Answer:
x=11 and x=18
Step-by-step explanation:
The given quadratic equation is;
[tex](x-8)^2-13(x-8)+30=0[/tex]
Let u=(x-8)
[tex]u^2-13u+30=0[/tex]
Split the middle term;
[tex]u^2-10u-3u+30=0[/tex]
Factor by grouping
[tex]u(u-10)-3(u-10)=0[/tex]
[tex](u-10)(u-3)=0[/tex]
We have either u=10 or u=3
This implies that;
x-8=10 or x-8=3
x=10+8 or x=3+8
x=18 or x=11
Answer:
The answer is D on EDGE 2020
Step-by-step explanation:
3/4 of Melissa's friends babysit for extra money. 2/3 of her friends babysit and pet sit. What fraction of those who babysit also pet sit?
A) 1/2
B) 1/4
C) 12/17
D) 8/9
Do 3/4 of 2/3
Turn the demoninator into 12 so:
9/12 8/12 so I’m guessing C
Answer: The correct option is (D) [tex]\dfrac{8}{9}.[/tex]
Step-by-step explanation: Given that [tex]\dfrac{3}{4}[/tex] of Melissa's friends babysit for extra money and [tex]\dfrac{2}{3}[/tex] of her friends babysit and pet sit.
We are to find the fraction of her friends those who babysits also pet sits.
Total fraction of Melissa's friends is given by
[tex]F=\dfrac{3}{4}.[/tex]
Therefore, the fraction of her friends those who babysits also pet sits is given by
[tex]f=\dfrac{\frac{2}{3}}{\frac{3}{4}}=\dfrac{2}{3}\times\dfrac{4}{3}=\dfrac{8}{9}.[/tex]
Thus, the required fraction is [tex]\dfrac{8}{9}.[/tex]
Option (D) is CORRECT.
Select the correct answer. Which inequality is true? A. |-5| > |-7| B. |-8| < |-5| C. |9| < |7| D. |-9| > |8|
To determine which inequality is true, compare the absolute values of the given numbers. The correct answer is B, |-8| < |-5|.
Explanation:To determine which inequality is true, we need to compare the absolute values of the given numbers. Absolute value is the distance of a number from zero on the number line. In this case:
A. |-5| is greater than |-7|, so |-5| > |-7| is true.B. |-8| is less than |-5|, so |-8| < |-5| is true.C. |9| is not less than |7|, so |9| < |7| is false.D. |-9| is greater than |8|, so |-9| > |8| is true.
Therefore, the correct answer is B, |-8| < |-5|.
what is the surface area of the right cylinder with a height of 20 and a radius of 5
Answer: The answer is 785.4
Step-by-step explanation: Equation is 2πrh+2πr²
Plug in your numbers and hit enter!
Hope this helps
For this case we have by definition, that the surface area of a cylinder is given by:
[tex]SA = 2 \pi * r * h + 2 \pi * r ^ 2[/tex]
Where:
A: It's the radio
h: It's the height
According to the given data we have:
[tex]SA = 2 \pi * (5) * 20 + 2 \pi * (5) ^ 2\\SA = 200 \pi + 50 \pi\\SA = 250 \pi\\SA = 785 \ units ^ 2[/tex]
ANswer:
[tex]785 \ units ^ 2[/tex]
Write -1/14,7/9,-4/5 in order from least to greatest
7/9 is going to be the greatest since it is the only positive number and the. it’s going to be -4/5 and then the least is going to be -1/14.
-1/14 , -4/5 , 7/9
The numbers -1/14, 7/9, -4/5 arranged from least to greatest are -4/5, -1/14, 7/9. This is found by converting fractions to decimals for easier comparison and then arranging them in order.
Explanation:To go about solving this, we first consider each number's location on the number line. The numbers closer to the left are smaller than those on the right. Given the numbers -1/14, 7/9, and -4/5, we can start by converting each fraction to a decimal for easier comparison.
-1/14 equals approximately -0.0714, 7/9 equals approximately 0.7777, and -4/5 equals -0.8. Therefore, from smallest to largest, these numbers can be arranged as -0.8, -0.0714, 0.7777. Converting these back to fractions gives us the desired result: -4/5, -1/14, 7/9.
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Please help will give brainliest
This relation is a function because a function, in fact this is a linear function. We have that:
[tex]\left[\begin{array}{cc}x & y\\2 & 3\\4 & 4\\6 & 5\\8 & 6\end{array}\right][/tex]
As you can see below, all the points have been plotted an this is a linear function. Therefore, with two points we can get the equation, so:
[tex]The \ equation \ of \ the \ line \ with \ slope \ m \\ passing \ through \ the \ point \ (x_{1},y_{1}) \ is:\\ \\ y-y_{1}=m(x-x_{1}) \\ \\ \\ y-3=\frac{4-3}{4-2}(x-2) \\ \\ \\ y-3=\frac{1}{2}(x-2) \\ \\ y=\frac{1}{2}x-1+3 \\ \\ y=\frac{1}{2}x+2 \\ \\ \\ Where: \\ \\ (x_{1},y_{1})=(2,3) \\ \\ (x_{2},y_{2})=(4,4)[/tex]
Finally, the equation is:
[tex]\boxed{y=\frac{1}{2}x+2}[/tex]
Answer:
y=0.5x +2
Step-by-step explanation:
A survey of pet owners found that on average, they spend $1,225 annually per pet, with a standard deviation of $275. Between which two amounts would you expect 95% of the survey’s respondents to spend annually per pet if the sample is approximately normal and comes from a normally distributed population? $675 and $1,500 $675 and $1,775 $950 and $1,500 $950 and $1,775
Answer:
B.$675 and $1,775
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
e2020 exam
A multiple choice test has 5 possible answers. Find the probability of answering all the questions correctly
The answer is 1/5
Step-by-step explanation:
You have the probability of getting 1/5 correct.
For this case, we have by definition, the calculation of probabilities:
[tex]probability = \frac {number\ of \favorable\ cases} {number\ of\ possible\ cases}[/tex]
We have 5 possible answers, and we have only one favorable case, that is, only one correct option among the 5 possible answers.
So, we have:
[tex]Probability = \frac {1} {5} = 0.2[/tex]
Answer:
0.2
Lines
m
and
n
are parallel. The equation of line m is =3+3
y
=
3
x
+
3
. What is the equation of line
n
?
Answer:
y = 3x + bStep-by-step explanation:
Parallel lines have the same slope.
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation of the line m:
[tex]m:\ y=3x+3\to m=3[/tex]
Therefore the equation of a line n parallel to the line m is:
[tex]y=3x+b[/tex]
where b is any real number
Answer y = 3x + b
Step-by-step explanation:
If
q
(
x
)
is a linear function, where
q
(
−
1
)
=
3
, and
q
(
3
)
=
5
, determine the slope-intercept equation for
q
(
x
)
, then find q(2).
The equation of the line is:
q(2) =
If
t
(
x
)
is a linear function, where
t
(
−
4
)
=
3
, and
t
(
4
)
=
4
, determine the slope-intercept equation for
t
(
x
)
, then find t(0).
The equation of the line is:
t(0) =
Answer:
[tex]\large\boxed{Q1.\ q(x)=\dfrac{1}{2}x+\dfrac{7}{2},\ q(2)=\dfrac{9}{2}}\\\boxed{Q2.\ t(x)=\dfrac{1}{2}x+\dfrac{7}{2},\ t(0)=\dfrac{7}{2}}[/tex]
Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{We have}\\\\q(-1)=3\to(-1,\ 3)\\q(3)=5\to(3,\ 5)[/tex]
[tex]\text{Calculate the slope:}\\\\m=\dfrac{5-3}{3-(-1)}=\dfrac{2}{4}=\dfrac{2:2}{4:2}=\dfrac{1}{2}\\\\\text{We have the equation:}\\\\y=\dfrac{1}{2}x+b\\\\\text{Put the coordinates of the point (-1, 3) to the equation:}\\\\3=\dfrac{1}{2}(-1)+b\\\\3=-\dfrac{1}{2}+b\qquad\text{add}\ \dfrac{1}{2}\ \text{to both sides}\\\\3\dfrac{1}{2}=b\to b=3\dfrac{1}{2}=\dfrac{7}{2}[/tex]
[tex]q(x)=\dfrac{1}{2}x+\dfrac{7}{2}\\\\q(2)-\text{put x = 2 to the equation:}\\\\q(2)=\dfrac{1}{2}(2)+\dfrac{7}{2}=\dfrac{2}{2}+\dfrac{7}{2}=\dfrac{9}{2}[/tex]
[tex]t(-4)=3\to(-4,\ 3)\\t(4)=4\to(4,\ 4)\\\\m=\dfrac{4-3}{4-(-4)}=\dfrac{1}{8}\\\\y=\dfrac{1}{8}x+b\\\\\text{put the coordinates of the point (4,\ 4):}\\\\4=\dfrac{1}{8}(4)+b\\\\4=\dfrac{1}{2}+b\qquad\text{subtract}\ \dfrac{1}{2}\ \text{from both sides}\\\\3\dfrac{1}{2}=b\to b=3\dfrac{1}{2}=\dfrac{7}{2}\\\\t(x)=\dfrac{1}{2}x+\dfrac{7}{2}\\\\t(0)=\dfrac{1}{2}(0)+\dfrac{7}{2}=0+\dfrac{7}{2}=\dfrac{7}{2}[/tex]
graph the function f(x) = cos(2x) +1
The graph of the function f(x) = cos(2x) + 1 is added as an attachment
Sketching the graph of the function
From the question, we have the following parameters that can be used in our computation:
f(x) = cos(2x) + 1
The above function is a cosine function that has been transformed as follows
Horizontally stretched by a factor of 1/2Shifted up by 1 unitNext, we plot the graph using a graphing tool by taking not of the above transformations rules
The graph of the function is added as an attachment
what is the y-coordinate of the image of P(3,-4) after a reflection in the x-axis?
Answer:
[tex]\boxed{4}[/tex]
Step-by-step explanation:
When you reflect a point (x, y) across the x-axis, the x-coordinate remains the same, but the y-coordinate gets the opposite sign.
Thus, the y-coordinate becomes [tex]\boxed{\textbf{4}}[/tex].
simplify please. i'm failing and grade cost 4 summitives.
|-10|+|5|
A)-15
B)-5
C)5
D)15
Answer:
D = 15
Step-by-step explanation:
|-10|+|5|=10+5=15
|-10|=10
|5|=5
Answer:
D)15
Step-by-step explanation:
| | these cancel out the negative in the ten making it a positive
so it would be 10+5
which is 15
Solve the following equation. Then place the correct number in the box provided. x - 5 = 10
Answer: [tex]x=15[/tex]
Step-by-step explanation:
You can observe in the exercise that the equation you need to solve is:
[tex]x-5=10[/tex]
You need to find the value of the variable "x" of this equation. To do this, you need to remember the Addition Property of equality, which states that:
[tex]If\ a=b\ then\ a+c=b+c[/tex]
Knowing this, to solve for the variable "x", you must add 5 to both sides of the equation. Therefore, you get this result:
[tex]x-5+5=10+5\\x=15[/tex]
Help me with these 2 problems
Answer:
Part a) The width of parking lot is 87m.
Part b) The length of rectangular pool is 94 m
Step-by-step explanation:
a) The area of parking lot Area= 8439 m^2
Length of Parking Lot = Length = 97 m
Width of Parking Lot = Width= ?
Area of rectangle = Length * Width
Putting the values,and finding width,
8439 = 97 * Width
=> Width = 8439/97
=> Width = 87 m
So, The width of parking lot is 87m.
b) Perimeter of rectangular pool = Perimeter= 344 m
Width of rectangular pool = Width = 78 m
Length of rectangular pool = Length = ?
The formula for perimeter is:
Perimeter = 2*(Length + Width)
Putting values in the formula:
344 = 2*(Length + 78)
344/2 = Length + 78
172 = Length + 78
=> Length = 172 - 78
Length = 94 m
So, the length of rectangular pool is 94 m.
I NEED HELP WHAT IS 100,00 X 100,00
10,000
x 10,000
________
100,000,000
Answer:
100,000,000
Step-by-step explanation:
Write an equation for the following points:
(1, 25) (2, 5) (3, 1)
Answer:
Use desmos.com/calculator. It is a graphing calculator that can do many things
Step-by-step explanation:
say thanks and vote
Find the surface area of each pyramid to the nearest whole number.
Your answer would be A = 444.72 Or 445
find the range of the following data set 31,31,22,28,23
Answer:
9
Step-by-step explanation:
since 2 is the minimum and 31 is the maximum you subtract 31 by 22
To find the range of the given data set, follow these steps:
1. Identify the maximum value in the data set.
2. Identify the minimum value in the data set.
3. Subtract the minimum value from the maximum value.
Let's apply these steps to the provided data set:
Data set: 31, 31, 22, 28, 23
Step 1: Find the maximum value.
Looking at the numbers, the maximum value is 31. (Both occurrences of 31 are considered, but since they are the same, the maximum is still 31.)
Step 2: Find the minimum value.
Looking at the numbers, the minimum value is 22.
Step 3: Calculate the range.
Subtract the minimum value from the maximum value: 31 - 22 = 9.
Hence, the range of the given data set is 9.
what is the similarity ratio of the smaller to the larger cones?
Answer:
that the are both have a right angle. And that the are both cones.
Step-by-step explanation:
Answer:
3 : 5
Step-by-step explanation:
The ratio can be determined using the radii or the heights of the 2 cones
radii 6 : 10 = 3 : 5 ← in simplest form
height 9 : 15 = 3 : 5 ← in simplest form
A system of two equations has no solution. One equation is -15x+y=18.
Select the equation that would make this system infinitely many solutions.
A) 3y-45x=54
B)3y+45x=54
C)45x+3y=-54
D)45x-3y=54
A.
If you multiply the original equation by 3 you get -45x+3y=54, which is the exact same as A, therefore they have infinite solutions.
What is the product of 2x + y and 5x – y + 3?
Answer:
The correct answer is 10x² + 3xy + 6x - y² + 3y
Step-by-step explanation:
It is given an expression (2x + y)(5x - y + 3)
To find the product
(2x + y)(5x - y + 3) = 2x * 5x - 2x*y + 2x*3 + y*5x -y² + 3y
= 10x² - 2xy + 6x + 5xy - y² + 3y
= 10x² + 3xy + 6x - y² + 3y
Therefore the correct answer is
10x² + 3xy + 6x - y² + 3y
The product of (2x + y) and (5x – y + 3) is found by using the distributive property of multiplication over addition, which gives us: 10x^2 + 3xy + 6x - y^2 + 3y.
Explanation:To find the product of (2x + y) and (5x – y + 3), we need to use the distributive property of multiplication over addition. This involves multiplying each term within the first parentheses by each term in the second parentheses.
The steps are as follows:
Multiply 2x by each term in the second parentheses: (2x*5x, 2x*-y, 2x*3)Multiply y by each term in the second parentheses: (y*5x, y*-y, y*3)Sum up all the products obtained.The result is 10x^2 -2xy + 6x + 5xy - y^2 + 3y. Simplifying further gives us: 10x^2 + 3xy + 6x - y^2 + 3y.
So, the product of (2x + y) and (5x – y + 3) is 10x^2 + 3xy + 6x - y^2 + 3y.
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Find the circumference if radius =26
Circumference can be found using [tex]C=2\pi r[/tex] formula. Where [tex]r[/tex] is radius.
Now we just put in the data.
[tex]C=2\pi\times26=52\pi\approx\boxed{163.36}[/tex]
If the radius is 26, firstly we have to calculate the diameter. The diameter is 2 times the radius.
Radius = 26
Diameter = 26 × 2 = 52
Circumference of circle = π × Diameter
= π × 52
= 163.3628 or 163.4 (to 1 dp)
create a circle with a centre of (0,0) and a radius of 13
Answer:
The equation would be:
[tex]x^2+y^2=169[/tex]
In the attachment!!!
Hope this helps!!!
[tex]Sofia[/tex]
Let F(x) 3x^2+2
The quadratic function g(x) is the function f(x) stretch vertically by a factor of 4
Enter the equation of g(x) in the box
Answer: g(x)=12x^2+8
Step-by-step explanation:
original function f(x)=3x^2+2
Now to stretch function vertically and rename to g(x) we just multiply the function by 4;
g(x)=4(3x^2+2)=12x^2+8
Any questions feel free to ask. Thanks
The equation of the function f(x) after stretching is g(x) = 12x² + 8.
What is a function ?A function is a law that relates a dependent and an independent variable.
The function given is
F(x) = 3x²+2
For when a function is vertically stretched
F'(x) = k .F(x)
k >1
here it is given that k = 4
The equation becomes
g(x) = 4( 3x²+2 )
g(x) = 12x² + 8
Therefore , The equation of the function f(x) after stretching is g(x) = 12x² + 8.
To know more about Function
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Name two three dimensional figures that produce a square when sliced horizontally by a plane
Answer:
A rectangular prism and a cube.
Step-by-step explanation:
A rectangular prism when sliced by a plane can have a square facing up, meaning that a square will be produced. A cube has all square faces and when cut horizontally will produce a square.
Algebra manipulation. Thank you! My answer is - 8/5 but I want to make sure :)
Start with
[tex]\dfrac{2a+3b}{a+b}=7[/tex]
Assuming [tex]a\neq -b[/tex], multiply both sides by [tex]a+b[/tex]
[tex]2a+3b = 7a+7b[/tex]
Solve for [tex]a[/tex]
[tex]5a = -4b \iff a = -\dfrac{4b}{5}[/tex]
Substitute this value for [tex]a[/tex] in the desired expression:
[tex]\dfrac{2a}{b} = \dfrac{\frac{-8b}{5}}{b} = -\dfrac{8}{5}[/tex]
You were correct! :)
what is the x-coordinate of the solution
Answer:
x=-4
Step-by-step explanation:
A total of 800 pre-sale tickets and tickets at the gate were sold to the football city championship game. if the number of tickets sold at the gate was thirteen less then twice the number of pre-sale tickets, how many pre-sale tickets were sold?
ANSWER
271 pre-sale tickets were sold.
EXPLANATION
Let p represent the number of pre-sale tickets and t represent the number of tickets sold.
According to the question,a total of 800 pre-sale tickets and tickets were sold .
This implies that,
[tex]p + t = 800[/tex]
Also the number of tickets sold is 13 less than twice the number of pre-sale tickets.
This gives another equation:
[tex]t = 2p - 13[/tex]
We substitute, the second equation into the first equation to obtain:
[tex]p + 2p - 13 = 800[/tex]
This implies that;
[tex]3p = 813[/tex]
Divide both sides by 3
[tex]p = \frac{813}{3} = 271[/tex]
Hence 271 pre-sale tickets were sold.
By setting up an algebraic equation and denoting pre-sale tickets as x, we discover that 271 pre-sale tickets were sold for the football city championship game.
To solve the problem of how many pre-sale tickets were sold for the football city championship game, we can set up an algebraic equation. Let's denote the number of pre-sale tickets as x. According to the question, the number of tickets sold at the gate is thirteen less than twice the number of pre-sale tickets, which we can express as 2x - 13. We are given that the total number of tickets sold is 800.
So, we set up the equation:
x + (2x - 13) = 800
Combining like terms, we get:
3x - 13 = 800
Adding 13 to both sides:
3x = 813
Then we divide both sides by 3 to find the value of x:
x = 813 / 3
x = 271
Therefore, 271 pre-sale tickets were sold.
determine if -1, 1, 4, 8 is a geometric sequence
ANSWER
No, because there is no common ratio
EXPLANATION
The given sequence is
-1, 1, 4, 8
If this sequence is geometric, then there should be a common ratio among the consecutive terms.
[tex] \frac{1}{ - 1} \ne \frac{4}{1} \ne \frac{8}{4} [/tex]
Hence the sequence
-1, 1, 4, 8
is not a geometric sequence.
Answer:
The sequence is not a geometric sequence
Step-by-step explanation:
In a geometric sequence you find the following term multiplying the current by a fixed quantity called the common ratio.
To prove if a sequence is geometric we need to check if the ratio is consistent across the sequence. To check for the ratio we use the formula:
[tex]r=\frac{a_n}{a_{n-1}}[/tex]
were
[tex]r[/tex] is the ratio
[tex]a_n[/tex] is the current term
[tex]a_{n-1}[/tex] is the previous term
Let's star with 1, so [tex]a_n=1[/tex] and [tex]a_{n-1}=-1[/tex]
[tex]r=\frac{a_n}{a_{n-1}}[/tex]
[tex]r=\frac{1}{-1}[/tex]
[tex]r=-1[/tex].
Now let's check 4 and 1, so [tex]a_n=4[/tex] and [tex]a_{n-1}=1[/tex]
[tex]r=\frac{a_n}{a_{n-1}}[/tex]
[tex]r=\frac{4}{1}[/tex]
[tex]r=4[/tex]
Since the ratios between two pair of numbers are different, we can conclude that the sequence is not geometric.
Please help its due tonight.
A bridge crosses a circular lake. The bridge is represented by the function
y −x = 2 and the lake is represented by the function x^2 +y ^2 = 100.
a. What is the radius of the lake?
b. Find the length of the bridge.
Answer:
a) The radius of the lake to be r=10 units.
b) [tex]14\sqrt{5}[/tex] units
Step-by-step explanation:
The lake has equation: [tex]x^2+y^2=100[/tex]
We can rewrite this as [tex]x^2+y^2=10^2[/tex]
Comparing this to [tex]x^2+y^2=r^2[/tex]
We have the radius of the lake to be r=10 units.
b) The bridge is represented by the function y −x = 2
This is the same as y=x+2
We substitute this into the equation of the circle to get:
[tex]x^2+(x+2)^2=100[/tex]
[tex]x^2+x^2+4x+4-100=0[/tex]
[tex]2x^2+4x-96=0[/tex]
[tex]x^2+2x-48=0[/tex]
[tex](x+8)(x-6)=0[/tex]
[tex]x=-8,x=6[/tex]
When x=8, y=2(8)+2=18
When x=-6, y=2(-6)+2=-10
The length of the bridge is the distance between the points (8,18) and (-6,-10)
[tex]=\sqrt{(8--6)^2+(18--10)^2}[/tex]
[tex]=\sqrt{196+784}[/tex]
[tex]=\sqrt{196+784}[/tex]
[tex]=\sqrt{980}[/tex]
[tex]=14\sqrt{5}[/tex]