Answer:
Part 1) [tex]f(x)=-5(x-10)(x+2)[/tex]
Part 2) After 10 seconds.
Step-by-step explanation:
We have the function:
[tex]f(x)=-5x^2+40x+100[/tex]
Where f(x) represents the height x seconds after it is released into the air.
Part 1)
First, let's distribute a -5 out of the function:
[tex]f(x)=-5(x^2-8x-20)[/tex]
Now, let's factor. We want to pick two number that multiplies to -20 and adds to -8.
We can use -10 and 2. So:
[tex]f(x)=-5(x^2+2x-10x-20)[/tex]
Factor:
[tex]\begin{aligned}f(x)&=-5(x^2+2x-10x-20) \\ f(x)&=-5(x(x+2)-10(x+2)) \\ f(x)&=-5(x-10)(x+2) \end{aligned}[/tex]
Hence, our factored form is:
[tex]f(x)=-5(x-10)(x+2)[/tex]
Part 2)
We want to find after how many seconds does it take for the projectile to reach the ground.
If it reaches the ground, the height above the ground, f(x), will be 0.
So, we can set f(x) equal to 0 and solve for x. Instead of using the original equation, we can use the factored form. So:
[tex]0=-5(x-10)(x+2)[/tex]
Zero Product Property:
[tex]x-10=0\text{ or } x+2=0[/tex]
Solve for x:
[tex]x=10 \text{ or } x=-2[/tex]
Since x measures time, -2 does not make sense in this context.
Therefore, our solution is x=10.
So, after 10 seconds, the projectile will hit the ground.
Piper is at the grocery store and plans on buying cans of soup and frozen dinners, but
is concerned about their sodium content. Each can of soup has 150 mg of sodium and peach frozen dinner has 450 mg of sodium.
How many milligrams of sodium are there in 4 cans of soup and 2 frozen dinners?
How many milligrams of sodium are there in c cans of soup and f frozen dinners?
Answer:
1,500 mg
150c + 450f
Step-by-step explanation:
Each can of soup has 150 mg of sodium and each peach frozen has 450 mg of sodium.
Piper plans to buy some of each product and wants to know how many milligrams of sodium are there in 4 cans of soup and 2 frozen dinners.
Since each can of soup has 150 mg of sodium, 4 cans have 4*150 = 600 mg of sodium.
Each frozen dinner has 450 mg of sodium, thus 2 of them have 2*450 = 900 mg of sodium.
There are 600 + 900 = 1,500 mg of sodium in this combination.
If Piper buys c cans of soup and f frozen dinners, they will have 150c + 450f milligrams of sodium.
Calculate the area of the triangle:
A=
(-2, 6)
(-2, 0)
(7,-5)
Helppp ASAP
Answer:
I got 27 as an answer
Step-by-step explanation:
Answer:
I hope this may help you ...
Carmen is printing an essay that is 9 pages long, and each page contains 45 lines of text. It takes her 5 minutes to print the essay. At what rate did the essay print?
Answer:
1.8 pages per minute and 81 lines per minute.
Plzz help!!!
What is the value of both these problems?
Problem 2
We have an isosceles triangle because of the two congruent sides (21 each).
The angles opposite the congruent sides are known as the base angles, and the base angles are congruent. For now, we don't know what they are. They are both x. I recommend writing 'x' onto the diagram where that missing unmarked angle is.
Then we'll use the idea that all three angles of any triangle always add to 180
x+x+38 = 180
2x+38 = 180
2x = 180-38
2x = 142
x = 142/2
x = 71
Answer: Choice A) 71=======================================================
Problem 3
We use the same ideas as the previous problem. This time the base angles are 56 degrees each. The remaining angle is x.
x+56+56 = 180
x+112 = 180
x = 180-112
x = 68
Answer: Choice A) 68Certain species of fish costs $4.49 each. You spend at most $35. How many of this type of fish can you buy for your aquarium?
Also how do you give the brainlyest answer to someone?
Answer:
7 fish
Step-by-step explanation:
1. 4.49x ≤ 35
2. Divide both sides by 4.49 so it cancels out the multiplication. x ≤ 7.79510022272
3. You can't split fish, so you can buy 7 fish.
Not sure how to give Brainliest, though.
Answer:
Do 4.49 times 8 it'll get your answer
Step-by-step explantion
NO it's 8 he can buy 8 Of them fishes
which of the following is the equation logx4=-2 written in exponential form
1. The exponential form of the equation [tex]log_{x} 4 = - 2[/tex] will be;
⇒ x⁻² = 4
2. The value of √e⁷/e⁵ will be;
⇒ e
3. The equivalent expression of 3 will be;
⇒ ln e³
What is an expression?
Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
1. The expression is the equation [tex]log_{x} 4 = - 2[/tex].
2. The equation is √e⁷/e⁵.
3. The number is 3.
Now,
The exponential form of the equation [tex]log_{x} 4 = - 2[/tex] is calculated as;
[tex]log_{x} 4 = - 2[/tex]
By the definition of logarithmic, we get;
4 = x⁻²
Hence, The exponential form of the equation [tex]log_{x} 4 = - 2[/tex] will be;
⇒ x⁻² = 4
2. The equation is √e⁷/e⁵.
Solve as;
√e⁷/e⁵ = √ e ⁷ ⁻ ⁵
= √ e²
= e
Thus, The value of √e⁷/e⁵ will be;
⇒ e
3. Since, by the definition of logarithmic;
[tex]ln_{e} e = 1[/tex]
So, By option 1;
[tex]ln_{e} e^3[/tex] = [tex]1 * 3[/tex] = [tex]3[/tex]
Thus, The equivalent expression of 3 will be;
⇒ ln e³
Learn more about the expression visit:
https://brainly.com/question/1859113
#SPJ2
A scale model of a building is 6in tall. The scale of the model is 1in. :50ft. How tall is the actual building?
Answer:
300 ft
Step-by-step explanation:
Estimate by rounding the largest number to hundreds and then divide.
869 ÷ 6 is approximately
Answer:
150
Step-by-step explanation:
Round: 869 → 900900 ÷ 6 = 150I hope this helps!
use patterns blocks to help fidn each of the fractions
Answer:1/2?
atleast that what i thought it was
Find an equation for the line below in y=mx+b
Answer:
y = -1/2x - 11/2
Step-by-step explanation:
Using slope intercept form y = mx + b, to determine the equation, first count the rise(vertical or change in y), and run(horizontal or change in x) of the line.
m is the slope, b is the y-intercept which will remain when x is 0 as this will cancel out the m.
Be careful when determining the slope, and pay attention to the steps(count) of the x, and y axis.
As this graph measures a line with a negative slope passing through the y axis at -5 1/2 → -11/2, with a step of 1, we can count the squares normally to determine the slope.
So since we know that this line has two obvious points (-5,-3) and (1,-6) we can use the equation for slope to measure it's steepness.
m = y2-y1/x2-x1
with (x1,y1) being the first point, and (x2,y2) being the second point.
So: (negative minus a negative makes a positive)
m = -6-(-3)/1-(-5) = -6 + 3/ 1 + 5 = -3/6 = -1/2.
Since m = -1/2, and b = -11/2, the line must be y = -1/2x - 11/2.
Lines g and h are parallel. What is the measure of ∠QRS?
Answer:
is there a diagram
Step-by-step explanation:
1/3 cups of butter?
(Hint:use a calculator to figure out how many tablespoons a 1/3 of a cup is,your answer will not be a whole number)
Answer:
Around 5 tablespoons or to be exact: 5.333333333333333
Elina is gathering up change she has saved. She has a total of $2.60. All of her change is in either nickles, dimes, or quarters. She has twice as many dimes as quarters and two less quarters than nickles. Is it possible that she has eight dimes, four quarters, and six nickels? Explain.
Answer:
sadsadwsd
Step-by-step explanation:
⚠️⚠️Can someone answer both of these? PLEASE I WANNA FINISHJSKSLWLA ⚠️⚠️
Write an equation
Answer:
j + 5 = s
a = l + 3
Step-by-step explanation:
What is the intermediate step in the form (x + a)? = b as a result of completing the
square for the following equation?
x2 + 18x + 57 = 12
Answer:
(x + 9)² = 36
Step-by-step explanation:
Given
x² + 18x + 57 = 12 ( subtract 57 from both sides )
x² + 18x = - 45
To complete the square
add ( half the coefficient of the x- term)² to both sides
x² + 2(9)x + 81 = - 45 + 81
(x + 9)² = 36
An equation uses the symbol.
True
False
Answer:
False
Step-by-step explanation:
Answer:
If you mean the symbol = then true.
Step-by-step explanation:
equation = equal sign
The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has a bell-shaped distribution. This distribution has a mean of 56 and a standard deviation of 10. Using the empirical rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 36 and 86?
Answer:
97.35%
Step-by-step explanation:
Empirical rule formula states:
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .
From the question, we have the mean of :
Mean of 56 and a standard deviation of 10.
For 36
36 = μ - xσ
36 = 56 - 10x
56 - 36 = 10x
20 = 10x
x = 20/10
x = 2
Hence, the data falls within 2 standard deviation of the mean
Hence, since it is one side,
= 95%
= 47.5%
For 86
86 = μ - xσ
86 = 56 - 10x
56 - 86 = 10x
-30 = 10x
x = -30/10
x = -3
Hence, the data falls within 3 standard deviation of the mean
Hence, since it is 99.7% one side,
= 99.7%
= 49.85%
Hence, we add up
= 47.5% + 49.85%
= 97.35%
The approximate percentage of 1-mile long roadways with potholes numbering between 36 and 86 is 97.35%
EASY POINTS
Kite LMNO is shown below.
Kite L M N O. Angle L is 130 degrees and angle N is 74 degrees. Angle L and N are opposite to each other.
What is the measure of Angle M?
