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Answer:

(a⁴+b⁴)(a²+b²)

Step-by-step explanation:

in the pictures

Answer:

3/4a -1/2a=8-4

1/4a=4

a=4/1/4

=16

Answer:

$16

1/2a=8

a=8*2

a=16

Answer:

They are similar by the definition of similarity in terms of a dilation

Step-by-step explanation:

The given vertices of triangle ΔABC are;

A(1, 5), B(3, 9), and C(5, 3)

The vertices of triangle ΔDEF are;

D(-3, 3), E(-2, 5), and F(-1, 2)

Therefore, we get;

The length of segment, [tex]\overline{AB}[/tex] = √((9 - 5)² + (3 - 1)²) = 2·√5

The length of segment, [tex]\overline{BC}[/tex] = √((9 - 3)² + (3 - 5)²) = 2·√10

The length of segment, [tex]\overline{AC}[/tex] = √((5 - 3)² + (1 - 5)²) = 2·√5

The length of segment, [tex]\overline{DE}[/tex] = √((5 - 3)² + (-2 - (-3))²) = √5

The length of segment, [tex]\overline{EF}[/tex] = √((2 - 5)² + (-1 - (-2))²) = √10

The length of segment, [tex]\overline{DF}[/tex] = √((2 - 3)² + (-1 - (-3))²) = √5

∴ [tex]\overline{AB}[/tex]/[tex]\overline{DE}[/tex] = 2·√5/(√5) = 2

[tex]\overline{BC}[/tex]/[tex]\overline{EF}[/tex] = 2·√10/(√10) = 2

[tex]\overline{AC}[/tex]/[tex]\overline{DF}[/tex] = 2·√5/(√5) = 2

The ratio of their corresponding sides are equal and therefore;

ΔABC and ΔDEF are similar by the definition of similarity in terms of dilation.

Answer:

Solution given:

area of semi circle h=½πr²=½×π×5²=39.27in²

area of rectangle EFHI=l×b=6×3=18in²

area of rectangle CDFG=l×b=17×2=34in²

Total area: 39.27+18+34=91.27 square inches

Answer:

.81 Repeating Decimal

Step-by-step explanation:

I think

Answer:

0.81

Step-by-step explanation:

18 divide by 22 is 0.81

Answer:

[tex]6a - 2[/tex]

Step-by-step explanation:

[tex]a - 2 + 5a[/tex]

[tex]6a - 2[/tex]

By definition of the focus of a parabola, the coordinates of the focus of the parabola - 8 · (x - 5) = (y + 1)² are represented by the point F(x, y) = (3, - 1). (Correct choice: A)

The standard equation of the parabola with an horizontal axis of symmetry is presented below:

[tex]x - h = \frac{1}{4\cdot p}\cdot (y - k)^{2}[/tex]     (1)

Where:

The coordinates of the focus is described by the following expression:

F(x, y) = (h + p, k)

If we know that h = 5, k = - 1 and p = - 2, then the coordinates of the focus are:

F(x, y) = (5 - 2, - 1)

F(x, y) = (3, - 1)

By definition of the focus of a parabola, the coordinates of the focus of the parabola - 8 · (x - 5) = (y + 1)² are represented by the point F(x, y) = (3, - 1). (Correct choice: A)

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Answer:

Either C or A

Step-by-step explanation:

Hope it help you have a good day

Answer: Number of hardback = 32

Number of paperback = 117

Step-by-step explanation:

Let the number of hardback books be represented by x.

Let the number of paperback books be represented by y.

Based on the information given, we can form an equation which will be:

x + y = 149 ......... i

3.50x + 0.75y = 199.75 ...... ii

Multiply equation i by 3.50

Multiply equation ii by 1

3.50x + 3.50y = 521.50 ...... iii

3.50x + 0.75y = 199.75 .....iv

Subtract equation iv from iii

2.75y = 321.75

y = 321.75 / 2.75

y = 117

Number of paperback = 117

Since x + y = 149

x = 149 - y

x = 149 - 117

x = 32

Number of hardback = 32

Answer:

It could be =15 or =0

Step-by-step explanation:Multiplying each side of −3x+4y=20

by 2 gives −6x+8y=40

. Adding each side of −6x + 8y = 40 to the corresponding side of 6x+3y=15

gives 11y=55,ory=5

. Finally, substituting 5 for y in 6x+3y=15

gives 6x+3(5)=15,orx=0

.

Answer:

x-3y=15 has a y-intercept of -5

Step-by-step explanation:

A y-intercept occurs when x = 0. So, when x = 0, which function has a y-value of -5?

Plug in 0 for all the values of x and solve for y.

1. 2(0)+y=-10; y=-10

2. (0)-y=-5; y = 5

3. (0)-3y=15; y = -5

4. -(0)+4y=20; y= 5

Answer:

x = 2

Step-by-step explanation:

2x−3-x+4=3

combine like terms:

x + 1 = 3

x = 2

The equation is true for the value of x = 2.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given equation is as given below.

2x − 3 - x + 4 = 3

We have to operate the like terms together.

Here 2x and x are like terms and 3 and 4 are like terms.

(2x - x) - 3 + 4 = 3

x - 3 + 4 = 3

x + 1 = 3

Subtracting 1 on both sides,

x = 3 - 1

x = 2

Hence the equation is true for x = 2.

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Answer:

[tex]A\simeq3399.41[/tex]

Step-by-step explanation:

The amount formula in compound interest is:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

where:

P = principal amount

r = annual interest

n = number of compounding periods

t = number of years

We already know that:

P = $3000

[tex]r = 6.25\% = \frac{6.25\%}{100\%}=0.0625[/tex]

t = 2

n = 365

Then,

[tex]A=3000(1+\frac{0.0625}{365} )^{(365)(2)}\\\\A=3000(1+\frac{0.0625}{365} )^{730}\\\\A=3399.408982\\\\A\simeq3399.41[/tex]

Answer:

Lateral Area = Area of 2 triangle + Area of slant rectangle + area of back rectangle

Lateral Area = (5m)(3m) + (6m) (36m) + (3m) (36m)

LA = 15m² + 216m² + 108m²

LA = 339 m²

SA = (5m)(3m) + (6m) (36m) + (3m) (36m) + (5m)(36m)

SA = 15m² + 216m² + 108m² + 180 m²

SA = 519 m²

Answer:

Step-by-step explanation:

Algebra Examples

Popular Problems Algebra Graph y=7x-8

y

=

7

x

−

8

Use the slope-intercept form to find the slope and y-intercept.

Tap for more steps...

Slope:  

7

y-intercept:  

(

0

,

−

8

)

Any line can be graphed using two points. Select two  

x

values, and plug them into the equation to find the corresponding  

y

values.

Tap for more steps...

x

y

0

−

8

8

7

0

Graph the line using the slope and the y-intercept, or the points.

Slope:  

7

y-intercept:  

(

0

,

−

8

)

x

y

0

−

8

8

7

0

y=7x-8

Answer:

a) 24

b) 10

c) 12/13

d) 5/13

e) 12/5

Step-by-step explanation:

a) We can see that the leg opposite <C is AB, and we are given AB = 24

b) We can see the leg adjacent to <C is AC, and we are given that AC = 10

c) The trig function sine is equal to

[tex]\frac{opposite}{hypotenuse}[/tex]

The opposite, AB, is 24, and the hypotenuse, BC, is 26. We can plug those numbers in:

[tex]sin(c) = \frac{24}{26} = \frac{12}{13}[/tex]

d)The trig function cosine is equal to

[tex]\frac{adjacent}{hypotenuse}[/tex]

The adjacent, AC, is 10, and the hypotenuse, BC, is 26. We can plug those numbers in:

[tex]cos(c) = \frac{10}{26} = \frac{5}{13}[/tex]

d)The trig function tangent is equal to

[tex]\frac{opposite}{adjacent}[/tex]

The opposite, AB, is 24, and the adjacent, AC, is 10. We can plug those numbers in:

[tex]tan(c) = \frac{24}{10} = \frac{12}{5}[/tex]

Answer:

$28.20

Step-by-step explanation:

11 bumper stickers = $10.34

per sticker = $0.94

30 bumper stickers = 30*0.94

=28.20

30 bumper stickers = $28.20

Answer:

$28.20

Step-by-step explanation:

First, find out how much each bumper sticker costs.

Assuming that the cost of each bumper sticker is the same, the following equation represents how much one number sticker costs.

11x = 10.34

Solve for x [divide both sides by 11]

x = 0.94

So, one bumper sticker costs $0.94

Now, find out how many 30 bumper sticker costs.

The following equation represents how much 30 stickers cost.

30x = y

X represents the cost of one sticker and y represents the cost of 30 stickers.

We already know the value of x [one bumper sticker's cost] which is $0.94, so subsitute that in for x.

30[0.94] = y

28.2 = y

So, 30 bumper stickers cost $28.20.

:)

Answer:

P (1 + r/n)^(nt)

Step-by-step explanation:

Answer:

A = P(1+r/n)nt

(note the r/n is a fraction)

Step-by-step explanation:

Answer:

the answer I think your looking for is C

Answer: it’s C

Step-by-step explanation:

Answer:

L=923.6 cm2 ; S =1231.5 cm2

Explanation:

L=2πR

L=14π

2πR=14π

R=14π/2π=7 - the radius

h=3R=3*7=21 -the height

S(l)=2πRh=Lh=14π*21=294π≈923,6 - the lateral area

S(s)=2πR²+Lh=2π*7²+294π=2π*49+294π=98π+294π=

     =392π≈1231,5 -the surface area

Answer:

20

Step-by-step explanation:

In an academic contest correct answers earn 12 points and incorrect answers lose 5 points. In the final round school A starts with 165 points and gives the same number of correct and incorrect answered. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. How many answers did each school get in the final round?

Let x = number correct answers

because school a , gives the same correct and wrong answers, their equation can be represented as :

165 - 5x + 12x =

165 + 7x

School b gives no wrong answer. their equation can be represented as

65 + 12x

to fing the number of correct answers given, equate the two equations

165 + 7x = 65 + 12x

collect like terms

165 - 65 = 12x - 7x

100 = 5x

x = 20

Answer:

The answer its A:

Step-by-step explanation:

I hope its correct.

Given here is a cube, whose one side is increased by a given percentage. The task is to find percentage increase in the volume of the cube. Below is the implementation of the above approach: