Consider the graph which function contains the points shown on the graph

Answer:

3/5^3 = 27

125

= 0.216

Step-by-step explanation:

Power: 3

5

^ 3 = 33

53

= 27

125

Answer:

13%

Step-by-step explanation:

Please use the $ sign.

The simple interest formula is i = p*r*t, where p is the principal amount, r is the interest rate as a decimal fraction, and t is the time in years.  Here, t = 1/4 year; r is unknown, p is $5004 and i is $162.63.

Writing this out with the given info, we get:

$162.63 = $5004*r*(1/4).

We can solve this for r by multiplying both sides by 4/$5004:

(4/$5004)($162.63)  = (4/$5004)($5004)*r*(1/4) = r

Evaluating r, we get (4)($162.63)/$5004 = 0.13

The interest rate, r, is 0.13, or 13%.

Answer:

m∠4 = 111°

Step-by-step explanation:

∠4 and ∠5 are same side (interior) angles, and since lines A and B are parallel, they will be congruent.

So, m∠4 = m∠5

Substitute: m∠4 = 111°

Answer:

$142500

Step-by-step explanation:

We are given that the resident of a certain University receives a salary that is three times the salary of one of the department heads.

Assuming [tex]x[/tex] to be the salary of the department head, if the total of the two salaries is $190000, we are to find the salary of the president of the University.

We can write an equation in terms of [tex]x[/tex]:

[tex]3x+x=190000[/tex]

[tex]4x=190000[/tex]

[tex]x=47500[/tex]

Salary of the president of the University = [tex]3(47500)[/tex] = $142500

Answer:

B is not necessarily true

Step-by-step explanation:

A) This is always true

B) This is not necessarily true

When two lines intersect, they form angles at the intersection as D says, but that does not mean that the angle will always be 90 degrees as is required for the two intersecting lines to be perpendicular

C) This is always true

D) This is always true

Option B) The lines are not perpendicular is not necessarily true.

When two lines intersect and following are the three different possibilities:

1) They are parallel, if lines are parallel they can never intersect.

2)They cross each at an angle and the point of intersection is unique that is they intersect at only one point.

3) Two lines coincide, that is every point on line 1 is a point on line 2.

Now

In option B it is given that lines are perpendicular that is the specific case of (2) When angle is 90°.

Therefore, it is not necessarily true.

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Answer:

12 gallons

Step-by-step explanation:

let x be the amount tank can hold, then

[tex]\frac{1}{3}[/tex] x + 2 = [tex]\frac{1}{2}[/tex] x

Multiply through by 6

2x + 12 = 3x ( subtract 2x from both sides )

12 = x

The tank can hold 12 gallons

Greg's gas tank can hold 12 gallons of gas. We know this because when Greg's tank is 1/3 full and he buys 2 gallons of gas it becomes 1/2 full. The difference between 1/2 and 1/3 of a tank, or 1/6 of the tank, is equal to 2 gallons.

The subject of this question is mathematics, specifically within the scope of fractions and simple algebra. The question tells us that when Greg's gas tank is 1/3 full and he adds 2 gallons, the tank becomes 1/2 full. This tells us that the difference between 1/2 and 1/3 of the tank's capacity is equal to 2 gallons. In mathematical terms, this can be represented as 1/2 - 1/3 = 2/6 - 2/6 = 1/6. Therefore, 1/6 of Greg's gas tank equals 2 gallons. If 1/6 of the tank equals 2 gallons, the entire tank (or 6/6) would hold 12 gallons of gasoline.

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Answer:

2800 cm^3, or 2.8 liters

Step-by-step explanation:

The base of the tank remains 14 cm × 25 cm. The remaining height is 15 -7 = 8 cm, so the remaining volume is ...

(14 cm)(25 cm)(8 cm) = 2800 cm^3 = 2.8 liters

_____

1 liter = 1000 cm^3

ANSWER

[tex]y = 3 \pm \sqrt{21} [/tex]

EXPLANATION

The quadratic equation is:

[tex] {y}^{2} - 6y - 12 = 0[/tex]

Group variable terms:

[tex] {y}^{2} - 6y = 12[/tex]

Add the square of half, the coefficient of y to both sides.

[tex] {y}^{2} - 6y + ( - 3) ^{2} = 12 + ( - 3) ^{2} [/tex]

[tex] {y}^{2} - 6y + 9= 12 + 9[/tex]

The LHS us now a perfect square trinomial:

[tex]{(y - 3)}^{2}= 21[/tex]

Take square root:

[tex]y - 3 = \pm \sqrt{21} [/tex]

[tex]y = 3 \pm \sqrt{21} [/tex]

The first choice is correct.

3±√21. The equation [tex]y^{2}-6y-12=0[/tex] has two possible solutions 3+√21 y 3-√21.

