Answer:
[tex]\displaystyle y-1=\frac{1}{3}(x+3)[/tex]
Step-by-step explanation:
Equation of a Line
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The table shows the relation between x and y. It contains the following points
(-3,1), (6,4), (12,6), (30,12).
Taking the two first points, we find the equation of the line:
[tex]\displaystyle y-1=\frac{4-1}{6+3}(x+3)[/tex]
[tex]\displaystyle y-1=\frac{3}{9}(x+3)[/tex]
Simplifying:
[tex]\displaystyle y-1=\frac{1}{3}(x+3)[/tex]
To ensure the rest of the points belong to the line, we test them:
For the point (12,6):
[tex]\displaystyle 6-1=\frac{1}{3}(12+3)[/tex]
[tex]\displaystyle 5=\frac{1}{3}(15)[/tex]
5=5
Since equality is true, the point belongs to the line.
For the point (30,12):
[tex]\displaystyle 12-1=\frac{1}{3}(30+3)[/tex]
[tex]\displaystyle 11=\frac{1}{3}(33)[/tex]
11=11
Since equality is true, the point belongs to the line.
Thus, the equation of the line is:
[tex]\mathbf{\displaystyle y-1=\frac{1}{3}(x+3)}[/tex]
Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Irene's car had 6.4 gallons in the 14-gallon tank on the coldest day of the year. Irene filled the tank with gas that cost $3.90 per gallon. How much did Irene spend on gas?
Answer:
$24.96
Step-by-step explanation:
Total number of gallons irede had in his tank = 6.4gallons
Price per gallon is $3.90
To get the cost of 6.4gallons;
If 1 gallon = $3.90
6.4gallons = $x
Cross multiply
1 * x = 3.90 * 6.4
x = 24.96
Hence Irene spent $24.96 on gas
Solve for the variable
-3/4b = 2
Answer:
b = 2.666.......
Step-by-step explanation:
[tex]-\frac{3}{4} b = 2[/tex]
------ -----
[tex]-\frac{3}{4}[/tex] [tex]-\frac{3}{4}[/tex]
b = 2.666.....
The number of avocados ( a ) (a) a particular tree produces each year can be modeled by the function a ( y ) a(y). What does a ( 12 ) = 364 a(12)=364 mean?
Answer:
[tex]a(12) = 364[/tex] means that 364 avocados are produced by a particular tree at 12-th year.
Step-by-step explanation:
Let [tex]a[/tex] the number of avocados that a particular tree produces at a year. [tex]a(y)[/tex] is the number of avocados that a particular tree produces at y-th year. Hence, [tex]a(12) = 364[/tex] means that 364 avocados are produced by a particular tree at 12-th year.
Haley bought 1.6 pounds of almonds for $13.20. How much did she pay per pound for the almonds? Record your answer and fill in the bubbles on your answer document. Be sure to use correct place value. +/- .
Answer:
She paid $8,25 per pound
Step-by-step explanation:
Given
[tex]Weight = 1.6\ lb[/tex]
[tex]Total= \$13.20[/tex]
Required
Determine the amount paid per pound
To do this, we simply divide the amount by the weight of Almonds.
[tex]Amount = \frac{Total}{Weight}[/tex]
[tex]Amount = \frac{\$13.20}{1.6\ lb}[/tex]
[tex]Amount = {\$8.25/\ lb[/tex]
Hence, she paid $8,25 per pound
Peter is painting his bedroom. His bedroom has four walls. Yesterday, he painted 1 2/5 walls. What fraction of the walls is left to paint?
Answer: 2 3/5ths are left or 13/5
Step-by-step explanation: 1 2/5 + 2 3/5 = 4 total walls
due soon will give brainalist no fake answers!!
