Which of the following options best describes an algebraic fraction?

Select all that apply.

common denominators
a variable in the numerator
a variable in the denominator
a variable with an exponent

Answer:

B 7

Step-by-step explanation:

Since the triangles are similar by AAA

We can use ratios to find the length x (which is PR)

5                 15

-------- = ------------

x               21

Using cross products

5 * 21 = 15 *x

Divide each side by 15

5/15 * 21 = 15x/15

1/3 * 21 =x

7 =x

Answer:

here is how i did it.

[tex]y+8=-11\qquad\text{subtract 8 from both sides}\\\\y+8-8=-11-8\\\\\boxed{y=-19}[/tex]

Answer:

-75.77

Step-by-step explanation:

finding the difference is just finding the distance between two points

your two points are 66.830 and 142.6

so subtract 66.830 from 142.6 and you will get -75.77 depending on the question it could be positive or negative.

Answer:

75.77

Step-by-step explanation:

Answer:

630.8 for the nearest tenth, and 631 for a whole number.

Step-by-step explanation:

[tex]\bf \textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=1.5\\ h=1.5 \end{cases}\implies SA=2\pi (1.5)(1.5+1.5) \\\\\\ SA=3\pi (3)\implies SA=9\pi[/tex]

Answer:

4.

a. base angle

b. leg

c. vertex

d. leg

e. base

f. base

5. You have 3 pairs of corresponding congruent sides, so the property that proves the triangles are congruent would be SSS.  

Answer:

It would take 675.2809 days or 675.3 days

Step-by-step explanation:

first you simplify your equations if possible which you can here.

6.01×10^8=601,000,000        8.9×10^5=890,000

Then you are going to divide 601,000,000 by 890,000 or you cancel the zeros and then divide (your choice)

601,000,000/980,000

You can cancel out the zeros that both share so you'll be left with

60,100/89

then you divide and you get

675.2809

or you can round to the nearest tenth and you get

675.3

Answer:

280 calories

Step-by-step explanation:

200 / 50 = 4

1 gram = 4 calories

70 * 4 = 280

Therefore, there are 280 calories in 70 grams of cheese.

Answer:

19800

Step-by-step explanation

5 * 60 =300

5 hrs is 300 minutes

300 + 30 = 330

5hrs and 30 min is 330 min

330*60= 19800

5hrs and 30 min is 19800 sec

Answer:

See below.

Step-by-step explanation:

The slope of the line is (5-1) / (3 - -3)

= 4/6  = 2/3

Point slope form:

y - y1 = m(x - x1)

Plugging in m = 2/3 and the point (-3,1):-

y - 1 = 2/3(x + 3) (answer)

Slope-intercept form:-

y - 1 = 2/3(x + 3)

y = 2/3x + 2 + 1

y = 2/3x + 3 (answer)

Standard Form:-

y = 2/3x + 3

Multiply through by 3:-

3y = 2x + 9

-2x + 3y = 9  (answer).

Answer:

a=4

Step-by-step explanation:

ax − 4 = 2y

We need to get the equation is slope intercept form  y= mx+b.

Lets solve for y

Divide each side by 2

a/2 x - 4/2 = 2y/2

a/2 x -2 = y

or y=a/2 x -2

The slope is a/2 and the y intercept is -2

We want a slope of 2  so a/2 =2

a/2=2

Multiply each side by 2

a/2 * 2 =2*2

a =4

Answer:

Ask away

Step-by-step explanation:

Answer:

Ill do the math

Step-by-step explanation:

Answer:

100:1

Step-by-step explanation:

To solve this, you must divide the two.

287 / 2.87 = 100

The scale factor of the model is 100:1.

The scale factor between a real building that is 287 feet tall and a model that is 2.87 feet tall is 0.01, or 1:100. This means that each unit on the model corresponds to 100 units on the actual building.

The subject here is regarding scale factor in mathematics. The scale factor is the ratio between the corresponding sides of two similar figures. In this case, the two figures are the actual capital building and its model. To calculate the scale, divide the height of the model by the height of the actual building. So, if an actual building is 287 feet and its model is 2.87 feet, then the scale is given by 2.87 / 287, which is 0.01.

So, the scale of the model to the building is 1:100, because for every one unit on the model, there are 100 units on the actual building. Remember this scale when considering the height and other dimensions of the model or the building.

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Answer:

The dot would be at (4, 6)

Step-by-step explanation:

To graph the line that represents the proportional relationship between the number of slices of pizza purchased and the total cost, divide the change in total cost by the change in the number of slices. In this case, the line passes through the points (4, 6) and (0, 0) with a slope of 1.5.

To graph the line that represents the proportional relationship between the number of slices of pizza purchased and the total cost, we need to identify the slope of the line. The slope represents the rate of change of the total cost with respect to the number of slices. In this case, we can calculate the slope by dividing the change in total cost by the change in the number of slices.

Given that the student bought 4 slices of pizza for $6.00, we can create two points on the line: (4, 6) and (0, 0). The first point represents 4 slices purchased for $6.00, and the second point represents 0 slices purchased for $0.00.

To calculate the slope, we use the formula (change in y)/(change in x), which gives us (6-0)/(4-0), resulting in a slope of 6/4 or 1.5.

Therefore, the line that represents the proportional relationship is a straight line passing through the points (4, 6) and (0, 0) with a slope of 1.5.

Answer: 700

Step-by-step explanation:

The required inequality to calculate the number of additional toys needed to meet the goal of more than 1000 toys and  additional condition is shown in the inequality '300 + x > 1000'.

The goal of the toy drive is to collect more than 1000 toys.

Given that 300 toys have already been collected, we want to find out how many more toys are needed to meet this goal.

To represent this situation, we can set up an inequality where x represents the number of toys still needed.

The inequality would be 300 + x > 1000.

Solving for x, we subtract 300 from both sides to isolate x, which gives us x > 700.

This means that the toy drive needs more than 700 additional toys to meet its goal of donating more than 1000 toys.

Answer:

55

Step-by-step explanation:

Given that a circle and inside two chords with same arc length.

We are to find the angle between the two chords.

Given that two arcs subtend angle 125 degrees at the centre.

Let us join the two ends of chords to make the figure as a triangle inside a circle.

The triangle is isosceles as two arcs and hence chords are equal.

By central angle theorem we have the two equal angles as 1/2 (125) = 62.5

Hence we have a triangle with two equal angles 62.5 and another angle 1.

By triangle sum of angles theorem

angle 1+62.5+62.5 = 180

Hence angle A = 180-62.5-62.5 = 55 degrees.

D) feet

A tree 1.5 x 10^3 is 1500 centimeters. That's about 300 inches, which would better be measured in feet.

You can use the fact that normally people use those measurements which are whole numbers or not elongated decimal number mostly and not much big numbers.

The most appropriate unit to measure the length of the tree out of the given options is

Option D:  feet

Normally people use those measurements which are whole numbers mostly and if not, then not too much long after decimal and not much big numbers.

A tree is measured suitably if we use feet. It is because the normal tree height is from few feet to few hundred feet.

If you measure tree height in centimetres, then as you can see in the question, the number before cm unit is quite big to handle by normal people.

If you measure in too big unit like kilometres, then the height would be expressed mostly like 0.some digits.

That's why we choose feet.

Since 1 cm = 0.0328 feet

thus, height of specified tree in feet would be

[tex]\rm 0.0328 \times 1.5 \times 10^{3} = 49.2 \: feet[/tex]

See the number before feet. Its not too big nor too small, and easy to remember and converse. That's why feet is appropriate.

Thus,

The most appropriate unit to measure the length of the tree out of the given options is

Option D:  feet

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Answer:

13 bowls

Step-by-step explanation:

To figure out how many bowls of nuts she can make, we divide how many cups of nuts she has by how many cups of nuts in a bowl

3 3/8 ÷ 1/4

Lets change 3 3/8 into an improper fraction

3 3/8 = (8*3 +3)/8 = 27/8

27/8 ÷ 1/4

Copy dot flip

27 /8 * 4/1

27/2

2 goes into 27 13 times with 1 left over

13 1/2

She will have 13 full bowls of nuts

The values of x and y that satisfy the system of equations are x = (1/3 ± i√(19))/1 and y = (±i√(19) + 2)/2.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

We are given that;

The equations 3x − 1 + 2y = 0 and 3x2 − y2 + 4 = 0

Now,

To find the corresponding values of y, we can plug these values of x into the expression for y that we found earlier:

[tex]y = -1/2(3x - 1). For x = (1/3 + i√(19))/1, we get: y = -1/2(3(1/3 + i√(19))/1 - 1) = -1/2(i√(19) - 2) = (i√(19) + 2)/2. For x = (1/3 - i√(19))/1, we get: y = -1/2(3(1/3 - i√(19))/1 - 1) = -1/2(-i√(19) - 2) = (-i√(19) + 2)/2.[/tex]

These are the values of y that satisfy the system of equations.

Therefore, by quadratic equations the answer will be x = (1/3 ± i√(19))/1 and y = (±i√(19) + 2)/2.

Learn more about quadratic equations;

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Answer:

6

Step-by-step explanation:

the rate of change is given by the slope of the line

the equation of a line in slope- intercept form is

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

f(x) = 6x - 5 is in this form

with slope m = 6 ← rate of change

Answer:

6

Step-by-step explanation:

We are given the function f(x) = 6x-5 for which we have to determine its rate of change.

The rate of change is given by the slope of a line.

We know that the standard form of an equation of a line is given by:

y = mx + c

where m is the slope.

If we observe the given function, we can notice that is in the form y = mx + c where the slope (m) is 6.

Therefore, the rate of change for the function f(x) = 6x - 5 is 6.

Answer:

the answer is -20/8 or A

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Answer:

-3/4 I think hope this helps

Answer:

88 percent because to get to 25*4 is 100 so whatever you do on the bottom you do on the top and you get 88

Step-by-step explanation:

Answer:

0.88

Step-by-step explanation:

this is easy!

divide 22 by 25.

the line between the numbers mean to divide

so you take the top number and put it outside the box then put the bottom on the inside of your box

Answer:

6.6 stone

Step-by-step explanation:

We will use conversions to change kilograms to stones

1 kilogram= 2.2 pounds,

1 stone= 14 pounds

42 kilogram          2.2 lbs           1 stone

---------------       * -------------   * ---------------

                           1 kg                 14 lbs

All the units cancel except stone

(42*2.2)/14  stone

6.6 stone

Answer:

Number of permutations = 5040

Step-by-step explanation:

We are given the word 'INNOVATIVE', that has total 10 letters.

Now, we are asked to form words using exactly 4 letters at a time i.e. out of 10 letters we are using 4.

Therefore, the number of permutations that can be formed using 4 letters are = P(10,4)

i.e. [tex]10_{P_{4} }[/tex]

= [tex]\frac{10!}{(10-4)!}[/tex]

= [tex]\frac{10!}{6!}[/tex]

= [tex]\frac{10*9*8*7*6!}{6!}[/tex]

= 10*9*8*7

= 5040

Answer: 5040

Step-by-step explanation:

npr = n! / (n - r)!

numbers of letters given = 10

permutation that can be formed using 4 letters at a time= 10 P ₄

=10! / (10 - 4)! = 10! / 6!

= 10 ×9 ×8×7 ×6! /6! ( the 6! will cancel out)

= 10×9 ×8×7=5040

Therefore, the number of permutations are 5040

Answer:

3/8

Step-by-step explanation:

The height is 9 in the drawing and the statue is 24

We want the scale factor from drawing to statue

The ratio is 9/24

Divide the top and bottom by 3

3/8

Answer:

18

Step-by-step explanation:

Let the side of the triangle be a and that of the new one be a'.

a'/a = 3/1      Insert the value of a

a'/6 = 3        Multiply each side by 6

  a' = 18

The measure of a side of the new triangle is 18.

Answer: 18 units.

Step-by-step explanation:

Given : An equilateral triangle is dilated by a scale factor of 3.

[Note an equilateral triangle has all its side-lengths are equal.]

Side-length of the original triangle = 6 units

Then, the measure of a side of the new triangle = Scale factor x Original side-length

= 3 x 6 = 18 units

Hence, the measure of a side of the new triangle = 18 units.

Answer:

Step-by-step explanation:

Three

3a

Two lines that have slopes where 1 is the negative of the other will intersect some where once and only once. I've included a graph for this.

3b

If you multiply the top line by 2 you get the bottom line. They are the same line. There's an infinite number of solutions.

3C

They will intersect once. On your paper just extend both lines. They intersect.

3D

If they are parallel, they never intersect. No solution.

Four

what's at the tail end of four. y = 1/2x - ???? I'll give it a value. You'll have to change the value to get it to work properly.

A

m: y = 1/2x - 4   The 4 is mine. Change it to what it says.

n: y =  1/2x - 8    Any value except - 4 will work.

B

m: y = 1/2x - 4

n : -2y = -x + 8           They are really the same equation. n = -2*m

C

m: y = 1/2 x - 4

n: y = x + 3

I'm going to let you work your way through 5. There should be enough in 3 and 4 to get five.

Five

A: False

B: This question is not true, but you probably don't have enough math to say why. Bend your right arm so it is parallel to your belt. Above that "line" bend your left arm so it is over the right arm in just one place. The left arm should be pointing towards the wall of your room. Those two are not parallel nor do they have  any meeting place.

C: True

D: False

Final answer:

The volume of a cylinder with a diameter of 6m and a height of 5m is calculated using the formula V = πr²h. With a radius of 3m, the volume is 141.39m³.

Explanation:

To find the volume of a cylinder with a diameter of 6m and a height of 5m, we first need to calculate the radius of the cylinder. The radius is half of the diameter, so in this case, the radius (r) is 3m. The formula for the volume (V) of a cylinder is V = πr²h, where π (pi) is approximately 3.142, r is the radius, and h is the height of the cylinder.

Using this formula, we get:

V = π × (3m)² × 5m

V = 3.142 × 9m² × 5m

V = 3.142 × 45m³

V = 141.39m³

Therefore, the volume of the cylinder is 141.39 cubic meters.