20 POINTS and BRAINLIEST
Solve the simultaneous equation!

Answer:

The maximum height it reaches is 20 meters

The time taken by it to reach the height is 2 seconds

Step-by-step explanation:

The formula of the height of the stone is h = u t - [tex]\frac{1}{2}[/tex] g t², where

∵ A stone is thrown vertically upwards with an initial velocity of 20 m/s

∴ u = 20 m/s

∵ g = 10 m/s²

→ Substitute them in the equation above

∴ h(t) = 20t - [tex]\frac{1}{2}[/tex] (10) t²

∴ h(t) = 20t - 5t²

→ Arrange the terms of the right side according to the greatest power of t

∴ h(t) = -5t² + 20t

To find the maximum height and the time of it find the vertex of the quadratic function (m, k), where m = [tex]\frac{-b}{2a}[/tex] and k is the value of h at t = m, a is the coefficient of t² and b is the coefficient of t

∵ The coefficient of t² is -5

∴ a = -5

∵ The coefficient of t is 20

∴ b = 20

→ Use them to find h

∵ m = [tex]\frac{-20}{2(-5)}[/tex] = [tex]\frac{-20}{-10}[/tex] = h

∴ m = 2

→ Substitute it in the equation above to find k

∵ h(m) = k

∵ k = -5(2)² + 20(2)

∴ k = -5(4) + 40

∴ k = -20 + 40

∴ k = 20

∴ The coordinate of the vertex of the function are (2, 20)

→ m represents the time of the maximum height and k represents

  the maximum height

∴ The maximum height it reaches is 20 meters

∴ The time taken by it to reach the height is 2 seconds

Answer:

slope = - [tex]\frac{3}{11}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, 7) and (x₂, y₂ ) = (6, 4)

m = [tex]\frac{4-7}{6+5}[/tex] = [tex]\frac{-3}{11}[/tex] = - [tex]\frac{3}{11}[/tex]

Answer:

140

Step-by-step explanation:

By inscribed angles, arc FPI = 2<FLI = 2*110 = 220. Since the entire arc of a circle is 360, we know that arc FLI + arc FPI = 360. Solving, we get arc FLI = 360 - 220 = 140.

I hope this helps!

Answer:

72

Step-by-step explanation:

Based on the table, the left and the right side have a pattern. When 3 is added to the left side, the right side is multiplied by 6. Since 12 multiplied by 6 is 72, the missing number is 72.

Answer:

[tex]\dfrac{1 - 6 \ln y}{2}[/tex]

Step-by-step explanation:

[tex] \ln \dfrac{\sqrt{e}}{y^3} = [/tex]

[tex] = \ln \dfrac{e^\frac{1}{2}}{y^3} [/tex]

[tex] = \ln e^\frac{1}{2} - \ln y^3 [/tex]

[tex]= \dfrac{1}{2} \ln e - 3 \ln y[/tex]

[tex]= \dfrac{1}{2} - 3 \ln y[/tex]

[tex]= \dfrac{1 - 6 \ln y}{2}[/tex]

The given logarithmic expression can be written as [tex]\frac{1-6ln\ y}{2}[/tex]

Given that,

Based on the above information, the calculation is as follows:

[tex]= ln \frac{\sqrt{e} }{y^3}\\\\= ln \frac{e^{1/2}}{y^3} \\\\= ln \e^{1/2} - lny3\\\\= \frac{1}{2}ln e - 3 ln y\\\\= \frac{1}{2} - 3 ln \ y \\\\= \frac{1- 6ln \y}{2}[/tex]

Therefore we can conclude that the given logarithmic expression can be written as [tex]\frac{1-6ln\ y}{2}[/tex]

Learn more: brainly.com/question/24169758

Answer:

D.$79.89

Step-by-step explanation:

Cost of one yard of fabric = $6.99

Length of fabric bought = 8 yards

Cost of one bag of polyester filling = $7.99

Number of bags of polyester filling bought = 3

Total cost of fabric = [tex]6.99\times 8=\$55.92[/tex]

Total cost of polyester filling = [tex]7.99\times 3=\$23.97[/tex]

Total cost of materials bought = Total cost of fabric + Total cost of polyester filling

[tex]=55.92+23.97=\$79.89[/tex]

Total cost of materials bought is [tex]\$79.89[/tex].

Answer:

[tex]y=\frac{5}{3}x+\frac{10}{3}[/tex]

Step-by-step explanation:

Firstly we rewrite the equation that is parallel to the line we need because parallel lines have the same slope by the rule

[tex]m_1=m_2[/tex]

so we rewrite the equation in slope-intercept form:

[tex]5x-3y=17\\-3y=-5x+17\\y=\frac{-5x+17}{-3}\\\\y=\frac{-5x}{-3}+\frac{17}{-3} \\\\y=\frac{5}{3}x-\frac{17}{3}[/tex]

and now we compare it with our slope-intercept form equation:

[tex]y=mx+b[/tex]

the coefficient of x which is m is the slope and since parallel lines have equal slopes the line that we need would also have the same slope which is 5/3.

now the next step is the line that we need passes through the point (-2,0) so it means that it should satisfy that specific point so we insert that point into our slope-intercept form and insert the slope which is 5/3 which is m.

[tex]y=mx+b\\y=\frac{5}{3}x+b\\\\0=\frac{5}{3}(-2)+b\\\\0=\frac{-10}{3}+b\\\\b=\frac{10}{3}\\[/tex]

now we know that the y-intercept(b) of the line we need is 10/3 and slope(m) is 5/3 insert these values into our slope-intercept form:

[tex]y=mx+b\\y=\frac{5}{3}x+\frac{10}{3} \\[/tex]

so this is our given line.

Answer: 40.8cm

Step-by-step explanation:

A hexagon is a polygon that is made up of 6 sides. The perimeter of a regular hexagon is calculated by multiplying the side given by 6

Since the length of a side of a regular hexagon is 6.8 cm, the perimeter will be:

= 6 × 6.8

= 40.8cm

Answer:

[tex]-8x^{2}+3x-6[/tex]

Step-by-step explanation:

The image below shows step-by-step on how to simplify the expression.

Hope this helps! :)

Answer:

Slope=2

y intercept= Length of spring without any weight

15 lbs= 38 inches

Step-by-step explanation:

slope=

18-12/5-2= 6/3 = 2

y intercept= 0=x and x=amount of weight

equation= 2x+8=y

2(15)+8=38

Answer:

700

Step-by-step explanation:

700

Answer:

4:3 or 4 to 3

Step-by-step explanation:

Answer:

is A B and D

Step-by-step explanation:

Answer:

So the slope is rise over run. You need the y intercept and the slope to write an equation. To find the y intercept, use the formula : 0=4(slope)*3+b and you get 0=12+b then you subtract twelve from both sides, getting b=-12. Thats your y intercept. So your equation will be y=4x-12

x= 6.32

y= 12

z= 18.97

I got my answer by; using the MCF and multiplying to see how many times 6/2 will go into x,y,z!

Hope this helps:)!

Answer:

x= 6.32

y= 12

z= 18.97

The amount of the sales tax is $2.24.

Given that,

Based on the above information, the amount of the sales tax rate is

[tex]= \$32 \times 7\%[/tex]

= $2.24

Here we simply multiply the cost with the sales tax rate.

Therefore we can conclude that the amount of the sales tax is $2.24.

Learn more: brainly.com/question/23461853

Answer:

The base is 0.1

The base is less than 1 so the function is decreasing

The x intercept is (3,0)

Step-by-step explanation:

The base of a logarithm refers to the number that must be raised to the power of the number on the right hand side of the logarithmic equation in order to yield the number on the left hand side of the logarithmic equation. It is always written as a subscript below the log symbol. In this case, the base is 0.1.

When the base of a logarithm is less than 1, it means that the function is decreasing as is the case in this question.

Looking at the graph, the x axis is cut at the point (3,0). This is the x-intercept of the graph.

sale price of the television is c

Answer/Step-by-step explanation:

5. 21x + 4 = 22x - 2 (corresponding angles)

Collect like terms

21x - 22x = -4 - 2

-x = -6

divide both sides by -1

x = 6

6. (x + 72) + (x + 132) = 180 (linear pair)

x + 72 + x + 132 = 180

Add like terms

2x + 204 = 180

2x = 180 - 204

2x = -24

x = -12

7. 90 = 22x + 2 (vertical angles)

90 - 2 = 22x

88 = 22x

Divide both sides by 22

4 = x

x = 4

8. 12x + 10 = 13x + 3 (vertical angles)

Collect like terms

12x - 13x = -10 + 3

-x = -7

Divide both sides by -1

x = 7

9. 17x = 16x + 5 (alternate exterior angles)

17x - 16x = 5

x = 5

✔️17x

Plug in the value of x

17(5) = 85°

10. 21x - 6 = 20x (corresponding angles)

Add like terms

21x - 20x = 6

x = 6

✔️20x

20(6) = 120°

Answer:

29.4x-70.56

Step-by-step explanation:

Answer:

let the marks obtained in maths be x

total marks obtained by susan=142+x

then

A/Q

60%of 450 =(142+x)

270=142+x

x=270-142

x=128

hence marks obtained in maths=128

OR

Max marks 120+150+180=450

60% of 450 is 270

70 +72+x=270

x=270-142

x=128

A

Step-by-step explanation:

Answer:

what questions? I dont see any

Answer:

there are no questions here but i am willing to see if i can help you with what you need

Step-by-step explanation:

Answer:

Wind speed = 30 mph

Plane speed = 270 mph

Step-by-step explanation:

Given that :

Distance = 600 miles

Let speed of airplane = a ; speed of wind = b

Net speed ; with wind = a + b

Net speed against wind = a - b

Time taken with wind = 2 hours

Time taken against wind = 2.5 hours

Recall :

Speed = distance / time ; distance = speed * time

(a + b) * 2 = (a - b) * 2.5

2a + 2b = 600

a + b = 300 - - - (1)

a = 300 - b

2.5a - 2.5b = 600

a - b = 240 - - - (2)

300 - b - b = 240

300 - 2b = 240

-2b = - 60

b = 30

a = 300 - 30

a = 270

Wind speed = 30 mph

Plane speed = 270 mph

Answer:

e. 2

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

let ones be x

tens is 4 + 2x

4 + 2x + x = 4

3x = 0

x = 0

tens is 4 + 2*0

tens = 4

40 candy canes

Answer:

The shadow of the pole is 1.2 feet long

Step-by-step explanation:

A little girl standing next to a telephone pole at 10 AM.

From the above question

Height of the girl = 4'6" tall = 4 feet and 6 inches tall

We convert to feet

= 12 inches = 1 foot

6 inches = x

Cross Multiply

12 × x = 6 × 1

x = 6/12 = 1/2 = 0.5 feet

Hence, the total height of the girl =

4 feet + 0.5 feet = 4.5 feet

The height of the telephone pole = 40 feet high.

The shadow of the telephone pole

= 8' 32 foot shadow

= 8 feet, 32 inches

We convert the inches to feet

12 inches = 1 foot

32 inches = x

Cross Multiply

12 × x = 32 × 1

x = 32/12 = 8/3 = 2.67 feet

Total length of the pole = 8 feet+ 2.67 feet = 10.67 feet

how long is a little girl shadow?

This is calculated using proportion

Shadow/Height

Shadow of the girl = x

Hence:

Shadow of the girl/Height of the girl = Shadow of the pole/Height of the pole

x/4.5 feet = 10.67 feet/40 feet

Cross Multiply

40 × x= 4.5 × 10.67

x = 4.5 × 10.67/40

x = 1.200375 feet

Approximately = 1.2 feet

Hence, the shadow of the pole is 1.2 feet long

Step-by-step explanation:

The equation of the line is y = 279.

Answer:

The scale factor is 18 to 1 for the painting

Step-by-step explanation:

Here we want to get the scale factor of the original to what is reproduced

Let us have same units first

Mathematically;

1 foot = 12 inches

3 feet = 36 inches

2 feet = 24 inches

So 36 to 2 and 24 to 1 1/3

That will be ratio 36/2 = 18 to 1

same as 25 divided by 1 1/3 = 18 to 1