Answer:
[tex]k=\frac{153}{124}[/tex]
Step-by-step explanation:
According to the Remainder Theorem; when P(y) is divided by y-a, the remainder is p(a).
The first polynomial is :
[tex]p(y)=ky^3+3y^2-3[/tex]
When p(y) is divided by y-5, the remainder is
[tex]p(5)=k(5)^3+3(5)^2-3[/tex]
[tex]p(5)=125k+75-3[/tex]
[tex]p(5)=125k+72[/tex]
When the second polynomial:
[tex]m(y)= 2y^3-5y+k[/tex] is divided by y-5.
The remainder is;
[tex]m(5)= 2(5)^3-5(5)+k[/tex]
[tex]m(5)= 225+k[/tex]
The two remainders are equal;
[tex]\implies 125k+72=225+k[/tex]
[tex]\implies 125k-k=225-72[/tex]
[tex]\implies 124k=153[/tex]
[tex]k=\frac{153}{124}[/tex]
if g(x)=2(x-4), find the value of x if g(x)=20
Answer:
32.64
Step-by-step explanation:
Answer:
hello : x = 14
Step-by-step explanation:
g(x)=20
solve this equation :
2(x-4) =20
divid by 2
x - 4 =10
add 4:
x = 14
Please help and thank you
Option B is the right answer.
What we're looking for is a hollow point on -3 going to the right and a hollow point on 2 pointing to the left.
The answer to this is B. The one that is shaded orange in the picture.
Let f(x)=e^x and g(x)=x+6. what are the domain and range of (g*f)(x)?
Answer:
(f of g)(x)=f(g(x))=f(x-3)=e^(x-3)
The domain of a real exponential function is all real, and
the corresponding range is y>0, i.e. (0,+∞)
Step-by-step explanation:
−k+2(−2k−5)
Simplify
Will give brainliest
Answer:-k+-4k-10; which is -5k-10
Step-by-step explanation:
first distribute.
then add.
done.
By simplifying the expression −k+2(−2k−5) we will get -5k-10
What is simplification?It means converting the complex expression, equation into a simple one from which it will be easy to calculate the value of variable.
How to simplify an expression?The given expression is
-k+2(-2k-5)
=-k-4k-10
=-5k-10
Hence the simplified value of the expression is -5k-10
Learn more about simplification at https://brainly.com/question/723406
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In the diagram below, what is the approximate length of the minor arc DE
Answer:
C. 6.3cm
Step-by-step explanation:
The length of the arc is calculated using the formula;
[tex]l=\frac{Central\:angle}{360\degree} \times 2\pi r[/tex]
The radius of the circle is r=10cm
The central angle is 36 degrees.
[tex]l=\frac{36\degree}{360\degree} \times 2\times3.14\times10[/tex]
We simplify to get;
[tex]l=\frac{1}{10} \times 3.14\times 20[/tex]
[tex]l=3.14\times 2=6.3cm[/tex]
Answer:
6.3 is the correct answer :D
Step-by-step explanation:
Determine the common ratio and find the next three terms of the geometric sequence. 8, -20, 50, ...
Answer:
see explanation
Step-by-step explanation:
The common ratio r of a geometric sequence is
r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex] = .....
r = [tex]\frac{-20}{8}[/tex] = [tex]\frac{50}{-20}[/tex] = - 2.5
Multiplying each term by - 2.5 gives the next term
50 × - 2.5 = - 125
- 125 × - 2.5 = 312.5
312.5 × - 2.5 = - 781.25
The next 3 terms in the sequence are - 125, 312.5, - 781.25
The common ratio is -2.5
Next 3 terms after 50 are -125, 312.5, -781.25
What is a geometric sequence and common ratio?A sequence ( increasing or decreasing) having a pattern that the next term is found by multiplying the previous term with a constant term called common ratio, is called a geometric sequence. Common ratio can be positive or negative.
Common ratio can be found by dividing a term by its previous term.How to find the common ratio of the given geometric sequence?The given sequence is 8, -20, 50......
The common ratio is [tex]\frac{-20}{8}= - 2.5[/tex]
How to find the next terms of the given geometric sequence?In a geometric sequence, a term multiplied by the common ratio gives ithe next term.Next term after 50 = {50 x (-2.5)} = -125
Next term after -125 = {(-125) x (-2.5)} = 312.5
Next term after 312.5 = {312.5 x (-2.5)} = -781.25
Next 3 terms after 50 are -125, 312.5, -781.25You can find more details on: https://brainly.com/question/8706084
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Suppose f(x) = x^2. what is the graph of g(x) = f(2x)?
Answer:
C
Step-by-step explanation:
Substitute 2x into the equation where x is located. G(x)= (2x)^2=4x^2. This will be a graph which has been vertically stretched has a very steep curve to it facing up. It is C.
Solve the inequality 3(4x+1)<39
it's x ≤ 3 :))) I found it out after realizing what you were asking
Pllllllzzzz Helpppppp!!!. I have class in an hour!!
Marcus is putting a border of mulch around a tree. The figure shows the top veiw of the mulch. The mulch is 3 in deep. Find the Volume of the mulch. (last problem shown in image.
Answer:
The volume of the mulch is [tex]528\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the mulch is equal to
[tex]V=Bh[/tex]
where
B is the area of the border of the mulch
h is the deep of the mulch
Find the area of the border B
The area of the border B is equal to the area of the complete square minus the area of the inside square
so
[tex]B=24^{2}-20^{2} = 176\ in^{2}[/tex]
we have
[tex]h=3\ in[/tex] -----> the deep of the mulch
substitute the values
[tex]V=(176)(3)=528\ in^{3}[/tex]
The formula for determining the frequency, f, of a note on a piano is f=440(2)^h/12 where h is the number of half-steps from the A above middle C on the keyboard. A note is six half-steps away from the A above middle C. The frequency of the A above middle C is 440 Hz. How much greater is the frequency of the new note compared with the frequency of the A above middle C?
A)29.3%
B)41.4%
C)70.7%
D)182.3%
Answer:
i think it is c
Step-by-step explanation:
Answer:
41.4%
Step-by-step explanation:
The formula for determining the frequency: [tex]f(h)=440(2)^{\frac{h}{12}}[/tex] --A
where h is the number of half-steps from the A above middle C on the keyboard.
A note is six half-steps away from the A above middle C.
Now we are supposed to find How much greater is the frequency of the new note compared with the frequency of the A above middle C?
Now initially there is no half steps .
So, substitute h =0
[tex]f(0)=440(2)^{\frac{0}{12}}[/tex]
[tex]f(0)=440[/tex]
Now we are given that A note is six half-steps away from the A above middle C
So, substitute h =6
[tex]f(6)=440(2)^{\frac{6}{12}}[/tex]
[tex]f(6)=622.25[/tex]
Now To find change percentage
Formula: [tex]=\frac{\text{final} - \text{initial}}{\text{Initial}} \times 100[/tex]
[tex]=\frac{622.25- 440}{440} \times 100[/tex]
[tex]=0.414 \times 100[/tex]
[tex]=41.4\%[/tex]
Hence the frequency of the new note is 41.4% greater with the frequency of the A above middle C.
Which two expressions are equivalent? PLZ HELP
Answer: I'm pretty sure it's a or c. I think its c.
Step-by-step explanation: Cuz 3x + 4x = 7x times 4x = 28x then we have
12x + 16x = 28x
Write the equation of the following graph in vertex form.
1) f(x) -0.4 (x + 2)(x - 5)
2) f(x) 0.4 (x + 2)(x - 5)
3) f(x) -0.4 (x - 2)(x + 5)
4) f(x) 0.4 (x - 2)(x + 5)
The quadratic equation in vertex form is f(x) = 0.4(x - 2)² + 5
How to determine the equation in vertex form
From the question, we have the following parameters that can be used in our computation:
The graph
Where, we have the vertex to be
(h, k) = (2, 5)
A quadratic equation in vertex form is represented as
f(x) = a(x - h)² + k
So, we have
f(x) = a(x - 2)² + 5
Using the points, we have
a = 0.4
Substitute the known values into the equation
f(x) = 0.4(x - 2)² + 5
Hence, the equation in vertex form is f(x) = 0.4(x - 2)² + 5
Which linear inequality is represented by the graph?
Answer:
The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.
Fifty percent of the surface area of the bread is crust. What is the height h?
