Answers
Answer:
A) 144 feet
[tex]\textsf{B)} \quad h(t)=16t(6-t)[/tex]
Step-by-step explanation:
Part A
Given polynomial:
[tex]h(t)=96t-16t^2[/tex]
where:
h(t) is the height of the debris (in feet).t is the time (in seconds) after the explosion.To find the height of the debris 3 seconds after the explosion, substitute t = 3 into the polynomial and solve:
[tex]\begin{aligned}\implies h(3)& = 96(3)-16(3)^2\\ & = 288 - 16(9)\\ & =288-144\\ & =144 \sf \:\: ft\end{aligned}[/tex]
Part B
To factor the polynomial, rewrite 96 as 6 × 16:
[tex]\implies h(t)=6 \cdot 16t-16t^2[/tex]
Rewrite t² as t × t:
[tex]\implies h(t)=6 \cdot 16t-16t \cdot t[/tex]
Factor out the common term 16t:
[tex]\implies h(t)=16t(6-t)[/tex]
Check
Substitute t = 3 into the factored expression:
[tex]\begin{aligned}h(3) & = 16(3)(6-3)\\& = 16(3)(3)\\& = 48(3)\\& = 144\:\: \sf ft \end{aligned}[/tex]
As the height is 144 ft when t = 3 is substituted into the original polynomial and the factored polynomial, this confirms that the factorization is correct.
Related Questions
solve X-2=7 answer the question pls pls
Answers
Answer:
x = 9
Step-by-step explanation:
x-2 = 7
you solve by adding 2 to both sides to maintain equality. and you add by 2 to cancel out the -2 to isolate the x.
x = 9
if you remove the X with 9 it would be 9-2=7
Identify the radius and the center of a circle whose equation is (x – 5)² + y² = 81.
The radius of the circle is
units.
The center of the circle is at
Answers
Answer:
centre (5,0)
radius:9
I hope it will be helpfulness
Does this graph show a function? Explain how you know.
O A. No; the graph fails the vertical line test.
O B. Yes; there are no y-values that have more than one x-value.
• C. No; there are y-values that have more than one x-value.
O D. Yes; the graph passes the vertical line test.
Answers
Answer:
letter c
Step-by-step explanation:
YOUR LUCKY THAT THIS QUESTION IS IN MY LEARNING & PLEASE NEXT TIME PUT THE GRAPH THAT YOU ARE TALKING ABOUTKEEP ON LEARNINGIs this correct?? If not then whats the answer.
(image below)
Brainly for the first person to answer
this question
Answers
Answer:
fair share
Step-by-step explanation:
all are equal.
Juan is making a fruit salad. He has grapes, watermelon, apples, pineapple, bananas, mangoes, honeydew, and cantaloupe. He wants his fruit salad to contain five different fruits. How many ways can he make the fruit salad if it must contain watermelon?
Answers
The number of ways that he can make the fruit salad if it must contain watermelon is 35.
What is Permutation and combination?Selection of the one object from the given samples with replacement or without replacement is called as the permutation. The selection of the items from the sample as they are different with each other.
The salad contains water melon, now we have to select 4 more fruits out of 7.
Using combination
[tex]^{n{C}_r[/tex] = n! / r! (n-r)!
[tex]^{7}C_4[/tex] = 7!/ 4! (7-4)!
= 7*6*5*4! / 4! * 3*2
= 35
Hence, number of ways that he can make the fruit salad if it must contain watermelon is 35.
Learn more about Permutation and combination here:
brainly.com/question/11732255
#SPJ1
Answer: 35 on edge got it right
Step-by-step explanation:
Explain what happens when you have an exponent to the power of another exponent.
Answers
Answer:
The "power rule" tells us that to raise a power to a power, just multiply the exponents. Here you see that 52 raised to the 3rd power is equal to 56.
Step-by-step explanation:
If m/BAD = 22°,
what is X?
A
C
22⁰
B
D
Answers
180 - 44 = 136
x is 136°.
Answer:
x = 136
Step-by-step explanation:
x = 180 - 22 - 22
= 136
Who is credited with creating an alphabet for several Slavic languages?
Answers
Answer:
the credit goes to create slavic language isSt. Cyril (or Constantine) and St. Methodius.
St. Cyril ( or Constantine) and St. Methodius are credited with creating an alphabet for several Slavic languages.
Here,
We have to find, Who is credited with creating an alphabet for several Slavic languages.
Who was Slavs?
Slavs are Indo-European people who speak the various Slavic languages of the larger Balto-Slavic linguistic group.
Now,
St. Cyril ( or Constantine) and St. Methodius are credited for creating an alphabet for several Slavic languages.
Learn more about the Slavic languages visit:
https://brainly.in/question/27181701
#SPJ6
In a basket, there are 52 apples or pears. The number of apples is 8 more than the number of
pears. How many numbers of apples and pears in the box?
Answers
Answer:
44 pears and 52 apples
Step-by-step explanation:
pears are 8 more than apple so 52-8 = 44
Number of apples and pears in a box is equals to [tex]30[/tex] and [tex]22[/tex] respectively.
What is number?" Number is defined as the count of any given quantity as per given condition."
According to the question,
Given,
Total number of apples [tex]= 52[/tex]
[tex]'x'[/tex] represents the number of pears
[tex]'x+ 8'[/tex] represents the number of apples
As per the given condition required equation we get,
[tex]x + x + 8 = 52\\\\\implies 2x = 52-8\\\\\implies x = \frac{44}{2} \\\\\implies x = 22[/tex]
number of pears [tex]= 22[/tex]
number of apples [tex]= 22+8[/tex]
[tex]=30[/tex]
Hence, number of apples and pears in a box is equals to [tex]30[/tex] and [tex]22[/tex] respectively.
Learn more about number here
https://brainly.com/question/17429689
#SPJ2
are any of these answers correct?
Of all video game players, 1/8 are men over age 50 and 2/5 are women. what fraction represents men younger than 50 years old?
13/40 are men under 50
21/40 are men under 50
17/40 are men under 50
23/40 are men under 50
please helm me out!
Answers
Answer:
19/40
Step-by-step explanation:
⅛ over 50
⅖ women
5 x 8 = 40
8 x 2 = 16
1 x 5 = 5
16 + 5 = 21
40 - 21 = 19
19/40
Answer:
19/40 are men under 50
Step-by-step explanation:
Given:
2/5 of all video game players are women1/8 of all video game players are men[tex]\begin{aligned}\textsf{Men under 50 yrs old} & = \textsf{total proportion of men} - \textsf{proportion of men over 50}\\\\& = \left(1-\dfrac{2}{5}\right)-\dfrac{1}{8}\\\\& = \dfrac{3}{5}-\dfrac{1}{8}\\\\& = \dfrac{3 \cdot 8}{5 \cdot 8}-\dfrac{1 \cdot 5}{8 \cdot 5}\\\\& = \dfrac{24}{40}-\dfrac{5}{40}\\\\& = \dfrac{19}{40}\end{aligned}[/tex]
To check this, let's assign a number to the total number of players and use this to help us calculate the proportion of players who are men under 50 years old.
Let the total number of video game players be 400.
If 2/5 of all video game players are women, then the proportion of all video game players that are men is: 1 - 2/5 = 3/5
⇒ total number of men = 3/5 of 400 = 3/5 × 400 = 240
If 1/8 of all video game players are men over 50 years old then:
⇒ number of men over 50 yrs old = 1/8 × 400 = 50
Therefore:
⇒ number of men under 50 yrs old = 240 - 50 = 190
Finally, the fraction of men under 50 years old from all video game players is the number of men under 50 divided by the total number of men.
⇒ men under 50 years old = 190/400 = 19/40
If a gas filled balloons rises 40 feet in the 1 minutes, 60 feet in the 2 minute, and 80 feet in the 3 minute, how many feet will the balloon rise during the 15 minute
Answers
Answer:
600
Step-by-step explanation:
15*40=600
An adult male cheetah runs at a speed of 26 mph. That is 30% faster than his average last month. How fast did the male cheetah run last month?
Sadie makes 1.5 liters of iced tea. She pours of a liter into a pitcher to take to her neighbor. Her sister drinks of the remaining iced tea. How much tea does Sadie’s sister drink?
Answers
An expression is defined as a set of numbers, variables, and mathematical operations. The male cheetah's average speed for the last month is 20 mph.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
A.) Let the male cheetah's average speed for the last month be represented by x.
Given the male cheetah runs at a speed of 26 mph, that is 30% faster than his average last month.
x + 30% of x = 26 mph
1.30x = 26
x = 20 mph
Hence, the male cheetah's average speed for the last month is 20 mph.
B.) Sadie makes 1.5 liters of iced tea. She pours a liter into a pitcher to take to her neighbor. Her sister drinks the remaining iced tea. Therefore,
Iced tea Sadie's sister drink = 1.56 liters - 1 liter = 0.56 liter
Hence, the amount of tea Sadie’s sister drinks is 0.56 liters.
Learn more about Expression:
https://brainly.com/question/13947055
#SPJ1
Using the following image, solve for JI.
J
2x + 28
x + 22
5
H
Answers
In the given image, the length of JI is 6
Solving linear equationsFrom the question, we are to solve for JI
From the given image, we can write that
JI + IH = JH
Then,
2x + 28 + 5 = x + 22
Solving for x
2x + 28 + 5 = x + 22
First, collect like terms
2x - x = 22 - 28 - 5
Simplifying
x = -11
But,
JI = 2x + 28
∴ JI = 2(-11) + 28
JI = -22 + 28
JI = 6
Hence, the length of JI is 6
Learn more on Linear equations here: https://brainly.com/question/27979747
#SPJ1
Tom sees an enormous thundercloud approaching
from the west. He sees a lightning flash at the top
of the cloud and hears thunder 15 seconds later. His
angle of sight to the top of the cloud is 65°. How
high is the top of the thundercloud off the ground?
Sound takes 5 seconds to travel 1 mile.
Answers
Using the slope concept, it is found that the thundercloud is 6.43 miles above the ground.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem, we have that:
The angle is of 65º.The vertical distance is the height h.The horizontal distance is of 3 miles, as the sound takes 5 seconds to travel 1 mile, and it took 15 seconds.Hence:
tan(65º) = h/3.
h = 3 x tan(65º)
h = 6.43 miles.
The thundercloud is 6.43 miles above the ground.
More can be learned about the slope concept at https://brainly.com/question/18090623
#SPJ1
Eugenia rolls a six-sided number cube. What is the probability that she gets a number greater than 4? A. 1/6 B. 1/3 C. 2/3 D. 5/6
Answers
The probability that she gets a number greater than 4 is 1/3
How to determine the probability?A six-sided number cube has the following properties:
Faces = 6
Numbers greater than 4 = 2
The probability that she gets a number greater than 4 is calculated as:
P = 2/6
Simplify
P =1/3
Hence, the probability that she gets a number greater than 4 is 1/3
Read more about probability at:
https://brainly.com/question/25870256
#SPJ1
please help me with my math
Answers
Answer:
x=115⁰
z=27⁰
Step-by-step explanation:
65+x=180 -> Due to same side interior being equal to 180 degrees
x= 115
x = 3z + 34 -> opposite interior being equal
115 = 3z + 34
81 = 3z
divide by 3 on both sides
z=27
Step-by-Step Solution:
We know, Adjacent or Consecutive Interior Angles are Supplementary and Alternate Interior Angles are Equal.
So,
=> x + 65 = 180 (Adjacent interior angles)
=> 3z + 34 = x (Alternate interior angles)
First solve Equation 1 :-
x + 65 = 180
x = 180 - 65
=> x = 115
Therefore, x = 115.
Now we got the value of ‘x’. Substitute this value in Equation 2 to find the value of ‘z’ hence completing our answer.
Substitute value of ‘x’ in Equation 2 :-
3z + 34 = x
3z + 34 = (115)
3z = 115 - 34
3z = 81
z = 81/3
=> z = 27
Therefore, z = 27.
Now we have the required answers.
Hence, x = 115 and z = 27.
Pls answer fast
(√3 + √11)² + (√3 - √11)²
Answers
(√3 + √11)² + (√3 - √11)²
(a+b)² = a² + b² + 2ab ( a - b )² = a² + b² - 2abNow ,
(√3 + √11)² + (√3 - √11)²
(3 + 11 + 2√3√11)+ (3 +11 - 2√3√11)
14 + 2√33+ 14 - 2√33
14 + 14 = 28
Hence , The value of (√3 + √11)² + (√3 - √11)² is 28 .
Answer:
28
Step-by-step explanation:
(a + b)² + (a - b)² = 2a² + 2b²
(√3 + √11)² + (√3 - √11)²
= 2√3² + 2√11²
= 28
A computer system is priced at $3200. A man buys
the computer system on hire purchase according
to the following terms: a down payment of $480
and the remaining to be paid in monthly
instalments over 2 years at a simple interest rate of
9.5% per annum.
(i) Find his monthly instalment.
(ii) Find the total amount the man pays for the
computer system.
(iii) How much more does he have to pay
for
buying the computer system on hire purchase?
dollar
Answers
(i) Monthly installment is $21.53 approximately.
(ii) Total amount man has to pay is $3716.8
(iii) Extra money he had to pay for buying the computer on hire is $516.8
Given,
Initial price of the computer(p) = $3200
Down payment = $480
Time period = 2 yrs
rate percent = 9.5%
(i) Monthly installment = ?
monthly installment =(capital amount × interest rate)/time in months
down payment to be paid = 3200 ₋ 480
= 2720
therefore, monthly payment = 2720 × 9.5 × 1/ 12
= $21.53
(ii) Total amount man has to pay = ?
= down payment ₊ remaining amount ₊ (remaining amount × t × r)
= 480 ₊ 2720 ₊ 2720 × 9.5 × 2
= $3716.8
(iii) If he buys the computer on hire then how much more he has to pay = ?
= total amount ₋ initial cost
= 3716.8 ₋ 3200
= $516.8
Hence the man has to pay $21.23 as a monthly installment, $3716.8 as a total cost of the computer system and $516.8 as an extra amount if he buys it on hire.
Learn more about "Interest rate problems" here-
brainly.com/question/2151013
#SPJ10
Estimate the sum of the decimals below by rounding to the nearest whole number. Enter your answer in the space provided
Answers
Answer:
18
Step-by-step explanation:
closest whole numberd are 5, 8 and 5. 5 + 5 = 10 + 8
= 18.
Solve: −0.06+7.6p<−127.74
A. p<−42.6
B. p<−34.57
C. p>−16.8
D. p<−16.8
Answers
Answer:
D
Step-by-step explanation:
- 0.06 + 7.6p < - 127.74 ( add 0.06 to both sides )
7.6p < - 127.68 ( divide both sides by 7.6 )
p < - 16.8
what is 52 + 6 × (5 − 3) − 10⁄2 =
Answers
Answer: 59
Step-by-step explanation:
Order of operations.
52+6x(2)-5
52+12-5
64-5
59
Step-by-step explanation:
52+6×2-10/2
52+6×2-10÷2
52+6×2-5
52+12-5
64-5 =59
my answer is 59.
Which is the simplified form of x-12?
O 12
O
O
*12
12
17/7/22
Answers
Applying the negative exponent rule, the simplified form of [tex]x^{-12}[/tex] is: [tex]\frac{1}{x^{12}}[/tex].
What is the Negative Exponent Rule?The negative exponent rule states that, if [tex]x^{-a}[/tex] then, it can be rewritten as, [tex]\frac{1}{x^a}[/tex].
Given the expression, [tex]x^{-12}[/tex], we can apply the negative exponent rule to rewrite the expression in simplified form as:
[tex]\frac{1}{x^{12}}[/tex].
Therefore, expressing [tex]x^{-12}[/tex] in a simplified form will give us: [tex]\frac{1}{x^{12}}[/tex].
Learn more about the negative exponent rule on:
https://brainly.com/question/11975096
#SPJ1
When water flow in two Hoses. The first is four times the second's speed, what is the ratio of the radius of the first to the second?
Answers
Answer:
4:1
Step-by-step explanation
this should be the answer from how u gave the question, also can i get brainliest ;)
True or false: The factor by which a row operation changed the determinant is equal to the determinant of the elementary matrix corresponding to that row operation.
Answers
The given statement is false.
What is the effect of a row operation on a determinant?
The factor by which a row operation intends to change the determinant is not equal to the determinant of the elementary matrix corresponding to that row operation. Rather, when a row is scaled up by a factor in a matrix, the determinant of that matrix also scales up by that factor.
Similarly, the factor by which a row operation changes the determinant is equal to the factor times the determinant of the elementary matrix corresponding to that row operation.
Learn more about a matrix here:
https://brainly.com/question/9967572
#SPJ4
Which expressions are equivalent to2 ( -6c+3) +4c
Answers
Answer:
-8c+6
Step-by-step explanation:
2(-6c+3)+4c = -12c+6+4c = -8c+6
100 PTS!! PLEASE HELP! OVER DUE
Answers
Answer:
[tex]-\frac{1}{2} \vec {c}[/tex]
Step-by-step explanation:
Look at the component form of each vector.
Note that vector c is <4,4> and vector d is <-2,-2>
If one imagined the line that contained each vector, the line for both would have a slope of 1, because [tex]\frac{4}{4}=1=\frac{-2}{-2}[/tex]
Since they have the same slope they are parallel, but since they are in opposite directions, we often call them "anti-parallel" (simply meaning parallel, but in opposite directions).
If two vectors are parallel, one vector can be multiplied by a scalar to result in the other vector. This means that there is some number "k", such that [tex]k \vec{c} = \vec {d}[/tex], or equivalently, [tex]kc_x=d_x[/tex] and [tex]kc_y=d_y[/tex].
If [tex]kc_x=d_x[/tex] and [tex]kc_y=d_y[/tex], we just need to substitute known values and solve for k:
[tex]kc_x=d_x\\k(4)=(-2)\\k=\dfrac{-2}{4}\\k=-\frac{1}{2}[/tex]
Double checking that k works for the y-coordinates as well:
[tex]kc_y=d_y[/tex]
[tex](-\frac{1}{2}) (4)[/tex] ? [tex](-2)[/tex]
[tex]-2=-2 \text{ } \checkmark[/tex]
So, [tex]-\frac{1}{2} \vec {c} = \vec {d}[/tex]
Answer:
Step-by-step explanation:
Look at the component form of each vector.
Note that vector c is <4,4> and vector d is <-2,-2>
If one imagined the line that contained each vector, the line for both would have a slope of 1, because
Since they have the same slope they are parallel, but since they are in opposite directions, we often call them "anti-parallel" (simply meaning parallel, but in opposite directions).
If two vectors are parallel, one vector can be multiplied by a scalar to result in the other vector. This means that there is some number "k", such that , or equivalently, and .
If and , we just need to substitute known values and solve for k:
Double checking that k works for the y-coordinates as well:
?
So,
Please help if you can
Answers
Wkwkkekekwkwkkskskwkw
any
ete the equivalent ratio table.
D
B
(Equivalent Ratio
21
35
20 50
27
70
12:13
17:5
23
S
9
11
2
18
22
Answers
Answer:
????????????????????????????????????????/
Step-by-step explanation:
Use graphing to determine the solution to the system of linear equations x=-1 y=3x+1
Answers
At x = -1 the value of y will be equal to -2 for the equation y = 3x + 1.
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given that:-
The system of linear equations x=-1 and y=3x+1.The equation will be solved as:-
Y = 3x + 1
Y = 3 ( -1 ) + 1
Y = -3 + 1
Y = -2
I have also plotted the graph of the two equations in the graph the two equations intersect at the point x = 1 and y = -2 so the solution of the equations will be ( -1, -2 ).
Therefore At x = -1 the value of y will be equal to -2 for the equation y = 3x + 1.
To know more about equations follow
https://brainly.com/question/2972832
#SPJ1
NEED HELP ASAP!!!!!
Triangle ABC and DEF are similar. Answer the following questions:
a. What relationship can you write for the angles of these two triangles?
b. What is the length of the missing side?
Answers
Answer:
a)<BAC = EDC,<DEC =ABC,ACB=DFE
b)7
Step-by-step explanation:
According to the definition, two triangles are similar if their corresponding angles are congruent and corresponding sides are proportional. Hence, we can find the dimensions of one triangle with the help of another triangle. If ABC and DEF are two similar triangles, then by the help of below-given formulas, we can find the relevant angles and side lengths.
∠A = ∠D, ∠B = ∠E and ∠C = ∠F
AB/DE = BC/EF= AC/DF