Mr Chan bought some pencils for a group of students. If he gives them 2 pencils each, he will have 10 pencils left. If he gives them 3 pencils each, he will have none left. How many students are in the group?

2w + 2l = 25

2 * 2 + 2l = 25

Simplfiy.

4 + 2l = 25

Subtract 4 from both sides.

2l = 21

Divide both sides by 2.

l = 10.5

Now that we have the value of l, we can find the area.

A = lw

A = 10.5 * 2

A = 21.

The length is 10.5cm.

The area of the rectangle is 21cm^2

If I understand what you're saying. It would be the absolute value of -37, which is 37. Also, the absolute value of 37 is 37.

The absolue valor of 37 is 37

Answer:

XY=8

Step-by-step explanation:

In △XYZ, XY=XZ

It is isosceles triangle whose equal sides are XY=XZ

We are given,  

XY=2a

YZ=3a+1

XZ=5a-12

XY=XZ

So, 2a=5a-12

Solve for a,  

2a-5a=-12

-3a=-12

a=4

Now we put a=4 into XY=2a  

So, XY=2(4)=8

Answer:

1.In △XYZ, XY=XZ.

We have to Find the length of XY of △XYZ if XY=2a, YZ=3a+1, and XZ=5a−12.

Now, X Y=X Z  [given]

→2 a= 5 a-12

Bringing like terms on same side

→2 a-5 a=-12

→-3 a=-12

→a=(-12)÷(-3)

a=4 is correct answer among all the options.

2.In △ABC, m∠A=(4x+7)° and m∠B=(5x−3)°.

What is m∠B?

Ans: as ∠ C not given we can't find ∠B.

Answer:

y = 0.15x+77 is the equation linear connecting total cost y and miles driven x

Step-by-step explanation:

Given that the leasing company charged a flat rental fee for the week, plus a charge for each mile driven.

Let flat rental fee be c and cost per mile driven = m and miles driven = x

Total cost =y

Then y = mx+C is the linear equation.

to find m and c, we use the fact that y =110.30 when x = 222

i.e. 110.30 = c+222x

and similarly 99.05 = c+147x

Subtract to eliminate c

11.25 = 75 x

0.15 =x

Substitute in I equation

110.30 = c+222(0.15)

c = 77

Hence y = 0.15x+77 is the equation linear connecting total cost y and miles driven x

Answer:

y = 0.15x+77

Step-by-step explanation:

i did it

Answer:

75,575 - ten-thousands place; this 7 is worth 70,000

75,575 - thousands place; this 5 is worth 5,000

75,575 - hundreds place; this 5 is worth 500

75,575 - tens place; this 7 is worth 70

75,575 - ones place; this 5 is worth 5

Answer:

Since discriminant is positive, therefore, the given quadratic equation has two real solutions. Correct answer is the last option.

Step-by-step explanation:

We have been given a quadratic equation and we need to figure out the number of real solutions of the equation.

[tex]2x^{2}+7x-15=0[/tex]

We know that discriminant of a general quadratic equation [tex]ax^{2}+bx+c=0[/tex] is given by [tex]D=b^{2}-4ac[/tex]

For the given quadratic equation [tex]2x^{2}+7x-15=0[/tex], we have [tex]a=2,b=7,c=-15[/tex]. Upon substituting these values in the formula for discriminant, we get:

[tex]D=7^{2}-4(2)(-15)[/tex]

[tex]D=49+120[/tex]

[tex]D=169[/tex]

Since discriminant is a positive number, therefore, the given quadratic equation has two real solutions. Hence, the last option is the correct answer.

Answer:

two real solutions

Step-by-step explanation:

Area is a squared number.  We know that from the label we use when we solve problems involving area.  Perimeter is a single unit label.  This single unit label can also be used to find scale factor, since single unit labels are one-to-one.  If the area of polygon F is 36, that means that the single unit measure was a number that was squared to get to the area.  Same goes for polygon G.  That means that in order to find the single unit measure of each of those we have to take the square root of the area.  The square root of 36 is 6, and the square root of 4 is 2.  6:2 is the scale factor, but that can be reduced to 3:1, larger to smaller.

