Answer:
At approximately x = 0.08 and x = 3.92.
Step-by-step explanation:
The height of the ball is modeled by the function:
[tex]f(x)=-16x^2+64x+5[/tex]
Where f(x) is the height after x seconds.
We want to determine the time(s) when the ball is 10 feet in the air.
Therefore, we will set the function equal to 10 and solve for x:
[tex]10=-16x^2+64x+5[/tex]
Subtracting 10 from both sides:
[tex]-16x^2+64x-5=0[/tex]
For simplicity, divide both sides by -1:
[tex]16x^2-64x+5=0[/tex]
We will use the quadratic formula. In this case a = 16, b = -64, and c = 5. Therefore:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Substitute:
[tex]\displaystyle x=\frac{-(-64)\pm\sqrt{(-64)^2-4(16)(5)}}{2(16)}[/tex]
Evaluate:
[tex]\displaystyle x=\frac{64\pm\sqrt{3776}}{32}[/tex]
Simplify the square root:
[tex]\sqrt{3776}=\sqrt{64\cdot 59}=8\sqrt{59}[/tex]
Therefore:
[tex]\displaystyle x=\frac{64\pm8\sqrt{59}}{32}[/tex]
Simplify:
[tex]\displaystyle x=\frac{8\pm\sqrt{59}}{4}[/tex]
Approximate:
[tex]\displaystyle x=\frac{8+\sqrt{59}}{4}\approx 3.92\text{ and } x=\frac{8-\sqrt{59}}{4}\approx0.08[/tex]
Therefore, the ball will reach a height of 10 feet at approximately x = 0.08 and x = 3.92.
PLS HELP!!!!! Combine like terms: x + 2x + 4
Answer:
3x+4
PLEASE MARK ME AS BRAINLIEST PLEASEEEEEE
Step-by-step explanation:
Negative ten is no less than two times a number plus forteen
What is the value of each expression?
7/8 + 4/8
Answer:
7/8 + 4/8 = 1 3/8.
Step-by-step explanation:
In words the answer is 1 and 3/8.
Find the circumcenter of ΔABC with vertices A(12, 0), B(0, -6), C(0, 0)
1. Benjamin is saving money for a new laptop. He
already has $50 in his account. Now he plans on
saving $25 per week. Which equation can be
used to calculate y, the total amount of money
Benjamin will have saved after x number of
weeks of saving.
A. y = 25x + 50
B. y = 50x + 25
C. x = 25y + 50
D. x = 50y +25
Give the slope between the points
(2,5) (14,-4)
Answer:
[tex]-\frac{3}{4}[/tex]
Step-by-step explanation:
Slope
(2, 5) and (14, -4)
_______________
When we solve for slope within two points, we have to follow the formula of slope.
[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]
X and Y - The first and second number in both points
1 and 2 - The first or second number within one point
Substitute :
[tex]\frac{-4-5}{14-2}[/tex]
[tex]\frac{-9}{12}[/tex]
Simplify :
[tex]-\frac{3}{4}[/tex]
Answer:
Rewritten in slope-intercept form
y = mx + b
The answer is
m = -3/4
Please need helppp asap!!!
Just answer True or False. Thank you
Answer:
True is my answer as well
Step-by-step explanation:
A rectangular living room is 6 meters long and 3 meters wide. What is its area?
do y’all know this one?
Step-by-step explanation:
For first triangle,
sin 45 = 3 / d
1 / root 2 = 3 / d
d = 3 root 2
For second triangle,
tan 60 = 7 / a
root 3 = 7 / a
a = 7 / root 3
8. Solve for x. Round to the nearest tenth. (4pts)
55°
7
x=
Answer: I think 2
Step-by-step explanation:
Because
Nine friends share 7 bags of trail mix equally what fraction of a bag of trail mix does each friend get
Answer:
Each person gets 7/9 of a bag
Step-by-step explanation:
7 bags between (divided by) nine people.
HELP i jus want a answer
The answer id D(102)
That is because to solve first you would figure out the area of the rectangle by doing 5 x 15 which is 75. Than you would figure out the area of the triangle. To figure ou the he8ght you would do 11 - 5 and for the base you would do 15 - 3 - 3 and that would be 9. Than you would do 9 x 6 divided by 2 and that would be 27. Than you would add 27 to 76 and that would get 102.
Please Help!
Give the largest whole number that could equal the length of the side in the picture.
Answer:
8
Step-by-step explanation:
We can use triangle inequality, let AC = x:
x+4 > 5
x+5 > 4
9 > x
Simplifying:
x>1
x>-1
9>x
Thus: 9>x>1
So the Largest whole number is 8
The cost of producing x units of a certain commodity is c() - 1000 +370x + 7x2,
What is the average rate of change of C with respect to x when the production
level is raised from x= 100 to x= 120?
Step-by-step explanation:
cost to produce 120 units
= C(120) = 1000+5.7(120) + .7(120^2) =
= 11764
cost to produce 100 units = C(100)
= 8570
rate of change = (11764-8570)/(120-100)
= 3194/20
= 159.70 dollars/unit
repeat the process for 100 to 101
ACTIVITY 2
Here are some equations that all have the same solution. Explain how you know
that each equation has the same solution as the previous equation.
x = -6
X-3= -9
-9 = x-3
900 = -100(x - 3)
900 = (x-3) (-100)
900 = -100x + 300
Answer:
Step-by-step explanation:
x = -6
subtract 3 from both sides: x-3 = -9
reflexive identity: x-3 = -9, so -9 = x-3
multiply both sides by -100: 900 = -100(x-3)
commutative law for multiplication: -100(x-3) = (x-3)(-100)
distributive rule: (x-3)(-100) = -100x + 300
Given 6, 8, and 11 as the three sides of a triangle, classify it as one of the following acute, right or obtuse. Please help and thank you
9514 1404 393
Answer:
obtuse
Step-by-step explanation:
You may remember that side lengths of 3, 4, 5 make a right triangle. Doubling those lengths to 6, 8, 10 will still give a right triangle.
The given triangle has a longest side (11) longer than would be appropriate for a right triangle (10), so the largest angle is larger than 90°.
The triangle is obtuse.
__
Comparison of a triangle to a right triangle with two sides the same is one of several ways the triangle can be classified. You can use the Law of Cosines to find the largest angle, or you can use a triangle solver (as we have below).
In case you don't recall that 3-4-5 makes a right triangle, you can use the Pythagorean theorem to find the longest side of a right triangle with the given shorter sides:
hypotenuse = √(6² +8²) = √100 = 10
Your long side is longer, so your largest angle is larger than 90°.
Law of Cosines:
angle = arccos((6² +8² -11²)/(2·6·8)) = arccos(-21/96) ≈ 102.6°
Name the form of the equation, then find the y-intercept of the following lines.....
y=2/5x+1
Answer:
y = 1
Step-by-step explanation:
To find the y-intercept (s), substitute in 0 for x and solve for y.
y = 2/5 x (0)+1
y-intercepts (0, 1)
Please help, the homework is due in a few hours
Answer:
the aswer is 2
Step-by-step explanation:
this is because 10/5=2
how do you convert 7/6 into a mixed number or how do you covert fractions into a number in general.
Answer:
1 1/6
Step-by-step explanation:
You can convert 7/6 into a mixed number by subtracting 1 from the improper fraction, because 1= 6/6
7/6 -6/6= 1 1/6
Answer:
7/6 would be 1 1/6
Step-by-step explanation:
To make it a number in general turn into a decimal.
Someone help me identify the quadrilaterals
PLEASE HELP ME ASAP I would appreciate it :((
12 points
95x4.5 please help!!!
Answer:
[tex]427.5[/tex]
Step-by-step explanation:
[tex]95\times4.5[/tex]
Multiply:
[tex]95\times4.5=427.5[/tex]
427.5 is your answer.
Deepa finds some dimes and quarters under the couch cushions. How much money
(in dollars) does she have if she has 10 dimes and 5 quarters? How much money in
dollars) does she have if she has a dimes and y quarters?
Answer:
$2.25
Step-by-step explanation:
10*0.10= $1.00
5*0.25= $1.25
1+1.25= $2.25
Estimate
1/8+4/9
A.5/17
B.3
C.1
D.1/2
Answer:
I would choose A
Step-by-step explanation:
Can someone help me find the area to this?
What do studies tell about people's way of life in traditional societies??
(Note: Please don't give me silly answer)
Step-by-step explanation:
buffet or tells about the beliefs values behaviour and material object that constitute a people's way of life
Answer:
In sociology, traditional society refers to a society characterized by an orientation to the past, not the future, with a predominant role for custom and habit. Such societies are marked by a lack of distinction between family and business, with the division of labor influenced primarily by age, gender, and status.
Step-by-step explanation:
Hope it is helpful.....
GIVING BRAINLIEST! The triangles below are similar. How tall is the tree? Please show process.
Answer:
18m tall?
Step-by-step explanation:
Answer:
20 m
Step-by-step explanation:
The scale factor between the two triangles is 1/10 because of how 3/30 is 1/10.
Therefore we can calculate the height of the tree by multiplying the height of the smaller triangle by 10 to find the height of the tree.
2*10 = 20m
Write an equation where the variable is divided by a number, and a solution is -4/5
Answer:
x/-5
Step-by-step explanation:
Just divide by 5 and the denominator will be 5 meaning x would have to be 4.
Make sure your 5 is negative so the whole equation also ends up negative. x/-5=-4/5
Please help me solve this
a waitress sold 17 ribeye steak dinners and 10 grilled salmon dinners, totaling $580.22 on a particular day. Another day she sold 21 ribeye steak dinners and 5 grilled salmon dinners, totaling $582.19 how much did each type of dinner cost.
Answer:
[tex]each \: ribeye \: costs \: \boxed{(r) \to \: \$23.3664} ......................... .. \\ each \: grilled \: salmon \: dinners \: costs \: \boxed{(r) \to \: \$18.29912}[/tex]
Step-by-step explanation:
[tex]let \: ribeye \: be \to \: (r).......................... \\ let \: grilled \: salmon \: dinners \: be \to \: (g) \\ \tt{hence} \to\\ (5) \times 17r + 10g = \$580.22 \\(10) \times 21r + 5g = \$582.19 \\ \to \\ (85r + 50g = 2,901.1) \\ - (minus)\\ (210r + 50g =5,821.9 ) \\ - 125r = - 2,920.8 \\ r = \frac{ -2,920.8 }{ - 125} \\ \boxed{r = \$23.3664} \\ \tt{hence} \to\\17r + 10g = \$580.22 \\ 17(23.3664) + 10g = \$580.22 \\1 0g = \$580.22 - \$397.2288 \\ 10g = \$182.9912 \\ g = \frac{\$182.9912}{10} \\ \boxed{g = \$18.29912}[/tex]
someone pls help:>>
Explanation:
Imagine that you cross out the top-most square for each step of each diagram. The squares not crossed out have the following counts: 1, 4, 9
This is the sequence of perfect squares. So the rule will have us take the number n, and square it to get n^2. Then we add on the squares we crossed out earlier. This explains the "plus 1" at the end to get the answer of n^2+1
Answer:
[tex] {n}^{2} + 1 \\ \: respresents \: the \: following \: \\ function[/tex]
i hope it helped.
8 + 69 + 9
word form