Solution
For this case we have the following:
x intercept 4: (4,0)
y intercept 2: (0,2)
Then we can find the slope like this:
[tex]m=\frac{2-0}{0-4}=-\frac{1}{2}[/tex]then the equation is given by:
y= -1/2 x+ 2
and we can use x= 1 and we have y= 3/2
x= 2 , y= 1
Then two other points could be:
(1,3/2) and (2,1)
An item is regularly priced at $43. Bill bought it on sale for 35% off the regular price. Hownmuch did he pay?
Given the regular price is $43.
S.P= 35% off on regular price i.e.
[tex]\begin{gathered} S\mathrm{}P=\text{ }\frac{65}{100}\times43 \\ S\mathrm{}P=27.95 \end{gathered}[/tex]Hence, after 35% off, the price is $27.95
Solve: - 4x + 1 ≤ 21 and 5x + 2 < 22A. x ≥ -5 and x < 4B. x > -5 and x ≤ 4C. x ≥ -5 or x < 4D. x > -5 or x ≤ 4
ANSWER
A. x ≥ -5 and x < 4
EXPLANATION
We have the two inequalities:
- 4x + 1 ≤ 21 and 5x + 2 < 22
Let us solve them separately:
FIRST ONE
-4x + 1 ≤ 21
Collect like terms:
-4x ≤ 21 - 1
-4x ≤ 20
Divide through by -4, the sign changes:
[tex]\begin{gathered} x\ge\text{ }\frac{20}{-4} \\ x\text{ }\ge\text{ -5} \end{gathered}[/tex]SECOND ONE
5x + 2 < 22
Collect like terms:
5x < 22 - 2
5x < 20
Divide through by 5:
x < 20 / 5
x < 4
The answer is Option A.
In a photograph, a skyscraper measures 5.8 in, tall. The scale of the photo to the actual skyscraper is 1:245. How tall is the actual skyscraper to the nearest foot?○ 118 ft ○ 183 ft○ 237 ft○204 ft
SOLUTION
In a photograph, a skyscraper measures 5.8 in, tall
The scale of the photo to the actual skyscraper is 1 : 245
That is 1 : 245 = 1 / 245 = 5. 8 / x
Cross- multiply we have:
1 X x = 5 . 8 X 245
x = 1421 inches in feet = 118.4167 feet
12. What is the equation in point-slope form of the
line that passes through the points (2, -3) and (-5, 8)?
⇒First step is to find the gradient
[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} } \\m=\frac{8-(-3)}{-5-2} \\m=\frac{8+3}{-7} \\m=-\frac{11}{7}[/tex]
In the general equation y=mx+c let us find the value of c by plugging in the known values
I will use the point (-5,8) Note you can use any .You will get the same value of c.
[tex]8=-\frac{11}{7} (-5)+c\\8=\frac{55}{7} +c\\c=8-\frac{55}{7} \\c=\frac{1}{7}[/tex]
The equation now is:
[tex]y=-\frac{11}{7} x+\frac{1}{7}[/tex]
Write the equation of the line that passes through the points(3,0) and(8,3)Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answer:
5/3
Step-by-step explanation:
rise over run
(8-3)/(3-0)
which graph of the following is yhe wquation of a line that is perpendicular to the graph of y=2/5×-1
hello
to solve this question, we need to plot the graph of this equation
Plot all of the points of the reflected figure. You may click a plotted point to delete
To reflect the figure, we have to draw the new vertex at the same distance from the line x = -4, the image below shows this reflection.
Notice that the new figure has the same distance from x = -4 as the pre-image.
What is the value of 2,783 +4,936?
Answer:7719
Step-by-step explanation:
Given f(x)=x^2 -3x +4
Find
f(2+h)
Find
f(2+h)-f(2)/h
Answer:
h² + h + 2h + 1====================
Given Function f(x) = x² - 3x + 4To findf(2 + h),[f(2 + h) - f(2)]/h.SolutionSolve by substitution
Find f(2 + h)f(x) = x² - 3x + 4f(2 + h) = (2 + h)² - 3(2 + h) = 4 = h² + 4h + 4 - 6 - 3h + 4 = h² + h + 2Find f(2)f(2) = 2² - 2*3 + 4 = 4 - 6 + 4 = 2Find [f(2 + h) - f(2)]/h(h² + h + 2 - 2)/h = (h² + h)/h = h + 1Felix is making a pattern with tiles shaped like parallelograms. He needs 5 black tiles
and 5 white tiles. The tiles cost $0.50 per cm².
What is the total area of the tiles Felix needs
to buy?
Answer: 80
Step-by-step explanation:
You do 2 times= 8 and multiply 8 to the 5 white and black tiles which equals 40+40=80.
The total area for the parallelogram shaped tiles Felix needs to buy is 80cm² at the price of $40.
Area of parallelogramIn calculating for the area of parallelogram, the base is multiplied by the height, as the same way for calculating the area of a rectangle.
Given that, the base of one parallelogram shaped tile is 4cm with height as 2cm.
Area of one parallelogram shaped tile = 4cm × 2cm
Area of one parallelogram shaped tile = 8cm²
Total area for the 5black and 5white tiles = 10 × 8cm²
Total area for the 5black and 5white tiles = 80cm²
Therefore, Felix needs to buy a total of 80cm² of 10 parallelogram shaped tiles.
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Leaming Diagnostic Analytics » Recommendations Language arts Science Social Studies Eighth grade Y.2 Find the slope from two points ZAC Find the slope of the line that passes through (9, 10) and (6, 12). Simplify your answer and write it as a proper fraction, improper fraction, or integer.
To find the slope of the line that passes through (9, 10) and (6, 12)
We will use the formula;
[tex]\text{slope =}\frac{y_2-y_1}{x_2-x_1}[/tex]From the points given;
x₁ = 9 y₁=10
x₂ = 6 y₂=12
Substitute the values into the formula;
[tex]\text{slope =}\frac{12-10}{6\text{ - 9}}[/tex]Evaluate;
[tex]\text{slope =- }\frac{2}{3}[/tex]21 -6 - NO a) D : {all real numbers}, R: {all real numbers Ob) D: {all real numbers), R; {y >0} O c) D: all real numbers), R: {y < 0} O d) D: {x>0}, R: {all real numbers
The domain is
[tex]D\colon\mleft\lbrace x\ge0\mright\rbrace[/tex]and the range
[tex]R=\text{all real numbers}[/tex]Then, the answer is d)
PLS HELP WILL GIVE 50 POINTS+ BRAINLIEST
Answer:
Please see the enclosed screenshot.
Step-by-step explanation:
Please see the enclosed screenshot.
Shiloh has 47 books. She wants to put them all on bookshelves. How many bookshelves will Shiloh need if each shelf holds 5 books?
A.
47
÷
5
=
7
R
2
Shiloh will need 8 shelves.
B.
47
÷
9
=
5
R
2
Shiloh will need 9 shelves.
C.
47
÷
5
=
7
R
2
Shiloh will need 7 shelves.
D.
47
÷
5
=
9
R
2
Shiloh will need 10 shelves.
The number of bookshelves needed if each bookshelves contain 5 books is 10.
How to find the number of shelves will hold the books?She has 47 books. . She wants to put them all on bookshelves.
Therefore, the number of bookshelves she will need if each shelf holds 5 books can be calculated as follows:
The total number of books she has in her possession is 47 books.
All the books must have a place in the bookshelves.
Each bookshelves can only contain 5 books.
Hence,
let
x = number of bookshelves
Therefore, the equation to find the number of bookshelves is as follows:
5x = 47
divide both sides by 5
x = 47 / 5
x = 9.4
Therefore, Shiloh will require 10 book shelves.
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does the ordered pair (-1, -9) satisfy the equation y=7-2x
Answer:
No
Step-by-step explanation:
In order to solve this, we plug in the values for x and y. Remember that x = -1 and y = -9
-9 = 7 - 2(-1)
-9 = 7 + 2
-9 ≠ 9
how do i find the final areahint: i have to square my units
Given:
A figure is given.
Required:
To find the area of the given figure.
Explanation:
The given figure is made up of three figures. So we will find the area of the three figures.
Area of square
[tex]\begin{gathered} A_1=(side)^2 \\ A_1=(3)^2 \\ A_1=9 \end{gathered}[/tex]Area of the triangle
[tex]undefined[/tex]I need help with this problem
Answer:
what is the problem text me
I can probably
Step-by-step explanation:
Please help solve!!
A football player kicks a football downfield. The height of the football increases until it reaches a maximum
height of 20 yards, 35 yards away from the player. A second kick is modeled by f(x) = -0.051x(x - 50),
where f is the height (in yards) and x is the horizontal distance (in yards). Compare the distances that the
footballs travel before hitting the ground.
The 1 first
The kick travels 1
Correct answers:
1
20
kick travels farther before hitting the ground.
10 X yards farther.
X
The distances that the footballs travel before hitting the ground is 50 yards.
What is defined as the quadratic function?A quadratic function has been one of the following: f(x) = ax² + bx + c, for which a, b, and c are positive integers and an is not equal to zero. A parabola is a curve that represents the graph of the a quadratic function. Parabolas can open up or down, and their "width" or "steepness" can vary, but they all share a basic "U" shape.For the given question;
The football is kicked by the player.
The second kick is modeled by f(x) = -0.051x(x - 50).
Where, f is the height (in yards) and x is the horizontal distance (in yards).
For calculating the distances that the footballs travel before hitting the ground, Put f(x) = 0.
As, the ball will reach the ground the height of ball above ground will be zero, thus f(x) = 0.
f(x) = -0.051x(x - 50) = 0
Simplifying;
-0.051x² + 2.25x = 0
Or, divide wole equation by x.
0.051x = 2.25
x = 50 yards.
Thus, the distances that the footballs travel before hitting the ground is 50 yards.
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H(x)=(x+5)^9 can be be expressed into the form f(g(x)) where f(x)=x^9, and g(x) is defined below
G(x)=?
The value of g(x) will be expressed as g(x) = (x + 5)
A function may be defined as an expression in which for one value of input variable x there is only one value of output variable y. The input variable is called as independent variable and output variable is called dependent variable. Composite functions are the functions which are written as combination of two functions. A function f(x) may be defined as composite function of another function g(x) when it can be written as either f(g(x)) or g(f(x)). We know that f(x) = x⁹ and the composite function H(x) = f(g(x)) = (x + 5)⁹. So, from this we can say that the function g(x) will be given as (x + 50 as we put (x + 5) as x in the function H(x).
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Draw triangle QRS with altitude RT. If m/RSQ = 43°, then find the m/TRS.
Do not include a degrees symbol on your answer.
The measure of angle TRS would be of 37º.
What is the measure of angle TRS?The vertices of the triangle can be attributed freely, hence we attribute as is in the drawing.
The altitude RT bisects the triangle forming a right angle, with R and T, hence the internal angles of the triangle TRS are as follows:
43º -> as given in the problem.90º -> due to the bisection.x. -> Angle TSR, which is the missing measure that we need to find to solve this problem.The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of the missing angle TSR can be found as follows:
43 + 90 + x = 180
133 + x = 180
x = 180 - 133
x = 47º -> m<TSR = 47º.
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f(x)=−x 2 −8 \text{Find }f(4) Find f(4)
IN THE PLACE OF x PLYG IN 4 AND SOLVE.
[tex]f(4) = - (4)^{2} - 8 \\ f(4) = - (16) - 8 \\ f(4) = - 16 - 8 \\ f(4) = - 24[/tex]
HOPE THIS HELPS
Slope =
y-intercept = (0,
Answer:
Solutions below.
Step-by-step explanation:
This question tests on the concept of graph reading.
To find the slope of a line, we have to use the following formula:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
Now, we can pick 2 random points on the line to substitute the values in to find the slope.
We will pick
(0, 3) as (x1, y1)
and
(2,0) as (x2, y2)
Therefore the slope will be:
[tex] \frac{0 - 3}{2 - 0} \\ = \frac{ - 3}{2} \\ = - \frac{3}{2} [/tex]
Now to find the y-intercept, as the name suggests, it is the point where the line intercepts the y-axis (vertical axis) , in this case, it is 3.
The point of this intercept is (0,3).
Answer:
slope = -5/3y-intercept = 3Step-by-step explanation:
You want the slope and the y-intercept of the line shown in the graph.
SlopeThe slope is the ratio of "rise" to "run". It is best found by identifying points on the graph where the line crosses grid intersections. The attachment shows two of those: (0, 3), (3, -2).
You can count grid squares or use the slope formula to find the slope.
slope = rise/run = (y2 -y1)/(x2 -x1)
slope = (-2 -3)/(3 -0)
slope = -5/3
Y-interceptThe y-intercept is the y-value of the point where the line crosses the y-axis. We have already found that to be 3, at one of the points used to find the slope.
y-intercept = 3 . . . . point (0, 3)
__
Additional comment
The slope-intercept form equation for the line would be ...
y = -5/3x +3
The standard-form equation would be ...
5x +3y = 9
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A lab assistant needs to create a 500 mL mixture that is 5% hydrochloric acid. The assistance has solutions of 3.5% and 6% in supply at the lab. Using the variables x and y to represent the number of milliliters of the 3.5% solution and the number of milliliters of the 6% solution respectively, determine a system of equations that describes the situation. Enter the equations below separated by a comma.How many milliliters of the 3.5% solution should be used? How many milliliters of the 6% solution should be used?
Let
x -----> the number of milliliters of the 3.5% solution
y ----> the number of milliliters of the 6% solution
we have that
3.5%=3.5/100=0.035
6%=6/100=0.06
5%=5/100=0.05
so
0.035x+0.06y=0.05(500) -------> equation A
and
x+y=500 -----> x=500-y ------> equation B
solve the system of equations
substitute equation B in equation A
0.035(500-y)+0.06y=0.05(500)
solve for y
17.5-0.035y+0.06y=25
0.025y=25-17.5
0.025y=7.5
y=300
Find out the value of x
x=500-300=200
therefore
the number of milliliters of the 3.5% solution is 200 mlthe number of milliliters of the 6% solution is 300 mlWhich of the following equations represents a line that passes through thepoints (-3, -14) and (0, –2)?Alg 1
Problem
Which of the following equations represents a line that passes through the
points (-3, -14) and (0, –2)?
Solution
For this case we want to create an equation with this general form:
y= mx+b
We can calculate the slope with this operation:
[tex]m=\frac{-2+14}{0+3}=4[/tex]And the intercept can be founded with the second point:
-2= 4(0)+b
b= -2
And the equation would be:
y= 4x -2
If we analyze the second option given we can see that we can write like this:
y-6 = 4(x-2)
y-6= 4x-8
y-6+8 =4x
y+2= 4x
y= 4x-2
So then the best option would be:
II. y-6 = 4(x-2)
The points (8, -9) and (0, -2) fall on a particular line. What is its equation in slope-
intercept form?
) Write your answer using integers, proper fractions, and improper fractions in simplest
form.
Video G
Answer:
y = -7/8x -2
Step-by-step explanation:
You want the slope-intercept equation of the line through the points (8, -9) and (0, -2).
SlopeThe slope of the line through points (x1, y1) and (x2, y2) is given by the formula ...
m = (y2 -y1)/(x2 -x1)
For the given points, the slope of the line is ...
m = (-2 -(-9))/(0 -8) = -7/8
InterceptThe y-intercept of the line is the y-value when x = 0. The point (0, -2) tells you the y-intercept is -2.
EquationThe slope-intercept equation is ...
y = mx +b . . . . . . where m is the slope, and b is the y-intercept
For a slope of -7/8 and a y-intercept of -2, the equation is ...
y = -7/8x -2
f(x) = integrate t ^ 4 dt from 3 to x
We have the function f(t) defined as:
[tex]f(x)=\int_3^xt^4dt[/tex]We have to find f'(x).
We can solve this integral as:
[tex]f(x)=\frac{t^5}{5}|^x_3=\frac{x^5}{5}-\frac{3^5}{5}[/tex]If we derive this expression for f(x) we obtain:
[tex]f^{\prime}(x)=\frac{d}{dx}(\frac{x^5}{5}-\frac{3^5}{5})=\frac{5}{5}x^4+0=x^4[/tex]NOTE: This expression could have been derived from the function inside the integral.
We can now find f'(3) as:
[tex]f^{\prime}(3)=3^4=81[/tex]Answer:
f'(x) = x^4
f'(3) = 81
1. Which of the following expressions can you factor using the reverse FOIL method? Select all that apply. (A) x²+x-6 (B) x^3 + 3x²+x-2 (C)4x^2 – 2x + 1 (D) x² + 8x + 12
We need to examine each expression at a time.
(A) x^2 + x - 6
notice the -6 has factors 3 and -2 which could be used to reverse the FOIL method:
x^2 + x - 6 = x^2 + 3 x - 2 x - 6 = x( x + 3) - 2 (x + 3) = (x+ 3) (x - 2)
(B) In this cubic expression we cannot use the reverse FOIL to extract factors.
(C) 4 x^2 - 2 x + 1 We cannot reverse the FOIL property either.
(D) x^2 + 8 x + 12
We notice that 12 has factors 2 and 6 which can be used to factor out this expression as shown below:
x^2 + 2 x + 6 x + 12 = x (x + 2) + 6 (x + 2) = (x + 2) (x + 6)
Therefore we were able to use the reverse of the FOIL property in expressions (A) and (D).
the table below shows the percentage of votes each sport received in a recent survey of student's favorite sports. will send image
Basketball 12 votes; Soccer 24 votes; Football 24 votes
Here, we want to select the options that could represent the percentage
From what we have, soccer and football are same value and basketball is half of these
So the option where we have the given outline is the correct answer
Looking at the options, the only place we have the outline is;
Basketball 12 votes; Soccer 24 votes; Football 24 votes
each side of a square is increasing at a rate of 4cm/s. At what rate is the area of the square increasing when the area of the square is 9 cm
The rate at which the area of this square increases when the area of the square is 9 cm is 24 cm²/s.
What is rate of change?The rate of change is a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.
How to calculate the area of a square?Mathematically, the area of a square can be calculated by using this formula;
A = s²
Where:
A represents the area of a square.s represents the side length of a square.Next, we would determine the side length of a square by making s the subject of formula as follows:
A = s²
s = √A
s = √9
s = 3 cm.
By applying chain rule of differentiation, the rate of change (da/dt) in area of this square with respect to time is given by:
dA/dt = 2 × s(t) × ds/dt
dA/dt = 2 × 3 × 4
dA/dt = 24 cm²/s.
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Answer the questions before. Show your work or explain your answers,1. A principal would like to estimate the percentage of students in the school whoplay video games. Which method should the teacher use to select the sample? Write the letter of your choice here:A. Use a computer to randomly select 30 students from all students.B. Use a computer to randomly select 30 students from all students who takecoding classes. C.select every other student from the classrooms close to her office. D. Select all students who are in the video game club. Explain. Your answer.
Given the following question:
The principal wants to estimate the percentage of students in the school who play video games, which is a good number of students. Selecting 30 random students and asking them if they play video games can represent the entire school. Asking 30 random students keeps it from being biased for example option B, asking 30 students who take coding classes is biased because they are in one specific class, they do not represent the majority of the school unless the school is a coding school.
The answer is the first option because it is a random sample of people to represent a population of people. This keeps the results from being biased so asking 30 random students is the way to go.