Simultaneous equations !
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Answer:

I believe it's 35 miles per gallon of gas

Answer:

35 miles per gallon

Step-by-step explanation:

Here we know that the car driven 402.5 miles on 11.5 gallons of gas, so we can write the following equivalence:

402.5 m = 11.5 g

With m being miles and g gallons.

We want to know the equivalent of miles for 1 gallon. So, lets take the equivalence and divide it by 11.5

402.5/11.5 m = 11.5/11.5 g

35 m = 1g

So, each gallon permits to travel 35 miles. If you want to verify it, just multiply 11.5 (the gallons) g by the number of miles, 35:

11.5 * 35 = 402.5

Answer:

Yes.

Step-by-step explanation:

A rational number is any number that can be expressed as a ratio of two integers. 1 and 3 are integers, and 1/3 is a ratio of them, so 1/3 is a rational number.

Answer: Yes it is

Step-by-step explanation: A rational number is a number that can be written in the form of a fraction, so yes it is a rational number.

Answer:

1,000

Step-by-step explanation:

60% of 1,000 is equal to 600

Answer:

its 600%

Step-by-step explanation:

The midpoint of a line segment with endpoints at (3,-1) and (8, -4) is [tex]\left(\frac{11}{2},-\frac{5}{2}\right)[/tex]

Solution:

We have been given 2 end points of a line which are: (3,-1) and (8, -4)

The midpoint of a line segment is half way from both the ends of the line segment.

The formula for midpoint for the two points [tex]P(x_1, y_1) \text{and} Q(x_2, y_2)[/tex] is given as:

[tex]\text {Midpoint}=(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})[/tex]

Here P(3, -1) and Q(8, -4)

[tex]\text { So } x_{1}=3 ; x_{2}=8 ; y_{1}=-1 ; y_{2}=-4[/tex]

Plugging in values in above formula, we get

[tex]\begin{array}{l}{\text {Midpoint}=(\frac{3+8}{2}, \frac{-1-4}{2}})\\\\ {\text {Midpoint}=(\frac{11}{2}, \frac{-5}{2}})\end{array}[/tex]

Hence, the midpoint of the line segment is [tex]\left(\frac{11}{2},-\frac{5}{2}\right)[/tex]

Answer:19.25

304.5

10000

Step-by-step explanation:

X+Y=100kg

X=100-Y

X*0.3+Y*0.55=100*0.5

(100-Y)*0.3+Y*0.55=50

30-0.3*Y+0.55*Y=50

0.25*Y=20

Y=80 kg

X=100-80

X=20 kg

The metal worker should use 20 kilograms of the metal alloy that is 30% copper and 80 kilograms of the metal alloy that is 55% copper.

Answer:

x=20kg

Step-by-step explanation:

Answer:

B. 2 x 3

Step-by-step explanation:

Answer:

b i got it right on test

Step-by-step explanation:

Answer: Multiplied by 10

Step-by-step explanation:

To find the common difference (rate or slope) we can divide the 2nd term to the 1st term.

54.2 / 5.42 = 10 (rule)

Since the common difference is the same throughout the sequence, we can name this as a "arithmetic sequence".

We can multiply 10 to 542 to find the 4th term: 542 * 10 = 5,420

______

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Answer:

Mrs. Dryson made 3 groups with 17 glasses of bears each or she made 17 groups with 3 glasses of bears each.

Step-by-step explanation:

Let the number of groups is x and each group gets y number of bears.

Now, Mrs. Dryson distributed 52 glass bears equally in groups and there was 1 bear left over.

Therefore, xy = 52 - 1 = 51

Now, x and y both must be whole numbers.

Now, we have 51 = 3 × 17, which is the only possible factorization of 51.

So, if x = 3 then y = 17 and if x = 17, then y = 3.

Therefore, Mrs. Dryson made 3 groups with 17 glasses of bears each or she made 17 groups with 3 glasses of bears each. (Answer)

1 1/2 meters is equivalent to 1500 millimeters.

The correct option is (b).

