solve
(2x-3) (x2+4x-5)

Answers

Answer 1

Answer: 2x^3 + 5x^2 - 10x + 15

Step-by-step explanation:

To multiply two polynomials, you can use the distributive property and multiply each term of one polynomial by each term of the other. In this case, the two polynomials are (2x - 3) and (x^2 + 4x - 5), so we have:

(2x - 3) * (x^2 + 4x - 5) =

2x * x^2 + 2x * 4x - 2x * 5 +(-3) * x^2 + (-3) * 4x - (-3) * 5

Expanding the products, we get:

2x^3 + 8x^2 - 10x - 3x^2 - 12x + 15

Combining like terms, we get: 2x^3 + 5x^2 - 10x + 15


Related Questions

Which shows how to solve the equation 3/4 X = -6 for x in one step?

Answers

To solve the equation 3/4 x = -6 for x in one step, you can multiply both sides of the equation by 4/3:

3/4 x = -6

4/3 * (3/4 x) = 4/3 * (-6)

x = 8

half as big as last night’s crowd ( c = size of last night’s crowd )
verbal expression to algebraic expression

Answers

Answer:       (1/2)c

To write an algebraic expression, convert parts of the verbal expression.

What is an expression?

An expression is numbers or variables with operations performed between them. It does not have an equal sign.

Operations

Operations are ways we change numbers, usually to make them bigger or smaller. Examples of operations are multiplication, division, subtraction, addition, and square root.

Write an expression

The question says:     "half as big as last night’s crowd"

last night's crowd = c

'half as big' = 1/2

This is a proper fraction with the top number smaller than the bottom number. When we multiply 'c' with a proper fraction, the answer would get smaller.

Therefore, we can represent the problem using the expression  [tex]\frac{1}{2}c[/tex].

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Please work the problem

Answers

Answer:

6x-7=3x-29

6x-3x=-29+7

3x=-23

x=-23/3

6x-7=8y+17

6(-23/3)-7=8y+17

-46-7=8y+17

8y+17+53=0

y=70/8

Y=8.75

ANS!!

Solve for x. Figures are not necessarily drawn to scale.
M
X
9
N
7
Q
10.5
9

Answers

The value of x is given as follows:

x = 13.5.

What are similar triangles?

Similar triangles are triangles that share these two features presented as follows:

Congruent angle measures.Proportional side lengths.

The proportional relationship for the side lengths is given as follows:

9/x = 7/10.5.

Applying cross multiplication, the value of x is obtained as follows:

7x = 9 x 10.5

x = 9 x 10.5/7

x = 13.5.

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Linda drove 567 miles in 9 hours.
At the same rate, how long would it take her to drive 693 miles?

Answers

The time taken by Linda to cover 693 miles is 11 hours.

What is rate of change?

Rate of change is the speed at which the variables changes with respect to time.

In 9 hours Linda drove 567 miles.

Miles travelled in 1 hour is,

[tex]speed=\frac{distance covered}{timetaken}[/tex]------(1)

         =[tex]\frac{567}{9}[/tex]

         = 63 miles per hour.

Linda drove 63 miles per hour.

She is travel in the same rate from the beginning.

Let  t be the time taken by her to travel 693 miles is,

By using (1),

[tex]speed=\frac{distance covered}{timetaken}[/tex]

[tex]t=\frac{693}{63}[/tex]

⇒t=11 hours.

Hence, the time taken by Linda to cover 693 miles is 11 hours.

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3. CONSTRUCTION
The diagram shows an
example of the Pratt truss used in bridge
construction.
Find m/1.

Answers

The angle ∠1 is 55 degrees.

What is Triangle?

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that  diagram shows an example of the Pratt truss used in bridge

construction.

We need to find the angle ∠1.

The given triangle is a right angle triangle which has one angle 90 degrees.

The adjacent angle to 145 degrees be angle 2.

145+∠2=180

∠2=180-145

∠2=35 degrees.

We know that the sum of three angles is 180 degrees

So ∠1+35+90=180

∠1+125=180

Subtract 125 from both sides

∠1=180-125

∠1=55

Hence, the measure ∠1 is 55 degrees.

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How much warmer is 92 than 40?

Answers

The temperature measure 92 is warmer than 40 by a measure of; 52.

