mystery question A=8+8 B= A-7 A=16 B=​

Answer:

[tex]y=\frac{1}{4}(x+1)^2-9[/tex]

Step-by-step explanation:

Method 1

we know that

The equation of a vertical parabola in vertex form is equal to

[tex]y=a(x-h)^2+k[/tex]

where

a is the leading coefficient

(h,k) is the vertex

we have

(h,k)=(-1,-9)

substitute

[tex]y=a(x+1)^2-9[/tex]

Remember that

one root is (-7,0)

substitute and solve for a

[tex]0=a(-7+1)^2-9[/tex]

[tex]0=a(-6)^2-9[/tex]

[tex]0=36a-9[/tex]

[tex]a=\frac{1}{4}[/tex]

therefore

[tex]y=\frac{1}{4}(x+1)^2-9[/tex]

Method 2

I use the fact that the roots are the same distance from the vertex

the distance from the given root to the vertex is equal to

6 units

so

If one root is x=-7

then the other root is

x=-1+6=5

The general equation of the quadratic equation is equal to

[tex]y=a(x+7)(x-5)[/tex]

we have the vertex (-1,-9)

substitute the value of x and the value of y and solve for a

[tex]-9=a(-1+7)(-1-5)[/tex]

[tex]-9=a(6)(-6)[/tex]

[tex]-9=-36a[/tex]

[tex]a=\frac{1}{4}[/tex]

[tex]y=\frac{1}{4}(x+7)(x-5)[/tex]

so

Expanded the equation, complete the square and rewrite as vertex form

Answer:

195.75

Step-by-step explanation:

Step-by-step explanation:

you can convert both inequalities to slope intercept form and then graph it.

So 4x+y>-1 would convert to y>-4x-1

And x+y ≥ 2 would be y≥-x+2

Then graph it

Working with the first one

4x+y > -1

Treat as an equation and find the x and y intercept

4x+y= -1

when x=0

4(0)+y = -1

y= -1

(0,-1)

when y=0

4x+0=-1

4x= -1

divide both sides by 4

x= -1/4 or -0.25

(-0.25, 0)

working with the second one

x+y≥2

same process

when x=0

0+y=2

y=2

(0,2)

when y=0

x+0=2

x=2

(2,0)

Now on your graph you have to plot the points (0, -1) ,( -0.25,0), (0,2) ,(2,0) using an appropriate scale

Answer:

About 14.29 minutes

Step-by-step explanation:

Each page has 125 words

There are 4 pages

SO, total number of words:

125 * 4 = 500 words

The rate of typing is 35 wpm (words per minute)

So, to find time it will take to type 500 words is found by dividing the number of words (500) by the rate (35), so we have:

500/35 = 14.2857 minutes

So, it will take about 14.29 minutes to type up the whole documentary

Step-by-step explanation:

[tex]\begin{array}{c|cc}12&2\\6&2\\3&3\\1\end{array}\qquad\qquad\begin{array}{c|cc}56&2\\28&2\\14&2\\7&7\\1\end{array}\\\\12=\boxed{2}\cdot\boxed{2}\cdot3\\\\56=\boxed{2}\cdot\boxed{2}\cdot2\cdot7\\\\GCF(12,\ 56)=\boxed{2}\cdot\boxed{2}=4\\\\LCM(12,\ 56)=\boxed{2}\cdot\boxed{2}\cdot3\cdot2\cdot7=168[/tex]

Answer:

The length of the rectangular field is (3 a - 3) meters

Step-by-step explanation:

Given as :

The Perimeter of rectangular field = p = ( 10 a - 6 ) meters

The width of the rectangular field = w = 2 a meters

Let The length of the rectangular field = L meters

Now From The perimeter formula

Perimeter of rectangular field = 2 × Length + 2 × width

Or, p =  2 × L +  2 × w

Or,  ( 10 a - 6 ) meters =  2 × L meters + 2 × 2 a meters

Or, 10 a - 6 =  2 × L + 4 a

Or, 10 a - 4 a - 6 = 2 L

Or, 6 a - 6 = 2 L

∴  L = [tex]\dfrac{6 a - 6}{2}[/tex]

i,e L = 3 a - 3

So, The length of the rectangular field = L = (3 a - 3) meters

Hence,The length of the rectangular field is (3 a - 3) meters  Answer

Answer: number 2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

91.6

Step-by-step explanation:

7786/85

Answer:

The equation to represent total number of pencils p that Rafael bought is 15 n .  

