Two consecutive positive numbers are such that the sum of their squares is 113. find the two numbers

Answer:

19 minutes.

Step-by-step explanation:

55-36=19.

For this case we have to indicate how much time the brownies are needed to bake, knowing that 55 minutes are given and Teresa reviewed them after 36 minutes.

For this we subtract:

[tex]55 \ minutes-36 \ minutes = 19 \ minutes[/tex]

So brownies have 19 minutes to bake

Answer:

19 minutes

Answer:

The expression equal to 2x^(2)+8 is:

First option (2x-4i)(x+2i)

Step-by-step explanation:

If we multiply

(2x-4i)(x+2i)=(2x)(x)+(2x)(2i)-(4i)(x)-4i(2i)

(2x-4i)(x+2i)=2x^(1+1)+4xi-4xi-8i^(1+1)

Simplifying:

(2x-4i)(x+2i)=2x^2-8i^2

and i^2=-1, then:

(2x-4i)(x+2i)=2x^2-8(-1)

Multiplying:

(2x-4i)(x+2i)=2x^2+8

Answer: (2x-4i)(x+2i)

Step-by-step explanation:

The two angles are corresponding angles, so they are congruent (due to the horizontal lines being parallel)

x+15 = 102

x+15-15 = 102-15 .... subtract 15 from both sides

x = 87

To calculate SUTA and FUTA for the first 12 weeks, calculate the taxable wages for each employee. Multiply the taxable wages by the respective tax rates to find the amount owed. Roger owes $371 for SUTA and $56 for FUTA for the first 12 weeks.

To calculate the amount that Roger owes for SUTA (State Unemployment Tax Act) and FUTA (Federal Unemployment Tax Act) for the first 12 weeks, we need to calculate the taxable wages for each employee. The taxable wages for SUTA is the first $7,000 and for FUTA is the first $7,000 as well.

Since the three employees earn $500, $550, and $700 respectively, their total wages for the first 12 weeks would be $17,100 (12 weeks x ($500 + $550 + $700)). However, since SUTA and FUTA only consider the first $7,000 of wages, we can calculate the amount for each tax.

For SUTA, the total taxable wages would be $7,000. Using the SUTA rate of 5.3%, we can calculate the amount owed: $7,000 x 0.053 = $371.

For FUTA, the total taxable wages would also be $7,000. Using the FUTA rate of 0.8%, we can calculate the amount owed: $7,000 x 0.008 = $56.

Therefore, Roger owes $371 for SUTA and $56 for FUTA for the first 12 weeks for his three employees.

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Answer:

b

Step-by-step explanation:

3.27 Times 10⁻⁴ in standard form is 0.000327. This is found by moving the decimal point in 3.27 four places to the left, resulting in the number 0.000327.

The number 3.27 TImes  10⁻⁴ into standard form.

To do this, we move the decimal point four places to the left, because the exponent on the 10 is negative four.

So, starting with the number 3.27, we move the decimal point to the left four times, which introduces three zeros after the decimal point and before the 327.

The correct answer is B: 0.000327.

This means that 3.27 times  10⁻⁴ is equivalent to 0.000327 when written in standard form.

Answer:

D

Step-by-step explanation:

f(x) - g(x) = -9x^2 - 7x + 12 - (3x^2 - 4x - 15)  Remove the brackets

f(x) - g(x) = -9x^2 - 7x  + 12 - 3x^2 + 4x + 15

f(x) - g(x) = -9x^2 - 3x^2 - 7x + 4x + 12 + 15

f(x) - g(x) = -12x^2- 3x + 27

Answer D

Answer:

Option D. -12x² - 3x + 27

Step-by-step explanation:

The given functions are f(x) = -9x² - 7x + 12 and g(x) = 3x² - 4x - 15

We have to find the value of f(x) - g(x)

f(x) - g(x) = (-9x² - 7x + 12) - (3x² - 4x - 15)

              = -9x² - 7x + 12 - 3x² + 4x + 15

              = (-9x² - 3x²) - (7x - 4x) + 12 + 15

              = -12x² - 3x + 27

This value of f(x) - g(x) matches with option D.

Therefore, Option D. is the correct option.

The slope-intercept form: y= mx + b

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (6, 2) and (5, 5). Substitute:

[tex]m=\dfrac{5-2}{5-6}=\dfrac{3}{-1}=-3[/tex]

Therefore we have y = -3x + b.

Put the coordinates of the point (5, 5) to the equation:

5 = -3(5) + b

5 = -15 + b     add 15 to both sides

20 = b

Answer:

y = -3x + 20

Step-by-step explanation:

(a) Slope

The point-slope formula for a straight line is

y₂ - y₁ = m(x₂ - x₁)     Insert the points  

2 - 5 = m(6 - 5)

    -3 = m×1

    m = -3

=====

(b) y-intercept

y₂ - y₁ = m(x₂ - x₁)

y₂ - 5 = -3(x₂ - 5)     Remove parentheses

y₂ - 5 = -3x₂ - 15       Add 5 to each side

      y = -3x + 20

Answer: x^3y^4 is the lowest common denominator.

Step-by-step explanation: To get both expressions to have a common denominator, multiply both of them to get them equal. For the first expression, multiply the numerator and denominator by y^3: 3y^3/x^3y^4

The second expression should be multiplied by the numerator and denominator by x^2: 7x^2/x^3y^4

(Add exponents when multiplying them) Now both expressions have common denominators.

Answer:

x^3*y^4

Step-by-step explanation:

The two denominators shown are x^3*y and x*y^4.  The LCD must involve the largest power of x, which is x^3, and the largest power of y, which is y^4.  Thus, the LCD is x^3*y^4.

Answer:

The answer c

Hope I helped :)

Step-by-step explanation:

Solve for x by simplifying both sides of the equation then isolating the variable.

Exact Form:

x=1/3

Decimal Form:

x=0.333333333

So for this, we will be setting up a system of equations with the information we have:

[tex]x+y=13\ \textsf{"The sum of two numbers is 13."}\\2x-3y=1\ \textsf{"Two times the first number minus three times the second number is 1."}[/tex]

Now we have our system of equations set up. Next, I will be using the substitution method to solve this system. So firstly, subtract y on both sides of the first equation:

[tex]x=13-y\\2x-3y=1[/tex]

Now, substitute x for (13 - y) in the second equation and solve for y as such:

[tex]2(13-y)-3y=1\\26-2y-3y=1\\26-5y=1\\-5y=-25\\y=5[/tex]

Now that we have the value of y, substitute it into either equation to solve for x:

[tex]x+5=13\\x=8\\\\2x-3(5)=1\\2x-15=1\\2x=16\\x=8[/tex]

In short, the first number (x) is 8 and the second number (y) is 5.

To solve this problem, plug 8250 in for b and 15 in for t and then solve for k:

[tex]8250=1000e^{15k}[/tex]

*Divide both sides by 1000*

[tex]8.25=e^{15k}[/tex]

*Take the natural log (ln) of both sides*

2.1102=15k

*Divide both sides by 15*

0.1406=k

0.1406 rounds to 0.141 which is close to a. 0.143.

Hope this helps!!

Answer:

y = 30

Step-by-step explanation:

We can use ratio's to solve this

40        20

-----  = -----------

100       20 + y

Using cross products

40 * (20+y) = 20*100

Distribute

800 + 40y = 2000

Subtract 800 from each side

40y = 2000-800

40y = 1200

Divide by 40

y = 1200/40

y =30

Answer:

False

Step-by-step explanation:

(-2,0)  x is equal to -2 and y = 0

y=x  

Substitute the values in.

-2 =0

False

Answer:

C is your answer

Step-by-step explanation:

Add every number by 14

The surface area of the cylinder is approximately 191.9 square inches.

The surface area of a cylinder is the sum of the areas of its curved surface and its two circular bases. The formula for the surface area of a cylinder is:

SA = 2πr² + 2πrh

where SA is the surface area, r is the radius of the circular base, h is the height of the cylinder, and π is the mathematical constant pi (approximately equal to 3.14159).

The first term on the right-hand side of the equation (2πr²) represents the area of the two circular bases of the cylinder. The second term (2πrh) represents the area of the curved surface of the cylinder.

The area of the square embedded in the circular base of the cylinder is 18 in², which means each side of the square has a length of √18 in = 3√2 in. Since the square is embedded in the circular base, the diameter of the base of the cylinder is equal to the diagonal of the square, which is 2 times the length of one side, or 6√2 in.

The radius of the circular base is half the diameter, or 3√2 in. The surface area of the cylinder consists of the area of the top circular base, the area of the bottom circular base, and the lateral area (the curved surface area) of the cylinder.

The area of each circular base is πr² = π(3√2)² = 18π in².

The lateral area of the cylinder can be found by multiplying the height (which is given as 10 inches) by the perimeter of the circular base (which is 2πr). The perimeter of the circular base is 2π(3√2) = 6π√2 in. Therefore, the lateral area is 10(6π√2) = 60π√2 in².

The total surface area of the cylinder is the sum of the areas of the two circular bases and the lateral area:

Surface area = 2(18π) + 60π√2

= 36π + 60π√2

≈ 191.9 in² (rounded to one decimal place)

Therefore, the surface area of the cylinder is approximately 191.9 square inches.

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When an exponent is negative, you move it to the other side of the fraction to make the exponent positive.

For example:

[tex]x^{-2}[/tex] or [tex]\frac{x^{-2}}{1} =\frac{1}{x^2}[/tex]

[tex]\frac{1}{y^{-3}} =\frac{y^3}{1}[/tex] or y³

f(-2) This means that x is -2, so you can plug in -2 for "x" in the equation

[tex]f(x)=3^x[/tex]

[tex]f(-2)=3^{-2}[/tex]

[tex]f(-2)=\frac{1}{3^2}[/tex]

[tex]f(-2)=\frac{1}{9}[/tex]

Your answer is D

The value of the function f(-2) will be 1/9

A mathematical relationship from a set of inputs to a set of outputs is called a function.

The given function is f(x) = [tex]3^{x}[/tex]

∴ f(-2) will be = [tex]3^{-2}[/tex]

So,  [tex]3^{-2}[/tex] will be equal to 1/9

∴ The value of f(-2) will be 1/9

Option D is correct.

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Answer:

The statement that most accurately represents the data given is the 'The mean and median age are more likely to be the same for the students in Math 1.'

Step-by-step explanation:

The box and whisker plots given for the two sets of data show a few different things.  Box and whisker plots first show us the median in a given set of data, which is the line in the middle of the box.  For both Math 1 and Math 2, this line occurs at 19.  The whiskers that extend from the box on either side represent the range, or lowest and highest numbers, in the data.  For Math 1, the range is 17-21 and for Math 2, the range is 17-23.  Since the range is more evenly distributed in Math 1, we can conclude that the mean, or average of the data, is most likely the same as the median of the data, which is 19.  

Answer:

its d

Step-by-step explanation:

its d

Answer:

[tex]\frac{(L x M)}{6}[/tex]

Step-by-step explanation:

The greatest common factor is the greatest number that will divide two values. We have two values L and M. Each has numbers which multiply together to give the number. The highest value or most in common they share is 6. This is the GCF.

The least common multiple is the smallest positive number which is a multiple of the two. This means both L and M divide into it evenly.

We know L x M is a multiple because L and M will be factors of it. But we don't know its the least.

As an example if L= 42 and M = 60, they have GCF 6. We can multiply them to find a multiple 42 x 60 = 2520 but we don't know this is the smallest or least multiple we can find. If we divide by the GCF, 2520/6=420. Interestingly, 42 x 10 =420 and 60 x 7 =420. This means 420 is the least common multiple.

We can multiply (L x M) and then divide by the GCF of L & M to find the least common multiple.

[tex]\frac{(L x M)}{6}[/tex]

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

rearrange 13x + 8y = 12 into this form

subtract 13x from both sides

8y = - 13x + 12 ( divide all terms by 8 )

y = - [tex]\frac{13}{8}[/tex] + [tex]\frac{3}{2}[/tex] ← in slope-intercept form

with slope m = - [tex]\frac{13}{8}[/tex] and y-intercept c = [tex]\frac{3}{2}[/tex]

Answer:

Anna

Step-by-step explanation:

Compare the answers, and when you do that then you can see that anna had more money come in then the others.

The number of cubes needed with an edge length of  [tex]\bold{\dfrac{1}{3}}[/tex] inches is needed to build a cube with an edge length of 1 inch is 27.

the edge length of smaller cube, a = [tex]\bold{\dfrac{1}{3}}[/tex] inches

the edge length of the cube to be built, S = [tex]\bold{\dfrac{1}{3}}[/tex] inches

we know that volume of a cube is given by (side)³.

[tex]\bold{Volume\ of\ cube = (side)^3}[/tex]

Volume of the smaller cube =  (edge length of the smaller cube)³

                                              =   a³

                                              =   [tex]\bold{(\dfrac{1}{3})^3}[/tex]

                                              =   [tex]\bold{\dfrac{1}{27}}[/tex] in.³

Volume of the cube to be build =  (edge length of the cube to be built)³

                                                    =   S³

                                                    =   1³

                                                    =   1 in.³

solving,

Cubes of smaller length are needed for the larger cube

                                                         [tex]\bold{=\dfrac{Volume\ of\ the\ Larger\ cube}{Volume\ of\ the\ Smaller\ cube}}[/tex]

                                                         [tex]\bold{=\dfrac{1}{\dfrac{1}{27}}}[/tex]

                                                         [tex]\bold{=27}[/tex]

Hence, the number of cubes needed with an edge length of  [tex]\bold{\dfrac{1}{3}}[/tex] inches is needed to build a cube with an edge length of 1 inch is 27.

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Answer:

slope = - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

y = - 2x is in this form

with slope m = - 2 and c = 0

Answer: 8?

Step-by-step explanation:

the value of the expression is approximately - 25.4349.

To find the value of the expression (- 3)³ + 6⁽³/¹²⁾, we follow the order of operations. First, we evaluate the exponentiation:

(- 3)³ = (- 3) × (- 3) × (- 3) = -27

Next, we simplify the second term:

6⁽³/¹²⁾ = 6⁽¹/⁴⁾ = √( √6) ≈ 1.5651

Finally, we add the two results:

(- 3)³ + 6⁽³/¹²⁾ = - 27 + 1.5651 ≈ - 25.4349

So, the value of the expression is approximately - 25.4349. The explanation highlights the steps of evaluating the exponentiation and simplifying the second term before performing the addition to get the final result.

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To find the length of the wall represented by a line that is 3 7/8 inches long on the blueprint, we can use the scale conversion. The length of the wall is 15 1/2 feet.

To find the length of the wall represented by a line that is 3 7/8 inches long on the blueprint, we need to use the scale conversion.

The given scale is 1 inch corresponds to 4 feet.

So, we can set up a proportion:

1 inch − 4 feet

3 7/8 inches − x feet

To solve for x, we can cross-multiply:

1 × x = 4 × 3 7/8

Multiply 4 by the whole number 3 and then add the product to the result of 4 multiplied by the fractional part 7/8.

x = 12 + 28/8

x = 12 + 3 1/2

x = 15 1/2 feet

Therefore, the length of the wall represented by a line that is 3 7/8 inches long on the blueprint is 15 1/2 feet.

Answer:

There are 8 cans on each of the equal shelves

Step-by-step explanation:

Total number of cans put in display = 35

Shelves with equal no of cans =  4 Shelves

And one shelf displays only 3 cans

Therefore, 4 shelves with equal no of cans + 1 shelf with 3 cans = 35 cans

Let us assume equal no. of cans be x

We get, 4x + 3 = 35

             4x = 35 - 3

             4x = 32

              x  = 32 ÷ 4

              x = 8

Thus, 4 shelves with equal no of cans contains 8 cans each.

The solution is: Area of actual Patio is:  170 ft²

Given:

Patio drawing of 4.25 in by 2.5 in

Scale of Patio to its drawing = 4ft to 1 in

Requires:

Area of actual Patio

SOLUTION:

Area of actual Patio = area of a rectangle = length × width

Given a scale drawing of 4ft to 1 in, therefore:

Length of actual Patio = 4.25 × 4 = 17 ft

Width of actual Patio = 2.5 × 4 = 10 ft

Therefore:

Area of actual Patio = 17 ft × 10 ft = 170 ft²

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complete question:

A contractor is given a scale drawing of a rectangular patio. The scale from the patio to the drawing is 4ft to 1in. What is the area of the actual patio?

Answer:

The company should charge $ 3.25 for the smaller size.

Step-by-step explanation:

The price per ounce of the 32-ounce product is required to be 25% greater than the larger-sized product.

We know that for the size of 48 ounces the price is $ 3.90

So, the price per ounce is:

[tex]\frac{3.90}{48}[/tex]= $ 0.08125

For the smallest size the price per ounce should be 25% higher.

So:

$ 0.08125 (1 + 0.25) = $ 0.10156

The total price for the smallest size is:

$ 0.10156 * 32 = $ 3.25

The company should charge $ 3.25 for the smaller size.

Answer:

3.25

Step-by-step explanation:

We could solve this problem by figuring out the per-ounce cost of the 48-ounce package, increasing it by $25\%$, and then multiplying that by 32 for the smaller package. However, if we simply increase the price by $25\%$, and then scale the package size down to 32 ounces from 48 ounces, these are the same calculations, but in a different order that makes it easier to calculate. Thus: $3.90 \times 1.25 \times \frac{32}{48} = \boxed{3.25\text{ dollars}}$