Select the two figures that are similar to the 5 by 10 figure that is shown

[tex]\underline{+\left\{\begin{array}{ccc}4x+5y=16\\-4x-10y=4\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad-5y=20\qquad\text{divide both sides by (-5)}\\.\qquad\qquad\boxed{y=-4}\\\\\text{Put the value of y to the first equation:}\\\\4x+5(-4)=16\\4x-20=16\qquad\text{add 20 to both sides}\\4x=36\qquad\text{divide both sides by 4}\\\boxed{x=9}\\\\Answer:\ \boxed{x=9\ and\ y=-4\to(9,\ -4)}[/tex]

To match the numbers to the letters for the equivalents, we can simplify each expression:

3(4x + 2) = 12x + 6 (A)

(2x + 3) - (4x + 5) = 2x + 3 - 4x - 5 = -2x - 2 (B)

8x + 5 - x + 4 = 8x - x + 5 + 4 = 7x + 9 (C)

7(3x - 2) = 21x - 14 (D)

Matching the numbers to the letters for the equivalents:

Expression 1 is equivalent to option A.

Expression 2 is equivalent to option B.

Expression 3 is equivalent to option C.

Expression 4 is equivalent to option D.

x, y - the numbers

x + y = 19

x - y = 3        add both sides of the equations

2x = 22      divide both sides by 2

x = 11

Substitute the value of x to the first equation:

11 + y = 19     subtract 11 from both sides

y = 8

The sum of the two numbers is 19 and their difference is 3. The two numbers are 11 and 8.

Let's use a system of equations to solve this problem.

Let's say the first number is x and the second number is y.

According to the given information, we have the following equations:

x + y = 19  (equation 1)

x - y = 3  (equation 2)

We can solve these equations simultaneously by either substitution or elimination method.

Let's use the elimination method.

Adding equation 1 and equation 2, we get:

(x + y) + (x - y) = 19 + 3

2x = 22

x = 11

Substituting the value of x in equation 1, we get:

11 + y = 19

y = 8

Therefore, the two numbers are 11 and 8.

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Answer:

Today Sally is 28 years old and her son is 10

Step-by-step explanation:

x= Sally's Age; y= Sally's son age

Sally is 18 years older than her son

x-y=18

And she was three times older

x=3y

Substituting and solving:

3y-y=18

2y=18

Last year they were:

y=9

x=27

This year

y+1=10 ; x+1=28

Answer:

Multiplication and Division in order from left to right

Step-by-step explanation:

PEMDAS

Parentheses

Exponents

Multiplication and Division in order from left to right

Addition and Subtraction in order from left to right

Final answer:

The operation that should be performed immediately after evaluating exponents using the order of operations is multiplication and division in order from left to right.

Explanation:

The operation that should be performed immediately after evaluating exponents using the order of operations is multiplication and division in order from left to right.

In the order of operations, exponents are evaluated first, followed by multiplication and division from left to right, and finally addition and subtraction from left to right. This means that after evaluating exponents, you should perform any multiplication or division operations in the expression if they exist.

For example, if you have the expression 2³ times 4 + 6, you would first evaluate 2³ = 8 and then perform the multiplication: 8 times 4 = 32. Finally, you would add the resulting 32 to 6 to get the final answer.

Answer:

18 times

Step-by-step explanation:

6/10= .6

So 60% of 30 is 18

Answer:

5x+5y

Step-by-step explanation:

Answer: 16.5 gallons of water should be mixed to make a 20% solution of [tex]H_2SO_4[/tex]

Step-by-step explanation: We are given the concentration of the solution in percentage, it can be taken as the molarity of the solution.

Now, to calculate the volume of water required, we use the formula:

[tex]M_1V_1=M_2V_2[/tex]

where,

[tex]M_1\text{ and }V_1[/tex] are the initial molarity and volume of the solution.

[tex]M_2\text{ and }V_2[/tex] are the final molarity and volume of the solution.

Given:

[tex]M_1=55\%\\V_1=6gallons\\M_2=20\%\\V_2=?gallons[/tex]

Putting values in above equation, we get:

[tex]55\times 6=20\times V_2\\V_2=16.5gallons[/tex]

Answer:

10.5 gallons of water should be added.

Step-by-step explanation:

Let [tex]C_{1} * V_{1} = C_{2} * V_{2}[/tex], where [tex]C_{i}[/tex] are the concentration of the solution and [tex]V_{i}[/tex] are the volume of the solution for i=1,2.

Now, substituting values, we have,

55*6 = 20*[tex]V_{2}[/tex]

i.e. [tex]V_{2}[/tex] = (6*55)/20

i.e. [tex]V_{2}[/tex] = 16.5

So, the final volume is 16.5 gallons.

Hence, we need to add 16.5 - 6 = 10.5 gallons of water.

150x + 400(1900-x) = 440250

150x + 760000 - 400x = 440250

250x = 319750

x = 1279

There were 1,279 children.

Answer:

Step-by-step explanation:

he used distributive property.

Answer:

Jack used distributive property

Answer:

(1,-5)

i plugged it into a graphing calc

Answer:

She can make two necklaces with 10 inches. 8 more inches

Step-by-step explanation:

Answer:

She can make 2.2 Necklaces, and needs 3.5 more inches of string.

Step-by-step explanation:

Let's carefully read the problem for information we need.

3 Friends, 4.5 Inches per friend. She only has 10 inches.

If each necklace is 4.5 inches, we need

4.5 (friend one) + 4.5 (friend 2) + 4.5 (friend 3). We can also just take 4.5 * 3 friends and get the same result. This equals 13.5.

But wait! We only have 10 inches... Jessica needs 3.5 more inches of string to be able too complete the 3rd necklace. This is the answer to "How much more string does she need to buy"

---

For "How many necklaces can she make". Well, we know she can't make a full 3 necklaces. We can find out the answer to this by dividing the 10 inches she does have, by the 4.5 inches it takes to make one necklace.

10/4.5=2.2

This means she could make 2 necklaces, and 2/10 (.2) of another necklace before she runs out of string.

To map triangle RST to triangle DEF, perform a translation, rotation, and possibly a reflection.

To map triangle RST to triangle DEF using rigid motions, we need to use a combination of translations, rotations, and reflections.

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What form of measurement do we convert it to?

Convert to what? Feet? Inches? Yards? Meters? Please tell me so i can answer this!

Answer:

1) Multiplying powers with the same base would be product rule. It where you just add the exponents. Dividing powers with the same base would be the quotient rule. Its where you subtract the exponents.

2)Where you multiply the two exponents together

3)The negative law is where for example, if it were in the numerator, then it would be placed at the denominator with a positive exponent whereas if it were in the denominator it would be on the numerator with the positive exponent. The zero law just states the anything to the power to zero is one.

Step-by-step explanation:

1) 3^3 x 3^4 = 3 ^3+4 = 3^7

3^9 ÷3² = 3^9-2 = 3^7

2) (3^2)^2 = 3^2×2 =3^4

3) 1/3^-5 = 3^5                 \

3^-7 =1/3^7

2^0 = 1

The exponent laws for multiplying and dividing powers with the same base involve adding or subtracting exponents, respectively. The power of a power law states you should multiply exponents. Negative and zero exponent laws indicate how to deal with powers that are negative or zero.

In mathematics, especially when dealing with exponents, there are specific laws that streamline the process of multiplication, division, and dealing with different powers. Below are the laws related to your questions:

Multiplying and Dividing Powers with the Same Base

For multiplication: When two powers with the same base are multiplied, you add the exponents. For example, a^m × a^n = a^(m+n).

For division: When two powers with the same base are divided, you subtract the exponents. For example, a^m ÷ a^n = a^(m-n), where a ≠ 0.

Power of a Power Law

When raising a power to another power, you multiply the exponents. This is known as the power of a power law. So, (a^m)^n = a^(m*n).

Negative and Zero Exponent Laws

A negative exponent indicates division by that base and the exponent turned positive, such as a⁻ⁿ = 1/aⁿ. For a zero exponent, any non-zero base raised to the power of zero equals one, signified as a⁰ = 1.

Answer:

its probably 8.5

Step-by-step explanation:

Answer:

Option B.

Step-by-step explanation:

Trigonometric area formula is Area = [tex]\frac{1}{2}\times absin(C)[/tex]

Where a and b are two sides of the triangle and C is the angle between these two sides.

As given in the figure, side a = 6 units, c = 2√2 units and ∠B = 80°

Then area of the triangle will be defined by the formula

Area = [tex]\frac{1}{2}\times acsin(B)[/tex]

        = [tex]\frac{1}{2}\times acsin(B)[/tex]

        = [tex]\frac{1}{2}\times 6\times 2\sqrt{2}\times sin(80)[/tex]

        = 6√2×sin80°

        = 6×(1.414)×0.9848

        = 8.36 square units

        ≈ 8.4 square units

Option B is the answer.

Answer:

-62

Step-by-step explanation:do multiplication 1st then work out problem left to right.

Answer:

8/3 = 1/x or x = 3/8

Step-by-step explanation:

Set up the ratio

(2/3)/(1/4) = 1/x  

solve for x  

8/3 = 1/x or x = 3/8

Answer:

Wax required for entire car = 3/8 bottle of wax

Step-by-step explanation:

We have given,

1/4 bottle of car wax can wax 2/3 of her car.

We need to find the wax required to wax her car completely.

Let's derive the relation between wax bottle and car waxing rate:

2/3 of car waxing needs 1/4 of bottle of wax.

for entire car waxing, i.e 1 car waxing needs (1/4) / (2/3) bottle of wax

            wax required for entire car     =    (1/4 )*(3/2)

                                                              =3/8 bottle of wax

ANSWER:

y = -2/3x + 2

ABOUT SLOPE INTERCEPT FORM:

You have to isolate or get y by itself:

2x + 3y = 6

-2x           -2x

3y = -2x + 6

3             3

y = -2/3x + 2 --- IN SLOPE INTERCEPT FORM

Hope this helps you!!! :)

Answer:

y=-2/3x +2

Step-by-step explanation:

y=mx+b

2x+3y-6

3y-6=-2x

3y=-2x+6

y=-2/3x+2

Answer:

m=-14 I hope this helps u

Step-by-step explanation:

Answer:

19.2 million.  

Step-by-step explanation:

Let us find the amount of savings per center by dividing 2.4 by 2.

[tex]\text{Amount of savings per center}=\frac{2.4\text{ Million}}{2\text{ Center}}[/tex]

[tex]\text{Amount of savings per center}=1.2\frac{\text{ Million}}{\text{ Center}}[/tex]

Hence, the company saved 1.2 million per center.

Let us multiply savings of each center by total number of company's distribution centers to find the total amount of money that the company can be expected to save.    

[tex]\text{Total amount of company's savings}=(1.2\times 16)\text{ million}[/tex]

[tex]\text{Total amount of company's savings}=19.2\text{ million}[/tex]

Therefore, Mr. Ortiz's company will save 19.2 million.

Answer:

Quarters = 47

Nickels = 83

Step-by-step explanation:

A) N + Q = 130

B) .05N + .25Q = 15.90

Multiplying equation A by -.05 equals

A) -.05N -.05Q = -6.50  then adding this to B)

B) .05N + .25Q = 15.90  Equals

.20Q = 9.40

Quarters = 47

Nickels = 83

.05*83 + .25*47 = 4.15 + 11.75 = 15.90

It ΔABC and ΔXYZ are similar, then the sides of the triangles are in proportion.

[tex]\dfrac{AB}{XY}=\dfrac{BC}{YZ}=\dfrac{AC}{XZ}[/tex]

We have BC = 8, AC = 7, Y = 28, XZ = 49 and YZ = 56. Substitute:

[tex]\dfrac{AB}{XY}=\dfrac{BC}{YZ}\to\dfrac{AB}{28}=\dfrac{8}{56}\qquad\text{cross multiply}\\\\56AB=(8)(28)\qquad\text{divide both sides by 56}\\\\AB=\dfrac{224}{56}\\\\\boxed{AB=4}[/tex]

Answer:

a.  4y =12x  the constant of variation is 3

Step-by-step explanation:

The equation for direct variation is y=kx

a.  4y =12x

 Divide each side by 4

4y/4 = 12x/4

 y = 3x

This is direct variation and the constant is 3

Equations b ,c, d  all have a constant added which make them something other than a direct variation

Answer:

A Constant of variation is 3

Step-by-step explanation:

Remark

Direct variations have an equation that looks like y = kx There is NO y intercept, or the y intercept = 0. If you solve for the slope of choices B C and D you get a y intercept that is not 0. For example Take C

Solution

Your only possible answer is A

The constant of variation =

The garden has a total of 14,208 plants, calculated by multiplying the area of the garden (3552 square feet) by the number of plants per square foot (4).

The student asked how many total plants are in a gardener's garden, which measures 96 feet long and 37 feet wide, with 4 plants per square foot. To determine the total number of plants, we must first find the area of the garden by multiplying the length and width.

The area of the garden in square feet is 96 feet × 37 feet = 3552 square feet. Since there are 4 plants per square foot, the total number of plants is 3552 × 4 = 14,208 plants.

Answer:

the integers are: 87, 89, and 91

Step-by-step explanation:

n+n+2+4=267

3n+6=267

3n=261

n=87.

can you please tell me where you got this question from

Final answer:

The three consecutive odd integers that sum up to 267 are 87, 89, and 91. By setting up an equation, we find the first integer and then determine the next two by adding 2 to each consecutive integer.

Explanation:

The sum of three consecutive odd integers is 267. To find these integers, let's first represent them algebraically. Assume the smallest integer is x. Then the second integer, being consecutive and odd, would be x + 2, and the third would be x + 4. The sum of these three integers is given by:

x + (x + 2) + (x + 4) = 267

Simplify this equation to find the value of x:

3x + 6 = 267

Subtract 6 from both sides:

3x = 261

Divide both sides by 3:

x = 87

Now that we have the smallest integer, the second and third integers are 87 + 2 = 89 and 89 + 2 = 91, respectively.

The three consecutive odd integers are 87, 89, and 91.

Answer:

$86.25

Step-by-step explanation:

You need to calculate 15% of $75, and then add it to $75.

To find a percent of a number, change the percent to a decimal and multiply by the number. To change a percent to a decimal, divide the percent by 100, which the same as moving the decimal point of the percent two places left.

For example, 15% = 15/100 = 0.15 (by dividing 15 by 100).

15% = 0.15 (by moving the decimal point of 15 two places to the left).

Now back to the problem. First, we find 15% of $75.

15% of $75 =

= 15% * $75

= 0.15 * $75

= $11.25

The tip of 15% of $75 was $11.25.

The total amount spent is the bill total, $75, plus the $11.25 tip.

Total spent = $75 + $11.25 = $86.25

Answer:

B

Step-by-step explanation:

Because Im MATHS SUPER MAN

Answer:

$82.55

Step-by-step explanation:

65 + (0.07×65) + (0.2×65)