Answer:
OTT →T.................
................... ............
y = -4(x + 6)(x - 8)
How do you write this in standard form?
Answer:
[tex]y = -4x^2 + 8x + 192[/tex]
Step-by-step explanation:
Hi there!
Standard form: [tex]y=ax^2+bx+c[/tex]
[tex]y = -4(x + 6)(x - 8)[/tex]
Use the distributive property to multiply (x+6) and (x-8)
[tex]y = -4(x(x - 8) + 6(x - 8))\\y = -4(x^2 - 8x + 6x - 48)\\y = -4(x^2 - 2x - 48)[/tex]
Multiply the parentheses by -4
[tex]y = -4x^2 + 8x + 192[/tex]
I hope this helps!
A 12-member jury is to be selected from 15 men and 13 women. Find the probability that this jury has 6 or 7 males.
Answer:
The right solution is "0.5545".
Step-by-step explanation:
According to the question,
The probability of having 6 or 7 males will be:
= [tex]P(6 \ males)+ P(7 \ males)[/tex]
= [tex]\frac{15_C_6\times 13_C_6}{28_C_{12}} + \frac{15_C_7\times 13_C_5}{28_C_{12}}[/tex]
= [tex]\frac{5005\times 1716+6435\times 1287}{30421755}[/tex]
= [tex]\frac{16870425}{30421755}[/tex]
= [tex]0.5545[/tex]
Can someone help me out
Answer: [tex]V=3369.3ft^3[/tex]
Step-by-step explanation:
[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}\pi (9.3)^3\\V=3369.3ft^3[/tex]
A force of 9 lb is required to hold 35lb crate on a hill. What angle does the hill make with the horizontal?
Answer: [tex]14.9^{\circ}[/tex]
Step-by-step explanation:
Given
Applied force is 9 lb to hold of 35 lb crate on a hill
Suppose the hill makes an angle of [tex]\theta[/tex] with horizontal
There will be two component of weights i.e. along and perpendicular to the hill
Only the component along the hill pulls the crate backwards
So,
[tex]\Rightarrow 35\sin \theta=9\\\\\Rightarrow \sin\theta =\dfrac{9}{35}\\\\\Rightarrow \theta =14.89^{\circ}\approx 14.9^{\circ}[/tex]
Write an equation for the line that passes through (-5, 4) and (-4, 2).
Answer:
y = - 2x - 6
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, 4) and (x₂, y₂ ) = (- 4, 2)
m = [tex]\frac{2-4}{-4-(-5)}[/tex] = [tex]\frac{-2}{-4+5}[/tex] = [tex]\frac{-2}{1}[/tex] = - 2 , then
y = - 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 4, 2 ) , then
2 = 8 + c ⇒ c = 2 - 8 = - 6
y = - 2x - 6 ← equation of line
What is the fraction called that is used to convert one unit to another?
Answer:
ratio
Step-by-step explanation:
by using a conversion factor and a fraction, a ratio can be created to convert one unit to another.
Match the number with its opposite -5.4
What is the explicit formula for the geometric sequence with this recursive formula
Answer:
Hello,
Answer A
Step-by-step explanation:
[tex]a_1=-6\\\\a_2=a_1*(\dfrac{1}{4} )^1\\\\a_3=a_2*(\dfrac{1}{4} )^1=a_1*(\dfrac{1}{4} )^2\\\\\\\\a_n=a_1*(\dfrac{1}{4} )^{n-1}\\\\Answer\ A\\[/tex]
How many units the function y = |x - 8| is translated from the parent function?
Answer:
8 Units, let me know if you didn't understand anything.
Step-by-step explanation:
Translation is the simple movement of just left, right, up or down. when dealing with the absolute value function here are the transformations.
A|B(x - C)| + D where A is the vertical stretch that multiplies all y values by A save where y=D. B is the horizontal shrink, so you divide all x values by B except for where x=C. C is the horizontal shift, which is a translation. C makes ALL points on the graph move to the right by C or if C is negative it moves them to the left. it could also look like |x + C|. keep in mind, +C is actually -C because - -C = C. D shifts up and down, so it is also a translation. if D is positive it moves up and if D is negative it moves down.
Nowthe only transformation in your problem is -8, which is a horizontal shift to the right. so the graph moves 8 to the right. There is your answer, 8 units.
Brown’s time for running a mile in gym class is 9.9 minutes, Ray’s time is 9.47 minutes and Malcolm’s time is 9.76 minutes. Who ran the mile in less time?
Given:
Brown’s time for running a mile in gym class = 9.9 minutes
Ray’s time for running a mile in gym class = 9.47 minutes
Malcolm’s time for running a mile in gym class = 9.76 minutes
To find:
Who ran the mile in less time?
Solution:
It is given that the time taken by Brown, Ray and Malcolm to cover a mile are 9.9 minutes, 9.47 minutes and 9.76 minutes respectively.
