The longest side of a triangle is twice the length of the shortest side. The remaining side is 20 cm longer than the shortest side. The perimeter of the triangle is 132 cm. What is the length of each side?
Answer:
The triangle has sides lengths 28, 56, 48
Step-by-step explanation:
Let x = the shortest side
So then the longest side will be 2x, because the question said that "the longest side... is twice the length of the shortest side" Then the third side would be x + 20.
The perimeter was given so add all the sides and set it equal to 132.
x + 2x + x + 20 = 132
Combine like terms.
4x + 20 = 132
Subtract 20
4x = 112
Divide by 4.
x = 28
Then use x = 28 to find the lengths of all the sides.
Shortest Side:
x = 28
Longest Side:
2x
= 2(28)
= 56
Third Side:
x + 20
= 28 + 20
= 48
Keith has $500 in a savings account at the beginning of Summer. He wants to have at least $300 in the account by the end of the summer. He withdraws $25 each week for food, clothes and movie tickets how many weeks can Keith withdraw money from his account?
Answer: 8 weeks
Step-by-step explanation: 25x4 =100 double it that makes 25x8=200 then 500 - 200 = 300
Answer:
12
Step-by-step explanation:
500 is what we are starting with and 300 is the endpoint.
if he spends 25 a week, we can multiply 25 12 times and we get 300
25•12= 300
Make a list of the factors of 18. Then make a list of the divisors of 18. Are the factors of the numbers also divisors of the number? Explain your reasoning
Answer:
Step-by-step explanation:
If you make a list of factors for 18 you will get 1, 2, 3, 6, 9 and 18.
If you make a list of divisors you will get 1, 2, 3, 6, 9 and 18.
yes the factors of the numbers are also divisors because factors are numbers that go into 18, and we can use those same numbers for dividing with the number 18.
what is the arcsin of 3
The value of the arcsin of 3 is 90 - 100.998i
From the question, we are to determine the inverse sine or arcsine of the given number
The given number is 3
All the values for the sine of angles are less than or equal to 1
That is,
Given an angle θ,
sinθ ≤ 1
From this, we can infer that the arcsine of 3 will be an imaginary number.
The arcsine of 3 is
sin⁻¹(3) = 90 - 100.998i
Hence, the value of the arcsin of 3 is 90 - 100.998i
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Arun bought 10 chicken wings for $10.00. How much would it cost for 3 wings?
Answer: 3 dollars
Step-by-step explanation: He bought 10 chicken wings. 10/10 is 1. If you buy 3 wings, it's 1+1+1 which is 3.
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Answer:
Hello.
Step-by-step explanation:
What is the solation to the equation?
√x+7= -2
√x+7 The solution to the equation is x=-3.
Square root: If we take the square root of a number and then take the square of the outcome, we get the original number back again.
e.g. 4 = 2 and 22 = 4.
We can say that the square root and the square cancel each other out. They are the inverse of each other.
If we have a number written with the index 2 ( squared) then taking the square root simply means that we leave out the 2 ( this only applies to positive numbers ).
We can therefore take any squared numbers that are under the square root sign out from under the root sign by leaving out the power 2.
The solution to the equation√x+7= -2.
√x+7= -2
First we take Squaring on both sides
(√x+7)2= (-2)2
x+7 = 4
x=-3.
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yazmin noticed her favorite workout tops were on sale for $6.00 off the original price. she purchased 4 of the tops and spent a total of $51.80. write and solve an equation to determine x, the original price of the workout tops?
the original price of the workout tops is $18.95
How to find the original price of the workout tops?
Let's say that the original price is x, we know that the tops are on sale for $6.00 off the original price, so if Yazmin buys 4 of these, the cost will be:
C(x) = (x - $6.00)*4
And we know that the cost is $51.80, replacing that we get:
$51.80 = (x - $6.00)*4
Now we need to solve this linear equation for x.
$51.80/4 = x - $6.00
$51.80/4 + $6.00 = x = $18.95
We conclude that the original price of the workout tops is $18.95
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1. Fill in the blanks to complete the description of the track. (2 points)
The track has ____ sides of the square and the distance around ____ complete circle(s).
2. The length of one side of the square is the square root of its area. Use the table to find the approximate length of one side of the square. Explain how you used the table to find this information. (2 points)
3. Use your answers above to find the total length of the part of the track that is made up of sides of the square. (2 points)
4. The circumference of (distance around) a circle is π times the diameter, or C = πd. A side of the square is the diameter of each half circle.
