Final answer:
Mr. Jimerson will earn $27.60 per hour after receiving a 15% raise on his original $24 per hour salary, resulting in a $3.60 increase per hour.
Explanation:
Mr. Jimerson earns $24 per hour working and qualifies for a 15% raise in salary. To calculate his new hourly salary after the raise, first determine the amount of the raise by finding 15% of his current hourly wage. Since 15% can be written as 0.15, we multiply his current wage by 0.15 to find the raise amount.
0.15 × $24 = $3.60
Next, add this raise amount to his original hourly wage to find his new salary:
$24 + $3.60 = $27.60 per hour
Therefore, Mr. Jimerson's salary after the raise will be $27.60 per hour.
decide whether the triangles are similar. If they are , write a similarity statement and state the reason justifying the similarity
I'll do the first one to get you started.
Start at point A as that is the first letter of the sequence ABC. The second letter is B so we'll record the length of segment AB, which is 4 units long.
Note how we have a segment that is also 4 units long in the other triangle; however, we won't use that one just yet. Instead, we'll go for the 2 unit segment. As it turns out, every piece of the triangle on the right side is half that of the left side triangle.
Segment ED is 2 units long. So AB and ED pair up
------------------------------
BC is 8 units long; DF is 4 units long (half of BC). So BC and DF pair up
I started at A, went to B, then to C in that exact order marking the side lengths of 4 and 8 respectively. At the same time for the other triangle, I started at E, moved to D, then to F recording the side lengths 2 and 4
So A pairs up with E, B pairs with D, and C pairs with F
Therefore, triangle ABC is similar to triangle EDF. The order is very important so that the points line up and correspond in the proper manner.
I used the SSS (side side side) similarity theorem to prove the triangles similar. This theorem says that if the sides are in proportion to one another, then the triangles are similar.
10(d+3)–(−9d–4)=d–5+3
What value of d makes the equation TRUE?
Answer:
d=-2
Step-by-step explanation:
We have
[tex]10(d+3)-(-9d-4)=d-5+3[/tex]
now we remove parenthesis and use distribution property
[tex]10d+30+9d+4=d-5+3[/tex]
now we combine like terms
[tex]10d+9d+30+4=d-2[/tex]
[tex]19d+34=d-2[/tex]
[tex]19d-d+34=-2[/tex] (subtract d from both side )
[tex]18d=-2-34[/tex] ( subtract 34 from both side )
[tex]18d=-36[/tex]
[tex]d=\frac{-36}{18}[/tex] ( divide both side by 18)
[tex]d=-2[/tex]
the ratio of the measures of three triangles is 2:5:4, and its perimeter is 165 units. find the measure of each side of the triangle
Answer:
30:75:60
Step-by-step explanation:
I'm not sure if this is how you're supposed to solve it, but I'll give it my best shot.
1. Think of the 2:5:4 as "chunks". 2 Chunks:5 Chunks:4 Chunks. 2+5+4 is 11. We obviously have to use all of the 165 perimeter units, and we know the ratio already.
2. We need to take 165, and divide it by 11. This will give us what one "chunk" is. It equals 15.
3. Now that we know what one chunk is equal to, we can simply multiply.
2 Chunks * 15 Per Chunk = 30
5*15=75
4*15=60
So, our final answer is 30:75:60
--
Checking, 30+75+60=165, so we used the whole perimeter.
The measure of sides of the triangle be 30, 75 and 60 unit.
Given,
the ratio of the measures three sides of triangles is 2:5:4.
The perimeter of triangle is 165 units.
Let the sides of triangle be 2x, 5x and 4x respectively.
We know that perimeter of triangle is sum of all sides, So
[tex]\rm P= 2x+5x+4x[/tex]
[tex]165=11x[/tex]
[tex]x=\dfrac{165}{11} \\\\[/tex]
[tex]x=15\\[/tex]
So the sides of triangle will be [tex]2\times15=30[/tex], [tex]5\times 15=75[/tex] and [tex]4\times15=60[/tex] units respectively.
