Find the value of m∠ACD. A. 30º B. 15º C. 60º D. 90º

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Explanation:

A graph is a nice addition (and it will likely help us see the vertex directly), but it isn't necessary because we can use the equation given to us. Though I recommend using a graphing calculator to confirm the answer.

The original function is the same as y = 1x^2+8x + (-2). We see that it is in the form y = ax^2+bx+c where

a = 1

b = 8

c = -2

Use the values of 'a' and b to get the value of h, which is the x coordinate of the vertex.

h = -b/(2a)

h = -8/(2*1)

h = -4

The x coordinate of the vertex is x = -4. Plug this into the original equation to get

f(x) = x^2+8x-2

f(-4) = (-4)^2 + 8(-4) - 2

f(-4) = -18

Plugging x = -4 into f(x) leads to y = -18. The point (-4, -18) is on the parabola. Furthermore, this is the vertex (h,k)

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

Alternatively, you can complete the square as shown below

y = x^2 + 8x - 2

y = (x^2 + 8x) - 2

y = (x^2 + 8x + 0) - 2

y = (x^2 + 8x + 16 - 16) - 2

y = (x^2 + 8x + 16) - 16 - 2

y = (x+4)^2 - 18

y = 1(x+4)^2 - 18

y = 1(x-(-4))^2 - 18

The last equation is in the form y = a(x-h)^2 + k with (h,k) = (-4,-18) being the vertex. The 16 is the result of taking half of 8 and squaring that result. We have 16-16 = 0 to make sure that we don't change the equation and keep things balanced. This is the same as adding 16 to both sides. All of this is done so we can end up with the (x+4)^2 perfect square portion.You can expand out (x+4)^2 - 18 and you should get x^2+8x-2 again.

Answer:

Step-by-step explanation: I hope it helps :)

[tex]-1.5(4-r)=-12\\\\\mathrm{Multiply\:both\:sides\:by\:}10\\\\-1.5\left(4-r\right)\cdot \:10=-12\cdot \:10\\\\= -15\left(4-r\right)=-120\\\\\mathrm{Divide\:both\:sides\:by\:}-15\\\\\frac{-15\left(4-r\right)}{-15}=\frac{-120}{-15}\\\\4-r=8\\\\\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}\\\\4-r-4=8-4\\\\-r=4\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\\\frac{-r}{-1}=\frac{4}{-1}\\\\r=-4[/tex]

Answer:

r = -4

Step-by-step explanation:

-1.5(4-r)=-12

Divide each side by -1.5

-1.5/-1.5(4-r)=-12/-1.5

(4-r)=8

Subtract 4 from each side

4-r-4 = 8-4

-r = 4

Divide each side by -1

r = -4

Answer:

A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at negative 0.5 and is pointing to the left.

Step-by-step explanation:

Required

[tex]2x - 6 \geq 6(x - 2) + 8[/tex]

Required

Determine the number line

[tex]2x - 6 \geq 6(x - 2) + 8[/tex]

Open the bracket

[tex]2x - 6 \geq 6*x - 6*2 + 8[/tex]

[tex]2x - 6 \geq 6x - 12 + 8[/tex]

[tex]2x - 6 \geq 6x - 4[/tex]

Collect Like Terms

[tex]2x - 6x \geq 6 - 4[/tex]

[tex]- 4x \geq 2[/tex]

Divide both sides by -4

[tex]\frac{- 4x}{-4} \geq \frac{2}{-4}[/tex]

[tex]x \leq -0.5[/tex]

From the list of given options, the correct answer is option C

Answer:

b

Step-by-step explanation:

Answer:

3/4 of the whole day(24 hours)

Step-by-step explanation:

1/3 of 24 hours equal to 8 hours. He slept for 8 hours. So his waking time equals 24-8=16

5/8 of his waking time (16 hours ) equal to 10 hours.

now total time spent in his house 10 + 8 = 18

in fraction 18/24 = 3/4

He slept 1/3 of the day, and is awake 2/3 of the day (note that 1/3 + 2/3 = 3/3 = 1)

2/3 of 5/8 = (2/3)*(5/8) = (2*5)/(3*8) = 10/24 = 5/12 of the day is spent at home when he is awake

Add 1/3 and 5/12 to get

1/3 + 5/12 = 4/12 + 5/12 = (4+5)/12 = 9/12 = 3/4

He spent 3/4 of a whole day at home (equivalent to 18 hours)

Answer:

No 1 would be 500 + 2400*30/100 = 500 + 720 = 1220

No 2 would be 500 + x*30/100

Step-by-step explanation:

Answer:

$1200 and 500+ .3x

Step-by-step explanation:

Use this equation: 500+ .3x and insert in 1200.

Made equation by taking garented amount, $500, and have that be added.  Sense you get 30 percent of of x (the amount of sales), have x be multiplied by .3 to get 30 percent.

Answer:

C. Two lines are perpendicular if they have opposite slopes

Step-by-step explanation:

Hey there!

Well 2 lines that are perpendicylar have reciprocal slopes for example,

2 and 1/2 are 2 slopes that are perpendicular.

Hope this helps :)

Answer:

VW=35

YZ=50

Step-by-step explanation:

As they are similar triangles with a ratio of 1:2 and we know VW:XZ=1:2, we can make the equation:

2(4y+7)=12y-14

8y+14=12y-14

4y=28

y=7

So, VW=4(7)+7=35.

Similarly, you can find YZ through VT:

2(7x-17)=8x+2

14x-34=8x+2

6x=36

x=6

Therefore, YZ=8(6)+2=50.

Answer:

18.0

Step-by-step explanation:

Note the tenth place value (underlined and bolded): 18.049

Look at the number to the direct right of the tenth place value (or the hundredth place value in this case). It is a 4.

Note the rules of rounding. If the number:

1) is 5 or greater, round up.

2) is 4 or less, round down.

In this case, it is 4, so you will round down.

18.049 rounded to the nearest tenth is 18.0

~

Answer:

18.0

Step-by-step explanation:

first time i put 18 and it was wrong so

Answer:

3/4

Step-by-step explanation:

We would like to find what 0.75 is as a fraction.

Remember that since there are two digits past the decimal point, the denominator will 100.

So, the numerator is 75 and the denominator is 100. We now have:

75/100

We would like to simplify this. Notice that the top and bottom (75 and 100) are both divisible by 25. So divide both by 25:

75 / 25 = 3

100 / 25 = 4

The answer is thus 3/4.

~ an aesthetics lover

Answer:

[tex]\Large \boxed{b=2}[/tex]

Step-by-step explanation:

-5+2(10b-2)=31

Expand brackets.

-5+20b-4=31

-9+20b=31

Add 9 on both sides.

20b=40

Divide both sides by 20

b=2

Answer:

Step-by-step explanation:

-5+2(10b-2)=31

Multiply the terms in the bracket

That's

- 5 + 20b - 4 = 31

Group like terms

Send the constants to the right side of the equation

That's

20b = 31 + 4 + 5

Simplify

20b = 40

Divide both sides by 20

We have the final answer as

Hope this helps you

Answer:

A ≈ 312.1

Step-by-step explanation:

[tex]A = \pi r(r+\sqrt{h^2 + r^2})[/tex]

r = 5

h = 14

[tex]A = \pi 5(5+\sqrt{14^2+5^2})[/tex]

A = 312.055478161

Answer:

just did this on a test and it was

The exponent 3 is an odd number.

Step-by-step explanation:

Hince the statements which justify it:

The base -2 is a negative number.

The exponent 3 is an odd number.

Julie gets a negative number for her final answer when solving the expression (-2)³ = -2 x -2 x -2

Because the base, -2, is a negative number.

When an odd number of negative numbers are multiplied together, the result is always negative.

In this case, there are three negative numbers (-2 x -2 x -2),

Which is an odd number, resulting in a negative answer.

However, since the base is negative, the result will always be negative for any odd exponent.

Therefore, the negativity of the base and the odd value of the exponent together lead to a negative final answer.

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Answer:

d

Step-by-step explanation:

Answer:

  Your table is filled in below.

Step-by-step explanation:

The scale factor is the ratio of image size to original size. In part (d), the image height is "blocks" while the original height is "feet". So, the units of the scale factor are "blocks/ft".

Sometimes a scale factor has units, like this, and sometimes it is expressed as a pure number. A map scale factor might be the pure number ratio 1 : 62500, or it could also be expressed with units as 1 in : 1 mile.*

__

* actually, these are slightly different scales. 1:62500 is about 0.98643 inches per mile.

Answer: Image

Step-by-step explanation:

took the test

Answer:

Area: [tex]50\pi -100[/tex]

Perimeter: 20[tex]\pi[/tex]

Step-by-step explanation:

If we take half of one of these "pedals" we can see that it is simply 1/4 of a circle with radius 5, subtracted by a triangle. Let's calculate this half-pedal.

[tex]1/4(25 \pi) - 1/2(5* 5)[/tex]

That means 4 pedals is equal to:

[tex]8(1/4(25\pi) - 1/2 (25))[/tex]

[tex]50\pi - 100[/tex]

So.. The area of the shaded region is [tex]50\pi -100[/tex]

Perimeter is even simpler. the half-pedal is just 1/4 of the circumference of the circle. The circumference is just [tex]10\pi[/tex], which means our half pedal is:

[tex]1/4(10\pi )[/tex]

Multiplying by 8, our perimeter is just 20[tex]\pi[/tex].

Answer:

23 years old

Step-by-step explanation:

Savannah's age = x

Selena's age = y

Right now, x = 2y + 1

In 13 years, x = 1.5y

Here, we must use simultaneous equations to work it out.

x = 2y + 1

x + 13 = 1.5 x (y + 13)   --> x + 13 = 1.5y + 1.5 x 13   --> x + 13 = 1.5y + 19.5

x + 13 = 1.5y + 19.5

- 13

x = 1.5y + 6.5

x = 1.5y + 6.5 = 2y + 1

1.5y + 6.5 = 2y + 1

- 1

1.5y + 5.5 = 2y

- 1.5y

5.5 = 0.5y

x 2

11 = y

We know that y = 11

Savannah is currently twice her cat's age plus 1, so...

11 x 2 + 1 = 22 + 1 = 23 years old

Hope this helps!

P.S. If the cat lives 13 more years after this, it will be a very old cat lol :)

Answer:

  504 in³

Step-by-step explanation:

The volume of the overall outside dimensions is their product:

  Voverall = (12 in)(8 in)(6 in) = 576 in³

The volume of the "slot" is the product of its dimensions:

  Vslot = (6 in)(6 in)(2 in) = 72 in³

Then the volume of the figure shown is ...

  Vfigure = Voverall -Vslot = 576 in³ -72 in³ = 504 in³

Answer:

504 inches cubed

Step-by-step explanation:

The area missing is 6*6*2=72

The whole area is 576

subtract the two and get 504

since we are talk about volume it is 50 inches cubed

Answer:

0.25 or 1/4

Step-by-step explanation:

1/3 * 75/100 = 75/300 = 1/4 = 0.25

[tex]75\%\cdot\dfrac{1}{3}=\dfrac{3}{4}\cdot\dfrac{1}{3}=\dfrac{1}{4}[/tex]

Answer:

No solution.

Step-by-step explanation:

Distribute.

-3(2x + 1) = 2(-3x - 1)

-6x - 3 = -6x - 2

Combine like terms.

-6x - 3 = -6x - 2 add 3 to both sides

-6x = -6x + 1 add 6x to both sides

0 = 1 this is false.

Because we ended up with a false equation, there is no solution to this equation.

Answer:

no solution

Step-by-step explanation:

Perform the indicated multiplication, using the distributive property.

-3(2x+1)=2(-3x-1)  becomes -6x - 3 = -6x - 2

This has no solution because -3 is never equal to -2.

Answer:

Isn’t it just 8/26

Step-by-step explanation:

Since 1 is 1/26 so 8 is just 8/26?

The part of a year is 8 fortnights is ( 8 / 26 ).

Multiplication is the process of determining the product of two or more numbers in mathematics.

It is given that a fortnight is 1/26 of a year. The part of the year for 8 fortnights is calculated as:-

⇒ 8 x ( 1 / 26 )

⇒( 8 / 26 )

Therefore, the part of a year is 8 fortnights is ( 8 / 26 ).

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Answer:

642/125

Step-by-step explanation:

and the other person got it

Answer:

(B) 99.229%

Step-by-step explanation:

If the probability of someone dying next year is [tex]\frac{771}{100000}[/tex], that means the probability of someone NOT dying next year is [tex]\frac{100000-771}{100000} = \frac{99229}{100000}[/tex].

To find the percent value of this fraction, we divide 99229 by 100000 and multiply by 100.

[tex]\frac{99229}{100000} = 0.99229\cdot100=99.229[/tex]

So, the answer is B, 99.229%.