9.47 < 9.76 < 9.9
Since, 9.47 minutes is the lowest time, therefore Ray can run a mile in less time.
To the nearest tenth of a second, the ball is in the air for s.
Answer:
2.4
Step-by-step explanation:
Took the assignment
Answer:
2.4 seconds is the correct answer.
Step-by-step explanation:
Just completed it.
Triangle ABC is shown below with line DE passing through the center:
Triangle ABC is shown with line DE running horizontally through the center of the figure.
If triangle ABC is dilated by a scale factor of three about the center of the triangle, dilated line D'E' will (6 points)
be parallel to the original line
shift three units to the right
be perpendicular to the original line
pass through points D and E
Answer:
D'E' be parallel to the original line
Step-by-step explanation:
Given
[tex]\triangle ABC[/tex]
Line [tex]DE[/tex]
[tex]k = 3[/tex] -- scale factor
Required
The relationship between [tex]DE[/tex] and [tex]D'E'[/tex]
When [tex]\triangle ABC[/tex] is dilated by a scale factor of 3, [tex]\triangle A'B'C'[/tex] will be three times as big as [tex]\triangle ABC[/tex].
Also:
Line [tex]D'E'[/tex] will be three times as long as [tex]DE[/tex]
Since no further transformation is done on [tex]\triangle ABC[/tex] and line [tex]DE[/tex], then [tex]D'E'[/tex] will be parallel to [tex]DE[/tex]
Complete the standard form equation representing the quadratic relationship displayed above, where a, b, and c are constants.
Answer:
Y =-10X +5
Step-by-step explanation:
x1 y1 x2 y2
1 -5 0 5
(Y2-Y1) (5)-(-5)= 10 ΔY 10
(X2-X1) (0)-(1)= -1 ΔX -1
slope= -10
B= 5
Y =-10X +5
Answer:
y = -2x2 + 8x + 5.
Step-by-step explanation:
If 1125 = 3^m × 5^n ;find the value of m and n.
9514 1404 393
Answer:
m = 2
n = 3
Step-by-step explanation:
1125 = 9·125 = 3^2 · 5^3
m = 2
n = 3
_____
Additional comment
Using divisibility rules, you can keep dividing by the obvious factors until the quotient is 1.
1125/5 = 225
225/5 = 45
45/5 = 9
9/3 = 3
3/3 = 1 . . . . . . 5 is a factor 3 times; 3 is a factor 2 times.
Which graph represents an odd function?
y
6
4
.
2
.
O
-6..
4
-2.
2.
.
B
х
لند
4
9
TV
Answer:
the odd graph represented is
y
6
4
1st graph represents the odd function because it is symmetric about origin
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
For a function f to be odd, it should satisfy the following equation:
f(-x) = -f(x)
For a function f to be even
f(-x)=f(x)
The graph of an odd function will always be symmetric about the origin.
By observing the graphs we can say that:
1st graph is symmetric about origin and hence it is an odd function.
2nd graph is symmetric about y-axis.Hence it is not an odd function.
Hence, 1st graph represents the odd function because it is symmetric about origin
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Pls help me with this problem
[tex]3x - 8 = 4x - 17 \\ \\ \sf \longmapsto \: 3x + 4x = - 17 + 8 \\ \\ \sf \longmapsto \: 7x = - 9 \\ \\ \sf \longmapsto \: x = \frac{ - 9}{7} [/tex]
Which of the following answer choices correctly expresses the number 64?
A. 4'6
B. 4'5
C. 4'4
D. 4'3
Answer:
4’3
Step-by-step explanation:
Took test
Answer:
4’3
Step-by-step explanation:
Use a number line to represent the following. (a) {-4,-1, 0, 2, 3}
Step-by-step explanation:
sorry I couldn't draw it properly but that is it...
I hope it helps
Answer:
Step-by-step explanation:
Draw a line and divide it into 13 equal parts.
Mark 0 in the middle of number line.
Mark negative numbers to the left of zero and mark positive numbers to the right of zero.
what is -10/19÷-5/7 but not converted into a decimal please!
Answer:
14/19
Step-by-step explanation:
Dividing fractions is the same as multiplying by the reciprocal:
-10/19 ÷ -5/7
-10/19 x -7/5
Multiply the numerators by each other, as well as the denominators:
70/95
Simplify by dividing both the numerator and denominator by 5:
= 14/19
So, the answer is 14/19
Go Long Telephone Company charges a flat rate of $18.75 per month plus $0.18 per minute. To Call Telephone Company charges a flat rate of$12.51 per month plus $0.42 per minute. How many minutes would a customer need to use in order for the bill from Go Long and Via Call to be equal at the end of the month?
9514 1404 393
Answer:
26 minutes
Step-by-step explanation:
Let x represent the number of minutes used. The charges will be equal when ...
