Linear equations are typically organized in slope-intercept form:
[tex]y=mx+b[/tex]
m is the slope of the lineb is the y-intercept (the value of y when the line passes through the y-axis)To find linear equations in slope-intercept form:
Determine the slopePlug the slope into the general formDetermine the y-intercept by isolating bPlug the b back into the equationSolving the QuestionWe're given:
The line passes through the points (2,6) and (4,16)First, determine the slope of the line.
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points that fall on the line
⇒ Plug in the given points (2,6) and (4,16):
[tex]m=\dfrac{16-6}{4-2}\\\\m=\dfrac{10}{2}\\\\m=5[/tex]
⇒ Therefore, the slope of the line is 5. Plug this back into the general form:
[tex]y=5x+b[/tex]
Now, determine the y-intercept.
[tex]y=5x+b[/tex]
⇒ Plug in one of the given points:
[tex]6=5(2)+b\\6=10+b\\b=-4[/tex]
⇒ Therefore, the y-intercept is -4. Plug this back into our original equation:
[tex]y=5x-4[/tex]
Answer[tex]y=5x-4[/tex]
Victoria is at an elevation of 150 feet. She hikes down to an elevation of 120 feet in 40 minutes.
Then she hikes down to an
elevation of 100 feet in 30 minutes.
What is her average rate of descent, in feet per minute, from 150 feet to 120 feet?
The Victoria's average rate of descent by hiking down from an elevation of 150 feet to an elevation of 120 feet in 40 minutes is equal to 0.75 feet per minute.
How to determine the average rate of descent of a hiker
Geometrically speaking, the average rate of descent (r), in feet per minute, is represented by a secant line, which represents in this case the change in elevation (Δz), in feet, divided by the change in time (Δt). A mathematical description of the formula is shown below:
r = Δz/Δt (1)
If we know that Δz = 30 ft and Δt = 40 min, then the average rate of descent is:
r = 30 ft/40 min = 0.75 ft/min
The Victoria's average rate of descent by hiking down from an elevation of 150 feet to an elevation of 120 feet in 40 minutes is equal to 0.75 feet per minute. [tex]\blacksquare[/tex]
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A recipe uses brown sugar and caster sugar in the ratio 3:2. What fraction of the sugar is caster?
Answer:
2/5 of the sugar is caster sugar
4 1/2 x 2 1/2 x 8 1/2 =
Answer:
[tex]95\frac{5}{8}[/tex]
Step-by-step explanation:
[tex]4\frac{1}{2} * 2\frac{1}{2} * 8\frac{1}{2}[/tex] = 9/2 * 5/2 * 17/2
765/8 = [tex]95\frac{5}{8}[/tex]
If it costs $.25 per square yard to seed an area of grass, how much does it cost to seed in the inside of this track
51yd, 102yd, 51yd, and 110yd
The price that it cost to seed the inside of this track is $1,040.4
How to calculate the area of a rectangleThe formula for calculating the area of a rectangle is expressed as:
A = length * width
Let the length be 51 and the width be 102 yd such that:
Area of the grass = 51 * 102
Area of the grass = 5202 square yard
If it costs $.25 per square yard to seed an area of grass, the price fror the area inside the track is:
Price = 0.2 * 5202
Cost of the track = $1,040.4
Hence the price that it cost to seed the inside of this track is $1,040.4
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Which of the following will form the composite function G(F(x)) shown
below?
G(Fx)) = 3(/* +1)
A. Fx) = x + 1 and G(x) = 13x
B. Fx) = 3x and G(x) = 5x + 1
C. F(x) = 3x and G(x) = 1
D. F(x) = 5x + 1 and G(X) = 3x
Answer:
Step-by-step explanation:
A
The given composition function is combination is F(x)=√x+1 and G(x)=3x. Therefore, option D is the correct answer.
The given function is G(F(x))=3(√x+1).
F(x)=√x+1 and G(x)=3x
The composite function is G(F(x))
Replace x by √x+1 in 3x, we get
3(√x+1)
Therefore, option D is the correct answer.
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You buy tomatoes in 25 lb cases one portion of salad requires. 75 oz of tomatoes how many portions can be made with one case
how many inches are in 12 ft
Answer:
the answer is 144
Answer:
144 inches
Step-by-step explanation:
There are 12 inches in 1 foot,
So 12 times 12 is 144 inches.
how long does it last for Fanger print
Answer:
A fingerprint can last on a surface from 2 hours to 40 years on average.
Step-by-step explanation:
Most fingerprints will get erased due to impact from humidity and heat.
For $1.80 a grocer buys a case of fruit which contains 12 dozen. He knows that 2 dozen will spoil before he sells them. At what price per dozen must he sell the good ones to gain 1/3 of the whole cost?
Answer:
i didnt understand the awnser fully but if i did the awnser is 5 cents a donut
Step-by-step explanation:
I neeed hellppppp plissss
Answer:
I believe C is the closest equation to the graph
Step-by-step explanation:
what is 6/4 in its simplst form
Answer:
Fraction form: [tex]\frac{3}{2}[/tex]
Decimal form: 1.5
Mixed number form: 1 [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Find the greatest common factor between the two numbers in the fraction, in this case the largest number both can be divided by equally is 2, so,
Take [tex]\frac{6}{4}[/tex] and divide both parts by 2:
6 ÷ 2 = 3
4 ÷ 2 = 2
Which gives you [tex]\frac{3}{2}[/tex]
Calculate the value of X
If you’re 16 how many months would you have to live to be 66
Answer:
ig 2 months
Step-by-step explanation:
If you were born in 1955 your full retirement age is 66 and 2 months. If you start receiving benefits at age 66 and 2 months you get 100 percent of your monthly benefit. If you delay receiving retirement benefits until after your full retirement age, your monthly benefit continues to increase.
PEMDAS 4+5 x (6-2) what the answer
Answer:4(5x+1)
Step-by-step explanation: you want to subtract the numbers 4+5x(6-2)/4+5x(4) so you'll need to multiply 5 and 4 so 4+5x*4 but i'm goin to make it smaller so it would be 4+20x but you have to rearrange it instead of it being 4+20x it would be 20x+4 .And the common factor would be 4(5x+1).
I hope this helps and makes sense.
Please help! I wish you a good day :)
Answer:
A=p2-2p-3
Step-by-step explanation:
The area for a triangle is given by:
A=1/2bh
The base is p + 1 and the height is 2p - 6. Therefore:
A=1/2(p+1)(2p-6)
Simplify the second term:
A=(p+1)(1/2)(2p-6)=(p+1)(p-3)
Distribute:
A=p(p-3)+1(p-3)
Distribute:
A=p2-3p+p-3
Combine like terms:
A=p2-2p-3
If r = 11, t = 3, s = 9, then 8r - 10s =
Answer:
-2
Step-by-step explanation:
plug values for r and s into the equation 8r - 10s.
so, 8(11) - 10(9)
88 - 90 = -2
hope this helps!
Which expression is equivalent to |x| < 11?
x > –11 or x < 11
x < –11 and x > 11
x < –11 or x > 11
x > –11 and x < 11
1. which expression is equivalent to 4(9+3).
Multiple Select three expressions
A. 4(12)
B. 36+3
C. 36+12
D. 4+(9+3)
E. (9+3) +(9+3) +(9+3) +(9+3)
Answer:
A. 4(12)
C. 36+12
E. (9+3) +(9+3) +(9+3) +(9+3)
Step-by-step explanation:
[tex]4(9+3)=48[/tex]
[tex]4*9=36\\4*3=12[/tex]
[tex]48[/tex]
[tex]4*12=48[/tex]
[tex]36+12=48[/tex]
[tex](9+3) +(9+3) +(9+3) +(9+3)\\12+12+12+12[/tex]
=48
Help please i cannot fail!! What is the surface area of the pyramid?
Answer:
800
Step-by-step explanation:
Check out the attached photo
Need help with the answer
Answer:
sine(∡DAB) = 0.5
Step-by-step explanation:
∡[tex]ACD=[/tex]∡[tex]ADB[/tex] = 60°
∡[tex]DAB=(180-90-60)^{o} =30^{o}[/tex]
[tex]sin(30^{o})= 0.5[/tex]
Hope this helps
Renee bought her mother 2 pounds of ground coffee. Her mother uses 4 ounces per
day to brew coffee. Did Renee buy her mother enough coffee for a week?
