Answers
Answer:
G !!! Have a good day BLOODY
Related Questions
Y=8x-11
Y=x-17
Solve the system of equations
Answers
Answer:
[tex]x=-\frac{6}{7}[/tex]
[tex]y=-17\frac{6}{7}[/tex]
Step-by-step explanation:
We are given the following system of equations that we are to solve:
[tex] y = 8 x - 1 1 [/tex] - (1)
[tex] y = x - 1 7 [/tex] - (2)
Since the left hand side of both the equations is the same so we will equate the right hand sides of both the equations to get:
[tex]8x-11=x-17[/tex]
[tex]8x-x=-17+11[/tex]
[tex]7x=-6[/tex]
[tex]x=-\frac{6}{7}[/tex]
Substituting this value of [tex]x[/tex] in (1) to find [tex]y[/tex]:
[tex]y=8(-\frac{6}{7})-11[/tex]
[tex]y=-17\frac{6}{7}[/tex]
Final answer:
The solution to the system of equations y = 8x - 11 and y = x - 17 is found by setting the equations equal to each other and solving for x, then substituting back to find y. The solution is x = -6/7 and y = -125/7.
Explanation:
To solve the system of equations, you want to find a single value for x and y that satisfies both equations simultaneously. The given equations are:
y = 8x - 11
y = x - 17
Since both equations are equal to y, we can set them equal to each other and solve for x:
8x - 11 = x - 17
Now, let's get all the x terms on one side and the numbers on the other:
8x - x = -17 + 11
7x = -6
Dividing both sides by 7 gives us:
x = -6/7
Now that we have x, we can substitute it back into one of the equations to find y:
y = 8(-6/7) - 11
y = -48/7 - 11
Convert -11 to a fraction,
y = -48/7 - 77/7
y = -125/7
The solution to the system of equations is x = -6/7 and y = -125/7.
The function f(x) = 2x is a logarithmic function. true or false
Answers
Answer:
False.
Step-by-step explanation:
The function f(x) =2x is not an logarithmic function. Rather, it is a linear function. The reason for this is that in f(x) = 2x, there is no log or ln involved on the right hand side of the equation. It is the polynomial of the first degree, which means it is a straight line function. It is important to note that for any value of x, the value of the function changes with the same proportion. This is because the derivative of the function is a constant, which means that the rate of change is constant. The graph of the function will be a line passing from the origin and (1,2) and will have the positive slope. Therefore, f(x) is not a logarithmic function, which means that the statement is false!!!
Which of the following represents "the difference between ten and a number is the sum of eight and a number"? 10 - N(8 + N) 8 - N = 10 + N 10 - N = 8 + N
Answers
Answer:
[tex]\Huge \boxed{10-N=8+N}[/tex]
Step-by-step explanation:
Algebraic expressionsDifference: should be subtract.
N: should be a number.
Sum: Add
Therefore, the correct answer is 10-N=8+N.
Hope this helps!
Answer:
10-N=8+N
Step-by-step explanation:
10-N=8+N represents "the difference between ten and a number is the sum of eight and a number''.
You should go in order of PEMDAS:
P - parenthesis
E - exponents
M - multiplication
D - division
A - addition
S - subtraction
Which of the following points lie in the solution set to the following system of inequalities?
[tex]y < - 3x + 3 \\ y < x + 2[/tex]
A.(1,-5)
B.(1,5)
C.(5,1)
D.(-1,5)
Answers
Answer:
A. (1, -5)Step-by-step explanation:
Put the coordinates of the points to the each inequality, and check the inequality:
A. (1, -5)
y < -3x + 3
-5 < - 3(1) + 3
-5 < -3 + 3
-5 < 0 CORRECT
y < x + 2
-5 < 1 + 3
-5 < 3 CORRECT
B. (1, 5)
y < -3x + 3
5 < -3(1) + 3
5 < -3 + 3
5 < 0 FALSE
C. (5, 1)
y < -3x + 3
1 < -3(5) + 3
1 < -15 + 3
1 < -12 FALSE
D. (-1, 5)
y < -3x + 3
5 < -3(-1) + 3
5 < 3 + 3
5 < 6 CORRECT
y < x + 2
5 < -1 + 2
5 < 1 FALSE
Let u = <-4, 1>, v = <-1, 6>. Find -2u + 4v
Answers
Answer:
<4,22>.
Step-by-step explanation:
This question involves the concepts of addition and scalar multiplication of vectors. It is given that the vector u = <-4, 1> and v = <-1, 6>. To find -2u, simply multiply -2 with the elements of u. This will give:
-2u = <-4*-2, 1*-2> = <8, -2>.
Similarly:
4v = <-1*4, 6*4> = <-4, 24>.
Hence,
-2u + 4v = <8, -2> + <-4, 24> = <8-4, -2+24> = <4,22>.
So the correct answer is <4,22>!!!
To find -2u + 4v, we will perform vector addition after scaling vectors u and v by -2 and 4, respectively.
First, we scale the vector u by -2. To do this, we multiply each component of vector u by -2:
u = <-4, 1>
-2u = -2 * <-4, 1> = <(-2)*(-4), (-2)*1> = <8, -2>
Now, we scale the vector v by 4. To do this, we multiply each component of vector v by 4:
v = <-1, 6>
4v = 4 * <-1, 6> = <4*(-1), 4*6> = <-4, 24>
Now that we have -2u and 4v, we can add these two vectors together. We do this by adding the corresponding components:
-2u + 4v = <8, -2> + <-4, 24>
Adding the x-components:
8 + (-4) = 4
Adding they-components:
-2 + 24 = 22
Hence, the resultant vector of -2u + 4v is:
-2u + 4v = <4, 22>
So the solution to -2u + 4v is the vector <4, 22>.
Segment AB the diameter of circle M. The coordinates of A are (-4,3). The coordinates of M (1,5) what are the coordinates of B
It’s number 4 but if you can answer all that would be even better
Answers
Answer:
The correct answer is option 1) (6,7)
Step-by-step explanation:
Points to remember
Mid point formula
Let (x₁, y₁) and (x₂, y₂) be the end points of a line segment, then the coordinates of the midpoint of the line segment is given by
[(x₁ + x₂)/2, (y₁ + y₂)/2]
To find the coordinates of B
Let A(x₁, y₁) = (-4, 3), and M(1, 5)
Coordinates of B be (x₂, y₂)
We have,
[(x₁ + x₂)/2, (y₁ + y₂)/2] = (1, 5)
(x₁ + x₂)/2 = 1
(-4 + x₂)/2 = 1
-4 + x₂ = 2
x₂ = 2 + 4 = 6
(y₁ + y₂)/2 = 5
(3 + y₂)/2 = 5
3+ y₂ = 10
y₂ = 10 - 3 = 7
Therefore coordinates of B(6,7)
The correct answer is option 1) (6,7)
Final answer:
The coordinates of point B, which lies diametrically opposite to A on circle M with a known center at (1, 5), are determined to be (6, 7).
Explanation:
Since segment AB is the diameter of circle M, and we know the coordinates of A (-4, 3) and center M (1, 5), we can find B by using the fact that the center of the circle is the midpoint of the diameter. The midpoint formula states that the midpoint M can be found using the following formulas:
Mx = (Ax + Bx) / 2
My = (Ay + By) / 2
Therefore, to find Bx and By, we can rearrange the formula:
Bx = 2Mx - Ax
By = 2My - Ay
Solving this gives us B as:
Bx = 2(1) - (-4) = 6
By = 2(5) - 3 = 7
So the coordinates of point B are (6, 7).
A:what are the solutions to the Quadratic equation
x^2 +4=0?
B:what is the factored form of the quadratic equation x^2+4?
Answers
Answer:
The correct answer for question A is x=2i or x= -2i
The correct answer for question B is (x+2i)(x-2i)
Step-by-step explanation:
Solution of question A:
x²+4=0
Subtract 4 from both sides.
x²+4-4=0-4
x²=-4
Take square root of both sides
√x²=+/-√-4
We know that i=√-1
So,
x=+/-(√4)(√-1)
x=+/-2i
Therefore x= 2i, x= -2i
Solution of question B:
x²+4
It cannot be factored using real number coefficient. You have to use complex numbers.
As we know -4 =(2i)², so we can write as:
x²+4=x² - (-4)= x²-(2i)²
Now factor using the difference of squares:
x²+4=(x+2i) (x-2i)....
Write an exponential function y = abx for a graph that includes (1, 15) and (0, 6).
Answers
Answer:
[tex] y = 6(2.5)^x [/tex]
Step-by-step explanation:
[tex] y = ab^x [/tex]
Use (0, 6) and solve for a:
[tex] 6 = ab^0 [/tex]
[tex] 6 = a \times 1 [/tex]
[tex] a = 6 [/tex]
Use a = 6 and (1, 15) and solve for b.
[tex] 15 = 6b^1 [/tex]
[tex] 15 = 6b [/tex]
[tex] 6 = 2.5 [/tex]
[tex] y = 6(2.5)^x [/tex]
Answer:
see explanation
Step-by-step explanation:
Obtain the exponential function by substituting the given points into the equation.
Equation in form
y = a [tex]b^{x}[/tex]
Using (0, 6), then
6 = a [tex]b^{0}[/tex] = a ⇒ a = 6
Using (1, 15), then
15 = 6 [tex]b^{1}[/tex] = 6b ( divide both sides by 6 )
[tex]\frac{15}{6}[/tex] = b, hence
b = [tex]\frac{5}{2}[/tex]
Exponential equation is y = 6 [tex](\frac{5}{2}) ^{x}[/tex]
How to solve this problem
Answers
Answer:
B: (2, -1)
Step-by-step explanation:
1) First isolate the y in both equations
2) Set the equations equal to each other
3) Solve for x (you should get 2 and 5)
4) Insert the x values back in to get your y values
5) You should have gotten (2, -1) and (5, 2)
These are your two answers, but the question is only asking for one solution and (5,2) isn't one of the options, so it has to be (2,-1).
How many gallons of gasoline that's 6 percent ethanol must be added to 2,000 gallons of gasoline with no ethanol to get a mixture that's 4 percent ethanol?
Answers
Because 2000 is 3 % then you divide it by three then multiply by 4 to get 4%
Final answer:
To make a 4 percent ethanol mixture, 4000 gallons of 6 percent ethanol gasoline must be added to 2000 gallons of gasoline with no ethanol.
Explanation:
To determine how many gallons of gasoline containing 6 percent ethanol must be added to 2,000 gallons of gasoline with no ethanol to achieve a mixture that is 4 percent ethanol, we can use a simple algebraic equation.
Let x be the number of gallons of 6 percent ethanol gasoline we need to add. The total amount of ethanol in the new mixture will be 0.06x gallons since 6 percent of the x gallons is ethanol. We need the mixture to have 4 percent ethanol overall, so we can set up the equation: 0.06x / (2000 + x) = 0.04. We're calculating the proportion of ethanol in the total mixture, which includes the initial 2000 gallons plus the x gallons we're adding.
Multiplying both sides of the equation by (2000 + x) to eliminate the fraction gives us 0.06x = 0.04(2000 + x), which simplifies to 0.06x = 80 + 0.04x. Subtracting 0.04x from both sides gives us 0.02x = 80, and dividing both sides by 0.02 gives us x = 80 / 0.02. This simplifies to x = 4000.
Thus, 4000 gallons of 6 percent ethanol gasoline must be added to the 2000 gallons of non-ethanol gasoline to achieve a 4 percent ethanol mixture.
Kate used 555 grams of wool to knit a sweater, a hat, and a scarf. She used 5 times fewer grams for the hat than for the sweater. She used 5 grams more for the hat than for the scarf. How many grams of wool did she use to knit each item?
Answers
Answer:
Sweater =400 grams
Hat =80 grams
Scarf =75 grams
Step-by-step explanation:
The amount of wool used to make a sweater, a hat and a scarf=555 grams
Let the amount of wool used to make a sweater be = x
The amount of wool for the sweater =x/5
The amount of wool used for the scarf=x/5 -5
Total amount of wool used = x+(x/5)+(x/5-5)
x+x/5 +x/5-5=555
Multiply all through by the LCM 5
5x+x+x-25=2775
7x=2800
x=400
Sweater =400 grams
Hat=400/5=80 grams
Scarf =400/5 -5=75 grams
What is the slope of the line whose equation is y−4=5/2(x−2)?
Answers
Answer:
[tex]m=\dfrac{5}{2}[/tex]
Step-by-step explanation:
If the equation of the line is
[tex]y=mx+b,[/tex]
then m represents the slope of the line and b represents the y-intercept of the line. This equation is called the equation of the line in the slope form.
Rewrite the equation of the line in the slope form
[tex]y-4=\dfrac{5}{2}(x-2)\\ \\y-4=\dfrac{5}{2}x-\dfrac{5}{2}\cdot 2\\ \\y-4=\dfrac{5}{2}x-5\\ \\y=\dfrac{5}{2}x-1[/tex]
Thus, the slope of the line is
[tex]m=\dfrac{5}{2}[/tex]
The slope of a line whose equation is [tex]y-4 = \frac{5}{2}(x-2)[/tex] is [tex]\frac{5}{2}[/tex]
Further ExplanationSlope/gradientSlope or the gradient of a line refers to the change along the y-axis divided by the change along the x-axis.The slope of the line can be calculated from two co-ordinates of the line in question or obtained from the equation of a lineEquation of a straight line Equation of a straight line is written in the form [tex]y=mx+ c[/tex], where m and c are numbers.m is the slope or gradient of the line while c is the y-intercept.Equation of a straight line can be found when given:A slope of the line and one point where the line is passing through Two points where the line is passing throughA slope of the line and the y-interceptIn this case;
The equation in question is;
[tex]y-4 = \frac{5}{2}(x-2)[/tex]
Combining like terms;
[tex]y= \frac{5}{2}x-5+4[/tex]
The equation of the line is
[tex]y= \frac{5}{2}x-1[/tex]
From the equation the slope of the line is [tex]\frac{5}{2}[/tex], while
The y-intercept is -1
Keywords: Slope, Equation of a straight line, y-intercept,
Learn more about: Equations of a straight line: brainly.com/question/4932386Slope of a straight line: brainly.com/question/4932386Double intercept: brainly.com/question/4932386Level: High school
Subject: Mathematics
Topic: Equation of a straight line
Sub-topic: Slope/gradient of a line
What angle is included by AB and BC?
Answers
Answer:
B
Step-by-step explanation:
The answer is in the the question "What angle is included by line segments AB and BC?".
I see B in both of those line segments so they both must share the angle B.
Answer:
<B
Step-by-step explanation:
The included angle is the angle between the two sides AB and BC
The included angle is angle B
PLZ QUICK ILL GIVE U BRAINLIEST I NEED HELP FAST!!!
Based on the figure below, what is the value of x? A right angle is shown divided in two parts. The measure of the angle of one part is 30 degrees and the measure of the other part is 5x plus 15 degrees. 3 9 12 15
Answers
Answer:
x=9
Step-by-step explanation:
90-30= 60
now set 60 = 5x + 15
solve for x
45= 5x
divide by 5
x = 5
30+(5x+15)=90
Now add all like terms so 45+5x=90
Then subtract 45 on both sides to get 5x=45.
Finally divide 5 on both sides to get x equal to 9.
Answer is 9
Jeff has a big scoop of ice cream that is 10 inches tall. It melts by 25% in a minute. What is the height of the ice cream after one minute
Answers
Answer:
2.5 inches
Step-by-step explanation:
If Jeff has a big scoop of ice cream that is 10 inches tall and it melts by 25% in a minute, the height of the ice cream after one minute is 2.5 inches.
You have to find what 25% of 10 inches is.
25% of 10 inches = 2.5 inches
Therefore, the height of the ice cream after one minute is 2.5 inches.
Answer: 7.5 inches tall
Step-by-step explanation: if 25% of the ice cream melted, it means 75% is remaining, therefore you say 75÷100 =0.75 then you multiply it by 10 inches to get 7.5 inches.
A circle with a radius of 10 inches is placed inside a square with a side length of 20 inches. Find the probability that a dart thrown will land inside the circle.
a. 87.5%
b. 75.8%
c. 57.8%
d. 78.5&
Answers
Answer:
The correct answer is last option 78.5%
Step-by-step explanation:
Points to remember
Area of circle = πr²
Where r is the radius of circle
Area of square = a²
Where 'a' is the side length of square
To find the area of circle
Here r = 10 cinches
Area = πr²
= 3.14 * 10²
= 3.14 * 100 = 314
To find the area of square
Here a = 20 inches
Area = a²
= 20²
= 400
To find the probability percentage
Probability = area of circle/Area of square
= (314/400)*100
78.5 %
Which of the following is the solution of 5e2x - 4 = 11?
A. X=In 3
B.In 27
C. X=In13/2
D.X=3/In3
Answers
Answer:
c on edge 2020
Step-by-step explanation:
i just did the assignment
The solution of the exponential function is option (C) [tex]x=\frac{ln3}{2}[/tex] is the correct answer.
What is of natural log function?The natural log is the logarithm to the base of the number e and is the inverse function of an exponential function. It is denoted by ln x.
For the given situation,
The function is 5e^2x - 4 = 11
⇒ [tex]5e^{2x} - 4 = 11[/tex]
⇒ [tex]5e^{2x} = 11+4[/tex]
⇒ [tex]5e^{2x} = 15[/tex]
⇒ [tex]e^{2x} = \frac{15}{5}[/tex]
⇒ [tex]e^{2x} = 3[/tex]
Taking ln on both sides,
⇒ [tex]ln e^{2x} = ln3[/tex] [∵ ln e = 1 ]
⇒ [tex]{2x} = ln3[/tex]
⇒ [tex]x=\frac{ln3}{2}[/tex]
Hence we can conclude that the solution of the exponential function is option (C) [tex]x=\frac{ln3}{2}[/tex] is the correct answer.
Learn more about natural log function here
https://brainly.com/question/27945885
#SPJ2
z varies directly with x4 and inversely with y.
When x = 2 and y = 4, z = 3.
What is the value of z when x = 4 and y = 9?
Answers
3=(k*2)/4
3=k/2
k=6
***
z=6x/y
***
z=6*4/9
z=8/3
Answer:
[tex]z=\frac{63}{4}[/tex]
Step-by-step explanation:
When two variables vary in a directly proportional way, it means that when one variable grows, the other also grows.
This is represented by the following equation
[tex]y = kx[/tex]
Where k is the constant of proportionality
When two variables vary in an inversely proportional way, it means that when one variable grows, the other decreases.
This is represented by the following equation
[tex]y = \frac{k}{x}[/tex]
In this case we know that:
z varies directly with [tex]x^4[/tex] and inversely with y.
We write this as:
[tex]z = k\frac{x ^ 4}{y}[/tex]
We know that When [tex]x = 2[/tex] and [tex]y = 4,\ z = 3[/tex].
So we use this information to find the constant k
[tex]3 = k\frac{2 ^ 4}{4}[/tex]
[tex]3 = k\frac{16}{4}[/tex]
[tex]3 = 4k[/tex]
[tex]k = \frac{3}{4}[/tex]
So the equation is:
[tex]z = \frac{3}{4}\frac{x ^ 4}{y}[/tex]
Finally when x = 4 and y = 9 then:
[tex]z = \frac{3}{4}\frac{4 ^ 4}{9}[/tex]
[tex]z = \frac{3}{4}\frac{4 ^ 4}{9}[/tex]
[tex]z=\frac{63}{4}[/tex]
what is the volume of a rectangular prism with the base area of 15m2 and height of 5cm?
a. 70m3
b. 60m3
c. 75m3
d. 65m3
Answers
Answer:
The correct answer is option C. 75 m³
Step-by-step explanation:
Points to remember
Volume of rectangular prism = Base area * Height
To find the volume of given prism
Here Base area = 15 m² and
Height = 5 m
Volume = base area * height
= 15 * 5
= 75 m³
Volume of prism = 75 m³
Therefore the correct answer is option C. 75 m³
Answer:
Rectangular Prism Volume = length x width x height
Rectangular Prism Volume = 15 x 5
Rectangular Prism Volume = 75 cubic meters
Step-by-step explanation:
10.
A bookstore is having a sale. All comic books are reduced 15%. Fill in the blank to show a
correct representation of this sale.
A $20 comic book is reduced to?
Answers
[tex]20-20\cdot0.15=\boxed{17}[/tex]
Comic book cost is reduced from 20 dollars to 17 dollars.
Hope this helps.
r3t40
Answer:
A $20 comic book is reduced to $17
Step-by-step explanation:
Consider the provided information.
A bookstore is having a sale. All comic books are reduced 15%.
We need to Fill the blank to show a correct representation of this sale.
A $20 comic book is reduced to?
The cost of books are reduced to 15% that means now you need to pay only 85% of the price.
Therefore,
[tex]\frac{85}{100}\times 20=0.85\times20 =17[/tex]
Hence, A $20 comic book is reduced to $17
The volume of a cone is 3.x cubic units and its height is x units.
Which expression represents the radius of the cone's base, in units?
Answers
Answer:
Radius of the cone's base is 3x ....
Step-by-step explanation:
We have given that the volume of a cone is 3πx³
Height = x units.
The volume of a cone of radius r and height h units is given by:
V= 1/3 π r² *h
Simply plug the values given in the question into the above mentioned equation:
1/3πr²*x = 3*π*x³
1/3r²*x= 3x³
r² = 3*3*x³/x
r²=9x²
Taking square root at both sides we get:
√r² =√9x²
r = 3x
Thus the radius of the cone's base is 3x.
Answer: The volume given is 3Pi(x^3) and the radius is x. The formula for the volume of a cone is V= [1/3]Pi(r^2)*height => [1/3]Pi (r^2) x = 3Pi(x^3) => (r^2)x = 3*3(x^3) => (r^2)x = 9(x^3) => (r^2) = 9x^2 => r = sqrt[9x^2] = 3x. So THE CORRECT Answer is: A) r = 3x
Step-by-step explanation: I just paid for this answer
Help!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Option C is correct.
Step-by-step explanation:
-10<3x-4<8
Solving the given equation,
we know that if a<b<c then a<b and b<c
s0, -10<3x-4 and 3x-4<8
Solving to find the value of x
-10<3x-4
Switching sides,
3x-4>-10
3x > -10 +4
3x > -6
x > -6/3
x > -2
3x-4 < 8
3x < 8+4
3x < 12
x < 12/3
x < 4
s0, x >-2 and x < 4
-2 < x <4
Option C is correct.
-10 < 3x-4 < 8
Isolate x
First add 4 to each side:
-6 < 3x < 12
Divide each side by 3:
-2 < x < 4
The inequality signs do not contain equal to, so you would have open circles on both -2 and positive 4.
This means x is greater than -2 and less than 4, which is shown as the 3rd choice.
help me please I only got 20 min left
Answers
Answer:
I is at -7
Step-by-step explanation:
Step 1 : Find the distance between point F and G.
Point G is at 2
Point F is at 8
The distance between them is of 6 points/numbers.
Step 2 : Find I
Point H is -1
Point I will be 6 points/numbers behind point H so you have to count backwards.
Going 6 points/numbers backwards will bring you to -7 which is point I.
Therefore, I is -7.
!!
What is the golden rule for solving an equation?
Answers
i don't know all about them but a few are
1) What you are doing on one side do it on other side
eg -
x-10 = 5
x-10 + 10 = 5 + 10 [adding 10 on both the sides]
x= 15
or
10x = 100
10x/10 = 100/10
x = 10
or
x/ 10 = 10
x/10 * 10 = 10 * 10
x = 100
I hope you have understood
Graph g(x), where f(x) = 4x − 2 and g(x) = f(x + 1).
Answers
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]f(x)=4x-2[/tex]
[tex]g(x)=f(x+1)[/tex]
so
Find the function f(x+1)
substitute the variable x for the variable (x+1) in the function
[tex]f(x+1)=4(x+1)-2[/tex]
[tex]f(x+1)=4x+4-2[/tex]
[tex]f(x+1)=4x+2[/tex]
so
[tex]g(x)=4x+2[/tex]
Find the y-intercept
The y-intercept of g(x) is the point (0,2) (value of y when the value of x is equal to zero)
Find the x-intercept
The x-intercept of g(x) is the point (-0.5,0) (value of x when the value of y is equal to zero)
therefore
The graph in the attached figure
Answer:
C: (-0.5,0), (0,2)
Step-by-step explanation:
The function that represents a geometric sequence.
Answers
Answer:
C
Step-by-step explanation:
c is the answer to your question
Answer:
C
Step-by-step explanation:
graph the equation by translating y=|x|
y=|X+2|
Answers
Answer:
Step-by-step explanation:
Graph the absolute value function y = |x|. This is v-shaped and opens up.
Now translate the entire graph 2 units to the left. You will then have the graph of y=|x+2|.
Find the x-intercepts of the parabola with
vertex (6,-5) and y-intercept (0,175).
Write your answer in this form: (x1,71),(x2,42).
If necessary, round to the nearest hundredth.
Enter the correct answer.
Answers
Answer:
The x-intercepts are (5,0) and (7,0)
Step-by-step explanation:
we know that
The equation of a vertical parabola in vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
a is a coefficient
(h,k) is the vertex
In this problem we have
(h,k)=(6,-5)
substitute
[tex]y=a(x-6)^{2}-5[/tex]
Find the coefficient a
with the y-intercept (0,175) substitute the value of x and the value of y in the equation
For x=0, y=175
[tex]175=a(0-6)^{2}-5[/tex]
[tex]175=36a-5[/tex]
[tex]36a=180[/tex]
[tex]a=5[/tex]
substitute
[tex]y=5(x-6)^{2}-5[/tex]
Find the x-intercepts
Remember that the x-intercepts are the values of x when the value of y is equal to zero
For y=0
[tex]0=5(x-6)^{2}-5[/tex]
[tex]5(x-6)^{2}=5[/tex]
simplify
[tex](x-6)^{2}=1[/tex]
square root both sides
[tex]x-6=(+/-)1[/tex]
[tex]x=6(+/-)1[/tex]
[tex]x=6(+)1=7[/tex]
[tex]x=6(-)1=5[/tex]
therefore
The x-intercepts are (5,0) and (7,0)
a^-4+b^2 when a=2 and b=3/4 answer as a reduced fraction
Answers
[tex]\bf a^{-4}+b^2\implies \cfrac{1}{a^4}+b^2\qquad \begin{cases} a=2\\ b=\frac{3}{4} \end{cases}\implies \cfrac{1}{2^4}+\left( \cfrac{3}{4} \right)^2\implies \cfrac{1}{16}+\cfrac{3^2}{4^2} \\\\\\ \cfrac{1}{16}+\cfrac{9}{16}\implies \cfrac{1+9}{16}\implies \cfrac{10}{16}\implies \cfrac{5}{8}[/tex]
What is the measure of angle C?
Answers
Answer:
B.
Step-by-step explanation:
The triangle is equilateral, therefore its angles are 60°.