By how much is 92 warmer than 40?

It follows from the task content that it is required to be determined, how much warmer is 92 than 40.

Since the greater temperature measure is; 92 while the lesser is 40.

It can be concluded that the temperature difference is; 92 - 40 = 52.

Ultimately, the measure 92 is 52 warmer than 40.

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Can someone please help me with this question

Answers

40 degrees Is the answer.

Hope this helps mate.

PLs give brainliest

Answer:

40

80 + (16x-4) + (9x +4) =180

x=4

BAC = (9*4+4)

BAC = 40

In order to ride a
roller coaster at the theme park, riders
must be at least 52 inches tall. Write
an inequality to show the
safe heights for riders.

Answers

The inequality to represent the height of roller coaster is x≥52.

What are inequalities?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that. in order to ride a roller coaster at the theme park, riders must be at least 52 inches tall.

Let the height be x.

Now, x≥52

Therefore, the inequality is x≥52.

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What is 168 cm to ft inch ?

Answers

From the information given, 168 cm is approximately equal to 5 feet and 6.14 inches (rounded to two decimal places).

To convert centimeters to feet and inches, you can use the following conversion factors:

1 inch = 2.54 cm

1 foot = 12 inches

First, convert the length in centimeters to inches by dividing by 2.54:

168 cm ÷ 2.54 cm/inch = 66.14 inches

Next, convert the total number of inches to feet and inches. To do this, divide the total number of inches by 12 to get the number of whole feet, and then use the remainder as the number of inches.

66.14 inches ÷ 12 inches/foot = 5 feet with a remainder of 6.14 inches

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Two polygons are similar if and only if there is a correspondence among their angles and among their sides so that all corresponding angles are congruent and all corresponding sides are proportional.

Which Postulate or Theorem is stated above?

Question 1 options:

Polygon Similarity Postulate


Polygon Congruence Postulate


Angle-Angle Similarity Postulate


Side-Side-Side Similarity Theorem


Side-Angle-Side Similarity Theorem

Answers

Angle-Angle Similarity Postulate states that  two polygons are similar if and only if they have two corresponding angles that are congruent.

What is Triangle?

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Given that two polygons are similar if and only if there is a correspondence among their angles and among their sides so that all corresponding angles are congruent and all corresponding sides are proportional.

The statement above is the Angle-Angle Similarity Postulate, which states that two polygons are similar if and only if they have two corresponding angles that are congruent.

Hence, Angle-Angle Similarity Postulate states that  two polygons are similar if and only if they have two corresponding angles that are congruent.

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Answer:

Angle-Angle Similarity Postulate

Step-by-step explanation:

9tailsminato9.

In the figure, the person is 5 ft tall and his shadow is 4 ft long. The tree's shadow is 22 ft long.

What is the height of the tree? Show all your work.

Answers

Answer:  The height of the tree is approximately 44 ft.

Step-by-step explanation:  Step 1: Calculate the ratio of the person's height to the length of their shadow.

Person's Height: 5 ft

Length of Shadow: 4 ft

Ratio: 5 ft/4 ft = 1.25

Step 2: Use the ratio to calculate the length of the tree's shadow.

Length of Tree's Shadow: 22 ft

Ratio: 1.25

Calculation: 22 ft/1.25 = 17.6 ft

Step 3: Multiply the length of the tree's shadow by the ratio to calculate the tree's height.

Length of Tree's Shadow: 17.6 ft

Ratio: 1.25

Calculation: 17.6 ft x 1.25 = 22 ft

Answer: The height of the tree is approximately 44 ft.

how do i solve -(-8q-8.7)

Answers

On solving the expression, we get -> (8q + 8.7).

What are algebraic expressions in mathematics?

In mathematics, an expression or mathematical expression is a combination of terms, both constants and variables. For example -

2x + 4y + z

Given is the algebraic expression as -

- (- 8q - 8.7)

The given expression is -

- (- 8q - 8.7)

- (- 8q) - (- 8.7)

8q + 8.7

Therefore, on solving the expression {- (- 8q - 8.7)}, we get -> (8q + 8.7).

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Please help!!!
I will give brainly if it gives me the opportunity

Answers

The expression that will help to find the area of the given shaded region is 3x²+27x+51.

