Answer:
k = 4
Step-by-step explanation:
In the equation: x² - 2x - 24
Replace the x with x + 3
(x+3)² - 2(x+3) - 24
x² + 6x + 9 - 2x - 6 -24
Let's rearrange it
x² + 6x -2x - 24 + 9 - 6
x² - 4x - 21
f(x+3) = x² - 4x - 21
The equivalent value of k from the function is k = -4
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the function be represented as A
Now , the value of A is
f ( x ) = x² - 2x - 24
Let the second function be represented as B
Now , the value of B is
f ( x + 3 ) = x² - kx - 21
On simplifying , we get
f ( x + 3 ) = ( x + 3 )² - 2 ( x + 3 ) - 24
f ( x + 3 ) = x² + 6x + 9 - 2x - 6 - 24
f ( x + 3 ) = x² + 4x - 21
So , from the equations , we get
-kx = 4x
Divide by -x on both sides , we get
k = -4
Hence , the equation is k = -4
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A rock is dropped from a height of 100 feet calculate the time between when the rock was strong and when he landed if we choose down as positive and ignore air friction the function is h(t)=16t^2-100
Answer:
[tex]2.5s[/tex]
Step-by-step explanation:
We are given a function which tells us at what time the rock is at a certain height. What should be the height of this function when the rock hits the ground? 0, because it has no height, it's on the ground!
So let's plug in 0, and see what value we get for the time.
[tex]0 = 16t^2-100\\100 = 16t^2\\\frac{100}{16} = t^2\\[/tex]
To solve for t we need to take the square root of both sides.
[tex]t = \sqrt{\frac{100}{16} } = \frac{10}{4} = 2.5s[/tex]
Does this graph show a function? Explain how you know.
Answer:
yes because the graph passes the vertical line test
ative section 3. a) The angle of elevation of the top of a tree observed from a point 60 m away from its foot is 45. Find the height of the tree, b) The angle of depression at a noint on 11
Answer:
The height of the tree is is 60m
Step-by-step explanation:
Let's answer a, as it is the only complete question.
We know that the angle of elevation of the top of a tree observed from a point 60m away, is 45°.
We can model this with a triangle rectangle, a sketch of it can be seen below (assuming that you are looking it from the ground).
You can see that the adjacent cathetus to the 45° angle is equal to 60m
And the opposite cathetus is the measure we want to find.
Now you can remember the trigonometric relation:
tan(a) = (opposite cathetus)/(adjacent cathetus).
So to find the height of the tree we need to solve:
tan(45°) = H/60m
This is just:
tan(45°)*60m = H =60m
The height of the tree is is 60m
1+1+2+2+3+3+4+4+5+5+6+6+7+7+8+8+9+9+0+0
90
6+6=12
12+8=20
20+10=30
30+12=42
42+14=56
56+16+18=90
1+1+2+2+3+3+4+4+5+5+6+6+7+7+8+8+9+9+0+0 would equal to 90 if you break it down.
Hope this helps!
Have a great day :)
Find the length of the side and area ot the square whose perimeter is given below a)44cm b)80cm
9514 1404 393
Answer:
a) 11 cm
b) 20 cm
Step-by-step explanation:
A square has four equal-length sides, so the perimeter is 4 times the side length. Then the side length is 1/4 of the perimeter.
a) s = (1/4)(44 cm) = 11 cm
b) s = (1/4)(80 cm) = 20 cm
PLEASE help!!! math coordinates
 PLEASE HURRY I WILL GIVE BRAINLIEST AND 5 STAR AND HEART! THANK YOU!
Answer:
I believe it is 55°.
I can't remember the exact steps for this tho.
I hope it is right! good luck!
The altitude of an equilateral triangle is 6v3 units long. The length of one side of the triangle is
units.
Answer:
Side = 2 * height / sqr root 3
Side = 2 * 6 * sqr root 3 / sqr root 3
Side = 12
Step-by-step explanation:
SEE QUESTION IN IMAGE
Answer:
d) 2y + x = 106Step-by-step explanation:
Mean of the data = sum of the data / number of frequencies:
(40 + 38 + y + y + x + 32)/6 = 362y + x + 110 = 36*62y + x = 216 - 1102y + x = 106Correct choice is d
How would I answer this: How many minutes are in a 30-day month.... use vertical multiplication to get the right answer
Answer:
43,200 minutes in 1months or 30 days
There are 43200 minutes in one month.
What is multiplication?The basic explanation of multiplication is adding a number, with respect to another number, repeatedly.
Given that, How many minutes are in a 30-day month,
We have, 60 minutes in 1 hour
And, 24 hours in 1 day,
Then, number of minutes in 1 day = 60 × 24 = 1440 minutes
Therefore, in 1 month = 1440 × 30 = 43200 minutes
Hence, there are 43200 minutes in one month.
