A ball is thrown through the air, following a parabola: y= -x^2 + 4x + 4.

The land slopes upward: y = 0.5x + 2

1. Using the graph what is a solution to the system of equations?

( , )

2. What does the solution represent in this scenario?


a The point the ball reaches maximum height.

b The point where the ball meets the ground.

c The point where the ball is thrown.

Answer:

C. y = -9x - 8

Step-by-step explanation:

Setting up the equation:

eight LESS (so minus sign before the 8) THAN (so 8 is being subtracted from the -9x) negative (-) nine TIMES (multiplication) a number, (variable) x.

We want to get the variable y alone, so this can be written as y = -9x - 8

The additive inverse of the complex number -12 + 4i is 12 - 4i

The complex number is given as:

-12 + 4i

The additive inverse of a complex number a + bi is -a - bi

This means that the additive inverse of -12 + 4i is 12 - 4i

Hence, the additive inverse of the complex number -12 + 4i is 12 - 4i

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Answer:

It's C

Step-by-step explanation:

Answer:

0.0308.

Step-by-step explanation:

There are 11 months out of the year which have a 29th day except for a leap year when all 12 have it.

Required probability = number of '29th' days in 4 years / total days in 4 years

= (3*11 + 12) / (3*365 + 366)

=  45/1461

= 0.0308.

Answer:

The answer choices are garbled.

Step-by-step explanation:

(18 pints)/(8 bottles) = (9/4) pint/bottle

2 and 1/4 pints per bottle

If Circle K has a radius of 8 inches. The figure that is closest to the length of FA is: 14.8.

MAC=1/2×360°=180°

mΔAFC=1/2×180°=90°

Circumference angle theorem

AK=8

AC=2

AK=16

Pythagorean theorem

FA²+FC²=AC²

Substitution

FA²+6²=16²

FA²+36=256

FA²=√220

FA=14.8

Therefore the figure that is closest to the length of FA is: 14.8.

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The number of balloons on each package will be 15

From the information, Jason is a party planner. In 124 packages, he has a total of 1,860 balloons and each package has the same number.

Therefore, the number of balloons on each package will be:

= 1860 / 124

= 15

When a plane has to travel 2,800 miles at an average speed of 560 miles per hour. The number of hours used will be:

= 2800/560

= 5

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Reason:

The mode is the number that shows up the most.

In this case, it would be 59 because it shows up twice, which is the most compared to any other number (which only show up once).

Answer:

segment AD is right one.

Answer:

Segment AD

Step-by-step explanation:

The only edge which lies on both planes and is shared by both is, Plane OAD and Plane BCD, is AD

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's evaluate ~

[tex]\qquad \sf  \dashrightarrow \: 5(z + 4) + 5(2 - z)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (5 \cdot z) + (5\cdot4) + (5\cdot2) - (5\cdot z)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 5z + 20 + 10 - 5z[/tex]

[tex]\qquad \sf  \dashrightarrow \: 5z - 5z+ 20 + 10[/tex]

[tex]\qquad \sf  \dashrightarrow \: 30[/tex]

So, the equivalent expression is 30

Answer:

30

Step-by-step explanation:

Let us divide the whole expression by 5. Then we must multiply the whole expression by 5 to obtain the same value as before.

Thus, we get the following expression:

[tex]\implies\huge\text{[}\dfrac{5(z+4)+5(2-z)}{5}\huge\text{]} \times 5[/tex]

[tex]\implies\huge\text{[}\dfrac{(z+4)+(2-z)}{1}\huge\text{]} \times 5[/tex]

Now, open the inner-most parentheses as the expression inside the inner-most parentheses, cannot be simplified further.

[tex]\implies\huge\text{[}\dfrac{z+4+2-z}{1}\huge\text{]} \times 5[/tex]

It should be noted that any number being subtracted from the same number is equivalent to 0. Therefore, we get the following expression:

[tex]\implies\huge\text{[}\dfrac{4+2}{1}\huge\text{]} \times 5[/tex]

Simplify the expression inside the long brackets.

[tex]\implies\huge\text{[}\dfrac{6}{1}\huge\text{]} \times 5[/tex]

Now, we can open the long brackets and simplify the product of 6/1 and 5.

[tex]\implies\huge\text{[}\dfrac{6}{1}\huge\text{]} \times 5 = \dfrac{6 \times 5}{1} = \dfrac{30}{1} = 30[/tex]

Therefore, the simplified expression is 30.

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Answer:

True

Step-by-step explanation:

Straight angles are straight lines which equal 180 degrees

Answer:

true it is equals 180 for that angle

[tex]\text{Arc length,}\\\\s = r \theta \\\\~~=12\cdot \left(30 \times \dfrac{\pi}{180} \right)\\\\~~=12\cdot \dfrac{\pi}6\\\\~~=2\pi[/tex]

Answer:

f(3) = 2

Step-by-step explanation:

Remark

The formula starts out as

f(x)= 2x - 4        

So what is telling you is that were ever you see a variable on the right, it can from the x on the left.

If you change the variable on the left, you must also do it on the right.

f(3) = 2*3 -4

f(3) = 6-4

f(3) = 2

Answer:

  72 cm²

Step-by-step explanation:

The shaded area is 1/4 of the rectangle, so the unshaded area is 3/4 of the rectangle--3 times the area that is shaded.

