Jacob tapes down a piece of red tape on a basketball court. The piece of tape is 3/5 yard long. He wants to divide it into sections that are each 1/10 yard long. How many sections will the piece of tape be divided into? 30 points if u answer

A) The time to travel 45 miles at a speed of 40 mph can be found from ...

... time = distance / speed

... time = (45 mi)/(40 mi/h) = 9/8 h = 1 hr 7 min 30 sec

B) The gas consumption can be found from ...

... (45 mi)/(54 mi/gal) = 5/6 gal

C) The cost of gas can be found from ...

... ($3.23/gal)×(5/6 gal) ≈ $2.69

_____

The units of the numbers tell you what needs to be multiplied or divided to give the answer quantity with correct units. It pays to keep the units with the numbers. They can be treated as though they were a variable.

If a square has an area of 45 square units its side has a length of

[tex]s=\sqrt{45} = 3 \sqrt{5}[/tex]

units.  Is that a perfect length?  I don't know, but I know it's perfect for a square whose area is 45.

Given rational expression is

[tex]-\frac{8x}{8x^2+2x}[/tex]

Now we need to find the restricted values if any for this rational expression.

Restricted values means the possible values of the used variable (x) that will make denominator 0 as division by 0 is not defined.

So to find the restricted values, we just set denominator equal to 0 and solve for x

[tex]8x^2+2x=0[/tex]

[tex]2x(4x+1)=0[/tex]

2x=0 or 4x+1=0

x=0 or 4x=-1

x=0 or x=-1/4

Hence final answer is x=0, -1/4

To find the restricted values of a rational expression, set the denominator equal to zero and solve for x.

To find the restricted values of the rational expression, we need to determine the values of x that will make the denominator of the expression equal to zero. When the denominator is zero, the expression is undefined.

In this case, the denominator is 8x2 + 2x. We set this equal to zero and solve for x:

8x2 + 2x = 0

Factor out 2x:

2x(4x + 1) = 0

Set each factor equal to zero:

2x = 0, 4x + 1 = 0

Solve each equation:

x = 0, x = -1/4

Therefore, the restricted values of x for the given rational expression are 0 and -1/4.

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If there are any three points on the graph that are not on the same line, the function is nonlinear. Such points might be ...

... (-5, 1), (-4, 0), (-3, 1)

one way is to factor the expressions

(a)

[tex]10^{5}[/tex] (1.2 + (5.35 × [tex]10^{1}[/tex]))

= [tex]10^{5}[/tex] (1.2 + 53.5)

= 54.7 × [tex]10^{5}[/tex] = 5.47 × [tex]10^{1}[/tex]× [tex]10^{5}[/tex] = 5.47 × [tex]10^{6}[/tex]

(b)

[tex]10^{-3}[/tex]((6.91 × [tex]10^{1}[/tex]) + 2.4)

= [tex]10^{-3}[/tex](69.1 + 2.4)

= 71.5 × [tex]10^{-3}[/tex] = 7.15 × [tex]10^{1}[/tex] × [tex]10^{-3}[/tex] = 7.15 × [tex]10^{-2}[/tex]

(c)

[tex]10^{5}[/tex]((9.7 × [tex]10^{1}[/tex]) + 8.3)

= [tex]10^{5}[/tex](97 + 8.3)

= 105.3 × [tex]10^{5}[/tex] = 1.053 × [tex]10^{2}[/tex] × [tex]10^{5}[/tex] = 1.053 × [tex]10^{7}[/tex]

(d)

[tex]10^{1}[/tex]((3.67 × [tex]10^{1}[/tex]) - 1.6)

= [tex]10^{1}[/tex](36.7 - 1.6)

= 35.1 × [tex]10^{1}[/tex] = 3.51 × [tex]10^{1}[/tex] × [tex]10^{1}[/tex] = 3.51 × [tex]10^{2}[/tex]

(e)

[tex]10^{-6}[/tex]((8.41 × [tex]10^{1}[/tex]) - 7.9)

= [tex]10^{-6}[/tex](84.1 - 7.9 )

= 76.2 × [tex]10^{-6}[/tex] = 7.62 × [tex]10^{1}[/tex] × [tex]10^{-6}[/tex] = 7.62 × [tex]10^{-5}[/tex]

(f)

[tex]10^{4}[/tex]((1.33 × [tex]10^{1}[/tex]) - 4.9 )

= [tex]10^{4}[/tex](13.3 - 4.9) = 8.4 × [tex]10^{4}[/tex]

Answer:

Cylinder C is the right answer.

Step-by-step explanation:

We have to find the storage capacity or the volume of cylindrical silos.

A. radius 6 feet; height 60 feet

Volume = [tex]\pi r^{2} h[/tex]

V = [tex]3.14\times6\times6\times60=6782.40[/tex] cubic feet

B. radius 8 feet; height 50 feet

V = [tex]3.14\times8\times8\times50=10048[/tex] cubic feet

C. radius 10 feet; height 34 feet

V = [tex]3.14\times10\times10\times34=10676[/tex] cubic feet

D. radius 12 feet; height 20 feet

V = [tex]3.14\times12\times12\times20=9043.20[/tex] cubic feet

Comparing all the volumes, we can see that cylinder C has the heighest volume.

Therefore, cylinder C is the right answer.

I would say the answer is b. It sounds like the best choice

hope i helped!

It is convenient to start with the point-slope form and then simplify it to the desired form.

The point-slope form of the equation for a line with slope m through point (h, k) can be written as ...

... y = m(x -h) +k

You have m=-7 and (h, k) = (-3, 16), so you can fill in the numbers to get ...

... y = -7(x +3) +16

... y = -7x -21 +16 . . . eliminate parentheses

... y = -7x -5 . . . . the form you are looking for

Answer:

9.5 lbs

Step-by-step explanation:

To find the total package weight, add up the weights of the packages, or use the shortcut to repeated addition that is called multiplication.

... 1.9 + 1.9 + 1.9 + 1.9 + 1.9 = 5×1.9 = 9.5 . . . pounds

There might be two ways to go about this

(1) I am going to assume that we can construct a second (reference) triangle - and you confirmed that it is ok to use trigonometry on that, and then we use the relationship between areas of similar triangles to get what we want. I choose a triangle DEF with same angles, 15, 75, and 90 degrees, and the hypotenuse DE a of length 1 (that is a triangle similar to ABC). I use sin/cos to determine the side lengths: sin(15)=EF and cos(15)=DF and then compute the area(DEF) =EF*DF/2. This turns out to be 1/8 = 0.125.

Now one can use the area formula for similar triangles to figure out the area of ABC - this without trigonometry now: area(ABC)/area(DEF)=(12/1)^2

so area(ABC)=144*area(DEF)=144*0.125=18

(2) Construct the triangle ABC geometrically using compass, protractor, and a ruler. Draw a line segment AB of length 12. Using the compass draw a (Thales') semi-circle centered at the midpoint of AB with radius of 6. Then, using the protractor, draw a line at 75 degrees going from point B. The intersection with the semicircle will give you point C. Finally. draw a line from C to A, completing the triangle. Then, using ruler, measure the length BC and AC.

Calculate the area(ABC)=BC*CA/2, which should come out close to 18, if you drew precisely enough.

Answer: 18 square cm

Step-by-step explanation:

*picture very note to scale im sorry lol*

Given: △ABC, m∠C=90°, m∠B=75°, AB=12 cm

m∠A = 15° (sum of all angles in a triangle is 180 degrees and 180-90-75=15)

CM - median to hypotenuse

CL - altitude

m<CLB = m<CLM = 90 degrees (def of altitude)

CM=MA=MB=1/2 AB = 6 cm (median to hypotenuse theorem)

m<MBC=m<BCM=75 degrees (base angles theorem of iso triangle)

m<BMC = 30 degrees (sum of all angles in a triangle, 180-75-75 = 30)

m<LCM = 60 degrees (sum of all angles in a triangle of triangle LCM, 180-90-30=60)

so now we know that triangle LCM is a 30-60-90 triangle with a hypotenuse of CM (6 cm)

LC = 1/2 of MC = 3 cm (leg opposite to 30 degree <)

So now we know that the height (altitude) of the triangle is 3 cm and the length is 12 cm.

Then, we can find the area by doing the (height * length)/2 = (3*12)/2, which brings us to our answer of 18 cm.

lmk if you don't understand anything in here i'm happy to clarify!

hope this helps!

Answer:

The answer would be 0.99/1 pound

Step-by-step explanation:

D

since the coefficient of the x² term is 1, then

add (half the coefficient of the x-term )² to both sides

that is ([tex]\frac{14}{2}[/tex])² = 49

620,000 = 620,000 it remains the same because of the 0.

it will be 600,000 your welcome

To solve a function like this, simply put the numerical value in place of the unknown variable for which you have to find the solution, for instance '-3' in this case.

g(x) = 2x-2

so to find g(-3), we just need to replace the x in the given expression by '-3'. Working is shown below:

g(x) = 2x-2

putting '-3' in place of x

g(-3) = 2(-3) - 2

g(-3) = -6 -2

g(-3) = -8

slope = - [tex]\frac{5}{2}[/tex]

the equation of a line in slope-intercept form is

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

y = - [tex]\frac{5}{2}[/tex] x - 5 is in this form

with slope m = - [tex]\frac{5}{2}[/tex]

The slope of the equation

[tex]Y=\dfrac{-5}{2}x-5[/tex] is [tex]-\dfrac{5}{2}[/tex]  .

A line's steepness or inclination can be measured by a line's slope. It specifies the amount of rise or fall a line experiences for each unit of horizontal distance. In other words, it measures how quickly the vertical (y) and horizontal (x) coordinates of points on a line change with time.

Given equation is

[tex]Y=\dfrac{-5}{2}x-5[/tex] consider it as equation (1)

This is in the form of slope-intercept equation y = mx +b consider it as equation (2).  

Where m represents the slope and b represents the intercept term.

On comparing the equation (1) and equation (2)

[tex]m=-\dfrac{5}{2}[/tex]

Hence, the slope of the given equation   is given by  [tex]-\dfrac{5}{2}[/tex] .

Learn more about slope here:

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Rewrite the equation so both sides have the same base, then equate exponents and solve for c.

[tex]\displaystyle\left(\frac{1}{4}\right)^{c-2}=64\\\\\left(4^{-1}\right)^{c-2}=4^{3}\\\\-(c-2)=3\\\\-1=c[/tex]

The value of c is -1.

c is the correct equation

given ΔABC is similar to ΔPQR

then the ratios of corresponding sides are equal.

the sides a, b and c inΔABC correspond to the sides p, q and r in ΔPQR

thus the following ratios are equal

[tex]\frac{a}{p}[/tex] = [tex]\frac{b}{q}[/tex] = [tex]\frac{c}{r}[/tex]

from this we can see that [tex]\frac{c}{r}[/tex] = [tex]\frac{a}{p}[/tex] → c

a no the corresponding angles are not congruent

∠A ≠ ∠E and ∠D ≠ ∠H

Answer:

No, the corresponding angles are not congruent.

Step-by-step explanation:

In the bigger model, the corresponding angles are 1 degree bigger

we know that

Corresponding angles:

the angles which occupy the same relative position at each intersection where a straight line crosses two others

If the two lines are parallel, the corresponding angles are equal

so, the angles with same positions to ∠1 are

∠13 and ∠5

so,

∠5 and ∠13..................Answer

Answer:

The answer is 5 and 13.

This is because they are on the same side but in other place. You can see this as a square, each square has 4 numbers.

Answer: B) 0

Step-by-step explanation:

1. When you add complex numbers you must add the whole parts and then the imaginary parts.

2. One of the properties of complex numbers is called "Additive identity" which is represented by:

[tex]0+0i[/tex]

3. Then, for the complex number [tex]14+5i[/tex], you have:

[tex](14+5i)+(0+0i)=(14+0)+(5+0)i=14+5i[/tex]

4. Therefore, the answer is the option B.

Answer:

The answer is B. 0

The amount Beth raised by swimming is ...

... x · $0.65

In addition, she had a contribution that was not related to the number of laps. Her total can be expressed as

... 15 + 0.65x = 80

_____

Subtract 15 and divide by 0.65 to find

... x = (80 -15)/0.65 = 65/0.65 = 100

Beth swam ...

... 100 Laps

24 rows of seats

let n be the number of rows

then the number of seats per row = n + 4

number of seats = number of rows × number of seats per row

n(n + 4 ) = 672

n² + 4n - 672 = 0 ← in standard form

the factors of - 672 which sum to + 4 are + 28 and - 24

(n + 28)(n - 24) = 0

equate each factor to zero and solve for n

n + 28 = 0 ⇒ n = - 28

n - 24 = 0 ⇒ n = 24

number of rows n > 0

number of rows = 24 and number of seats per row = 28

24 × 28 = 672 as a check

Answer:

What does the multiplication property of equality allow us to do while solving equations?

C. The multiplication property of equality allows us to multiply both sides of the equation by the same value to maintain equivalent equations.

~batmans wife dun dun dun...

The multiplication property of equality in Mathematics allows us to multiply both sides of an equation by the same value without affecting the equality. This property is useful for simplifying equations and finding unknown variables.

The multiplication property of equality is a crucial concept in solving equations. It states that if you have an equation, you can multiply the same quantity to both sides of the equation without affecting the equality. Essentially, what it says is captured in option C: The multiplication property of equality allows us to multiply both sides of the equation by the same value to maintain equivalent equations.

For example, if we have an equation 2x = 8, we can apply the multiplication property of equality by multiplying both sides of the equation by 1/2 (the reciprocal of 2) to find the value of x, without changing the balance of the equation. So, 2x * 1/2 equals 8 * 1/2, simplified gives us x = 4. This helps in simplifying complex equations and reaching the solution.

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Answer:

y = 2.5(x + 2)^2 - 3

The answer is A

Step-by-step explanation:

The general equation for the vertex is

y  =  a (x + b)^2 + c

a we are not certain about

b = 2

c = - 3

y = a(x + 2)^2 - 3 Now we have to solve for a.

a is found by using the one point we know (0,7) It means when x = 0 y = 7 so just put those two numbers in.

7 = a(0 - 2)^2 - 3

7 = a (- 2)^2 - 3       Add 3 to both sides.

7 + 3 = a(4)              Combine 7 and 3

10 = 4a                     Divide by 4

10/4 = a                    Do the actual division    

2.5 = a

Answer: See above

A

the equation of a parabola in vertex form is

y = a(x - h )² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here the vertex = (- 2, - 3 ), thus

y = a(x + 2 )² - 3

to find a substitute (0, 7 ) into the equation

7 = 4a - 3 ( add 3 to both sides )

10 = 4a ( divide both sides by 4 )

a = [tex]\frac{10}{4}[/tex] = [tex]\frac{5}{2}[/tex]

y = [tex]\frac{5}{2}[/tex](x + 2 )² - 3

(I have answered this question about half an hour before - repeating here)

In order to show the correct time again, the clock has to be exactly 12 hours, or 12*60=720 minutes, behind. With 2 minutes per 3 hours, the clock will have to run for 3 * 720/2 = 1080 hours. 1080 hours = 45 days. The shortest interval the clock need to show the correct time is 45 days.

The shortest interval of time after which the clock will show the correct time is 1.5 hours.

To find the shortest interval of time after which the clock will show the correct time, we need to determine the total time it takes for the clock to lose 2 minutes and reset to the correct time. Since the clock loses 2 minutes every 3 hours, it loses 1 minute per 1.5 hours. Therefore, it will take 1.5 hours for the clock to lose 2 minutes and show the correct time again. So, the shortest interval of time is 1.5 hours.

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5/50 = x / 170

solve for x by multiplying both sides by 170

Jesse used 5 gallons of gasoline to drive 50 miles. the gasoline he will need to travel 170 miles will be 17 gallons.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Jesse used 5 gallons of gasoline to drive 50 miles.

Let x be the gasoline he will need to travel 170 miles

5/50 = x / 170

x = 170 (1/10)

x = 17

Hence, the gasoline he will need to travel 170 miles will be 17 gallons.

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- 28[tex]p^{5}[/tex] - 7[tex]p^{4}[/tex] + 7p³

distributing and adding exponents of like terms gives

- 28[tex]p^{3+2}[/tex] - 7[tex]p^{3+1}[/tex] + 7p³

= - 28[tex]p^{5}[/tex] - 7[tex]p^{4}[/tex] + 7p³

Answer:

Given is that Lance rotates the figure 180° and Celina rotates the figure 90°

Now, when the figure is rotated 180 degrees, it will be turned around the origin in a way that the new place of the image will lie in a straight line in accordance to the original position. So, the second image is Lance's image.

When a figure is rotated 90 degrees counterclockwise, this means the figure will turn to the left and the point of the figure will be downwards. So, the first image is Celina's image.  

Answer:

See below:  Brainliest would help?

Step-by-step explanation:

Answer:

Maximum value of the expression = 5

X value it occurs at = 2

Step-by-step explanation:

Please view the image I provided.

Answer:

The maximum height is reached after 3.75 seconds.

Step-by-step explanation:

Assuming the deceleration due to gravity is unaided by air resistance, gravity causes the ball to lose vertical speed at the rate of 32 ft/s every second. The initial vertical speed of 120 ft/s will decline to zero when t satisfies ...

... 120 ft/s - (32 ft/s²)t = 0

... (120 ft/s)/(32 ft/s²) = t = 3.75 s

The ball will not go any higher after its vertical speed is zero.