Hope this helped!

A-

1 box --- 6 minutes

y boxes --- 1 minute

y = 1/6

B-

1 box --- 9 minutes

t boxes --- 1 minute

t = 1/9

So...

r - used time

r(1/9 + 1/6)=100

r=(100.18)/5

r= 360 minutes

1/6 . 360 = 60 boxes

answer: 60 boxes

In total, machine A filled 66 boxes, and machine B filled 66 boxes, resulting in a total of 100 boxes filled.

Let's use the concept of the rate of work to solve this problem. The rate of work is the amount of work done per unit of time.

Machine A's rate of work is 1 box of nails every 6 minutes.

Machine B's rate of work is 1 box of nails every 9 minutes.

Let's assume that machine A filled x boxes, and machine B filled y boxes. Since they worked for the same amount of time, the total number of boxes filled by both machines is 100.

So, the equation representing the total work is:

x (boxes filled by A) + y (boxes filled by B) = 100

Now, let's use their rates of work to form two more equations:

Rate of work of A = 1 box every 6 minutes

Rate of work of B = 1 box every 9 minutes

Since work = rate × time, we can write two equations:

x (boxes filled by A) = (1/6) * t (time in minutes)

y (boxes filled by B) = (1/9) * t (time in minutes)

Since they both worked for the same time, we can set the time for both machines as equal:

t = t

Now, we have a system of equations:

x + y = 100

x/6 = y/9

t = t

Let's solve the system of equations. We can start by substituting the value of y from the second equation into the first equation:

x + (x/6)*3 = 100

x + (x/2) = 100

Multiply both sides by 2 to eliminate the fraction:

2x + x = 200

3x = 200

x = 200/3

Now, let's find the value of y using the second equation:

y = (x/6)*3

y = (200/3)/6 * 3

y = 200/3

So, machine A filled 200/3 boxes of nails, which is approximately 66.67 boxes.

Machine B filled 200/3 boxes of nails, which is also approximately 66.67 boxes.

Since they cannot fill a fraction of a box, we can distribute the remaining 2/3 box between machine A and machine B, giving one extra box to each.

In total, machine A filled 66 boxes, and machine B filled 66 boxes, resulting in a total of 100 boxes filled.

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Answer:

3.2 ft

Step-by-step explanation:

the only thing you need to know is that congruent means that all the side and the same and the shape can be flipped and still look the same so the measure of the line segment is 3.2ft

Answer:

3.2 ft

Step-by-step explanation:

The answer above is correct.

Hey there!

5/8 + 14 = ?

We can say 14 is equal to 14/1 beause it doesn't have a denominator and we will need to solve for your equation

14 * 8 = 112 (upcoming numerator for now)

8 * 1 = 8 (upcoming denominator for now)

5 stays alone

New equation 5 + 112 / 8

5 + 112 = 117 (numerator)

8 = 8 (demominator)

Answer: 117/8 (if you're looking for the improper fraction version) ; 14 5/8 (if you're looking for the mixed number version) ; 14.625 (if you're looking for the decimal version of it)

⬆ ANY one of these choices SHOULD work

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

Answer: I dont know if this is right but the is 8 Ive never done this before.

Step-by-step explanation:

1 =

4 =

1 =

4 =

r− 5 ⋅ 2 = 1 = r = 11

8 = r = 11

Answer:

x = -4

Step-by-step explanation:

16 + x = 12

16 - 16 + x = 12 - 16

x = -4

The table is a partial representation as we only see three data points. This is a limited view. Because of this, the answer is between C and D. However, we can rule out choice C as the equation will give us the complete view of what's going on. We can plug in any x value we want to find the corresponding y value (keep in mind that x and y can't be negative though). So that means the graph is a partial representation. This is true if the line segment doesn't extend forever upward. If we had a line segment through the endpoints (0,4) and (3,7), and it stopped at (3,7), then this is a limited view. It does not show what the bill would be if x were say x = 5.

Half of the number 65 is [tex]32\frac{1}{2}[/tex].

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given fraction is [tex]32\frac{1}{2}[/tex].

Let x be unknown number.

Then, the equation is

1/2 of x=[tex]32\frac{1}{2}[/tex]

x/2 =32.5

x=65

Therefore, half of the number 65 is [tex]32\frac{1}{2}[/tex].

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