18.75 +0.18x = 12.51 +0.42x
6.24 = 0.24x . . . . . . . . . . . . . . . subtract 0.18x+12.51
26 = x . . . . . . . . . . . . . . . divide by 0.24
A customer using 26 minutes will receive the same bill from either company.
Help me to solve this fast ( prove it)
Step-by-step explanation:
sec⁴A + tan⁴A = 1 + (2tan²A/cos²A)
LHS = sec⁴A + tan⁴A
= (sec²A)² + (tan²A)² {using formula of a²+b²)
= (sec²A-tan²A) + 2tan²A.sec²A
= 1 + {2tan²A.(1/cos²A)}
= 1 + (2tan²A/cos²A)
Independent Practice
x
0
1
2
3
4
y
2
1.5
1
0.5
0
Which kind of function best models the data in the table? Write an equation to model the data.
A.
linear; y= 1 2 x+2
B.
quadratic; y=− x 2
C.
quadratic; y=− 1 2 x 2
D.
linear; y=− 1 2 x+2
Answer:
D. linear; y = - 1/2x + 2
Step-by-step explanation:
As the values of x increase by 1, the values of y decrease by 0.5. This means that we have a negative linear relationship of 1/2. In other words, the slope is -1/2. Our y-intercept is 2 since when x = 0, y = 2. So, D is the correct choice.
Find range
of
f(x) =
[tex]1 \div ( |x| - x)[/tex]
Step-by-step explanation:
We need to find thr range if
[tex] \frac{1}{ (|x| - x)} [/tex]
The absoulte value of something is positive.
So
[tex] \frac{1}{x - x} = \frac{1}{0} [/tex]
This function isn't possible so no range exist.
Rewrite the series as a sum (show all work)
Answer:
1144
Step-by-step explanation:
100 + 98 + 96 +.... + 78+76 =
(12-0)/2 (176)
(6.5) (176) = 1144
The sum of the series will be 1068.
We have the following expression -
[tex]\sum_{i=0}^{12} 100 - 2i[/tex]
We have to rewrite the series as the sum.
What do you mean by Series ?A series in mathematics is the sum of a list of numbers that are generated according to some pattern.
We have the following expression -
[tex]\sum_{i=0}^{12} 100 - 2i[/tex]
The terms of this series can be calculated by calculating the value of the function at different values of i.
The series is as follows -
100 + 98 + 96 +.... + 78+76
This is an arithmetic progression with a = 100 and d = - 2 and n = 12. The sum of this series is -
[tex]S = \frac{n}{2} \times {2a + (n-1)d}[/tex]
S = [tex]\frac{12}{2} [{2 \times 100 + (12 -1)(-2)] = 6[200+ 11 \times -2] = 6[200 -22][/tex]
S = 6 x 178 = 1068
The sum of the series will be 1068.
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If a block weighs 8kg PLUS half a block.
What is the weight of a block and a half?
Answer:12kg
Step-by-step explanation:
8kg+4kg=12kg
the 4kg came from the half block
se um bloco pesa 8 kg meio bloco pesa 4 kg então é só juntar 8+4=12
What is the area of the obtuse triangle below?
11
13
A. 12 sq. units
7
B. 71.5 sq. units
C. 24.5 sq. units
D. 143 sq. units
find the length of x
Answer:
7/2 =x
Step-by-step explanation:
The triangles are similar so we can write a ratio to solve
2 4
---- = -------
x 7
Using cross products
2*7 = 4x
14 = 4x
14/4 = 4x/4
7/2 =x
Answer:
[tex]x=3\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{4}{2} :\frac{7}{x}[/tex]
x · 4 = 7 · 2
4x = 14
4x ÷ 4 = 14 ÷ 4
x = 3.5
A pitcher of juice holds 6 cups. How many 2/3 -cup servings of juice are in the pitcher?
serving-
please help ill give brainliest
Answer:
Step-by-step explanation:
6 ÷ (⅔) = 6 × (3/2) = 9
There are nine ⅔-cup servings per pitcher.
Type the correct answer in each box. Use numerals instead of words.
The domain of this function is {-12, -6, 3, 15}.
y = -2/3x + 7
Complete the table based on the given domain.
Answer:
hope it helps plz mark me brainliest!
Step-by-step explanation:
4x² - 3, x less than/equal to 0
Step-by-step explanation:
y = (-1/2)[(x+3)^½]
(x+3)^½ = -2y
Square both sides,
(x+3) = (-2y)²
x+3 = 4y²
x = 4y²-3
Interswitch x and y
Inverse is 4x²-3
Domain of inverse is the range of f.
The range of f is less than/equal to 0
Because at x = -3, f(x) = 0
For x > -3, f(x) is negative
Domain of inverse is x less than/equal to 0
Which expression gives the surface area of a sphere with radius 3x?
Answer:
=> 12πr²
Step-by-step explanation:
The Surface area of sphere is 4πr²
so the surface area of sphere with radius 3x will be
=> 4×3πr²
=> 12πr²
