5^-4 over 5^3
simplify
A. 5^7
B. 5^-1
C. 1/5
D. 1/5^7​

Answer:

HT = 17 cm

<T = 58°

<H = 32°

Step-by-step explanation:

✔️Find HT:

Since it's a right triangle, we would apply the Pythagorean Theorem given as c² = a² + b²

Where,

a = HW = 15 cm

b = WT = 8 cm

c = HT

Plug in the values:

HT² = 15² + 8²

HT² = 289

HT = √289

HT = 17 cm

✔️Find <T by applying trigonometric ratio formula:

Recall: SOH CAH TOA

Reference angle (θ) = <T

HW = 15 cm = Opposite side length

WT = 8 cm = Adjacent side length

Apply CAH:

Cos θ = Adj/Hyp

Substitute

Cos T = 8/15

T = [tex] cos^{-1}(0.5333) [/tex]

T ≈ 58°

✔️Find <H:

Sun of interior angles of a triangle = 180°

Therefore,

m<H + m<T + m<W = 180°

Substitute

m<H + 58° + 90° = 180°

m<H + 148° = 180°

m<H = 180° - 148°

m<H = 32°

Answer:

B.) x^12

Step-by-step explanation:

You don't multiply the exponents when multiplying x^7 × x^5, you add them.

If we add the exponents, we get x^12.

Hope this helps!

If there is something wrong, just let me know.

Answer:

D

Step-by-step explanation:

We are given the two functions:

[tex]f(x) = 5x^2-x+1 \text{ and } g(x) = -3x[/tex]

And we want to find:

[tex](f \circ g)(1)[/tex]

Recall that this is equivalent to:

[tex]=f(g(1))[/tex]

Evaluate g(1):

[tex]g(1) = -3(1) = -3[/tex]

Substitute:

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

Evaluate f(-3):

[tex]f(-3)=5(-3)^2-(-3)+1=49[/tex]

Therefore:

[tex](f \circ g)(1) =49[/tex]

Our answer is D.

Answer:

49

Step-by-step explanation:

ƒ(x) = 5x2 – x + 1 and g(x) = –3x

(ƒ ∘ g)(1)

First find g(1) = -3(1) = -3

Then find f(g(1) = f(-3)

f(-3) = 5(-3)^2 - (-3) +1 = 5(9) +3+1 = 45+4 = 49

Answer:

x=5, y=3

Step-by-step explanation:

Answer:

B. False

Step-by-step explanation:

There is not enough information to make that conclusion. The two statements are completely unrelated, so the transitive property cannot be used. None of the given statements say that ABC is congruent to MNO or PQR. That means that nothing can be assumed about DEF. To use the transitive property you would need proof that ABC=MNO or ABC=PQR. But neither of those statements are there so the answer is false.

Answer:

true

Step-by-step explanation:

a pe c

Answer:

y = 2x - 9

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 2 , then

y = 2x + c ← is the partial equation

To find c substitute (2, - 5) into the partial equation

- 5 = 4 + c ⇒ c = - 5 - 4 = - 9

y = 2x - 9 ← equation of line

Answer: is 3

Step-by-step explanation:

Very easy man !!!

Answer:

504 cm²

Step-by-step explanation:

Let the length and the width of the rectangle be L cm and W cm respectively.

Perimeter= 2(L +W)

2(L +W)= 108

L +W= 108 ÷2

L +W= 54

L= 54 -W -----(1)

[tex] \frac{L}{W} = \frac{7}{2} [/tex]

Cross multiply:

2L= 7W -----(2)

Substitute (1) into (2):

2(54 -W)= 7W

Expand:

108 -2W= 7W

+2W on both sides:

9W= 108

Divide both sides by 9:

W= 108 ÷9

W= 12

Substitute W= 12 into (1):

L= 54 -12

L= 42

Area of rectangle

= length ×width

= LW

= 42(12)

= 504 cm²

First, we'll set up two equations. One for the amount of each coin and another for the value of the coins.

N will represent nickels

D will represent dimes

N + D = 30

---The problem tells us that there are 30 total coins

0.05N + 0.10D = 2.95

---Nickels are worth 5 cents and dimes are worth 10 cents, and the total value of the coins is 2.95

Now that we have our equations, we need to solve for one of the variables in the first equation. I will solve for N.

N + D = 30

N = 30 - D

Then, we take that equation and substitute our new value for N into the second equation (value) and solve for D.

0.05(30 - D) + 0.10D = 2.95

1.5 - 0.05D + 0.10D = 2.95

1.5 + 0.05D = 2.95

0.05D = 1.45

D = 29

Now that we know how many dimes there are, we can plug that value into our equation for N and solve for N.

N = 30 - D

N = 30 - 29

N = 1

Therefore, there are 29 dimes and 1 nickel.

Hope this helps!

Answer:

2663.0 cm³ (3 s.f.)

Step-by-step explanation:

[tex]\boxed{volume \: of \: sphere = \frac{4}{3}\pi {r}^{3} }[/tex]

Radius= diameter ÷2

Radius of sphere

= 17.2 ÷2

= 8.6 cm

Volume of sphere

[tex] = \frac{4}{3} (3.14)(8.6)^{3} [/tex]

= 2663.0 cm³ (3 s.f.)

Angle ECD and Angle FDC are same-side interior angles. They lie on the same side of the transversal and are on the inside of the two parallel lines. Same-side interior angles are supplementary, meaning that they add up to 180.

(40x + 15) + (5x + 30) = 180

45x + 45 = 180

45x = 135

x = 3

Angle ECD = 40(3) + 15 = 120 + 15 = 135

Angle FDC = 5(3) + 30 = 15 + 30 = 45

Hope this helps!

Answer:

32 years

Step-by-step explanation:

8x12 because there are 12 inches in a foot

8x12=96

96/3

96/3=32

Answer:

32 years

Step-by-step explanation:

y = years

1 foot  = 12 inches

12 × 8 = 96

Now, plug in random numbers into the expression below to find how long it takes for the tree to grow 8 feet.

3y

3 × 10 = 30

3 × 20 = 60

3 × 30 = 90

3 × 31 = 93

3 × 32 = 96

It will take the pine tree 32 years to grow 8 feet, or 96 inches.

The function is negative for all real values of x where x < -3 or x > -1 and the domain of the function is -∝ < x < ∝

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = - ( x + 3 ) ( x - 1 )   be equation (1)

Now , the values of x which makes the function negative are

when x < -3

f ( x ) = - ( -ve ) ( -ve ) = -ve

when x > 1

f ( x ) = - ( +ve ) ( +ve ) = -ve

So , the domain of the function is all real numbers and -∝ < x < ∝

Hence , the function is solved

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Answer:

100-35=65

15*0.65=9.75

so the price now is 9.75

Hope This Helps!!!

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

see this attachment

Answer:

An inverse variation give a harder one next time

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

y coordinates must be at the numerator, while x coordinates at the denominator

Answer: 1⅓ batch of cookies

Step-by-step explanation:

From the question, we are given the information that a cook has 4 cups of raisins to make oatmeal cookies and that the recipe requires 3 cup of raisins for each batch of cookies.

Therefore, the number of batches of cookies that the cook can make will be the number of cups of rasins that the cook has divided by the number of reasons needed for each cookie. This will then be:

= 4/3

= 1⅓ batch of cookies

Answer:

x = 7.535 and y = 0.307

Step-by-step explanation:

Given that,

Two equations,

2x + 3y = 8 ...(1)

x – 5y = 6....(2)

Multiply equation (2) by -2.

-2x + 10y = -12....(3)

Now, adding equations (1) and (2),

2x + 3y -2x + 10y = 8-12

13y = 4

y = 0.307

Put the value of y in equation (2).

x – 5(0.307) = 6

x = 6 + 1.535

x = 7.535

So, the solutions of the given equation are x = 7.535 and y = 0.307.

Answer:

Value of given expression x is -4

Step-by-step explanation:

Given equation in question;

4 + 2|3x + 4| = -4

Find:

Value of given expression

Computation:

4 + 2|3x + 4| = -4

Using BODMAS rule;

⇒ 4 + 2|3x + 4| = -4

⇒ 2|3x + 4| = - 4 - 4

⇒ 2|3x + 4| = - 8

⇒ |3x + 4| = - 8 / 2

⇒ |3x + 4| = - 4

⇒ 3x + 4 = - 8

⇒ 3x = -8 - 4

⇒ 3x = -12

⇒ x = -12 / 3

⇒ x = -4

Value of given expression x is -4

Answer:

Following are the solution to the given question:

Step-by-step explanation:

For question 1:

Calculating the speed between A and B:

[tex]Time\ (t)= 1 \ hours\\\\Distance\ (d)= 10 \ km\\\\V=\frac{d}{t}=\frac{10}{1}= 10 \ kmph[/tex]

For question 2:

Calculating the speed between B and C:

[tex]Time\ (t)= (2-1)=1 \ hours\\\\Distance\ (d)= (15-10)= 5\ km\\\\V=\frac{d}{t}=\frac{5}{1}= 5 \ kmph\\[/tex]  

For question 3:

In this the speed between A and B is the double to speed between B and C.

Answer:

The equation of the circle is given by:

(x-a)^2+(y-b)^2=r^2

where:

(a,b) is the center  of the circle

given that the center of our circle is (2,3) with the radius of 5, the equation will be:

(x+2)^2+(y+3)^2=5^2

expanding the above we get:

x^2+4x+4+y^2+6y+9=25

this can be simplified to be:

x^2+4x+y^2+6y=25-13

x^2+y^2+4x+6y=12

Answer:

[tex]\sf\longrightarrow \boxed{\sf x^2+y^2-4x-6y-12=0}[/tex]

Step-by-step explanation:

Here we are given the radius of circle as 5cm and the centre of the circle is (2,3) . We need to find the equation of the circle. Here we can yse the Standard equation of circle to find the equation .

Standard equation of circle :-

[tex]\sf\implies \green{ (x - h )^2+(y-k)^2 = r^2 }[/tex]

Substitute the respective values ,

[tex]\sf\longrightarrow ( x - 2 )^2 + ( y - 3)^2 = 5^2 [/tex]

Simplify the whole square ,

[tex]\sf\longrightarrow x^2 + 4 -4x + y^2+9-6y = 25[/tex]

Rearrange and add the constants ,

[tex]\sf\longrightarrow x^2 + y^2 -4x -6y +13 = 25 [/tex]

Subtract 25 on both sides ,

[tex]\sf\longrightarrow x^2 +y^2-4x-6y+13-25=0[/tex]

Simplify ,

[tex]\sf\longrightarrow \boxed{\blue{\sf x^2+y^2-4x-6y-12=0}}[/tex]

Answer:

There are 8 bottles in each box.

Step-by-step explanation:

Victor has 12 boxes with 'n' number of water bottles in each box.

A dozen is same as 12.

Now, 12 boxes and each with 'n' number of bottles. Total number of bottles in '12' boxes is 12n bottles.

Now, it is removing 12(a dozen) bottles from 12n bottles which gives 84.

So, 12n -12=84

Add both sides 12

12n= 96

Divide both sides by 12

n=8

So, there are 8 bottles in each box.

Answer:

46°

Step-by-step explanation:

arcsin(5/7)

Answer:

-3 =x

Step-by-step explanation:

The angles are corresponding angles and corresponding angles are equal if the lines are parallel

2x+9 = 7x+24

Subtract 2x from each side

2x+9-2x = 7x+24-2x

9 = 5x+24

Subtract 24 from each side

9-24 = 5x

-15 = 5x

Divide by 5

-15/5 = 5x/5

-3 =x

Answer:

[tex]4x^3-2x^2+5x-6+\frac{1}{x}[/tex] is a polynomial

Step-by-step explanation:

a polynomial is a set of numbers with multiple terms that are not simplify able

[tex]9x^7y^{-3} z[/tex] is not a polynomial because its actually one term, there is no addition/subtraction of different terms.

-13 is a single number, so not a polynomial

13x^-2 is also a single number, not a polynomial

Step-by-step explanation:

1. The length is one more thrice it's width. The height is 4 more than it width. We can represent the

[tex](3x + 1)(x + 4)[/tex]

[tex](3 {x}^{2} + 13x + 4)x = 720[/tex]

Multiply it by x.

[tex]3 {x}^{3} + 13 {x}^{2} + 4x = 720[/tex]

[tex] 3{x}^{3} + 13 {x}^{2} + 4 x - 720[/tex]

The possible roots

The possible roots are plus or minus is1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, and 720. By a long list of substitution, 5 is a root. So this means that x=5. So the width has to be

[tex]x = 5[/tex]

2. First. we apply the Rational Root Theorem so the possible roots are plus or minus 1,2,3,6.

Let check via synethic division to see which are roots.

Let try 1 and -1 first. If we plug 1 into the equation, we get

[tex]1 - 2 - 5 + 6 = 0[/tex]

So 1 or (x-1) is a solution. Since it's a solution we can divide this into our original polynomial to get us a new polynomial that is more simplified. If we apply synthetic division, we get a new polynomial in

[tex] {x}^{2} - x - 6[/tex]

We can then factor this into

[tex](x - 3)(x + 2)[/tex]

So our roots or factors is

[tex](x - 1)(x - 3)(x + 2)[/tex]

Answer:

21x+4

Step-by-step explanation:

X’s: 21x

#’s: 4

So it will be 21x+4

Answer:

There is overwhelming evidence that human activities, especially burning fossil fuels, are leading to increased levels of carbon dioxide and other greenhouse gases in the atmosphere, which in turn amplify the natural greenhouse effect, causing the temperature of the Earth's atmosphere, ocean, and land surface to ...

Answer:

V =48 cm^3

Step-by-step explanation:

The volume of a prism is given by

V = l*w*h

V = 3*4*4

V =48 cm^3

V =48 cm^3

Step-by-step explanation:

The volume of a prism is given by

V = l*w*h

V = 3*4*4

V =48 cm^3

An ellipse is a plane curve that surrounds two focus points and has a constant sum of the two distances to the focal points at all places on the curve. In the graph, the A represents the minor axis of the ellipse.

Suppose that the major axis is of the length 2a units, and that minor axis is of 2b units, and let the ellipse is centered on (h,k) with major ellipse parallel to x-axis, then the equation of that ellipse would be:

[tex]\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2} =1[/tex]

Coordinates of its foci would be: (h±c, k) where c² = a² - b²

If its major axis is parallel to y-axis, then,

coordinates of its foci would be:  (h, k±c) where c² = a² - b² and its equation would be:

[tex]\dfrac{(x-h)^2}{b^2} + \dfrac{(y-k)^2}{a^2} =1[/tex]

An ellipse is a plane curve that surrounds two focus points and has a constant sum of the two distances to the focal points at all places on the curve. Since an ellipse has two diameter, the major and the minor diameter. Therefore, in the graph, the A represents the minor axis of the ellipse.

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