Step-by-step explanation:

Given as :

The total numbers of pencils packs bought by Rafael = n

The number of pencils in each pack = 15 pencils

Let The total number of pencil does Rafael bought = p

Now, According to question

The total number of pencil does Rafael bought =  total numbers of pencils packs bought by Rafael × number of pencils in each pack

i.e p = n × 15

So, The  total number of pencil does Rafael bought = p = 15 n

Hence, The equation to represent total number of pencils p that Rafael bought is 15 n .  Answer

Final answer:

The equation to represent the total number of pencils Rafael bought is p = 15 × n, where p is the total number of pencils and n is the number of packs bought.

Explanation:

To represent the total number of pencils p that Rafael bought, we create an equation that multiplies the number of packs n by the number of pencils in each pack.

Since each pack contains 15 pencils, the equation is:

p = 15 × n

Using this equation, if you know the number of packs Rafael bought, you can calculate the total number of pencils by substituting n with the number of packs.

Answer:

OPTION B: {5, 7, 9}

Step-by-step explanation:

D [tex]$ \cap $[/tex] E is the collection of elements that are present in both D and E.

Given the set D = {5, 6, 7, 8, 9, 10}

and                 E = {1, 3, 5, 7, 9, 11}

So, the elements present in both D and E are: {5, 7, 9}.

Hence, D [tex]$ \cap $[/tex] E = {5, 7, 9}.

OPTION B is the answer.

The statement which describes the meaning of the slope is " The boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet " ⇒ D

Step-by-step explanation:

The boiling point of water (measured in degrees), at altitude (measured in feet), is modeled by the function T(a) = −0.0018 a + 212, where

The form of the linear function is f(x) = mx + b, where m is slope (the rate of change), and b is the y-intercept (the value of f(x) at x = 0)

By comparing between the form of the function and the given function

∴ m = -0.0018 ⇒ degrees per foot

∵ The sign of the slope is negative

∵ The slope = Δf(x)/Δx

- That means T(a) is decreasing function

∴ The boiling point is decreases when the altitude increasing

∵ -0.0018 = [tex]-\frac{18}{10,000}[/tex] degrees per feet

∴ The boiling point decreases by 18 degrees as the altitude

    increases by 10,000 feet or the boiling point decreases by 1.8

     degrees as the altitude increases by 1,000 feet

The statement which describes the meaning of the slope is " The boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet "

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The meaning of slope is best described by the boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet. The option (D) is correct.

To understand the meaning of the slope in the given function[tex]\( T(a) = -0.0018a + 212 \)[/tex], where [tex]\( T \)[/tex] represents the boiling point of water in degrees and [tex]\( a \)[/tex] represents the altitude in feet, we need to analyze the slope of the function.

The slope of the function is given by the coefficient of [tex]\( a \)[/tex], which is [tex]\( -0.0018 \)[/tex]. This slope tells us how the boiling point of water changes with altitude. To interpret the slope in terms of degrees per foot:

A slope of [tex]\( -0.0018 \)[/tex] means that for every 1 foot increase in altitude, the boiling point decreases by 0.0018 degrees.

To find out how much the boiling point changes over an increase of 1,000 feet in altitude, we multiply the slope by 1,000:

[tex]\( \text{Change in boiling point} = \text{slope} \times \text{change in altitude} \)[/tex]

[tex]\( \text{Change in boiling point} = -0.0018 \times 1000 \)[/tex]

[tex]\( \text{Change in boiling point} = -1.8 \)[/tex]

Therefore, the correct interpretation of the slope is that the boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet, which corresponds to option D.

The complete question is:

The boiling point of water, T (measured in degrees), at altitude a (measured in feet) is modeled by the function T(a)=-0.0018a+212. In terms of altitude and temperature, which statement describes the meaning of the slope?

A. The boiling point increases by 18 degrees as the altitude increases by 1,000 feet.

B. The boiling point increases by 1.8 degrees as the altitude increases by 1,000 feet.

C. The boiling point decreases by 18 degrees as the altitude increases by 1,000 feet.

D. The boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet.

Answer:

[tex]3-\frac{1}{2}n[/tex]

Step-by-step explanation:

We will use the distributive property shown below to break it down first.