__

  Unshaded area = 3 × 24 cm² = 72 cm²

The region that is not shaded has an area of 72 cm².

_____

You can mark the midpoint of MR as point S, and draw segment PS. That will divide the rectangle into 4 congruent triangles, one of which is shaded. The congruent triangles all have the same area, so the shaded area is 1/4 of the total area, and the unshaded area is 3 times the shaded area.

Answer:

This is incorrect because 1 meter is 100 centimeters. But then when you keep going and when you get to 4 meters, you would get 400.

For example:

1 meter - 100 centimeters

2 meters - 200 centimeters

3 meters - 300 centimeters

4 meters - 400 centimeters

Hope this helps!

Answer:

Jace did not make a mistake, because the answers are the same. Jace just did the problem in a unique way.

Answer:

Step-by-step explanation:

88 / 184 ≈ 0.48

96 / 184 ≈ 0.52

104 / 166 ≈ 0.63

62 / 166 ≈ 0.37

Answer: Use pemdas to solve

Friday:

(13.5 + 18.5) ÷ 2

= 16

Saturday:

18 - (2 x 4)

= 10

Sunday:

20 - (5 - 3)

= 18

Step-by-step explanation:

Phillipa rode her bicycle the most on Sunday.

Hope this helps.

Answer:

put x= 2 and y = 1

and see this inequality will holds

Answer:

36.32 m

Step-by-step explanation:

perimeter = 2(l+b) = 2(10.5 + 7.66)

=2(18.16)= 36.32 m

Answer:(x-4)^2+(y+2)^2=121

Step-by-step explanation:

eqaution of circle is this

(x-h)^2+(y-k)^2=r^2

(x-4)^2+(y--2)^2=r^2

and 2 negatives make positive

(x-4)^2+(y+2)^2=r^2
and r^2=121

(x-4)^2+(y+2)^2=121

Area of hexagon

Now

area of upper 6 triangles

Total area

Answer:

770 m²

Step-by-step explanation:

The surface area of a regular pyramid comprises the area of the base (regular polygon) and the area of each of the slanted sides (triangles).

Apothem:  The line segment from the center of the regular polygon to the midpoint of one of its sides.

Area of the base

The base of the prism is a regular polygon with 6 sides (hexagon).

[tex]\textsf{Area of a regular polygon}=\sf \dfrac{1}{2}nsa[/tex]

where:

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Base area}& =\sf \dfrac{1}{2}\cdot 6 \cdot 12 \cdot 6\sqrt{3}\\ & = \sf 216\sqrt{3}\:m^2\end{aligned}[/tex]

Area of one side

The sides of the regular pyramid are congruent triangles.

[tex]\textsf{Area of a triangle} = \sf \dfrac{1}{2} \times base \times height[/tex]

Given:

Substitute the given values into the formula:

[tex]\implies \textsf{Area of a triangle} = \sf \dfrac{1}{2} \times 12 \times 11=66\:m^2[/tex]

Total Surface Area

[tex]\begin{aligned}\implies \textsf{Total Surface Area} & = \sf base \: area + 6 \times side \: area\\& = \sf 216\sqrt{3}+6 \cdot 66\\& = \sf 216\sqrt{3}+396\\& = \sf 770\:m^2\:(nearest\:whole\:number)\end{aligned}[/tex]

The length of the shorter diagonal is 5.241 units and the length of the longer diagonal is 14.371 units

An equation is an expression that shows the relationship between two or more numbers and variables.

Let p and q represent the length of the diagonals.

Hence:

[tex]p=\sqrt{9^2+6^2+2(9)(6)cos(34)}=14.371\ units\\\\q=\sqrt{9^2+6^2-2(9)(6)cos(34)}=5.241\ units[/tex]

The length of the shorter diagonal is 5.241 units and the length of the longer diagonal is 14.371 units

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Answer:

[tex] {2x}^{3} - 3yz[/tex]

[tex]2 {( - 1)}^{3} - 3( - 2)(3)[/tex]

[tex] - 2 +6(3)[/tex]

[tex] - 2 +18[/tex]

(-)+(+)=(-)

[tex]-16[/tex]

Answer:

Step-by-step explanation:

a straight line equals 180°. so if one side is 117°, the other side would have to add up to 180.

180-117=63

And you can kind on figure out what is the same as the other angles. Hope his helps

The median of the number recorded in the question is 51.5 feet. This is obtained by dividing the sum of two numbers that occur centrally in half.

The central value in a list ordered from smallest to largest is the median of a set of values.

The formula for the Inter-quartile range is given as:

IQR = Q₃- Q₁ (that is Median of the Upper Half Less the Median of the lower half)

Step 1 - First, let's arrange the numbers sequentially

→  40, 40, 47, 49, 50, 53, 55, 57, 63, 76

Step 2 - Determine the upper and lower halves and their median

If the Lower half is  40, 40, 47, 49, 50, then it's median is 47

If the Upper half is   53, 55, 57, 63, 76, then its median is 57.

Hence:

IQR = 57 - 47

= 10 feet.

No, the friends didn't perform better in the second round because the was a significant drop in the median and the IQR. The median dropped from 51.5 to 47 and the IQR from 10 to 6.

It can be concluded that the distance in the second set of data is less variable when juxtaposed with those form the first set.

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Answer:

No solution or Undefine

Step-by-step explanation: