Answer:
a=16
Step-by-step explanation:
Given
(y-4)(y^2+4y+16)
To find the value of a in the resulting polynomial we have to solve the given expression
=y(y^2+4y+16)-4(y^2+4y+16)
= y^3+4y^2+16y-4y^2-16y-64
To find the value of a, both the polynomials will be compared
y^3+4y^2+16y-4y^2-16y-64
y^3+4y^2+ay-4y^2-ay-64
Comparing the coefficients of both polynomials gives us that
a=16
So, the value of a is 16 ..
Please help asap!!!!!!!!!!!
ANSWER
[tex]16\pi \: sq.in[/tex]
EXPLANATION
The area of a sector is calculated using the formula,
[tex]Area = \frac{arc \: measure}{360 \degree} \times \pi {r}^{2} [/tex]
The arc measure is given as 45°
The radius of the circle is 8 inches.
We substitute to obtain,
[tex]Area = \frac{45 \degree}{360 \degree} \times \pi \times {8}^{2} [/tex]
[tex]Area = \frac{1}{4} \times 64\pi = 16\pi[/tex]
The answer is:
The correct option is the second option:
[tex]SectorArea=8\pi in^{2}[/tex]
Why?To answer the question, we need to calculate the total area of the circle (which corresponds to 360°) and then, calculate the equivalent area to the sector of the arc that measures 45°
Calculating the total area, we have:
[tex]TotalArea=\pi radius^{2} \\\\TotalArea=\pi 8^{2} =64\pi in^{2}[/tex]
Now, we need to consider that the calculated area (total area) correspondes to all 360° that conforms the interior angle of a circle, now, if we want to calculate the area that represents a sector of the arc that measures 45°, we have to use the following formula:
[tex]SectorArea=\frac{360\°}{45\° }*TotalArea\\\\SectorArea=\frac{45\°}{360\° }*64\pi in^{2}=\frac{1}{8} *64\pi in^{2}\\\\SectorArea=8\pi in^{2}[/tex]
Hence, we have that the correct option is the second option:
[tex]SectorArea=8\pi in^{2}[/tex]
Have a nice day!
A circle with radius r is inscribed into a right triangle. Find the perimeter of the triangle if the length of the hypotenuse is 24 cm and r=4 cm;
Answer: 56
Step-by-step explanation:
4=(a+b-24)/2
32=a+b
32+24=56
Answer:
The perimeter of the triangle is 56 cm.
Step-by-step explanation:
Given:
The length of the hypotenuse is 24 cm
Radius of the circle r=4 cm
To Find:
The perimeter of the triangle=?
Solution:
Let us see the below diagram representing situation.
Here, first we have drawn the radius of circle perpendicular to the sides of triangle,
We have Taken PB = 4 because, it is a side of square formed there, and we take OC as x.
Then, QC also becomes x as they are tangents from single point, so they are equal.
Now, AQ becomes 24 – x as AC is 24 according to given information.
So, perimeter = AB + BC + CA
Perimeter = (24 – x + 4) + (4 + x) + (24 – x + x)
Perimeter = 28 – x + 4 + x + 24
Perimeter = 28 + 28 = 56
Hence, the perimeter of the triangle is 56 cm.
What are the solution(s) to the quadratic equation 50 – x2 = 0?
x = ±2
x = ±6
x = ±5
no real solution
Answer:
No real solution
Step-by-step explanation:
There is no perfect squares in 50
ANSWER
[tex]x = \pm5\sqrt{2} [/tex]
EXPLANATION
The given equation is:
[tex]50 - {x}^{2} = 0[/tex]
Group the constant term to get:
[tex]- {x}^{2} = 0 - 50[/tex]
[tex] - {x}^{2}=- 50[/tex]
[tex]{x}^{2}=50[/tex]
Take square root to get:
[tex]x = \pm \sqrt{50} [/tex]
We simplify further to remove the perfect square.
[tex]x = \pm \sqrt{25 \times 2} [/tex]
[tex]x = \pm \sqrt{25} \times \sqrt{2} [/tex]
[tex]x = \pm5\sqrt{2} [/tex]
Help me pleasssseeeeeee
Answer:
d. Distributive property
Step-by-step explanation:
The Distributive property of multiplication over addition is what allows you to multiply each of the terms in parentheses by the factor outside parentheses. It tells you ...
a(b +c) = ab + ac
It works both ways, also allowing you to remove a common factor to outside parentheses.
If the translation maps point (3,2) to (4,5); or T: (3,2) —> (4,5), then what is the image of point (0,0)? (4,5) (-1,-3) (1,3)
Answer:
(1, 3)
Step-by-step explanation:
If the translation is ...
(3, 2) + (a, b) = (4, 5)
Then we can find (a, b) by subtraction:
(4, 5) -(3, 2) = (a, b) = (4-3, 5-2) = (1, 3)
Not the image of point (0, 0) will be ...
(0, 0) + (a, b) = image
(0, 0) + (1, 3) = (0+1, 0+3) = (1, 3)
The image of the point is (1, 3).
Barry buys 6 loaves of bread. Each loaf weighs 1 1 4 pounds. What is the total weight of the bread in pounds? in ounces? A. 6 1 4 pounds; 100 ounces B. 7 1 2 pounds; 112 ounces C. 7 1 2 pounds; 120 ounces D. 9 pounds; 144 ounces
Answer:
C. 7 1/2 pounds; 120 ounces
Step-by-step explanation:
I'll assume you wanted to write each loaf weighs 1 and 1/4 (1.25) pounds and not 114 pounds... since that makes sense considering the choices for answer.
So, to get the total weight of the 6 loafs, we multiply by 6 the weight of one...
TP = 6 * 1.25 = 7.5 or 7 1/2 pounds
To get that in ounces, we just have to remember there are 16 ounces per pound... so
TO = 7.5 lbs * 16 ounces/lbs = 120 ounces
sin E =
Whats the answer
B is correct. I’ve noticed that you’ve posted a lot of questions like this, so here’s how I remember it. Soh-Cah-Toa
Soh stands for Sin=Opposite (the side opposite to the angle) over hypotenuse (the side opposite to the right angle)
Cah stands for Cos=Adjecent (the side next to the angle that is not the hypotenuse) over the hypotenuse
Toa stands for Tan=opposite over adjacent
Good luck! Hope I helped you understand.
is 3x^2 + 2x + 10 = 0 written in standard form?
Answer:
in the US, yes
in some other English-speaking countries, no
Step-by-step explanation:
"Standard form" depends on where you live. In the UK, the "standard form" of a quadratic equation is what is called "vertex form" in the US. That form is ...
3(x +1/3)^2 +29/3 = 0
In the US, the equation you show is in standard form.
Which system of linear inequalities is shown in the graph?
A)
y < x + 4
y ≥ -3x - 2
B)
y < x + 4
y ≤ -3x - 2
C)
y > x + 4
y ≤ -3x - 2
D)
y > x + 4
y ≥ -3x - 2
Any help would be greatly appreciated, thanks!
Answer:
D)
y > x + 4
y ≥ -3x - 2
Step-by-step explanation:
Blue line's boundary is above the line and dotted (>) so the equation: y > x + 4
Red line's boundary is above the line and solid (≥) so the equation: y ≥ -3x - 2
Answer
D)
y > x + 4
y ≥ -3x - 2
Answer:
D
Step-by-step explanation:
graph the function f( x ) = |x+2| - 3
Answer:
Find the attached
Step-by-step explanation:
To graph the given function, we would need to obtain pairs of points (x, f(x)). We can let x be;
-5, -4, -3, 3, 4, 5
we simply substitute each value of x in the given function to obtain the value of the function corresponding to the given x value;
when x = -5, f(-5) = |-5+2| - 3 = 0
when x = -4, f(-4) = |-4+2| - 3 = -1
when x = -3, f(-3) = |-3+2| - 3 = -2
when x = 3, f(3) = |3+2| - 3 = 2
when x = 4, f(4) = |4+2| - 3 = 3
when x = 5, f(5) = |5+2| - 3 = 4
The graph of the function is as shown in the attachment below.
Answer:
Find the attached
Step-by-step explanation:
To graph the given function, we would need to obtain pairs of points (x, f(x)). We can let x be;
-5, -4, -3, 3, 4, 5
we simply substitute each value of x in the given function to obtain the value of the function corresponding to the given x value;
when x = -5, f(-5) = |-5+2| - 3 = 0
when x = -4, f(-4) = |-4+2| - 3 = -1
when x = -3, f(-3) = |-3+2| - 3 = -2
when x = 3, f(3) = |3+2| - 3 = 2
when x = 4, f(4) = |4+2| - 3 = 3
when x = 5, f(5) = |5+2| - 3 = 4
A triangular plot of land is shown.
What is the longest dimension of the plot?
Enter your answer in the box.
Round only your final answer to the nearest foot.
___
Check the picture below.
make sure your calculator is in Degree mode.
Question Part Points Submissions Used Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.) cos(2θ) + sin^2(θ) = 0
[tex]\bf \textit{Double Angle Identities} \\\\ cos(2\theta)= \begin{cases} cos^2(\theta)-sin^2(\theta)\\ \boxed{1-2sin^2(\theta)}\\ 2cos^2(\theta)-1 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ cos(2\theta )+sin^2(\theta )=0\implies \boxed{1-2sin^2(\theta)}+sin^2(\theta )=0 \\\\\\ 1-sin^2(\theta )=0\implies 1=sin^2(\theta )\implies \pm\sqrt{1}=sin(\theta ) \\\\\\ \pm 1=sin(\theta )\implies sin^{-1}(\pm 1) = \theta \implies \theta = \begin{cases} \frac{\pi }{2}\\\\ \frac{3\pi }{2} \end{cases}[/tex]
To solve the equation cos(2θ) + sin^2(θ) = 0 using a double- or half-angle formula, rewrite the equation and combine like terms to simplify.
Explanation:To solve the equation cos(2θ) + sin^2(θ) = 0 using a double- or half-angle formula, we can rewrite the equation as:
2cos^2(θ) - 1 + sin^2(θ) = 0
Using the identity sin^2(θ) = 1 - cos^2(θ), we can substitute and simplify:
2cos^2(θ) - 1 + (1 - cos^2(θ)) = 0
Combining like terms, we have:
-cos^2(θ) + cos^2(θ) = 0
This simplifies to:
0 = 0
Since 0 = 0 is a true statement, the equation is satisfied for all values of θ within the interval [0, 2π).
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Use your calculator to find sin 52º.
Use your calculator to find cos 47°.
Answer:
sin of 52 is 0.98662759204
cos of 47 is 0.99233546915
Step-by-step explanation:
Find an equation of the tangent line to the curve at the given point. y = x , (4, 2) Step 1 To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (4, 2), we know that (4, 2) is a point on the line. So we just need to find its slope. The slope of a tangent line to f(x) at x = a can be found using the formula m tan = lim x→a f(x)-f(a)/ x-a
Answer:the answer is C
Step-by-step explanation:
The yearly attendance at a ballpark is shown in the table. Which answer describes the average rate of change from Year 2 to Year 5?
Answer:
A
Step-by-step explanation:
The average rate of change is the change in attendance over change in time.
Δy / Δx
(333.7 - 298.3) / (5 - 2)
11.8
So the average rate of change is an increase of 11.8 thousand people per year.
The average rate of change from Year 2 to Year 5 is 11.8 if at year 2 the attendance is 298.3 and at year 5 the attendance is 333.7
What is the rate of change?It is defined as the change in values of a dependent variable with respect to the independent variables.
We have to find the average rate of change from Year 2 to Year 5:
At year 2 the attendance = 298.3
At year 5 the attendance = 333.7
Average rate of change = (333.7-298.3)/(5-2)
= 11.8
Thus, the average rate of change from Year 2 to Year 5 is 11.8 if at year 2 the attendance is 298.3 and at year 5 the attendance is 333.7
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Help me pleassssseeeee
Hello There!
Martha’s first step would represent “Associative Property Of Addition”
This basically means that you can add or multiply these numbers regardless of how they are grouped in a sequence.
Please help me asap
math
Answer:
I think 478.4 ._.
Step-by-step explanation:
First, find out how many gallons of gasoline she can buy with $18.50 by dividing 18.50 by 1.25 to get 14.8 gallons. Then, since he already has 6 gallons in his tank, add 6 to 14.8 = 20.8. Finally multiply this by the ratio of gallons to miles (23) to get 478.4
HELP ASAP WILL MAKE YOU THE BRAINLIST
The height of one right circular cylinder is 7 centimeters and its radius is 2 centimeters. The height of the second right circular cylinder is 28 centimeters and its radius is also 2 centimeters. What is the ratio of the volume of the larger cylinder to the volume of the smaller cylinder?
A. 4:1
B. 5:1
C. 10:1
D. 25:1
These two right circular cylinders have the same height, 45 centimeters. The radius of the smaller cylinder is 22 centimeters and the radius of the larger cylinder is 6 times greater than that of the smaller cylinder. What is the ratio of the volume of the larger cylinder to the volume of the smaller cylinder?
A. 6:1
B. 12:1
C. 36:1
D. 150:1
A right square prism has a volume of 220 cubic meters. The prism is enlarged so its height is increased by a factor of 10, but the other dimensions do not change. What is the new volume?
Suppose that the volume of a right circular cylinder is 225 cubic meters and the area of its base is 25 square meters. What is the height of the cylinder?
A. 12 m
B. 9 m
C. 11 m
D. 35 m
There are two right circular cylinders. The radius of the first cylinder is 4 centimeters, and its height is 5 centimeters. The radius of the second cylinder is 12 centimeters, and its height is also 5 centimeters. What is the ratio of the volume of the larger cylinder to the volume of the smaller cylinder?
A. 3:1
B. 5:1
C. 6:1
D. 9:1
Answers:
#1: A
#2:C
#4:D
35,417 written in numerals
Answer:
30,000 5,000 400 10. 7
---------- ----
XXX V CD. X VII
The question appears to be a misunderstanding as the number '35,417' is already represented as numerals, which are symbols used to denote numbers. Therefore, '35,417' is already in its correct numeral form.
Explanation:The student is asking for the number '35,417' to be written in numerals but it is already written in numerals. Numerals are symbols used to represent numbers. For example, the numeral for the number one is 1, and the numeral for the number two is 2. Therefore, the numeral representation for '35,417' is simply 35,417.
The question appears to be a misunderstanding as the number '35,417' is already represented as numerals, which are symbols used to denote numbers. Therefore, '35,417' is already in its correct numeral form.
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Completer the blank with a <, >, or =
-2 _ -4
-10 _ -5
-3 _ 0
l -8 l _ l -5 l
4 _ l -8 l
I know which ones are bigger, but i always get confused what <, > means?
Answer:
>,<,<,>,<
Step-by-step explanation:
The bigger side in the >/< Symbols mean that value is larger
help please ..............
Answer:
6x is indeed the Greatest Common Factor.
Step-by-step explanation:
6x[3 - y² + 2y⁶]
law of sines? .
.
.
.
.
.
.
.
.
.
.
.
Answer:
b ≈ 3.1
Step-by-step explanation:
The law of sines tells you ...
b/sin(B) = c/sin(C)
Here, you have to find angle C based on the sum of the angles of a triangle being 180°.
C = 180° - A - B = 180° - 69° - 32° = 79°
Multiplying the above law of sines equation by sin(B), you have ...
b = c·sin(B)/sinc(C) = 5.7·sin(32°)/sin(79°) ≈ 3.07707
b ≈ 3.1 . . . . . rounded to tenths
Answer:
[tex]\displaystyle 3,1 ≈ b[/tex]
Step-by-step explanation:
First, find [tex]\displaystyle m∠C,[/tex]accourding to the Triangle-Sum Theorem:
[tex]\displaystyle 180° = 32° + 69° + m∠C \hookrightarrow 180° = 101° + m∠C; 79 = m∠C[/tex]
Now that we have all three angles, we can solve for edge b
[the second edge], using the Law of Sines:
[tex]\displaystyle \frac{c}{sin∠C} = \frac{b}{sin∠B} = \frac{a}{sin∠A} \\ \\ \frac{5,7}{sin\:79°} = \frac{b}{sin\:32°} \hookrightarrow 3,0770743283... = \frac{5,7sin\:32°}{sin\:79°} \\ \\ 3,1 ≈ b[/tex]
I am joyous to assist you at any time.
One number is 10 times as large as another, and their difference is 81. Find the numbers.
If x represents the smaller number, then the larger number is
10
10x
X - 10
Answer:
90
Step-by-step explanation:
10x - x = 81
9x = 81
x = 9
larger number = 10 x 9 = 90
For this case we have that "x" is the variable that represents the smallest number to find. Let and the variable that represents the largest number, then:[tex]y = 10x\\y-x = 81[/tex]
Substituting the first equation in the second:
[tex]10x-x = 81\\9x = 81\\x = \frac {81} {9}\\x = 9[/tex]
So, the biggest number is:
[tex]y = 10 * 9 \\y = 90[/tex]
Answer:
10x
90
–x + 5y = –2; {(7, 1.6), (5, 0.6), (6, 3.6), (4, –1.4)}
a.
{(5, 0.6)}
c.
{(6, 3.6)}
b.
{(4, –1.4)}
d.
{(7, 1.6)}
Answer:
a. {(5, 0.6)}
Step-by-step explanation:
A graph is a useful tool. It can help you find that the set of points that satisfies both functions is ...
{(5, 0.6)}
_____
Comment on the graph
Strictly speaking, the points connecting the dots of the second function are not part of the function. They are there simply to provide a visual aid in locating the points. As we see, the line goes through point (5, 0.6) exactly.
Which measurement is the measure of an obtuse angle?
Answer: An obtuse angle is any angle greater than 90° and less than 180°
Step-by-step explanation:
Answer:
An obtuse angle is more than 90 degrees so anything above 90 degrees is obtuse while anything below is either an acute, strait, or right angle.
Step-by-step explanation:
PLEASE HELP ME!!
1. What are the mean, median, mode and range of the data set given the altitude of lakes in feet: -12,-9,-14,-39,-49,-18, and -43?
2. Given the data 21,13,13,37,13,23,25,15:
a. What is the outlier in the data?
b. What is the mean with the outlier?
c. What is the mean without the outlier?
First put your numbers in order from least to greatest (These are negative numbers so that means that the smallest number is the one farthest away from zero)
-49, -43, -39, -18, -14, -12, -9
Mean is adding all the numbers together and dividing the sum by how many numbers there are in the data set
-49 + (-43) + (-39) + (-18) + (-14) + (-12) + (-9) = -184
There are seven numbers so divide -184 by 7:
-184 ÷ 7 ≈ 26.29
Median is the number in the middle. Take away the smallest number and the biggest number on each layer until you get to the middle
-49, -43, -39, -18, -14, -12, -9
-43, -39, -18, -14, -12
-39, -18, -14
-18 <-------------------Median
Mode is whatever number appears the most often in the data. In this case all the numbers appear only once so there is no mode
Range is subtracting the largest number by the smallest number
-9 - (-49) = 40
2. Data in order
13, 13, 13, 15, 21, 23, 25, 37
Outlier is the number that is a number that is rather far from the other number in the data
a. In this case the outlier is 37
b. 13 + 13 + 13 + 15 + 21 + 23 + 25 + 37 = 160
160 ÷ 8 = 20
c. 13 + 13 + 13 + 15 + 21 + 23 + 25 = 123
123 ÷ 7 = 17.57
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
Mean = 26.29
Median = -18
Mode = 40
2 a. 37
2 b. 20
2 c. 17.57
Step-by-step explanation:
Mean = -49 + (-43) + (-39) + (-18) + (-14) + (-12) + (-9) = -184
There are seven numbers so divide -184 by 7:
-184 ÷ 7 ≈ 26.29
Median =
-49, -43, -39, -18, -14, -12, -9
-43, -39, -18, -14, -12
-39, -18, -14
-18
Mode =
-9 - (-49) = 40
2.