Distributive Property:  [tex]a(b-c)=ab-ac[/tex]

The expression is:

[tex]\frac{1}{2}(n-8)+7-n[/tex]

Let's distribute:

[tex]\frac{1}{2}(n-8)+7-n\\=\frac{1}{2}(n)-\frac{1}{2}(8)+7-n[/tex]

Now, we multiply:

[tex]\frac{1}{2}(n)-\frac{1}{2}(8)+7-n\\=\frac{1}{2}n-4+7-n[/tex]

Now we combine like terms (variables and numbers separately):

[tex]\frac{1}{2}n-4+7-n\\=-4+7-n+\frac{1}{2}n\\=3-\frac{1}{2}n[/tex]

This is the simplified expression.

Answer: The total price of a bench is 1.008x.

Step-by-step explanation:

Since we have given that

Let the cost price be 'x'.

Mark up % = 120%

So, Mark up value would be

[tex]\dfrac{120}{100}x\\\\=1.20x[/tex]

Discount % = 20%

Amount of discount is given by

[tex]\dfrac{20}{100}\times 1.2x\\\\=0.2\times 1.2x\\\\=0.24x[/tex]

So, it becomes,

Amount after discount is given by

[tex]1.2x-0.24x\\\\=0.96x[/tex]

Sales tax = 5%

Amount of sales tax would be

[tex]\dfrac{100+5}{100}\times 0.96x\\\\=\dfrac{105}{100}\times 0.96x\\\\=1.05\times 0.96x\\\\=1.008x[/tex]

Hence, the total price of a bench is 1.008x.

Answer:X=5/3

Step-by-step explanation:

(2∧(3*x-4))2=(-2)²

2∧2*(3*x-4)=2²

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

2*(3*x-4)=2

3*x-4=1

3*x=5

x=5/3

Answer:

After evaluating the expression, the result is 2/3

Step-by-step explanation:

Let's evaluate the expression given to us:

-2 + 12 - 2³/ 2⁰ * 3

-2 + 12 - 8/ 1 * 3 ⇒ 2⁰ = 1 and 2³ = 8

-10 + 12/ 3

2/3

After evaluating the expression, the result is 2/3

The other parallel side is 44 m

Step-by-step explanation:

Let us revise the formula of the area of a trapezium

[tex]A=\frac{1}{2}(b_{1}+b_{2})h[/tex] , where

∵ The area of a trapezium is shaped field is 480 m²

∴ A = 480 m²

∵ The distance between two parallel sides is 15 m

∴ h = 15 m

∵ One of the parallel side is 20 m

∴ [tex]b_{1}[/tex] = 20 m

We need to find [tex]b_{2}[/tex]

Substitute all these value in the rule of the area below

∵ [tex]A=\frac{1}{2}(b_{1}+b_{2})h[/tex]

∴ [tex]480=\frac{1}{2}(20+b_{2})(15)[/tex]

- Multiply the two sides by 2

∴ [tex]960=(20+b_{2})(15)[/tex]

- Divide both sides by 15

∴ [tex]64=20+b_{2}[/tex]

- Subtract 20 from both sides

∴ [tex]44=b_{2}[/tex]

The other parallel side is 44 m

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Answer:

The triangles are congruent by Angle Side Angle congruency statement and the reason is below.

Step-by-step explanation:

Given:

∠ VUW ≅ ∠ XYW

VW ≅ YW

To Prove:

Δ VUW ≅ Δ XYW

Proof:

In Δ VUW and Δ XYW

∠ VUW ≅ ∠ XYW      ……….{Given}

VW ≅ YW                 ............{Given}

∠ VWU ≅ ∠ XWY    …………..{Vertically Opposite Angles are equal}

Δ VUW ≅ Δ XYW   .….{ By Angle-Side-Angle congruence test}

......Proved

Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line ⇒ 1st

Step-by-step explanation:

Parallel lines have:

The formula of the slope of a line which passes through points [tex](x_{1},y_{1})[/tex] and [tex](x_{1},y_{1})[/tex] is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

∵ The given line passes through points (-12 , -2) and (0 , -4)

∴ [tex]x_{1}[/tex] = -12 , [tex]x_{2}[/tex] = 0

∴ [tex]y_{1}[/tex] = -2 , [tex]y_{2}[/tex] = -4

- Use the formula of the slope above to find the slope of the given line

∵ [tex]m=\frac{-4-(-2)}{0-(-12)}=\frac{-4+2}{12}=\frac{-2}{12}=\frac{-1}{6}[/tex]

