Answer:
y = [tex]\frac{6}{5}[/tex]x + 4
Step-by-step explanation:
Use the slope formula and slope-intercept form y=mx+b to find the equation.
f(x)= 3x^2-7 over
4x^2-3
-find f(2)
Answer:
5/13
Step-by-step explanation:
f(x) = [tex]\frac{3x^{2}-7 }{4x^{2}-3 }[/tex]
Substitute x for 2.
[tex]\frac{3(2)^2-7}{4(2)^2-3}[/tex]
Solve
[tex]\frac{3(4)-7}{4(4)-3}[/tex]
[tex]\frac{12-7}{16-3}[/tex]
f(2)= [tex]\frac{5}{13}[/tex]
The value of f(2) is 5/29.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x) = 3x² -7/ 4x² - 3
Now, find the value of the function at x= 2
So, f(2)= 3(2)² -7/ 4(2)² - 3
f(2) = 3 x 4 -7 / 4 x 8 - 3
f(2) = 5/29
Hence, the value of f(2) is 5/29.
Learn more about function here:
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"57 more than 3 times Kate's score" Use the variable g to represent Kate's score.
If y varies directly as x, and y = 15 when x = 5. Find x when y = 9
Answer:
x=3
Step-by-step explanation:
If y is 15 when x is 5, and y =f(x), then the equation is y=3x. Substitute in 9 for y, and do the algebra, and you will get 3. Hope this helped :D
The value of x is 3 when y = 9.
What is Proportionality?When two quantities are proportional, it means that they can be expressed as a ratio or a fraction, and this ratio remains constant as the values of the quantities change.
If y varies directly as x, it means that the ratio of y to x remains constant.
We can express this relationship as y = kx, where k is the constant of variation.
To find the value of k, we can use the given information that y = 15 when x = 5:
15 = k . 5
Dividing both sides of the equation by 5, we get:
k = 15/5
k = 3
Now that we have the value of k, we can substitute it into the equation
y = kx to find x when y = 9:
9 = 3x
Dividing both sides of the equation by 3, we get:
x = 9/3
x = 3
Therefore, when y = 9, x = 3.
Learn more about Proportionality here:
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An average swimming pool contains 19200 gallons of water. The pool needs drained at the end of the summer. Water drains from the pool at the rate of 12 gallons per minute. Which equation can be used to find the volume, V, of the water in the pool m minutes after draining begins?
Answer:
V = 19200 - 12m
Step-by-step explanation:
The pool contains 19200 gallons of water.
Now we are told that water drains from the pool at the rate of 12 gallons per minutes.
Now, we want to find the volume, V, of the water in the pool, "m" minutes after draining begins.
Since water drains at 12 gallons per minutes, it means that after "m" minutes, the total amount that would have been drained is 12m gallons.
Thus, total volume V left after m minutes can be expressed as;
V = 19200 - 12m
If a point P(x,y) is the equidistant from the points A(2,3) and B(6,1), find the equation of locus of moving point P.
please answer it and I will mark your answer as the brainliest..please..!!!
Answer:
[tex]y=2x-6[/tex]
Step-by-step explanation:
A locus can be defined as a curve or figure formed by all the points satisfying a particular equation of the relation between coordinates.
The condition stated in the question is such that a generic (x,y) point of the curve is equidistant from the points A(2,3) and B(6,1).
The distance d1 from (x,y) to (2,3) is:
[tex]d_1=\sqrt{(x-2)^2+(y-3)^2}[/tex]
The distance d2 from (x,y) to (6,1) is:
[tex]d_2=\sqrt{(x-6)^2+(y-1)^2}[/tex]
Since d1=d2:
[tex]\sqrt{(x-2)^2+(y-3)^2}=\sqrt{(x-6)^2+(y-1)^2}[/tex]
Squaring both sides:
[tex](x-2)^2+(y-3)^2=(x-6)^2+(y-1)^2[/tex]
Operating:
[tex]x^2-4x+4+y^2-6y+9=x^2-12x+36+y^2-2y+1[/tex]
Simplifying all the squares:
[tex]-4x+4x+4-6y+9=-12x+36-2y+1[/tex]
Moving the variables to the left side and the numbers to the right side:
[tex]-4x+12x-6y+2y=36+1-4-9[/tex]
Simplifying:
[tex]8x-4y=24[/tex]
Dividing by 4:
[tex]2x-y=6[/tex]
Or, equivalently:
[tex]\boxed{y=2x-6}[/tex]
Anything would really help! Due soon!
Answer:
y=mx+b
Step-by-step explanation:
subtract from both sides -6- (8.4) =1.2x +8.4 - (8.4)
Answer: -6- (8.4) =1.2x +8.4 - (8.4)
X = - 12
If Karis can run 1 mile in 10 minutes, how many
miles could he run in 1 hour at this same rate?
Answer:
6 miles per hour or 6 miles
Step-by-step explanation:
If Karis can run 1 mile in 10 minutes, how many miles could he run in 1 hour at this same rate?
1 mile = 10 minutes
there are 60 minutes in 1 hour
10 minutes × 60 minutes = 6
6 × 1 mile = 6 miles so the answer is 6 mile per hour
Three girls cut out decimal models of hundredths. Amber doesn't shade any of her models. Grace qualifies three fifths of a model. Marsha shades one model and seven-tenths of another model. What decimal represents the number of shadows of each girl? Click on the icon to view the decimal models of hundredths. The decimal represents the number of shades of amber. The decimal represents the quantity that represents the quantity that Marsha qualifies. Tones of grace. The decimal (write whole numbers or decimals).
Answer:
[tex]Amber = 0[/tex]
[tex]Grace = 0.60[/tex]
[tex]Marsha =1.70[/tex]
Step-by-step explanation:
Given
Decimal Grid = Hundredths
[tex]Amber = None[/tex]
[tex]Grace = \frac{3}{5}th[/tex]
[tex]Marsha = 1 + \frac{7}{10}th[/tex]
To solve for each:
We have:
For Amber:
[tex]Amber = 0 * 100[/tex]
[tex]Amber = 0[/tex]
For Grace:
[tex]Grace = \frac{3}{5}th[/tex]
[tex]Grace = \frac{3}{5} * 100[/tex]
[tex]Grace = \frac{300}{5}[/tex]
[tex]Grace = 60[/tex]
This means that Grace shaded 60 of the hundredth models.
Decimal shaded is:
[tex]Grace = 60 * \frac{1}{100}[/tex]
[tex]Grace =\frac{60}{100}[/tex]
[tex]Grace = 0.60[/tex]
For Marsha:
[tex]Marsha = 1 + \frac{7}{10}th[/tex]
[tex]Marsha = \frac{10 + 7}{10}th[/tex]
[tex]Marsha = \frac{17}{10}th[/tex]
[tex]Marsha = 1.7th[/tex]
Multiply this by 100, to get the number of shaded
[tex]Marsha = 1.7 * 100[/tex]
[tex]Marsha = 170[/tex]
This means that Marsha shaded 170 of the hundredth models.
Decimal shaded is:
[tex]Marsha = \frac{170}{100}[/tex]
[tex]Marsha =1.70[/tex]
1
2
3
What is the slope of the line represented by the equation y
Y = 4/5x - 3
Show all work to identify the asymptotes and zero of the function f(x)=5x (over) x^2-25
9514 1404 393
Answer:
asymptotes: x = ±5; y = 0zero: x = 0Step-by-step explanation:
The function will have a zero where the numerator is zero:
5x = 0
x = 0 . . . . divide by 5
The zero of the function is x=0.
__
The function will have vertical asymptotes where the denominator is zero:
x^2 -25 = 0
x^2 = 25 . . . . add 25
x = ±5 . . . . . . take the square root
The function will have vertical asymptotes at x = -5 and x = 5.
__
When x gets large, the magnitude of the function is approximately ...
5x/x^2 = 5/x
As x approaches infinity, this value approaches zero.
The function will have a horizontal asymptote at y = 0.
Please help me solve this. :)
Answer:
40
Step-by-step explanation:
Given problem:
x² - y²
x+ y = 10
x - y = 4
Solution:
Using the concept of differences of two squares;
x² - y² = (x + y)(x - y)
So;
x² - y² = 10 x 4 = 40
Need help ASAP!!!!!!!
Which pair of numbers has an LCM of 60?
a. 2 and 12
b.5 and 12
c.6 and 12
d.3 and 12
Pls answer ASAP
Answer: 5 and 12
Step-by-step explanation:
i did the quiz
Find the distance between each pair of points.
M(-2,5) N(-2,-4)
Answer:
9
Step-by-step explanation:
I need help with this urgently!!
Answer:
c
Step-by-step explanation:
your welcome
Please help!!!! thank youuuu
2hr+20min+60sec are equal to _____ minutes
It is correct
Find the measure of the "?" or "X". Explain or show your
Answer:
66⁰ + x = 111⁰
x = 111⁰ - 66⁰
x = 45⁰
Answer:
First, I am taking the interior angle E as 'y' to be able to use the angle sum property to find 'x'.
So we can find 'y' by using 'linear pair'.
So Exterior angle 'E'+y=180 Degree.
= 111+y=180
By transposing: y=180-11
And y= 69 degrees.
And now have angles y & 'Angle G' we can use Angle sum property to find 'x'
ACCORDING TO ANFLE SUM PROPERTY OF TRIANGLE: "THE SUM OF ALL THE ANGLES OF A TRIANGLE IS 180 DEGREE"THEREFOR, y+x+angle G=180 degrees.
= 69 degrees+66 degrees+x=180 degrees
= 135 degrees+x=180 degrees
by transposing,
x= 180 degrees-135 degrees
And, x= 45 degrees
ANOTHER METHOD:BY USING EXTERIOR ANGLE PROPERTY.
ACCORDING TO EXTERIOR ANGLE PROPERTY OF TRIANGLE: "An exterior angle of a triangle is equal to the sum of its interior opposite angles"
So, Exterior Angle E= x+ Angle G
= 111 degrees= x+ 66 degrees
By transposing, x= 111 degrees-66 degrees
= x=45 degrees.
So no matter whichever method is used, the value of x= 45 degrees.
What is the equation of the line that passes through the point (-1, -5) and has a
slope of -3?
Answer:
[tex]y=-3x-8[/tex]
Step-by-step explanation:
The Baltic Sea is almost completely surrounded by countries in Europe. The average depth of the Baltic Sea is 52 meters below the surface. The deepest point in the Baltic Sea is 407 meters lower than this. What is the deepest point in the Baltic Sea relative to the surface?
Answer:
The deepest point in the Baltic Sea relative to the surface is 459 meters.
Step-by-step explanation:
The average depth of the Baltic Sea is:
[tex] d_{1} = 52 m [/tex]
The deepest point in the Baltic Sea is (lower than this):
[tex] d_{2} = 407 m [/tex]
Hence, the deepest point in the Baltic Sea relative to the surface is given by:
[tex] d_{T} = d_{1} + d_{2} = 52 m + 407 m = 459 m [/tex]
Therefore, the deepest point in the Baltic Sea relative to the surface is 459 meters.
I hope it helps you!
Anna runs three over4 mile in six minutes. Assuming she runs at a constant rate what is her speed in miles per hour
Answer:
7.5 mph
Step-by-step explanation:
6 times 10 is 60 minutes which is an hour
3/4 times ten is 7.5
Solve for x: 3(x + 1) = −2(x − 1) − 4.
Answer:
x = -1
Step-by-step explanation:
3(x+1) = -2(x-1) - 4 (Use the distributive property on both sides)
3x + 3 = -2x + 2 - 4 (collect like terms on the right side)
3x + 3 = -2x - 2 ( add 2x on both sides)
5x + 3 = -2 ( subtract 3 on both sides)
5x = - 5 (divide by 5 on both sides)
x = -1
Which pair of lines are perpendicular
Answer:
D
Step-by-step explanation:
Explain why three-dimensional graphs can be misleading. What would be a better type of graph to
use?
three-dimensional graphs wouldn´t give you the right information but two-dimensional graphs would give you the actual size of the shape.
Which equation has a constant of proportionality equal to ?
1/2
Choose 1 answer:
Answer:it’s c or 3/6
Step-by-step explanation:
Answer:
C. y = 3/6x
Step-by-step explanation:
The number by the x is the constant of proportionality. 3/6 is the same thing as 1/2, because when you divide the numerator and denominator by 3 it equals to 1/2.
I need help fast I’m timed!
Answer:
-5
Step-by-step explanation:
Last year the cost of Mr. patten’s car insurance was 86.80 per month. This year it inscreased by 5 percent. What was the cost of his insurance after the increase?
Answer:4.34
Step-by-step explanation:
Marissa is choosing a four-digit PIN for her ATM card. The first digit must be a digit from 1 through 9. For the other three digits, she can choose any combination of digits 0 through 9, but may not repeat a digit. Which shows part of the sample space for Marissa's PIN?
Answer:
2345, 2034, 2134
Step-by-step explanation:
From the choices available the only options that would samples would be 2345, 2034, 2134. These three samples meet all of the requirements of the ATM cards pin system. Each of them starts with a 2 which is between 1 and 9. The last 3 digits of each of these samples are between 0 and 9 and are also not repeated from any of the other digits in the pin. All of the other options available either start with a 0 or have at least one repeating digit in its pin code.
The diameter of a cylinder is doubled, and the height is cut in half. what will happen to the volume of the cylinder? please!
Answer:
The volume will be four times the original volume.
Step-by-step explanation:
V = (pi)r2h is the formula for the volume of a cylinder. The formula becomes V = (pi)(2r)2h if the radius is doubled and the height remains the same. V = 4(pi)r2h after simplifying. ... Therefore the new volume would be 4 times the original volume.
create a predictable sequence of at least 4 numbers that is not arithmetic or geometric.
Answer:
1,2,3,5,8,13,.......
Step-by-step explanation:
We can have a sequence that adds the previous two terms to get the next term
1,2,3,5,8,13,.......
This is neither geometric nor arithmetic