The equation of a line in the point slope form is expressed as
y - y1 = m(x - x1)
Where
m represents slope
y1 represents intial value of y
x1 represents initial value of x
The formula for determining slope is expressed as
m = (y2 - y1)/(x2 - x1)
y2 and x2 are final values of y and x respectively.
From the information given,
x1 = - 1, x2 = - 4
y1 = 4, y2 = 2
Slope = (2 - 4)/(- 4 - - 1)
Slope = - 2/ (- 4 + 1)
Slope = - 2/- 3
m = 2/3
Substituting m = 2/3, y1 = 4 and x1 = - 1 into the point slope equation, it becomes
y - 4 = 2/3(x - - 1)
= y - 4 = 2/3(x + 1)
The quotient of a number and -15 is equivalent to 100
SOLUTION
The quotient of a number and -15, simply means the number divided by -15.
So, let the unknown number be x,
This statement can be written mathematically as
[tex]\frac{x}{-15}\equiv100[/tex]This becomes
[tex]\begin{gathered} \frac{x}{-15}\equiv100 \\ \frac{x}{-15}=100 \\ m\text{ultiplying -15 to both sides } \\ \frac{x}{-15}\times-15=100\times-15 \\ -15\text{ cancels -15} \\ x=100\times-15 \\ x=-1500 \end{gathered}[/tex]Hence, the number is equivalent to -1,500
translating english Phrases to mathematical expression
the square of a number y subtracted by 1
The mathematical expression for the given English phrase is given by [tex]x^{2}-1[/tex]
What is a mathematical expression?
In mathematics, a mathematical expression is a combination of finite symbols that is well-formed according to rules depending on the context.
We are given an English phrase as the square of a number subtracted by 1
Let the given number be 'x'
The square of the number i.e. x will be [tex]'x^{2} '[/tex]
Now square of the number subtracted by 1 is [tex]x^{2}-1[/tex]
Hence the mathematical expression for the English phrase is [tex]x^{2} -1[/tex]
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Answer:
Domain: A, [1, 7]
Range: [-4, 2]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
7 friends each run an equal part of a 5km relay race. What fraction of a kilometer does each friend complete?
Solution
For this case we can do this:
5/7 km
The reason is because we just need to divide the total distance (5km) by the 7 friends
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The function g(3) has a value of 0
How to evaluate the function?The given parameters are the graphs in the figure
From the question, we have the function definition to be g(3)
Next, we analyze the functions of the graphs
The function on the first graph is a function of f(x), while the second graph is a function of g(x)
This means that we use the second graph to calculate the value of the function g(3)
The function g(3) means the value of x is 3
On the second graph, we have
g(x) = 0 when x = 3
So, we have
g(3) = 0
Hence, the value of the function is 0
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7. Tina's mother always purchases the family size box of her favorite cinnamon breakfast cereal.The family size box has a height of 14 inches, a length of 8 inches, and a width of 4 inch.lUnfortunately, the store only had medium boxes of Tina's favorite cereal. The dimensions arehalf the size of the family size box of cereal. What is the difference in the volume of the boxesof cereal?
Given:
A statement is given
Required:
What is the difference in the volume of the boxes
of cereal?
Explanation:
The family size box has a height of 14 inches, a lenght of 8 inches, and a width of 4 inches
So the volume of family size is
[tex]V_1=14\times8\times4=448inches^3[/tex]Becausr the dimensions are half the size of family size
box of cereal is the combination of volume
So the medium box has a height of 7 inches, length 4 inches, width 2 inches
volume
[tex]V_2=7\times4\times2=56inches^3[/tex]So the volume of family size box of cereal is layer than that of the medium box. The volume of family of family size base is eight times the volume of medium box. That is
the different in the volume of boxes of cereal
Required answer:
Above explanation
Two pools are being filled with water. To start, the first pool has 1900 liters of water and the second pool had 1372 liters of water. Water is being added to the first pool at a rate of 31 liters per minute. Water is being added to the second pool at a rate of 42 liters per minute.Let x be the number of minutes water has been added(a) For each pool, write an expression for the amount of water in the pool after x minutes.Amount of water in the first pool (in liters) = Amount of water in the second pool (in liters) =(b) Write an equation to show when the two pools would have the same amount of water.
For the first pool, we start with 1900 liters, and add water at a rate of 31 liters per minute, So the equation for the total amount of water in liters in terms of minutes is given by:
Water in Pool 1 = 1900 + 31 x
The other pool (Pool 2) starts with 1372 liters and the rate of water added is 42 liters per minutes, then after "x" minutes of being filled at this rate be have:
Water in Pool 2 = 1372 + 42 x
(b) For this part of the problem, when we assume that both amounts of water are the same, we equal the amount of water on each pool, connecting them via an equal sign:
Water in Pool 1 = Water in Pool 2
1900 + 31 x = 1372 + 42 x
Given the point and slope write the equation of the line (-2, 11); slope = 4
Let:
(x1,y1) = (-2,11)
m = 4
Using the point-slope equation:
[tex]undefined[/tex]A ball is thrown 24 m/s into the air. How high does it go?556.4 m0 m29.4 m-556.4 m
the initial speed of the ball is u = 24 m/s
the acceleration is a = 9.8 m/s^2
also the ball will have zero velocity at the top,
so final velocity is v = 0
so the distance(s) covered by the ball is ,
[tex]\begin{gathered} v^2=u^2-2gs \\ 0=24^2-2\times9.8\times s \end{gathered}[/tex][tex]\begin{gathered} 19.6s=576 \\ s=\frac{576}{19.6}=29.4 \end{gathered}[/tex]so the ball was 29.4 m high.
Drag each label to the correct location on the figure. Not all labels will be used. Find the missing angle measurements. 60° 64° 45° 49° 53° 56° 64° 719
we know that
In any triangle the sum of the interior angles must be equal to 180 degrees
so
In the first triangle (bottom) we have
64+71+x=180
Solve for x
x is the missing angle
135+x=180
x=180-135
x=45 degrees
The first missing angle is 45 degrees
step 2
triangle of the top
we know that
The first missing angle is 64 degrees by vertical angles
so
we have that
64+56+y=180
solve for y
120+y=180
y=180-120
y=60 degrees
Twelve (12) more than a number is five (5). What is the number?
ANSWER
[tex]-7[/tex]EXPLANATION
Let the number be x.
Twelve more than the number is:
[tex]12+x[/tex]That value is equal to five. This implies that:
[tex]12+x=5[/tex]To find the number (x), subtract 12 from both sides of the equation:
[tex]\begin{gathered} 12+x-12=5-12 \\ x=-7 \end{gathered}[/tex]That is the number.
Which of the following represents "the product of 7 and a number k"?
a. 7 - k
b. 7 + k
c. 7/k
d. 7k
Answer:
um it's option ( d )
7k
:)
-w/5+9=13 what does w equal
Answer:w=-20
Step-by-step explanation: well, you start off by canceling the 9 subtracting 9 from both sides, to get a new equation of -w/5=4. Then, to cancel. Then, to cancel out dividing by 5, you multiply both sides by 5 to get a new equation of -w=20. Then, to cancel out the negative sign, just multiply both sides by -1, to get w=-20.
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find the area of a trapezoid whose height is 7 in in whose bases are 14 in in 10 inches
The area of a trapezoid is the average of the bases multiplied by the height
[tex]\begin{gathered} A=\frac{a+b}{2}\cdot h \\ \text{Where} \\ a\colon\text{ long base} \\ b\colon\text{ short base} \\ h\colon\text{ height} \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} a=14\text{ in} \\ b=10\text{ in} \\ h=7\text{ in} \end{gathered}[/tex][tex]\begin{gathered} A=\frac{a+b}{2}\cdot h \\ A=\frac{14in+10in}{2}\cdot7\text{ in} \\ A=84\text{ square inches} \end{gathered}[/tex]Therefore, the area of a trapezoid w
total amount 20 year term
Answer:
I think you just multiply the amount of the house by the interest rate (.52), and then also multiply the length of the loan. so
$62,000(.52)(20)=$64,400
if the ratio of tourists to locals is 2:5 and there are 50 tourists at the opening of a new museum how many locals are in attendance
Ratio: 2 tourist: 5 locals
To find the number of locals you multiply the given number of tourits by 5/2:
[tex]50\text{tourist}\cdot\frac{5\text{locals}}{2\text{touritst}}=125\text{locals}[/tex]Then, when there are 50 tourist, there are 125 localsSuppose that J and K are points on the number line. If JK=6 and J lies at -3, where could K be located? them with commas. If there is more than one location, separate
Answer:
15, -9
Step-by-step explanation:
Which of the following explains how to use partial quotients to find
832
÷
26
?
A.
Subtract
20
×
40
from 832 to get 32. Then subtract
1
×
26
from 32 to get 6.
Then add the partial quotients 20 + 1 + 6 to get 27. The quotient is 27.
B.
Subtract
30
×
25
from 832 to get 82. Then subtract
3
×
26
from 82 to get 0.
Then add the partial quotients 30 + 3 to get 33. The quotient is 33.
C.
Subtract
30
×
26
from 832 to get 52. Then subtract
2
×
26
from 52 to get 0.
Then add the partial quotients 30 + 2 to get 32. The quotient is 32.
D.
Subtract
30
×
26
from 832 to get 52. Then subtract
4
×
13
from 52 to get 0.
Then add the partial quotients 30 + 4 to get 34. The quotient is 34.
Partial quotients can be used to find 832 ÷ 26 by the explanation that follows. C. Subtract 30 × 26 from 832 to get 52. Then subtract 2 × 26 from 52 to get 0. Then add the partial quotients 30 + 2 to get 32. The quotient is 32
How to do division using partial quotientsPartial quotient is the method that is sued to solve the big division problems in mathematics. It is one that is done through the use of logic in order to get the solution
For instance
832 ÷ 26 ⇒ 30
30 * 26 = 780
832 - 780 = 52
52 ÷ 26 ⇒ 2
2 * 25 = 52
52 - 52 = 0
The quotient is gotten by adding up the values gotten during the division
= 30 + 2
= 32
32 is the quotient and option C is the correct option
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For the equation
3x+2y=6
a) Complete the table:
x y
0
0
b) Plot the two points you found in the table.
Answer:
Step-by-step explanation:
68
Brad wants to buy flowers for his friend with $39. The daisies are $1 each and the roses are $3 each. He buys 3 more daisies that roses. How much did the roses cost
The amount that each rose costs is $9
How to determine the amount of each rose?From the question, we have the following parameters
Total purchase = $39
Daisies = $1 each
Roses = $3
Represent the rose with x and the daisies with y
From the question, we understand that:
He buys 3 more daisies that roses.
This means that
y = x + 3
3x + y = 39
Substitute y = x + 3 in the equation 3x + y = 39
So, we have
3x + x + 3 = 39
Evaluate the like terms
4x = 36
Divide by 4
x = 9
Recall that:
The rose is represented with x
Hence, the cost of each rose is $9
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9. The formula for the area of a trapezoid is A = {h(b2 + b2). Express bị in terms ofA, h and bz. The area of a trapezoid is 60 square feet, its height is 6 ft, and one base is 12ft. Find the number of feet in the other base.
9.The area of a trapezoid is given as;
A={1/2h{b2 +b2}} where b2 and b2 are the lengths of the sides and h is the height
To express b2 in terms of A ,h, and b2 will be to make b2 the subject of the formular of trapezoid area.This will be
A={1/2h{b2 +b2}} ------ collect like terms and add
A={1/2h{2b2}} --------cancel the 2 in the 1/2 and that in brackets to get
A={h{b2}}
Divide both sides by h to remain with b2 on the right-hand side as
A/h = b2
So the expression will be :
b2 = A/h ---------answer
Divide (41°48') = 4.
Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.
What does division look like?The opposite of multiplication is division. Knowing a division truth enables us to find a multiplication fact
Before moving on, keep in mind that the numbers in the equation 41 divided by 48 are defined as follows:
dividend = 41,48 = dividend.
Step 1: Arrange it so that the dividend 41 is on the right side and the divisor 48 is on the left as shown:
4 8 ⟌ 4 1
Step 2: The divisor (48) is multiplied by the dividend's initial digit (4) by 0 times (s). Hence, place 0 at the top:
0 \s 4 8 ⟌ 4 1
Step 3: Write the result of multiplying the divisor by the outcome of the previous step (48 x 0 = 0), underneath the dividend.
0 \s 4 8 ⟌ 4 1 \s 0
Step 4: Write the result below after subtracting the previous step's result from the dividend's first digit (4 - 0 = 4).
