We solve as follows:
[tex]\frac{2}{3}+\frac{5}{6}=\frac{3}{2}[/tex]10. What is the equation of the directrix for the parabola-8(y - 3)=(x +4)2?A) y=5B) y=1C) y=-2D) y=-6
SOLUTION:
Step 1:
In this question, we are given the following:
The equation of the directrix for the parabola:
[tex]-8\text{ \lparen y-3\rparen= \lparen x+ 4\rparen}^2[/tex]Step 2:
The details of the solution are as follows:
Next, we can see that the equation of the directrix for the parabola is at:
[tex]\text{y = 5 }[/tex]This is because:
[tex]\begin{gathered} y\text{ -3 = \lparen}\frac{-1}{8})\text{ \lparen x + 4 \rparen}^2 \\ y\text{ = \lparen-}\frac{1}{8})\text{ \lparen x + 4\rparen}^2+\text{ 3} \end{gathered}[/tex]Then, y = k - p
y = 3 - p
p = 1/ 4a
p = 1 / 4(-1/8)
p = -2
y = 5
1. A contractor is building a new room onto the back of
Darnell's house. The contractor adds a diagonal brace to
the frame of one of the walls. The frame is 15 feet long
and 8 feet tall. How long is the diagonal brace?
Answer:
the answer is 23
Step-by-step explanation: use the formala of a triangle
which means you either add or subtract the sides and since it is the big side you are missing you have to add and when you do you get 23
A ferry travelled from Jetty A to Jetty B in 3 h. It then travelled from Jetty B back to
Jetty A in 2 h. The distance between the two jetties was 80 km.
Find the total time taken for the whole journey.
Find the average speed for the whole journey.
Average Speed = 160÷5= 32km/hr
Given,
A ferry traveled from Jetty A to Jetty B in 3 h. It then traveled from Jetty B back to Jetty A in 2 h. The distance between the two jetties was 80 km.
To find,
Total time for the whole journey,
Solution: Time is taken from Jetty A to Jetty B = 3 hours
and Jetty B to Jetty A = 2 hours
Total time = 3 h + 2 h = 5 h
Average Speed = Total Distance ÷ Total Time
Since, Total distance = 80×2= 160
Average Speed = 160÷5= 32km/hr
a) 5 hours
b) 32km/hr
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graph the linear function identify the x-intercept.
y=-x
The x-intercept of the given linear function is 0 and the graph of the linear ufnction is shown.
What is the x-intercept?A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = MX + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.So, plot the linear function:
Plot y = -x as follows:(Refer to the graph attached below)
We can clearly see that the x-intercept is 0.Therefore, the x-intercept of the given linear function is 0 and the graph of the linear ufnction is shown.
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find area and perimeter
Answer:
Area: 20cm^2
perimeter: 20cm
(4*2) + (4*3) =
8 + 12 = 20cm^2
Which answer choice uses exponents to show the expression below?
10(5 · 5 + 10) − 2 · 2 · 2
Answer:
5² · 10 + 10² - 2³
Step-by-step explanation:
10(5 · 5 + 10) − 2 · 2 · 2 =
= 5² · 10 + 10² - 2³
what is 95% of 40?part. ___ = ___. percentwhole. 100 percent
1) According to that table we can write:
40-------100
x-------95
100x = 40*95
x= 38
2) So filling in we have:
Cross multiplying it we can find that 38 is 95% of 40.
Exit Ticket : Submit on Schoology Write an equations that represents the proportional relationship between the time in class x and the number of pages y. Hotebo... Create a table & graph to represent the proportional relationship. 5/29/21 Liana takes 2 pages of notes during each hour of class.
Given that;
Liana takes 2 pages of notes during each hour of class.
To write a proportional relationship, let x represent the time in class and y represent the number of pages.
[tex]y=kx[/tex]according to the question, the constant of proportionality is equal to 2. ( 2 pages per hour).
So, the equation becomes;
[tex]y=2x[/tex]Therefore, an equation to represent the proportional relationship is;
[tex]y=2x[/tex]We can represent the equation on the graph as;
We can also represent it on the table as;
[tex]\begin{gathered} x\text{ y} \\ 1\text{ 2} \\ 2\text{ 4} \\ 3\text{ 6} \\ 4\text{ 8} \\ 5\text{ 10} \end{gathered}[/tex]Where x is in hours and y is in pages.
A rock is thrown vertically from the ground with a velocity of 28 meters per second, and it reaches a height of -5.2t2 + 28.6t + 4 after t seconds. How many seconds after the rock is thrown will it reach maximum height?
After 2.75 seconds of motion in the upward direction, the stone will reach maximum height.
What is the general equation of a parabola?The general equation of a parabola is given by y = a(x – h)² + k or
x = a(y – k)² + h. Here (h, k) denotes the vertex
We have a rock which is thrown vertically from the ground with a velocity of 28 meters per second, and it reaches a height of -5.2t² + 28.6t + 4 after t seconds.
We have -
y = - 5.2t² + 28.6t + 4
dy/dx = - 10.4t + 28.6
For maximum height -
dy/dx = 0
- 10.4t + 28.6 = 0
28.6 = 10.4t
t = 28.6/10.4
t = 2.75 seconds
Therefore, after 2.75 seconds of motion in the upward direction, the stone will reach maximum height.
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what 6y=3x-9, in the simplest form
Answer: x=2y+3
Step-by-step explanation:
Switch around the 6y
3x-9=6y
Add 9 to both sides
3x-9+9=6y+9
3x=6y+9
Divide everything by 3
x=2y+3
the lengths of the upper end lower bases of a trapezoid are 6 centimeters and 10 centimeters respectively, and the distance between them is 15 centimeters. what is the area of the trapezoid
Given data:
The upper end length of the trapezoid is: a=6 cm
The lower end length of the trapezoid is: b=10 cm
The height of the trapezoid is: h=15 cm
The expression to calculate the area of the trapezoid is,
[tex]A=\frac{1}{2}\times h\times(a+b)[/tex]Substitute vall known values in the above expression.
[tex]\begin{gathered} A=\frac{1}{2}\times15\times(6+10) \\ =\frac{1}{2}\times15\times16 \\ =\frac{240}{2} \\ =120cm^2 \end{gathered}[/tex]Thus, the area of the trapizoid is 120 square centi meter.
JJ decides to leave a tip that is 15% of the original price for his meal. How much should he leave as tip for the $5.50 cheeseburger and $2.50 milkshake? Express your answer to the hundredths place.
JJ should leave $1.20 as a tip for the meal.
What is a tip?Gifts or amounts offered for services provided or expected.Below are some of the most common ways to calculate a tip:Method 1: Hover over the decimal point on your bill total and double the number.Method 2: Double the tax amount on the invoice.Method 3: Double the Input Tax Invoice, then shift the decimal point by one place.Some places add a tip to the bill, so check your bill carefully.For waiters in sit-down restaurants, the tip is 15-20% of the bill before tax.
According to the question:
Tip = 15% of the original priceTip = 15 % × $8Tip = $1.20Therefore, JJ should leave $1.20 as a tip for the meal.
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Clarissa had 72 candy bars to sell. She sold 4 per day for 8 days. She ordered 15 more candy bars to share with her 3 friends. The following expression can be used to find the number of candy bars Clarissa had left.
(I need the answer ASAP please!
72 – 4 • 8 – 15 ÷ 3
Based on this expression, how many candy bars did Clarissa have left?
The number of candy bars Clarissa had left are 55
Given,
In the question:
Clarissa had 72 candy bars to sell. She sold 4 per day for 8 days. She ordered 15 more candy bars to share with her 3 friends.
To find the number of candy bars Clarissa had left.
Now, According to the question:
Total candy sells is 72
Sold candy = 4 per day for 8 days
Sharing candy is 15
Based on the given conditions,
Formulate:
15 + 72 - 8 x 4
Calculate the product or quotient:
15 + 72 - 32
calculate the sum or difference
87 - 32
= 55
Hence, the number of candy bars Clarissa had left are 55.
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Answer: 35
Step-by-step explanation:
Solve for x. Enter the solutions from least to greatest.
(x-7)²-25= 0
lesser =
greater x =
The values for the lesser and greatest are:
-14 and 0
Step 1: Define
(x + 7)² - 49 = 0
Step 2: Solve for x
Add 49 to both sides: (x + 7)² = 49
Square root both sides: x + 7 = ±7
Subtract 7 on both sides: x = -7 ± 7
Evaluate: x = -14, 0
Step 3: Check
Plug in x values into original equation to verify they are a solution.
x = -14
Substitute in x: (-14 + 7)² - 49 = 0
Add: (-7)² - 49 = 0
Exponents: 49 - 49 = 0
Subtract: 0 = 0
Here we see that 0 does indeed equal 0.
∴ x = -14 is a solution of the equation
x = 0
Substitute in x: (0 + 7)² - 49 = 0
Add: 7² - 49 = 0
Exponents: 49 - 49 = 0
Subtract: 0 = 0
Here we see that 0 does indeed equal 0.
∴ x = 0 is also a solution of the equation.
Hence we get the required answer.
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Solve each system of equations by SUBSTITUTION. Clearly identify your solution.5x + 3y = 15) (x - 6y = 3
x = 3, y = 0
Explanation:5x + 3y = 15 ...equation 1
x - 6y = 3 ...equation 2
Using substitution method:
We can use any of the variables to work out the substitution method
let's make x the subject of formula in equation 2:
x - 6y = 3
x = 3 + 6y ...equation 3
Now we substitute 3+6y for x in equation 1:
5(3+6y) + 3y = 15
Expand the paranthesis:
15 + 30y + 3y = 15
collect like terms:
30y + 3y = 15 - 15
33y = 0
Divide both sides by 33:
33y/33 = 0/33
y = 0
We substitute 0 for y in any of the equation:
Using equation 2:
x - 6(0) = 3
x - 0 = 3
x = 3
3. In the figure below, XU is the midsegment of TVW and is parallel to VW, determine the length of XU. (3 points) 11x + 2 U 10x + 16
If XU is the midsegment of TVW, then, it is necessary that:
(11x + 2)/(10x + 16) = 1/2
multiply the previous equation by 10x + 16:
11x + 2 = 1/2(10x + 16)
11x + 2 = 5x + 8 subtract 5x and 2 both sides
11x - 5x = 8 - 2
6x = 6
x = 6/6
x = 1
THe length of XU is:
XU = 11x + 2 = 11(1) + 2
XU = 13
Im doing a practice assignment and im not the best at word problems Im not understanding the question
A sample statistic is is any quantity from the sample of a population.
We can see in the last option, that from the population (total of subjects of study) Kaisa, selected 84 of the total students. This fits in to the definition of sample statistic.
Thus, the correct option is the last one.
can someone turn 5x + 20y = 500 into slope intercept form
Answer:
y=-1/4x+25
Step-by-step explanation:
Answer: y=-1/4x + 25
Step-by-step explanation: If you don't understand how i got this remember the formula
y = mx + b
Good luck!
What would the monthly payment be on a $9,000 car loan at 8.85% interest for a five-year term?
Answer:
186.17
Step-by-step explanation:
Factor the expression using the GCF.
60−36
Answer:
12
Step-by-step explanation:
12x3=36, 12x5=60 shazam
Use the diagram below to find the area of the shaded sector
SOLUTION
We need to get the slopes of the lines A and B.
Slope of A considering the points (-4, 3) and (0, 0) which is at the origin, we have
[tex]\begin{gathered} m=\frac{0-3}{0-(-4)} \\ m=\frac{-3}{4} \\ m=-\frac{3}{4} \end{gathered}[/tex]Since line B is a horizontal line, the slope is 0.
angle between two slopes is given as
[tex]\begin{gathered} tan\theta=|\frac{m_2-m_1}{1+m_1m_2}| \\ where\text{ }\theta\text{ is the angle between them and } \\ m_1\text{ and m}_2\text{ are slopes of the line } \end{gathered}[/tex]So, we have
[tex]\begin{gathered} tan\theta=|\frac{m_2-m_1}{1+m_1m_2}| \\ tan\theta=|\frac{0-(-\frac{3}{4})}{1+0(-\frac{3}{4})}| \\ tan\theta=|\frac{\frac{3}{4}}{1}| \\ tan\theta=|\frac{3}{4}| \\ tan\theta=\frac{3}{4} \\ \theta=tan^{-1}\frac{3}{4} \\ \theta=36.86989 \\ \theta=36.87\degree \end{gathered}[/tex]Hence the angle between A and B is 36.87 degrees
Area of a sector is given as
[tex]A=\frac{\theta}{360\degree}\times\pi r^2[/tex]Note that the radius r is the length of line B, which is 5 units. So, the area becomes
[tex]\begin{gathered} A=\frac{\theta}{360\degree}\times\pi r^2 \\ A=\frac{36.87}{360}\times\pi\times5^2 \\ A=8.04376\text{ units}^2 \end{gathered}[/tex]Hence the answer is 8.04 square units. The last option is the answer
I need help check the picture
The value that does not belong in the domain of the set is 7 and the value that does not belong in the range of the set is 10.
Given set of values:-
{(2,7), (8,12), (5,9), (10,15)}
Domain : {2,5,7,8,10}
Range: {7,9,10,12,15}
We have to determine the numbers which do not belong in the domain and range of the relation.
We know that in a set of values (x,y) , x is the part of the domain and y is the part of the range.
Hence, the domain of the relation is given by:-
{2,8,5,10}
The range of the relation is given by:-
{7,12,9,15}
Hence, 7 does not belong to the domain of the set and 10 does not belong to the range of the set.
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Janelle plays on her community basketball team, the Raging Rabbits. During their big game against the Porcupines, the Rabbits score 35 points in the first half. They add to their score in the second half. In all, the Rabbits score 90 points. Use an equation for to find the number of points the Rabbits score in the second half.
Answer:
90-35=x 90-35=55
Step-by-step explanation:
To find your value of X, subtract your score of the first half from your total score.
what is the slope of the line that passes through the points (-4,2) and (-5,0). answer in simplest form
The line which passes through (-4,2) and (-5,0) has a slope of 2.
Let,
[tex](x_{1},y_{1})[/tex] = (-4,2)
[tex](x_{2},y_{2})[/tex] = (-5,0)
If the points are equal to each other, their x-coordinates are equal to each other:
[tex]x_{1}[/tex]=-4
[tex]x_{2}[/tex]=-5
If the points are equal to each other, their y-coordinates are equal to each other:
[tex]y_{1}[/tex]=2
[tex]y_{2}[/tex]=0
The slope, m is the steepness of a line and it is measured as the ratio of the change in vertical distance, rise over the change in horizontal distance, run.
The slope of the line, m:
m = ([tex]y_{2}[/tex]-[tex]y_{1}[/tex])/([tex]x_{2}[/tex]-[tex]x_{1}[/tex])
m=(0-2)/(-5-(-4))
m=(-2)/(-1)
m=2
The slope of the line for the two points is 2.
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I'm having some problems with this logarithmic question I will upload a photo
The Solution.
[tex]Let\log _{\frac{1}{9}}(\frac{1}{9})=x[/tex]Writing the above equation in index form, we have
[tex]\begin{gathered} (\frac{1}{9})^1=(\frac{1}{9})^x \\ Then\text{ it follows that} \\ 1=x \\ x=1 \end{gathered}[/tex][tex]\begin{gathered} \text{Let }\log _749=x \\ So\text{ we have} \\ 49=7^x \\ \text{Making the base of both sides equal, we have} \\ 7^2=7^x \\ x=2 \end{gathered}[/tex][tex]\begin{gathered} \text{Let }\log _{\frac{1}{4}}16=x \\ \\ 16=(\frac{1}{4})^x \\ 16=4^{-1\times x} \\ 4^2=4^{-x} \\ -x=2 \\ x=-2 \end{gathered}[/tex][tex]\begin{gathered} \text{Let }\log _{125}5=x \\ \text{cross multiplying, we have} \\ 5=125^x \\ 5^1=5^{3x} \\ 3x=1 \\ \text{Dividing both sides by 3, we get} \\ x=\frac{1}{3} \end{gathered}[/tex][tex]\begin{gathered} \text{ Let }\log _8(\frac{1}{8})=x \\ \\ \frac{1}{8}=8^x \\ \\ 8^{-1}=8^x \\ -1=x \\ x=-1 \end{gathered}[/tex][tex]\begin{gathered} \text{ Let }\log _9(1)=x \\ 1=9^x \\ 9^0=9^x \\ x=0 \end{gathered}[/tex][tex]\begin{gathered} \text{ Let }\log _{\frac{1}{9}}(-1)=x \\ \\ -1=(\frac{1}{9})^x \\ \\ No\text{ solution because it has no real value.} \end{gathered}[/tex]A toy rocket was fired into the air. The height, h,of the rocket at time t seconds is recorded in the tablebelow. Using an equation to model the data, find theheight of the rocket after 5 seconds.
we have the ordered pairs
(0,0)
(1,76)
(2,120)
(3,132)
(4,112)
Plot the given points
see the attached figure
In this problem we have a vertical parabola open downward
The vertex represents a maximum
The equation is of the form
y=ax^2+bx+c -----> quadratic equation
using a quadratic regression calculator
we have that
a=-16
b=92
c=0
therefore
y=-16x^2+92x
For x=5 sec
substitute
y=-16(5)^2+92(5)
y=60
the answer is
the height is 60 unitsAlternative method (approximate solution)
The quadratic equation in vertex form is equal to
y=a(x-h)^2+k
where
(h,k) is the vertex
I will assume that the vertex in this problem is the point (3,132)
so
(h,k)=(3,132)
substitute
y=a(x-3)^2+132
Find out the value of a
we have the point (0,0)
substitute in the equation
0=a(0-3)^2+132
0=9a+132
a=-132/9
a=-14.67
therefore
y=-14.67(x-3)^2+132
For x=5
y=-14.67(5-3)^2+132
y=73.33 units
Third Method
using the equation
y=ax^2+bx+c
points (0,0), (1,76) and (2,120)
(0,0) --------> 0=a(0)^2+b(0)+c ----------> c=0
y=ax^2+bx
(1.76) ------> 76=a(1)^2+b(1) ----------> a+b=76 ------> equation 1
(2,120) ----> 120=a(2)^2+b(2) ----> 4a+2b=120 ----> equation 2
solve the system of equations
the solution of this system is
a=-16
b=92
therefore
the equation is
y=-16x^2+92x (same first method)Find the equation of the linear function represented by the table below in slope-intercept form.
Answer:
y= 6x-8
Step-by-step explanation:
you pick two y values and subtract them. then take two x values and subtract them. divide those two awnsers with y on top. the -8 is the y intercept because when x is 0, the y is -8.
Answer:
Step-by-step explanation:
recall slope m is:
slope = m
m = (y2-y1) / (x2-x1)
point P1 (0,-8) in the form (x1,y1)
point P2(1,-2) in the form (x2,y2)
m = { -2-(-8) } / { 1-0 }
m = { -2+8 } / 1
m = 6 /1
m = 6
then plug in any point, I'll use P1
y - y1 = m(x -x1) (point-slope formula)
y - (-8) = 6*(x-0)
y+8 = 6x
y= 6x -8 (slope-intercept formula) :)
For each ordered pair, determine whether it is a solution to 4x + 5y = -13.
(-7,4)
(8,- 9)
(-1, -2)
(6, 3)
Is it a solution ?
Answer:
4x-5y=-13. 4x−5y=−13 4 x - 5 y = - 13.
Step-by-step explanation:
Step 1. Solve the equation for y y . Tap for more steps.
Enter the answer in the space provided.
Consider the figure.
142
68
N
Enter the measure of anglez, in degrees, in the space provided.
Step-by-step explanation:
as simple as it sounds, we need to do a few steps to actually get the result.
first the outer angle 142° and the corresponding inner angle in the triangle are a linear pair of angles, and together they have 180°.
so, the inner angle is 180 - 142 = 38°.
then, remember, the sum of all angles in a triangle is always 180°.
so, the third inner angle is 180 - 38 - 68 = 74°
now, this third inner angle is with z (the corresponding outer angle) again a linear pair (sum 180°).
so,
z = 180 - 74 = 106°
I need help with this problem. the answer i got was that there is no solution. is that correct?
Explanation:
To solve the equations by Elimination we can multiply the first equation by -2.5 as follows:
[tex]\begin{gathered} (2x+8y=6)\cdot(-2.5) \\ -2.5\cdot2x-2.5\cdot8y=-2.5\cdot6 \\ -5x-20y=-15 \end{gathered}[/tex]Now, we can add this equation to the second equation as follows:
- 5x - 20y = - 15
5x + 20y = 15
0 + 0 = 0
0 = 0
When we get 0=0, the system has infinite solutions
So, this system has solutions with the form:
(x, y) where 2x + 8y = 6
It also means that both equations, 2x + 8y = 6 and 5x + 20y = 15 are equivalent equations and the solutions of the first one are also the solutions of the second one.