Answer:
90gr strawberry jelly
6 sponge fingers
315ml custard
135gr tinned fruit
Step-by-step explanation:
120/4 = 30 * 3 = 90
8/4 = 2 * 3 = 6
420/4 = 105 * 3 = 315
180/4 = 45 * 3 = 135
Name a ray with an endpoint of A.
okay so i got (1,1) but it's not on here ;-;
A circular garden has a diameter of 8 feet, and a rectangular garden has side lengths of 5 feet by 9 feet.
find the difference in square feet between the two gardens
Answer:
rectangular
Step-by-step explanation:
Answer:
The square of a number decreased by 8 times the number equals 9. Determine the two possible values of the number. X2-8x=9. +1-9 ... 9. Basic Area of Rectangles. 16 The length of a rectangular room is 5 less than ... 17 The total area of Jon's backyard is 144 square feet. ... the length of a side of the original square garden.
Step-by-step explanation:
i hope this helps!
Given: m || n and p is a traversal.
Prove: m<2=m<7
What is the missing reason in the proof?
Answer:
Alternate exterior angles
Step-by-step explanation:
Alternate exterior angles are congruent.
Jamie tossed a coin 50 times. The coin landed on heads 27 times and landed on tails
23 times. What is the relative frequency of landing on heads?
Answer: 54%
Step-by-step explanation:
The relative frequency of landing on heads is 0.54 or 54%.
Given that Jamie tossed a coin 50 times.
Head showed for 27 times.
Tails showed for 23 times.
We need to find the relative frequency of landing on heads,
The relative frequency of an event is calculated by dividing the number of times the event occurred by the total number of trials or occurrences.
In this case, Jamie tossed a coin 50 times, and it landed on heads 27 times.
To find the relative frequency of landing on heads, we divide the number of times the coin landed on heads (27) by the total number of tosses (50):
Relative Frequency of landing on heads = Number of heads / Total number of tosses
Relative Frequency of landing on heads = 27 / 50
Simplifying this fraction, we get:
Relative Frequency of landing on heads = 0.54
This means that, based on the given data, the coin landed on heads approximately 54% of the time in the 50 tosses performed by Jamie.
Therefore, the relative frequency of landing on heads is 0.54 or 54%.
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Please Hurry! Due by tonight!
Step-by-step explanation:
the y-intercept is 1 because it's on the y(axis). the line from 1 goes down 1 over three so the slope is 1/3.
your equation would be y=1/3x+1
Solve the following equation:
a/3.5 - 4.8 = 6.3
a= ______
Answer:
a= 38.85
Step-by-step explanation:
Answer:
[tex]\boxed {a = 38.85}[/tex]
Step-by-step explanation:
Solve for the value of [tex]a[/tex]:
[tex]\frac{a}{3.5} - 4.8 = 6.3[/tex]
-Add both sides by [tex]4.8[/tex]:
[tex]\frac{a}{3.5} - 4.8 + 4.8 = 6.3 + 4.8[/tex]
[tex]\frac{a}{3.5} = 11.1[/tex]
-Multiply both sides by [tex]3.5[/tex]:
[tex]a = 11.1 \times 3.5[/tex]
[tex]\boxed {a = 38.85}[/tex]
Therefore, the value of [tex]a[/tex] is [tex]38.85[/tex].
please someone help me please??!!!
Answer:
how should I know?
Step-by-step explanation:
Answer:
a.)
x= -2 , -1, 0, 1, 2, 3
y=8 , 7, 6, 5, 4, 3
and for b just plot the point and then connect them. im not sure how i can show you
Step-by-step explanation:
What is the total number of servings the modified recipe will make?
9514 1404 393
Answer:
B. 4
Step-by-step explanation:
Equating exponents, we have ...
2x +7 = 15
2x = 8 . . . . . subtract 7
x = 4 . . . . . . divide by 2
The equation is true when the value of x is 4.
hope this helps enjoy.
The ratio of blueberries to strawberries in a fruit salad is 4:3. If there are 45 strawberries in a salad, how many blueberries are there.. Blueberries 4 Strawberries 3
Answer:
60 blueberriesStep-by-step explanation:
Given the ratio of blueberries to strawberries in a fruit salad to be 4:3. The total ratio = 4+3 = 7
If there are 45 strawberries in the salad then we can first calculate the total mixture of both as shown;
amount of strawberries = 3/7 * x = 45
x is the total amount of mixture
from the expression;
3x/7 = 45
cross multiply
3x = 7*45
3x = 315
x = 315/3
x = 105
The amount of blueberries present = 105 - 45 = 60
Hence the amount of blueberries present is 60 blueberries
For a party, Samantha bought eight half gallon bottles of soda. About how many cups of soda did Samantha buy???
Answer: 4 and a half
Step-by-step explanation:
there are 1,920fence posts used in a 12-killometer strech fence how many fence posts are used in one kilometer
Answer:
160
Step-by-step explanation:
Just divide 1920 into 12
Need help in math ASAP
Answer:
B
Supplementary means they add to make 180 deg, so solve (4x-8)+(2x+2)=180
Answer:
angle a + angle b=180
4x-8+(2x+2)=180
6x-6=180
6x=180+6
x=186/6
{x=31°}
A 14 foot long ramp is being built to access a front door in a house. The door is 5 feet above the ground. How far away from the base of the house must the ramp be placed? What angle will the ramp make with the ground?
Answer:
The ramp must be placed 13.08 feet from the base of the house.
The angle the ramp will make with the ground is 20.92°.
Step-by-step explanation:
An illustrative diagram for the scenario is shown below.
In the diagram, d represents the distance of the door from the ground, r represents the length of the ramp and x represent the distance of the ramp from the base of the house.
To determine how far away from the base of the house the ramp must be placed, that is to determine x in the diagram.
The diagram is a right angle triangle and x can be determine using the Pythagorean theorem which states " the square of the hypotenuse equals sum of the squares of the other two sides"
In the diagram, the hypotenuse is r
∴ r² = d² + x²
r = 14 ft
d = 5 ft
∴ 14² = 5² + x²
196 = 25 + x²
Then, x² = 196 - 25
x² = 171
x = √171
x = 13.08
Hence, the ramp must be placed 13.08 feet from the base of the house.
Now, to determine what angle the ramp will make with the ground, that is θ in the diagram.
From the formula
Sinθ = Opposite / Hypotenuse
In the diagram, opposite = d = 5ft
and Hypotenuse = r = 14ft
∴ Sinθ = 5ft / 14ft
Sinθ = 0.3571
∴ θ = Sin⁻¹(0.3571)
θ = 20.92°
Hence, the angle the ramp will make with the ground is 20.92°.
Felix can grow 6 plants with every seed packet. Write an equation that shows the relationship between the number of seed packets x and the total number of plants y. Write your answer as an equation with y first, followed by an equals sign.
Answer:
I believe it’s:
Y= 6x
Step-by-step explanation:
if if x equals 3 and Y equals negative 2 - x 3 - Y2
Answer:
13
Step-by-step explanation:
x=3, y=-2 so 3(3)-(2)2=13
maria wanted to invest $10,000 at the bank. she invested part of her money in a cd account paying 2.1% simple interest and invest the rest of her money in a checking account paying 1.5% simple interest. After 1 year, her interest income was $195. How much did Maria invest in each account
Answer:I = ?, P = $500, r = 6%, t = 3 years
Step-by-step explanation:
Use the quadratic formula to solve the equation.
5x2-3x + 1 = 0
X=
Answer:
x= 11/3
Step-by-step explanation:
Simply.
[tex] \frac{ab - a}{a} = [/tex]
[tex] \frac{2x + y}{y} = [/tex]
I mainly forgot how to do it. Do I divide -ab to get it alone? How do I do it?
Answer:
Required Answer:-First go to first equation[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac{ab-a}{a}}[/tex]
Take common[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {{\bcancel {a }}(b-1)}{{\bcancel {a}}}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]{\underline{\boxed{\bf b-1)}}}[/tex]
Solve each equation. For each step. Identify the property used.
14 + 3n = 8n - 3(n-3)
22x + 11 = 4x - 7
(P.S. The properties that the problem is asking for are the properties of equality. Division property of equality, etc, etc.)
Answer:
Solution of [tex]14 + 3n = 8n - 3(n-3)[/tex] => x = 5/2
Solution of [tex]22x + 11 = 4x - 7[/tex] => x=-1
Step-by-step explanation:
We will solve the equations one by one
So,
[tex]14 + 3n = 8n - 3(n-3)[/tex]
Applying Distributive property
[tex]14 + 3n = 8n - 3n+9\\14+3n = 5n+9[/tex]
Subtraction property of equality (Subtracting 14 from both sides)
[tex]14+3n-14 = 5n+9-14\\3n = 5n-5[/tex]
Subtraction property of equality (Subtracting 5n from both sides)
[tex]3n-5n = 5n-5-5n\\-2n = -5[/tex]
Division property of equality (Dividing both sides by -2)
[tex]\frac{-2n}{-2} = \frac{-5}{-2}\\n = \frac{5}{2}[/tex]
Second Equation:
[tex]22x + 11 = 4x - 7[/tex]
Subtraction property of equality (Subtracting 11 from both sides)
[tex]22x + 11-11 = 4x - 7-11\\22x = 4x-18[/tex]
Subtraction property of equality (Subtracting 4x from both sides)
[tex]22x-4x = 4x-18-4x\\18x = -18[/tex]
Division property of equality (Dividing both sides by 18)
[tex]\frac{18x}{18} = \frac{-18}{18}\\x = -1[/tex]
Hence
Solution of [tex]14 + 3n = 8n - 3(n-3)[/tex] => x = 5/2
Solution of [tex]22x + 11 = 4x - 7[/tex] => x=-1
The matrices show the number of indoor and outdoor volunteers in different age groups
create a matrix that shows the total number of indoor and outdoor volunteers in different age groups. name the matrix T.
what is the value of the element t11 and what does the value indicate?
create a matrix by subtracting the women's matrix from the mens matrix. name the matrix D.
what is the value of the element at d12 and what does that value indicate?
Answer:
(a) M + W = Indoor= [26 55] Outdoor = [32 49]
(b) The value indicates the sum of the indoor volunteers ages 18-39 so the Value would be, 34.
(c) M – W = Indoor = [8 15] Outdoor = [-16 3]
(d) This value indicates the difference of the volunteers indoors 40. So the value would be 15.
Step-by-step explanation:
If this is wrong my apologies i tried LOL
but i will let you know when i get the results back asap!
The value of the element t11 is 34 and the value of the element at d12 is 15.
When are two matrices called being equal?Two matrices are equal if and only if their shapes are same, and they've got the same elements for each corresponding row and column positions.
M + W = Indoor= [26 55] Outdoor = [32 49]
The value indicates the sum of the indoor volunteers ages 18-39,
Therefore, the Value would be, 34.
To create a matrix by subtracting the women's matrix from the mens matrix.
Now the difference;
M – W = Indoor = [8 15] Outdoor = [-16 3]
This value indicates the difference of the volunteers indoors 40 so
Therefore the value would be 15.
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Please quickly! Out of 5,500 people who attended the football game, fifty-six percent were rooting for the home team. How many people rooted for the home team?
how do I do this?
I don't understand geometry and it's really confusing can one of you help me?
Answer:
lol im stuck too
Step-by-step explanation:
which of the following is an arithmetic sequence with common difference 2
A. 1, -3, 5, -7, 9
B. 2, 4, 8, 16, 32
C. 10, 8, 6, 4, 2
D. 13, 15, 17, 19, 21
Answer:
C is the answer.
C has a common difference of "2"
Step-by-step explanation:
You could say that the word "difference" also means Subtraction, so in a simpler way of saying "The common difference of 2" you could say, "Which one of the following is subtracting by 2?"
PLEASE MARK BRAINLIEST