Answer:

1/3

Step-by-step explanation:

khan academy answer

y^5 is your answer hope it helps!

Final answer:

The expression 16 x (-3/8) + 16 x 1/4 is evaluated using the distributive property to get -6 + 4, which equals -2.

Explanation:

To evaluate the expression 16 x ( -3/8) + 16 x 1/4 using the distributive property, we will distribute the 16 into the terms inside the parentheses.

Here is the step-by-step process:

Multiply 16 by (-3/8): 16 × (-3/8) = -6.

Multiply 16 by 1/4: 16 × 1/4 = 4.

Add these two results together: -6 + 4 = -2.

Therefore, the evaluation of the expression 16 x ( -3/8) + 16 x 1/4 is -2.

The equation of a parallel line through point (h, k) can be found by altering the given line's equation this way:

To change this equation to point-slope form, solve for y (without expanding the x-term). If there is any constant added to the x-term, add its opposite (so it appears with y).

Here, that looks like ...

... 2(x+9) -5(y-9) = 0

... -5(y-9) = -2(x+9) . . . . add the opposite of the x-term

... y - 9 = 2/5(x +9) . . . . this is the point-slope form you want

_____

To put the equation in general form, multiply by the common denominator of any fractions, and subtract the stuff on the right side of the equal sign. Factor out any common factors of the integer coefficients and constant, and multiply by -1 if the leading coefficient is negative.*

Here, we multiply by 5 (and eliminate parentheses) to get

... 5y -45 = 2x +18

... -2x +5y -63 = 0 . . . . right side subtracted

... 2x -5y +63 = 0 . . . . . leading coefficient made positive. This is your general form.

___

* Actually, I can find no requirement that General Form have a positive leading coefficient. Nor is there a requirement that the coefficients be mutually prime. However, these are requirements for the very similar Standard Form, which has the constant on the right side of the equal sign, instead of the left. Since leading minus signs tend to get lost, IMO, it is a good idea to make the leading coefficient positive, even if it is not a requirement.

ANSWER TO QUESTION 1.

We plot the points:

[tex]P(8,0)[/tex]

[tex]Q(6,2)[/tex]

and

[tex]R(-2,-4)[/tex]

We plot the image triangle also with the points,

[tex]P'(4,0)[/tex]

[tex]Q'(3,1)[/tex]

and

[tex]R(-1,-2)[/tex]

See graph in attachment.

ANSWER TO QUESTION 2.

The scale factor is the ratio of the image length to the object length.

[tex]Scale\: factor=\frac{|P'Q'|}{|PQ|}[/tex].

We need to use the distance formula to determine the two lengths.

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]|P'Q'|=\sqrt{(3-4)^2+(1-0)^2}[/tex]

[tex]|P'Q'|=\sqrt{(-1)^2+(1)^2}[/tex]

[tex]|P'Q'|=\sqrt{1+1}[/tex]

[tex]|P'Q'|=\sqrt{2}[/tex]

[tex]|PQ|=\sqrt{(6-8)^2+(2-0)^2}[/tex]

[tex]|PQ|=\sqrt{(-2)^2+(2)^2}[/tex]

[tex]|PQ|=\sqrt{4+4}[/tex]

[tex]|PQ|=\sqrt{8}[/tex]

[tex]|PQ|=2\sqrt{2}[/tex]

Therefore the scale factor of the dilation is

[tex]Scale\: factor=\frac{\sqrt{2}}{2\sqrt{2}}[/tex].

[tex]Scale\: factor=\frac{1}{2}[/tex].

ANSWER TO QUESTION 3

For a reflection in the y-axis we negate the x-coordinates. That means we are using the y-axis as our mirror line. The mapping is given as follows:

[tex]P'(4,0)\rightarrow P''(-4,0)[/tex]

[tex]Q'(3,1)\rightarrow Q''(-3,1)[/tex]

and

[tex]R(-1,-2)\rightarrow R''(1,-2)[/tex]

ANSWER TO QUESTION 4

We can see from the diagram that, PQR is bigger than P"Q"R".

The reason is that PQR was reduced by scale factor of half and then reflected in the y-axis to obtain P"Q"R".

Since dilation is not a rigid motion, the two triangles PQR and P''Q''R" are not equal in all respect, therefore they are not congruent.

Answer: 747

Step-by-step explanation:

16x9+67x9

First multiply 16 and 9 which is equal to 144

144+67x9

now multiply 67 and 9 which is equal to 603

144+603

Now add 144 and 603 which is equal to 747

So the answer to 16x9+67x9 is 747

use PEMDAS

16 * 9 + 67 * 9 =

144 + 603 =

747

It is known that 60 minutes equals 1 hour.

Therefore, the first thing we do to solve the problem is to calculate how many hours are equivalent to 96 minutes.

For that we calculate:

[tex]96 minutes * \frac{1 hour}{60minutes}=\frac{96}{60}=1.6hours\\[/tex]

Thus:

96 minutes = 1.6 hours.

1.9 ounces of water are lost every 1.6 hours.

Therefore, in 8 hours the amount of water lost  is:

[tex]\frac{8hours}{1.6hours}*1.9 = 9.5\\[/tex] ounces of water

After 8 hours, 9.5 ounces of water are lost

Therefore, the amount of water left in the tank after 8 hours is:

[tex]80 000-9.5=79990.5[/tex] ounces

For this case, we have:

The generic definition of the distributive property is:

[tex]a (b + c) = ab + ac\\[/tex]

Therefore, the option that fits the definition is given by:

[tex]9 (t + 5) = 9t + 45[/tex]

where the property is verified.

Thus, the correct option is A.

Answer:

Option A

Part a)

we know that

to find the equation of the line, I will use the two points that are closest to the line

Let

A(1,14)

B(7,7)

Part b)

Find the slope

we know that

the formula to find the slope between two points is equal to

[tex]m=(y2-y1)/(x2-x1)[/tex]

substitute

[tex]m=(7-14)/(7-1)[/tex]

[tex]m=(-7)/(6)[/tex]

[tex]m=-7/6=-1.167[/tex]

the answer part b) is

the slope is [tex]m=-7/6=-1.167[/tex]

Part c)

we know that

the equation of the line in point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

use the point B (7,7)

[tex]y-7=(-7/6)*(x-7)[/tex]

therefore

the answer part c) is

[tex]y-7=(-7/6)*(x-7)[/tex]

Part d)

we know that

the equation of the line in slope-intercept for is equal to

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

we have

[tex]y-7=(-7/6)*(x-7)[/tex]

[tex]y=(-7/6)x+(49/6)+7[/tex]

[tex]y=(-7/6)x+(91/6)[/tex]

therefore

the answer Part d) is

[tex]y=(-7/6)x+(91/6)[/tex] or [tex]y=-1.167x+15.167[/tex]

There is 1 serving of lemon juice to 3 cups water. Hence why it's 1:3 ratio.

Since it's 1:3, then 2 servings to 6 cups of water, so on and so forth.

Multiply your lemon juice servings by 3 to find out how many cups of water for the table.

To find how much lemon juice for 36 cups of water, just divide 36 by 3 to get 12. 12 servings of lemon juice is just right for your 36 cups of water.

Answer: There is 12 servings of lemon juice needed for 36 cups of water.

Step-by-step explanation:

Since we have given that

Number of cups of water to make lemonade = 36

Ratio of lemon juice to water = 1 : 3

So, number of lemon juice cups be x

number of cups of water be 3x.

According to question, it becomes,

[tex]3x=36\\\\x=\dfrac{36}{3}\\\\x=12[/tex]

Hence, there is 12 servings of lemon juice needed for 36 cups of water.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.

so 13

13.  A prime number is a number which cannot be factored anymore.  4 can be factored as 2 x 2, 26 can be factored as 13 x 2, and 15 can be factored as 3 x 5.

1/2(4x-5) + 5/2 = 10

Use the distributive property:

2x - 5/2 + 5/2 = 10

Use addition property:

2x = 10

Divide both sides by 2:

x = 10/2

x = 5

First, let's convert the radical terms to exponents. Remember the following:

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

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

[tex]\sqrt[4]{x^9} = x^{\frac{9}{4}}[/tex]

[tex]\sqrt[6]{x^5} = x^{\frac{5}{6}}[/tex]

After substituting in the values we just found, our expression looks like:

[tex]\dfrac{(x^{\frac{5}{2}})(x^{\frac{9}{4}})}{x^{\frac{5}{6}}}[/tex]

Now, remember that we can add the exponents of terms that have the same base and are being multiplied by each other. Also, remember that we can subtract the exponents of terms with the same base that are being divided by each other. This is represented as:

[tex]x^a \cdot x^b = x^{(a + b)}[/tex]

[tex]\dfrac{x^c}{x^d} = x^{(c - d)}[/tex]

Thus, we can simplify our expression even more:

[tex]\dfrac{(x^{\frac{5}{2}})(x^{\frac{9}{4}})}{x^{\frac{5}{6}}}[/tex]

[tex]\dfrac{x^{\frac{19}{4}}}{x^{\frac{5}{6}}}[/tex]

[tex]x^{\frac{47}{12}}[/tex]

Our answer is [tex]\boxed{m = \dfrac{47}{12}}[/tex].

100 can go into 750  7.5 times :)

750 divided by 100 is 7.5 so 100 goes into 750 7.5 times

I started off by changing 4 1/5 into 21/5 to make the division easier.

To divide the mixed number 4 1/5 by the fraction 2/3, first convert the mixed number to an improper fraction. The operation becomes (21/5) ÷ (2/3). By multiplying 21/5 by the reciprocal of 2/3, which is 3/2, we find that the result is 63/10. When converted back to a mixed number, 63/10 is expressed as 6 3/10.

The task is to do the operation 4 1/5 divided by 2/3 and expressing the answer as a mixed number in simplest form. To divide fractions, we usually multiply by the reciprocal. First, convert 4 1/5 to an improper fraction which gives us 21/5.

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To find the constant 'a' in the function g(x) = 5x + a, you can substitute the known values into the function. Here, it leads us to the equation 5*4 + a = 31. Solving this equation gives 'a' = 11.

The question gives us the value of g(4) and asks us to find the constant 'a' in the function g(x) = 5x + a.

To solve for 'a', we can substitute the known values into the equation. We know that g(4) = 31, and the function g(x) is defined as 5x + a. Therefore, we replace 'x' with 4 in the function. This gives us 5*4 + a = 31.

Solving this equation, we find that 20 + a = 31. By subtracting 20 from both sides of the equation, we can solve for 'a', giving us 'a' = 31 - 20 = 11.

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In probability, the outcomes of rolling a die are considered. The probability of getting a number less than 7 is 1 or 100% and the probability of rolling a number greater than or equal to 3 is 2/3 or approximately 66.67%

This question falls under the topic of probability in Mathematics. In the case of a single die, there are 6 possible outcomes because a die has 6 faces.

For the probability of getting a number less than 7, all outcomes (1,2,3,4,5,6) are less than 7. Thus, the probability is 6 out of 6 or 1.

For the probability of getting a number that's greater than or equal to 3, the favorable outcomes are 3,4,5,6. So, there are 4 such outcomes. The probability, in this case, is 4 out of 6, which simplifies to 2/3.

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x-intercept: (4,0)

y-intercept: (0,2)