Answer:
a = 9
Step-by-step explanation:
Step 1: Add 3 to both sides
2a – 3 = 15
2a – 3 + 3 = 15 + 3
Step 2: Simplify
add the numbers ( 2a = 18 )
Step 3: Divide both sides by the same factor
2a = 18
2a 18
––– = –––
2 2
Step 4: Simplify
l
Cancel the terms that are in both the numerator and the denominator
l
l
Divide the numbers
l
a = 9
Answer: a = 9
An angle measures 138° less than the measure of its supplementary angle. What is the
measure of each angle?
The measure of each angle is 159° and 21°.
What are supplementary angles?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates.Two angles are considered to be supplementary if their sums total 180 degrees. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°.So, supplementary angles = 180
Then,
2x + 138 = 1802x = 180 - 1382x = 42x = 2121 + 138 = 159Therefore, the measure of each angle is 159° and 21°.
Know more about supplementary angles here:
https://brainly.com/question/12919120
#SPJ9
Find an equation of the line passing through the point (6,-1) that is parallel to the line y = -3/2x- 3
Step-by-step explanation:
parallel means it has the same slope.
the slope is always the factor of x : -3/2
I guess the needed equation is in slope-intercept form :
y = ax + b
"a" being the slope, "b" being the y intercept (the y value when x = 0).
but since we have a point on the line and its slope, we can start with the point-slope form
y - y1 = a(x - x1)
"a"is again the slope, (x1, y1) is the given point.
and then we transform this into the slope-intercept form.
in our case we have
y - -1 = -3/2 × (x - 6)
y + 1 = -3x/2 + 18/2 = -3x/2 + 9
y = -3x/2 + 8
or
y = -3/2 x + 8
or
y = -1/2 × (3x - 16)
please help im giving 60 points on my most recent question earn another 10 here :D
Find the midpoint given the endpoints:
(___),(___)
Note: 1.5 = 3/2
=======================================================
Explanation:
The two points shown on the graph are located at (-3, -2) and (1, 5)
Let's focus on the x coordinates for now.
To find the midpoint of -3 and 1, we do two things in the order shown
Add up the values: -3+1 = -2Divide in half: -2/2 = -1Therefore, -1 is the midpoint of -3 and 1 on the number line.
It is also the x coordinate of the midpoint.
------------
Repeat these steps for the y coordinates of the given points.
Add: -2+5 = 3Divide in half: 3/2 = 1.5This is the y coordinate of the midpoint.
-------------
The midpoint overall is located at (-1, 1.5)
I used GeoGebra to confirm the answer as correct.
? 4 cm Area = 20 cm² 6 cm
The height of the triangle whose base is 4 cm and area is 20 cm² is 10 cm .
The area of a triangle is defined as the total space occupied by the three sides of the triangle in a two-dimensional plane. The basic formula for the area of a triangle is half the product of the base and the height, or A = 1/2 × b × h.It is given that base is 4 cm and area is 20 cm² .
Putting above values in area formula , we get
Area = 1 / 2 × base × height
20 = 1 / 2 × 4 × height
20 = 2 × height
10 cm = height
Learn more about area of triangle here :
https://brainly.com/question/17335144
#SPJ9
The complete question is given below :
Find the height of the triangle whose base is 4cm and area is 20 cm².
Determine if each statement is true or false. Justify your answer.
log₃3/2 = 1/2 log₃3
The logarithm statement log₃ 3 / 2 = 1 / 2 log₃ 3 is a false statement as 1 / 2 log₃ 3 is equal to log₃ √3 and not log₃ 3 / 2.
We are given the logarithm as:
log₃ 3 / 2 = 1 / 2 log₃ 3
We need to tell if it is true of not.
We get that, it is false as 1 / 2 log₃ 3 is equal to log₃ √3 and not log₃ 3 / 2.
So, the statement given will be a false statement.
Therefore, we get that, the logarithm statement log₃ 3 / 2 = 1 / 2 log₃ 3 is a false statement as 1 / 2 log₃ 3 is equal to log₃ √3 and not log₃ 3 / 2.
Learn more about logarithm here:
https://brainly.com/question/25710806
#SPJ4
An elementary school collected 1,705 bottles for a recycling program. A high school also collected some bottles. Both schools collected 3,627 bottles combined. How many bottles did the high school collect?
answer choices
5,332
5,333
2,122
1,922
The number of bottles collected by the high school is 1922 bottles since the total collected bottles is 3627.