13, 13, 13, 15, 21, 23, 25, 37
Outlier is the number that is an odd number
a. In this case the outlier is 37
b. 13 + 13 + 13 + 15 + 21 + 23 + 25 + 37 = 160
160 ÷ 8 = 20
c. 13 + 13 + 13 + 15 + 21 + 23 + 25 = 123
123 ÷ 7 = 17.57
I what are the values of the coefficient of each term and the constant term?
Step-by-step explanation:
[tex](4x - 2).6(2x + 7) \\ = (4x - 2)(12x + 42) \\ = 48 {x}^{2} + 168x - 24x - 84 \\ = 48 {x}^{2} + 144x - 84[/tex]
then
[tex]a = 48 \\ b = 144 \\ c = - 84[/tex]
Which inequality is graphed below?
ANSWER
[tex]y \geqslant \frac{1}{4} x - 1[/tex]
EXPLANATION
The graph has a solid boundary line.
The region above the boundary line is shaded
Therefore the inequality sign involved is '≥'
The boundary line has equation
[tex]y = \frac{1}{4} x - 1[/tex]
We can now conclude that, the inequality graphed above is
[tex]y \geqslant \frac{1}{4} x - 1[/tex]
Answer:
The answer is
Step-by-step explanation:
The inequality in the graphed above is y≥1/4x-1
Help me with ixl please
Answer:
$33.00
Step-by-step explanation:
You find out how much the sale price is by subtracting 25% of 40 from 40:
40 - [(.25)(40)] and that equals 30. So the sale price is $30. Now if the tax is 10% (.1 in decimal form), we find the total cost by adding .1(30) to 30:
30 + [(.1)(30)] which is $33
Samantha wanted to fill her new fish tank with goldfish and guppies. She bought 26 total fish. Each goldfish cost $3, and each guppy cost $4. She spent $86 total. How many guppies did she buy? 4 7 8 16
Answer:
8 guppies
Step-by-step explanation:
Let:
x = number of goldfishes
y = number of guppies
We can come up with two equations:
x + y = 26
3x +4y = 86
We use the first equation to come up with a solution for one of the unknowns:
x = 26 - y
We can use this to substitute the x on the second equation:
[tex]3x + 4y = 86\\\\3(26-y) + 4y=86\\\\78 - 3y + 4y = 86\\\\78 + y = 86\\\\y = 86 - 78\\\\y = 8[/tex]
So she bought 8 guppies.
The total guppies Samantha buys are 8 and the total goldfish she buys are 18 and this can be determined by forming the linear equation.
Given :
Samantha wanted to fill her new fish tank with goldfish and guppies. She bought 26 total fish. Each goldfish cost $3, and each guppy cost $4. She spent $86 in total.Let the total number of goldfish be 'x' and the total number of guppies be 'y'. Then the linear equation that represents the total number of fish is given by:
x + y = 26
x = 26 - y ---- (1)
The linear equation that represents the total spent $86 is given by:
3x + 4y = 86 --- (2)
Now, substitute the value of 'x' in equation (2).
3(26 - y) + 4y = 86
Simplify the above equation.
78 - 3y + 4y = 86
y = 86 - 78
y = 8
Now, substitute the value of 'y' in equation (1).
x = 26 - 8
x = 18
So, Samantha buys 8 guppies.
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