The equation of a line is y=4x+7 write down the gradient of the line and write down the y-intercept of the line.
Answers
y = mx + b
slope m = 4 and y-intercept b = 7
The gradient of the line y=4x+7 is 4 and the y-intercept is 7. This line rises by 4 units vertically for every 1 unit it moves horizontally, and it intersects the y-axis at the point (0,7).
Explanation:In the given line equation y=4x+7, the coefficient of x is the gradient (or slope) of the line and the constant term is the y-intercept. So, in this case, the gradient of the line is 4 and the y-intercept is 7. This means the line rises by 4 units vertically for every 1 unit it moves horizontally, and it intersects the y-axis at the point (0,7).
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Related Questions
In the figure, BC and AD are line segments. What is the sum of x and y?
Answers
x = 54
when added, they equal (62 + 54) = 116
Answer:
The correct option is 2.
Step-by-step explanation:
Given information: BC and AD are line segments.
According to the angle sum property, the sum of interior angles of a triangle is 180°.
In triangle DOC,
[tex]\angle C+\angle COD+\angle D=180^{\circ}[/tex]
[tex]y+64^{\circ}+54^{\circ}=180^{\circ}[/tex]
[tex]y+118^{\circ}=180^{\circ}[/tex]
[tex]y=180^{\circ}-118^{\circ}[/tex]
[tex]y=62^{\circ}[/tex]
The value of y is 62°.
If two lines intersect each other then vertical opposite angles are equal.
[tex]\angle COD=\angle AOB=64^{\circ}[/tex]
In triangle AOB,
[tex]\angle A+\angle AOB+\angle B=180^{\circ}[/tex]
[tex]x+64^{\circ}+62^{\circ}=180^{\circ}[/tex]
[tex]x+126^{\circ}=180^{\circ}[/tex]
[tex]x=180^{\circ}-126^{\circ}[/tex]
[tex]x=54^{\circ}[/tex]
The value of x is 54°.
The sum of x and y is
[tex]54^{\circ}+62^{\circ}=116^{\circ}[/tex]
The sum of x and y is 116°. Therefore the correct option is 2.
The 100-meter race times at a state track meet are normally distributed with a mean of 14.62 seconds and a standard deviation of 2.13 seconds. Using the Standard Normal Probabilities table, what is the approximate probability that a runner chosen at random will have a 100-meter time less than 15.5 seconds? a.0.1894
b. 0.3409
c. 0.6591
d. 0.7910
e. 0.8106
Answers
To solve this problem, we use the t statistic. The formula for z score is:
z = (x – u) / s
where x is the sample value = 15.5 seconds or below, u is the sample mean = 14.62 seconds, s is standard dev = 2.13 seconds
z = (15.5 – 14.62) / 2.13
z = 0.41
Using standard distribution tables at z = 0.41, the value of P is:
P = 0.6591 = 65.91%
Hence there is a 65.91% chance the runner will have less than 15.5 seconds of time
answer:
c. 0.6591
Answer:
c. 0.6591
Step-by-step explanation:
You earned $34,000 and your total tax due was $6,200. what was your average tax rate?
a.8%
b.10%
c.18%
d.20%
Answers
0.1823 * 100 = 18.23 rounds to 18% <=
A number cube is rolled 30 times, and a number less than five comes up 20 times. What is the experimental probability that a number GREATER than four is rolled?
A.1/20
B.2/3
C.1/10
D.1/3
Answers
Answer:
The answer is 2/3. Probably to late but i thought i might as well share!
Hope it helps haha!
Brainliest?
I don’t understand what and how to solve these
Answers
A baby elephant weighs 250 lb,
What is the elephant's weight in tons and kilograms (1 kg= 2.2 lb.)? Round to the thousandths place.
Answers
and Kg would be 113.636
If the population of a country grows at a rate of approximately 5 percent per year, the number of years required for the population to double is closest to
Answers
The population of the country will double its population in approximately 14 years at a rate of 5 % growth rate every year
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the population be = x
Let the number of years be time = t
Let the percentage of increase be = 5 %
Now , dx / dt = rate of increase of population per change in time
Here, ( dx/dt ) ∝ x
where , x is the population at any time t
Then ( dx/dt ) = Ax
where A is the proportionality constant.
Now , the equation is dx / x= A dt
On , Integrating with respect to x , we get
ln x = At + c
where c is the integration constant
So , on simplifying the equation , we get
Taking exponents on both sides of the equation ,
[tex]x=e^{rt + c}[/tex]
Let [tex]k=e^{c}[/tex]
So , the equation is
[tex]x= ke^{rt}[/tex]
Now , r is the rate of increase, and k is the initial population be x₀
And to find the time t taken to attain double population, so x = 2x₀
[tex]x= ke^{rt}[/tex]
Substituting the values in the equation , we get
[tex]2x_{0} =x_{0} e^{0.05t}[/tex]
[tex]2 = e^{0.05t}[/tex]
Taking logarithm on both sides,
[tex]ln 2=ln ( e^{0.05t} )[/tex]
0.69314=0.05t
t = 0.69317 / 0.05
t = 13.86294 years
Therefore , it takes 13.86294 years to double population
And , 13.86294 ≈ 14 years
Hence , The population of the country will double its population in approximately 14 years at a rate of 5 % growth rate every year
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What is 7,433,654 Rounded to the nearest 100,000
Answers
33,654 does not round up because the highest valued digit is not 5 or higher.
What is the equation of a line that passes through the point (9, −3) and is parallel to the line whose equation is 2x−3y=6 ?
Enter your answer in the box
Answers
-3y = -2x + 6
y = 2/3x - 2....the slope here is 2/3. A parallel line will have the same slope
y = mx + b
slope(m) = 2/3
(9,-3)...x = 9 and y = -3
now we sub and find b, the y int
-3 = 2/3(9) + b
-3 = 6 + b
-3 - 6 = b
-9 = b
so ur parallel equation is : y = 2/3x - 9 <== or 2x -3y = 27
The equation of the line, in slope-intercept form, that is parallel to 2x - 3y = 6 and passes through (9, -3) is: [tex]\mathbf{y = \frac{2}{3}x - 9}[/tex]
Given:
Points the line passes through, (9, -3)
The equation of the line it is parallel to: 2x - 3y = 6
Note:
Parallel lines have the same slope valueEquation of a line in slope-intercept form is: y = mx + b. (m is slope; b is y-intercept)Point-slope form is; y - b = m(x - a)First, rewrite 2x - 3y = 6 in slope-intercept form to determine its slope.
[tex]2x - 3y = 6\\\\-3y = -2x + 6\\\\y = \frac{2}{3}x - 2[/tex]
The slope of 2x - 3y = 6 is therefore 2/3.Thus, the slope of the line that passes through (9, -3) is also 2/3.
Write the equation of the line in point-slope form:
Substitute m = 2/3, and (a, b) = (9, -3) into y - b = m(x - a)
Thus:[tex]y - (-3) = \frac{2}{3}(x - 9)\\\\y + 3 = \frac{2}{3}(x - 9)[/tex]
Rewrite in slope-intercept form[tex]y + 3 = \frac{2}{3}(x - 9)\\\\y + 3 = \frac{2}{3}x -\frac{2}{3}(9)\\\\y + 3 = \frac{2}{3}x - 6\\\\y = \frac{2}{3}x - 6 - 3\\\\\mathbf{y = \frac{2}{3}x - 9}[/tex]
Therefore, the equation of the line, in slope-intercept form, that is parallel to 2x - 3y = 6 and passes through (9, -3) is: [tex]\mathbf{y = \frac{2}{3}x - 9}[/tex]
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Cole viewed paintings in 3 rooms in the museum. Each room had 12 paintings. He viewed paintings in 5 more rooms that each had 9 paintings. How many paintings did Cole view at the museum?
Answers
Point V lies between points U and W on UW.
If UW = 9x – 9, what is UW in units?
5 units
6 units
30 units
36 units
Answers
hope this helps :)))))
Answer: The correct option is (D) 36 units.
Step-by-step explanation: Given that point V lies between points U and W on UW, where
[tex]UV=2x-4,~~VW=4x+10~~~\textup{and}~~~UW=9x-9.[/tex]
We are to find the length of UW in units.
Since point V lies on the line segment UW, so we must have
[tex]UV+VW=UW\\\\\Rightarrow (2x-4)+(4x+10)=9x-9\\\\\Rightarrow 6x+6=9x-9\\\\\Rightarrow 9x-6x=6+9\\\\\Rightarrow 3x=15\\\\\Rightarrow x=5.[/tex]
Therefore, the length of UW is
[tex]UW=9x-9=9\times5-9=45-9=36~\textup{units}.[/tex]
Thus, the length of UW is 36 units.
Option (D) is correct.
I need help.....
1. A triangle has vertices at A(−7, 6), B(4, 9), C(−2, − 3). What are the coordinates of each vertex if the triangle is translated 4 units right and 6 units down?
1. A′(−3, 12), B′(8, 15), C ′(2, 3)
2. A′(−11, 0), B′(0, 3), C ′(−6, − 9)
3. A′(−3, 0), B′(8, 3), C ′(2, − 9)
4. A′(−11, 12), B′(0, 15), C ′(−6, 3)
Answers
A(-7,6) so adding 4 to the x would give you -3, and subtracting 6 to the y would give you 0. -> (-3,0)
B(4,9), add 4 to the x would give you 8, subtract 6 would give you 3. -> (8,3)
C(-2,-3), add 4 to the x would give you 2, subtract 6 would give -9. -> (2,-9)
Wallace received a 28 percent discount on an item priced at $275. What is the total price that he paid for it? cost after discount = price × (1 – discount percentage)
Answers
$275*(1-28%)
275*0.72
=198
(Basically just remember if you want to find the cost of something after discount just minus it off 100% , for example, 60% discount then times the original price to 0.4 to find the cost after the discount)
Hope this helps!
Answer: $198
Step-by-step explanation:
Given: The discount percentage : 28 % =0.28
The price of item = $275
The given formula for total cost of item after discount :
[tex]\text{Cost after discount = Price *(1 – Discount percentage)}[/tex]
Substitute the value of price =$275 and discount percent = 0.28 in the above formula , we get
[tex]\text{Cost after discount =}275\times(1-0.28)\\\\\Rightarrow\ \text{Cost after discount =}275\times0.72\\\\\Rightarrow\ \text{Cost after discount =}\$192[/tex]
Hence, he paid the total price of $198 for it.
determine the equation of the graph and select the correct answer below.
Answers
The hypergeometric distribution can be approximated by either the binomial or the poisson distribution. let x have the hypergeometric distribution:
Answers
I have this problem on a textbook that doesn't have a solution. It is:
Let
f(x)=(rx)(N−rn−x)(Nn),f(x)=(rx)(N−rn−x)(Nn),and keep p=rNp=rN fixed. Prove thatlimN→∞f(x)=(nx)px(1−p)n−x.limN→∞f(x)=(nx)px(1−p)n−x.Although I can find lots of examples using the binomial to approximate the hypergeometric for very large values of NN, I couldn't find a full proof of this online.
Anyway... I hoped this helped!
Faye’s bank charges her a $2.25 service fee every time she uses an out-of-network ATM. If Faye uses an out-of-network ATM twice a week, how much money does she pay in service fees every year?
a.
$240.25
b.
$225.00
c.
$200.75
d.
$234.00
Answers
If you multiply $2.25 by two (because she gets the fee twice a week) then multiply that number (4.5) by 52 (because there are 52 weeks in a year) you get your answer D. Hope this helps!
The amount of money that is being paid by Faye as service fee every year is: d. $234.00.
Given the following data:
Service fee = $2.25Number of times = 2Time = 1 yearTo determine the amount of money that is being paid by Faye as service fee every year:
How to solve a world problem.First of all, we would calculate the amount of money she pays for the service in a week as follows:
[tex]Cost = 2.25 \times 2[/tex]
Cost per week = $4.50
Note: There are 52 weeks in a year.
Thus, we would multiply the cost per week by 52:
[tex]Total \;cost = 52 \times 4.5[/tex]
Total cost = $234.00
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Expression that dissolves an answer from a particular experience that can only be solved by an amount given to the perimeter. Please tell me in a good form from a perspective that can only be solved for once person
Answers
Hope this helps
the total surface area of a cube is 726 in^2 what is the length of each side of the cube? it is. in
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so each edge = sqrt 121 = 11 inches
−px+r=−8x−2
solve for X
Answers
-8x=2
8x=-2
x=-1/4
Answer:
[tex]\frac{-2-r}{-p+8}[/tex].
Step-by-step explanation:
-px+r= -8x-2
-px+8x = -2-r
x(-p+8) = -2-r
x = [tex]\frac{-2-r}{-p+8}[/tex].
What are families of functions and how are they useful?
Answers
Alternatively, we can define a family by a formula that involves the argument and one or more parameters. For each specific value of the parameter(s) we'll then get one function in the family.
hope this is helpfull....
NOT MY ANSWER>>>>>>
Mike and Kate plan to save money for their wedding over a 20 month period. They will need to save $8,000 to help pay for the wedding. They set aside the same amount each month. After a year they saved $4,000. Mike and Kate know they must adjust their plan in order to meet their goal, so they came up with the following options: Option A: Stay with saving the same amount they've been saving each month but postpone the wedding 2 months. Option B: Increase the amount of money they save each month by $80 from what they've been saving. Which of the following is a true statement? a. Only option A will allow them to meet their goal. b. Only option B will allow them to meet their goal. c. Both options A and B will allow them to meet their goal. d. Neither option A nor option B will allow them to meet their goal.
Answers
Jordan was driving down a road and after 4 hours he had traveled 82 miles. At this speed, how many miles could Jordan travel in 14 hours?
Answers
4 hours is to 82 miles as 14 hours is to x miles
4/82 = 14/x
Cross multiply to get
4x = 14 * 82
4x = 1148
x = 287
287 miles
What is the contrapositive of the conditional statement? If two variables are directly proportional, then their graph is a linear function.
Answers
Answer:
(D) Last option
if the graph of two variables is not a linear function, then the two variables are not directly proportional.
Step-by-step explanation:
The required contrapositive of the given statement is, "If the graph is not a linear function, then the two variables are not directly proportional."
What is the contrapositive of the conditional statement?The contrapositive of a conditional statement is a statement that is formed by negating both the hypothesis and the conclusion of the original statement and then reversing the order of the resulting statement.
Here,
The contrapositive of the conditional statement is:
"If the graph is not a linear function, then the two variables are not directly proportional."
Note that the contrapositive of a conditional statement has the same truth value as the original statement. In other words, if the original statement is true, then its contrapositive is also true, and if the original statement is false, then its contrapositive is also false.
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6a - 10 = 3a + 17 please explain how you got your answer
Answers
Put similar things together
First step is to subtract 3a from both sides
3a - 10 = 17
Second step is to add 10 to both sides
3a = 27
Third step is to divide both sides by 3
a = 9
That's the answer.
To solve the equation 6a - 10 = 3a + 17, we first move all 'a' terms to one side and constants to the other, then simplify and solve for 'a', resulting in a = 9.
The student has asked to solve the equation 6a - 10 = 3a + 17. To find the value of 'a', we need to consolidate all the 'a' terms on one side and the constants on the other side. Here's the solution step-by-step:
Subtract '3a' from both sides of the equation to get '6a - 3a - 10 = 17'.
Simplify the left side to get '3a - 10 = 17'.
Add '10' to both sides to isolate the 'a' term and get '3a = 17 + 10'.
Simplify the right side to get '3a = 27'.
Divide both sides by '3' to solve for 'a', getting 'a = 27 / 3'.
Finally, 'a = 9'.
The correct answer is a = 9.
A ball is thrown vertically upward from the top of a 200 foot tower, with an initial velocity of 5 ft/sec. Its position function is s(t) = –16t2 + 5t + 200. What is its velocity in ft/sec when t = 3 seconds?
Answers
at t = 3 velocity = -96 + 5 = -91 ft/sec answer
Answer:
The velocity would be - 91 ft/sec.
Step-by-step explanation:
Given,
The function that shows the position of the ball after t seconds,
[tex]s(t) = -16t^2 + 5t + 200[/tex]
Since, velocity is the changes in position with respect to time,
That is, if v(t) is the velocity of the ball after t second,
[tex]\implies v(t)=\frac{d}{dt}(s(t))[/tex]
[tex]=\frac{d}{dt}(-16t^2 + 5t + 200)[/tex]
[tex]=-32t+5[/tex]
Hence, the velocity after 3 seconds is,
[tex]v(3)=-32(3)+5=-96+5=-91\text{ ft per seconds}[/tex]
What is the product of −2 2/5 and −3 5/6 ?
Answers
1. The value -2 is a lower bound for the zeros of the function shown below. f(x)=4x^3-12x^2-x+15
True
False
2. Express the polynomial as a product of linear factors. f(x)=2x^3+4x^2-2x-4
A. (x-2)(x+1)(x-1)
B. (x-2)(x-2)(x-1)
C. (x-4)(x+1)(x-1)
D. 2(x+2)(x+1)(x-1)
Answers
It is true that the value -2 is a lower bound for the zeros of the function f(x) = 4x³ - 12x² - x + 15
The polynomial as a product of linear factors is d. 2(x+2)(x+1)(x-1)
How to determine the true statement
From the question, we have the following parameters that can be used in our computation:
f(x) = 4x³ - 12x² - x + 15
Also, we have
x =-2
Calculate f(-2)
f(-2) = 4(-2)³ - 12(-2)² - (-2) + 15
f(-2) = 4 * -8 - 12 * 4 + 2 + 15
f(-2) = -32 - 48 + 2 + 15
f(-2) = -63
The above value is negative
This means that -2 is a lower bound for the zeros of the function.
Expressing the polynomial as a product of linear factors.
Here, we have
f(x) = 2x³ + 4x² - 2x - 4
Factorize in 2's
So, we have
f(x) = 2x²(x + 2) - 2(x + 2)
This can be expressed as
f(x) = (2x² - 2)(x + 2)
Factor out 2
f(x) = 2(x² - 1)(x + 2)
Express as difference of two squares
f(x) = 2(x - 1)(x + 1)(x + 2)
Hence, the polynomial as a product of linear factors is d. 2(x+2)(x+1)(x-1)
Use the square root property of equality to solve (x – 3)2 = –4. The solutions are a. -1 or 7 b. 1 or 5 c. 3+- 2i d. 3+-4i
Answers
(x-3)[tex] (x-3)^{2} = -4 \sqrt{(x-3)^2} = +- \sqrt{-4 x - 3 = i \sqrt{4} x - 3 = +-2i x = 3 +-2i[/tex]
Answer:
The solution is 3 ± 2i . The correct option is C.
Step-by-step explanation:
using the square root property of equality to solve (x - 3)² = -4
we have;
(x - 3)² = -4
Take the square root of both-side
√(x - 3)² = ±√-4
x - 3 = ±√4 × √-1
Not that square root of -1 is i
x - 3 = ±2i
Add 3 to both-side of the equation
x -3 + 3 = 3 ± 2i
x = 3 ± 2i
Therefore, the solution are 3 ± 2i
I am having trouble figuring out this math problem. I have tried every equation that I can think of the problem states 6×-3=5×+7 then x
Answers
6x - 3 = 5x + 7
You would subtract 5x from both sides. Remember, x = 1x
x - 3 = 7
Lastly, you would add 3 to both sides.
x = 10
I hope this helps!
Jennifer ran 4/5 of a mile on Monday. She ran 1 2/3 times as far on Tuesday. How far did she run on Tuesday?
1 4/15 miles
1 1/3 miles
2 7/15 miles
3 1/3 miles
Answers
Jennifer ran [tex]1\frac{1}{3}[/tex] miles on Tuesday.
What is multiplication?Multiplication is when you take one number and add it together a number of times. Example: 5 multiplied by 4 = 5 + 5 + 5 + 5 = 20.
Given that, Jennifer ran 4/5 of a mile on Monday. She ran [tex]1\frac{2}{3}[/tex] times as far on Tuesday, we need to find how far did she run on Tuesday,
Since, she ran 4/5 times mile,
And, on Tuesday she ran [tex]1\frac{2}{3}[/tex] times as far Monday,
On Tuesday she will run = 4/5 × [tex]1\frac{2}{3}[/tex]
= 4/5 × 5/3
= 4/3
= [tex]1\frac{1}{3}[/tex]
Hence, Jennifer ran [tex]1\frac{1}{3}[/tex] miles on Tuesday.
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