Essentially, when it's asking "find the maximum height and the time it occurs at," it wants you to use the vertex formula. This is a formula that gives you the x-coordinate of the vertex, or the maximum or minimum height of a parabola.
x-coord of vertex = \(\frac{-b}{2a}\)
A quadratic equation is structured with 3 parts
for this one, a = -16, b = 104, c = 5
finding the x-coord just plug those into the formula
\(-\frac{104}{2(-16)}\)
simplify to
- 104/ - 36
negative cancels
104/32
at time = 13/4, there is a relative maximum.
to find its height, just plug that value into your calculator using the original equation
plugging in t = 13/4 yields a value of 174
Coords of rel. max. (13/4 , 174)
What is the property of 22•1-22?
the expression 22 • 1 - 22 demonstrates the Distributive Property, and the result is 0. The property that is being demonstrated in the expression 22•1 - 22 is the Distributive Property of Multiplication over Addition (or Subtraction).
The Distributive Property states that when you multiply a number by the sum (or difference) of two or more numbers, you can distribute the multiplication across each term inside the parentheses.
In this case, the expression is:
22 • 1 - 22
We can distribute the multiplication as follows:
(22 • 1) - (22)
Since any number multiplied by 1 is equal to itself, we get:
22 - 22
And finally, when you subtract a number from itself, the result is always zero:
22 - 22 = 0
So, the expression 22 • 1 - 22 demonstrates the Distributive Property, and the result is 0.
To know more about Property:
https://brainly.com/question/26683487
#SPJ3
Rectangle A measures 9 inches by 3 inches. Rectangle B is a scaled copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B.
OPTIONS:
A: 13.5 inches by 4.5 inches
B: 90 inches by 30 inches
C: 4.5 inches by 1.5 inches
D: 8 inches by 2 inches
E: 10 inches by 4 inches
Answer:
A, B and C
Step-by-step explanation:
A: A is. If you multiply both numbers by 1.5 you get
9*1.5 = 13.53*1.5 = 4.5B is. If you multiply 9 by 10 and 3 by 10 you
9*10 = 903*10 = 30C is. If you multiply 9 by 0.5 and 3 by 0.5 you get
9*0.5 = 4.53*0.5 = 1.5D and E don't work.
PLS HELP IF U TAKE THE POINTS IM REPORTING U
QUESTION IN PIC
Quadrilateral ABCD has the following angle measures: m∠A = ?°, m∠B = 97°, m∠C = 47°, m∠D = 90° What is m∠A?
Answer:
m<A is 126 degrees
Step-by-step explanation:
Assuming that the whole entire quadrilateral is 360 degrees, I can say that part A is 126 degrees.
Item 4
Find the surface area of the prism.
The surface area is
a
square feet.
Answer:
xnxnxnzznchamschdntjekdfurnthsjdnfjdjdjdkdkr
Step-by-step explanation:
xmxmxnxmxmxnxmxnxndmsndfhakxufmrjdkxddjrf7sjrifxisufkf8dhrkfdkshgshdbfjdddnfjfkdnfmcmcmdmdkfkfkkfdkfkfkfkfkfkfkfkkfkfkfkfkfkdkdkdmdkdkdkdkdmdmrmddmrm1520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126
The high temperature for one town last year was 79°F The low temperature for the same town was - 3°F What was the difference between the high and low
temperatures for the town last year.
Answer:
79°c - (-3°c) = 82°c
Step-by-step explanation:
this is because we need to calculate the total gap between those numbers through number line. I have attached the photo, have a look over there.
10. Suppose y = x2 - 2x - 3. What is a linear equation that intersects the graph of
y=x²-2x-3 in exactly two places? Name the two points of intersection.
well, let's pick any two random x-values on the quadratic, hmmm say let's use x = 4 and x = 7, so hmm f(4) = 5 and f(7) = 32, that'd give us the points of (4, 5) and (7 , 32).
To get the equation of any straight line, we simply need two points off of it, let's use those two above.
\((\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{32}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{32}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{4}}} \implies \cfrac{ 27 }{ 3 } \implies 9\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{ 9}(x-\stackrel{x_1}{4}) \\\\\\ y-5=9x-36\implies {\Large \begin{array}{llll} y=9x-31 \end{array}}\)
Check the picture below.
Refer to the attached images.
4) Graph f(x) 2(3)*. Compare the graph to the
graph of the parent function. Describe the domain
and range of f.
Answer it is 65
Step-by-step explanation:
What is the measure of arc QSR?
Answer:
i need a picture for this problem.
Step-by-step explanation:
Answer:
250°
Step-by-step explanation:
Got it right on edge
Solve the following word problem. (4 pts)
6. Ava's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3
student tickets and 3 adult tickets for a total of $45. On the second the school sold 6 student tickets
and 11 adult tickets and took in a total of $130. What is the price of a student and an adult ticket?
Answer:
student = $7 ; adults = $8
Step-by-step explanation:
3s + 3a = 45
6s + 11a = 130
s + a = 15
s = 15 - a
6(15-a) + 11a = 130
90 - 6a + 11a = 130
5a = 130 - 90
5a = 40
a = 40/5
a = 8
s = 15 - 8
s = 7
At the beginning of the summer, Jenna had saved $166. To earn money over the summer, she is working part time at the local
community center. She will earn $23 per day of work. If x represents the number of days she works, which of the following
equations represents how much money she will have, including her savings?
Jenna will have total money, y= 166 + 23x.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Jenna had saved $166.
She will earn $23 per day of work
If x represents the number of days she works the she will earn
= 23x
So, She will have total
= 166+ 23x
Learn more about Equation here:
https://brainly.com/question/29657992
#SPJ1
CAN ANYONE HELP PELASE THIS IS DUE I need step by step distribution on the math equation
Answer:
Step-by-step explanation:
Use distributive property, then combine like terms. Don't forget if you divide by a negative number you have to reverse the symbol. Very important! See image.
Please answer I am struggling
(For question 1 you have to do it yourself, get a ruler and measure the actual length of the drawing, then multiply it by 8 to get the actual dimensions in the exercise. )
Example, if you measure 4 inches, the actual dimension will be 4 x 8 = 32 ft
2. (Scale drawing 1:5 is that every 1 (length units) will be equal to 5(length units) in the actual dimensions)
Model : 3ft ; 7m
Actual : 15ft ; 35m (corresponding)
Actual : 20yd ; 12.5 cm
Model : 4yd ; 2.5 cm
6. 1.5 ft = 1.5 x 12 = 18 inches.
The model is 3 inches, and the actual rose is 18 inches -> The scale of the drawing is 6. (enlargement)
Same goes to the scale factor, but this time is the quotient of the corresponding side -> 3 : 18 = 1:6.
(If I got any parts wrong just tell me, I actually kinda forgot these kind of stuff)
I need help it ends in 42 minutes.
Answer:
Step-by-step explanation:
Because p is a function of hours.
People are a function of hours.
The middle school is holding a food drive for a local food pantry. If each student commits to bringing 9 cans of food, write an expression for the total number of cans for an unknown number of students, s
The expression for the total number of cans of food would be: 9s
Define the term variable?A variable is a symbol or letter that denotes a possible range of values or quantities. It is used to express relationships between numbers and to solve equations and problems, and is typically represented by a letter like x, y, or z.
A variable's value can be determined by its context of use or by resolving an inequality or equation that it appears in. Variables are frequently used in algebra to represent unknowns or to simplify challenging formulas.
Let's use the variable "s" to represent the number of students participating in the food drive.
Then, the expression for total number of cans of food would be: 9s
This is because each student is committing to bringing 9 cans of food, so if there are "s" students participating, then the total number of cans of food would be 9 times the number of students (9s).
To know more about expression, visit:
https://brainly.com/question/1859113
#SPJ1
Area involving
A rectangular paperboard measuring 35 in long and 24 in wide has a semicircle cut out of it, as shown below.
Find the area of the paperboard that remains. Use the value 3.14 for x, and do not round your answer. Be sure to include the
correct unit in your answer.
24 in
35 in
0
808
in
X
in² in³
The area of the paperboard that remains is 613.92 square inches.
To find the area of the paperboard that remains after a semicircle is cut out, we need to calculate the area of the rectangular paperboard and subtract the area of the semicircle.
The rectangular paperboard has dimensions of 35 inches long and 24 inches wide. Therefore, the area of the rectangular paperboard is:
Area_rectangular = length * width = 35 in * 24 in = 840 in²
Now, let's calculate the area of the semicircle. The semicircle is cut out of the rectangular paperboard, and the diameter of the semicircle is equal to the width of the rectangular paperboard (24 inches).
The formula to calculate the area of a semicircle is:
Area semicircle = (π * r²) / 2
where r is the radius of the semicircle.
Since the diameter of the semicircle is 24 inches, the radius is half of that, which is 12 inches.
Plugging in the values into the formula, we get:
Area_semicircle = (3.14 * 12²) / 2 = (3.14 * 144) / 2 = 226.08 in²
Finally, to find the area of the paperboard that remains, we subtract the area of the semicircle from the area of the rectangular paperboard:
Area remaining = Area rectangular - Area semicircle = 840 in² - 226.08 in² = 613.92 in²
Therefore, the area of the paperboard that remains is 613.92 square inches.
For more questions on area
https://brainly.com/question/25292087
#SPJ8
If ∆ABC≅∆DEF, and AB=15, BC=20, and FE=3x-7, then x=?
Answer:
x= 29
Step-by-step explanation:
Since, ∆ABC is congruent to ∆DEF,
AB= DE....(i)
BC= EF....(ii)
AC= DF....(iii)
From (ii), BC= EF,
So, 3x-7 = 20
3x= 20+7= 27
x= 27/3 = 9
Hope it helps you
From the congruent triangles value of x is 9 units.
Given that, ∆ABC≅∆DEF, and AB=15, BC=20, and FE=3x-7.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Since, ∆ABC is congruent to ∆DEF,
AB= DE --------(I)
BC= EF --------(II)
AC= DF --------(III)
From (II), BC= EF,
So, 3x-7 = 20
3x= 20+7= 27
x= 27/3 = 9 units
Therefore, from the congruent triangles value of x is 9 units.
To learn more about the congruent theorem visit:
https://brainly.com/question/24033497.
#SPJ2
need HELP ON THIS A S AP !!!!!
Answer:
803.84yd²
Step-by-step explanation:
Surface Area of A Sphere: \(A=4\pi r^2\)
We are given the radius of 8 yards.
Using 3.14 for pi:
\(A=4*3.14*8^2\\\\A=4*3.14*64\\\\A=12.56*64\\\\\boxed{A=803.84}\)
The correct answer should be 803.84yd².
Brainilest Appreciated.
Answer:
803.84 yd^2
Step-by-step explanation:
4*3.14*8^2
12.56*64
803.84
brainliest pls
hope i helped
-ZYLYNN
Christina is making a necklace using beads. She has 20 red, 14 blue, 10 purple, 28 green, and 8 yellow beads. She randomly chooses a bead to start the necklace. What is the probability of Christina choosing a purple bead?
Answer:
10/70
Step-by-step explanation:
Please help I’m being timed on this! ://
Write an algebraic rule to describe the translation P(-8,6) ► P(-10,2).
A (x,y) (- 18.y+8)
B. (x,y) → (x+2,y+4)
C. (x,y) → (x +4,y - 2)
D. (x,y) → (x-2,y-4)
Answer:
its going to be D (x,y) - (x-2,y-4)
Step-by-step explanation:
Show that f is continuous on (−[infinity], [infinity]). f(x) = 1 − x2 if x ≤ 1 ln(x) if x > 1
On the interval
(−[infinity], 1),
f is function; therefore f is continuous on
(−[infinity], 1).
On the interval
(1, [infinity]),
f is function; therefore f is continuous on
(1, [infinity]).
The function \($$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$\) is continuous on (-∞, ∞).
As per the given data the function f(x) is given by:
\($$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$\)
Here we have to determine that the function f(x) is continuous on (-∞, ∞)
If we show that f(x) is continuous at x = 1 then f(x) is continuous on (-∞, ∞)
What are continuous function?
A continuous function in mathematics is one where changes in the parameter cause constant changes in the function's value (i.e., a change without a leap). This shows that there are no abrupt changes in value or discontinuities.
To show f(x) is continuous at x = 1
\(\lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1^{+}}\) f(x)
\(\rightarrow \lim _{x \rightarrow 1^{-}} f(x) & =\lim _{x \rightarrow 1^{-}}\left(1-x^2\right) \\\)
= 1 - 1
= 0
\(\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{+}} \ln (x) \\\)
= ln 1
= 0
Therefore \(\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{-}} f(x)-0\).
Hence f(x) is continuous on (-∞, ∞)
For more questions on Limits
https://brainly.com/question/20067425
#SPJ4
VOLUME-Find the Volume of the rectangular prism.
Answer:
144
Step-by-step explanation:
base x length x height
12 x 4 x 3
144
9x + 5 - 3x = 5x - 14
Answer: The answer is x = -19
Answer:
-19
Step-by-step explanation:
9x - 5x -3x = -14 -5
1x = -19
what are the two square roots of 9
Answer:
-3, 3
Step-by-step explanation:
(a) should the fiber be judged acceptable? use the p-value approach. (b) what is the probability of not rejecting the null hypothesis at 0.05 if the fiber has a true mean breaking strength of 102 psi? (c) find a 95% one-sided lower ci on the true mean breaking strength. (d) use the ci found in part (d) to test the hypothesis. (e) what sample size is required to detect a t
The z value is calculated by using the equation (x- μ)/ σ/ √n. Here the true value lies between the confidence interval. So null hypothesis is accepted.
The data which is given are, mean of the sample (x) = 100.6 psi
Standard deviation, σ = 2 psi
Number of specimens tested, n = 9
Let us consider the mean breaking point of yarn of the population = μ
Since it is said that the mean breaking point should at least be 100,
Null hypothesis, H₀ , μ ≥ 100
Alternate hypothesis, H₁ μ < 100
a. Z value = (x- μ)/ σ/ √n = \(\frac{100.6-100}{\frac{2}{\sqrt{9}} }\) = 0.89
So P ( z ≥ 0.89) = 0.1711
If significance level,α is greater than P(z ≥ 0.89), we cannot reject the null hypothesis.
b. If significance level is 0.05
Critical value for the breaking point , (x-μ)/σ/√n = 1.64
\(\frac{x- 100}{\frac{2}{\sqrt{9} } }\) = 1.64
x = 101.093
Z value = \(\frac{101.09-102}{\frac{2}{\sqrt{9} } }\) = -1.378
P(z< -1.378) = 0.0885
Probability of committing type 2 error = 8.85%
c. Required confidence interval level = \(x-z_{0.05}(\frac{2}{\sqrt{n} })\) = \(102-1.64(\frac{2}{\sqrt{9} } )\) = 102 - (1.64× 0.67) = 100.9
d. If true value lies between the two confidence interval, null hypothesis is accepted. Here 100.9 < 102 < α
So null hypothesis is accepted.
For more information regarding probability and z-value kindly refer
https://brainly.com/question/22068540
#SPJ4
The complete question is
The mean breaking strength of yarn used in manufacturing drapery material is required to be at least 100 psi. Past experience has indicated that the standard deviation of breaking strength is 2 psi. A random sample of nine specimens is tested, and the average breaking strength is found to be 100.6 psi.
a) Should the fiber be judged acceptable? Use the P-value approach.
b) What is the probability of not rejecting the null hypothesis at
α=0.05
if the fiber has a true mean breaking strength of 102 psi?
c) Find a 95% one-sided lower CI on the true mean breaking strength.
d) Use the CI found in part (d) to test the hypothesis.
If angle 3 is 54 degrees what is the measure of each angle
Answer:Si es un triangulo y el tercer angulo es de 54 grados los otros dos angulos son de 63 grados
Step-by-step explanation:
180-54= 126
126/2=53
eso si el triangulo es isosceles.
. what is the value of the 30th percentile for the data set? 7 12 3 14 17 20 5 3 17 4 13 2 15 9 15 18 16 9 1 6
The required value of the 30th percentile of the given data set 7 12 3 14 17 20 5 3 17 4 13 2 15 9 15 18 16 9 1 6 is equal to 5.
To find the value of the 30th percentile,
We need to sort the data set in ascending order first,
1, 2, 3, 3, 4, 5, 6, 7, 9, 9, 12, 13, 14, 15, 15, 16, 17, 17, 18, 20
The 30th percentile is the value below which 30% of the data falls.
To find this value, we can use the formula,
P = (n / 100) × x
where P is the desired percentile (30th percentile in this case),
n is the total number of data points,
And x is the rank of the value corresponding to the desired percentile.
Here,
The total number of data points n = 20
x = (30 / 100) × 20
= 6.
This means that the value corresponding to the 30th percentile is the 6th value in the sorted data set, which is 5.
Therefore, the value of the 30th percentile for the given data set is 5.
Learn more about percentile here
brainly.com/question/29113797
#SPJ4
Why are most personal loans much smaller than mortgages and home equity loans?.
Answer:
Most personal loans are smaller than mortgages and equity loans because the percentage of the interest rate on a home is higher than that of a personal loan.
Step-by-step explanation:
What is remainder when x3 2x² X 1 is divided by x 1?
When x^3+2x^2+x+1 is divided by (x+1) then remainder is 1.
In the given question, we have to find what is remainder when x^3+2x^2+x+1 is divided by (x+1).
To find the remainder there are two ways. First we divide the x^3+2x^2+x+1 by (x+1). Second we find the value of from (x+1) by equating (x+1) equal to zero. The put the value of x in the expression x^3+2x^2+x+1.
In this we ca easily find the remainder.
Now we firstly find the value of x;
(x+1) = 0
Subtract 1 on both side we get;
x= −1
Now put x= -1 in the expression x^3+2x^2+x+1.
x^3+2x^2+x+1 = (−1)^3+2(−1)^2+(−1)+1
x^3+2x^2+x+1 = −1+2−1+1
x^3+2x^2+x+1 = 1
Hence, when x^3+2x^2+x+1 is divided by (x+1) then remainder is 1.
To learn more about division of polynomial link is here
brainly.com/question/29718477
#SPJ4
The right question is:
What is remainder when x^3+2x^2+x+1 is divided by (x+1)?
Maggie buys a dress and a pair of shoes at The Home Store. Before adding the sales tax, she pays $48 for a dress that normally sells for $62 and she pays $34 for a pair of shoes that normally sells for $46. a) Before the sales tax, how much does Maggie save on her purchases by buying at the sale price? Show all work. b) To the nearest percent, what percent discount did Maggie get on her total purchase? Show all work. c) Including a 15% sales tax, what total amount will Maggie pay?
Answer:
a) $26
b) 24.07%
c) $94.3
Step-by-step explanation:
Given that:
Before tax:
Normal price of dress = $62
Discounted price of dress = $48
Normal price of a pair of shoes = $46
Discounted price of a pair of shoes = $34
a) Before the sales tax, total savings = ($64 - $48) + ($46 - $34) = $26
b) Total percentage discount on total sales.
Total bill for original price = $62 + $46 = $108
Percentage discount can be found by the formula:
\(\dfrac{\text{Total discount}}{\text{Total bill for original price}}\times 100\\\Rightarrow \dfrac{26}{108} \times 100 = 24.07\%\)
c) Total amount paid if the sales tax is 15%.
Amount paid with tax = Amount after discount + 15% of amount after discount
Amount after discount = $48 + $34 = $82
15% of $82 = $18.29
Amount paid with sales tax = $82 + $12.3 = $94.3