3y - 8 = -3(4 - 2x)
Step 2 of 2: Find the equation of the line which passes through the point (- 12. -3) and is parallel to the given line Express
your answer in slope-intercept form. Simplify your answer.

Answer:

v=-7

Step-by-step explanation:

13v-5v=-27-29

8v=-56

v=-56/8=-7

The cost of one ounce of peanuts is $0.20

The cost of one ounce of cashew is $0.35

15p + 5c = 4.75 equation 1

5p + 15c = 6.25 equation 2

Where:

Multiply equation 2 by 3

15p + 45c = 18.75 equation 3

Subtract equation 1 from equation 3

40c = 14

c = 14/40

c = $0.35

Substitute for c in equation 1

15p + (5 x 0.35) = $4.75

15p + 1.75 = 4.75

15p = 4.75 - 1.75

15p = 3

p = 3/15

p = $0.20

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The first three statements are not a negation. Only the last statement is a negation.

The opposite of the given mathematical statement is the negation of a statement in mathematics. If "P" is a statement, then "P" is the statement's negation. The words negation is used to denote a statement's denial.

It's vital to know the opposite of a given mathematical statement from time to time in mathematics. This practice is known as "negating" a statement. Remember that if a statement is true, then its negation must be false (and if a statement is false, then its negation is true).

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that log4x=2log16x. (ii)Show that log x=3logb³ x. (iii) Show that log₂x=(1+log₂3)logix

The expanded form of the given exponential equation is 6718464

Exponential equations are inverse of logarithmic equations. The standard exponential equation is expressed as. y = ab^x

where

a is the base

x is the exponent

Given the expression below;

a = 4(6)^8​

Expand to have:

a = 4 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6

a = 4 * 1679616
a = 6718464

Hence the expanded form of the given exponential equation is 6718464

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Answer: -5

Step-by-step explanation:

-3x+9y=-57                x=4

-3(4)+9y=-57

-12+9y=-57

             +12

9y=-45

    9y

y=-5

The number of people who can go to the game only on Sunday by applying the concept of set theory is equal to 5.

Total number of people for a trip to a baseball game = 15

Number of people planning to go on Saturday = 10

Number of people planning to go Sunday = 12

Let x be the number of people who can go on both Saturday and Sunday.

Then, the number of people who can go only on Saturday is 10 - x.

And the number of people who can go only on Sunday is 12 - x.

Total of 15 people are going to the baseball game.

Using set theory we have,

Number of people going on Saturday only + number of people going on Sunday only + number of people going on both = 15

Substitute the value we have,

⇒(10 - x) + (12 - x) + x = 15

Simplifying the above equation, we get,

⇒22 - x = 15

⇒ x = 7

The number of people who can only go to the game on Sunday is

= 12 - x

= 12 - 7

= 5

Therefore, using set theory number of people can only go to the game on Sunday is equal to 5 .

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By algebra, if one solution for the second order polynomial b² - 9 = 0 is 3, then the other solution to the expression is - 3.

Herein we have a quadratic equation, that is, a second order polynomial, of the form b² - a² = 0. By algebra we know that the polynomial of such form have the following equivalence:

b² - a² = (b - a) · (b + a), which means that the roots of the interval are x₁ = a and x₂ = - a.

If we know that a² = 9, then the roots of the second order polynomial are:

b² - 9 = (b - 3) · (b + 3)

By algebra, if one solution for the second order polynomial b² - 9 = 0 is 3, then the other solution to the expression is - 3.

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Answer:

80 square units

Step-by-step explanation:

These are rectangles and triangles.

The formula to get the area of a rectangle is its length multiplied by its width.

The formula to get the area triangle is its base multiplied by its height, then divided by 2.

The 3 rectangles all share the width of 6 units, so we can combine the 3 rectangles and consider it as 1 large rectangle.

The lengths of the rectangles are 2, 8, and 2 units.

We can add them together to get a total height of 12 units.

So, the formula to get the area of this rectangle is:
[tex]6\times12= A[/tex]

By solving this, we get:
A = 72 square units

There are 4 triangles remaining.

The base and height of all the triangles are 2 units.

So, by plugging these values into the triangle area formula, as mentioned from the beginning, we get:

[tex](2\times2)\div2=A[/tex]

So, the area of 1 triangle is 2 square units.

But since there are 4 triangles with the same bases and heights, we will multiply the area of 1 triangle by 4.

So, [tex]4 \times 2 = A[/tex]

This means the area of all the triangles together is 8 square units.

By adding the area of the triangles and rectangles together, we will get the answer.

[tex]72+8 = A[/tex]

So, the total area of this box is 80 square units.

Answer:

16.7 degrees

Step-by-step explanation:

Someone may think this graph is misleading because it does not start from the origin

As a general rule, graphs are to begin from the origin

The origin of a graph is

(x, y) = (0, 0)

From the given graph, the origin is

(x, y) = (0, 60)

This means that someone may think this graph is misleading because it does not start from the origin

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Answer: option (2)

Step-by-step explanation:

The slanted line has a negative slope.

Also, the line is shaded below.

This leaves option (2) as the correct answer.

Adding the difference between [tex]$\frac{9}{16}[/tex] and [tex]$\frac{5}{4}[/tex] we get [tex]$1 \frac{13}{16}[/tex].

Find the least common denominator or LCM of the two denominators:

LCM of 4 and 16 exist 16.

Subsequently, estimate the equivalent fraction of both fractional numbers with denominator 16.

For the 1st fraction, since 16 × 1 = 16,

9/16 = (9 × 1) / (16 × 1) = 9/16

For the 2nd fraction, since 4 × 4 = 16,

5/4 = (5 × 4) / (4 × 4) = 20/16

Add the two like fractions, then we get

(20/16) + (9/16) = (20 + 9)/16 = 29/16

So, [tex]$\frac{5}{4}+\frac{9}{16} =\frac{29}{16}[/tex]

In mixed form: [tex]$1 \frac{13}{16}[/tex].

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Answer:

Step-by-step explanation:

A) The median number is just the middle number so it should be 2.8

B) Bottom 30% are the six lowest amounts. The highest of the bottom six numbers is 2.3. Not sure what it means by calculating them. 1.8, 1.9, 1.9, 2.0, 2.1, and 2.3 are the lowest six. If you need to add them up the answer is 12.
C) I don’t know what your Q1 is.

Answer:

t + 3

Step-by-step explanation:

adding 3 years onto t amount of years

The number of mice that didn't get a tumor is 9 mice out of the 25 mice.

Identify the total mice who did not have any effects or the effects did not include a tumor.

Repiratory failure: 9 mice

Based on this, it can be concluded 9 mice did not have a tumor, while 21 mice hat at least a tumor and some of them had a tumor and respiratory failure.

Note: This question is incomplete; here is the missing section:

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The number must be between 20 and 30.

The square of the whole number can be found as follows;

The square of the whole number is between 500 and 900. The number must be between 20 and 30.

The number is an whole number.

Therefore, the number will be between 20 and 30.

20² = 400

30² = 900

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The weight of toys a toddler owns has a population mean of 15.8kg and a population standard deviation of 4.2kg. then the probability a toy store owner could select a sample of 49 toddlers and find the sample mean to be 15.1kg or less is 0.121 and 15.1kg or more is 0.879.

Given Information:

Population mean, μ = 15.8 kg

Population standard deviation, σ = 4.2 kg

For finding the probability for the sample mean, we first need to find the standard score.

(a) For sample mean to be 15.1kg or less,

z = (x - μ) / (σ/√n)

Here, x = 15.1

⇒ z = (15.1 - 15.8) / (4.2/√49

z =-0.7 / (4.2/7)

z = -1.17

Now, we can use the z-table to find the probability of the sample mean to be 15.1kg or less.

∴ P(x ≤ 15.1) = 0.121

(b) Now, to find the probability of sample mean to be 15.1kg or more, we can simply subtract P(x ≤ 15.1) from 1.