Begin by converting 2 pounds to ounces. Choose the words and numbers to
complete the statements.
Part A
A pound is a Choose...
v unit than an ounce, so Choose...
the
number of pounds by 16 to find the number of ounces. Therefore, 2 pounds is equal
to Choose...
ounces.
Answer:
I do know Part B. No, Renees mom does not have enough, since 4 ounces per day, isn't enough coffee. Hope this helped!
Step-by-step explanation:
what is this sphere’s volume? radius is given, please round to nearest tenth
Answer:
179.59438
rounded to the nearest tenth would be 179.6
Step-by-step explanation:
use this formula
volume = (4/3) · π · r3
Kevin has a part time job. he earns £9 an hour. he wants to buy a new bike costing £306. how many hours does Kevin have to work to earn enough to buy it?
Answer:
34
Step-by-step explanation:
306/9=34
Solve the following:
four and seven twelfths plus six and nine twelfths
Ans:
11 and four twelfths
Step-by-step explanation:
please help me on this
Answer:
monkey is monkey so monkey and monkey conbided = baby little happy monkey
Step-by-step explanation:
Help please! I have to turn this in today.
:)
Answer:
Integer: 9
Nearest 10th: 9.5
Step-by-step explanation:
Grandma baked 96 cookies and gave them to her grandchildren. One of the grandchildren, Cindy, received c fewer cookies than she would have received had all of the cookies been evenly divided among the 8 grandchildren.How many cookies did Cindy receive? Write your answer as an expression.
Answer: 29 cookies.
Step-by-step explanation: 96/8=32 32-3=29 boom. maths.
The number of cookies baked by Grandma= 96
If she divides them evenly amount 8 children, then by division operation the number of cookies received by each child = (number of cookies) ÷ (number of children)
= (96) ÷ (8) = 12
Since, Cindy, received c fewer cookies than she would have received had all of the cookies been evenly divided among the 8 grandchildren.
Hence, the number of cookies received by Cindy = 12-c
Find the exact value of tan 195°.
[tex]\tan 195^{\circ}\\\\=\tan\left(3 \times 90^{\circ} - 75^{\circ} \right)\\\\=\cot 75^{\circ}\\\\=\left(\tan 75^{\circ} \right)^{-1}\\\\= \textbf{[}\tan \left(30^{\circ} + 45^{\circ}\right) \right \textbf{]}^{-1}\\\\=\left(\dfrac{\tan 30^{\circ} +\tan 45^{\circ}}{1- \tan 45^{\circ} \cdot \tan 30^{\circ}} \right)^{-1}\\\\\\=\left( \dfrac{\dfrac 1{\sqrt 3}+1}{1- \dfrac 1{\sqrt 3}} \right)^{-1}\\\\\\=\left( \dfrac{\sqrt 3+1}{\sqrt 3-1}\right)^{-1}\\\\\\=\dfrac{\sqrt 3-1}{\sqrt 3 +1}\\[/tex]
[tex]=\dfrac{\left( \sqrt 3-1\right)^2}{\left( \sqrt 3+1\right)\left( \sqrt 3-1\right)}\\\\\\=\dfrac{3+1-2\sqrt 3}{3-1}\\\\\\=\dfrac{4-2\sqrt 3}{2}\\\\\\=2-\sqrt 3[/tex]
For the equation z – 14 = 29. Jaun says that the solution is 33.Check solution work by substitutions it into the equation .Is his solution correct. Explain
Answer:
Jaun's solution is incorrect.
Step-by-step explanation:
If Jaun's solution to the equation is 33, we can check this by substituting z=33 and solving 33 - 14 = 29. Since 33-14=19 and 19 does not equal 29, Jaun's answer is incorrect.
Hope this helps! :)
Use rounding to estimate the product of 296 and 2, 423. Round both
numbers to the nearest hundred to find your answer.
The solution is
Answer:
Step-by-step explanation:
no problem
296 rounded to the nearest hundred would be 300 and 2423 would be 2400 there hope it helps
The product of 296 and 2.423 rounded to the nearest hundred would be 717.20
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of trimmed from the right in terms of exact digits.
We need to find the product of 296 and 2.423
296 x 2.423 = 717.20
Thus, 717.20 rounded to the nearest hundred .
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