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3. Find f(x) - g(x)
4 options to pick from
Answer:
Answer is 13x⁴ - x³ - 9x²( the last option)
Step-by-step explanation:
f(x) = 8x⁴ - x³ - 4x²
g(x) = -5x⁴ + 5x²
so,
f(x) - g(x)
=(substituting the value)
= (8x⁴ - x³ - 4x²) - (-5x⁴ + 5x²)
= 8x⁴ - x³ - 4x² + 5x⁴ - 5x²
= 8x⁴ + 5x⁴ - x³ - 4x² - 5x²
= 13x⁴ - x³ - 9x²
Answer:
The 4th option would be correct.
Step-by-step explanation:
No complex calculations are needed. Just pay attention to what the problem is asking for. Notice that f(x) is positive while g(x) is negative. So instead of adding, you're subtracting.
Now look at the last coefficients in each function. Notice that they're the same term, since both of their variables are x^2. Since we're subtracting, that 5x^2 in function g is actually going to be negative. This is why the answer would be the last option, since it's the only one that shows that -4x^2 and -5x^2 is being combined.
Also, at the start, I said no complex calculations are needed. This is because the problem didn't say 'Show your work' or something along those lines. Only do it if it asks, or if your teacher does.
Instructions: Given the following constraints, find the maximum and minimum values for z.
x + 3y < 0
Constraints: X – Y > 0
3x – 7y < 16
Optimization Equation: 2 = -x + 5y
Maximum Value of z:
Minimum Value of z:
Check
Answer:
[tex]x+3y\leq 0[/tex]
[tex]x-y\geq 0[/tex]
[tex]1) x+3y=0[/tex]
[tex]x-y=0[/tex]
[tex]-----[/tex]
[tex]4y=0[/tex]
[tex]y=0[/tex]
[tex]x=0[/tex]
[tex](0,0)[/tex]
[tex]2)(x+3y=0)3[/tex]
[tex]3x-7y=16[/tex]
[tex]3x+9y=0[/tex]
[tex]3x-7y=16\\------\\16y=-16[/tex]
[tex]y=-1[/tex]
[tex](3,-1)[/tex]
[tex]3)(x-y=0)3[/tex]
[tex]3x-7y=16[/tex]
[tex]3x-3y=16[/tex]
[tex]3x-3y=0[/tex]
[tex]3x-7y=16\\------\\4y=-16[/tex]
[tex]y=-4[/tex]
[tex]x=4[/tex]
[tex](4,-4)[/tex]
[tex]Z=-x+5y[/tex]
[tex](0,0):z=0[/tex]
[tex](3,-1):z=-8[/tex]
[tex](4,-4):z=-24[/tex]
[tex]Maximum \:Value\: of\: z:0[/tex]
[tex]Minimum\: Value\: of\: z:-24[/tex]
OAmalOHopeO
18
The length of a rectangle is twice as long as the width of the rectangle.
The area of the rectangle is 32 cm.
Draw the rectangle on the centimetre grid.
.
4
54
B2
%
I did it wrong can someone help me
Answer:
Width = 4 cm
Length = 8 cm
Step-by-step explanation:
Hi there!
Let [tex]l[/tex] be equal to the length of the rectangle.
Let [tex]w[/tex] be equal to the width of the rectangle.
1) Determine equations to find the length and width
We're given that the length is two times the length of the width:
[tex]l=2w[/tex]
We're also given that the area of the rectangle is 32 cm². Recall that the area of a rectangle is [tex]A=lw[/tex]:
[tex]A=lw\\32=lw[/tex]
Now, we have our two equations:
[tex]\displaystyle \left \{ {{l=2w} \atop {32=lw}} \right.[/tex]
2) Solve for the width using substitution
[tex]\displaystyle \left \{ {{l=2w} \atop {32=lw}} \right.[/tex]
Replace [tex]l[/tex] in the second equation with [tex]2w[/tex] from the first equation:
[tex]32=(2w)w\\32=2w^2[/tex]
Divide both sides by 2 to isolate w²:
[tex]16=w^2[/tex]
Take the square root of both sides to isolate w:
[tex]\pm4=w[/tex]
Because width cannot be negative, w=4. Therefore, the width of the rectangle is 4 cm.
3) Solve for the length
[tex]\displaystyle \left \{ {{l=2w} \atop {32=lw}} \right.[/tex]
Now, that we have the width (4 cm), we can solve for the length by plugging it back into one of the equations. Either of the equations work, but we can use the first:
[tex]l=2w\\l=2(4)\\l=8[/tex]
Therefore, the length of the rectangle is 8 cm.
3) Draw the rectangle
We can use what you had before as a foundation. You drew a rectangle with width 4 cm and length 7 cm. To draw the correct rectangle, add another row on top to make it 4 cm by 8 cm.
I hope this helps!
BOYS AND GIRLS, HELP ME PLEASE!!
5,6,7,8 PLEASE
factor this examples
Answer:
5) 4а²+8ас=4а(а+2с)
6) 3m²-6mn=3m(m-2n)
7) ab-ac+yb-yc=a(b-c)+y(b-c)=(a+y)(b-c)
8) ab+ac+xb+c=b(a+x)+c(a+1)
Asha found that a vertical line intersects the graph of x = StartAbsoluteValue y EndAbsoluteValue at two points. What can Asha conclude about x = StartAbsoluteValue y EndAbsoluteValue?
It is a function of x but not a relation.
It is a relation but not a function of x.
It is both a function of x and a relation.
It is neither a function of x nor a relation.
Answer:
what can i help u with
Step-by-step explanation:
The graph of x = |y| is as shown in the figure.
When we draw a vertical line, it intersects the graph at two points.
This means for the same value of x , we have two values of y.
Or in other words, for the same pre image, we have two images.
Hence it is not a function.
But for every value of x, we do have a value of y, hence it is a relation.
x = |y| is a relation but it is not a function
Answer:
:B
Step-by-step explanation:
hope that can help
Will give brainliest need quick answers
Answer:
u=1
v = 10
Step-by-step explanation:
For the triangles to be congruent
IG = PR
50 = u+49
50 - 49 = u
1 = u
GH = RQ
v+6 = 16
v = 16-6
v = 10
6(2x-11)<-3+5x Need help asap
Answer:
x <9
Step-by-step explanation:
6(2x-11)<-3+5x
Distribute
12x -66 < -3+5x
Subtract 5x from each side
12x-5x -66 < -3+5x-5x
7x -66< -3
Add 66 to each side
7x-66+66<-3+66
7x<63
Divide by 7
7x/7 <63/7
x <9
PLEASE HELP ASAP !! IF I DONT FINISH THIS HOMEWORK ILL GET GROUNDED .
A group of 11 students participated in a quiz competition. Their scores are shown below:
Scores
7 8 3 6 3 14 4 3 2 3 5
Part A: Would a dot plot, a histogram, or a box plot best represent the range of scores of the students by quartiles. Explain your answer. (4 points)
Part B: Provide a step-by-step description of how you would create the graph named in Part A. (6 points)
Answer:
A) Histogram
Step-by-step explanation:
A) The first step would be to look at the purpose and use for each type of plotting method;
Dot Plot: Used to represent the distribution of data (for ex; #of Strawberries, Blueberries, and Raspberries.
Histogram: A histogram is used to summarize discrete or continuous data. In other words, it provides a visual interpretation of numerical data by showing the number of data points that fall within a specified range of values
Box Plot: Summerizes a set of data measured on an interval scale.
Best choice: Histogram- The reason why a histogram is the best representation of the student quartiles is because a histogram is used to summarize discrete or continuous data, and the given data is discrete
B)
To create your histogram you first have to create a frequency table like the one below;
On the vertical axis, place frequencies. Label this axis "Frequency".
On the horizontal axis, place the lower value of each interval. Label this axis with the type of data shown (Score, etc.)
Draw a bar extending from the lower value of each interval to the lower value of the next interval. The height of each bar should be equal to the frequency of its corresponding interval.
That's how it's done!
Answer:
this is only for part a: a histogram
Step-by-step explanation: a histogram is like a bar graph and instead of putting dots or X's just graph it its much easier
For a one-way within-subjects ANOVA, the mean difference attributed to the manipulation is in the ________, and the mean difference attributed to individual differences is in the ________ of the test statistic. numerator; numerator denominator; numerator numerator; denominator denominator; denominator
Answer:
1. numerator;
2. denominator
Step-by-step explanation:
For a one-way within-subjects ANOVA, the mean difference attributed to the manipulation is in the NUMERATOR, and the mean difference attributed to individual differences is in the DENOMINATOR of the test statistic.
The bill before tax at a restaurant is $32, and the sales tax is 10%. You decide to leave a 15% tip based on the pre-tax amount. What will be the amount of the total bill, including tax and tip?
Bill before tax = $32
Tax = 10/100×32
= $3.2
Tip = 15/100×32
= $4.8
Total cost = 32 + 3.2 + 4.8
= $40
Answered by Gauthmath must click thanks and mark brainliest
describe the rule that describes the relationship between the numbers in the top row (x) and the bottom row (y) in the following table
Answer:
y(x) = 2x+3
Step-by-step explanation:
the rule is y(x) = 2x+3
sector abc sits inside a circle with a radius of 9cm and is a 80 degree angle what is the area of sector abc
Answer:
56.52 cm²Step-by-step explanation:
Area of sector:
S = πr²θ/360Substitute the values and find the area:
r = 9 cmθ = 80°S = 3.14*9²*80/360 = 56.52 cm²1. A football goal post casts a shadow 120 inches long. You are 5 feet 6 inches tall and cast a shadow 16.5 inches long. Find the height of the goal post in feet. Round your answer to the nearest whole number.