Thus the sides of triangle are 30, 75 and 60 units.
For more details on perimeter of triangle follow the link:
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Solve by elimination. 7x+3y=25 -2x-y=-8
Answer:
x=1 , y=6
Step-by-step explanation:
7x+3y = 25
-2x-y = -8
Multiply the second equation by 3 so we can eliminate y
3(-2x-y )= -8*3
-6x -3y = -24
Add this equation to the first equation
-6x -3y = -24
7x+3y = 25
----------------------
x = 1
But we still need to find y by substituting x =1
-2x -y = -8
-2(1) -y = -8
-2-y = -8
Add 2 to each side
-2+2 = -8+2
-y = -6
Multiply by -1
y = 6
Sounds travel at a speed of about 1,087 feet per second when the temperature is 32 F at this speed how far does sound travel in 8 second
Answer:
The answer is 8696
Step-by-step explanation:
This answer is obtained by multiplying the speed per second by 8
Answer:
8696 feet
Step-by-step explanation:
We are given that the sound travels at a speed of nearly 1087 feet per second when the temperature is 32 F. And we are supposed to find the distance the sound travels in 8 seconds.
We know the formula of the speed:
[tex]Speed = \frac{distance}{time}[/tex]
Putting in the values to find the distance:
[tex]1087=\frac{distance}{8}[/tex]
[tex]distance = 1087*8\\\\distance=8696[/tex]
Therefore, the speed travels for 8696 feet in 8 seconds.
One evening 1400 concert tickets were sold for the Fairmont Summer Jazz Festival. Tickets cost $20 for covered pavilion seats and $15 for lawn seats. Total receipts were $24,000. How many tickets of each type were sold?
To determine the number of each type of ticket sold, a system of linear equations is set up and solved using the substitution method. The answer is 600 covered pavilion seats and 800 lawn seats were sold.
To solve this problem, we can set up a system of linear equations based on the given information. Let x be the number of covered pavilion seats sold and y the number of lawn seats sold. We have two equations:
x + y = 1400 (since 1400 tickets were sold in total)20x + 15y = 24000 (since the total receipts from ticket sales were $24,000)Now we can solve this system of equations using either substitution or elimination method. For simplicity, let's use the substitution method:
From equation 1, we can express x as:
x = 1400 - y
Now substitute x in equation 2:
20(1400 - y) + 15y = 24000
Simplify and solve for y:
28000 - 20y + 15y = 24000
-5y = -4000
y = 800
Since we know y, we can find x by substituting the value of y in x = 1400 - y:
x = 1400 - 800
x = 600
So, the number of covered pavilion seats sold was 600 and the number of lawn seats sold was 800.
( 4 over 4 )x = 4/32 what is the value of x
Answer:
x = [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
The fraction [tex]\frac{4}{4}[/tex] is equal to 1, so putting this into the equation:
1x = [tex]\frac{4}{32}[/tex]
So x = [tex]\frac{4}{32}[/tex]
Or simplified down by dividing the fraction by 4:
x = [tex]\frac{1}{8}[/tex]
Answer:
1/8
Step-by-step explanation:
for this problem, you just have to think about how many times 4 goes into 32, so what times 4 equals 32? the answer is 8. so by simplifying the 4 and 32, you get 1/8
12a + 12b + 12c + 12d Michael writes the expression shown here as 12(a + b + c + d). He is correctly using the ___________ property.
Answer:
He should be using distributive property
Sorry if im wrong
Step-by-step explanation:
Answer:
Michael used distributive property
Step-by-step explanation: I got it correct on my test and I'm also in K12
Use synthetic division to solve (4x-3x+5x+6)/(x+6). What is the quotient?
The correct solution: 4x^2 -27x +167 - 996/(x+6)
Step-by-step explanation:
3(-2x-1)=2(x+5)
A) -13/8
B) -3/4
C) 13/8
D) 3/4
(64/125) to the power of -2/3
Solve x+2/x-4<0
A)–4 < x < –2
B)–2 < x < 4
C)–2 < x < –4
[tex]Domain:\ x\neq-2\\\\\dfrac{x+2}{x-4}<0\iff(x+2)(x-4) < 0\\\\x+2=0\to x=-2\\x-4=0\to x=4\\\\(x+2)(x-4)=x^2-4x+2x-8\\\\\text{parabola op}\text{en up}\\\\\text{Look at the picture}\\\\Answer:\ \dfrac{x+2}{x-4}<0\ for\ x\in(-2,\ 4)\to\boxed{B)\ -2 < x < 4}[/tex]
Other method:
[tex]\dfrac{x+2}{x-4}<0[/tex]
zeros of numerator and denominator are x = -2 and x = 4.
Look at the second picture.
for x < -2 → x + 2 < 0 and x - 4 < 0
therefore [tex]\dfrac{x + 2}{x - 4}=\dfrac{(-)}{(-)}>0[/tex]
for -2 < x < 4 → x + 2 > 0 and x - 4 < 0
therefore [tex]\dfrac{x+2}{x-4}=\dfrac{(+)}{(-)} < 0[/tex]
for x > 4 → x + 2 > 0 and x - 4 > 0
therefore [tex]\dfrac{x+2}{x-4}=\dfrac{(+)}{(+)} > 0[/tex]
Answer: B) -2 < x < 4Answer:
-2 < x < 4
Step-by-step explanation:
Based on the given information, choose the similarity statement
Answer:
SSS
Step-by-step explanation:
For the triangle to be considered similar, 2 sides and an angle must be similar or two angles and a side or three angle or the three sides are similar.
For the case above the three are similar and this makes triangle ABC similar to DEF.
Answer:
Third option SSS is the correct answer.
Step-by-step explanation:
It is given the BC/EF = 1/2
Consider Two triangle ABC and DEF
To find the ratio of sides
From the given data, we get
AC/DF = 3/6 = 1/2 and AB/DE = 12/24 =1/2
The ratio of sides are equal then the triangles are similar.
Based on the given data we can conclude that triangle ABC and DEF are similar.
Find the nth term of 3,12,27,48,75
Answer:
3n^2
Step-by-step explanation:
3, 12, 27, 48, 75
List the differences between terms:-
9, 15, 21, 27
Now find the second differences:-
6, 6, 6
The sequence in the question is quadratic and the first coefficient ( that of n^2) = 6/2 = 3. The first term in the nth term formula is 3n^2.
Now we write out the original sequence and the 3n^2 values as follows:-
3 12 27 48 75
3 12 27 48 75
They are the same so the formula for the nth term is 3n^2.
The nth term of the given sequence is 3n².
What is a series?A sequence's series is the total number of terms in the sequence.
A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.
Given the series,
3,12,27,48,75
Since all terms are multiplied of 3
3 × 1 = 3
3 × 4 = 12
3 × 9 = 27
3 × 16 = 48
3 × 25 = 75
It is clear that it is forming a series by 3 and the product of the square root of a natural number.
So, it will be 3n².
Hence "The nth term of the given sequence is 3n²".
For more information about the series,
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a submarine travels 90 kilometers in 4 hours find the submarines rate of speed in kilometers per hour
Answer:
22.5
Step-by-step explanation:
To find the rate of speed per hour, you need to divide the kilometer (90) by the hours (4).
90/4=
22.5
The submarine's rate of speed is found by dividing the distance traveled (90 kilometers) by the travel time (4 hours), resulting in a rate of 22.5 kilometers per hour.
You need to use the formula for speed which is speed = distance ÷ time. In this case, the submarine travels 90 kilometers in 4 hours.
To calculate the rate of speed, divide the distance by the time:
Speed = 90 kilometers ÷ 4 hours = 22.5 kilometers per hour.
This means the submarine's rate of speed is 22.5 kilometers per hour.
It takes a student 11 seconds to scan their hand at lunch. During one 30 min lunch period, approximately how many students can be scanned??? Is it 18,1008,180,1800. Plzzz I will give you 100 points
It takes 11 seconds to scan one person. So we have this ratio to start with
11 seconds: 1 person
Divide both sides by 11 to get this new ratio
1 second: 1/11 person
1 second: 0.0909 person
So in 1 second, 0.0909 of a person can be scanned. This statement seems silly because we can't have a fraction of a person, but it helps with the next part as shown below. The next step is to multiply both sides by 1800 to get....
1 second: 0.0909 person
1800*1 second: 1800*0.0909 person
1800 seconds: 163.62 persons
In a span of 1800 seconds (equivalent to 30 minutes), about 163 people's lunches can be scanned. Unfortunately, none of the answer choices are 163. The closest thing is 180, but that is an overestimate. So I would ask your teacher if there is a typo somewhere.
Note: if it took exactly 10 seconds for each student (instead of 11), then the answer would be 1800*(1/10) = 1800*0.10 = 180.
In order for two triangles to be similar, all corresponding pairs of angles must be
last weekend,5% of the tickets sold at seaworld were discount tickets. if seaworld sold 60 tickets in all , how many discount ticket did it sell? use the percent proportion
Answer:
3
Step-by-step explanation:
to do this you need to figure out 5 percent of 60
in order to do this you need to find 95 percent of 60 and subtract it from 60
.95x60=57
60-57=3
they sold 3 discount tickets
3/60=5%
Katie's orange tree has 30 oranges. Katie's tree has three times as many fruits as Lisa's did before Lisa harvested half of her limes on the tree. How many limes does Lisa have on her tree now?
Lisa has 5 limes left on her tree after harvesting half. So, the correct answer is option 5) 5.
Let's break down the problem step by step:
1. Katie's orange tree has 30 oranges.
2. Katie's tree has three times as many fruits as Lisa's did before Lisa harvested half of her limes.
3. Let's denote the number of limes Lisa originally had as x .
4. After Lisa harvested half of her limes, she was left with [tex]\( \frac{x}{2} \)[/tex] limes.
5. Since Katie's tree has three times as many fruits as Lisa's tree originally had, the total number of fruits on Katie's tree is 3x .
6. The problem states that Katie's tree has 30 oranges, so 3x = 30 .
7. Solving for x , we find [tex]\( x = \frac{30}{3} = 10 \).[/tex]
So, Lisa originally had 10 limes on her tree. After harvesting half of them, Lisa is left with [tex]\( \frac{10}{2} = 5 \)[/tex] limes.
Therefore, the correct answer is option 5) 5.
The Correct question is:
Katie's orange tree has 30 oranges. Katie's tree has three times as many fruits as Lisa's did before Lisa harvested half of her limes on the tree. How many limes does Lisa have on her tree now?
1)10
2)45
3)90
4)15
5)5
Lisa initially had 10 limes on her tree. After harvesting half, she has 5 limes remaining. Therefore, Lisa now has five limes on her tree.
To find out how many limes Lisa has on her tree now, we need to break down the problem step-by-step:
Katie's tree has three times as many fruits as Lisa's: 30 = 3x
Solving for x: x = 10
So, Lisa originally had 10 limes on her tree.
Next, we calculate how many limes Lisa has after harvesting half:
Lisa harvested half of the 10 limes:Number of limes harvested = 10 / 2 = 5 The remaining limes on Lisa's tree: Remaining limes = 10 - 5 = 5Therefore, Lisa has five limes on her tree now.
7.19 divided by 58 estimate the quotients
Answer:
0.124
Step-by-step explanation:
[tex]\frac{7.19}{58}[/tex]
To divide the numbers, we need to remove the decimal point
To remove decimal point , we multiply top and bottom by 100
[tex]\frac{719}{5800}[/tex]
Use long division. After using decimal point at the top we can include any number of zeros with 719
. 1 2 3 9
---------------------
5800 7190
5800
------------------------(subtract)
13900
11600
---------------------------(subtract)
2300 0
1740 0
--------------------------(subtract)
56000
52200
---------------------------(subtract)
3800 0
Division goes on ............
Estimate the quotient to 3 decimal places
Quotient = 0.124
Do not round your answer. Type in just the number. 36 is what percent of 288?
36 is 12.5% of 288
I hope this helps!
Which set of coordinates satisfies the equations 3x − 2y = 15 and 4x − y = 20?
A. (2, -7)
B. (1, -6)
C. (5, 0)
D. (0, -7.5)
Answer:
C. (5,0)
Step-by-step explanation:
you can check the graph at the point where those two lines meet
or
solve the simultaneous equation
you will solve for x=5 and y=0 if you use elimination/substitution
Answer:
(5,0)
Step-by-step explanation:
we have two equations with two unknown variables
equation 1 : 3x -2y =15
equation 2: 4x - y =20
we can multiply the equation 2 for two in order to add the equations and eliminate a term
(-2)*(equation 2)= -2(4 x- y) =-2*20
-8x +2y=-40 equation 3
now, let´s add the equation 3 to equation 1
-8x +2y = -40
3x -2y = 15
___________
-5x +0 =-25
[tex]x=\frac{-25}{-5} \\x=5[/tex]
and leaving y from equation 2
4 x - y =20
4x -20 =y
y=4(5)-20
y=20-20=0
y = 0
the only coordinate that satisfies the equation is (5,0)
have a great day
write 4.59% as a decimal
Answer: .0459
Step-by-step explanation:
What is the slope intercept form in equation form of this graph?
Answer:
y = 7/2x+5
Step-by-step explanation:
To find the slope we need two points
(-2,-2) and (0,5)
We can find the slope from the formula
m = (y2-y1)/(x2-x1)
m = (5--2)/(0--2)
m = (5+2)/(0+2)
m = 7/2
The slope is 7/2
The y intercept, or where it crosses the y axis, is 5
Using the slope intercept formula for a line
y= mx+b
y = 7/2x+5
Someone pls help me with this
The anwser is ten because the number i saw is 14 estimate is ten.
Ella has 5 balloons.Taylor had 7 balloons.Write the ratio of Ella’s balloons to Taylor’s balloons
The ratio of Ella’s balloons to Taylor’s balloons is 5:7. Then the correct option is B.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
Division means the separation of something into different parts, sharing of something among different people, places, etc.
Ella has 5 balloons. Taylor had 7 balloons.
Then the ratio of Ella’s balloons to Taylor’s balloons is given by the division of the numbers 5 and 7. Then we have
Ratio = 5 / 7
The ratio of Ella’s balloons to Taylor’s balloons is 5:7. Then the correct option is B.
More about the ratio and the proportion link is given below.
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if I had 20 apples but 5 are gone and 2 came back but my friend took 7 and TWO OTHER friends took 2 EACH, how many do I have left?
Answer:
6 apples
Step-by-step explanation:
20 - 5 = 15
15 + 2 = 17
17 - 7 = 10
10 - (2 x 2) = 6
Your answer is 6 apples
Yum yum!!
Identify an equation in slope-intercept from for the line parallel to y=-3x + 7 that passes through (2, -4)
The slope-intercept form:
y = mx + b
m - slope
b - y-intercept
The parallel lines have the same slope.
We have y = -3x + 7 → m = -3. Therefore y = -3x + b.
Put the coordinates of the point (2, -4) to the equation of a line:
[tex]-4=-3(2)+b[/tex]
[tex]-4=-6+b[/tex] add 6 to both sides
[tex]2=b\to b=2[/tex]
Answer: y = -3x + 2The graph of the equation Ax+3y=48 passes through the point (-18,7) What value of A accurately completes the equation?
please help
Answer:
A = -1.5
Step-by-step explanation:
Ax+3y=48
Plug in (-18,7)
A(-18) +3(7)=48
-18A + 21 = 48
-18A = 27
A = - 27/18
A = - 3/2
A = -1.5
Please help !!evaluate the algebraic expression 7x - 5 when x = 4/7