∴ The slope of the given line is [tex]\frac{-1}{6}[/tex]

∵ The two lines are parallel

∴ Their slopes are equal

∴ The slope of the parallel line = [tex]\frac{-1}{6}[/tex]

∵ The parallel line passes through point (0 , 6)

- The form of the linear equation is y = mx + b, where m is the slope

  and b is the y-intercept (y when x = 0)

∵ m = [tex]\frac{-1}{6}[/tex] and b = 6

∴ The equation of the parallel line is y = [tex]\frac{-1}{6}[/tex] x + 6

Let us check which point is on the line by substitute the x in the equation by the x-coordinate of each point to find y, if y is equal the y-coordinate of the point, then the point is on the line

Point (-12 , 8)

∵ x = -12 and y = 8

∵ y = [tex]\frac{-1}{6}[/tex] (-12) + 6

∴ y = 2 + 6 = 8

- The value of y is equal the y-coordinate of the point

∴ Point (-12 , 8) is on the line

Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line

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The point on the line that passes through (0, 6) and is parallel to the given line is (2, 8).

To find a point on a line parallel to the given line, we can use the slope of the given line, which is equal to the slope of the parallel line.

The slope of the given line can be calculated using the coordinates (-12, -2) and (0, -4):

Slope (m) = (change in y) / (change in x) = (-4 - (-2)) / (0 - (-12)) = (-2) / (12) = -1/6.

Now that we know the slope of the parallel line is -1/6, we can use the point-slope form of a linear equation to find the equation of the parallel line:

y - y1 = m(x - x1),

where (x1, y1) is the point (0, 6) and m is the slope (-1/6). Plugging in these values:

y - 6 = (-1/6)(x - 0),

y - 6 = (-1/6)x,

y = (-1/6)x + 6.

Now, we can choose any x-value to find the corresponding y-value. If we plug in x = 2 into the equation, we get:

y = (-1/6)(2) + 6 = -1/3 + 6 = 8.

So, the point (2, 8) is on the line that passes through (0, 6) and is parallel to the given line.

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Answer:

Find the complete table in attached file.

Step-by-step explanation:

Find the Incomplete table in attached file

Given:

A car travels 55 miles per hour for 2 hours.

So the speed of the car 55 miles per hour is constant for 2 hours.

Using speed  formula.

[tex]Speed=\frac{distance}{time}[/tex]

Second row.

From the second row of the table [tex]time = \frac{1}{2}=0.5\ sec[/tex] and speed is constant [tex]speed = 55\ mi/hr[/tex], so we need to find only distance.

[tex]Speed=\frac{distance}{time}[/tex]

[tex]55=\frac{distance}{0.5}[/tex]

[tex]distance = 55\times 0.5[/tex]

[tex]distance = 27.5\ mi[/tex]

Third row.

From the third row of the table [tex]time =1\frac{1}{2}=\frac{3}{2} = 1.5\ sec[/tex] and speed is constant [tex]speed = 55\ mi/hr[/tex], so we need to find only distance.

[tex]Speed=\frac{distance}{time}[/tex]

[tex]55=\frac{distance}{1.5}[/tex]

[tex]distance = 55\times 1.5[/tex]

[tex]distance = 82.5\ mi[/tex]

Fourth row.

From the fourth row of the table [tex]distance =110\ miles[/tex] and speed is constant [tex]speed = 55\ mi/hr[/tex], so we need to find time.

[tex]Speed=\frac{distance}{time}[/tex]

[tex]time=\frac{distance}{speed}[/tex]

[tex]time=\frac{110}{55}[/tex]

[tex]time = 2\ sec[/tex]

Therefore we complete the table from the above calculation.

Answer:

An acute triangle, because [tex]22^2 + 51^2 >54^2[/tex]

Step-by-step explanation:

Given:

The distance between city A and city B is 22 miles.

The  distance between city B and city C is 54 miles.