What is area?

Area is a measure of the amount of space inside a two-dimensional shape or surface. It is usually expressed in square units, such as square inches, square feet, or square meters. The area of a shape can be calculated by multiplying its length by its width, or by using a specific formula for that shape. For example, the area of a rectangle is found by multiplying its length and width, while the area of a circle is found by multiplying the square of its radius by pi (3.14). Area is an important concept in mathematics, and it is used in many real-world applications such as calculating the amount of paint needed to cover a wall, or the amount of land needed to build a house.

Here,

area of rectangle=(x+10)(2x+5)

area of square=(x+1)²

area of shaded region=area of rectangle-area of square

=(x+10)(2x+5)-(x+1)²

=2x²+20x+5x+50+x²+2x+1

=3x²+27x+51

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Yvette is saving money to buy holiday gifts. She will save the money she makes at her part-time job. However, she borrowed $25 from her sister that she has to pay back before she can start saving.

This relationship can be shown by a linear function. Below is a table showing how many hours Yvette has worked (input), and how much money she's saved (output).

Hours Worked (x) Amount Saved (y)
0 -$25
4 $14
8 $53
12 $92
16 $131

Which of the following statements are true regarding the graph of this linear function? Select all that apply.

Group of answer choices:

A. The slope of the line, 25, is the amount of money she makes per hour of work.

B. The slope of the line, 9.75, is the amount of money she starts with having worked 0 hours.

C. The y-intercept of the line, 0, is the amount of money she starts with, since she's worked 0 hours.

D. The y-intercept of the line, -25, is the amount of money she starts with, since she owes her sister $25 and has worked 0 hours.

E. The slope of the lines, 9.75, is the amount of money she makes per hour of work.

Answers

The slope of the line is 9.75 and the y-intercept is -25.

What is a linear function?

Two distinct but related concepts are referred to by the phrase "linear function": A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

Here, we have

Given: Yvette is saving money to buy holiday gifts. She will save the money she makes at her part-time job. However, she borrowed $25 from her sister which she has to pay back before she can start saving.

Let the linear function that models the given situation be y = ax + b. Here, a and b are constants.  We can use this information to find the values of a and b.

We put x = 0 and y = -25 into y = ax + b

b = -25

Substitute the value of b into y = ax + b

y = ax -25...(1)

Now we put x = 4 and y = 14 in equation(1) and we get

14 = 4a - 25

4a = 39

a = 9.75

Substitute the value of a in equation (1):

y = 9.75x - 25

Compare the above function with the slope-intercept form of a line y = mx + c

m = 9.75, c = -25

Hence, the slope of the line is 9.75 and the y-intercept is -25.

A. From the previous calculations, it is clear that the slope of the line is 9.75. Hence, the first statement is not true.

B. From the given table, it is known that person Y had started working with -25 dollars. Clearly, 9.75 is the slope of the line, but it does not represent the initial amount that person Y had at x = 0. Hence, the second statement is not true.

C.  From the previous calculations, it is clear that the y-intercept is -25, not 0. Hence, the third statement is not true.

D. From the previous calculations and the given table, it is clear that the y-intercept is -25, and it does represent the initial amount that person Y had at x = 0. Note that the y-intercept is negative as the person has borrowed 25 dollars from her sister. Hence, the fourth statement is true.

E. From the previous calculations, it is clear that the slope of the line is 9.75. It is known that the slope of a line represents the rate of change in the value of y with respect to x. So, it can be concluded that 9.75 represents the amount that person Y earns per hour. Hence, the fifth statement is true.

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Select all the equations that are equivalent to this equation

Answers

The equations equivalent to the given equation 3x - 4 = 5 are A) 3x = 9, B) 3x - 4 + 4 = 5 + 4 and E) -4 = 5 - 3x.

What is an Equation?

An equation is defined as a mathematical statement containing two expressions on either sides which are connected with an equal to sign.

Either sides of an equation are called as left hand side and right hand side.

Given equation is 3x - 4 = 5.

Adding the number 4 on both sides, we get,

3x - 4 + 4 = 5 + 4, which is the equation B.

Simplifying,

3x = 9, which is the equation A.

x = 3

3x - 4 = 5

Subtracting 3x on both sides of the equation,

3x - 4 - 3x = 5 - 3x

-4 = 5 - 3x, which is the equation E.

Hence the equivalent equations are A, B and E.

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Your question is incomplete. Probably the correct question is as follows.

Select ALL the equations that are equivalent to the equation 3x - 4 = 5.

A) 3x = 9

B) 3x - 4 + 4 = 5 + 4

C) x - 4 = 2

D) x = 9

E) -4 = 5 - 3x

aiden earns 16.00 per hour if he gets a 4% raise, what will be his new hourly wage

Answers

Aiden's new hourly wage would be 16.64 per hour.

Solution:

We have been given that Aiden's hourly wage is 16.00 per hour

So, If he gets a 4% raise then his hourly wage will be,

16* (100+ 4) / 100 = 16.64

Therefore, Aiden's new hourly wage will be 16.64 per hour.

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There are 400 eighth graders at Wilson Middle SchoolIn the class president election, 296 students voted for Luke, 60 students voted Alice, and 44 students voted for Chris.who voted for luke

Answers

Answer: In the class president election at Wilson Middle School, 296 students voted for Luke.

Step-by-step explanation:

Determine which of the following properties are always true by dragging them to the right:
-All four sides are congruent
-Opposite sides are congruent
-Opposite sides are parallel
All four angles are congruent
-Opposite angles are congruent
Diagonals are congruent
-Diagonals bisect each other
-Diagonals intersect at a right angle
diagonals bisect interior angles
-Sum of all angles equals 360

Answers

The properties that are always true are: Opposite sides are congruent. Opposite sides are parallel. Opposite angles are congruent. Sum of all angles equals 360. Diagonals bisect each other.

What are diagonals?

A diagonal in mathematics is a line that joins two solids or polygons whose vertices are not on the same edge. Generally speaking, a diagonal is a sloping or slanting line that joins the vertices of a form. The term "diagonal" refers to lateral forms with sides, edges, and corners.

The properties that are always true are:

Opposite sides are congruent.

Opposite sides are parallel.

Opposite angles are congruent.

Sum of all angles equals 360.

Diagonals bisect each other.

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How do you find the limit of a function on a calculator?

Answers

Answer:

Step-by-step explanation:

The method for finding the limit of a function on a calculator depends on the specific calculator you are using. Here are the general steps for finding the limit of a function using a graphing calculator:

Enter the function: Most graphing calculators have a function editor where you can enter the function you want to find the limit of.

Set the limit: To find the limit of the function at a particular point, you need to specify the value at which you want to find the limit. This is done by entering the limit expression, for example: limit(f(x), x, a) where f(x) is the function, x is the variable, and a is the value at which you want to find the limit.

Evaluate the limit: After entering the limit expression, you can evaluate it by pressing the "enter" or "=" button. The calculator will then display the limit of the function at the specified value.

It's important to note that a graphing calculator can only estimate the limit of a function based on the accuracy of the graph, so the result may not be exact. Additionally, some functions may have limits that cannot be evaluated using a calculator. In these cases, you may need to use analytical methods to determine the limit.

Ayana is
1
1
2
1
2
1

1, start fraction, 1, divided by, 2, end fraction meters tall. Her little sister Chike is
1
1
4
1
4
1

1, start fraction, 1, divided by, 4, end fraction meters tall.

Answers

Ayana is 6/5 times as tall as Chike.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Height of Ayana = 1 1/2 meter

And, Height of Chike = 1 1/4 meter

Now, We can simply solve the above problem as follows;

Height of Ayana = 1(1/2) meters

We can also write it as;

= 3/2 meters

And, Height of Chike = 5/4 meters

Hence, To compare the given fractions we will first make the denominator equal by taking the LCM.

LCM of 2 and 4 = 8

Hence, Heights of Ayana can be rewritten as, 12/8 meters

And, Height of Chike can be rewritten as, 10/8

Now, Comparing the height of Ayana and Chike as;

= (12/8) ÷ (10/8)

= 12/10

= 6/5

Hence, Ayana is 6/5 times as tall as Chike.

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Complete question is this,

Ayana is 1(1/2) meters tall. Chike is 1(1/4) meters tall. Complete the comparison.

Ayana is ____ times as tall as chike.