Answer:
The height h is [tex]5\ cm[/tex]
Step-by-step explanation:
we know that
The surface area of the bread is equal to
[tex]SA=2B+Ph\\[/tex]
where
B is the area of the base
P is the perimeter of the base
h is the height
In this problem
If fifty percent of the surface area of the bread is crust
then
[tex]2B=Ph\\[/tex]
substitute the values
[tex]2(10)(10)=4(10)h\\[/tex]
[tex]200=40h\\[/tex]
[tex]h=200/40=5\ cm[/tex]
Find the degree of the monomial 8ab^3
Answer:
B: 4
Step-by-step explanation:
#first
Answer:
A, 3
Step-by-step explanation:
The degree, otherwise known as the power, is 3.
I need help on this I am just going to use the picture
Answer:
D
Step-by-step explanation:
let y = f(x), that is
y = [tex]\frac{2x-3}{5}[/tex]
Rearrange making x the subject
Multiply both sides by 5
5y = 2x - 3 ( add 3 to both sides )
5y + 3 = 2x (divide both sides by 2 ) , then
x = [tex]\frac{5y+3}{2}[/tex]
Change y back into term of x, hence
[tex]f^{-1}[/tex](x) = [tex]\frac{5x+3}{2}[/tex] → D
D is the correct answer
At the beach, Pancho and his sister both built sandcastles and then measured their heights. Pancho's sandcastle was 3/5 of a foot tall and his sister's was 2/5 of a foot tall. How much taller was Pancho's sandcastle than his sister's?
1/5 of a foot
Simply subtract the height of Pancho’s sandcastle (3/5 of a foot) minus the height of his sister’s sandcastle (2/5 of a foot) to find a difference of 1/5 of a foot, meaning Pancho’s sandcastle was 1/5 of a foot taller than his sister’s sandcastle.
Solve by factoring 3x^2-3x-60=0
Answer:
x = 5 or x = -4
Step-by-step explanation:
3x^2 - 3x - 60 = 0
Factor out 3 from the left side.
3(x^2 - x - 20) = 0
Divide both sides by 3.
x^2 - x - 20 = 0
Factor the trinomial.
(x - 5)(x + 4) = 0
x - 5 = 0 or x + 4 = 0
x = 5 or x = -4
Find any 3 (x,y) pairs that are solutions for the equation 2x-5y=10 . Show your work
Answer:
(0,-2), (5,0) and (10,2).
Step-by-step explanation:
Given equation is [tex]2x-5y=10[/tex].
Now we need to find 3 pairs of solutions in (x,y) form for the given equation.
As [tex]2x-5y=10[/tex] is a linear equation so we are free to pick any number for x like x=0, 5, 10
Plug x=0 into [tex]2x-5y=10[/tex], we get:
[tex]2(0)-5y=10[/tex]
[tex]0-5y=10[/tex]
[tex]-5y=10[/tex]
[tex]y=\frac{10}{-5}[/tex]
[tex]y=-2[/tex]
Hence first solution is (0,-2)
We can repeat same process with x=5 and 10 to get the other solutions.
Hence final answer is (0,-2), (5,0) and (10,2).
The answers is:
The three points that are solution for the equation are:
[tex](5,0)\\(0,-2)\\(6,0.4)[/tex]
Why?To find 3 pairs (x,y) or points that are solutions for the equation, we could find where the function intercepts the x-axis and y-axis, we must remember that the domain of a line is all the real numbers, so by using any input, we will find a solution, which means finding a point that belongs to the line.
So,
Finding the axis intercepts of the line, we have:
x-axis intercept:
Making "y" equal to 0, we have:
[tex]2x-5y=10[/tex]
[tex]2x-5*(0)=10[/tex]
[tex]2x=10[/tex]
[tex]x=\frac{10}{2}=5[/tex]
We have that the interception point with the x-axis is (5,0)
y-axis intercept:
Making "x" equal to 0, we have:
[tex]2x-5y=10[/tex]
[tex]2*(0)-5y=10[/tex]
[tex]0-5y=10[/tex]
[tex]5y=-10[/tex]
[tex]y=\frac{-10}{5}=-2[/tex]
We have that the interception point with the y-axis is (0,-2)
As we know, the domain of a line is equal to the real numbers, Now, we have that any between the points (5,0) and (0,-2) will belong to the line, so, let's try with a point wich x-coordinate (input) is equal to 6 and then find the y-coordinate (output) if the point satisfies the equality, it belongs to the equation to the line.
