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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It is given that the volume of a size 5 football is larger than that of a size 4 football by 72.8%.find the ratio of the radius of the size 5 football to that of the size 4 football.
Answer:
6/5
Step-by-step explanation:
Let size 4 football radius = x,
and size 5 football radius = y,
Volume of size 5 = Volume of size 4 × (1 + 0.728)
Using the sphere volume formula,
V = (4/3)πr³
(4/3)πy³ = (4/3)πx³ × (1.728)
y³ = 1.728x³
y = ³√1.728 x
y/x = 6/5
Therefore, ratio of the radius of the size 5 football to that of the size 4 football is 6/5
Answer:
6/5
Step-by-step explanation:
According to the Rational Root Theorem, the following are potential roots of f(x) = 2x2 + 2x – 24.
–4, –3, 2, 3, 4
Which are actual roots of f(x)
Answer:
The answer is 3 and (-4).
Step-by-step explanation:
We are given an equation 2x² + 2x – 24.
Let us assume that the equation is equal to zero.
2x² + 2x – 24 = 0
Now, divide whole equation by 2 we get,
x² + x – 12 = 0
x² + 4x – 3x – 12 = 0
x(x + 4) – 3(x + 4) = 0
(x – 3) (x + 4) = 0
x = 3, -4
Thus, The actual roots of f(x) are 3 and (-4).
Answer:
-4 AND 3
Step-by-step explanation:
find area of rhombus . please./.
Answer: 126
Step-by-step explanation:
Pls help! I really need help! This is the question..
A sample of iron has dimensions of 2 cm x 4 cm x 6 cm and a mass of 100g. What is the density of the sample?
Answer:
2.083 g/[tex]cm^{3}[/tex]
Step-by-step explanation:
Density is mass / volume
volume = length * width * height
(In this case since iron is usually in a block unless stated otherwise)
100g / (2*4*6)cm^3 = density
100g / [tex]48 cm^{3}[/tex] = 2.083 g/[tex]cm^{3}[/tex]
What is the volume of the cardboard container
i need help with this
Two independent variables that can affect the cost of the supplies are:
x = number of pencils bought.y = number of notebooks bought.What is an independent variable?An independent variable is a variable that can change freely.
For example in the given situation, we could define the independent variables:
x = number of pencils bought.y = number of notebooks bought.Notice that these variables are independent because these don't depend on each other.
Then if each pencil costs A, and each notebook costs B, the cost function will be:
C(x, y) = A*x + B*y
So there you have two independent variables that affect the cost of the supplies.
If you want to learn more about independent variables, you can read:
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16. The population density of football stadium is.57 people per square foot. If the area of the stadium is 1,750,000 ft?,
then about how many people are in the stadium?
Answer:
99750000 people
Step-by-step explanation:
1,750,000*57=99750000
Express as a fraction in the simplest form: 43.5%
a. 435/1000
b. 870/200
c. 87/200
Answer:
C
Step-by-step explanation:
43.5 x 10 = 435
435/1000 = 87/200 (simplified)
Why wont anyone give me just the answers when i need them?
Answer:
id.k maybe because people are busy ,
i think the same as you.
Step-by-step explanation:
Choose the correct answer in each number.
1. It is the sum of all areas of lateral faces
and bases of solid figure.
A. Base area B. Lateral area C. Surface area D. None of the above
2. A flat pattern that you can fold to form a solid figure is called a/an _____.
A. Area B. Edge C. Face D. Net
3. The surface area of a cube is _____ times the area of its face.
A. Three B. Four C. Five D. Six
4. In a cylinder, the edge or length of the lateral surface is equal to _____ of its base.
A. Circumference B. Perimeter C. Radius D. All of the above
5. The lateral surface of a cylinder when it is unrolled will be _____
A. Rectangle B. Trapezoid C. Triangle D. All of the above
6. The solid figure that has surface area equivalent to for times the areas of circles of the same radii is _____.
A. Cube B. Cone C. Tetrahedron D. Sphere
7. To get the lateral area of a cone, we use the formula _____.
A. L.A.=πr2 B. L.A.=πrs C. L.A.=πrh D. L.A.=rh
8. The sum of the area of the square base and four triangular lateral faces is the surface area of _____.
A. Cube B. Rectangular prism C. Pyramid D. Cone
9. The unit for surface area is _____.
A. Cubic unit B. Linear unit C. Square unit D. Weight unit
10. A cone has a radius of 5 cm and slant height of 7.1 cm. What is the unit of measure appreciate for its surface area?
A. Square milimiter (mm2) B. Square centimeter (cm2) C. Square decimeter (dm2) D. Square meter (m2)
Answer:
A
B
A
C
D
C
A
B
B
D
Step-by-step explanation:
Determine algebraically whether the function is even, odd, or neither even nor odd. f(x) = x^2
Answer:
The function is even
good luck
Use the equation A = bh to calculate the height of a parallelogram with an area of 36 square inches and a base of 9 inches
Answer:
4 inches
Step-by-step explanation:
A = b x h
A = 36
b = 9
36 = 9 x h
4 = h
height = 4 inches
What is the sum? 2x/x2 + x-4/9x
Answer:
(x² + 14x)/(9x²)
Step-by-step explanation:
To do this calculation process:
The first term: 2x/x² = 2/x.
Then: (2/x) + (x - 4)/(9x).
We should common the denominator by multiplying the denominators of the two terms (9x)(x) = 9x² and dividing each denominator by the common denominator.
So, it will be equal:
[(2)(9x) + (x - 4)(x)]/9x² = (18x + x² - 4x)/9x² = (x² + 14 x)/9x².
What is the slope of a line that goes through the points (3, 7) and (8, 11)
Question 4 options:
11/7
5/4
−8/3
4/5
Answer:
5/4
Step-by-step explanation:
Since the formula of finding the slope is y2-y1/x2-x1, you plug ithe numbers into the equation which is 8-3/11-7 which equals 5/4.
A sphere has a volume of 33.5 cubic inches. Which value is closest to the radius of this sphere in inches?
Answer:
3.26
Step-by-step explanation:
33.5/3.14 = 10.66 ( when rounded to the nearest tenth).
10.66 square rooted is 3.26
The required radius of the sphere is 2 inch.
Volume of sphere = 33.5 cubic inches . Radius of sphere to be determine.
Volume, is defined as mass gained per unit cube of density.
Here, area of sphere = [tex]4/3\pi r^3[/tex]
33.5 = 4/3 πr³
r³ = 33.5 * 3/4π
r = 2
Thus, the required radius of the sphere is 2 inch.
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Help me quickly!!
Brainliest + 50 points
No spammers allowed
Thanks in advance
:) :)
Answer:
x = 5
Step-by-step explanation:
Given coordinates: (3, 4) (x, 6)
Slope: 1
Use the slope formula to find the value of x:
Slope = y2 - y1 / x2 - x1
Substitute the given information into the formula:
1 = [tex]\frac{6-4}{x-3}[/tex]
1 = [tex]\frac{2}{x-3}[/tex]
Multiply both sides of the equation by the common denominator:
[tex]\frac{2(x-3)}{x-3} = x-3[/tex]
Reduce the fraction:
2 = x - 3
Rearrange variables to the left side of the equation:
-x = -3 - 2
Calculate:
-x = -5
Divide both sides with the coefficient of the variable:
x = 5
hope this helps!! p.s. i really need brainliest :)
Answer:
x = 5
Step-by-step explanation:
Slope formula
[tex]\sf slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\sf let\:(x_1,y_1)=(3,4)[/tex]
[tex]\sf let\:(x_2,y_2)=(x,6)[/tex]
[tex]\sf \implies slope=\dfrac{6-4}{x-3}=\dfrac{2}{x-3}[/tex]
As the slope equals 1:
[tex]\begin{aligned}\sf \implies \dfrac{2}{x-3} & =1\\\sf 2 & =\sf x-3\\ \sf 2+3 & =\sf x\\ \sf x & = \sf 5\end{aligned}[/tex]
Therefore, x = 5
On a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 20. Find the z-score of a person who scored 270 on the exam.
Answer:
z = -1.5
Step-by-step explanation:
To Find z-score
z = (X - μ) / σX = Test scoreμ = Mean σ = Standard DeviationGiven
X = 270μ = 300σ = 20Solving
z = 270 - 300 / 20z = -30/20z = -1.5help please, I need it fast
Answer:
(d) 1 / 2^8
this is the answer
both equations answers are kind of same, so (d) is the answer for your question
if this helped you please brainliest?
Answer:
A
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]\frac{2^{-3} }{2^{-5} }[/tex] = [tex]2^{-3-(-5)}[/tex] = [tex]2^{(-3+5)}[/tex] = 2² → A
state how the graph will change
. mervin needs cash and he needs it now. he goes to advanced financial and takes out a loan of 300.00. advanced financial calls their loans mirco-loans and get to choose their own interest rates. if they set the rate at 70% per year, how much interest will mervin need to pay back in 5 months if interest compounds monthly? how much will he owe in 5 months using approximate equivalent growth?
Mervin's loan of $300 is an illustration of compound interest
The interest to pay back in 5 months is $74.2, and the amount to pay back in 5 months is $374.2
The interest to pay back in 5 monthsThe given parameters are:
Principal, P =$300.00Rate, r = 70%Time, t = 5 monthsThe compound interest is calculated as:
CI = P * (1 + r)^(t/12) - P
Substitute known values
CI = 300 * (1 + (0.70))^(5/12) - 300
Evaluate the expression
CI = 74.2
Hence, the interest to pay back in 5 months is $74.2
The amount to pay back in 5 monthsThe amount (A) is calculated using:
A = CI + P
This gives
A = 74.2 + 300
A = 374.2
Hence, the amount to pay back in 5 months is $374.2
Read more about compound interest at:
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0=x^2-8x-32 solve by completing the square
Answer:
x = 4.65 or x = -0.65 (to 2 d.p)
Step-by-step explanation:
To complete the square, use the formula x² + bx + c = (x + b/2)² - (b/2)² + c
In this case, x² - 8x - 32 = (x - 4)² - 16 - 32This simplifies to (x - 4)² - 48 = 0To solve this:
First, add 48 to both sides → (x - 4)² = 48Next, square root both sides → x - 4 = ± √48 (remember that the square root of a number always has a positive and negative value)Finally, add 4 to both sides → x = 4 ± √7x has 2 solutions
x = 2 + √7 or x = 2 - √7
x = 4.65 or x = -0.65 (to 2 d.p)
Hope this helps!