Answer:
40 feets
Step-by-step explanation:
Given that :
Person's height = 5feet 6 inches ;
Person's height in inches ;
1 foot = 12 inches ;
5 feets = (12 * 5) = 60 inches
Person's height = 60 + 6 = 66 inches
Height of person's shadow = 16.5 inches
Height of post shadow = 120 inches
Height of goal post = x
(Height of goal post / height of post shadow) = (person's height / person's shadow)
x / 120 = 66 / 16.5
Cross multiply :
16.5x = 120 * 66
16.5x = 7920
x = 7920 / 16.5
x = 480 inches
To feets ;
1 foot = 12 inches
480 inches = 480/12 feets = 40 feets
J.W. is an artist and sells hisnpottery each year at a local Renaissance Festival. He keeps track of his sales and the 7.75% sales tax he collects by making notations in a ledger. Every evening he checks his records by counting the total money in his cash drawer. After a day of selling pottery, the cash totaled $1253.68. How much is from the sale of the merchandise and how much is sales tax? Round your answer to the nearest cent.
The amount from tax is $97.16 while the amount from sales is $1156.52
Tax is a compulsory sum levied on the sales of goods and services
Taxes increases the price of a good
The price of J.W.'s pottery would be 7.75% higher as a result of the tax
Amount of tax collected = percentage of sales tax x total of cash
0.0775 x $1253.68 = $97.16
Amount from the sale = total cash - taxes
$1253.68 - $97.16 = $1156.52
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Guys help please I am struggling
9514 1404 393
Answer:
14.1 years
Step-by-step explanation:
Use the compound interest formula and solve for t. Logarithms are involved.
A = P(1 +r/n)^(nt)
amount when P is invested for t years at annual rate r compounded n times per year.
Using the given values, we have ...
13060 = 8800(1 +0.028/365)^(365t)
13060/8800 = (1 +0.028/365)^(365t) . . . . divide by P=8800
Now we take logarithms to make this a linear equation.
log(13060/8800) = (365t)log(1 +0.028/365)
Dividing by the coefficient of t gives us ...
t = log(13060/8800)/(365·log(1 +0.028/365)) ≈ 0.171461/0.0121598
t ≈ 14.1
It would take about 14.1 years for the value to reach $13,060.
Complete the table to investigate dilations of
exponential functions.
3.2*
23x
-2
NAN
62
-1
2 / 를
0
a
b
с
1
d.
e
f
2
4
12
64
a =
b
с
e
f=
d =
DONE
Intro
Answer:
a= 1
b= 3
c= 2
d= 2
e= 6
f= 8. These are the answers for the question. Love from Gauthmath
The standard exponential function is expressed as y =ab^x. The values of the variables are: b = c = 3, a = 1, d = 2,e = 6, f = 9
Functions and valuesThe standard exponential function is expressed as:
y =ab^x
wherex is the exponent
a is the base
According to the question, we are to fill the given table based on the given exponential functions.
If the exponential function is 2^x
a = 2^0 = 1
d = 2^1 = 2
If the exponential function is 3*2^x
b = 3* 2^0 = 3
e = 3 * 2^1 = 6
If the exponential function is 2^3x
c = 3^2(0) = 3^1 = 3
f = 3^2(1) = 3^2 = 9
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Which of the following is equivalent to (16^3/2)^1/2
Answer:
8
Step-by-step explanation:
(16^3/2)^1/2
We know a^b^c = a^(b*c)
16 ^(3/2*1/2)
16 ^3/4
Rewriting 16 as 2^4
2^4^3/4
2^(4*3/4)
2^3
8
if the rate store is constant which statement correctly compares the cost of a package 20 cd's
Answer:
rufvkslvUtepgsohch. h,kh jblfc.Suppose TM ≈ GL and angle M ≈ G What additional information is needed to prove triangle MTD≈ GLS by SAS?
Answer:
the second option
Step-by-step explanation:
SAS is side angle side. so, we need 2 sides and the enclosed angle.
since G is the transformed M, and GL is the transformed side TM, that also means L correlates to T and S to D.
for SAS we need both sides of the angles M and G.
TD and SL are not satisfying this condition.
only MD and SG do.
Question 15 of 41
What is the ratio for the volumes of two similar spheres, given that the ratio of their radii is 3:5?
A. 9:25
B. 27:125
C. 125:27
D. 25:9
SUBMIT
Answer:
B
Step-by-step explanation:
the radii have to be cubed cause a volume is cubed
3^3:5^3
27:125
I hope this helps and sorry if it's wrong