Substituting x equal to 6, we have:
[tex]2*(6)-5y=10[/tex]
[tex]12-5y=10[/tex]
[tex]12-10=5y[/tex]
[tex]y=\frac{12-10}{5}=\frac{2}{5}[/tex]
So, the obtained point is:
[tex](6,\frac{2}{5})[/tex]
or
[tex](6,0.4)[/tex]
Now, let's prove that it belongs to the equation of the line by substituting it into the equation:
[tex]2*(6)-5*\frac{2}{5}=10[/tex]
[tex]12-2=10[/tex]
[tex]10=10[/tex]
We can see that the equality is satisfied, it means that the point belongs to the line.
Hence, the three points that are solutions for the equation are:
[tex](5,0)\\(0,-2)\\(6,0.4)[/tex]
Have a nice day!
The radius of a sphere is 6 units. Which expression represents the volume of the sphere, in cubic units? π(6)2 π(6)3 π(12)2 π(12)3
Answer: [tex]\frac{4}{3}\pi (6)^3[/tex]
Step-by-step explanation:
The formula for calculate the volume of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Where "V" is the volume of the sphere and "r" is the radius of the sphere.
In this case the radius of the sphere is 6 units. Knowing this radius, you can substitute into the formula [tex]V=\frac{4}{3}\pi r^3[/tex]
Therefore, you get that the expression that represents the volume of this sphere is:
[tex]V=\frac{4}{3}\pi (6)^3[/tex]
Answer:
4/3π(6)3
Step-by-step explanation:
A particular lawn mower is on sale at two different stores the original price at both stores was $130. Watson’s garden shop is advertising the lawn mower for 50% off. Hartman’s home center reduced the mower 40%, and then took an additional 15% off the reduced price. Which lawn mower is the better deal?
Answer:
Watson's garden shop has the better deal on the lawn mower.
Hope this helped :)
Step-by-step explanation:
Watson's $130 - 50% = $65
Hartman's $130 - 40% = $78
$78 - 15% = About $66
Answer:
The deal of Watson’s garden shop is better.
Step-by-step explanation:
Given,
The original price = $ 130,
After 50% off,
The new price would be,
[tex]P_1=130\times \frac{(100-50)}{100}[/tex]
[tex]=\frac{130\times 50}{100}[/tex]
[tex]=\frac{6500}{100}[/tex]
[tex]=\$ 65[/tex]
While, after 40% off then additional 15% off,
The new price would be,
[tex]P_2= 130\times \frac{(100-40)}{100}\times \frac{(100-15)}{100}[/tex]
[tex]=130\times \frac{60}{100}\times \frac{85}{100}[/tex]
[tex]=\frac{663000}{10000}[/tex]
[tex]=\$ 66.30[/tex]
∵ 66.30 > 65
Hence, first deal is better.
4. What is the median of this data set?
Shield Darter
Number of Sites
1
2
3
4
5
6
7
8
9
10
Number of Shield Darter
The median for this given data set is 5.
To find the median for a set of data, you need to first arrange the data in numerical order. Then, you locate the middle value to find the median. Therefore the median is 5.
Plz help me with this
Answer: D) 10 sin (πx) - 5
Step-by-step explanation:
The range (maximum - minimum) is 5 - (-15) = 20
The amplitude (A) is range (20) ÷ 2 = 10
The vertical shift (D) is maximum (5) - amplitude (10) = -5
Of the given options, only A & D are candidates. Now we need to decide if it is a cos graph (A) or a sin graph (D). If we shift the graph up 5 units (to eliminate the vertical shift) , the graph would pass through the origin. Thus it is a sin graph and the answer must be option D.
How to make these !!!!help me !! Urgente
The Pythagorean Theorem is
[tex]a^2+b^2=c^2[/tex]
Where a and b are legs and c is the hypotenuse.
If we had the measurements 27, 36, and 45...