0 \s 4 8 ⟌ 4 1 \s - 0 \s 4
Step 5: Decrease the dividend (1)'s second digit as follows:
0 \s 4 8 ⟌ 4 1 \s - 0 \s 4 1
Step 6: The bottom number (41), which is the divisor, is multiplied by 0 times (s). Hence, place 0 at the top: 0 0 \s 4 8 ⟌ 4 1 \s - 0 \s 4 1
Step 7: Divide the result from the previous step by the divisor (48 x 0 = 0), and then write the result at the bottom:
0 0 \s 4 8 ⟌ 4 1 \s - 0 \s 4 1 \s 0
Step 8: Subtract the outcome from Step 7 from the number displayed above. Put the solution at the bottom (41 - 0 = 41). 0 0 \s 4 8 ⟌ 4 1 \s - 0 \s 4 1 \s - 0 \s 4 1
There are no more digits to shift down from the dividend, thus you are finished.
The top number is the solution, and the remaining value is the bottom one.
As a result, when 41 is divided by 48 using long division, the result is:
0.
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Find the slope of the line determined by the following equation. Simplify your answer.
-2x - 7y = 22
Answer:
Slope=—2/7
Step-by-step explanation:
[tex]-2x-7y=22\\-7y=2x+22\\y=-\frac{2}{7} x-\frac{22}{7} \\[/tex]
Consider the following linear function and graph it:y = 4x − 5y = _______x, y = ______
ANSWER:
y = -13
x, y = -2, 13
y = -5
x,y = 0, -5
y = 3
x, y = 2, 3
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]y=4x-5[/tex]We will choose some values of y and then calculate x and establish the point (x, y)
[tex]\begin{gathered} y=-13 \\ -13=4x-5 \\ 4x=-13+5 \\ x=-\frac{8}{4}=-2\rightarrow(-2,13) \\ \\ y=-5 \\ -5=4x-5 \\ 4x=0 \\ x=0\rightarrow(0,-5) \\ \\ y=3 \\ 3=4x-5 \\ 4x=5+3 \\ x=\frac{8}{4}=2\rightarrow(2,3) \end{gathered}[/tex]Help!!! I have Math homework that needs to be turned in tomorrow.
Find the Difference. Write the fractions in the simplest form.
3/4 - 9/4
Work Shown:
3/4 - 9/4 = (3-9)/4 = -6/4 = -3/2
Please help:A rectangular flower bed is enlarged so that its area increases by 24 ft². The enlarged flower bed is a rectangle and its area is x^2 + 11x + 24 ft².Which expressions represent the dimensions of the flower bed before the increase?Enter your answers in the boxes. __ft by __ ft
Enlarged area = x^2 + 11x + 24 ft²
Original area =
a + 24 ft^2 = x^2 + 11x + 24 ft²
a = x^2 + 11x + 24 ft² - 24 ft^2
a = x^2 + 11x
Factored:
a = x (x + 11 )
Dimensions before the increase
x ft by (x-11) ft
melissa loves to read. she finished 6 books this weekend, 5 books last weekend, and 7 books the weekend before that. If the books averaged 120 pages each, about how many pages did she read in 3 weekends
She read 2160 pages in 3 weekend
Given,
Melissa finished 6 books this weekend, 5 books last weekend, and 7 books the weekend before that.
Average of books pages is 120 each.
To find the how many pages she read in 3 weekend?
Now, According to the question:
Based on the given condition,
120 x (7 + 6 + 5)
= 120 x 18
= 2160
Hence, She read 2160 pages in 3 weekend
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Use technology to find points and then graph the line y=\frac{1}{2}(x+2)-4,y= 21(x+2)−4, following the instructions below.
Answer:
The two points: (6, 0) and ( 0, -3).
Explanation:
To plot the line of the equation, we first find two points t
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The equation of a line passing through two points that is (-2 , 11) and (1 , -4) is equal to f(x) = -5x + 1.
What is the point slope form of a line ?
Point slope form is used to represent a straight line using its slope and a point on the line.
A line is passing through two points that is (-2 , 11) and (1 , -4).
These points can be represented by :
([tex]x_{1}[/tex] , [tex]y_{1}[/tex]) = (-2 , 11)
([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = (1 , -4)
We know that the slope is given by :
m = [tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}}[/tex]
m = [tex]\frac{-4 -11 }{1 -(-2)}[/tex]
m = -15 / 3
m = -5
We know that the point -slope form of a line is given by :
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex])
y - 11 = -5 ( x + 2)
y = -5x - 10 + 11
y = -5x + 1
or
f(x) = -5x + 1
Therefore , the equation of a line passing through two points that is (-2 , 11) and (1 , -4) is equal to f(x) = -5x + 1.
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