What is total of all bottles collected by both groups?The total number of bottles collected by both elementary and high schools is 3627 bottles, which means that the number of bottles collected by the high school can be determined as the total bottles minus the ones collected by the elementary school:
bottles collected by high school = total bottes - bottles collected by elementary schoolbottles collected by high school = 3627 - 1705bottles collected by high school = 1922Find out more about subtraction on: brainly.com/question/134255
#SPJ1
Determine if each statement is true or false. Justify your answer.
log₂4+log₂8=5
The statement [tex]log_{2} 4 + log_{2} 8 = 5[/tex] is true.
We have been given two logarithm terms that is the first term is [tex]log_{2} 4[/tex] and second term is [tex]log_{2} 8[/tex].
The properties of logarithm that we are going to use are
[tex]log a^{m} = m *log a[/tex] and [tex]log_{a} a = 1[/tex]
First we will find the value of the two terms by operating the above mentioned properties of logarithm to obtained the values of the logarithm.
Thus,
[tex]log_{2} 4 = log_{2} 2^{2} \\ = 2* log_{2} 2\\ = 2*1\\ = 2[/tex]
Similarly,
[tex]log_{2} 8 = log_{2} 2^{3} \\ = 3* log_{2} 2\\ = 3*1\\ = 3[/tex]
Now adding both the terms by substituting its respective values which we have calculated above, we get
[tex]log_{2} 4 + log_{2} 8 = 2+3 = 5[/tex]
Thus, we have proved that R.H.S = L.H.S
Hence the statement is [tex]log_{2} 4 + log_{2} 8 = 5[/tex] is true.
Learn more about logarithm here : https://brainly.com/question/10208274
#SPJ4
Simplify each expression. Rationalize all denominators. 1-√3 x / √6 x
After simplifying and rationalizing the expression 1 - √ 3 x / √ 6 x, we get the result as - (√ 2 / 2) + (√6 / 6) x .
We are given the expression:
1 - √ 3 x / √ 6 x
We need to simplify each expression by rationalizing the denominator.
Multiply √ 6 in both numerator and denominator, we get that:
(1 - √ 3 x) / √ 6 x × ( √ 6 / √ 6)
We get that:
= (√ 6 - 3 √ 2 x) / 6 x
= - (√ 2 / 2) + (√6 / 6) x
Therefore, after simplifying and rationalizing the expression 1 - √ 3 x / √ 6 x, we get the result as - (√ 2 / 2) + (√6 / 6) x .
Learn more about rationalization here:
https://brainly.com/question/790315
#SPJ4
Add or subtract if possible. 10√27 - 4√12
The subtraction of the expression 10√27 - 4√12 is 22√3.
Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more integers together.
In mathematics, subtraction involves removing anything from a group or a number of objects. What is left in the group gets smaller when you subtract.
Consider the expression,
y = 10√27 - 4√12
Now, the number in the root can also be written as:
27 = 3 × 3 × 3
12 = 2 × 2 × 3
Therefore,
y = 10√27 - 4√12
y = 10[ √(3 × 3 × 3) ] - 4[ √( 2 × 2 × 3 ) ]
y = 10 × 3√3 - 4 × 2√3
y = √3 ( 10 × 3 - 4 × 2 )
y = √3 ( 30 - 8 )
y = 22√3
The value of the expression 10√27 - 4√12 is 22√3.
Learn more about subtraction here:
https://brainly.com/question/4721701
#SPJ4
Divide using long division or synthetic division:
(10x^3-x^2-29x-30)/(x^2-x-2)
Answer:
10 x^3 - x^2 - 29 x - 30 = (10 x + 9)(x^2 - x - 2) + -12
Step-by-step explanation:
Compute (10 x^3 - x^2 - 29 x - 30) ÷ (x^2 - x - 2) using polynomial long division:
x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30
To eliminate the leading term of the numerator, 10 x^3, multiply x^2 - x - 2 by 10 x to get 10 x^3 - 10 x^2 - 20 x. Write 10 x on top of the division bracket and subtract 10 x^3 - 10 x^2 - 20 x from 10 x^3 - x^2 - 29 x - 30 to get 9 x^2 - 9 x - 30:
| | | | | 10 x | |
x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30
| -(10 x^3 | - | 10 x^2 | - | 20 x) | |
| | | 9 x^2 | - | 9 x | - | 30
To eliminate the leading term of the remainder of the previous step, 9 x^2, multiply x^2 - x - 2 by 9 to get 9 x^2 - 9 x - 18. Write 9 on top of the division bracket and subtract 9 x^2 - 9 x - 18 from 9 x^2 - 9 x - 30 to get -12:
| | | | | 10 x | + | 9
x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30
| -(10 x^3 | - | 10 x^2 | - | 20 x) | |
| | | 9 x^2 | - | 9 x | - | 30
| | | -(9 x^2 | - | 9 x | - | 18)
| | | | | | | -12
The quotient of (10 x^3 - x^2 - 29 x - 30)/(x^2 - x - 2) is the sum of the terms on top of the division bracket. The remainder is the expression that remains after the final subtraction step.
| | | | | 10 x | + | 9 | (quotient)
x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30 |
| -(10 x^3 | - | 10 x^2 | - | 20 x) | | |
| | | 9 x^2 | - | 9 x | - | 30 |
| | | -(9 x^2 | - | 9 x | - | 18) |
| | | | | | | -12 | (remainder) invisible comma
(10 x^3 - x^2 - 29 x - 30)/(x^2 - x - 2) = (10 x + 9) - 12/(x^2 - x - 2)
Write the result in quotient and remainder form:
Answer: 10 x^3 - x^2 - 29 x - 30 = (10 x + 9)(x^2 - x - 2) + -12
Your friend invested $1000 in an account that pays 6% annual interest. How much interest will your friend have after her college graduation in 4 years?
c. Is the solution of the equation the final answer to the problem?
The solution of the equation is the final answer to the problem , $ 240 .
Calculating Simple Interest :
Simple Interest = ( P * R * N ) / 100
where P = Principal Amount
R = Rate of Interest
and N = No. of years for which investment is done
According to question :
P = 1000
R = 6
N = 4
Hence ,
Simple Interest = ( 1000 * 6 * 4 ) / 100
= 240
Therefore , after college graduation in 4 years the interest received would be $240 .
The solution of the equation is the final answer to the problem .
To learn more on Simple Interest follow link :
https://brainly.com/question/19088526
#SPJ4
y varies directly with x .
If x=1 when y=5 , find y when x=3 .
After direct variation y = 15 when x = 3.
What exactly do we mean when we say "direct variation"?To give the reader a hint, direct variation equations use the same phrase.Either "directly proportional" or "directly varies" is the phrase.For example, the area of a square is proportional to the square of its side.The variational constant is k = 3 if y varies directly as x and y = 6 when x = 2.As a result, y = 3x is the direct variation equation.So,
The initial statement is y = kx
Then to find y when x = 3.
K constant will be y/x ⇒ 5/1That is y = kx ⇒ y = 5/1 × xWhen x = 3:
y = 5/1 × 3 ⇒ y = 15Therefore, after direct variation y =15 when x = 3.
Know more about direct variation here:
brainly.com/question/6499629
#SPJ4
3 A trader buys some goods for $820. When he sells them, he makes a profit of 35%.
a Work out the profit, in dollars.
b Work out how much he sells them for
Based on the amount that the trader bought the goods for, when he sells them, he would make a profit of $287
The amount that the trader will sell the goods for is $1,107
How to find the dollar profit?The dollar profit that the trader will make from selling the goods is:
= Cost of the goods x Percentage profit
= 820 x 35%
= 820 x 0.35
= $287
The amount that the trader will sell the goods for is:
= Cost of the goods + Profit on the goods
= 820 + 287
= $1,107
Find out more on profit percentage at https://brainly.com/question/19104371
#SPJ1
A triangle has side lengths of (8w + 8x) centimeters, (3w+10y) centimeters, and
(4y + 8x) centimeters. Which expression represents the perimeter, in centimeters,
of the triangle?
Answer:
(8w+8x)(8w+8x)+(3w+10y)(3w+10y)+(4y+8x)(4y+8x)
Step-by-step explanation:
20 POints!!!
PLSSSSSSS
Answer: ab = 3a + 2b + c subtract 3a from both sides. ab - 3a = 2b + c factor the left side. a (b - 3) = 2b + c divide both sides by ( b - 3).
sorry but only one for then second screenshot :/
Hope this helps! :)
WILL GIVE BRAINLIST TO BEST ANSWER
Julia drove a car 10 miles in 30 minutes. Jasmine drove a motorcycle 3 miles in 12 minutes. who drove faster? show work!
A student states that a triangle can be formed with side lengths 2 in, 3 in, and 6 in. is the student correct? why, or why not? yes, because 2 3 < 6 yes, because 6 2 > 3 no, because 2 3 < 6 no, because 6 2 > 3
A student is not correct when he stated that a triangle can be formed with side lengths 2 in, 3 in, and 6 in because 2 + 3 < 6.
A triangle is a polygon with three sides and three vertices.
To know if a set of numbers is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
Let a = 2, b = 3 , c = 6
a + b > c : 2 + 3 > 6 5 > 6 False
a + c > b : 2 + 6 > 3 8 > 3 True
b + c > a : 3 + 6 > 2 9 > 2 True
If at least one of these statements does not hold true, the measurements can't be the sides of a triangle.
Learn more about Triangle Inequality Theorem at:
https://brainly.com/question/507331
#SPJ1
What’s the algebraic expression of:
Six times the sum of a and b squared minus four times the product of a and b squared
Answer:
6(a+b)^2 + 4ab^2
Step-by-step explanation:
sum is addition (a+b)
product is multiplication (ab)
6(a+b)^2 + 4ab^2
3(4x - 5) - 2 (x - 3) = 7
Can you please simplify this for me?
Step-by-step explanation:
12x - 15 - 2x + 6 = 7
10x - 9 = 7
10x = 16
x = 16/10
x = 8/5
Please help!!! 4(3x + 2)= -76, show your work pleaseee!!!
Answer:
x=-7
Step-by-step explanation:
Divide both sides by 4: 4(3x+2)/4=-76/4
Simplify; 3x+2=-19
Subtract 2 from both sides: 3x+2-2=-19-2
Solve:3x=-21
divide side by 3: 3x/3=-21/3
simplify: x=-7 B)
Answer:
x = -7
Step-by-step explanation:
Given equation:
[tex]4(3x+2)=-76[/tex]
Distribute:
[tex]\implies 4 \cdot 3x+4 \cdot 2=-76[/tex]
[tex]\implies 12x+8=-76[/tex]
Subtract 8 from both sides:
[tex]\implies 12x+8-8=-76-8[/tex]
[tex]\implies 12x=-84[/tex]
Divide both sides by 12:
[tex]\implies \dfrac{12x}{12}=\dfrac{-84}{12}[/tex]
[tex]\implies x=-7[/tex]
Find the inverse of each function. Is the inverse a function? f(x)=4 x-1
We need to know about inverse of a function to solve this problem. The inverse of the given function is (x+1)/4.
The inverse of a function is a function for whom the range of the function becomes it's domain. The domain of a function is the set of values that the function can take as input. The range of a function is the set of values that the function can have as possible output. The inverse of a function is a function that finds the pre-image of it's function. If the function is in terms of x, then the inverse of the function will be in terms of y. The inverse of a function can be found by making y the independant variable and expressing x in terms of y.
f(x)=4x-1
write this function in terms of y and wquating to x
x=4y-1
x+1=4y
y=(x+1)/4
[tex]f^{-1} (x)[/tex]=(x+1)/4
Therefore we found the inverse of the function to be (x+1)/4.
Learn more about inverse of function here:
https://brainly.com/question/15066392
#SPJ9
The job paid 25$ for every 2 hours of work.
Write an equation that represents how much the job pays, y, for x hours of work
Answer:
$12.5xy
Step-by-step explanation:
y = how much the jobs pays
x = hours of work
25/2
= 12.5xy
quadrilateral A'B'C'D. Describe a sequence F. Quadrilateral ABCD is congruent to of rigid motions that takes A to A, B to B, C to C, and D to D. (Lesson 1-17) A' B' C' A D C B
The sequence of transformations that take quadrilateral ABCD to quadrilateral A'B'C'D' is given by:
Rotation 90º clockwise.Translation left.What are examples of transformations in the graph of a function?Examples of transformations are given as follows, along with explanations on the changes caused by the transformations.
Translation: Can be either left/right or down/up, changing the position of the figure.Reflections: Can be over one of the axes or over a line, changing the orientation of the figure.Rotations: Happens over a degree measure, changing the inclination, along with the orientation, of the figure.Dilation: Happens when the coordinates of the vertices of the original figure are multiplied by the scale factor, changing the side lengths of the figure.As a dilation changes the side lengths the figure, a dilated figure is not congruent to the original figure, hence a dilation does not happen for this problem.
The first change was in the inclination and orientation of the figure, hence it underwent a rotation. From the movement of the vertices, for example, A to the bottom to the top, B from right to left, the rotation was of 90º clockwise.
Then, the function had the base at the same position, however it moved left, hence the second transformation was a translation left.
More can be learned about transformations at https://brainly.com/question/28174785
#SPJ1
you will get 100 points if you get this right
Answer:12.5 Km/L
Step-by-step explanation:[tex]\frac{100km}{8L}[/tex]
=12.5Km/L
Answer: 12.5
100 / 8 = 12.5
CHECK
12.5 x 8 = 100
Hope this helps 0v0
Hi please help me!!!!!!
The slope and y-intercept of the line are -3 and -6 respectively.
How to find the slope and y-intercept of a line?The graph is a linear function.
The graph can be represented in a slope intercept form as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore, using (1, -9)(-4, 6)
m = 6 - (-9) / -4 - 1
m = 6 + 9 / -5
m = 15 / -5
m = -3
Therefore,
slope = -3
Let's find the y-intercept as follows;
(1, -9)
y = -3x + b
-9 = -3(1) + b
b = -9 + 3
b = -6
Therefore, the slope and y-intercept of the line are -3 and -6 respectively.
learn more on y-intercept and slope here: https://brainly.com/question/12763756
#SPJ1
Review the graph. A student spends 16.5 hours studying and receives a mark of 61.4%. Which statement describes this result?
Using the line of best fit, the correct statement that describes this result is given by:
D. The result is an outlier and there is no gap in the data.
What is the missing information?The statements are missing, and are given as follows:
A. The result is not an outlier and there is a gap in the data.
B. The result is not an outlier and there is no gap in the data.
C. The result is an outlier and there is a gap in the data.
D. The result is an outlier and there is no gap in the data.
What does the line of best fit mean?The line of best fit gives the expected exam score for a student that studies x hours. For example, for a student that studies 16 hours, the expected score is of 90.
The actual score is 61.4%, which is significantly less than the expected score, meaning that there is an outlier. However, there are no gaps in the data-set, as as the line considers students between 0 and 20 hours, and 16 is in this interval.
This means that option D is correct.
More can be learned about a line of best fit at https://brainly.com/question/22992800
#SPJ1
Please help I will give brainliest
The congruent figures are given as follows:
LMNOP and YAHFS.EFCD and XUYW.MON and TUE.What are congruent figures?Congruent figures are figures whose outer side lengths have the same measures. They may have different orientations, but the outer side lengths have to be the same.
Hence the congruent figures in this problem are given as follows:
LMNOP and YAHFS.EFCD and XUYW.MON and TUE.They have different orientations(rotated), but same side lengths.
More can be learned about congruent figures at https://brainly.com/question/1675117
#SPJ1
Given a term in the sequence and the common ratio find the first term:
Please show work!! ASAP!! I’m desperate
============================================================
Explanation:
[tex]g_3 = 6.25[/tex] tells us that the third term is 6.25
The common ratio r = 5/4 = 1.25 tells us how to get the next term. We multiply the third term by 1.25 to get the next term
4th term = (3rd term)*(r) = (6.25)*(1.25) = 7.8125
--------------
To go backwards and find the second term, we will divide by r, which is the inverse operation of multiplication.
2nd term = (3rd term)/r = (6.25)/(1.25) = 5
Use the same idea to find the 1st term
1st term = (2nd term)/r = 5/(1.25) = 4 is the final answer
help me out asap pls
Answer:
I don't think any are parrallel.
Step-by-step explanation:
If you look at the angles, they are different. Just slightly. So the rays making the angles would be at different angles. If they were the same angles the rays making the angles would be the same not allowing them to touch making them parallel. But since they are not I don't think they are parallel.
Solve by substitution
3x-y=12
Y=4x-14
The value of x is 2 and the value of y is -6.
What is the solution of the equations?The substitution method is one of the methods used to solve simultaneous equations. It entails making one of the variables the subject of the equation in one of the equations.
Then the variable is substituted for in the first equation:
3x-y=12
Second equation :
1Y=4x-14
Substitute for y in equation 1 using equation 2 :
3x - (4x - 14) = 12 3x -4x + 14 = 12
Combine similar terms:
14 - 12 = 4x -3x
Add similar terms;
2 = x
Substitute for x in equation:
2y = 4(2) - 14 y = 8 - 14 y = -6
learn more about system of equations at brainly.com/question/25802822
#SPJ1
The value of x is 2 and the value of y is -6.
What is the value of x and y?The substitution method is one of the methods that is used to solve for simultaneous equations. It entails making either of the variables the subject of the formula and then replacing for the variable in the other equation.
Other methods that can be used to solve simultaneous equations are the graph method and the elimination method.
3x - y = 12 equation 1
Y= 4x - 14 equation 2
y is the subject of the formula in equation 2
Substitute for y in equation 1
3x - (4x - 14) = 12
3x -4x + 14 = 12
Combine similar terms together:
14 - 12 = 4x -3x
Add similar terms together
2 = x
In order to determine the value of y, take the following steps
Substitute for x in equation 2
y = 4(2) - 14
8 - 14
y = -6
To learn more about the substitution method, please check: https://brainly.com/question/12544602
#SPJ1