Determine if the triangles can be proved congruent by SSS, SAS, ASA, AAS, or HL.
SSS

For two numbers to be proportional, they need to be directly increasing or decreasing in a constant ratio.

If Donny makes $9.75 per lawn, we can make a table that looks like this:

1 Lawn = $9.95

2 Lawns = $19.90

3 Lawns = $29.85...

And so on.

You can see this is proportional because it has a constant ratio between both elements.

(1 to 9.95)

So, it is proportional.

Answer: -120

6 less than is 6 - and 3 times a number 42 is 3 x 42 so...

6 - (3 x 42) = -120

Answer: It looks like you are trying to find the value of the function h(x) = √ (x-3) - 2.

To find the value of this function for a given value of x, you need to substitute the value of x into the function definition and simplify the expression.

For example, if you want to find the value of h(x) for x = 5, you would substitute 5 for x in the function definition and simplify the expression to get:

h(5) = √(5-3) - 2

= √2 - 2

= 1.4 - 2

= -0.6

Therefore, the value of h(x) for x = 5 is -0.6.

You can follow this same process to find the value of h(x) for any other value of x. Just be sure to substitute the correct value of x into the function definition and simplify the expression to find the final result.

Step-by-step explanation:

Answer:

g[f(x)]

Step-by-step explanation:

Given functions:

[tex]f(x)=x-3[/tex]

[tex]g(x)=\sqrt{x}-2[/tex]

Composite functions are when the output of one function is used as the input of another.

Therefore, to create √(x-3)-2, substitute the function f(x) in place of the x in function g(x):

[tex]\begin{aligned}\implies g[f(x)]&=\sqrt{f(x)}-2\\&=\sqrt{x-3}-2\end{aligned}[/tex]

The value of 'y' in the isosceles trapezoid ABCD is 14 and this can be determined by using the properties of isosceles trapezoid.

What is Triangle ?

Triangle can be defined as which contains three sides, three angles and the sum of the angles is 180 degrees.

Given ,

ABCD is an isosceles trapezoid with legs AB and CD and base BC.

If the length of AB is (7y - 4),

the length of BC s (4y - 6),

and the length of CD is (8y - 18).

The two legs are of equal length In any isosceles trapezoid that means:

7y - 4 = 8y - 18

Add 18 on both sides in the above equation.

7y - 4 + 18 = 8y - 18 + 18

7y + 14 = 8y

Now, subtract 7y on both sides in the above equation.

7y + 14 - 7y = 8y - 7y

Simplify the above expression in order to get the value of 'y'.

y = 14

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Answer:

perpendicular

Step-by-step explanation:

Yes, because as x increases, y increases and because all of the pairs represent the same ratio.

When two sets of provided numbers change in proportion, the ratios are said to be directly proportional if they do so in the same direction.

If two ratios or fractions are equivalent, it may be shown using the proportion formula. By dividing the supplied numbers, we may determine the value that is missing. You may write the percentage formula as a: A and d are the extreme terms, and b and c are the middle terms, according to the formula b::c: d = a/b = c/d.

Yes, because as x increases, y increases.

Yes, because all of the pairs represent the same ratio.

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To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.

Let's begin with a straightforward equation: x + 2 = 7.

How do you obtain X on your own?

Take away two from both sides.

⇒ x + 2 - 2 = 7 - 2\s⇒ x = 5

Check the solution, x = 5, by reentering it into the equation. We get 5 + 2= 7.

R.H.S. L.H.S.

Utilizing triangle properties or the Pythagorean theorem, we can get a solution for the unknown side or angle of a triangle.

With the aid of an example, let's clarify how to solve for x in a triangle.

Two of ABC's legs, which measure 7 units and 24 units respectively, are right-angled at B. Look for the hypotenuse X.

By using the Pythagorean theorem to ABC,

We obtain AC2 = AB2 + BC2, where x2 = 72 + 242, 49 + 576, and 625 where x2 = 625.

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Answer:

Step-by-step explanation:

2

Answer:

2/3 + 1/6 + 2/8

=(2×8+1×4+2×3)/24

=(16+4+6)/24

=26/24

=13/12

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The height of the person is approximately 0.426 meters or 42.6 cm.

We can use the concept of similar triangles to solve this problem. The height of the building and the length of its shadow form a right triangle, with the height as the opposite side and the shadow as the hypotenuse. The person and their shadow also form a similar right triangle, with the height of the person as the opposite side and the shadow as the hypotenuse.

We can set up the following proportion:

(Height of building)/(length of shadow) = (height of person)/(length of shadow)

48/30 = h/0.8

Solving for h, we get:

h = (48/30) * 0.8 = 0.533 * 0.8 = 0.426

Therefore, the height of the person is approximately 0.426 meters or 42.6 cm.

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An equation for the function g(x) when g(x) = f(-x) is g(x) = -x/3 - 6, which is shown in the graph attached below.

In Mathematics, a reflection can be defined as a type of transformation which moves every point of the geometric figure by producing a flipped, but mirror image of the geometric figure.

In Geometry, a reflection across the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By reflecting the given function across the across the y-axis (y = x), we have the following:

f(x) = x/3 - 6

g(x) = f(-x)

g(x) = -x/3 - 6.

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Answer:

Y-intercept: (0, -7)

X-intercept: (-14,0)

Step-by-step explanation:

To find the y-intercept, we need to put 0 in for x

0 + 2y = -14

2y = -14

y = -7

So, the y-intercept is located at (0, -7)

To find the x-intercept, we need to put 0 in for y

x + 2(0) = -14

x = -14

So, the x-intercept is located at (-14,0)

Step-by-step explanation:

To find the y-intercep, we need to put 0 in for x

0 + 2y= -14

2y = -14

y = - 7

So, the y - intercept is located at ( 0, - 7)

Answer:

Step-by-step explanation: 2.922

Answer: 2.922

Step-by-step explanation: (Look at the attachment for the best experience, or idea) So, as you can see in the attachment below, we first need to line up the decimal points with one another. They subtract in line with the other decimals and borrow. As we know, our answer is 2.922.

The number of groups of like terms is 3

An algebraic expression is defined as an expression made up of terms, variables, coefficients, constants, and factors.

These algebraic expressions are also composed of mathematical operations, such as;

A term can be described a single variable, number or numbers and variables that are multiplied together.

From the information given, we have the terms;

3x¹³, 9x¹⁰, -1x¹³, -16x¹³, 3x¹⁰, 3¹³, 10x¹⁰, 13x¹⁰

The similar terms are;

3x¹³,  3x¹⁰,  3¹³

Hence, the number is 3

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Answer:

y=4x+12

Step-by-step explanation:

if a line is parallel to another they have the same slope ,,

y=mx+c

where m represents the slope

and c represents the intercepted part of y axis

so the slope equals 4 from y=4x+11

to find the intercepted part c ,, substitute by the given point in the equation y=mx+c

(-2,4),, and slope is 4

4= 4×-2+c

4= -8+c

c= 12

so the equation is

y=4x+12

Answer:

y =4x-18

Step-by-step explanation:

y +2 = 4(x - 4)

y +2 =4x-16

y = 4x-18

The description of a solution to the problem modeled by the function y = 2x + 8 is given as follows:

The time needed to complete 40 parts  is of 16 minutes.

The function for this problem is defined as follows:

y = 2x + 8.

In which the variables are defined as follows:

Hence, solving the function for x, we are going to obtain the time needed to produce y parts, giving the description of a solution for this problem.

When y = 40, the solution for x is given as follows:

40 = 2x + 8

2x = 32

x = 32/2

x = 16 minutes.

The interpretation of this solution is that a time of 16 minutes is needed to obtain a production of 40 parts.

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The solution indicates 40 positive three-digit integers of this kind are available.

The numbers used for counting as well as organizing are known as natural numbers in mathematics. Cardinal numbers and ordinal numbers are two different types of numbers that are used for counting and ordering, respectively.

Left of zero on the number line, a negative number is an integer. It is not zero, though.

Any solution x will mod 23 will also have x+23n as a solution, for some integer n.

Since;

900/23 = 39 3/23,

we know:

There are 39 or 40 three-digit integers of this form.

As it happens,

100 is the smallest 3-digit solution. So, there are 40 three-digit numbers that are of the form 100 +23n,

hence 40 solutions to the equation.

The equation reduces, mod 23, to

10x = 11

Its solutions are x = 23n +8.

This shows There are 40 three-digit positive integers of this form.

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This probability does not support the Trump/Farage claim that 60% of all immigrants are male.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes, and how likely they are.

The probability of obtaining 257 or fewer males in a sample of 583 immigrants can be found using the binomial probability formula, which calculates the probability of a specific number of successes (male immigrants) in a fixed number of trials (sample size) with a fixed probability of success (p = 0.60).

Using the binomial formula, the probability of obtaining 257 or fewer males in a sample of 583 immigrants can be found by summing the probabilities of obtaining 257 males, 256 males, 255 males, etc. up to 0 males.

Using a binomial calculator, we can find that the probability of obtaining 257 or fewer males in a sample of 583 immigrants is about 0.04.

This probability is quite low, which suggests that it is unlikely to obtain 257 or fewer males in a sample of 583 immigrants if the proportion of male immigrants is actually 60%.

Therefore, this probability does not support the Trump/Farage claim that 60% of all immigrants are male.

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It is given that a 45-45-90 triangle whose each leg is 12 cm, then the length of the hypotenuse can be found out as 12/√2

since the hypotenuse is one of the legs multiplied by √2.

dividing the hypotenuse by √2 will get the length of one leg. since it is a 45 45 90 triangle, the length of the two legs are the same.

It is given that  a 45-45-90 triangle whose each leg is 12 cm, then the length of the hypotenuse can be found out as:

By using the Pythagoras theorem, we have

a^2+b^2= c^2

Substituting the given values, we have

12/√2

Thus, the length of the hypotenuse will be

12/√2

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Leo's balance after 8 months is $1725.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

Example:

2, 4, 8, 16 is a geometric sequence.

We have,

1500, 1530, and 1560 is a geometric sequence.

First term.

a = 1500

Common ratio.

r = 1.02

The nth term of a geometric sequence is a[tex]r^{n-1}[/tex].

Now,

For n = 8,

8th term.

= 1500 x [tex]1.02^7[/tex]

= 1500 x 1.15

= 1725

Thus,

The balance after 8 months is $1725.

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Answer:

If x-3 is directly proportional to the square of y, then we can say that:

(x-3) = ky^2

Where k is a constant of proportionality.

If x=5 when y=2, we can substitute these values into the equation to find the value of k:

(5-3) = k(2)^2

2 = 4k

k = 0.5

Now that we have the value of k, we can use it to find the value of x when y=6:

(x-3) = (0.5)(6)^2

x-3 = 18

x = 21

So, if x is directly proportional to the square of y and x=5 when y=2, then x=21 when y=6.

To the nearest percent, the percent by which the population grew from 2010 to 2020 is; 2%

Percentage increase is defined as the difference between the final value and the initial value, expressed in the form of a percentage.

Now, we are told that;

Initial Population in 2010 = 59000

From 2010 to 2015, the population grew by 7.3%. Thus;

Population in 2015 = 1.073 * 59000 = 63307

Now, we are told that from 2015 to 2020, it fell by 5.3%. Thus;

Population in 2020 = 63307 * (100% - 5.3%)

= 59952

Thus, percentage increase from 2010 to 2020 = (59952 - 59000)/59000) * 100% = 1.61% ≈ 2%

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Answer:

#1

Step-by-step explanation:

boxes   apples

3            6

6           12

9          18

10         20

ratio of apples to boxes is 2:1.   2 apples each box.  Divide the number of apples by 2 to get the number of boxes.  multiply boxes by 2 to get apples.

#2

boxes    cherries

3             12

5           20

6            24

7            28

if you divide cherrie by 4 you get the number of boxes.

Multiply boxes by 4 to get cherries.

Ratio of cherries to boxes is 4 to 1.

By adding a duplicate of the identity matrix to the augmented matrix, which was formed, it is possible to find the inverse of a square matrix using row reduction.

If the matrix is capable of being reduced to the identity, the identity matrix will simultaneously change into the inverse matrix. A rectangular array of numbers, arranged in rows and columns, is referred to as a matrix. The dimension, or order, of a matrix, indicates how many rows and columns there are in the array. For example, if a matrix has m rows and n columns, its order is expressed as mxn.

Correct Question :

How do you find the inverse of a 4x4 matrix?

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Answer:

[tex] \sf \: \frac{75}{12} \: (or) \: 6.25[/tex]

Step-by-step explanation:

Given problem,

[tex] \sf \rightarrow \: 15 \times \frac{5}{12} [/tex]

Let's solve the problem,

[tex] \sf \rightarrow \: 15 \times \frac{5}{12} [/tex]

[tex] \sf \rightarrow \: \frac{(15 \times 5)}{12} [/tex]

[tex] \sf \rightarrow \: \frac{75}{12} = 6.25[/tex]

Hence, the product is 6.25.

Using the fact that the triangles are similar, we will see that:

x = 5.626

On the image we can see two triangles, such that one is inscribed on the other.

Just because of that, it is obvious that the two triangles are similar.

And because the triangles are similar, the quotients between correspondent sides must be equal, that allows us to write the equation:

3/x = 8/15

The quotient is "left side over the bottom side"

We can solve that equation for x:

3/x = 8/15

3 = (8/15)*x

(15/8)*3 = x

45/8 = x

5.625 = x

That is the value of x.

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Answer:

90670998.89999999999999

NA (There is not enough information given to determine the value of MZ)

In this question, we are given that WY is 4.6 for us to find the value of MZ We need more information to be in a position to answer this. More information includes maybe we know the value of M or at least having some relationship between WY and MZ for us to draw a conclusion and come up with the value of MZ. If at all we had a common value in WY and MZ say M then it could be easier to come to a conclusion and finally get the value of MZ.

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