If we have a general quadratic equation [tex]ay^{2} +by+c=0[/tex] we can solves the equation by completing the square. First, we divide the quadratic equation by a, we obtain [tex]y^{2} +\frac{b}{a} y+\frac{c}{a} =0[/tex].

For this problem, we have [tex]y^{2}-6y-12=0[/tex]

We can skipped division in this example since the coefficient of [tex]x^{2}[/tex] is 1.

Move the term c to the right side of the equation

[tex]y^{2}-6y=12[/tex]

Completing the square on the left side of the equation and balance this by adding the same number to the right side of the equation, with b = -6.

[tex](\frac{b}{2})^{2} =(\frac{-6}{2})^{2}=(-3)^{2} =9[/tex]

[tex]y^{2}-6y+9=12+9[/tex]

[tex](y-3)^{2}=21[/tex]

Take the square root on both sides of the equation:

y - 3 = ±√21

Add 3 from both sides:

y = 3 ± √21

Hello wendywagor!

Let x = the original price of the sneakers

x - .60x = 22.40

.40x = 22.40

x = $56

Thanks For Using Brainly.com

Have A Great rest of Your Day!

Answer:

Step-by-step explanation:

Without a second equation relating x and y, we can solve 3x - 1/2y = 2 ONLY for x in terms of y or for y in terms of x:

x in terms of y:    Multiply all three terms of 3x - 1/2y = 2 by 2, to eliminate the fraction:  6x - y = 4.  Now add y to both sides to isolate 6x:  6x = 4 + y.

Last, divide both sides by 6 to isolate x:

x = (4 + y)/6

y in terms of x:    

y = 6x - 4

If you want a numerical solution, please provide another equation in x and y and solve the resulting system.

Answer:

Step-by-step explanation:

just did the question and got it right.

Answer:

x=−7+√130 or x=−7−√130

Step-by-step explanation:

Answer:

Step-by-step explanation:

x²+14x+17=-98

add 98 to each side

x²+14x+115=0

Solve with quadratic formula

a=1

b=14

c=115

\frac{-14 ±\sqrt{14^2-4*1*115} }{2*1}

Find the circumference:

Circumference = 2 x PI x radius

Circumference = 2 x 3.14 x 19 = 119.32

Divide by 4: 119.32 / 4 = 29.83 rounded to 29.8

The answer is C.

Answer:

C. 29.8 inches

Step-by-step explanation:

Length of complete hula hoop(L)= circumference of hoop

=>[tex]L=2\pi r[/tex]

where radius, r= 19 inches

Therefore length of arc(l) subtending 1/4 of the hoop is

=>[tex]l=\frac{1}{4}\times L=\frac{1}{4}\times2\pi r=\frac{\pi r}{2}[/tex]

=>[tex]l=\frac{\pi \times 19}{2}inches=29.8 inches[/tex]

Thus the length of the arc subtending 1/4 of the hoop is 29.8 inches

Answer:

the answer is 37.7 so the point closest to 40.

Step-by-step explanation:

Answer: the one between 30 and 40

Step-by-step explanation:

Answer:

7.782352941

Step-by-step explanation:

4.2 divided by 1.02 the multiply the out come of that by 1.89 to get 7.782352941

Answer:

First option: (1, 1)

Second option: (-3, 4)

Step-by-step explanation:

Substitute each point into the inequality:

Point (1,1):

[tex]x + 2y \geq3\\\\(1) + 2(1) \geq3\\\\3\geq3[/tex]

(The inequality is satisfied with this point)

Point (-3, 4):

[tex]x + 2y \geq3\\\\(-3) + 2(4) \geq3\\\\5\geq3[/tex]

 (The inequality is satisfied with this point)

Point (-2, 2):

[tex]x + 2y \geq3\\\\(-2) + 2(2) \geq3\\\\2\geq3[/tex]

(The inequality is not satisfied with this point)

Point (5, -2):

[tex]x + 2y \geq3\\\\(5) + 2(-2) \geq3\\\\1\geq3[/tex]

(The inequality is not satisfied with this point)

Answer:

Your answer would be A and B

Step-by-step explanation:

For this case we must simplify the following expression:

[tex]\sqrt {\frac {16} {25}}[/tex]

We can rewrite 16 as:[tex]2 ^ 4 = 2 * 2 * 2 * 2[/tex]

We can rewrite 25 as:[tex]5 ^ 2 = 5 * 5[/tex]

[tex]\sqrt {\frac {2 ^ 4} {5 ^ 2}} =\\\frac {\sqrt {2 ^ 4}} {\sqrt {5 ^ 2}} =[/tex]

By definition of properties of powers and roots we have:

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

Then, rewriting the expression:

[tex]\frac {2 ^ 2} {5} =\\\frac {4} {5}[/tex]

Answer:

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

Answer:

Step-by-step explanation:

[tex]k - \text{scale of similar}[/tex]

[tex]\text{If}\ AB\sim CD\ \text{in scale}\ k,\ \text{then}\ \dfrac{length_{AB}}{length_{CD}}=k[/tex]

[tex]\text{If}\ A\sim B\ \text{in scale}\ k,\ \text{then}\ \dfrac{area_A}{area_B}=k^2[/tex]

[tex]\text{If}\ A\sim B\ \text{in scale}\ k,\ \text{then}\ \dfrac{volume_A}{volume_B}=k^3[/tex]

[tex]\text{We have}\ B\sim A\ \text{in scale}\ k=5.\ V_A=12\ m^3,\ \text{therefore}\\\\\dfrac{V_B}{V_A}=k^3\to\dfrac{V_B}{12}=5^3[/tex]

[tex]\dfrac{V_B}{12}=125[/tex]            multiply both sides by 12

[tex]V_B=1500\ m^3[/tex]

Answer:

w=18 minutes per mile, r=12 minutes per mile

Step-by-step explanation:

Let w and r represent the rates, in minutes per mile, that Carly walked and ran on the treadmill, respectively.

1. On Monday, Carly walked 3 miles and spent 3w minutes, ran 2 miles and spent 2r minutes. In total Carly spent 78 minutes, so

3w+2r=78

2. On Thursday, Carly walked 2 miles and spent 2w minutes, ran 3 miles and spent 3r minutes. In total Carly spent 72 minutes, so

2w+3r=72

Solve the system of two equations:

[tex]\left \{ {{3w+2r=78} \atop {2w+3r=72}} \right.[/tex]

Multiply the first equation by 2, the second equation by 3 and subtract them:

[tex]2(3w+2r)-3(2w+3r)=2\cdot 78-3\cdot 72\\ \\6w+4r-6w-9r=156-216\\ \\-5r=-60\\ \\r=12[/tex]

Substitute it into the first equation:

[tex]3w+2\cdot 12=78\\ \\3w=78-24\\ \\3w=54\\ \\w=18[/tex]

Answer:

(x + 6)²

Step-by-step explanation:

This is a perfect square of the form

(x + a)² = x² + 2ax + a²

here a² = 36 ⇒ a = 6 and 2ax = 2 × 6x = 12x

Hence

x² + 12x + 36 = (x + 6)²

Answer:

(x+6)(x+6)

Step-by-step explanation:

ANSWER

[tex](-8, - 3)[/tex]

EXPLANATION

Given that: (-8,-8) is on f(x).

Then we can write (-8,f(-8)) is on f(x).

The corresponding point on

[tex]f(x) + 5[/tex]

will be

[tex](-8,f(-8)+5)[/tex]

We substitute f(-8)=-8 to obtain;

[tex](-8, - 8+5)[/tex]

This simplifies to

[tex](-8, - 3)[/tex]

Therefore the corresponding point on f(x)+5 is (-8,-3).

Answer:

For the first pic its mode interval and median for the second pic its frequency table.

Step-by-step explanation:

Answer:

The missing image from the problem is attached

The answer is (C) Each of the lateral faces has an area of 464 square inches.

Step-by-step explanation:

Base is a square that is 32 in

The height of one of the 4 lateral faces is 29 in

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

Base is L*W --> 32*32 = 1024 square inches

(1) Lateral face is 1/2*b*h = 0.5*32*29 = 464 square inches

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

Since the answers are about the face and/or one lateral face only, those two numbers are important. (C) is the only answer that matches

Each of the lateral faces has an area of 464 square inches , Option C is the correct answer

A square pyramid is a three dimensional figure , having square as the base and four triangular faces which meet at a single point called at a single point.

It is given in the question (figure is attached )

Base of the square pyramid is 32 in

The height of one of the 4 triangle is 29 in

Area of the base = 32* 32

= 1024 sq.in

Area of the lateral face (triangle ) =  1/2*b*h

= (1/2) * 32 * 29

= 464 sq. in

Therefore Option C is the correct answer , Each of the lateral faces has an area of 464 square inches.

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[tex]

\frac{\sqrt{9}}{\sqrt{81}}=\frac{3}{9}=\boxed{\frac{1}{3}}

[/tex]

The answers are A and B.

Hope this helps.

r3t40

Hey there!

If we have two white marbles and seven purple marbles, our first probability is out of nine.

First of all, we have the probability of selecting a purple marble, 7/9.

Now, if we do not replace it, there are only eight marbles left. Therefore, getting a white marble is 2/8, or 1/4.

We multiply these probabilities together to get our answer to a.

7/9(1/4)= 7/36

a. 7/36

Now, let's do b. We have 2/9, and then 1/8, giving us 1/36.

b. 1/36

Now, let's calculate selecting two purple to help us with C.

We have 7/9, and then 6/8, or 3/4.

7/9(3/4)= 7/12

Since there is a majority of purple marbles, there is a C) greater probability of selecting two purple marbles in a row.

I hope this helps!

Answer:

A. 7:9 B. 1:4 C. Purple

Step-by-step explanation:

A. Because there are 7:9 B. Because 1:4 C. Because Purple has more

Answer:

x=-1/2

Step-by-step explanation:

Given:

8x^3+12x^2+6x+1=0

Making factors of the given polynomial by using cube formula, given as

(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

Re-writting the given polynomial:

(2^3.x^3) + 3(2^2.x^2)(1)+3(2x)(1) + (1^3)=0

Hence (2^3.x^3) + 3(2^2.x^2)(1)+3(2x)(1) + (1^3) can be written as (2x+1)^3

(2x+1)^3= 0

2x+1= 0

2x= -1

x= -1/2 !

Hey there! :D

f(-3)= 4(2)^x

Just plug in -3 as x and solve.

4(2)^-3

First do the exponent, and then multiply the four on the outside.

4(1/8)

=1/2

I hope this helps!

~kaikers

Final answer:

To calculate f(-3) for the function f(x) = 4(2)ˣ, substitute -3 into the function, yielding f(-3) = 1/2 after simplifying 4 times 2 raised to the power of -3.

Explanation:

To find f(-3) for the function f(x) = 4(2)ˣ, simply substitute -3 for x in the equation. Here's How:

Start with the original function f(x) = 4(2)ˣ.

Replace every x with -3 to get f(-3) = 4(2)⁻³.

Calculate 2⁻³, which equals 1/8 because negative exponents represent the reciprocal of the base raised to the positive exponent.

Now, multiply 4 by 1/8 to get f(-3) = 4 * 1/8 = 1/2.

Therefore, f(3) for the given function equals 1/2.

Answer:

The missing words

# x ⇒ # y ⇒ # 4 ⇒ # 0

Step-by-step explanation:

* Lets revise how to find the inverse function

- At first write the function as y = f(x)

- Then switch x and y

- Then solve for y

- The domain of f(x) will be the range of f^-1(x)

- The range of f(x) will be the domain of f^-1(x)

* Now lets solve the problem

∵ f(x) = √(x - 4)

∴ y = √(x - 4) ⇒ switch x and y

∴ x = √(y - 4) ⇒ square the two sides

∴ x² = [√(y - 4)]² ⇒ cancel the root by squaring

∴ x² = y - 4 ⇒ add 4 to the both sides

∴ y = x² + 4

∴ f^-1(x) = x² + 4

* To find the domain of the inverse, find the range of the function

∵ The domain of f(x) is ⇒ x - 4 ≥ 0 (no negative value under√)

∴ the domain is x ≥ 4

- Substitute this value in the function to find the range

∵ x = 4

∴ y = √(4 - 4) = 0

∴ y ≥ 0

- The range of f(x) is y ≥ 0

∴ The domain of the inverse f^-1(x) is x ≥ 0

- The missing words

# x

# y

# 4

# 0

Answer:

[tex]1.\ m<6\\2.\ g\leq-4\\3.\ y<41\\4.\ b<4\\5.\ h<-30\\6.\ x>-2\\7.\ t>9\\8.\ w<28[/tex]

Step-by-step explanation:

1. Subtract 10 from both sides. Then:

[tex]m+ 10< 16\\ m+ 10-10< 16-10\\m<6[/tex]

2. Divide both sides by -2. Notice that the direction of the symbol of the inequality will change. Then:

[tex]-2g\geq8\\\\\frac{-2g}{-2}\geq\frac{8}{-2}\\\\g\leq-4[/tex]

3. Add 22 to both sides. Then:

[tex]y-22< 19\\ y-22+22<19+22\\y<41[/tex]

4. Divide both sides by -7. Notice that the direction of the symbol of the inequality will change. Then:

[tex]-7b>-28\\\\\frac{-7b}{-7}>\frac{-28}{-7}\\\\b<4[/tex]

5. Subtract 30 from both sides. Then:

[tex]h+30<0\\ h+30-30<0-30\\h<-30[/tex]

6. Divide both sides by -5. Notice that the direction of the symbol of the inequality will change. Then:

[tex]-5x<10\\\\\frac{-5x}{-5}<\frac{10}{-5}\\\\x>-2[/tex]

7. Subtract 13 from both sides. Then:

[tex]t+13>22\\ t+13-13>22-13\\t>9[/tex]

8. Add 12 to both sides. Then:

[tex]w-12< 16\\ w-12+12<16+12\\w<28[/tex]

Answer:

y=-1x+5

Step-by-step explanation:

[tex]\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{0}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{0-1}{5-4}\implies \cfrac{-1}{1}\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-1=-1(x-4) \\\\\\ y-1=-x+4\implies y=-x+5[/tex]