There is a $30 fee to rent a tool from the local hardware store plus $6 per day. If Joe rents a jackhammer for 5 days, what is his total bill? The correct function for this situation is f(x) = 30x + 6.
O False
O True

Answer:

42 + 2/3

Step-by-step explanation:

First, to calculate the sum of an infinite geometric series, our formula is

a₁/(1-r), with a₁ being the first term of the series and r being the common ratio. Therefore, we want to find both a₁ and r.

To find r, we can first determine that 2 * r = a₄ and a₄ * r = a₅, as the ratio separates one number from the next in a geometric series. Therefore, we have

2 * r * r = a₅

2 * r² = 1/8

divide both sides by 2 to isolate the r²

r² = 1/16

square root both sides to isolate r

r =± 1/4. Note the ± because r²=1/16 regardless of whether r = 1/4 or -1/4. However, because all terms are positive, r must be positive as well, or a₄, for example, would be 2 * (-1/4) = -0.5

Therefore, r = 1/4 .

To find the first term, we know that a₁ * r = a₂, and a₂ * r = a₃. Therefore, a₁ * r² = a₃ = 2

a₁ * 1/16 = 2

divide both sides by 1/16 to isolate a₁

a₁ = 2 * 1/ (1/16)

= 2 * 16

= 32

Plugging a₁ and r into our infinite geometric series formula, we have

a₁/(1-r)

= 32  / (1-1/4)

= 32/ (3/4)

= 32/ 0.75

= 42 + 2/3

Answer:

84°

Step-by-step explanation:

angles in a quadrilateral add to 360°. 360-(114+76)=5x =170°. 170°/5 = 32°. x=32°

angles on a straight line add to 180°.

2x = 64°. 180-64=116°. y=116°.

y-x = 116-32 = 84°

Answer:

[tex]78[/tex]

Step-by-step explanation:

The inner angles of a quadrilateral all add up to 360. This means we can write the following

[tex]114 + 76 + 3x + 2x = 360\\190 + 5x = 360\\5x = 170\\x = 34[/tex]

Now that we have x we can find y. Notice that y and 2x are on the same line. Any line cutting another straight line will create two angles that add up to 180.

Therefore we can write

[tex]2x + y = 180\\2(34) + y = 180\\y = 112[/tex]

Finally computing y - x

[tex]y - x = 112 - 34 = 78[/tex]

Answer:

huh?

Step-by-step explanation:

Answer:

-4

they wanted you to compute using x as 3

-2*3 + 2 = -4

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

13 mi

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

5^2 +12^2 = c^2

25+144 = c^2

169 = c^2

Taking the square root of each side

sqrt(169) = sqrt(c^2)

13 = c

Answer:

[tex](x+1)^2+(y+4)^2=9\\[/tex]

Step-by-step explanation:

The general format for the equation of a circle is the following:

[tex](x-h)^2+(y-k)^2=a^2\\[/tex]

Where [tex](h,k)[/tex] is the center of the circle and ([tex]a[/tex]) is the circle's radius. Please note, that the circle ([tex](x-h)^2+(y-k)^2=a^2\\[/tex]) has a center that is (h) units to the right of the origin, and (k) units above the origin.

The given circle has a center at [tex](-1,-4)[/tex], moreover, its radius is (3) units. Therefore, one must substitute these points into the equation of a circle and simplify to find its equation:

[tex](x-h)^2+(y-k)^2=a^2\\[/tex]

[tex](x-(-1))^2+(y-(-4))^2=(3)^2\\[/tex]

[tex](x+1)^2+(y+4)^2=9\\[/tex]

Answer:

Step-by-step explanation: Let's first determine the center of the circle

which is represented by the red dot and it has the coordinates (-1, -4).

The radius of the circle is a segment that joins the center of the

circle to a point on the circle and all radii of a circle are congruent.

The radius of the circle shown here is 3.

Now, the equation of a circle is (x - h)² + (y - k)² = r² where

(h, k) is the center of the circle and r is the radius.

Now we plug all our given information into the formula.

So we have [x - (-1)]² + [y - (-4)]² = (3)².

Notice that I changed the parentheses in the formula to brackets

so that we wouldn't be dealing with too many sets of parentheses.

Changing the brackets back to parentheses,

our equation is (x + 1)² + (y + 4)² = 9.

Answer:

Does the answer help you?

Answer:

[tex]\textbf{No, the answer is not correct }[/tex].

Step-by-step explanation:

The student didn't use the quotient of powers property correctly. Instead of subtracting, the student divided the exponents within the parenthesis. So, x to the two-fifths power is the correct simplified form.

[tex](\frac{x^{2/5}\times x^{4/5} }{x^{2/5} } )[/tex]

[tex]=(\frac{x^{6/5} }{x^{2/5} } )^{1/2}[/tex]

[tex]=x^{6/5-2/5} )^{1/2}[/tex]

[tex]=(x^{4/5} )^{1/2} =x^{2/5}[/tex]

OAmalOHopeO

Answer:

a1=3, a2=6, a3=12, a4=24, a5=48

Step-by-step explanation:

a7=a*r^6=192

a10=a*r^9=1536, r^3=8, r=2 and a=3

a1=3, a2=6, a3=12, a4=24, a5=48

Answer:

At most, Liam can only buy lunch for 6 people.

Step-by-step explanation:

It isn't going to be a decimal answer because there can't be half of a person

All you have to do is divide 50 by 8 and round down because you don't want to spend more than 50 dollars.

Writing it mathematically, it would be:

p [tex]\leq[/tex] 6

Answer:

Nicole should take 13 1/8 cups of snack mix.

Step-by-step explanation:

If a serving size is 7/8 and Nicole wants to take 15 serving sizes (15 7/8's), then we must multiply 7/8 by 15:

15 × 7/8

Write 15 over 1 (15 = 15/1) to make the calculations easier:

15/1 × 7/8

Multiply the numerators and denominators separately:

15 × 7 / 1 × 8

105 / 8

Instructions don't say you have to do this but I will convert this improper fraction into a mixed number:

105/8 = 13 1/8

Answer:

VERTICALLY OPP ANGLES

Step-by-step explanation:

Answer:

W = 7 - x

Step-by-step explanation:

The perimeter is P= 2L + 2×W , where L is the length and W is the width.

If L = (x+2) , replacing L with the expression x+2 we have

P= 2×(X+2) + 2W ⇔ 18 = 2x + 4 + 2W ⇔ 2W =18 - 2x - 4 ⇔ 2W = 14 - 2x

⇔ W = 7 - x

Answer:

Step-by-step explanation:

We can see that there are roots at (-2,0) and (-1,0)

also, the root at (-2,0) should bounce right off

and the root at (-1,0) should go through

With all that being said it has to be B

Answer:

The rea of walk way is 32 ft^2.

Step-by-step explanation:

width, w = 8 feet

length, L = 10 feet

width of walkway, d = 2 feet

length of outer, L' = 10 + 2 + 2 = 14 feet

Area of outer, A' = L' x w = 14 x 8 = 112 ft^2

Area of inner, A = L x w = 10 x 8 = 80 ft^2

The area of walkway = A' - A = 112 - 80 = 32 ft^2

The rea of walk way is 32 ft^2.

Answer:

X+y=7

Step-by-step explanation:

i  remember  doing something like this but mines had the word onion rings .

Answer:

Step-by-step explanation:

If you plot those coordinates in your calculator in the stat plot function under "stat", you will see that the dots are almost but not quite in a straight line going from upper left to lower right. This indicates a strong negative linear association, third choice down.

Answer:

D. Nonlinear Negative Association

Step-by-step explanation:

Answer:

answer is 21..............

Explanation:

p(x) = x⁴ + 2x³- 3x² + x - 1

Factor of p(x)

x-2=0

x=2

Then by using synthetic division

Answer:

This would be a .04 or 4% decay.....

for every "time unit" (x in this case) you will be multiplying

the amount by .96 ... in other words if you started with one dollar

the results would be 96 cents... after two "time" steps you would have

only 92 cents (.96 *.96)

Step-by-step explanation:

Answer: The range is  [tex]\{y \in \mathbb{R}\ | \ y \le -6\}[/tex]

Explanation:

The parabola opens down, forming a "frowny face" in a way (just without the eyes). Or you can think of it as a hill or mountain. This means that the vertex (-3,-6) is at the top of that mountain. It's the highest point of that parabola.

The range is the set of all possible y values. We see that y = -6 is the largest it can get. So y = -6 or y is smaller than this. We would then write [tex]y \le -6[/tex] to describe all the possible y values.

Therefore, the range is [tex]\{y \in \mathbb{R}\ | \ y \le -6\}[/tex]

This translates to "y is a real number such that y is -6 or smaller".

So the second answer you wrote is close, but you forgot the "or equal to" portion of the inequality sign.

See below for a visual example of what's going on.

Step-by-step explanation:

[tex]s = \pi \times {r}^{2} = \pi \times {6}^{2} = 36\pi[/tex]

[tex]h = 18 \times \sin(60) = 9 \sqrt{3} [/tex]

[tex]v = s \times h = 36\pi \times 9 \sqrt{3} = 324 \sqrt{3} \pi[/tex]

Answer:

2 is the answer . the explanation is in the attachment .

Answer: A x> -2

Step-by-step explanation:

Answer:

Area of the slice of pie = 22.09 ft²

Step-by-step explanation:

Area of the slice of pie = Area of the sector of the circle with the central angle 45°

Area of the sector = [tex]\frac{\theta}{360^{\circ}}(\pi r^{2} )[/tex] [Here, r = radius of the circle]

                              = [tex]\frac{45^{\circ}}{360^{\circ}}(\pi )(\frac{15}{2})^2[/tex]

                              = 22.09 ft²

Area of the slice of pie = 22.09 ft²

Answer:

22.08ft^2

Step-by-step explanation:

A = πr^2(x/360) d = 15

Since r is half of diameter this means that r = 15/2 =7.5

so Lets use the Area of Sector formua

A =3.14(7.5)^2 (45/360)

A =3.14(56.25) (45/360)

A = 176.625 (45/360)

A = 176.625 (0.125)

A = 22.078125

rounded to the nearest 10th would make it 22.08

Answer:

2 × 2 × 3 × 5

Step-by-step explanation:

Given that,

The number = 60

To find,

Factors of 60 greater than 1 = ?

Procedure:

As we know,

Any of various numbers multiplied together to form a whole.

To find the factors of a number, we will have to do its prime factorization.

So,

The prime factorization of 60:

1 * 2 * 2 * 3 * 5 = 60

Since the factors greater than 1 are asked, the factors would be;

2 * 2 * 3 * 5

Thus, 2 * 2 * 3 * 5 is the correct answer.

Answer:

[tex]{ \tt{ \tan {}^{4} \theta + { \sec }^{2} \theta }} \\ { \tt{ = ({ \tan }^{2} \theta ){}^{2} + { \sec }^{2} \theta }} \\ = { \tt{ {-(1 - { \sec }^{2} \theta) }^{2} + { \sec }^{2} \theta }} \\ { \tt{ = -(1 - 2 { \sec }^{2} \theta + { \sec }^{4} \theta) + { \sec}^{2} \theta}} \\ { \tt{ = -(1 - { \sec }^{2} \theta) + { \sec }^{4} \theta}} \\ { \tt{ = -{ \tan}^{2} \theta + { \sec }^{4} \theta }} \\ = { \tt{ { \sec}^{4} \theta - { \tan }^{2} \theta}} \\ { \bf{hence \: proved}}[/tex]