⇒ P(x ≥ 15.1) = 1 - P(x ≤ 15.1)

P(x ≥ 15.1) = 1 - 0.121

P(x ≥ 15.1) = 0.879

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Answer:3/7

Step-by-step explanation:There are total 7 days in a week. 3 days were dry so the fraction is 3/7 . The dry days over the total days of the week

After rounding to the nearest tenth, we get:

[tex]\frac{2.1}{1.488} = 1.5[/tex]

We have the quotient:

[tex]\frac{2.1}{1.488}[/tex]

If you multiply the numerator and denominator by 1000, you will get the simpler quotient:

[tex]\frac{2100}{1488}[/tex]

It gives:

[tex]\frac{2100}{1488} = 1.45[/tex]

Now we want to round it to the nearest tenth, which is the first digit after the decimal point.

To do so, we need to look at the number at the right of it.

In this case, we can see a 5, so we should round up, then we have:

[tex]\frac{2100}{1488} = 1.5[/tex]

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Answer:

180°

cuz when a line (I forgot the name) and radius meet at the circumference they from an angle of 90°

The solution to the system of inequalities is (-3.375, 1.75)

The system of inequalities is given as:

3y > 2x+12

2x+y < -5

Next, we plot the graph of the system using a graphing tool

From the graph, both inequalities intersect at

(-3.375, 1.75)

Hence, the solution to the system of inequalities is (-3.375, 1.75)

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The missing angle is B = 65° and the missing sides are a ≈ 7.461 and c ≈ 6.762.

In this case, we know two angles (A = 25°, C = 90°) and a side of a triangle (b = 16) and Euclidean properties and the law of the sines must be used to find the rest of variables:

B = 180° - A - C

B = 180° - 25° - 90°

B = 65°

a = 16 × (sin 25°/sin 65°)

a ≈ 7.461

c = 16 × (sin 25°/sin 90°)

c ≈ 6.762

The missing angle is B = 65° and the missing sides are a ≈ 7.461 and c ≈ 6.762.

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Answer:

+5

Step-by-step explanation:

There is a length of 5 between all numbers, meaning that 5 is added to each number to get the next one.

I hope this helps!

Answer:

[tex]\implies y=(x-2)^2-6[/tex]

Step-by-step explanation:

Vertex form of a quadratic equation:

[tex]y=a(x-h)^2+k[/tex]

where:

Given vertex:  (2, -6)

⇒ h = 2 and k = -6

Substitute the values of h and k into the formula:

[tex]\implies y=a(x-2)^2+(-6)[/tex]

[tex]\implies y=a(x-2)^2-6[/tex]

As we have not been given a value for the constant [tex]a[/tex], assume this is 1.

Therefore, the vertex form of the quadratic function with vertex (2, -6) is:

[tex]y=(x-2)^2-6[/tex]

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Vertex form

a=1

Put values

One tree is 31.044 m taller than the other one in height.

Given Information and Formula Used:

The distance between the trees, BC (from the figure) = 120 m

Elevation of angles to the top of the trees,

∠AMB = 52°

∠DMC = 36°

In a right angled triangle,

tan x = Perpendicular/Height

Here, x is the angle opposite to the Perpendicular.

Calculating the Height Difference:

Let's compute the height of the taller tree first.

In ΔAMB,

tan 52° = AB / BM

Now, since M is the point halfway between the trees,

BM = CM = BC/2

BM = CM = 60 m

⇒ 1.2799 = AB / 60

AB = 1.2799 × 60

Thus, the height of the taller tree, AB =  76.794 m

Now, we will compute the height of the smaller tree.

In ΔDCM,

tan 36° = DC / CM

⇒ 0.7625 = DC / 60

DC = 0.7625 × 60

Thus, the height of the smaller tree, DC = 45.75 m

The difference in the heights of the trees, AP = AB - DC

AP = (76.794 - 45.75)m

AP = 31.044m

Hence one tree is 31.044m taller in height than the other.

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The measure of the angle x is 77 degrees if two lines are parallel to each other or p ll q option (A) is correct.

Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have two lines that are parallel to each other or p ll q

The angle made by transversal t is 136 degrees

The measure of the other angle = 180 - 136 = 44 degrees

Draw a line parallel to p and q and passes through the intersection point of line t and v

The angle made by the transversal and the line drawn is the same as 44 degrees.

The measure of the other angle = 121 - 44 = 77 degrees

Thus, the measure of the angle x is 77 degrees if two lines are parallel to each other or p ll q option (A) is correct.

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