Enter your answer and show all the steps that you use to solve this problem in the space provided.

Eliza and Jamie are making cupcakes for a bake sale at school. Eliza needs 213
c of flour for her recipe and Jamie needs 134 c for her recipe. They have 4 c of flour. Do they have enough flour for both recipes? Explain.

Answer:

[tex]3y-6=18\\\\3y=24[/tex]

The value of "y" is: [tex]y=8[/tex]

Step-by-step explanation:

Given the following equation:

[tex]3(y-2) = 18[/tex]

1. You must apply the Distributive property on the left side of the equation (This is: [tex]a(b\±c)=ab\±ac[/tex]). Then:

[tex](3)(y)+(3)(-2) = 18\\\\3y-6=18[/tex]

2. Now you need to apply the Addition Property of Equality. Remember that this states that:

[tex]If\ a=b,\ then\ a+c=b+c[/tex]

So, adding 6 to both sides of the equation, you get:

[tex]3y-6+(6)=18+(6)\\\\3y=24[/tex]

3. Finally, you can apply the Division Property of Equality, which states that:

[tex]If\ a=b,\ then\ \frac{a}{c}=\frac{b}{c}[/tex]

So, dividing both sides of the equation by 3, you get:

[tex]\frac{3y}{3}=\frac{24}{3}\\\\y=8[/tex]

Answer:

[tex]f(t) = 2430(1 + \frac{0.16}{4} )^{7 \times 4}[/tex]

The APR is 16%.

Step-by-step explanation:

Jason writes the following function to represent the amount of money in his account after 7 years given quarterly compounding of the $2430 initial deposit as  

[tex]f(t) = 2430(1.04)^{28}[/tex] ......... (1)

a. If we want to rewrite the equation in the form  

[tex]f(t) = A(1 + \frac{r}{n} )^{nt}[/tex] .......... (2)

Then comparing equation (1) and (2) we get, A = 2430 and t = 7

Hence, 7n = 28

⇒ n = 4

Now, [tex]1 + \frac{r}{4} = 1.04[/tex]

⇒ r = 0.16 i.e. 16%  

Therefore, the expression is  

[tex]f(t) = 2430(1 + \frac{0.16}{4} )^{7 \times 4}[/tex] (Answer)

b. The APR is 16%. (Answer)

Answer:

-4, 3.

Step-by-step explanation:

x^2 + x - 12 = 0

(x + 4)(x - 3) = 0

x = -4, 3.

Answer:

1. [tex]m\angle KLP+m\angle PLM=180^{\circ}[/tex]

2. [tex]3x+m\angle PLM=180^{\circ}[/tex]

3. [tex]m\angle PLM=180^{\circ}-3x[/tex]

4. [tex]m\angle PMN=m\angle P+m\angle PLM[/tex]

5. [tex]2x+72^{\circ}=x+180^{\circ}-3x[/tex]

6. [tex]x=27^{\circ}[/tex]

Step-by-step explanation:

Please find the attached diagram for the complete question.

We are supposed to complete the given blanks.

1. [tex]m\angle KLP+m\angle PLM=...[/tex]

We can see from our given diagram that angle KLP and angle PLM are linear angles, so their measure will be equal to 180 degrees. Therefore, the correct expression for blank in 1st step would be [tex]180^{\circ}[/tex].

2. [tex]...+m\angle PLM=180^{\circ}[/tex]

Now, we will substitute the measure of angle angle KLP in our equation. We can see that measure of angle angle KLP is [tex]3x[/tex]. Therefore, the correct expression for blank in 2nd step would be [tex]3x[/tex].

3. [tex]m\angle PLM=180^{\circ}...[/tex]

Our next step is to find the measure of angle PLM in terms of x by subtracting [tex]3x[/tex] from both sides as:

[tex]3x-3x+m\angle PLM=180^{\circ}-3x[/tex]

[tex]m\angle PLM=180^{\circ}-3x[/tex]

Therefore, our 3rd step would be [tex]m\angle PLM=180^{\circ}-3x[/tex].

4. [tex]m\angle PMN=m\angle P+m\angle ...[/tex]

We can see that angle PMN is an exterior angle of our given triangle, so its measure will be equal to the sum of the opposite interior angles.

We can see that angle P and angle PLM are opposite interior angle of angle PMN, so we can set an equation as:

[tex]m\angle PMN=m\angle P+m\angle PLM[/tex]

Therefore, the correct expression for blank in 4th step would be [tex]]angle PLM[/tex].

5. [tex]...=...+180^{\circ}-3x[/tex]

Our next step is to substitute the values of angle PMN and angle P as given in the diagram.

[tex]2x+72^{\circ}=x+180^{\circ}-3x[/tex]

Therefore, our 5th step would be [tex]2x+72^{\circ}=x+180^{\circ}-3x[/tex].

6. [tex]x=[/tex]

Now, we need to solve for x using algebra as:

[tex]2x+72^{\circ}=x-3x+180^{\circ}[/tex]

[tex]2x+72^{\circ}=-2x+180^{\circ}[/tex]

[tex]2x+2x+72^{\circ}=-2x+2x+180^{\circ}[/tex]

[tex]4x+72^{\circ}=180^{\circ}[/tex]

[tex]4x+72^{\circ}-72^{\circ}=180^{\circ}-72^{\circ}[/tex]

[tex]4x=108^{\circ}[/tex]

[tex]\frac{4x}{4}=\frac{108^{\circ}}{4}[/tex]

[tex]x=27^{\circ}[/tex]

Therefore, the value of x is 27 degrees.

Answer:

1,215

Step-by-step explanation:

39/13=3

45*(3)^x

45*(3)^3

45*(27)

1,215

Final answer:

To find the number of foxes after 39 years, use the population growth function y = 45 *[tex]3^x[/tex]. Since 39 years corresponds to 3 periods of 13 years each, the equation becomes y = 45 * [tex]3^3,[/tex] resulting in 1215 foxes.

Explanation:

The student has asked how many foxes will there be after 39 years, given the population growth function y equals 45 times 3 to the x power, where x represents the number of 13-year periods. To solve this, we calculate the value of x by dividing the total time of population observation (39 years) by the duration of one population tripling period (13 years). This gives us:

x = 39 years / 13 years/period = 3 periods

We then substitute x into the equation and get:

y = 45 *[tex]3^3,[/tex] = 45 * 27 = 1215 foxes

Therefore, there will be 1215 foxes in the wildlife preserve after 39 years.

Answer:

[tex]\sqrt[7]{x^{4}}[/tex]

[tex](x^{\frac{1}{7}})^{4}[/tex]

[tex](\sqrt[7]{x})^{4}[/tex]

Step-by-step explanation:

we have

[tex]x^{\frac{4}{7}}[/tex]

Remember the properties

[tex]\sqrt[n]{a^{m}}=a^{\frac{m}{n}}[/tex]

[tex](a^m)^{n}=a^{m*n}[/tex]

so

Verify each case

Part 1) we have

[tex]\sqrt[4]{x^{7}}[/tex]

we know that

[tex]\sqrt[4]{x^{7}}=x^{\frac{7}{4}}[/tex]

Compare with the given expression

[tex]x^{\frac{7}{4}} \neq x^{\frac{4}{7}}[/tex]

Part 2) we have

[tex]\sqrt[7]{x^{4}}[/tex]

we know that

[tex]\sqrt[7]{x^{4}}=x^{\frac{4}{7}}[/tex]

Compare with the given expression

[tex]x^{\frac{4}{7}} = x^{\frac{4}{7}}[/tex]

therefore

Is equivalent to the given expression

Part 3) we have

[tex](x^{\frac{1}{7}})^{4}[/tex]

we know that

[tex](x^{\frac{1}{7}})^{4}=x^{\frac{4}{7}}[/tex]

Compare with the given expression

[tex]x^{\frac{4}{7}} = x^{\frac{4}{7}}[/tex]

therefore

Is equivalent to the given expression

Part 4) we have

[tex](x^{\frac{1}{4}})^{7}[/tex]                      

we know that

[tex](x^{\frac{1}{4}})^{7}=x^{\frac{7}{4}}[/tex]

Compare with the given expression

[tex]x^{\frac{7}{4}} \neq x^{\frac{4}{7}}[/tex]

Part 5) we have

[tex](\sqrt[4]{x})^{7}[/tex]

we know that

[tex](\sqrt[4]{x})^{7}=(x^{\frac{1}{4}})^{7}=x^{\frac{7}{4}}[/tex]

Compare with the given expression

[tex]x^{\frac{7}{4}} \neq x^{\frac{4}{7}}[/tex]

Part 6) we have

[tex](\sqrt[7]{x})^{4}[/tex]

we know that

[tex](\sqrt[7]{x})^{4}=(x^{\frac{1}{7}})^{4}=x^{\frac{4}{7}}[/tex]

Compare with the given expression

[tex]x^{\frac{4}{7}} = x^{\frac{4}{7}}[/tex]

therefore

Is equivalent to the given expression

Answer:

First side; 5 in

second side: 12 in

third side: 11 in

Step-by-step explanation:

A: first side     B: second side     C: third side

b = a + 7

c = 3a -4

a + b + c = 28

a + (a + 7) + (3a -4) =28

5a + 3 =  28

5a = 28 -3 = 25

a = 5

b = 12

c = 11

The length of the sides of a triangle is 5, 12, and 11.

A triangle is a 3-sided shape that is occasionally referred to as a triangle.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.

Let's say the first second and third side of the triangle is a, b and c respectively.

Now,

The second side of a triangle is 7 inches more than the first side.

b = a + 7

The third side is 4 inches less than 3 times the first.

c = 3a - 4

Now,

Perimeter = 28

a + b + c = 28

By substituting,

a + a + 7 + 3a - 4 = 28

5a + 3 = 28

a = 5

b = 5 + 7 = 12

c = 3(5) - 4 =11

Hence "The length of the sides of a triangle is 5, 12, and 11".

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Answer:

[tex]\large\boxed{x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi,\ k\in\mathbb{Z}}[/tex]

Step-by-step explanation:

[tex]\sin x-(3\sin x-1)=0\\\\\sin x-3\sin x+1=0\qquad\text{subtract 1 from both sides}\\\\-2\sin x=-1\qquad\text{divide both sides by 2}\\\\\sin x=\dfrac{1}{2}\Rightarrow x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi,\ k\in\mathbb{Z}[/tex]

[tex]\text{Equation:}\\\\\sin x=a\\\\\text{has solutions}\\\\x=\theta+2k\pi\ \vee\ x=(\pi-\theta)+2k\pi\\\\\text{Why}\ 2k\pi?\\\text{Because the sine function has a period of}\ 2\pi.[/tex]

[tex]\text{look at the table}\\\\\sin x=\dfrac{1}{2}\to x=\dfrac{\pi}{6}\ \vee\ x=\pi-\dfrac{\pi}{6}=\dfrac{5\pi}{6}[/tex]

[tex]\text{Other solution:}\\\\\sin x=\dfrac{1}{2}\Rightarrow x=\sin^{-1}\dfrac{1}{2}\\\\x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi[/tex]

Answer:

Step-by-step explanation:

(23 - 3) + (6 * 9) =

20 + 54 =

74 <===

Answer:

C

Step-by-step explanation:

The pair of functions are f(a) = 5 + a² and g(a) = √(a - 5) - 2 option third is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

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

(gof)(a) = |a| - 2

Let f(a) = 5 + a²

g(a) = √(a - 5) - 2

(gof)(a) = g(f(a)) = √(5 + a² - 5) - 2

(gof)(a) = |a| - 2

Thus, the pair of functions are f(a) = 5 + a² and g(a) = √(a - 5) - 2 option third is correct.

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Answer:

1373 r 4

Step-by-step explanation:

Given that Ahmad is riding his bike. The distance he travels varies directly with the number of revolutions (turns) his wheels make. A) Ahmed travels 8 feet per revolution. B) the slope here is 8.

The slope is the measure of rate of change in y (dependent variable) due to change in x (independent variable).

In the given question, a graph is given.

On y axis we are given distance travelled, making it the dependent variable.

On x axis we are given the number of revolutions, making it the independent variable.

On reading from the graph, coordinate (2,16) clearly lies on the graph.

It implies, distance travelled in 2 revolutions = 16 feet.

By unitary method,

distance travelled in 1 revolution = [tex]\frac{16}{2} = 8[/tex] feet.

Since, distance travelled in 1 revolution is 8 feet, the change in distance travelled on unit change of revolution is 8, making the slope of the line equals to 8.

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We know that Kayla is level 12 and gains 6 levels everyday. We know that Maddy is level 28 and gains 2 levels everyday. To find which day they are both the same level we can add.

-------------------------

Day 1:

Kayla is level 12

Maddy is level 28

Day 2:

Kayla is level 18 (12 + 6)

Maddy is level 30 (28 + 2)

Day 3:

Kayla is level 24 (18 + 6)

Maddy is level 32 (30 + 2)

Day 4:

Kayla is level 30 (24 + 6)

Maddy is level 34 (32 + 2)

Day 5:

Kayla is level 36 (30 + 6)

Maddy is level 36 (34 + 2)

-------------------------

They willl be at the same level on level 36.

-------------------------

Best of luck!

Answer:

The carpenter will need 2 plywood to build the prism.

Step-by-step explanation:

Given:

The size of the plywood = 4 ft x 8 ft

1 Unit = 4 feet

To Find :

Number of plywood sheets the carpenter would need = "

Solution:

Step 1: Find the area of  square

Area of the square is

=>[tex]4^2[/tex]

=>[tex]16 cm^2[/tex]

Here we have 3 square, so

[tex]3 \times 16[/tex]

=>[tex]48 ft^2[/tex]

Step 2 : Area of the triangle

Area of the triangle is

=>[tex]\frac{1}{2} \times b\times h[/tex]

=>[tex]\frac{1}{2} \times 4 \times 4[/tex]

=>[tex]\frac{16}{2} [/tex]

=>[tex]8ft^2[/tex]

[tex]2 \times 8 = 16ft^2[/tex]

Step 3: Finding the plywood needed

the total area of the  triangular prism is

48 + 16=  [tex]64 ft^2[/tex]

Area of the plywood wood is

=> [tex]4 \times 8[/tex]

=> [tex]32 ft^2[/tex]

Number of plywood required = [tex]\frac{\text {area of the prism}}{\text{area of one plywood}}[/tex]

=> [tex]\frac{64}{32}[/tex]

=> 2

yes, through distribution 4(n+3) n becomes 4n and 3 becomes 12

Final answer:

By applying the distributive property to 4(n+3), it simplifies to 4n + 12, showing that the expressions 4n+12 and 4(n+3) are indeed equivalent.

Explanation:

When we compare the two expressions 4n+12 and 4(n+3), we need to determine if they are equivalent. By applying the distributive property to 4(n+3), we multiply 4 by both n and 3, giving us 4n + 4×3, which simplifies to 4n + 12. This is exactly the same as the original expression 4n+12, thus the two expressions are equivalent.

Understanding this equivalence is crucial in algebra. It shows how the distributive property allows us to simplify or expand expressions, ensuring that we can see different forms of the same equation. This foundational skill is key to solving more complex algebraic problems, as it helps in recognizing patterns and simplifying equations.

Answer:

[tex]m\angle x=120^o[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of angle y

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

In the bottom triangle of the figure

[tex]30^o+30^o+m\angle y=180^o[/tex]

solve for y

[tex]60^o+m\angle y=180^o[/tex]

[tex]m\angle y=180^o-60^o[/tex]

[tex]m\angle y=120^o[/tex]

step 2

we know that

[tex]m\angle x=m\angle y[/tex] ----> by vertical angles

we have

[tex]m\angle y=120^o[/tex]

therefore

[tex]m\angle x=120^o[/tex]

Answer:

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of angle y

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

In the bottom triangle of the figure

solve for y

step 2

we know that

----> by vertical angles

we have

therefore

Step-by-step explanation:

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In the right triangle ABC of the figure, the tangent of angle C is equal to divide the opposite side to angle C (side AB) by the adjacent side to angle C (side BC)

so

[tex]tan(C)=\frac{AB}{BC}[/tex]

substitute the given values

[tex]tan(C)=\frac{11}{22}[/tex]

simplify

[tex]tan(C)=\frac{1}{2}[/tex]

Answer:

[tex]sd(X)=\sqrt{np(1-p)}=\sqrt{250*0.427*(1-0.427)}=7.82[/tex]

The best option is:

B.7.82

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

Data given

[tex]p_C[/tex] represent the real population proportion for residents born in Colorado  

[tex]\hat p_C =0.427[/tex] represent the estimated proportion for rsidents born in Colorado

[tex]n_C=250[/tex] is the sample size selected

Solution to the problem

Let X the random variable of interest (number of residents in the sample), on this case we now that:  

[tex]X \sim Binom(n=250, p=0.427)[/tex]  

The probability mass function for the Binomial distribution is given as:  

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]  

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

The expected value is given by this formula:

[tex]E(X) = np=250*0.427=106.75[/tex]

And the standard deviation for the random variable is given by:

[tex]sd(X)=\sqrt{np(1-p)}=\sqrt{250*0.427*(1-0.427)}=7.82[/tex]

The best option is:

B.7.82

The standard deviation of the number of residents in the sample who were born in Colorado

B.7.82

hence option B is correct

Given

42.7 % of Colorado residents were born in Colorado.

If a sample of 250 Colorado residents is selected at random

We have to find out  the standard deviation of the number of residents in the sample who were born in Colorado

The options are given below  

A.6.75

B.7.82

C.10.33

D.11.97

E.61.17

This problem is given problem of binomial distribution  is a discrete probability distribution of two independent events for the given parameters.

Number of Colorado students taken in sample = n =  250

Let, the percentage of Colorado residents that were born in Colorado be p

Let, the percentage of Colorado residents that were not  born in Colorado be q

The percentage of Colorado residents that were born in Colorado = 42.7% = p = 0.427

[tex]\rm \m for \; a \; binomeal\; distribution \to p = 1-q ......(1)\\Equation \ (1)\; holds\; good[/tex]

So The percentage of Colorado residents that were not born in Colorado =   q = (100-42.7) =  57.3 %

The standard deviation for binomial distribution is given by the formula as formulated in the equation number (1)

[tex]\rm \sigma = \sqrt{ n\times p\times q } .......(1)[/tex]

So we can write

Standard deviation of binomial distribution

[tex]\rm \sigma = \sqrt{ 250 \times \0.427 \times 0.573 } = 7.82[/tex]

The standard deviation of the number of residents in the sample who were born in Colorado

B.7.82

hence option B is correct

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Answer:

This ratio means for every boy there are two girls.

There are twice as many girls as there are boys. Backwards, it's there are half as many boys as there are girl.

The simplified ratio is found by reducing the ratio to the lower terms.

5/10 = 1/2

Both sides on the unsimplified ratio are division by 5. When done, it became 1/2.

Answer:5

Step-by-step explanation:The area of a 5x5 square is 25, and the perimeter would be 20. A 5x5 square's area is 5 more than the perimeter.

Answer:

I think you meant

Step-by-step explanation:

The ninth graders are hosting the next school dance. They would like to make at least a $500 profit from selling tickets. The ninth graders estimate that at most 300 students will attend the dance. They will earn $3 for each ticket purchased in advance and $4 for each ticket purchased at the door. Write a system of inequalities to represent this situation. Suppose only 30 people buy advance tickets. How many people would need to buy tickets at the door?

The common difference is basically the number at which the pattern increases.

A's common difference: 2

B's common difference: 9

C's common difference: 5

answer: A, C, B

Answer:

Step-by-step explanation:

10, 20, 30, 40

Answer:25

Answer: x = -1 and y = 5

Step-by-step explanation:

7x + 3y = 8 ........................... equation 1

4x - y = - 9 ............................ equation 2

Solving the simultaneous linear equation by substitution method , make y the subject of the formula from equation 2 , we have

y = 4x + 9 ............................. equation 3

substitute y = 4x + 9 into equation 1 , we have;

7x + 3 ( 4x + 9 ) = 8

7x + 12x + 27 = 8

19x + 27 = 8

subtract 27 from both sides

19x = -19

divide through by 19

x = -1

substitute x = -1 into equation 3 , we have

y = 4 ( -1) + 9

y = -4 + 9

y = 5

Therefore :

x = -1 and y = 5

The volume is approximately 1130.5 m³.

A cylinder's volume can be calculated using the formula

V = π r² h

Given a base diameter of 12m (radius = 6m) and a height of 10m,

we substitute these values into the formula and get the volume:

V = 3.142 × (6m)² × 10m

V = 1130.52 m³

Answer:

C

Step-by-step explanation:

Rather than picking, let's try to construct one from the description.

reflected over the x axis means -[tex]\sqrt{x}[/tex]

the vertex is usually at (0,0), now how do we move a graph?  or in other words  translating it.

To move left and right you use [tex]\sqrt{x-h}[/tex] where if you subtract h you move right and if you add h you move left.  we go from (0,0) to (-4,2).  so 0 to -4 is 4 left, so that means we add 4.

To move up and down we use [tex]\sqrt{x}+v[/tex] Here if v is positive you move up and if v is negative you move down.  going from (0,0) to (-4,2) it moves up 2

So now we put them all together [tex]-\sqrt{x+4}+2[/tex]  And if you look, C matches that exactly.

The correct equation is option C: y = -√(x + 4) + 2, which describes a square root function reflected across the x-axis with a vertex at (-4, 2).

We are given a square root function that is reflected across the x-axis and has a vertex at (-4, 2). Let's analyze which of the provided options fits this description step by step.

Thus, option C is the correct equation that describes the square root function reflected across the x-axis with a vertex at (-4, 2).

Answer:   [tex]PQ=16\ units[/tex]

Step-by-step explanation:

The missing figure is attached.

The perimeter of a rectangle is:

[tex]P=2l+2w[/tex]

Where "l" is the lenght and "w" is the width.

You can identify in the figure that:

[tex]w=SR=PQ=2z+2\\\\l=QR=PS=3z+1[/tex]

Then, knowing the perimeter of the rectangle, you can make the subsitution into the formula:

 [tex]76=2(3z+1)+2(2z+2)[/tex]

Now you must simplify and solve for "z"

[tex]76=6z+2+4z+4\\\\76-6=10z\\\\70=10z\\\\\frac{70}{10}=z\\\\z=7[/tex]

Finally, substituting the value of "z" into  [tex]PQ=2z+2[/tex], you get:

 [tex]PQ=2(7)+2=16\ units[/tex]

Answer:

13/7, 221/182 and expansion, 507 inches

Step-by-step explanation:

If the two quadrilaterals are similar, you can take the diagonal length as a similar side to find the scale factor. In this case, the scale factor would be 13/7. For simplicity, we can keep this a factor for now. Because the quadrilaterals are similar, the scale factor is the same for all sides, 13/7. Because you are going from ABCD to EFGH and the scale factor is 13/7 (otherwise the other way around would be 7/13) and so the scale factor is greater than 1, you are expanding aka expansion. So, to find EF from side AB and you have the length 17/26, just multiply that by 13/7 to get 221/182 as the length.

To find the area of EFGH, you square the scale factor 13/7 and equal it to the area of EFGH A is over the area of the ABCD (you ratio them and set them equal) so 169/49 = A/147 and solve for A which is then 49A = 169 x 147 which is then 507 inches.  

Final answer:

Explaining how to find the scale factor, determine expansion/contraction, calculate side length, and find the area in similar quadrilaterals.

Explanation:

Scale factor: To find the scale factor, we compare the diagonal lengths. AC:EG = 7:13. The scale factor from BC to FG is 7/13.

Expansion or Contraction: Since the scale factor is greater than 1, this dilation is an expansion.

Side EF length: If AB is 17/26, then EF = (13/7) * (17/26) = 221/182 inches.

Area of EFGH: Since the scale factor is 7/13, the area is scaled by (7/13)^2 = 49/169 of the original area. Area of EFGH = 147 * 49/169 = 42 square inches.

Answer:

The 9th term for given sequence is 16.777

Therefore the 9th term is [tex]a_{9}=16.777[/tex].

Step-by-step explanation:

Given first three terms of a sequence are 100,80,64,...

Given [tex]a_{1}=100[/tex] ,[tex]a_{2}=80[/tex] , [tex]a_{3}=64[/tex],...

Given sequence is of the form of Geometric sequence

Therefore it can be written as [tex]{\{a,ar,ar^2,...}\}[/tex]

therefore a=100 , ar=80 , [tex]ar^2=64[/tex] ,...

To find common ratio

[tex]r=\frac{a_{2}}{a_{1}}[/tex]

[tex]r=\frac{80}{100}[/tex]

[tex]r=\frac{4}{5}[/tex]

[tex]r=\frac{a_{3}}{a_{2}}[/tex]

[tex]r=\frac{64}{80}[/tex]

[tex]r=\frac{4}{5}[/tex]

Therefore [tex]r=\frac{4}{5}[/tex]

The nth term of the geometric sequence is

[tex]a_{n}=ar^{n-1}[/tex]

To find the 9th tem for the given geometric sequence is

[tex]a_{n}=ar^{n-1}[/tex]

put n=9, a=100 and  [tex]r=\frac{4}{5}[/tex]

[tex]a_{9}=100(\frac{4}{5})^{9-1}[/tex]

[tex]=100(\frac{4}{5})^{8}[/tex]

[tex]=100(\frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5})[/tex]

[tex]=100(\frac{256\times 256}{625\times 625})[/tex]

[tex]=100(\frac{65536}{390625})[/tex]

[tex]=100(0.16777})[/tex]

[tex]=16.777[/tex]

Therefore [tex]a_{9}=16.777[/tex]

The 9th term is 16.777

Answer:

The required equation of line is 3x + 2y =13

Step-by-step explanation:

Here we are given two points are we are supposed to find the line passing through the two points.

The given points are (3,2) and (5,-1).

There is only one line passing through these two points.

The slope of the given line = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

                                              = [tex]\frac{-3}{2}[/tex]

y - [tex]y_{1} = m(x - x_{1})[/tex]  

y - 2 = [tex]\frac{-3}{2}[/tex](x - 3)

2y - 4 = - 3x + 9

3x + 2y = 13

The required line is 3x + 2y = 13