A rectangle has a length of 19 inches and a
vidth of 15 inches. What is the perimeter
of the rectangle?
The perimeter is
inches.

Answers

Answer:

Step-by-step explanation:

So when solving for the perimeter you need to add up all the sides. So 15 + 15 = 30 and 19 + 19 = 38. So 38 + 30 = 68 inches. So there is your answer. 68 inches is the perimeter.

in a triangle ABC, E and F are mid points of equal sides AB and AC of triangle ABC. Show that BF = CE

Answers

BF=CE in a triangle ABC, E and F are mid points of equal sides AB and AC of triangle ABC.

What is Triangle?

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given E and F are mid point of equal sides AB and AC of triangle ABC

In ΔABF and  ΔACE

AB=AC  (given )

∠A=∠A  (common angle )

The side FA is equal to EA

If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent

∴ΔABF≅ΔACE (SAS rule)

∴BF=CF ( Corresponding parts of Congruent triangles.)

Hence, in a triangle ABC, E and F are mid points of equal sides AB and AC of triangle ABC then BF=CE.

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Fill in each blank with the correct number or variable.

7 (x + 2) = 7 x ___ + 7 x ___

Answers

Answer: x,2

Step-by-step explanation:

Answer:

7 x x + 7 x 2

Step-by-step explanation:

7(x + 2)

7x + 7(2)

7x + 14

Please help! Make you brainliest and 15 points!

Answers

Answer:

b value is 3

rise = 3 run = -2

another point could be (2,0)

Step-by-step explanation:

A group of 10 Science Club students is on a field trip. That number of students represents
20% of the total number of students in the Science Club. What is the total number
of students in the Science Club?
A
B
D
20
30
50
80

Answers

The total number of students in the science club will be 50. The correct option is C.

What is the percentage?

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

If 10 students represent 20% of the total number of students in the Science Club, then 10 / 0.2 = 50 students is the total number.

Therefore, The total number of students in the science club will be 50. Then the correct option is C

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Wayne earns 5.3% simple interest for 5 years on $3000. How much interest does he earn on the account? I=prt
*
1 point
$883.86
$795
$3,883.86
$1,795

Answers

Answer: I would say it’s D. $1,795

Step-by-step explanation: why not pick D….

Hope this helps^^

The simple interest earned on $3000 after 5 years at 5.3% rate of interest is $795. The correct option is C .

Given,

Principal amount = $3000

Rate of interest = 5.3%

Time = 5 years

Now,

Simple interest = Principal × ROI ×Time/100

Substitute the values ,

Simple interest = 3000 * 5.3 * 5/ 100

Simple interest = 79500/100

Simple interest = $795

Total amount after 5 years = $3000 + $795

= $3795

Hence simple interest earned on $3000 at ROI of 5.3% after 5 years will be $795 .

Therefore option C is correct.

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Find an expression that represents the difference when (-4x+4) is subtracted from (-9x-7) in simplest terms.

Answers

The required simplified expression result of (-4x+4) is subtracted from (-9x-7) is -5x -11.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,

The expression (-9x-7) - (-4x+4) can be simplified as follows:
First, we'll combine the like terms:

-9x - 7 - (-4x + 4)

Next, we'll use the distributive property to simplify the right side:
-9x - 7 - (-4x) + 4

Combining like terms on the right side:
-9x - 7 + 4x - 4

Combining the remaining terms:
-5x -11

Thus, the requried simplified expression is given as -5x-11.

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How is matrix multiplication done in MATLAB?

Answers

The " * " operator is used in MATLAB to do matrix multiplication. In MATLAB, the matrix multiplication process is based on linear algebraic principles.

So the " * " operator is used in MATLAB to do matrix multiplication. In MATLAB, the matrix multiplication process is based on linear algebraic principles. In MATLAB, the standard syntax for multiplying matrices is:

When the dimensions of A and B satisfy the matrix multiplication rule, the css copy code C = A * B can be used. Particularly, the number of rows in matrix B and the number of columns in matrix A must match.

The resulting matrix C will be the same size in terms of both rows and columns as matrix A and matrix B. Here is an illustration of how matrix multiplication functions in MATLAB:

A = [1 2; 3 4];% Define matrix A B = [5 6; 7 8];% specify matrix.

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Micaela bought a concert ticket online for $76. She used a coupon code to get a 20%
discount. The website also applied a 5% processing fee to the price after the discount.
How much did Micaela pay, in the end? Round to the nearest cent.

Answers

Micaela paid the amount of $63.8 in the end for a concert ticket.

How to calculate the percentage discount?

Subtract the final price from the original price then Divide this number by the original price. Finally, multiply the result by 100. You've obtained a discount in percentages.

Reformulate the basic equation to:

% discount = 100 × (original price - discounted price) / original price

To calculate the final price that Micaela paid, we need to apply the discount and the processing fee to the original price of the ticket.

The discount is 20% of the original price of $76, which is:

discount = 0.2 x $76 = $15.20

So Micaela paid:

price after discount = $76 - $15.20 = $60.80

Now we need to apply the processing fee. The processing fee is 5% of the price after the discount, which is:

processing fee = 0.05 x $60.80 = $3.04

So the final price that Micaela paid is:

final price = $60.80 + $3.04 = $63.84

Therefore, she paid $63.8 in the end, rounded to the nearest cent.

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Which branch of government controls the bureaucracy? determine the required tension in cable ac, knowing that the resultant of the three forces exerted at point c of boom bc must be directed along bc. (you must provide an answer before moving on to the next part.) the corresponding magnitude of the resultant is which branch of the government appoints justices to the u.s. supreme court? while martha nussbaum thinks it is important to study philosophy, she does not believe that the study of religions will be necessary in a modern, secular world. True or False this is kinda complex ngl could any high schoolers help me? this is the problem.Solve for aaa.Give an exact answer.3+0.5(4a+8)=92a3+0.5(4a+8)=92a. A= ? what is thermal boundary layer thicker than velocity boundary layer? Which codon is the code for the amino acid histidine (His)? 2.Solve for x. Round to onedecimal place (nearesttenth).11X45 Read the sentence.The painting depicts a young boy as he plows the fields on his familys farm in Oklahoma in the early 1950s.Which type of language is used in this sentence?informal, subjectiveinformal, objectiveformal, subjectiveformal, objective Which expression can be used to find thesurface area of the triangular prism?4-2+3.2+5.222.3.4+4-2+32+5-21/2-3-4) -2+4-2+3.2+5.23.4+4-2+3-2+5-224 ft4 ft3 ft3 ft5 ft2 ft5 ft2 ft 2In paragraph 13, the chef writes a proof to answer the professor's exam question. What does he sayabout the idea of equidistant bodies in his proof?A Everything is the same distance from the sun.B All heavenly bodies move slowly around the Earth.His cigarette is the same distance from everything in the universe.The sun is the center of the universe and Earth revolves around it. The discovery that DNA from killed virulent bacterial can transform live harmless bacteria into virulent forms means that DNA: A) is double stranded. B) is transcribed into RNA. C) codes for proteins. D) contains information that controls an organism's traits. what two principles are considered the miranda triggers? Select all the characteristics that apply to an atomic orbital. Defined by the wave function (Psi). A region around the nucleus of an atom where the probability of finding an electron is high A shell in an atom containing the valance electrons Identified by a unique combination of four quantum numbers; identified by a unique combination of three quantum numbers Defined by the square o' the wave function what is difference between mission and vision What does the Starbucks logo mean? the walls are fixed to the ground which wall is the most stable when the same lateral force is applied Who is dana sue gray? (a) Determine a theme or central idea of a text. In Act II, Scene 4, of The Diary of Anne Frank, Anne says to Peter, "I still believe, in spite of everything, that people are really good at heart. " Annes Voice repeats this thought at the very end of the act. To what main theme of the play do these words point? (b) Analyze the development of theme, including its relationship to setting. Explain how the theme you have identified relates to the setting of the play and the circumstances of the characters. (c) Analyze the development of theme, including its relationship to plot. Explain how events of the play help to develop this theme. (d) Analyze the development of theme, including its relationship to characters. Explain how this theme relates to the character of Anne. In your answer, consider Mr. Franks final words, "She puts me to shame. "\ Justifying a Claim Based on a Confidence Interval for a Population Proportion Based on the simulation, what proportion of the 95 percent confidence intervals capture the population proportion of 0.3? Explain how you determined your answer.