Part A: State the vertical angles theorem.

Part B: Identify the pairs of vertical angles in the figure.

Part C: Determine the measures of triangle a triangle b and triangle c in this figure. Show your work.

Answer:

It got colder by 9 degrees

Step-by-step explanation:

The equation of the parabola in vertex form is y = - (1 / 4) · x².

In this problem we find a parabola whose axis of symmetry is on the y-axis and the directrix is above the parabola, which means that the least distance between the vertex and the directrix is negative. The equation of the parabola in vertex form is described below:

4 · p · (y - k) = (x - h)²

Where:

If we know that p = - 1 and (h, k) = (0, 0), then the equation of this parabola is:

4 · (- 1) · y = x²

- 4 · y = x²

y = - (1 / 4) · x²

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The absolute value will always be a positive number while solving an equation that does not involve an absolute value could be any number.

The absolute value of a number n, written |n|, can be described

geometrically as the distance of n from 0 on the number line.

For instance, |42| = 42 and |–42| = 42. Both 42 and –42 are 42 units

from zero.

Algebraically, the absolute value of a number can be defined

piecewise as follows.

|x| = {

 x, for x ≥ 0

–x, for x < 0

Examine the definition carefully. Because –x is the opposite of x,

–x is positive when x is negative. For instance, |–7.4| = –(–7.4) = 7.4.

Thus |x| are |–x| are never negative, and, in fact, |x| = |–x|.

On many graphing utilities, spreadsheets, and CAS, the absolute–

the value function is denoted abs. For example, abs(x–3) = |x–3|.

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Answer:

the answer is 90⁰ ok that

Answer: 40 hours

Step-by-step explanation:

As stated in the question the total amount spent in the month of august is $35.

First of all you have to subtract 15 out of the entire amount spent so that you can start calculating how many hours did Julie use the pool.

(35-15) = 20 (divide the answer with 0.50)

(20/0.50) = 40 (We have to divide to get the amount of hours she spent in pool)

Answer:

A) [tex]y = \frac74x[/tex]

Step-by-step explanation:

Since the equation's graph passes through the origin, its [tex]c[/tex] value is equal to 0, and, therefore, you will only need to find the slope as the equation is of the template [tex]y = mx[/tex] where [tex]m[/tex] is the slope.

To find the slope, you can substitute the coordinates of the given points into the formula for a line's slope: [tex]y = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]y = \frac{7 - 0}{4 - 0} \to \frac74[/tex]

Therefore, the line's equation is [tex]y = \frac74x[/tex]

Answer:

number is - 4

Step-by-step explanation:

let the number be n then 4 times the sum of the number and 2 is 4(n + 2)

4(n + 2) = 2n

4n + 8 = 2n ( subtract 2n from both sides )

2n + 8 = 0 ( subtract 8 from both sides )

2n = - 8 ( divide both sides by 2 )

n = - 4

the number is - 4

[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]

- - - - - - - - - - - - - - - - - - - - -

[tex]\textsf{Let the number be t.}[/tex]

[tex]\textsf{The Sum means adding two numbers together.}[/tex]

[tex]\textsf{Then,}[/tex]

[tex]\textsf{4 times the sum of a number and 2 = 4 times t+2 = 4(t+2).}[/tex]

[tex]\textsf{Remember to write the parentheses when you're multiplying something times}\\\textsf{a sum or a difference.}[/tex]

[tex]\textsf{You know how to write "is equal to", don't you? It's =}[/tex]

[tex]\therefore\\\textsf{4(t+2)=}[/tex]

[tex]\textsf{Next, twice the number is written as 2t.}[/tex]

[tex]\textsf{\textbf{Our expression looks like this:}}[/tex]

[tex]\Large\boldsymbol{\rm{4(t+2)=2t}}[/tex]

[tex]\textsf{Now let's find the number: }[/tex]

[tex]\Large\begin{gathered} \sf{4(t+2)=2t}\\\sf{4t+8=2t}\\\sf{4t-2t=-8}\\\sf{2t=-8}\\\sf{t=-4} \end{gathered}[/tex]

[tex]\ddot\smile[/tex]

[tex]\Large\overbrace{\underbrace{\boldsymbol{\rm{Reflection - RoSe}}}}^\star_\star[/tex]

Answer: 2 laps four minutes

explanation:

The inequality for the load in truck is 300r + 425p ≤ 6300.

11 refrigerators and 8 pianos will overload the truck.

Given,

The carrying capacity of truck = 6300 lbs

The truck is used to transport refrigerators and pianos.

The weight of 1 refrigerator = 300 lb

The weight of 1 piano = 425 lb

We have to find an inequality which shows the number of refrigerators and pianos could the truck carry.

Let's take the number of refrigerators as r and number of pianos as p.

We can equate by using their weights:

That is,

300r + 425p ≤ 6300

Next, we need to determine that, will 11 refrigerators and 8 pianos overload the truck:

We have to multiply the given number with their weights:

That is,

(300 × 11) + (425 × 8) = 3300 + 3400 = 6700

6700 is greater than 6300.

So, we can conclude that 11 refrigerators and 8 pianos will overload the truck.

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Answer: 2 6/7

Step-by-step explanation:

Answer:

Answer is 75/32

Step-by-step explanation:

Convert the mixed number to an improper fraction so 7 1/2 changes to 15/2 divided by 2x5/8 but then you change the 2 to 1/2 so 15/2 x 1/2 x 5/8

then you multiply the fractions then you get 75/32

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Remember that we're using absolute values. A negative number plus a positive number is the same as a positive number subtracted by another positive number.

Based on the constant average rates of change. , the missing value in the table is 16

Linear relationships are relationships that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

The table of values is given as

x    y

1     4

2     7

3     10

4     13

5

The constant average rates of change of linear relationships imply that:

As the x values constantly change by a value, the y values constantly change by another value (could be the same value)

On the given table, we can see the trend to be;

As x increase by 1, y increase by 3

So, the missing y value is

y = 13 + 3

Evaluate the sum

y = 16

Hence, the missing value in the table is 16

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Answer: 4r + 4s - 16s

Step-by-step explanation:

r +3r = 4r

-10s -6s =16s

2t + 2t =4t

key when you see the word perimeter than think of addition

The time it took to fly through ah fro is 21 hours

x=21 hrs

This is further explained below.

Generally, A cargo aircraft traveled to the repair facility and returned again, and the flight there took an hour less of its total time than the flight back did.

The voyage there had an average speed of 220 miles per hour, whereas the return back had an average speed of 200 miles per hour. I was wondering how many hours the journey took.

Generally, the equation for the distance is  mathematically given as

Dist = speed * time

Therefore

Dist to = dist back

220t = 200(t+1)

220t = 200t + 200

220t - 200 = 200

20t = 200

t = 200/20

t = 10 hrs to

Considering for hours back

10 + 1 = 11 hrs back

Total hrs: 10 + 11 = 21 hrs for the round trip

In conclusion, The trip took

21 hrs

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CQ

a cargo plane flew to the maintenance facility and back it took one hour less time to get there than it did to get back. the average speed on the trip there was 220mph the average speed on the way back was 200mph how many hours did the trip take

Answer:

[tex] \sf \large \: x = -1[/tex]

Step-by-step explanation:

4x + 7 = 3

Substract 7 from both sides

4x + 7 - 7 = 3 - 7

4x = -4

Divide both sides by the coefficient of x

4x/4 = -4/4

calculate

x = -1

Answer:

x=6.28 0r 0.72

Step-by-step explanation:

The explanation is in the image

Answer:

[tex] \sf{x=−12}[/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

90+x+67+35=180

Step 1: Simplify both sides of the equation.

90+x+67+35=180

(x)+(90+67+35)=180(Combine Like Terms)

x+192=180

x+192=180

Step 2: Subtract 192 from both sides.

x+192−192=180−192

x=−12

Step-by-step explanation:

You could use a calculator to make it simple

(0.067 × 42.1) ÷ (17.4 - 4.19). to 1s.f

=(2.8207) ÷ (13.21)

= 0.213527 to 1s.f

= 0.2

*you could also check using your own calculator

*let me know if you want me to expand it if you don't have a calculator

Answer:

[tex]\sf \bf h^{21}[/tex]

Step-by-step explanation:

  We have to multiply the powers.

[tex]\sf \boxed{\bf (a^m)^n=a^{m*n}}[/tex]

       [tex]\sf (h^3)^7=h^{3*7}[/tex]

                [tex]\sf = h^{21}[/tex]

The extraneous solution is √2 and -√2

Extraneous solutions refer to the ones which when found the roots appear to be right, but are not exactly valid roots.

We have to check, whether the given solution is an extraneous one or not. We have to solve this equation,

√x+1 + √2 x = √5 x+3

or, √x + √2 x - √5 x = 3 - 1

or, - √2 x = 2Now, we have to square both sides,

∴ 2x² = 4

or, x² = 4/2

or, x² = 2

or, x = + √2 and - √2

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Firstly we will convert the percent R into a decimal value r. For that, we will divide with a hundred,

r = R/100

r = 6/100

r = 0.06 rate per year,

Then solve the equation for A

A = P(1 + r/n) ^ nt

A = 500.00(1 + 0.06/12) ^ (12 x 10)

A = 500.00(1 + 0.005)^ 120

A = $909.70

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $500.00 at a rate of 6% per year compounded 12 times per year over ten years, is $909.70.

I = A - P = $2,000.00

Equation:

A = P(1 + rt)

Calculation:

First, converting R percent to r a decimal

r = R/100 = 4%/100 = 0.04 per year.

Solving our equation:

A = 5000(1 + (0.04 × 10)) = 7000

A = $7,000.00

The total amount accrued, principal plus interest, from simple interest on a principal of $5,000.00 at a rate of 4% per year for ten years is $7,000.00.

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The properties used to simplify the problem are associative property of addition, additive inverse, and additive identity.

Consider the given problem;

( 38 + 677 ) + ( - 38 )

The associative properties can be represented as:

( A + B ) + C = A + ( B + C )

Now, we need to check all the options to determine the properties used:

( 38 + 677 ) + ( - 38 ) = 38 + ( 677 - 38 )

( A + B ) + C = A + ( B + C )

Therefore, this is the associative property.

Now,

677 + 0 = 677

A + 0 = A

Thus, this is the additive identity.

Similarly,

677 + [ 38 + ( -38 ) ]

Here, 38 + ( -3 8 ) represents,

A + ( - A ) = 0.

Therefore, this is the additive inverse.

Thus, the properties used to simplify the problem are the associative property of addition, additive identity, and additive inverse properties.

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The graph at:

x=-6,-4→intersects directly

x=0→passes through

x=1→tangent

At different x-intercepts, graphs exhibit varying behaviours. On occasions, the graph will intercept the x-axis and cross it. On occasions, the graph will contact the x-axis and then deviate from it. The graphs contact or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities. Higher even powers, such as 4, 6, and 8, will still cause the graph to contact and deviate from the x-axis, but as even power increases, the graph will appear flatter as it does so.The graph will still cross through the x-axis for higher odd powers like 5, 7, and 9, but for each rising odd power, the graph as it approaches and departs the x-axis, it seems flatter.

∴x=-6,-4→intersects directly

x=0→passes through

x=1→tangent

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There are two types of exponential functions. For x or y increases as the value of y increases, the value of y decreases, approaching zero. For

approaching zero as the value of {x} increases, the value of y increases.

Which two forms of exponential functions are there?

What does Y mean in the exponential growth equation?

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Answer:

NOT GREATER!!!

Step-by-step explanation:

0.6667 is NOT greater than 0.6667 which also means that 2/3 is NOT greater than 4/6.

The value of x using the change of base formula of logarithm is 25.

What are the various properties of the logarithm?

Out of several properties of logarithms, some of the main properties are given below:

Product Rule

log (ab) = log a + log b

Change of base

log ₇ x = log x / log 7

Power Rule

log a² = 2 log a

Quotient Rule

log (a / b) = log a - log b

Solving the given equation by using the change of base formula

We are given a logarithmic expression: log ₉ x = log ₃ 5

Using properties of the logarithm, we have

log x / log 9 = log 5 / log 3

log x = (log 5 × log 9) / log 3

= (log 5 × 2 log 3) / log 3

= 2 × log 5

= log 5²

log x = log 5²

Applying exponent both sides, we get,

x = 25

Hence, the value of x is 25.

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Answer:

100 and 10

Step-by-step explanation:

The value of x would be 28 and the measure of angle M will be 90 degrees.

That parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.

A rectangle is always a parallelogram and a quadrilateral but reverse statement may or may not be true.

WE have been given the Quadrilateral MNOP is a rectangle, and ∠M = 3x + 6.

WE know that interior angle of the rectangle are 90 degrees each.

Therefore,

∠M = 3x + 6 = 90

3x + 6 = 90

3x = 90 - 6

3x = 84

x = 84/3

x = 28

Hence, the value of x would be 28 and the measure of angle M will be 90 degrees.

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Answer: 3c^2  +4 -5c

Step-by-step explanation:

-2c^2 -c +1 -(-5c^2 -3 +4c)

3c^2  +4 -5c