In your answer to question 1, you gave the number of complete circles included in the track. Use this answer and C = πd to find the approximate length of the circular part of the track to the nearest tenth of a foot. Use 3.14 for π and show your work. (2 points)
5. Find the approximate length of the track, including the straight and circular sections. (2 points)
Answer:2 and 5
Step-by-step explanation:
i don't know a lot but hope it helped
x+2)4x²+10x+2(
SOLVE THIS QUADRATIC EQUATION PLS
Step-by-step explanation:
4x^2 +10+ 2(2x+4)
4x^2 + 10x+4x+8
4x^2 +14x+8
4x^2+16x-2x -8
4(x+4)+2(x+4)
4+2(x+4)
6(x+4)
B is between A and C. If AC = x-31, AB = x-6 And BC = 2x+10, find the value of x
Answer:
AB +BC + AC = 180
x - 6 + 2x + 10 + x - 31 = 180
3x - 27 =180
3x= 207
x=69
what is inverse of matrix
Answer:
linear algebra, an n-by-n square matrix A is called invertible, if there exists an n-by-n square matrix B such that \mathbf {AB} =\mathbf {BA} =\mathbf {I} _{n}\ where Iₙ denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.
Answer:
Brainliest pls
Step-by-step explanation:
The inverse of a square matrix A, denoted by A-1, is the matrix so that the product of A and A-1 is the Identity matrix.
Determine the truth value of the following conditional statement. If true, explain your reasoning. If false, give a counterexample.
If ∠1 and ∠ 2 form a linear pair, they are supplementary angles.
∠1 and ∠ 2 are linear pairs and have a sum of 180° so they will be supplementary angles.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
In the given image ∠1 and ∠ 2 are linear pairs.
Now,
∠1 = ∠3 (opposite angle)
∠2 = ∠4 (opposite angle)
Now,
∠1 + ∠2 + ∠3 +∠4 = 360°
(∠1 + ∠2) + 180° = 360°
(∠1 + ∠2) = 180°
If the sum of two angles is 180° then they will be supplementary angles.
Hence "∠1 and ∠ 2 are linear pairs and have a sum of 180° so they will be supplementary angles".
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calculate the percent of population each situation represents b) 90 out of a population of 450 people
The percent of population in the situation is 20 %.
Percentage means a number or a ratio represented in the form of fractions of 100. It is represented using the percentage sign ‘%’. In other words, the percentage is defined as how much of one quantity is made by another quantity and it is evaluated in terms of 100.
We have to find the percentage of population 90 out of a population of 450 people represents.
We know that, the formula for percentage will be:-
(Given people/ Total people)*100
Here,
Given people = 90
Total people = 450
Hence, the percentage will be :-
= (90/450)*100 = (1/5)*100 = 20 % .
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solve the system by using any method. if a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. 2(3x y)
By solving the equations, We get
[tex](\frac{34}{31} ,\frac{10}{31} )[/tex]
Explain Unique solution?
A unique solution to a set of linear simultaneous equations exists if and only if,
(A) There are the same number of equations and unknowns.
(b) Each equation is valid.
(c) All equations are independent and there is no linear connection between any two or more equations.
Given:
[tex]2(3x+y)=y-x+8[/tex]
[tex]x-\frac{4}{3}\;y=\frac{2}{3}[/tex]
Solving the equations,
[tex]2(3x+y)=y-x+8[/tex]
[tex]6x+2y=y-x+8[/tex]
[tex]7x+y=8\;\;\;\;\;------equation(1)[/tex]
[tex]x-\frac{4}{3}\;y=\frac{2}{3}[/tex]
[tex]\frac{3x-4y}{3}=\frac{2}{3}[/tex]
[tex]3x-4y=2 \;\;\;\;\;------equation(2)[/tex]
By solving equation(1) and (2), We get
[tex]x=\frac{34}{31}[/tex]
Substitute the value of x in equation(1),
[tex]7\;(\frac{34}{31}) +y=8[/tex]
[tex]y=8-7(\frac{34}{31} )[/tex]
[tex]y=8-\frac{238}{31}[/tex]
[tex]y=\frac{248-238}{31}[/tex]
[tex]y=\frac{10}{31}[/tex]
Therefore, The points (x, y) is,
[tex](\frac{34}{31} ,\;\frac{10}{31} )[/tex]
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What is the value of x?
Answer: x = 7
Step-by-step explanation:
1. Set line PS equal to QR
2x - 3 = 11
2. Add 3 to both sides:
2x = 14
3. Divide both sides by two:
2x/2 = 14/2
4. Simplify
x = 7
Which of these fractions is equal to 1? A 31/31 B 17/18 C 1/5 D 7/4
Answer:
A
Step-by-step explanation:
31 divided by 31 is 1 (Since fractions are basically division)
Angelo drove home from college traveling an average speed of 71.7 mph and drove back to the college the following week at an average speed of 64.1 mph. if the total round trip took 5 hours, how much time did it take angelo to drive from home back to college? express the time in hours and minutes. round to the nearest minute.
When Angelo drove home from college with an average speed of 71.7 mph and back to college with an average speed of 64.1 mph, she took 5 hours for full trip then the time taken to travel from home to college is 2.63 hours
Given,
The average speed from college to home = 71.7 mph
The average speed from home to college = 64.1 mph
We know,
Speed = Distance / Time
Consider the total distance as x
Time taken = Distance / Speed
Then the time taken to travel from college to home = [tex]\frac{x}{71.7}[/tex] hours
time taken to travel from home to college = [tex]\frac{x}{64.1}[/tex] hours
Total time taken = 5 hours
Then the equation will become
[tex]\frac{x}{71.7}+\frac{x}{64.1}=5[/tex]
Cross multiply the terms
[tex]\frac{64.1x+71.7x}{(71.7)(64.1)}=5\\ \frac{135.8x}{4595.97}=5[/tex]
135.8x= 5×4595.97
135.8x=22979.85
x=169.21
Time taken to travel from home to college =[tex]\frac{169.21}{64.1}[/tex]
=2.63 hours
Hence, When Angelo drove home from college with an average speed of 71.7 mph and back to college with an average speed of 64.1 mph, she took 5 hours for full trip, then the time taken to travel from home to college is 2.63 hours
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Help! factoring out the gcf from the equation 4w with an exponent of 3 subtracted from 12w with an exponent of 2
The GCF of [tex]12w^{2} - 4w^{3}[/tex] is [tex]4w^{2}[/tex].
The Greatest Common Factor (GCF) of two or more numbers is defined as the factors which is common and highest .
For Example The GCF of 6 and 8
express 6=2*3
8=2*2*2. since 2 is common in both the GCF is 2.
In the given question
we need to factor out gcf from [tex]12w^{2} - 4w^{3}[/tex]
first express both terms in prime factors
[tex]12w^{2} =3*4*w*w[/tex]
and
[tex]4w^{3} =4*w*w*w[/tex]
the equation becomes
[tex](3*4*w*w-4*w*w*w)[/tex]
we can see that [tex]4*w*w[/tex] is common in both the terms .
So we can write [tex]4w^{2} (3-w)[/tex]
Therefore [tex]4w^{2}[/tex] is the gcf by factoring of [tex]12w^{2} - 4w^{3}[/tex].
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ZA and ZB are
supplementary angles. If mA = (x + 4)° and m
LB = (2x - 7)°, then find the measure of ZA.
Supplementary angles have a sum of 180°
Therefore, we can add the expressions for Angles A and B and set their sum equal to 180.
( 7x - 15 ) + ( 2x - 3 ) = 180
Now we can combine like terms and use inverse operations to find the value of x:
( 7x - 15 ) + ( 2x - 3 ) = 180
9x - 18 = 180
9x - 18 + 18 = 180 + 18
9x = 198
9x/9 = 198/9
x = 22
Then Angle A will have a measure of 7x - 15 or 7• 22 -15 = 154 - 15 = 139°
m∠A = 139°
The measure of Angle b will be 2x - 3 = 2 • 22 - 3 = 44 - 3 = 41°
m∠ B = 41°
NOTE: 139 + 41 = 180
Solve for x in the equation x2-10x+25= 35-
X=5+2√ √5
O x=5± √√35
x=10+2√√/5
x = 10+ √√√35
0 0 0 0
The solution of the quadratic equation is x=5±√35 .
A quadratic equation is given by the equation which can be written in the form ax²+bx +c.
There are two solution of x for a quadratic equation. the graph of a quadratic equation is in the shape of a parabola in the cartesian plane.To solve a quadratic equation various methods are used:Completing of squaresMiddle term factorizationusing the quadratic formulathe given quadratic equation is :
x²-10x+25=35
Simplifying the equation we get:
or, x²-10x+25-35=0
or, x²-10x-10=0
Now we will solve the equation by completion squares method:
x²-10x-10=0
or, x²-2×x×5+5²-5²-10=0
or, (x-5)²=35
or, x-5=±√35
or, x= 5±√35
Therefore the solution of the quadratic equation is 5+√35 and 5-√35 .
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Use the graph to determine the input value for which f(x) = g(x) is true.
The input value is x = 1.5
An intersection is the point where two lines or curves meet We can find intersections graphically by plotting curves on the same graph and determining their intersection. We can find an intersection algebraically by following these steps: Solve each equation for one of the variables, calling it y. Set the expressions for y found in the first step equal and solve for the other variable, calling it x. This is the x-value of the intersection. Return the x value of the intersection back to one of the original equations and solve for y.This is the y variable for the intersection.In the graph the intersection both functions is the point when f(x)=g(x)
the point of intersection both graphs is (1,5,2)
that means
for the input value of x = 1.5
f(1.5) = g(1.5) = 2
The input value is x = 1.5
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The question is incomplete, the complete question is
Use the graph to determine the input value for which f(x) = g(x) is true.
A. x = 0.5
B. x = 1
C. x = 1.5
D. x = 2
Answer:
x=1.5
Step-by-step explanation:
edge 2022
The speed of sound is approximately 760 mph in air. If a gun is fired 1/2 mile away, how long will it take the sound to reach you?
which of the following is an advantage of a cumulative frequency polygon over a histogram or frequency polygon?
The significant benefit of a cumulative frequency polygon above a histogram and frequency polygon is that it can demonstrate the total number of observations that are less than the upper limit of a specific class.
What is cumulative frequency polygon?A line segment-joined plot of a cumulative frequency against by the upper class boundary. An ogive would be any continuous cumulative frequency curve, along with a cumulative frequency polygon.
Some main points related to cumulative frequency polygon are-
The cumulative frequency graph can graphically represent data organized in the pattern of a cumulative frequency distribution. The method for drawing cumulative frequency polygons as well as cumulative frequency curves and perhaps ogives is similar. The only distinction in that a cumulative frequency polygon is formed by connecting points with line segments, whereas the cumulative frequency polygon is formed by connecting points with a free hand smooth curve.The cumulative frequency polygon is primarily a line graph drawn on graph paper by projecting the actual lower and upper limits of a class intervals on the x-axis and their respective cumulative frequencies on the y-axis.To know more about the cumulative frequency polygon, here
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what is the answer? pls, help me do it. :)
Answer:The answer would be 14 squishy cupcakes
Step-by-step explanation:Please give brainliest if right.
Answer: 14 (Im assumning you want to know what 14% of 100 is)
Step-by-step explanation:
100 * 14% (0.14) = 14
Add 100 into a calculator, hit multiply, type 14 then the percent button. Press equal and you should get 14.
Usually a percentace of 100 is that number.
40) SHOPPING Stevenson's Market is selling 3 packs of stylus pens for $5.00. How
much will 10 packs of stylus pens cost at this price?
The cost of ten pack of stylus pen is $(50/3).
This problem can be solved by unitary method and can be understood by the following process.
In this method we have to determine the cost of a unit of product and then the total amount by multiplying the unit cost by the desired quantity what we want.
Here, it is given that three packs of stylus pen costs $5.
Cost of one pack of stylus pen = $ 5/3
Therefore cost of 10 packs of stylus pen = $(5/3)*10
= $(50/3)
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pls help how do u solve for x
so this is complicated
1)
y = 180°-(21°+34°)
y = 180°-55°
y = 125°
x = 180°-125°
x = 55°
Under her cell phone plan, violet pays a flat cost of $38 per month and $3 per gigabyte. she wants to keep her bill under $80 per month. which inequality can be used to determine xx, the maximum number of gigabytes violet can use while staying within her budget? a) 80>3x+38 b) 80>3(38+x) c) 80<3x+38 d) 80<3(38+x)
Answer:
a) 80>3x+38
Step-by-step explanation:
Gigabyte cost + flat cost < $80
Flat cost = $38
x = number of gigabytes
$3 = money charged per gigabyte
Gigabyte cost = 3x
Answer:
3x + 38 < 80 OR 80 > 3x + 38
What is the midpoint of the segment shown below
Which of the following is an equation to the tangent line to the graph of (fx) = -2x+4 at 1
A) y= -2(x-1) + 2
B) y= 2(x-1) + 2
C) y= -2(x+1) + 2
D) y= 2(x-1) - 2
Please show how to find this as I really want to learn!
Answer:
nuts
Step-by-step explanation: