What angle corresponds to angle AFG?

Answer:

Step 2: 4(2) + 4(3x)

Step-by-step explanation:

By definition, the area of a rectangle is given by:

Area = Length × Width

In this case, we know that:

Area = 8 + 12x

Width = 4

Therefore:

Step 1: 8 + 12x

Step 2: 4(2) + (4)(3x)

Step 3: 4(2 + 3x)

Therefore, the dimensions of the rectangle are 4 and 2 + 3x.

The mistake was made in STEP 2. Instead of 4(2) + 4(x2) it should be  4(2) + 4(3x). Which is the second option.

Answer:

2.5 Days

Step-by-step explanation:

Answer:

2.5 days

Step-by-step explanation:

[tex]\bf \qquad \qquad \textit{joint compound proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{\underline{y} varies directly as \underline{u} and inversely as }p^4}{y=\cfrac{ku}{p^4}}[/tex]

first term =36

second term=69

So common difference=69-36=33

checking. 69+33=102

36=3+33

so the series in AP Becomes as...

(3+33) ,(36+33) ,(36+2(33)) ... (36+7(33))

So The Answer is...

(refer above attachment.)

Hope it helps...

Regards,

Leukonov/Olegion.

Answer:

Step-by-step explanation:

For angle A we have

opposite = 8

adjacent = 6

hypotenuse = 10

sin A = opposite/hypotenuse

cos A = adjacent/hypotenuse

tan A = opposite/adjacent

cot A = adjacent/opposite

6/10 = adjacent/hypotenuse = cos A

The trigonometric function of the triangle is given by cos A = 6/10

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔABC

where the measure of ∠ABC = 90°

Now , from the trigonometric relations ,

cos θ = adjacent / hypotenuse

So , on simplifying , we get

The measure of BC = 6 units

The measure of AB = 8 units

The measure of AC = 10 units

cos A = 6 / 10

Hence , the measure of cos A of triangle is cos A = 6 / 10

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Answer:

see explanation

Step-by-step explanation:

Given the 2 equations

x² + y² = 5 → (1)

2x + y = 4 → (2)

Rearrange (2) expressing y in terms of x by subtracting 2x from both sides

y = 4 - 2x → (3)

Substitute y = 4 - 2x in (1)

x² + (4 - 2x)² = 5 ← expand factor on left side

x² + 16 - 16x + 4x² = 5

5x² - 16x + 16 = 5 ( subtract 5 from both sides )

5x² - 16x + 11 = 0 ← in standard form

(5x - 11)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

5x - 11 = 0 ⇒ 5x = 11 ⇒ x = [tex]\frac{11}{5}[/tex]

Substitute each of these values into (3) for corresponding values of y

x = 1 : y = 4 - 2 = 2 ⇒ P(1, 2)

x = [tex]\frac{11}{5}[/tex] : y = 4 - [tex]\frac{22}{5}[/tex] = - [tex]\frac{2}{5}[/tex]

Hence Q( [tex]\frac{11}{5}[/tex], -[tex]\frac{2}{5}[/tex] )

Answer:

b

Step-by-step explanation:

it makes sense because they all are going down by 1 side each time

B) the triangle because each figure is loosing one side

Answer:

White: 2/5

Dark: 3/5

Step-by-step explanation:

There are 5 sections and there are 2 white spots and 3 dark spots.

So, 2 out of the 5 sections are white which is 2/5 and 3 out of the 5 sections is dark which is 3/5.

Answer:

Step-by-step explanation:

Given : The total number of sections = 5

The number of white sections = 2

The number of dark sections =3

Now, the probability that the spinner lands on a white section is given by :-

[tex]\text{P(white)}=\dfrac{\text{Number of white sections}}{\text{total sections}}\\\\=\dfrac{2}{5}[/tex]

Now, the probability that the spinner lands on a dark section is given by :-

[tex]\text{P(dark)}=\dfrac{\text{Number of dark sections}}{\text{total sections}}\\\\=\dfrac{3}{5}[/tex]

Answer:

10 ounces of water

Step-by-step explanation:

16=8/5

z=1

16*1=16

8/5*z=8/5z

16=8/5z

16/1.6z=10

z = 10

Answer:

10 ounces of water

Step-by-step explanation:

Answer: $40.80

Explanation: 60*.68=40.8

Answer:

Sale price = $40.80

Step-by-step explanation:

The original price = $60

After mark down of 32% is applied,

The selling price becomes 100% - 32% = 68%

The selling price = 68% of $60 = [tex]\frac{68}{100}[/tex] × $60 = $40.80

Answer:

68.7

Step-by-step explanation:

We need only estimate (approximate) the value of f(x) at x = 5:

f(x)=6.87(2.5)(x – 1)   →   f(5)=6.87(2.5)(5 – 1).

Note that 2.5(4) = 10, so now we have (exactly) f(5)=6.87(10), which, in turn, is

equal to 68.7.

Answer:

About 1 dollar.

Step-by-step explanation:

First we must establish the possible values that 96 cents can be rounded to.

We know that 96 cents is more than nothing, or 0. We also know that a dollar is 100 cents. This means 96 cents is in between 0 and 1 dollar. We just have to determine whether 96 is closer to 100 cents or 0 cents.

To do this find the difference between 96 and each value.

100-96 = 4

96-0 =96

The difference between 96 and 100 is smaller, so the values are closer and 96 should be rounded to a dollar.

Answer:

B: 4x − 2y = 2

B: 4x − 2y = 2  equation completes the system that is satisfied by the solution (1, 1).

A linear equation has one or two variables.

solving this we will get the valve of Y if x is given.

explanation:

line R = x + y = 2

putting the value of X=1 & y=1 as given (1,1)

x+y =2

1+1= 2

therefore, 4x - 2y = 2

4(1) - 2(1)= 2 answer

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Answer:

sin(81)

Step-by-step explanation:

Since the sine of something is the ratio of the opposite side to the hypotenuse, to get the same ratio in cosine, you take the complement of the angle. So the answer is sin(90 - 9) or sin(81).

The expression in terms of cosine cos 81°. The expression is obtained by the trigonometric rules.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

The given expression is;

sin9°

The expression in terms of cosine.

sin 9°= sin(90-81°)

sin 9°= cos 81°

Hence,the expression in terms of cosine cos 81°.

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Answer:

  4. Your working and answers are correct: x = 44, y = 43.

  5. GH = 60°

Step-by-step explanation:

5. Arc GH is double the inscribed angle GFH, so we have ...

  2(4x+2) = 9x-3

  8x +4 = 9x -3 . . . . . simplify

  7 = x . . . . . . . . . . . . add 3-8x

Then the arc's measure is ...

  (9·7 -3)° = (63 -3)° = 60°

Answer:

Step-by-step explanation:

Your working and answers are correct: x = 44, y = 43.

5. GH = 60°

Answer:

∠A ≅ ∠A'  and CB ~ C'B'

Step-by-step explanation:

In a dilation, you get a SIMILAR figure. It will have the same shape, but a different size.

Similar figures have the same angle measures but the side lengths will change.

Any of the answers with congruent (≅) angles are correct:

∠A ≅ ∠A'

Any of the answers with SIMILAR (~) side lengths are correct:

CB ~ C'B'

Answer:

∠A ≅ ∠A'  and CB ~ C'B'

Step-by-step explanation:

Answer:

The expression which is equivalent to (k ° h)(x) is [tex]\frac{1}{(5 + x)}[/tex] ⇒ 2nd answer

Step-by-step explanation:

* Lets explain the meaning of the composition of functions

- Composition of functions is when one function is inside of an another

 function

# If g(x) and h(x) are two functions, then (g ° h)(x) means h(x) is inside

  g(x) and (h ° g)(x) means g(x) is inside h(x)

* Now lets solve the problem

∵ h(x) = 5 + x

∵ k(x) = 1/x

- We need to find (k ° h)(x), that means put h(x) inside k(x)

* Lets replace the x of k by the h(x)

∵ k(x) = [tex]\frac{1}{x}[/tex]

∵ h(x) = 5 + x

- Replace the x of k by 5 + x

∴ k(5 + x) = [tex]\frac{1}{5 + x}[/tex]

∴ The expression which is equivalent to (k ° h)(x) is [tex]\frac{1}{5+x}[/tex]

Answer:

the answer would be y=2x+4

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I just finished the quiz, and this was my only incorrect one. The correct answer is A. Also, think logically. If the sun is spread out over more area, then it must be at a smaller angle. This leads to cooler temperatures, of course.

Final answer:

To evaluate the expression (-5+7x1)-9x5, follow the order of operations: calculate inside the parentheses, multiply, and then subtract, resulting in a final answer of 47.

Explanation:

To evaluate the expression (-5+7×1)-9×5, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). Let's break down the expression step by step:

Inside the parentheses: -5 + (7 × 1) = -5 + 7 = 2.

Multiply: -9 × 5 = -45.

Subtract the value obtained from step 2 from the result of step 1: 2 - (-45).

Change the subtraction of a negative value to addition: 2 + 45 = 47.

Thus, the expression (-5+7×1)-9×5 evaluates to 47.

Line graph because it shows differences

So this equation is in slope intercept form:

y = mx + b

m is slope

b is y-intercept

This means that for this equation the slope is 6/5 and the y-intercept is (0 , 1)

Look at image below for the graph

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

B.[tex]14in^{2}[/tex]

Step-by-step explanation:

Solve this by using one of two methods.

Split up into different shapes:

This method uses the sum of the areas of a rectangle and two triangles to find the area of the parallelogram:

[tex]A=(b*h)_{rectangle} +2*(0.5*b*h)_{triangle} \\A=(5*2)+2(0.5*2*2)\\A=10+4\\A=14in^{2}[/tex]

Use Parallelogram formula:

This formula is the same as the formula for a rectangle where you multiply the base by the height.

[tex]A=b*h\\A=(5+2)*2\\A=14in^{2}[/tex]

Answer: The answer is 14 in2

Answer:

The answer is actually C. here's proof:

It also makes sense since 2.5 is very unlikely, so the change is significant.

Answer:

Step-by-step explanation:

If you use pemdas, you would do 3÷1/3 which equals 9. Then do 9-9, which equals 0. Then, do 0+1, which equals 1. Hope this helps! <3

[tex]9 - 3 \div \frac{1}{3} + 1 = [/tex]

Divisions go first, to do it we have to reverse the fraction and turn ÷ into ×

[tex] = 9 - 3 \times 3 + 1 = [/tex]

Now the multiplication

[tex] = 9 - 9 + 1 = [/tex]

[tex] = 1[/tex]

Answer:7

Step-by-step explanation:

In the first store, you pay 12.5+1.5x per x movies

In the second store, you pay 3.5x per x movies

The first store offers a better deal when:

12.5 + 1.5x > 3.5x

12.5 > 2x

6.25 > x

Which means if you rent minimum 7 movies in month, you should go to the first store

Answer:

Step-by-step explanation:

We know that the first store charges $12.50 per month, which is a initial condition, and charges additionally $1.50 per movie, which is variable, this represents the ratio of change, so this can be expressed as

[tex]\$12.50 + \$1.50x[/tex]

Where [tex]x[/tex] represents movies.

Now, the second store doesn't charge and membership fee, just it charges a cost per movie which is $3.50.

Then, to solve the minimum number of movies needed to Plan A be the best choice, we just have to solve the following inequality

[tex]\$12.50 + \$1.50x> \$3.50[/tex]

Which expresses the case where Plan A is a better choice, solving for [tex]x[/tex], we have

[tex]\$12.50 + \$1.50x> \$3.50x\\\$1.50x - \$3.50x >-\$12.50\\(-1)(-2x)>(-12.50)(-1)\\2x<12.50\\x<\frac{12.50}{2}\\ x<6.25[/tex]

Which means that the minimum number of movies is 7, which is the next whole number after 6.

Answer:

She'll need 8143 cubic inches of foam and 1,809.6  square inches of fabric.

Step-by-step explanation:

Assuming you want to know how much foam and fabric she will need...

First the foam... so we need to determine the volume of that footstool.  The Volume of a cylinder is given by:

V = π * r² * h

So, we plug in the numbers:

V = π * 12² * 18 = π * 144 * 18

V = 2,592 π  = 8143 cubic inches.

Now for the fabric... we'll assume Maria wants to cover the side of the stool and the top, but not the bottom.

The side of the stool is basically a rectangle of width of 18 inches and a length of the circumference of the base of the stool.  The circumference is given by: C = 2 π * r of course, so C = 24π = 75.14 inches.

So the lateral surface of the cylinder is:

LS = 18 * 75.14 = 1,357.2 sq inches.

Then we need to calculate the area of the top... which is easy:

A = π * r²  = π * 12²  = 144 π = 452.4 sq inches

So, to cover the lateral side of the footstool and its top, she needs to use:

TA = 1,357.2 + 452.4 = 1,809.6 sq inches of fabric.

Answer:

The fabric needed = 2260.8 square inches

Step-by-step explanation:

Points to remember

Surface area of cylinder = 2πr(r + h)

It is given that,

Maria want to make a footstool in the shape of a cylinder.

radius of cylinder = 12 in and height = 18 in

To find the surface area

Here r = 12 in and h = 18 in

Surface area = 2πr( r + h)

 = 2 * 3.14 * 12 (12 + 18)

 = 2260.8 square inches

P means permutation, so using the permutation formula:

8P4 = 8! / (8-4)!

= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (4 x 3 x 2 x 1)

= 8 x 7 x 6 x 5

= 1680

The answer is C.

Answer:

C

Step-by-step explanation:

Its C

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{6}{ h},\stackrel{-3}{ k})\qquad \qquad radius=\stackrel{5}{ r}\\[2em] [x-6]^2+[y-(-3)]^2=5^2\implies (x-6)^2+(y+3)^2=25[/tex]

Answer:

Step-by-step explanation:

The x value for the center is part of the x^2 part of the equation.

The y value for the center is part of the y^2 part of the equation.

The radius is squared.

(x - 6)^2 + (y + 3)^2 = 5^2  

Notice the sign change for the center. When you move horizontally the sign of the center changes sign in the circle's equation.

The graph is included to show you that.

let's firstly convert the mixed fractions to improper fractions and proceed from there.

[tex]\bf \stackrel{mixed}{8\frac{2}{3}}\implies \cfrac{8\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{26}{3}}~\hfill \stackrel{mixed}{7\frac{x}{3}}\implies \cfrac{7\cdot 3+x}{3}\implies \stackrel{improper}{\cfrac{21+x}{3}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \cfrac{26}{3}=\cfrac{21+x}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3\left( \cfrac{26}{3} \right)=3\left( \cfrac{21+x}{3} \right)}\implies 26=21+x\implies \boxed{5=x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 8\frac{2}{3}=7\frac{5}{3}~\hfill[/tex]

7 5/3 if that’s what your asking

8 2/3 is equal to 7 5/3