The distance  between city A and city C is 51 miles.

thus we have a triangle ABC with side lengths :

AB = 22 miles (shortest side)

BC= 54 miles  (longest side)

AC = 51 miles (shorter side)

For an obtuse triangle :

[tex](Shorter\ side)^2+(Shortest\ side)^2<(Longest\ side)^2[/tex]

For acute triangle :

[tex](Shorter\ side)^2+(Shortest\ side)^2>(Longest\ side)^2[/tex]

Comparing sum of squares of shorter sides with the square of longest side:

[tex]AB^2+AC^2=22^2+51^2=484+2601=3085[/tex]

[tex]BC^2=54^2=2916[/tex]

We see that:

[tex]22^2+51^2>54^2[/tex]

Thus, the condition [tex](Shorter\ side)^2+(Shortest\ side)^2>(Longest\ side)^2[/tex]  fulfills proving this triangle to be an acute triangle.

Answer:

The answer is B on Edge 2020 Thank me Later!

Step-by-step explanation:

I did the Exam

Answer:

Step-by-step explanation:

a>−64/3

Hope this helps mark me as brainiest pls

The solution of the a is greater than negative 21 and one-third. Then the correct option is A.

Inequality is simply a type of equation that does not have an equal sign in it. Inequality is defined as a statement about the relative size as well as is used to compare two statements.

The inequality equation is given below.

[tex]\dfrac{3}{4} \times a > -16\\[/tex]

On solving the inequality, the value of the a will be

[tex]\rm a > -16 \times \dfrac{4}{3}\\\\a > - \dfrac{64}{3}\\\\a > - 21 \dfrac{1}{3}[/tex]

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Answer: z = 3

Step-by-step explanation: To solve this equation for z, we can first combine our like terms on the left side of the equation. Since 12 and 7 both have z after their coefficient, we can subtract 12z - 7z to get 5z.

Now we have 5z - 2 = 13.

To solve from here, we add 2 to the left side of the equation in order to isolate 5z. If we add 2 to the left side, we must also add 2 to the right side. On the left side, the -2 and +2 cancel out. On the right, 13 + 2 simplifies to 15.

Now we have 5z = 15.

Solving from here, we divide both sides of the equation by 5 to get z alone. On the left side, the 5's cancel out and we are simply left with z. On the right side, 15 divided by 5 simplifies to 3 so we have z = 3.

Answer:

-41/36

Step-by-step explanation:

-5/9 + -7/12

x4        x3

-20/36 + -21/36

Negative + Negative = Negative

-41/36

Simplfy - > Can't, it's in the simpliest form.

Answer:

(-4,2)

Step-by-step explanation:

Answer:

(-4,2)

Step-by-step explanation:

Answer:

30 or 52

I'm not sure. Sorry. I tried my best. Don't let the "Helping Hand" fool you. You see you said 6 forks and twice as many spoons which equals 12+6. Then "as" knives. I got confused there. I think there it's either 12 or twice as many knives as spoons. In other words, 12×2.

6 + (6 × 2) + (6 × 2) = 30

6 + (6 ×2) + (12 × 2) = 52

Answer:

[tex]h=\frac{SA}{2\pi r}-r[/tex]

Step-by-step explanation:

The surface area of a cylinder is equal to

[tex]SA=2\pi r^{2} +2\pi rh[/tex]

Solve for h

That means ----> isolate the variable h

subtract  2πr² both sides

[tex](SA-2\pi r^{2})=2\pi rh[/tex]

Divide by 2πr both sides

[tex]\frac{SA-2\pi r^{2}}{2\pi r}=h[/tex]

Rewrite

[tex]h=\frac{SA-2\pi r^{2}}{2\pi r}[/tex]

Simplify

[tex]h=\frac{SA}{2\pi r}-r[/tex]

Of the possible numbers (1,2,3,4,5,6), 3 are greater than 3. The probability to roll a number greater than 3 is 3 over the 6 total. That can be simplified to 1/2 for the probability. If she rolls the dice 90 times 90 x 1/2 or 45 rolls will receive a number greater than 3.

answer: 45

Answer:

B

Step-by-step explanation:

85+156+34+127=402

10+18+2+14=44

44/402=10.95%

Answer is B. 10.95%

Answer:

-8 i think

Step-by-step explanation:

The y-intercept of the graph for the function y = (x - 2)(x + 4) is found by setting x to zero, which results in a y-intercept of -8.

The y-intercept on a graph represents the point where the curve or line crosses the y-axis.

To find the y-intercept of the graph of y = (x - 2)(x + 4), you need to determine the value of y when x is zero. By substituting x with 0 in the equation,

we calculate the y-intercept:

Therefore, the y-intercept of the graph is -8.