[tex]a^2+b^2=c^2 \\ \\ 27^2+36^2=45^2 \\ \\ 729+1296=2025 \\ \\ 2025 = 2025[/tex]
So it is a right triangle because [tex]a^2+b^2=c^2[/tex]
The values of a, b, and c are given.
[tex]a=27 \\ b=36 \\ c=45[/tex]
Converse blanks: the sum of the legs squared is equal to the square of the hypotenuse; right.
a = 27, b = 36 (a and b can be switched), c = 45 --> the hypotenuse is always the longest side.
a² + b² = c²
Substitute: 27² + 36² = 45²
Simplify: 729 + 1296 = 2025
Simplify: 2025 = 2025
This is a right triangle because the sum of the lengths of the legs squared is equal to the length of the hypotenuse squared.
(also good note, the sides have a ratio of 3 : 4 : 5, which will always make a right triangle)
Plz help me with this
Answer: D) x⁻²
Step-by-step explanation:
x³ ÷ x⁵
= x³⁻⁵
= x⁻²
The span of the Benjamin Franklin suspension bridge in Philadelphia, Pennsylvania, is 1750 feet. A model of the bridge has a span of 42 inches. What is the scale factor of the model to the span of the actual Benjamin Franklin Bridge?
I think the ratio is 3:125
Answer:
1746.5
Step-by-step explanation:
please help fast i dont know what to do
Answer:
y = -3x + 2, or C
Step-by-step explanation:
So, slope intercept form is y = mx + b.
m = (y2 - y1)/(x2 - x1). So (5 - (-1))/(-1 - 1) = -3
b = (0,2), according to the graph, or just 2.
So y = -3x + 2
Joe and mike both ran the same race. Joe finish the race 4 minutes before mike. If mike finish the race at 4:02pm what time did joe finish the race
joe finished 3:58 pm
Joe finished the race at 3:58 PM, 4 minutes before Mike, who finished at 4:02 PM. Subtract 4 minutes from 4:02 PM to get Joe's finish time. The result is 3:58 PM.
Joe and Mike both participated in the same race, but Joe finished 4 minutes earlier than Mike. We know that Mike finished the race at 4:02 PM. To determine Joe's finish time, we need to subtract 4 minutes from 4:02 PM.
Here are the steps:
Start with Mike's finish time: 4:02 PM.Subtract 4 minutes from 4:02 PM: 4:02 PM - 4 minutes = 3:58 PM.Therefore, Joe finished the race at 3:58 PM.
HELP PLEASE!! The following data shows the weight in ounces of 10 different bags of candy.
10, 3, 7, 3, 4, 21, 6, 10, 1, 2, 3.
After removing the outlier what does the mean absolute deviation of this data set represent???
A. On average the weight of a bag of candy varies 3.2 ounces from the mean of 4 ounces
B. On average the weight of a bag of candy varies 2.6 ounces from the mean of 5 ounces
C. On average the weight of a bag of candy varies 3.2 ounces from the mean of 5 ounces
D. On average the weight of a bag of candy varies 2.6 ounces from the mean of 4 ounces
Answer:
C.
Mean= 4.9
Mean Absolute Deviation (MAD): 4.099173553719
Step-by-step explanation:
An outlier is a value that is very different from the other data in your data set. This can skew your results. As you can see, having outliers often has a significant effect on your mean and standard deviation. Because of this, we must take steps to remove outliers from our data sets.
outlier: 21
Answer:
the answer is C :D
Step-by-step explanation:
Can someone please help!!? Now!!!
What are the domain and range of f(x) = log(x-1) + 2
domain: x > 1; range: y > 2
domain: x > 1; range: all real numbers
domain: all real numbers; range: y > 1
domain: all real numbers; range: all real numbers
ANSWER
domain: x > 1; range: all real numbers
EXPLANATION
The given logarithmic function is
[tex]f(x) = log(x - 1) + 2[/tex]
The domain of this function refers to all values of y for which x is defined.
This function is defined argument is greater than 1.
[tex]x - 1 \: > \: 0[/tex]
[tex]x \: > \: 1[/tex]
The range refers to all values of y for which x is defined.
x is defined for all values of y.
The range is all real numbers.
Answer:domain: x > 1; range: all real numbers
Step-by-step explanation:
Edge