Using the vertex of the quadratic equation, it is found that a maximum height of 78.75 feet is reached after 2.13 seconds.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]
Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the height is modeled by:
h(t) = -16t² + 68t + 6.5.
The coefficients are a = -16, b = 68, c = 6.5, and the vertex will be given by:
[tex]x_v = -\frac{b}{2a} = -\frac{68}{-32} = 2.13[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a} = -\frac{68^2 - 4(-16)(6.5)}{-64} = 78.75[/tex]
A maximum height of 78.75 feet is reached after 2.13 seconds.
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If the given is DEFG is a kite how do I prove that triangle EFH is congruent to triangle GFH
Answer:
They both have H hoel
Step-by-step explanation:
\
Tyrell and Marianne start at the same point. Tyrell walks 2.5 miles north in a straight path. Marianne walks 6.0 miles east in a straight path. How many miles apart are they at the end of their walks rounded to the nearest hundredth mile?
Answer: 6.5 is the answer.
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPPPPP ASAP
Answer:
The answers are D and then B.
Step-by-step explanation:
The first question asks which team has the youngest members on average. This is easily answered because the "mean" is simply the average of all the ages. Therefore the youngest "mean" age will also have the youngest members on average.
The second question asks what team has the most variability in ages. Range is the difference between the highest and lowest number. Therefore the team with the highest range should, logically, also have the most variability.
Yo I need to bring up my math grade bad so
y>-x+1
(please show it graphed already :D)
Answer:
Step-by-step explanation:
Hakeem has a points card for a movie theater. he receives 45 rewards points just for signing up. he earns 11. 5 points for each visit to the movie theater. he needs 206 points for a free movie ticket. how many visits must hakeem make to earn a free movie ticket?
Answer:
14visists
Step-by-step explanation:
206 points= 45points + 11.5points(number of visits)
let number of visits=x
206points-45points=11.5x
161=11.5x
x=161/11.5
x=14 visits
Which value represents |26|?
OA) -26
OB) O
OC) 26
OD) 126
Find the surface area of the prism.
9 m
5 m. 12m
Answer:
the surface area of the prism is equal to 202 m^2
Step-by-step explanation:
The surface area of the prism is equal to
SA=2B+Ph
where
B is the area of the base
P is the perimeter of the base
h is the height of the prism
Find the area of the base B
B=LW=4*5=20m^2
Find the perimeter of the base P
P = 2(L+W) = 2 (4+5) = 18 m
Find the surface area ---->
SA = 2B + Ph = 2(20) + 18(9) = 202 m^2
btw m^2 is stand for square meter, also called the meter squared! (just if ur wondering)
This table gives a few (x,y)(x,y)left parenthesis, x, comma, y, right parenthesis pairs of a line in the coordinate plane.
xxx yyy
-94−94minus, 94 242424
-74−74minus, 74 181818
-54−54minus, 54 121212
What is the xxx-intercept of the line?
((left parenthesis
,,comma
))
From the linear function formed by the points given in the table, it is found that the x-intercept is of -14.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem, when x increases by 20, y decays by 6, hence the slope is given by:
[tex]m = -\frac{6}{20} = -0.3[/tex]
Then:
y = -0.3x + b.
When x = -54, y = 12, hence:
y = -0.3x + b
12 = -0.3(-54) + b.
b = -4.2.
Thus, the equation is:
y = -0.3x - 4.2.
The x-intercept is the value of x when y = 0, hence:
-0.3x - 4.2 = 0.
x = -4.2/0.3
x = -14
More can be learned about linear functions at https://brainly.com/question/24808124
Answer:
Step-by-step explanation:
rate plsss
How many rearrangements are there of the letters in the word "great?"
Evaluate the expression for x = 3 and y = 6.
5(x2 + y) + y2
Answer:
48
Step-by-step explanation:
5(x2+y)+y2
5 x (3 x 2 + 6) + 6 x 2
5 x 6 + 6 + 6 x 2
30 + 6 + 6 x 2
30 + 6 + 12
36 + 12 = 48
Solve for x and round to the nearest tenth for both (please:) )
Answer:
see explanation
Step-by-step explanation:
using the sine ratio in the right triangle.
sin23° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{7}[/tex] ( multiply both sides by 7 )
7 × sin23° = x , then
x ≈ 2.7 ( to the nearest tenth )
----------------------------------------------------
using the tangent ratio in the right triangle
tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{27}{17}[/tex] , then
x = [tex]tan^{-1}[/tex] ( [tex]\frac{27}{17}[/tex] ) ≈ 57.8° ( to the nearest tenth )
The owner of a video game store creates the expression −2x2 28x 20 to represent the store's weekly profit in dollars, where x represents the price of a new video game. choose the equivalent expression that reveals the video game price that produces the highest weekly profit, and use it to determine that price. −2(x − 7)2 118; x = $7 −2(x − 7)2 118; x = $118 −2(x2 − 14x) 20; x = $14 −2(x2 − 14x − 10); x = $10
The given expression is equivalent to [tex]\rm -2(x-7)^2+118[/tex]price is $7 option first is correct.
What is a quadratic expression?A quadratic expression is a second-degree algebraic expression represented by the:
[tex]\rm ax^2+bx+c=0[/tex] ........(1)
Where a, b, and c are the constants and
We have a quadratic expression:
[tex]\rm f(x)=-2x^2+28x+20[/tex]
Convert it to perfect square by perfect square trinomial:
[tex]\rm f(x)=-2(x^2+14x)+20[/tex]
[tex]\rm f(x)=-2(x^2+14x+49-49)+20[/tex] (adding and subtracting by 49)
[tex]\rm f(x)=-2(x-7)^2+2(49)+20[/tex]
[tex]\rm f(x)=-2(x-7)^2+118[/tex]
Here [tex]\rm (x-7)^2[/tex] is the positive term and -2 is the negative term so in order to get the highest weekly profit it should be zero, so
[tex]\rm -2(x-7)^2=0[/tex]
x = $7
Thus, the given expression is equivalent to [tex]\rm -2(x-7)^2+118[/tex] and the price is $7.
Learn more about quadratic expression here:
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Answer:
First option A. −2(x − 7)^2 + 118; x = $7
Step-by-step explanation:
Took the test and it's correct, trust me :)
Mr. Red's first year salary is $30,000 and it increases by $500 each year. What is the explicit rule for this sequence in simplified form?
Question 1 options:
an=29,500(n)+500
an=500(n)+29,999
an=500(n)+29,500
an=500(n)+30,000
Mr. Red's salary is an illustration of an arithmetic sequence
The explicit rule of Mr. Red's salary is an = 500n + 29500
How to determine the explicit formula?Mr. Red's salary is an arithmetic sequence with the following parameters:
First term, a1 = 30000
Common difference, d = 500
The explicit rule is calculated as:
an = a1 + (n - 1) * d
This gives
an = 30000 + (n - 1) * 500
Evaluate the product
an = 30000 - 500 + 500n
This gives
an = 29500 + 500n
Rewrite as:
an = 500n + 29500
Hence, the explicit rule of Mr. Red's salary is an = 500n + 29500
Read more about arithmetic sequence at:
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which statement is true about credit cards?
Answer:
it doesnt say any statement at all can you add them
how to find the area of a circle
A=πr²
where
π -> pi (3.14...)
r - radius
r² means you multiply r times itself
Hope it helps!
1. The sample mean weight of 100 chimpanzees was measured to be 82.4 pounds, with a standard deviation of 12.6 pounds. Using a 1% level of significance, what could we claim about the population mean weight for all chimpanzees so that it will fail to be rejected?
Using the t-distribution, as we have the standard deviation for the sample, we could claim that the mean weight in pounds is in the interval (79.1, 85.7).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 100 - 1 = 99 df, is t = 2.6259.
The other parameters have values given by:
[tex]\overline{x} = 82.4, s = 12.6, n = 100[/tex].
We could claim that the mean is any value in the 99% confidence interval, which has bounds given by:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 82.4 - 2.6259\frac{12.6}{\sqrt{100}} = 79.1[/tex]
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 82.4 + 2.6259\frac{12.6}{\sqrt{100}} = 85.7[/tex]
More can be learned about the t-distribution at https://brainly.com/question/16162795
Since spring started, Kareem has been surveying the growth of leaves on his neighborhood trees. He goes out every day and computes the average number of leaves on a sample of trees. He created a scatter plot where the y-axis represents the average number of leaves on the trees, and the x-axis represents the number of weeks since spring started. Use the 2 given points to write a linear equation that can be used to approximate the data distribution.
Answer:
y = 1566.67x + 1716.67
is the actual answer..
The linear equation that can be used to approximate the data distribution is y = 1566.67x + 1716.67.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Given two points on the line.
(0.5, 2500) and (3.5, 7200)
Slope intercept form of a linear equation is y = mx + c, where m is the slope and c is the y intercept.
Slope = (7200 - 2500) / (3.5 - 0.5)
= 4700 / 3
= 1566.67
So the equation is, y = 1566.67x + c
Substitute the point (0.5, 2500) to the equation.
2500 = (1566.67 × 0.5) + c
c = 1716.67
So the equation is, y = 1566.67x + 1716.67
Hence the required equation is y = 1566.67x + 1716.67.
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#SPJ2
Ex. 1 Write an equation in slope-intercept form for the line that passes through (3, 8) and is
perpendicular to the line with equation y = -1/3x+8
Answer:
Step-by-step explanation:
The line perpendicual to a reference line will have a slope that is the negative inverse of the reference line. In this case, the reference line is y= -(1/3)X+8, with a slope of -(1/3). The negative inverse would be 3. So the new line would have the form:
y = 3x + b
To find b, the y-intercept, use the given point and solve for b:
y = 3x + b
or 8 = 3*3 + b for the point (3,8)
8=9+b
b= -1
Thje equation of the line perpendicualr to the reference line and going through point (3,8) is:
y = 3x - 1
See attached graph.
In the relation (a+c)^2=t make C the subject
Answer:
See below
Step-by-step explanation:
(a+c)^2 = t
(a+c) = sqrt t
c = sqrt(t) - a
Solve for xx. Round to the nearest tenth, if necessary.
sin U= |TS| / |US|
-> |US| = |TS| / sinU
-> x= 0.6 / sin 37°
-> x≈1,0
Is this correct please give correct answer but no links
Answer:
I give answers I think their correct but as humans we make mistakes so there may be errors
Pls help pls pls ple
Answer:
10.5 ft
Step-by-step explanation:
This problem is using scaling.
Basically:
2.5(RV) = WZ
Meaning our scale factor is 2.5.
Multiply 4.2 * 2.5
Your answer is 10.5 ft.
What is the answer to -50 +x<-35
Answer:
x < 15
Step-by-step explanation:
1) Regroup terms.
⇒ x - 50 < - 35
2) Add 50 to both sides.
x < - 35 + 50
3) Simplify - 35 + 50 to 15.
x < 15
Answer:
x < 15
Step-by-step explanation:
-50 + x < -35
+50 +50
________________
x < 15
Hope this helps :)
5. The relationship between temperature in degrees Fahrenheit and degrees Celsius is
shown in the graph below
SAT math scores for a particular year are normally distributed with a mean of 510 and a standard deviation of 80.
What is the probability that a randomly selected score is greater than 590? Enter the numerical answer only (no percent sign).
Using the normal distribution, it is found that there is a 16% probability that a randomly selected score is greater than 590.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In this problem, the mean and the standard deviation are, respectively, given by [tex]\mu = 510[/tex] and [tex]\sigma = 80[/tex].
The probability that a randomly selected score is greater than 590 is one subtracted by the p-value of Z when X = 590, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{590 - 510}{80}[/tex]
Z = 1
Z = 1 has a p-value of 0.84.
1 - 0.84 = 0.16.
0.16 = 16% probability that a randomly selected score is greater than 590.
More can be learned about the normal distribution at https://brainly.com/question/24663213
Use the properties of logarithms to write the logarithm in terms of
log5(2) and log5(3).
log5(12)
[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_5(12)\implies \log_5(4\cdot 3)\implies \log_5(2^2\cdot 3) \\\\\\ \log_5(2^2)~~ + ~~\log_5(3)\implies 2\log_5(2)~~ + ~~\log_5(3)[/tex]
The pilot of a small plane is flying at an altitude of 2000 ft- The pilor plans to start the final descent toward a runway when the horizontal distance between the plane and the runway is ? mi. To the nearest degree what will be the angle of depression 19 from the plane to the runw'y at this point?
Using the slope concept, supposing the horizontal distance is of 1500 feet, the angle of depression will be of 37º.
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 suppose an horizontal distance of 1500 feet, with a vertical distance of 2000 feet, hence:
[tex]\tan{\alpha} = \frac{1500}{2000}[/tex]
[tex]\alpha = \tan^{-1}{\left(\frac{1500}{2000}\right)}[/tex]
[tex]\alpha = 37^\circ[/tex]
The angle of depression will be of 37º.
More can be learned about the slope concept at https://brainly.com/question/18090623
Will mark brainly!!! Please help me with this. Thank you! :)
Can you please explain how you get the answer. I really appreciate it!!!
5510 ÷ 27 with remainder
Answer:
204, there is no remainder.
Step-by-step explanation:
Answer: 204 Rem 2
Step-by-step explanation: Use long division
find a, b, and c please and thank u
