Answer:
(x-3)/4=y
Step-by-step explanation:
substitute x for y and y for x
x=4y+3
subtract 3 from both sides
x-3=4y
divide both sides by 4
(x-3)/4=y
A wall is 22 feet tall. A ladder is leaned against that wall. The top of the ladder touches the top of the wall and the bottom of the ladder rests on the ground 8 feet from the base of wall. What is the length of the ladder?
Answer:
23.41 feet
Step-by-step explanation:
The ladder forms a right angle triangle with the wall
Height of the wall (opposite) = 22 feet
Bottom of the ladder from the wall (adjacent) = 8 feet
What is the length of the ladder?
Length of the ladder (hypotenuse)
Using Pythagoras theorem
Hypotenuse ² = opposite ² + adjacent ²
= 22² + 8²
= 484 + 64
= 548
Hypotenuse ² = 548
Hypotenuse = √548
= 23.41 feet
The length of the ladder is 23.41 feet
Write 142% as a mixed number in simplest form.
Answer:
71/50
Step-by-step explanation:
142 100
Both numbers are even. Divide by two.
71 50
Can't be simplified any further
Make it a mixed number.
1 21/50
The number 142 % in mixed number form is 1 21/50
What are Mixed Numbers?
A mixed number is a whole number, and a proper fraction represented together. A mixed number is formed by combining three parts: a whole number, a numerator, and a denominator. The numerator and denominator are part of the proper fraction that makes the mixed number.
Given data ,
The number given is = 142 %
On simplifying , we get
142 % = 100 % + 42%
We know that 100 % = 1
So ,
42 % = 42 / 100
Divide by 2 on both numerator and denominator , we get
21 / 50
So , the number 142 % is written as 1 21/50
Or ,
Simplifying 142 / 100 , we get
142 / 100 = 71 / 50
Converting 71 / 50 into mixed number , we get 21 as the remainder ,
Therefore , the mixed number form of 71 / 50 is 1 21/50
Hence , the mixed number form is 1 21/50
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Solve the inequality below 3-1/2x ≤ 11
PLEASE HELP ASAP I HAVE A TEST IN 2 MINUTES!!!!!!
The graph below models the value of a $20,000 car t years after it was purchased.
Which statement best describes why the value of the car is a function of the number of years since it was purchased?
A. Each car value, y, is associated with exactly one time, t.
B. Each time, t, is associated with exactly one car value, y.
C. The rate at which the car decreases in value is not constant.
D. There is no time, t, at which the value of the car is 0.
B. Each time, t, is associated with exactly one car value, y.
Answer:
B
Step-by-step explanation:
I got it right on the test
Helpppppppppppppppp ill mark you brainlist write in y=mx+b form
Answer:
The equation of the line in slope-intercept form is:
[tex]y\:=\:\frac{-10}{7}x-\frac{45}{7}[/tex]Step-by-step explanation:
Given the points
(-8, 5)(-1, -5)Finding the slope
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-8,\:5\right),\:\left(x_2,\:y_2\right)=\left(-1,\:-5\right)[/tex]
[tex]m=\frac{-5-5}{-1-\left(-8\right)}[/tex]
[tex]m=-\frac{10}{7}[/tex]
We know the slope-intercept form of the line equation is
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
substituting m = -10/7 and (-8, 5) in the slope-intercept form to determine the y-intercept
[tex]5\:=\:\frac{-10}{7}\left(-8\right)+b[/tex]
[tex]\frac{80}{7}+b=5[/tex]
[tex]b=-\frac{45}{7}[/tex]
now substituting m = -10/7 and b = -45/7 in the slope-intercept form
[tex]y = mx+b[/tex]
[tex]y\:=\:\frac{-10}{7}x+\left(-\frac{45}{7}\right)[/tex]
[tex]y\:=\:\frac{-10}{7}x-\frac{45}{7}[/tex]
Thus, the equation of the line in slope-intercept form is:
[tex]y\:=\:\frac{-10}{7}x-\frac{45}{7}[/tex]Find the minimum value of the function. [Hint: Let t = x³.] f(x) = 1 + 12x³ + 3x⁶
===========================================
Work Shown:
t = x³
f(x) = 1 + 12x³ + 3x⁶
f(x) = 1 + 12x³ + 3(x³)²
f(t) = 1 + 12t + 3t²
f(t) = 3t² + 12t + 1
f(t) = 3(t² + 4t) + 1
f(t) = 3(t² + 4t + 4 - 4) + 1 .... see note below
f(t) = 3( (t²+4t+4) - 4) + 1
f(t) = 3( (t+2)² - 4) + 1
f(t) = 3(t+2)² - 3*4 + 1
f(t) = 3(t+2)² - 12 + 1
f(t) = 3(t+2)² - 11
The smallest that t² can get is 0. By extension, the smallest (t+2)² can get is also 0, and same goes for 3(t+2)².
So effectively we replace the 3(t+2)² portion with 0 and end up with 3(t+2)²-11 = 0-11 = -11 as the minimum value of f(x)
This is the smallest output possible. Confirmation of such is shown in the graph below.
------------
Note: Recall that (A+B)² = A²+2AB+B². If we use this rule on (t+2)², then we get t²+4t+4. Earlier we simply had t²+4t without the extra +4 at the end. So I added 4 and subtracted 4 to balance things out. This completed the square.
Consider the similar triangle below.
ABC is the per-image and PQR is the image.
Answer:
Scale factor: 2
PR = 14
Perimeter = 34
Step-by-step explanation:
Similar Triangles
Similar triangles are those who have their corresponding side lengths proportional, i.e. the ratio of the corresponding sides is equal.
The figure shows similar triangles ABC and PQR. We can also see corresponding sides BC and QR have lengths 6 and 12 respectively.
The scale factor is [tex]\frac{12}{6}=2.[/tex]
The rest of the sides can be calculated by using the per-image triangle ABC side lengths and the new-found scale factor. Thus:
PR = AC*2 = 7*2 = 14
PR = 14
PQ = AB*2 = 4*2 = 8
The perimeter of the triangle PRQ is the sum of its side lengths:
P = 12 + 14 + 8 = 34
Answers:
Scale factor: 2
PR = 14
Perimeter = 34
A linear function has a slope of
у
and an x-intercept of -4. What are the coordinates of the y-intercept of the function?
Answer:
( 0, -4)
Step-by-step explanation:
The y-intercept in a linear function will always have 0 as the x-coordinate.
A 6-meter wire will be cut into pieces that are each 0.15 meter in length. A 3-meter rope will be cut into pieces that are each 0.25 meter in length.
How many more pieces of wire than pieces rope will there be?
Answer:
that will be 40(wire)-12(rope)=28parts
Step-by-step explanation:
6meter wire div by 0.15 eq to 40
3meter rope div 0.25 eq to 12
so we use 40-12=28parts
PLEASE HELP FAST! Solve for Y in the following system of equations!
X-y=-1
3x+5y=21
A.) 2
B.) 3
C.) 9
D.) 12
Answer:
B.) 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
x - y = -1
3x + 5y = 21
Step 2: Rewrite Systems
x - y = -1
Add y to both sides: x = y - 1Step 3: Redefine Systems
x = y - 1
3x + 5y = 21
Step 4: Solve for y
Substitution
Substitute in x: 3(y - 1) + 5y = 21Distribute 3: 3y - 3 + 5y = 21Combine like terms: 8y - 3 = 21Add 3 to both sides: 8y = 24Divide 8 on both sides: y = 3Write seventy thousand three hundred twenty and sixteen thousandths in standard form
Answer:
27,328.016
Step-by-step explanation:
Find the constant rate of change from the table
Answer:
going on by 2 every
Step-by-step explanation:
Find the next term in the sequence 3,7,10,17,27,44,___
Find the next term in the sequence
-1,4,-16,64,____
The historical records state that the long-lost temple of the sun had a perimeter of about 220 meters and an area of about 2,100 square meters. Do you think the archaeologists actually discovered the lost temple?
Answer:
The archaeologists dis not actually discovered the lost temple
Step-by-step explanation:
For us to be able to determine if the archaeologist actually discovered the lost temple, we need to find the dimension of the temple first.
Area of the temple = LW
Perimeter = 2L + 2W
L is the length
W is the width
If the perimeter is 220m
220 = 2L + 2W
110 = L+W ... 1
If the area is 2100 square meters
A = LW
2100 = LW ... 2
From 1;
L = 110 - W .... 3
Substitute 3 into 2
From 2;
2100 = LW
2100 = (110-W)W
2100 = 110W - W²
- W² + 110W - 2100 = 0
W² - 110W + 2100 = 0
Using the general formula;
W = -(-110)±√(-110)²-4(1)(2100)/2
W = 110±√3700/2
W = 110±60.83/2
W = 110±60.83/2
W = 110+60.83/2 and W = 110-60.83/2
W = 170.83/2 and 49.17/2
W = 85.415m and 24.585m
Substitute the width into the formula to get the length;
LW = 2100
L = 2100/W
L = 2100/85.415
L = 24.59 m
If the width is 24.585m;
L = 2100/24.585
L = 85.42m
Since we have different dimension of the temple, this show shat the archaeologists dis not actually discovered the lost temple
Which type of transformation is describe by (x,y) and (x+2,y+3)?
Answer:
fing the variable that is what u need
Aidan drives to school and back each day. The school is 16 miles from his home. He averages 40 miles per hour on his way to school. If his total trip takes 1 hour, at approximately what average speed does Aidan drive home?
Distance (mi)
Rate (mph)
Time (hr)
Trip to School
16
40
Trip Home
16
x
17 mph
27 mph
32 mph
56 mph
Aidan's average speed on his drive home is 26 2/3 miles per hour
What is Aidan's average speed?
Average speed is the total distance travelled per time. It indicates how fast an object is moving.
Average speed = total distance / total time
The first step is to determine the time it would take Aidan to drive to school :
Time = distance / speed
16 / 40 = 2/5 hours = 2/5 x 60 = 24 minutes
The second step is to determine the time it would take Aidan to drive from school
Time it would take to drive home from school = 60 minutes - 24 minutes = 36 minutes = 36/60 = 3/5 hours
Aidan's average speed to drive home = 16 miles ÷ 3/5
16 x 5/3 = 80 / 3 = 26 2/3 miles per hour
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Answer:
answer is 27 B, on edge.
Step-by-step explanation:
Rewrite as a monomial in standard form: (-2/3x^2y)^3*(-3/4xy^2)^2
Answer:
-1/6x^8y^7
Step-by-step explanation:
Answer both questions please! [ Brainliest ]
-
1. The measure of an angle is 63.5°. The measure of its supplementary angle is ___
degrees.
2. The measure of an angle is 64°. The measure of its complementary angle is ___
degrees.
Answer:
1. 116.5 degrees
2. 26 degrees
this pictureeeeeeeee??!!!!!
Answer:all real numbers your welcome
Step-by-step explanation:
A school is organizing a weekend trip to a nature preserve. for each student, there is a $40 charge, which covers food and lodging. there is also a $30 charge per student for the bus. the school must also pay a $20 cleaning fee for the bus. if the total cost of the weekend is $4,220, how many students will be going on the trip?
The number of students going on the trip is 60.
Given that, total cost = $4220
Cost per student= $30+$40=$70
Additional cost = $20
We need to find the number of students.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of students be x.
Cost paid by students = 4220-20 = 4200
Number of students = cost paid by students/cost per student
x = 4200/70
⇒x= 60
Therefore, the number of students going on the trip is 60.
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How do you get from one number to the next using multiplication or division?
From 100 to 106.
We can move from 100 to 10^6 by multiplying with 10^4.
How do you use multiplication?We know that it is possible to move from one value to another by the use of multiplication or division. Now in either case, there is a value that we have to us to multiply or divide another number order to move from one number to another.
Now we have the number 100 and we want to change it to 10^6. The implication of this is that the number 100 must have to be multiplied by the number 10^4 in order to arrive at the expected destination.
Thus;
100 * 10^4 = 10^6
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A circle with a 12 in diameter is folded in half and then folded in half again. What is the area of the resulting shape in terms of pi?
As an estimation we are told 5 miles is 8 km.
Convert 57.5 miles to km.
Answer:
5 miles=8km
1miles=8/5=1.6km
57.5 miles=(57.5×1.6)km
=92km
Which way will water move in this example shown below?
The water will not move
Water will move into the cell
The water will evaporate
The water will move out of the cell
Answer: it will move down.
Step-by-step explanation:
because of gravity.
HELP ASAP!! GIVING BRAINLY
Answer:
1) D
2)A
Step-by-step explanation:
Number 1) Don’t get confused with the -10 and 10, we already know that the value is already 20 so that narrows it to 2 choices. Now everytime you move on, it subtracts 10 so its 20:-10
Number 2) This one is pretty easy, we know that he drives about 12,000 miles a year but we don’t know how many years, so that unknown variable would be (x), now the 40,000 miles was already on it so that can’t change, only The years change so therefore the equation could be 12,000x+40,000
graph the following state and show the a h and k values.
y=2(x+3)^2-4
Does anyone know what the solution to −1.3≥2.9−0.6r is??
Answer:
yes its r>7
Step-by-step explanation:
-1.3>2.9-0.6r subtract 2.9 on both sides and do KCC keep change change
-2.9 -2.9
__________
-4.2>0.6r
________ divide by -0.6 on both sides to get
.6 .6
________
7<r or r>7 either way is fine
Work out the equation of a line which has a gradient of 3 and passes through the point (-1,3)
The equation of line is given as : y = 3x + 6
According to the question we have been given that the line passes through the points (-1,3) and has gradient 3
We need to find the equation of line. The general form of slope intercept form is
y = mx + c
where, m = slope
c = intercept
When a point and slope is given then the expression for the equation of line is given as:
[tex](y - y_{1})=m(x-x_{1})\\[/tex] (1)
where (x1,y1) are the coordinates which is (-1,3)
m = slope or gradient = 3
Putting the required values in equation (1) we get
(y-3) = 3(x+1)
y-3 = 3x + 3
y = 3x + 6
Hence the equation of line is given as : y = 3x + 6
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Answer: y=3x+6
Step-by-step explanation:
10. A washing machine repairer charges a total of £T for a repair which takes H hours. The formula
connecting T and H is
T = 35 + 20H.
Find H when T is 85.
The value of H when T is 85 is 2.5 hours which is calculated from the linear equation in two variables.
The linear equation in two variables is defined as an equation which defines the relationship between two unknown variables.
The general form of linear equation is of the form ax + by = c where a and b are constant co-efficient and c is a constant. Here y is the dependent variable and x is the independent variable.The graph of a linear equation in two variables is a straight line in the cartesian plane.Given the linear equation for total amount of money(T) which is the dependent variable using the independent variable H(number of hours worked) .
T=35 + 20 H
At T = 85 , we substitute the value of T in the linear equation to find H .
T=35 + 20 H
or, 85 = 35 + 20H
or, 50=20H
or, H=2.5
Therefore the value of H is 2.5 hours when T is 85.
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You have $20 to spend at the dollar store for Jake and Julian's birthdays. You want to buy 2 sodas for Jake, 4 candy bars for Julian, and an equal number of balloons b for them both with the rest of your money. Which equation below will determine how many balloons each friend receives?
Answers
2+4+b/2 =20
2+4+b =20
2+4+2b =20
20-4-2 =b
2(2+4+b) =20
Using a system of equations, the equation that determines how many balloons each friend receives is given by:
2 + 4 + 2b = 20.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable s: number of sodas bought.Variable c: number of candy bars bought.Variable b: number of balloons bought.You want to buy 2 sodas for Jake, 4 candy bars for Julian, hence:
s = 2, c = 4.
An equal number of balloons b, hence 2b is added to the equation, as the amount has to be 2, 4, 6, and so on, considering one balloon for each.
The total amount of money is of $20, hence the equation is:
2 + 4 + 2b = 20.
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