Answer:
The rocket will hit the floor at 9.57 seconds
Step-by-step explanation:
Given
[tex]G(x) = -16x^2 + 150x + 30[/tex]
Take off height = 30ft
Initial velocity= 150ft/s
Required [Missing from the question]
Time to hit the ground
The rocket will hit the ground at:
[tex]G(x) = 0[/tex]
So, we have:
[tex]0 = -16x^2 + 150x + 30[/tex]
Rewrite as:
[tex]16x^2 - 150x - 30=0[/tex]
Solve using quadratic formula, we have:
[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
Where:
[tex]a= 16\\ b = -150\\ c = -30[/tex]
So, we have:
[tex]x = \frac{-(-150) \± \sqrt{(-150)^2 - 4*16*(-30)}}{2*16}[/tex]
[tex]x = \frac{150 \± \sqrt{22500 +1920}}{32}[/tex]
[tex]x = \frac{150 \± \sqrt{24420}}{32}[/tex]
[tex]x = \frac{150 \± 156.27}{32}[/tex]
Split:
[tex]x = \frac{150 + 156.27}{32}\ or\ \frac{150 - 156.27}{32}[/tex]
[tex]x = \frac{306.27}{32}\ or\ \frac{-6.27}{32}[/tex]
Time cannot be negative;
So:
[tex]x = \frac{306.27}{32}[/tex]
[tex]x = 9.57[/tex]
Hence, the rocket will hit the floor at 9.57 seconds
The current temperature is 48F. It is expected to drop 1.5F each hour. Determine how many hours the temperature will be 36 F.
Answer: 6 hours
Step-by-step explanation:
48/6 = 8
36/6 = 6
Help please. It’s due at 2pm
Answer:
X = 64
Step-by-step explanation: The square in the corner indicates a 90 degree angle. by adding everything but X and subtracting that from 360 degrees we can get X. 180+90+26=296 360-296=64
Answer:
64°Step-by-step explanation:
We know that this need to total to 360°. Since we know this, it is simple and straight forward.
To find x, we need to add up all the known degrees.
180 + 90 + 26 = 296
Also if you do not know how I got 90, there is a right angle which is 90 degrees.
Now that we have the sum of the known degrees, we take that number and subtract that from 360
360 - 296 = 64
So our final answer is 64°
A circle with a radius of 4 inches has a diameter that is 3x+5 inches long. What is the value of x?
Answer:
x=1
Step-by-step explanation:
The radius of a circle is half of the diameter.
Because we know this, we can multiply the radius by 2 to equal the diameter:
4*2=3x+5
Then we solve for x:
8=3x+5
3=3x
x=1
1. Use the given key to answer the questions.
0.1
tenth
0.01
hundredth
0.001
thousandth
0.0001
ten-thousandth
a.
What number does this diagram represent?
b. Draw a diagram that represents 0.216.
c. Draw a diagram that represents 0.304.
Answer:
please where is the diagram
Find the distance between the two points.
Answer:
[tex]\sqrt{61}[/tex]
Step-by-step explanation:
Calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 2,- 4) and (x₂, y₂ ) = (4, 1)
d = [tex]\sqrt{(4-(-2))^2+(1-(-4))^2}[/tex]
= [tex]\sqrt{(4+2)^2+(1+4)^2}[/tex]
= [tex]\sqrt{6^2+5^2}[/tex]
= [tex]\sqrt{36+25}[/tex]
= [tex]\sqrt{61}[/tex]
Erica babysits for 4 1/2 hours and is paid $27 . If the people she babysits for have $31.50 to pay her, how long can they stay out?
Answer:
5.25 hours or 5 1/4 hours
Step-by-step explanation:
According to the scenario, calculation of given data are as follows,
Total time = 4 1/2 hours or 270 mins
Total payment = $27
First we calculate the time for $1, then
So, $27 = 270 mins
$1 = 270 ÷ 27 = 10 mins
Now, we can calculate total time in $31.50 by using following formula,
Total time in $31.50 = 10 mins × 31.50
= 315 mins
= 5.25 hours or 5 1/4 hours
At a car wash fundraiser, $168 was raised for washing 24 cars. The next day, $280 was raised for washing 40 cars. Are the rates equivalent? Explain your reasoning.
Step-by-step explanation:
168/24 = 7 dollars per car
280/40 = 7 dollars per car
the rates are equivalent.
Completely simplify the rational expression LaTeX: \frac{7x}{3y} + \frac{12x}{9y}
Answer:
[tex]\frac{11x}{3y}[/tex]
Step-by-step explanation:
[tex]\frac{7x}{3y} + \frac{12x}{9y}[/tex]
To add the two fractions, you need a common denominator. In this case, the lowest common denominator (LCD) is 9y. That's because 9y is divisible by both 3y and 9y.
The first fraction must be changed so that its denominator is 9y. Do this by multiplying both numerator and denominator by 3.
[tex]\frac{7x}{3y}\cdot\frac{3}{3}+\frac{21x}{9y}=\frac{21x}{9y}+\frac{12x}{9y}\\=\frac{21x+12x}{9y}\\=\frac{33x}{9y}[/tex]
Finally, this answer can be simplified ("reduced") by dividing both numerator and denominator by 3, their greatest common factor.
Watch help video
Which of the following equations represents a line that passes through the points
(2,0) and (1, -4)?
I. 4.x - y = 9
II. y +4 = 4(x + 0)
Neither
I only
II only
I and II
Answer:
I think neither
Step-by-step explanation:
Jennifer buys a desk on sale for $478.60. If the regular price was $684.00, what is the percentage of discount?
Answer:
30%
Step-by-step explanation:
Find the percent discount by dividing the change in the price by the original price:
(684 - 478.6) / 684
205.4 / 684
= 0.3
So, the percent discount was approximately 30%
Find the inverse of the following function.
f(x) = + 12
OA (1) = x
= 1 – 12
OB. (v) = 12 - Foto
oc. 5- (6) = x3 – 12
OD. 1-() =
= 1 + 12
Answer:
c
Step-by-step explanation:
exchange y and x
then find y
Draw a line to match each fraction, decimal, or percent in Column A to the equivalent value in Column B.
A B
40/50 1 3/4
13% 1 11/20
1.75 0.13
155% 80%
Answer:
This is the answer
Step-by-step explanation:
40/50 - 80%
13% - 0.13
1.75 - 1 3/4
155% - 1 11/20
Hope this helps
Jane used a Venn diagram to sort shapes. Select a plane shape that belongs inside the overlap region of the diagram.
Answer:
c
Step-by-step explanation:
Which of the following is equivalent to 16 ^3/4
Answer:
83/5
Step-by-step explanation:
83/5 would be equivalent to 16 3/4.
Answer:
8, or B on Edge.
Just took the quiz. Have a great day
based on the area of the squares determine whether the triangle shown is a right triangle.
Answer:
No, it is not a right triangle.
Step-by-step explanation:
Answer:
not a right triangle
Step-by-step explanation:
A factory makes car batteries. The probability that a battery is 1/14. If 400 batteries are tested how many are defective
Answer:
1/14 of 400 batteries = 56 batteries
Step-by-step explanation:
[tex]400 \times 0.14[/tex]
Answer:
Actual: 28.57
Rounded: 29
Step-by-step explanation:
400/14 = 28.57
Round to nearest whole number: 29
Correct on A P E X
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
-4 x 3/2
Step-by-step explanation:
It will end up being -6 which is less than -4.
Tell me if it is wrong.
Have a nice day!
Answer:
We can use the numbers -4 and [tex]\frac{3}{2}[/tex] to get a product less than -4.
-4 x [tex]\frac{3}{2}[/tex] = -6
So, the answer is less than -4.
Please give Brainliest!
Have a great day!
Which expression is equivalent to 7x + 4x2 – 5x?
Answer:
2x+8
Step-by-step explanation:
Answer:
[tex]4x^{2} +2x[/tex]
Step-by-step explanation:
I'm not sure what you want, because it says "which expression", but you didn't provide any answer choices.
So all you have to do for this is combine like terms, and the only ones were 7x and -5x, which equals 2x.
*ANSWER THESE PROBLE
Show your work to earn credit for your solution.
1. When Carlos bought a new office phone, he borrowed $1,000 at a rate of 7% for 8 months.
How much interest did he pay?
Show your work here:
1 = Prt
Please help
Step-by-step explanation:
The interest will be $560
Choose the measure that best represents the data. Explain your reasoning.
12, 15, 16, 18, 20, 90
A number multiplied by 7 is less than 21. Which of the following expressions correctly identifies this sentence?
Answer:
Step-by-step explanation:
Find the minimum value of the function f(x) = 0.8x2 + 11.2x + 42 to the
nearest hundredth.
Answer:
The minimum value is 2.8. The vertex is (-7, 2.8).
Step-by-step explanation:
Through the x^2 term we identify this as a quadratic function whose graph opens up. The minimum value of this function occurs at the vertex (h, k). The x-coordinate of the vertex is
-b 11.2
x = --------- which here is x = - ------------ = -7
2a 2(0.8)
We need to calculate the y value of this function at x = -7. This y-value will be the desired minimum value of the function.
Substituting -7 for x in the function f(x) = 0.8x^2 + 11.2x + 42 yields
f(-7) = 0.8(-7)^2 + 11.2(-7) + 42 = 2.8
The minimum value is 2.8. The vertex is (-7, 2.8).
Select the correct answer. What are the solutions of this quadratic equation?
6x^2 + 6 = 12x + 18
[tex]x = 1 + \sqrt{3} [/tex]
[tex]x = 2 + 2 \sqrt[]{3} [/tex]
[tex]x = 2 + \sqrt{6} [/tex]
[tex]x = - 1 \: and \: x = 3[/tex]
Answer:
x=1+√3
Step-by-step explanation:
Let's solve your equation step-by-step.
6x^2+6=12x+18
Step 1: Subtract 12x+18 from both sides.
6x^2+6−(12x+18)=12x+18−(12x+18)
6x^2−12x−12=0
For this equation: a=6, b=-12, c=-12
6x^2+−12x+−12=0
Step 2: Use quadratic formula with a=6, b=-12, c=-12.
x=−b±√b2−4ac/2a
x=−(−12)±√(−12)2−4(6)(−12)/2(6)
x=12±√432/12
x=1+√3
Find the radius of a hemisphere with a volume of 106.1 cubic inches. Round to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
help needed asap will give brainliest
Answer:
the corect answer for this question is (-x,y)
what is a non example substitution method?
Answer:
The substitution method consists of solving for in one of the equations, basically the one that is easiest, and substituting the resulting expression in the other. With this, the second equation is converted into a linear equation with one unknown, which is solved by simply solving for.
Step-by-step explanation:
l hope and this can help you
Do you like math? If you do solve this simple equations
[tex]2 + 2 + 4 + 4 + 8 + 8 + 16 + 16[/tex]
Answer:
60 ?
Step-by-step explanation:
SOMEONE PLEASE HELP ME WITH THIS QUESTION ASAP AND SHOW WORK
Answer:
m∠XCY = 60°
Step-by-step explanation:
From the figure attached,
Circle has been given with the inscribed angles ∠XWY and ∠XCY formed by the same arc XY.
By the property of the inscribed angles,
"Measure of the inscribed angle formed by the same arc are equal"
m∠XWY ≅ m∠XCY
60x = 61x - 1
61x - 60x = 1
x = 1
Therefore, m∠XCY = 61x - 1
= 61(1) - 1
= 60°
The maximum walking speed S, in feet per second of an animal can be modeled by the equation S= √gL , where g=32ft/sec
Answer:
1.41
Step-by-step explanation:
The maximum walking speed S, in feet per second, of an animal can be modeled by the equation S= √(gL), where g = 32ft/sec² and L is the length, in feet, of the animal's leg. To the nearest hundredth, how many times greater is the maximum walking speed of a giraffe with a leg of 6 feet than a hippopotamus with a leg of 3 feet?
Step 1: Calculate the maximum walking speed of a giraffe
The leg of a giraffe measures L = 6 ft.
Sg= √(g × Lg)
Sg= √(32 ft/s² × 6 ft) = 13.86 ft/s
Step 2: Calculate the maximum walking speed of a hippopotamus
The leg of a hippopotamus measures L = 3 ft.
Sh= √(g × Lh)
Sh= √(32 ft/s² × 3 ft) = 9.80 ft/s
Step 3: Determine how many times greater is the maximum walking speed of a giraffe than a hippopotamus
We will make the ratio Sg/Sh
Sg/Sh = (13.86 ft/s)/(9.80 ft/s) = 1.41
The maximum walking speed of a giraffe is 1.41 times greater than the maximum walking speed of a hippopotamus.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
The leg of a giraffe measures L = 6 ft.
S(g)= √(g×L)
S(g) = √(32 ft/s² × 6 ft)
S(g) = 13.86 ft/s
The maximum walking speed of a hippopotamus:
The leg of a hippopotamus measures L = 3 ft.
S(h)= √(g×L)
S(h) = √(32 ft/s² × 3 ft)
S(h) = 9.80 ft/s
The ratio S(g) to S(h)
S(g)/S(h) = 13.86/9.80 = 1.41
S(g) = 1.41S(h)
Thus, the maximum walking speed of a giraffe is 1.41 times greater than the maximum walking speed of a hippopotamus.
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The table shows the blood pressures of 16 clinic patients. What is the interquartile range of the data?
A) 7.75
B) 8.50
C) 9.25
D) 10.75
The interquartile range of the data will be 9.1.
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The table shows the blood pressures of 16 clinic patients.
Now,
Since, The data set is,
⇒ 81.6, 84.1, 87.6, 82.8, 82.0, 88.9, 86.7, 96.4, 84.6, 104.9, 90.8, 94.0, 69.4, 78.9, 75.2, 91.0
Arrange in ascending order as;
⇒ 69.4, 75.2, 78.9, 81.6, 82.0, 82.8, 84.1, 84.6, 86.7, 87.6, 88.9, 90.8, 91.0, 94.0, 96.4, 104.9
Clearly, There are 16 clinic patients.
Hence, The lower quartile (Q₁) = 81.6 + 82 / 2
= 81.8
And, The Upper quartile (Q₃) = 90.8 + 91 / 2
= 90.9
Thus, The interquartile range of the data = Q₃ - Q₁
= 90.9 - 81.8
= 9.1
Therefore, The interquartile range of the data = 9.1
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