Solve the system of equations.​

Answer:

[tex]g(x) = \sqrt[4]{x-7},~ x\geq 7[/tex]

Step by step explanation:

[tex]y= f(x) = x^4+7\\\\\text{Replace x with y and solve for y:}\\\\~~~~~~~x = y^4 +7\\\\\implies y^4 = x-7\\\\\implies y = \pm\sqrt[4]{x-7}\\\\ \implies f^{-1}(x) = \pm\sqrt[4]{x-7}[/tex]

The approximate difference in years for Calvin and Makayla is that B. Makayla invests her money 2 years longer.

Given:

We use the compound interest formula,

[tex]A= P(1 + r/t)^t[/tex]

[tex]658.8/400= (1205/1200)^1^2^c[/tex]

c= 10 years approx.

For Makayla,

We use the same formula:

[tex]A= P(1 + r/t)^t\\[/tex]

[tex]613.4/300= (1206/1200)^1^2^m[/tex]

m= 12 years approx.

Hence, the difference in the years would be:

12-10

= 2 years.

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Answer:

Makayla invests her money 2 years longer

Step-by-step explanation:

b on edge

Answer: x = 0, 8

Step-by-step explanation:

x = 0

x - 8 = 0 ⇒ x = 8 (move 8 to the right)

x = 0, 8

Answer:

6.4

Step-by-step explanation:

E bisects side MO, plot it in the center of M and O

MO is 8, split into two even parts, 4 and 4

TE is 5

set up Pythagorean theorem, 5^2 + 4^2 = x^2 to find MT

25+16=x^2

41=x^2

x=6.403

Answer:

x ≈ 0.5

Step-by-step explanation:

using the tangent ratio in the right triangle

tan63° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{IJ}{JK}[/tex] = [tex]\frac{1}{x}[/tex] ( multiply both sides by x )

x × tan63° = 1 ( divide both sides by tan63° )

x = [tex]\frac{1}{tan63}[/tex] ≈ 0.5 ( to the nearest tenth )

Answer:

x = 0.5

Step-by-step explanation:

We can use tan Θ to find the value of x.

tan Θ = Opposite ÷ Adjacent

Let us solve it now

tan 63 = 1 ÷ x

1.9626 = 1 ÷ x

x = 1 ÷ 1.9626

x = 0.5095

x ≈ 0.5  ( nearest 10th )

Answer:

360 people out of 1200 are likely to have red hair.

Step-by-step explanation:

So I just saw that 100 x 120 equals 1200. So I just need to multiply 3 x 120 and I got 360. I think this is how to solve?

Answer:

=4x³-4x²+4x-3

Step-by-step explanation:

(f+g)(x)=4x³+2x²-6x²+4x-6+3

=4x³-4x²+4x-3

Answer:

the green box is 0

Step-by-step explanation:

we are asked to find the x-intercept, which means y = 0

(x, y)

Another way to test this is plug it in 1 for x!  (1, y) where x = 1

[tex]y = \frac{2x^{2} -3x+1}{2x^{2} +8x+6} \\\\[/tex]

[tex]y = \frac{2(1)^{2} -3(1)+1}{2(1)^{2} +8(1)+6}[/tex]

[tex]y = \frac{2(1) -3(1)+1}{2(1) +8+6}[/tex]

[tex]y = \frac{2 - 3 + 1}{2 + 8 + 6}[/tex]

[tex]y = \frac{-1+1}{10 + 6}[/tex]

[tex]y = \frac{0}{16}[/tex]

y = 0

After 10 years, there will be 108 rabbits left in the park.

An exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Here, the given equation;

       R = 120 (0.99)ⁿ

where, n is the number of years

n = 10 years (given)

R = 120 (0.99)¹⁰

R = 120 X 0.904

R = 108.52

Thus, After 10 years, there will be 108 rabbits left in the park.

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Answer:

122x + 37

Step-by-step explanation:

hope this helps u

Answer:

[3×2⁵+13×2]+2³(-2²+3²)-3=

[3×32+26]+2³(-4+9)-3=

[96+26]+2³(5)-3=

122+40-3

162-3=

159...

note:-a×(-b)=+ab

The value of n from the triangle = 2.5

Perimeter of a triangle= a +b+c

Where,

a= n

b= 5n - 6

C= 2n + 1

P= 15

Therefore n

15 = n + 2n + 1 + 5n - 6

15 = 8n-5

8n= 15+5

8n = 20

n= 20/8

n= 2.5

Therefore, the value of n = 2.5

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Answer:

34/48

Step-by-step explanation:

So to answer this problem, we need to know two things:
1) The number of people who made a purchase
2) The number of people who came into the store

The problem gives us 1), which is 34.
The answer for 2) is 34+14, since that's the total number of people who came into the store. This means that the ratio is 34/48.

Answer:

Step-by-step explanation:

jenny spin a fair-4 spinner

The probability that the spinner will land on a or b will be 0.50.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

Jenny spins a fair 4-sided spinner.

Let the section be marked as a, b, c, and d.

Then the total number of the event will be given as,

Total events = 4

Then the probability that the spinner will land on a or b will be given as,

P = 1/4 + 1/4

P = (1 + 1)/4

P = 2/4

P = 1/2

P = 0.50

The probability that the spinner will land on a or b will be 0.50.

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Step-by-step explanation:

the area of a triangle is

baseline × height / 2

in our case

baseline × 5 / 2 = 20 in²

baseline × 5 = 40

baseline = 8 in

The area of a 2D form is the amount of space within its perimeter. The correct option is D.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The area of the L block will be the sum of the area of A and B. Therefore, the area can be written as,

Area of L block = Area of A + Area of B

                          = (7×2) units² + (1 × 5) units²

                          = 14units² + 5units²

                          = 19units²

Hence, the correct option is D.

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Answer: 210

Step-by-step explanation:

      ! means, for example, 6! = 6 * 5* 4 * 3 * 2 * 1

Given:

[tex]\displaystyle \frac{10!}{6!(12-8)!}[/tex]

Subtract:

[tex]\displaystyle \frac{10!}{6!(4)!}[/tex]

Distribute:

[tex]\displaystyle \frac{10!}{6!*4!}[/tex]

Expand:

[tex]\displaystyle \frac{10 * 9 * 8 * 7 * 6 * 5* 4 * 3 * 2 * 1}{(6 * 5* 4 * 3 * 2 * 1)*(4 * 3 * 2 * 1)}[/tex]

Cancel out (6*5*4*3*2*1) in both the top and bottom as they equal 1:

[tex]\displaystyle \frac{10 * 9 * 8 * 7 }{4 * 3 * 2 * 1}[/tex]

Multiply:

[tex]\displaystyle \frac{5,040 }{24}[/tex]

Divide:

210

Answer:

35%

Step-by-step explanation:

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

The percentage of people who supported the home team is 35%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

20% = 20/100 = 1/5

25% = 25/100 = 1/4

We have,

Number of people who attended the basketball game = 1940

Number of people who supported the home team = 679

Number of people who supported the visiting team = 1261

The percentage of people who supported the home team.

= [ Number of people who supported the home team / Total number of people who attended the basketball game ] x 100

= [679 / 1940] x 100

= 67900 / 1940

= 35%

Thus,

The percentage of people who supported the home team is 35%.

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Using the triangle sum theorem, the value of angle ACB in the triangle is: B. 50°.

According to the triangle sum theorem, the sum of all the angles in a triangle equals 180 degrees.

90 + 7x - 20 + 4x = 180

70 + 11x = 180

11x = 180 - 70

11x = 110

11x/11 = 110/11

x = 10

m∠ACB = 7x - 20

Plug in the value of x

m∠ACB = 7(10) - 20

m∠ACB = 50° (option B).

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Answer:

-[tex]\frac{17}{3}[/tex]

Step-by-step explanation:

Answer: 60 square units

Step-by-step explanation: i hope that helps buddy :)

Answer:

Statement 1 and 2

Step-by-step explanation:

If you take t^2 - 16t + 55 and find some of its graphical values, you will get:

Turning point: (8,-9)

Roots: (5,0) and (11,0)

When this graph is plotted and you imagine the x axis to be time (as stated in the question), each of the roots (x - intercept) must be when the swimmer goes under and when they come back up.

This means that the swimmer dived under the water at 5 seconds and came back up at 9, making the first 2 statements correct.

Now the fourth statement is ruled out.

The fifth statement is not plausible as the graph would have to have more than 2 roots for the swimmer to enter the water twice.

That leaves the third statement. If you imagine the depth of the swimmer to be the y axis of our imaginary graph, and we know that the y axis of the turning point is -9, that means that the swimmer's deepest dive was 9 feet under the water, ruling out the third statement too.

Hope this helps :D

Answer:

[tex]h(t)= (t-5)(t-11)[/tex]

The swimmer comes back up 11 seconds after the timer is started.

The swimmer dives into the water 5 seconds after the timer is started.

Step-by-step explanation:

Given function:

[tex]h(t)=t^2-16t+55[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex],

find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:

[tex]\implies ac=55[/tex]

[tex]\implies b=-16[/tex]

Two numbers that multiply to 55 and sum to -16 are: -11 and -5

Rewrite b as the sum of these two numbers:

[tex]\implies t^2-11t-5t+55[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies t(t-11)-5(t-11)[/tex]

Factor out the common term (t - 11):

[tex]\implies (t-5)(t-11)[/tex]

Therefore, the given formula in factored form is:

[tex]h(t)= (t-5)(t-11)[/tex]

The swimmer's depth is modeled as h(t).  Therefore, when h(t) = 0 the swimmer will be at the surface of the water.

[tex]\implies h(t)=0[/tex]

[tex]\implies (t-5)(t-11)=0[/tex]

[tex]\implies t-5=0\implies t=5[/tex]

[tex]\implies t-11=0 \implies t=11[/tex]

Therefore, the swimmer will be at the surface of the water at 5 s and 11 s.

The swimmer's maximum depth is the vertex of the function. The x-value of the vertex is the midpoint of the zeros.  Therefore, the x-value of the vertex is t = 8.

Substitute t = 8 into the function to find the maximum depth:

[tex]\implies h(8)=8^2-16(8)+55=-9[/tex]

So the swimmer's maximum depth is 9 ft.

True Statements

The swimmer comes back up 11 seconds after the timer is started.

The swimmer dives into the water 5 seconds after the timer is started.

Answer:

3

Step-by-step explanation:

got it on edge

Answer: 5%

Step-by-step explanation:

[tex]6615=6000(1+r)^{2} \\ \\ 1.1025=(1+r)^{2} \\ \\ 1.05=1+r \\ \\ r=0.05=\boxed{5\%}[/tex]

The class which has a greater percent of students who ride the bus is Walter's class

Walter's class:

Percentage of students who ride bus = 14 / 15 × 100

= 0.933 × 100

= 93.3%

Sasha's class:

Percentage of students who ride bus = 11 / 20 × 100

= 0.55 × 20

= 55%

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The area of the triangle will be 3240 square centimeters.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The diagram is given below.

The height of the triangle is 120 cm and the base of the triangle is 54 cm.

Then the area of the triangle will be

Area = 1 / 2 x 120 x 54

Area = 3240 square cm

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Answer:

0.324

Step-by-step explanation:

Answer: See the screenshots below

I'm answering in this format because the questions aren't numbered, so its hard to reference them consistently (so we're both on the same page).

All decimal values are approximate. I decided to round to 4 decimal places, but feel free to use another level of precision.

Answer:

x = -2

Step-by-step explanation:

[tex]2x(x-5)-x(3+2x) = 26\\2x^{2} -10x-3x-2x^{2} = 26\\-13x=26\\x=\frac{26}{-13} \\=-2[/tex]

Its basically the order of operations, from left to right , evaluate brackets (if possible), then multiplication or division, lastly followed by addition or subtraction.

2x2-10x-3x-2x2=26

Eliminam opusele

reducem termenii

-13x=26

imparte ambele parti

x=-2

Step-by-step explanation:

Recall that (a + b)² = a² + 2ab + b².

Let a = x² and b = y². Then

(x² + y²)² = (x²)² + 2x²y² + (y²)²

⇒   x⁴ + y⁴ = (x² + y²)² - 2 (xy)²

Given that x² + y² = 13 and xy = 6, we have

x⁴ + y⁴ = 13² - 2×6² = 97

Answer:

7. 13.6

8. 19.5

9. 6.5

10. 12.6

Step-by-step explanation:

Recall the three main trig functions

Sine = opposite / hypotenuse

Cosine = adjacent / hypotenuse

Tangent = opposite / adjacent

( remember hypotenuse = longest side length , opposite = side length opposite of angle , and adjacent = side length thats not the opposite or hypotenuse )

We will use these to solve each problem

7.

We are given :

When dealing with opposite and adjacent we use tangent

We have tan = opp / adj

==> plug in opp = 11 and adj = x as well as given angle 39

tan(39) = 11/x

==> multiply both sides by x

xtan(39) = 11

divide both sides by tan(39)

x = 11/tan(39)

plugging this into a calculator , we get x = 13.6 ( rounded )

8.

We are given :

When dealing with adjacent and hypotenuse we use cos

We have cos = adj / hyp

==> plug in given angle 46 , adj = x and hyp = 28

cos(46) = x/28

==> multiply both sides by 28

x = 28cos(46)

plugging this into a calculator we get  x = 19.5 ( rounded )

9.

We are given :

When dealing with the opposite and adjacent we use tangent

We have tan = opp / adj

==> plug in 51 degrees for angle , opp = 8 and adj = x

tan(51) = 8/x

==> multiply both sides by x

xtan(51) = 8

==> divide both sides by tan(51)

x=8/tan51

plugging this into a calculator we get that x = 6.5 ( rounded )

10.

We are given:

When dealing with the opposite and hypotenuse we use sine

We have sin = opp / hyp

==> plug in angle as 24 , opp = x and hyp = 31

sin(24) = x / 31

==> multiply both sides by 31

31sin(24) = x

plugging this into a calculator we get that x = 12.6 ( rounded )

And we are done!

Let me know if you have any doubts in the comments ! : )