Answer:
x = 4 ± 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
x² - 8x - 32 = 0 ( add 32 to both sides )
x² - 8x = 32
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 4)x + 16 = 32 + 16
(x - 4)² = 48 ( take square root of both sides )
x - 4 = ± [tex]\sqrt{48}[/tex] = ± 4[tex]\sqrt{3}[/tex] ( add 4 to both sides )
x = 4 ± 4[tex]\sqrt{3}[/tex]
The measure of Vis 94°. What is the measure of _XYZ, the tangent-chord angle? O A. 440 X O B. 47° C. 1889 2 Z O D. 940
Answer:
B
Step-by-step explanation:
the tangent- chord angle XYZ is half the measure of its intercepted arc XY
∠ XYZ = [tex]\frac{1}{2}[/tex] × 94° = 47°
Answer:
I think that the correct answer would be B. 47 degrees
Step-by-step explanation:
hope this helps
pls mark brainliest
Tell which set or sets the number below belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers.
26
Part 1
Select all that apply.
A.
irrational numbers
B.
whole numbers
C.
real numbers
D.
natural numbers
E.
integers
F.
rational numbers
Answer:
26 is a:
B. Whole number
D. Natural number
E. Integer
F. Rational number
Answer:
B, C, D, E, F or all options except A
Step-by-step explanation:
26 is not an irrational number since irrational numbers cant be put in fraction form while 26 can be. ex: 26/1, 52/2 and so on
26 is a whole number.
whole numbers are 0 1 2 3 4 and so on
26 is a real number
imaginary number example: sqrt of -2
natural numbers are numbers going from 1 to infinity
integers are any number that is not a decimal.
26 is rational since it's not irrational.
what expression is equivalent to 1/4 (x+24)
Use the Distributive Property, which states the following:-
[tex]\sf{a(b+c)=ab+ac}[/tex]
Where
we distribute a by multiplying it times b and c
a, b, and c can be either constants (numbers) or variables (letters)
Distribute:-
[tex]\sf{\displaystyle\frac{1}{4}(x+24)}}[/tex]
Multiply the term before the parentheses by the terms inside the parentheses:-
[tex]\sf{\displaystyle\frac{1}{4} x+6}}[/tex]
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
Write an equation in slope-intercept form that is parallel to y - 5x = 10 and passes through the point (2, -4).
Answer:
y = 5x - 14
Step-by-step explanation:
*Parallel lines have the same slopes*
Rewrite your equation to slope-intercept form: y = mx + b
y = mx + b
m = slopeb = y-intercept (when x = 0)y - 5x = 10 <== add 5x to both sides
+ 5x + 5x
y = 5x + 10
The slope of the line that is parallel to this line is 5.
We need to find the y-intercept (b) for the parallel line using (2, -4):
y = 5x + b <== substitue 2 for x and -4 for y
-4 = 5(2) + b
-4 = 10 + b <== subtract 10 from both sides to isolate b
-10 -10
-14 = b
y = 5x + b changes to y = 5x - 14
Hope this helps!
Slope:-
m=5Parallel lines have equal slope
passes through (2,-4)Equation in point slope form
y-y1=m(x-x1)y+4=5(x-2)y+4=5x-10y=5x-14Find the length of the third side. If necessary, round to the nearest tenth
Answer:
9.21954445729
Step-by-step explanation:
A^2 + B^2 = C^2
7^2 = 6^2 = 85
The square root of 85 is...
9.21954445729
find the perimeter of polygon
Answer:
22
Step-by-step explanation:
4+7+4+7=22
what is the answer forAt a sale, suits were sold for $72 each. This price was 45% of a suit's original price. How much did a suit originally cost?
Answer:
160
Step-by-step explanation:
72=0.45x
72/0.45=x
x=160
h(x)= {1/x-5 , x=0
{-(x-4)^2, x=7
{ 3x-2, x~0,7
h(6)
Answer:
16
Step-by-step explanation:
h(x)=3x-2 in (0,7)
h(6)=3(6)-2=18-2=16
What is the answer this math problem. -6+ -(8x - 3)
Answer:
x = -3÷8
or x = -0.375
Explanation:
-6+ -(8x-3)= -6-8x+3
= -8x -3
-8x-3= 0
-8x = 3
8x = -3
x = -3÷8