side length z =

angle d =

Answer:

B) y - 2 = (-1/4)(x - 2)

Step-by-step explanation:

Start with the equation of the given line: y = 4x + 7.

Determine the slope of the given line, which is 4.

Since the perpendicular line has a negative reciprocal slope, the perpendicular line's slope is -1/4.

Use the point-slope form of a linear equation: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.

Substitute the values x₁ = 2 and y₁ = 2 into the point-slope equation: y - 2 = (-1/4)(x - 2).

Simplify by distributing -1/4 to (x - 2): y - 2 = (-1/4)x + 1/2.

Add 2 to both sides to isolate y: y = (-1/4)x + 1/2 + 2.

Simplify further: y = (-1/4)x + 5/2.

The equation in point-slope form for the line passing through (2, 2) and perpendicular to y = 4x + 7 is y - 2 = (-1/4)(x - 2), which matches option B.

Answer:

Step-by-step explanation:

3( -2p +2);  distribute 3 over parenthesis

-6p + 6

The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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a) The data is not symmetric

b) The complete table:

  Class interval         Frequency         Relative Frequency

c) Proportion of subdivisions has total length less than 2000 is 0.49

Proportion of the subdivisions has total length between 2000 and 4000 is 0.36

a) To draw the stem and leaf plot we take the thousandth place digit as stem and the leaf is obtained by remaining digits.

       Stem     Leaf

The data is not symmetric

b) To draw the histogram first we form the frequency distribution and the relative frequency using the formula

Relative Frequencies are given by

Relative frequency = Frequency / Total frequency

     Class interval         Frequency         Relative Frequency

                                       = 47

Histogram attached at end of solution

The histogram is approximately positively skewed.

c) Proportion of lengths less than 2000 = sum of relative frequency from 0 to 2000

= 0.26 + 0.23

Proportion of subdivisions has total length less than 2000 = 0.49

Proportion of length between 2000 and 4000 = sum of relative frequency between 2000 and 4000

= 0.21 + 0.15

Proportion of the subdivisions has total length between 2000 and 4000 = 0.36

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Answer:

Step-by-step explanation:

The answer is B

g(x)=|x+4|-10

The equation that represents this graph is g(x) = | x + 4 | - 10.

We know the absolute value function of the modulus function always outputs a positive value irrespective of the sign of the input.

In piecewise terms  | x | = x for x ≥ 0 and | x | = - x for x < 0.

We know the graph of the modulus function y = | x |.

By observing the graph we can conclude that the graph has been shifted along the x-axis by 4 to the left.

∴ y = | x + 4 |.

The graph has also shifted down 10 units along the x-axis.

∴ y = | x + 4 | - 10 is the equation that represents this graph.

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Answer:

a. y = 0.15x + 20

b. the slope (0.15) represents how much the energy company charges per hour.

c. the y-intercept (20) represents the connection fee that you pay starting out.

d. the independent variable is the y-intercept (20) because it only relys on itself

e. the dependent variable is the slope (0.15) it relys on the x variable and the y-intercept (20).

f. 21 hours of usage will cost $23.15 + 20

so the final cost for 21 hours of usage will be $43.15.

Answer:

r=30

Step-by-step explanation:

first expand:

4r+60+4r=300

8r+60=300

8r=300-60

8r=240

r=30

hope this works:)

Answer:

A)  7 ft

Step-by-step explanation:

The definition of a tangent to a circle is a straight line that touches the circle at only one point.

If two segments originating from a common exterior point are tangent to a circle, then those segments are equal in length.

The top segment of ED is 2 ft.

Therefore, the top segment of EF is also 2 ft.

The bottom segment of ED is 4ft.

Therefore, the left segment of DF is also 4 ft.

As DF is 9 ft, then the right segment of DF is 5 ft, since 9 - 4 = 5.

Therefore, the bottom segment of EF is also 5 ft.

Therefore, the two segments of EF are 2 ft and 5 ft.

So the length of EF is 7 ft.

Answer:

1/2 cup

Step-by-step explanation:

Answer:

x = 3, 2

Explanation:

⇒ x² - 5(x) + 6 = 0

breakdown

⇒ x² - 3(x) - 2(x) + 6 = 0

takeout common terms

⇒ x(x - 3) - 2(x - 3) = 0

factor

⇒ (x-3) ( x-2) = 0

simplify

⇒ (x-3)=0, ( x-2) = 0

final answer

⇒ x = 3, 2

Answer: A

Step-by-step explanation:

X+y=1550

Y=4x

The system of equations used are:

x + y = 1550

y = 4x

Option A is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 5 is an equation.

We have,

Number of yards by x = x

Number of yards by y = 4x

Total yards = 1550

Now,

Two equations are:

x + y = 1550

y = 4x

Thus,

The system of equations are:

x + y = 1550

y = 4x

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Answer:

61%

Step-by-step explanation:

Counted the squares by across and down, 6*10=60, and the extra 1 square means 61.

Since it's 61 out of the 100 squares it's 61%

Answer:

-12a - 16

Step-by-step explanation:

\(-3(4a+6)+2=\\-12a-18+2=\\-12a-16\)

Answer:

-12a-16

Step-by-step explanation:

This Should be correct

Using the addition rule with different signs, we know that the resultant answer will have the same sign.

A general example to help you recognize patterns:

Adding Integers:

Subtracting Integers:

Therefore, using the addition rule with different signs, we know that the resultant answer will have the same sign.

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Using a system of equations, for Madelyn to add a certain number of charms to her bracelet, where the cost will be the same at either jewelry shop, the number of chams would be 5.

When two or more equations are solved concurrently, they are described as a system of equations.

Another description of a system of equations is simultaneous equations.

                                       Oxford Fine    Espinoza

Unit cost per charm              $12                 $14

The cost of the bracelet      $40                $30

Let the number of charms = c

Equation 1: (Costs at Oxford Fine) 12c + 40

Equation 2: (Costs at Espinoza) 14c + 30

For the cost to be the same at either jewelry shop, Equation 1 must equal Equation 2:

12c + 40 = 14c + 30

-2c = -10

c = 5

Check:

12c + 40

12(5) + 40 = $100

14c + 30

14(5) + 30 = $100

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The 2 angles total 120

The 2x angle is 120 - 70 = 50 degrees.

2x = 50

Divide both sides by 2:

x - 25

Answer:

\(2x + 70 = 120 \\2x = 120 - 70 \\ 2x = 50 \\ x = \frac{50}{2} \\ \boxed{x = 25}\)

In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, when the CPI was 33.4 the estimated cost of a 30-second commercial during the first Super Bowl in 1967 would be approximately $68,900.

To calculate the cost of the 30-second commercial during the first Super Bowl in 1967, we can use the concept of inflation and the Consumer Price Index (CPI).

The CPI measures the average price change of a basket of goods and services over time. By comparing the CPI values of two different years, we can estimate the relative increase in prices due to inflation.

Given data:

Cost of a 30-second commercial in 2021 = $5.6 million

CPI in 2021 = 271.4

CPI in 1967 = 33.4

To calculate the cost in 1967, we need to adjust the 2021 cost for inflation using the CPI ratio:

Cost in 1967 = (Cost in 2021) * (CPI in 1967 / CPI in 2021)

Cost in 1967 = ($5.6 million) * (33.4 / 271.4)

Cost in 1967 ≈ $0.689 million

To round the cost to the nearest hundred dollars, we can multiply the cost by 100 and round it to the nearest whole number:

Cost in 1967 ≈ $68,900

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0.005m

Measuring properties of a given entity is always prone to error and hence leads to inaccuracy in the resulting measurement. One of such errors is the absolute error.

Absolute error is the difference between the actual/exact value and measured value.

The classroom has been measured to have a perimeter of 62.25m. This shows that it is accurate to 0.01 of a meter. This means that the actual measurement of the classroom could either be 0.005m more or less than the measured value.

In other words, the actual value of the classroom is

62.25 ± 0.005 m

This difference of 0.005 m gives the absolute error.

22π  m²  is the exact surface area of a cylindrical propane tank.

What are volume and surface area?

The entire area of all the faces makes up the surface area of a three-dimensional form. We measure the areas of each face and put them together to determine the surface area of a shape.

                    The surface-area-to-volume ratio, also known as the surface-to-volume ratio or abbreviated as SA:V, refers to how much surface area there is in each unit volume of an object or collection of objects.

A=2πrh+2πr²

 =2π * 1* 10 +2π* 1²

  = 2π( 10 + 1)

  = 2π * 11

  = 22π  m²

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Answer:

\(64 \times 63fctorial \\ = 64 \times (1 \times 2 \times .......63) \\ = 1 \times 2 \times .......63 \times 64 \\ = 64factorial \\ thank \: you\)

Answer:

64!

Step-by-step explanation:

n * (n-1)! = n!

64 * 63! = 64 * (64-1)! = 64!

The number she'd have is:

Explanation:

First, let's see which number is in the tens place and which number is in the ones place (the units place).

In the number 548, the place value of 5 is hundreds, the place value of 4 is tens, and the place value of 8 is ones (or units).

So if Sera adds two to the units, she'll have 10. But, since we can't write the number as 5410 (that would be a totally different number), we just write 0 in the units place, and shift 1 to the tens place, which gives us :

550

That's not all, since we also add 1 to the tens:

560

Answer:

The answer is down below

Step-by-step explanation:

v-u=◇velocity

\( = 9 - 5\)

◇velocity =4ms‐¹

acceleration =◇velocity/time

\(a = \frac{4}{5} \)

\(a = 0.8m {s}^{ - 2} \)

Change in velocity:

\( \sf \:final \: velocity - initial \: velocity = change \: in \: velocity\)

\( \therefore \tt \delta \: v = 9 - 5 \\ \tt = 4m {s}^{ - 1} \)

To find acceleration:

\( \rm \: a = \frac{ \triangle \: v}{\triangle \: t} \)

\( \rm \: a = \frac{ 4}{5 - 0} = \frac{4}{5} = 0.8m {s}^{ - 1} \)

Answer: D

Step-by-step explanation:

Hope it helps

The equivalent cost will be $5.4 per gallon.

The equivalent is the expression that is in different forms but is equal to the same value. Conversion means to convert the same thing into different units.

In September 2016, the cost of gasoline in Berlin was around 1.25 euros per liter.

We know that 1 U.S. dollar = 0.876 euros and 1 gallon = 3.785 liters.

The equivalent cost would be dollars per gallon will be

⇒ 1.25 euros per liter

⇒ 1.25 x [(1/0.876) / (1/3.785)] dollars per gallon

⇒ 1.25 x 1.1415 / 0.2642

⇒ $5.4 per gallon

The equivalent cost will be $5.4 per gallon.

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Answer:

52^6 , there u go hopw this helps ask me anything u want im always here to help

Answer:

52^6

Step-by-step explanation:

Answer:

B. - √2 + √6 / 4

Step-by-step explanation:

I don't know if it's for edge but here's an answer :)

Answer:

320

Step-by-step explanation:

Is the 3 to 2 part to part?  Out of every 5 people, 3 prefer pizza and 2 do not.  We can us this to set up a proportion.

3/5 = 120/x  The 3 represent the part that like pizza over the whole of 5.  The second ratio is showing the actual number of people that liked pizza over the total number of people.

What would be multiply 3 by to get 120? 40.  So, we will multiply 5 times 40 to get the total number of people.  5 x 40 = 200