A. 56Degrees
B. 78Degrees
C. 156Degrees
D. 204Degrees
Step-by-step explanation:
Find QR
QR + RS = QS
18 + x + 2x + 24 = 17
Answer:
QR = 10
Step-by-step explanation:
QR + RS = QS , substitute values
18 + x + 2x + 23 = 17 , that is
3x + 41 = 17 ( subtract 41 from both sides )
3x = - 24 ( divide both sides by 3 )
x = - 8
Thus
QR = 18 + x = 18 - 8 = 10
Five cubic meters of copper has a mass of 44,800 kilograms. What is the density of copper?
Answer:
i thin it is 8960
Step-by-step explanation:
44800 divided by five = 8960
With a coupon, you get a pair of shoes that normally cost $80.00 for 30% off. How much is the discount?
Answer: The discount is 24$ so the 80$ shoes are now 56$.
Please help! Drag the tiles to the correct boxes to complete the pairs...
how do u find the sum of (5x-2) + (4x+6)
[tex] \: \: \: \: \: \: \: \: (5x - 2) + (4x + 6) \\ \\ = > 5x - 2 + 4x + 6 \\ \\ = > 5x + 4x - 2 + 6 \\ \\ = > \green{\boxed { 9x + 4}}[/tex]
Answer:
9x+4
Step-by-step explanation:
First, remove the unnecessary parentheses from (5x-2)+(4x+6) making it 5x-2+4x+6 because when there is a + in front of an expression in parentheses, the expression remains the same.
Next, collect like terms, turning 5x-2+4x+6 into 9x-2+6.
Now, calculate the sum and you should get 9x+4.
Anthony earned $131 in tips last night while working at the restaurant. If his tips
consisted of $1 bills and $5 bills only and he counted 47 bills in total, then how
many $5 bills did Anthony receive?
Given:
Total income form tips = $131
His tips consisted of $1 bills and $5 bills only.
Total number of bills = 47
To find:
The number of $5 bills.
Solution:
Let x be the number of $1 bills and y be the number of $5 bills.
Total bills : [tex]x+y=47[/tex] ...(i)
Total income : [tex]x+5y=131[/tex] ...(ii)
Subtract (ii) from (i), we get
[tex]x+5y-(x+y)=131-47[/tex]
[tex]x+5y-x-y=84[/tex]
[tex]4y=84[/tex]
[tex]y=21[/tex]
Therefore, the number of $5 bills is 21.
What is a pre-image?
Answer:
an image before the image your seeing
Step-by-step explanation:
log(x+1)−log(x−8)=log(10)
How do i solve this?
9514 1404 393
Answer:
x = 9
Step-by-step explanation:
The applicable rule of logarithms is ...
log(a) -log(b) = log(a/b)
__
Use the rules of logarithms to simplify the left side to a single log, then take the antilogs and solve the resulting equation.
log(x+1) -log(x-8) = log(10)
log((x+1)/(x-8)) = log(10)
(x +1)/(x -8) = 10 . . . . . . . take antilogs
x +1 = 10(x -8) . . . . multiply by x-8
81 = 9x . . . . . . . add 81-x, simplify
9 = x . . . . . . . . . divide by 9
_____
When the equation is rewritten to the form f(x) = 0, the x-intercept is the solution.
Guys plz help Answer this Question!!!!!
Answer:
X intercept is (-40,0) why intercept is (0,15)
Step-by-step explanation:
youyou will be able to tell this by looking at the graph and counting where the points are
The points (-1, r) and (2, 1) lie on a line with slope 2. Find the missing coordinate r
Please help!!!
Answer:
r = -5
Step-by-step explanation:
Slope = (y2 - y1)/(x2 - x1)
(-1, r)
(2, 1)
r - 1/-1 - 2 = r - 1/-3
Slope = 2
-3 x 2 = -6
-6 -(-1) = -5
-5 - 1 = -6
-6/-3 = 2
So:
r = -5
Hope this helps!
9514 1404 393
Answer:
r = -5
Step-by-step explanation:
The x-coordinate of the partially-defined point is 3 units less than the x-coordinate of the given point. The slope of 2 tells you the y-coordinate of the partial point (r) will be 2·3 = 6 units less than the y-coordinate of the given point. That is ...
r = 1 - 2·3
r = -5
__
You are given the slope of the line and a point on it, so you can write the point-slope equation of the line:
y -y1 = m(x -x1) . . . . . . . line with slope m through point (x1, y1).
For the given point and slope, this is ...
y -1 = 2(x -2)
For an x-value of -1, the corresponding y-value will be ...
r = 2(-1-2) +1 = -6 +1
r = -5
a cone has a volume of 33 cubic inches. of a cylinder has the same height and radius as the cone, what is the volume of the cylinder
Answer: 40 cubic inch
Step-by-step explanation:
Uniforms are sold in packages of 8. The store's 137 employees will each be given 4 uniforms. How many uniforms will the store need to order all together?
Answer:
552 uniforms (69 packages)
Step-by-step explanation:
since each employee will be given 4 uniforms and each package contains 8 uniforms, you need 1 package of uniforms for every 2 employees.
Total number of employees = 137
total number of uniform packages = 137 / 2 = 68.5 packages which must be rounded up since you need to have enough uniforms for everyone = 69 packages
69 packages x 8 uniforms per package = 552 uniforms