To find out which option is equivalent to 1 1/2 meters, we need to convert 1 1/2 meters to millimeters.

Given:

- Gretta's height is 11/2 meters.

To convert meters to millimeters, we'll use the fact that 1 meter is equal to 1000 millimeters.

So, to convert 1 1/2 meters to millimeters:

[tex]\[ \text{1 1/2 meters} = (1 + 1/2) \times 1000 \text{ millimeters} \][/tex]

[tex]\[ = (1.5) \times 1000 \text{ millimeters} \][/tex]

[tex]\[ = 1500 \text{ millimeters} \][/tex]

So, 1 1/2 meters is equivalent to 1500 millimeters.

Therefore, the correct option is:

b. 1500 millimeters

complete question given below:

Gretta is 11/2 meters tall. Which of the following is equivalent to 1 1/2 meters?

a.150 millimeters

b.1,500 millimeters

c.100 millimeters

d.1,000 millimeters

Answer:

12:45 pm and 7:30 pm

Step-by-step explanation:

In a 24 hour clock, we don't use pm or am to identify time. But in a 12 hour clock , am or pm is used. Given time is in 24 hour clock.

So, for 12:45, in 12 hour clock it will be 12:45 pm because, when the time crosses 11:59, it becomes pm.

For, 19:30, it will 19:30-12:00= 7:30 pm.

Final answer:

To convert 12:45 from the 24-hour clock to the 12-hour clock, it remains 12:45 AM. To convert 19:30, you subtract 12 hours, making it 7:30 PM because it is after noon.

Explanation:

To convert times from the 24-hour clock to the 12-hour clock, you need to remember that the 24-hour clock runs from 0:00 (midnight) to 23:59, while the 12-hour clock repeats the cycle of AM and PM hours from 1 to 12.

Solution to (a):

12:45 in the 24-hour clock is straightforward. Since it's already in the AM range, it's the same in the 12-hour clock - 12:45 AM.

Solution to (b):

To convert 19:30 from the 24-hour clock to 12-hour clock format, subtract 12 hours from the 24-hour time if it is greater than 12. Thus, 19:30 becomes 7:30 PM because 19 - 12 = 7, and any time past noon is in the PM.

Answer:

97.5 sq. ft.

Step-by-step explanation:

Im presuming the question asks to find area of the shaded region.

First of all, the total figure is a rectangle. We can write an expression(in words) for the shaded area.

Shaded Area = Area of Rectangle - Area of Small Triangle(White) - Area of Large Triangle(White)

Now, we find respective areas.

Area of rectangle:

length * width = (5+10) * (12) = 15 * 12 = 180

Area of Small Triangle (white):

A = (1/2) * base * height = (1/2) * 5 * (12-3) = (1/2) * 5 * 9 = 22.5

Area of Large Triangle (white):

A = (1/2) * base * height = (1/2) * 10 * (12) = 60

Now, we find area of shaded region:

Shaded Area = Area of Rectangle - Area of Small Triangle(White) - Area of Large Triangle(White)

Shaded Area = 180 - 22.5 - 60 = 97.5 sq. ft.

Answer:

97.5 sq. ft.

Step-by-step explanation:

See the given diagram with given measurements.

The area of the shaded portion is to be determined.

Now, we have to first find the area of the two right triangles formed at the left and right sides.

We know that the area of a right triangle = [tex]\frac{1}{2} \times (\textrm {Base})\times (\textrm {Height})[/tex]

Then the area of the left side triangle = [tex]\frac{1}{2} \times 5 \times (12 - 3) = 22.5[/tex] sq. ft.

Now, the are of the right side triangle = [tex]\frac{1}{2} \times 10 \times 12 = 60[/tex] sq. ft.

Now, the area of non-shaded region = Total are of the two right triangles  

= (60 + 22.5) = 82.5 sq. ft.

Therefore, the area of the shaded region is = (Area of the total rectangle - Area of the non-shaded region)

= [(10 + 5) × 12] - 82.5

= 97.5 sq. ft. (Answer)

Answer:

3 7/12

Step-by-step explanation:

first you have to make both denominators the same through multiplication but remember if you do that you have to multiply the numerator by the same number as the denominator. then after you do that you can add them and if it comes out improper then you need to simplify your fraction and you have the answer.

Answer: 3⁷/₁₂

Explanation:

Numerator- number on top of fraction

Denominator- number on bottom of fraction

First find a common denominator. A number that both denominators can go into. In this case we'll use 12. Because both of the denominators, 6 and 4, fit into 12.

6 goes into 12 twice. And 4 goes into 12 three times.

To convert to a common denominator, multiply both the numerator and the denominator by the same number. Do not multiply the whole number.

So because 6 goes into 12 twice, we multiply by 2.

⁵/₆ x 2 = ¹⁰/₁₂

And because 4 goes into 12 three times, we multiply by 3.

2³/₄ × 3 = 2⁹/₁₂

Okay so now that both numbers have a common denominator, we can add.

¹⁰/₁₂ + 2⁹/₁₂ = 2 ¹⁹/₁₂

Simplified as 3 ⁷/₁₂

Answer:

8.75 minutes

Step-by-step explanation:

This is a simple linear relation between two variables, time and depth

We can solve it by simple inspection like this.

If the diver is 5 feet deep and plans to go 75 feet deep, he must move 70 feet deeper.

At a rate of 8 feet/minute, it will take him/her

70/8= 8.75 minutes

It is 8 minutes and 45 seconds

[tex](-22)^{\frac{1}{2}}[/tex] and [tex](-10)^{\frac{1}{4}}[/tex] are not real numbers

A real number is any positive or negative number. This includes all integers and all rational and irrational numbers

They are called "Real Numbers" because they are not Imaginary Numbers.

When you take an even root of a negative number, there is no real answer. (2 is an even number)

In the real number set, you can't take an even-indexed root of a negative number.

Given options are:

[tex]\begin{array}{l}{\text { A) }(-22)^{\frac{1}{2}}} \\\\ {\text { B) }(-16)^{\frac{1}{3}}} \\\\ {\text { C) }(-16)^{\frac{1}{5}}} \\\\ {\text { D) }(-10)^{\frac{1}{4}}}\end{array}[/tex]

Looking at the answer choices here, we can see that A and D use even roots, so they will give non-real answers.

Thus [tex](-22)^{\frac{1}{2}}[/tex] and [tex](-10)^{\frac{1}{4}}[/tex] are not real numbers

Answer:

(-16)^1/3 and (-6)^1/5

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Two pyramids are similar. It means that their side lengths are proportional.

So, let's see the proportionality constant from SMALL PYRAMID to LARGE PYRAMID.

The corresponding length of 8 in small pyramid is 24 in large pyramid. We ask ourself:  "8 times WHAT gives us 24?"

This is the proportionality constant (aka "k").

So, 8 times "3" is 24. So the proportionality constant is "3".

k = 3

Now, the height of small pyramid is 6 and height of large pyramid is "x". These sides will be same way proportional. So, we can say:

6 times the proportionality constant (3) would give us x

So,

6 * 3 = x

x = 18

Correct answer is C

Answer: the lowest common multiple of 3 and eight is 24

Step-by-step explanation:

Answer:its 24 :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

100/16 = 25/4 = 6(whole number )1/4

Answer:

20 cups

Step-by-step explanation:

15 / 6 = 5/2

8 * 5/2 = 20

20 cups of milk would be required by Brian to prepare 15 dozen brownies. By utilizing ratios and proportions, this conclusion has been obtained.

To solve this problem, we can use both proportions and ratio. Brian uses 8 cups of milk for every 6 dozen (or 72) brownies. This can be written as the ratio 8:72 or the proportion 8/72 = x/180. From the proportion, we know the cross products are equal, so 8*180 = 72*x. Solving for x gives us x = (8*180)/72. Therefore, Brian would need 20 cups of milk to make 15 dozen brownies.

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Answer:

22m²

Step-by-step explanation:

Area of parallelogram is simply the base length x height.

In this case, base length = 4m and height = 5.5m

hence,

Area = 4 x 5.5 = 22m²

Answer:

22 m^2

Step-by-step explanation:

A = (base)(height), so:

A = (4 m)(5.5 m) = 22 m^2

Answer:

We can conclude that Δ XYZ ≅ Δ RST by ASA postulate.

Step-by-step explanation:

Δ XYZ and Δ RST are congruents by ASA postulate because:  

1. Their included sides XZ  and RT are equal.  

2. Their angles ∠Z and ∠T are equal (92° = 92°)

3. Their angles ∠X and ∠R are equal.  

4. Their non-included sides XY and RS are equal.

Now, we can conclude that Δ XYZ ≅ Δ RST by ASA postulate.

Answer:

Carlton caught 2072 more fish than Will

Step-by-step explanation:

First you add how much fish Will caught: 7+13+8=28. Then you Subtract Carlton's number of fish minus Wills number of fish:

2100-28=2072! Hope it helped :) Please Mark Brainliest :)

Answer:

2 and 2/5 candy bars

Step-by-step explanation:

To figure this out, simply add the fractions together 6 times or multiply 2/5 by 6.

(2/5)(6/1)

Multiply the numerator

2*6=12

Multiply the denominator

5*1=5

so the answer is 12/5 or 2 and 2/5 candy bars.

Answer:

[tex]\frac{1}{16}[/tex]

Step-by-step explanation:

Given

[tex](-1/4)^{2}[/tex]

= - [tex]\frac{1}{4}[/tex] × - [tex]\frac{1}{4}[/tex]

= [tex]\frac{1(1)}{4(4)}[/tex]

= [tex]\frac{1}{16}[/tex]

Answer:

262

Step-by-step explanation:

If x is the first integer, then x+1 is the second, x+2 is the third, and so on.  Meaning the 7th term in the list is x+6.

x + x + 6 = 518

2x = 512

x = 256

The first integer is 256, so the last integer is 262.

Answer:

Step-by-step explanation:

The vertices of triangle ABC are A(−5, 1), B(−2.5, 7), and C(0, 1).

The given translation of vertices,

This translation shows shift x-coordinate 3 unit right and y-coordinate 1 unit down.

[tex]A(-5,1)\rightarrow A'(-5+3,1-1)[/tex]

New vertices A'(-2,0)

[tex]B(-2.5,7)\rightarrow B'(-2.5+3,7-1)[/tex]

New vertices B'(0.5,6)

[tex]C(0,1)\rightarrow C'(0+3,1-1)[/tex]

New vertices C'(3,0)

Hence, the new coordinate of the vertices are A'(-2,0) , B'(0.5,6) and C'(3,0)

Answer:

[tex]y \leq -\frac{3}{4}x+2[/tex]

y is less than or equal to negative three fourths times x plus 2

Step-by-step explanation:

step 1

Find the equation of the solid line

we have the coordinates (0,2) and (4,-1)

Find the slope m

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{-1-2}{4-0}[/tex]

[tex]m=\frac{-3}{4}[/tex]

[tex]m=-\frac{3}{4}[/tex]

Find the equation of the line in slope intercept form

[tex]y=mx=b[/tex]

where

m is the slope

b is the y-intercept (value of y when the value of x is equal to zero)

we have

[tex]m=-\frac{3}{4}[/tex]

[tex]b=2[/tex] ---> is given

substitute

[tex]y=-\frac{3}{4}x+2[/tex]

Remember that

The shading area is below the line

therefore

The inequality is

[tex]y \leq -\frac{3}{4}x+2[/tex]

y is less than or equal to negative three fourths times x plus 2

Answer:

Y is less than or equal to negative three fourths times x plus 2

Step-by-step explanation:

Answer: Rational

Step-by-step explanation: -44 is an integer and all integers are rational numbers. Therefore, -44 is classified as a rational number.

The set of integers includes the set of whole numbers {0, 1, 2, 3...} and they also include their negative counterparts.

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Answer:

605100

Step-by-step explanation:

6.051*10^5=605100