Final answer:
The maximum number of hours a tutor can work at $35 an hour within a $420 budget is 12 hours per month.
Explanation:
The student asked how many hours a math tutor could work each month within a budget of $420 if the tutor charges $35 an hour. To calculate the maximum number of tutoring hours, divide the total budget by the hourly rate. This can be expressed as Maximum Hours = Total Budget / Hourly Rate.
In this case, the calculation would be:
Maximum Hours = $420 / $35 per hour
So, the math tutor can work a maximum of 12 hours per month on this budget since:
$420 / $35 per hour = 12 hours
if angle 1 and angle 2 form a linear pair. if m<1=5x+9 and m<2=3x+11, find the measure of both angles
Answer: [tex]m\angle 1=109\°\\m\angle 2=71\°[/tex]
Step-by-step explanation:
It is important to remember the definition of "Linear pair angles".
By definitiion "Linear pair angles" are two angles which are adjacents and supplementary.
Based on this, we know that the angles [tex]\angle1[/tex] and [tex]\angle2[/tex] are supplementary, which means that they add up to 180 degrees.
So, knowing that:
[tex]m\angle 1=5x+9\\m\angle 2=3x+11[/tex]
We can write the following expression and solve for "x":
[tex](5x+9)+(3x+11)=180\\\\8x=180-20\\\\x=\frac{160}{8}\\\\x=20[/tex]
Therefore, substituting, we get that the measures of the angles [tex]\angle1[/tex] and [tex]\angle2[/tex] are:
[tex]m\angle 1=5(20)+9=109\°\\\\\\m\angle 2=3(20)+11=71\°[/tex]
Measures of both the angles are 109° and 71°. We found the measures of two angles forming a linear pair, then solving the equation 8x + 20 = 180, which gives x = 20. Substituting x finds the angles.
If angle 1 (∡1) and angle 2 (∡2) form a linear pair, their measures add up to 180° because linear pairs are supplementary angles. Given that the measures are m∡1 = 5x + 9 and m∡2 = 3x + 11, we can set up the equation:
5x + 9 + 3x + 11 = 180Combine like terms:
8x + 20 = 180Subtract 20 from both sides:
8x = 160Divide both sides by 8:
x = 20Now, substitute x back into the expressions for
∡1 and ∡2:
Therefore, the measures of the angles are :
∡1 = 109° and ∡2 = 71°.
The length of a rectangle is 10 units longer than its width. If the total perimeter of the
rectangle is 44 units, what is the width?
The width of the rectangle will be equal to 12 units.
What is a perimeter?Perimeter is defined as the sum of all the sides of the given shape. The rectangle has four sides then the perimeter of the rectangle will be the sum of all the sides of the rectangle.
Given that length of a rectangle is 10 units longer than its width. The total perimeter of the rectangle is 44 units.
The width of the rectangle will be calculated as below:-
2l + 2w = P
2(10) + 2w = 44
20 + 2w = 44
2w = 24
w = 12
Therefore, the width of the rectangle will be equal to 12 units.
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What is 2.6666 as a fraction
To write 2.6666 as a fraction, write 2.6666 as the numerator with 1 as the denominator.
2.6666/1
Now you multiply numerator and denominator by 10000 to make the numerator a whole number ( no decimals)
26666/10000
Both numbers are even and can be divided by 2:
The fraction becomes: 13333/5000
It is -9° now. The temperature will drop 5° in two hours. What will the
temperature be in two hours?
Answer:
-14°
Step-by-step explanation:
-9 - 5
-9 + (-5)
-14
Hey!
----------------------------------------------
Solution:
If the temperature is -9 degrees now and it drops 5 degrees in two hours you just want to subtract.
-9 - 5 = -14 degrees
----------------------------------------------
Answer:
-14 degrees
----------------------------------------------
Hope This Helped! Good Luck!
What is the slope of the line passing through (1, -5) (4, 1)
[tex]\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{1}}}\implies \cfrac{1+5}{3}\implies \cfrac{6}{3}\implies 2[/tex]
For a field trip 20 students rode in cars and
the rest filled nine buses. How many
students were in each bus if 236 students
were on the trip?
it is 11 students in the bus
Solve for xxx.
-9x+5< 17\quad \maroonC{\text{ AND}} \quad 13x+25<-1−9x+5<17 AND13x+25<−1
To solve the inequalities, isolate x in each. The solution for -9x + 5 < 17 is x > -4/3 and the solution for 13x + 25 < -1 is x < -2. The intersection of these solutions, and thus the solution to the compound inequality, is x < -2.
Explanation:We can solve the inequalities separately, then find the intersection of their solution sets. First, let's solve the inequality -9x + 5 < 17. To do this, we subtract 5 from both sides to isolate the term with x which gives -9x < 12. Finally, we divide both sides by -9, remembering to flip the inequality sign since we divided by a negative. This gives x > -4/3.
The second inequality 13x + 25 < -1 can be solved similarly. Subtracting 25 from both sides will get 13x < -26. Divide both sides by 13 to find that x < -2.
The final answer will be the intersection of the two solutions. Since x < -2 is a stricter condition than x > -4/3, the solution to the compound inequality is x < -2.
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Question:
15 5/12 - 11 1/8
A. 4 7/28
B. 4 7/12
C. -4 1/3
D. -4 7/24
Two stores sell the same refrigerator for the same original price. Store A advertises that the refrigerator is on sale for 15% off the original price. Store B advertises that it is reducing the refrigerator’s price by $150. When Stephanie compares the sale prices of the refrigerator in both stores, she concludes that the sale prices are equal. What is the refrigerator’s original price? Write and solve an equation.
Answer:
150 dollhairs
Step-by-step explanation:
Answer:
Refrigerator’s original price = 1000 $
Step-by-step explanation:
Let the original price of refrigerator be r.
Store A advertises that the refrigerator is on sale for 15% off the original price.
[tex]\texttt{Price of refrigerator in store A = }r-\frac{15}{100}r=0.85r[/tex]
Store B advertises that it is reducing the refrigerator’s price by $150.
Price of refrigerator in store B = r - 150
Stephanie compares the sale prices of the refrigerator in both stores, she concludes that the sale prices are equal
That is
0.85r = r - 150
0.15r = 150
r = 1000$
Refrigerator’s original price = 1000 $
Nathan and his brother Zach love to play video games. Right
of
each love to play video games. Right now, Nathan's score is 11 less than 2 times Zac's score
example, if Zach has 80 points, then Nathan has 149 points. Find four more possibilities for the brothe
out more possibilities for the brothers' scores and fini
the table below Then write a rote relating than's score N. Zachy's score, Z.
Answer:
[tex]N=2Z-11[/tex]
[tex]\begin{array}{cc}\text{Zac's score}&\text{Natan's score}\\ 6&1\\7&3\\8&5\\9&7\end{array}[/tex]
Step-by-step explanation:
Nathan's score is 11 less than 2 times Zac's score.
Let Z points be Zac's score and N points be Natan's score. then
2 times Zac's score = 2Z
11 less than 2 times Zac's score = 2Z -11
So, N = 2Z - 11
1. If Z=6, then [tex]N=2\cdot 6-11=12-11=1[/tex]
2. If Z=7, then [tex]N=2\cdot 7-11=14-11=3[/tex]
3. If Z=8, then [tex]N=2\cdot 8-11=16-11=5[/tex]
4. If Z=9, then [tex]N=2\cdot 9-11=18-11=7[/tex]
Thus, four other possibilities are
[tex]\begin{array}{cc}\text{Zac's score}&\text{Natan's score}\\ 6&1\\7&3\\8&5\\9&7\end{array}[/tex]
What is the simplified form of the fraction 108/162 ?
Answer:
Reduced fraction: 2/3
Answer: 2/3
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 108 and 162 is 54
Divide both the numerator and denominator by the GCD
108 ÷ 54
162 ÷ 54
Reduced fraction:
2
3
Therefore, 108/162 simplified to lowest terms is 2/3.
Solve for x. |x| – 5 = 7
A. x = –12 or 12
B. x = –2 or 2
C. x = 2
D. x = 12
Answer:
x=12 or x= -12 (answer A)
Step-by-step explanation:
|x| – 5 = 7
|x| = 12
x=12 or x= -12 (answer A)
d. The total cost for 22 gallons of gas is $68.30. How many dollars per gallon of gas did
you spend?
Answer:
$3.10 per gallon
Step-by-step explanation:
You are trying to find how many dollars per one gallon.
You divide $68.30 by 22 so you can get dollars per one gallon.
68.30 ÷ 22 = 3.10
Therefore it cost $3.10 per gallon you spend.
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Final answer:
You spent $3.10 per gallon of gas.
Explanation:
To determine how many dollars per gallon of gas was spent, we can divide the total cost by the number of gallons. The question states that the total cost for 22 gallons of gas is $68.30.
So we perform the following calculation:
Cost per gallon = Total cost / Number of gallons
Cost per gallon = $68.30 / 22 gallons
Now, dividing $68.30 by 22 gives us:
Cost per gallon = $3.10
Therefore, the cost was $3.10 per gallon.
I’m looking for the answer to number 2
Answer: w = a/l
Step-by-step explanation:
If a = lw, then w = a/l
W = a/l is an equation to find the width if you already know both the a and l
Six more than the product of a number and 7 is 4.
Answer:
[tex]- \frac{1}{2}[/tex]
Step-by-step explanation:
6x+7=4
6x+7-7=4-7
6x=-3
[tex]\frac{6x}{6}[/tex]=[tex]\frac{-3}{6}[/tex]
x=[tex]-\frac{1}{2}[/tex]
Solve the equation-2x+8=-3x+14
Answer:
x = 6
Step-by-step explanation:
-2x + 8 = -3x + 14
Add 3x to both sides.
x + 8 = 14
Subtract 8 from both sides.
x = 6
Both sides of the equation are equal, the solution [tex]x = 6[/tex] is correct.
To solve the equation [tex]-2x + 8 = -3x + 14[/tex], you can follow these steps:
Move the variables to one side of the equation:
Add 3x to both sides of the equation to get the variables on one side:
[tex]-2x + 8 + 3x = -3x + 14 + 3x[/tex]
Simplify:
[tex]x + 8 = 14[/tex]
Isolate the variable:
Subtract 8 from both sides to isolate [tex]x[/tex]:
[tex]x + 8 - 8 = 14 - 8[/tex]
Simplify:
[tex]x = 6[/tex]
Check your solution:
Substitute [tex]x = 6[/tex] back into the original equation to ensure it satisfies the equation:
[tex]-2(6) + 8 = -3(6) + 14[/tex]
Simplify both sides:
[tex]-12 + 8 = -18 + 14[/tex]
[tex]-4 = -4[/tex]
X divided by 6 is 4. What is Z?
Answer:
this is so hard
Step-by-step explanation:
find the width and height of an older 40 inch television that has an aspect ratio of 4:3 find the area of this screen
Answer:
768 square inches
Step-by-step explanation:
see attached
The width and height of the 40 inch television with a 4:3 aspect ratio are 32 inches and 24 inches respectively. The area of the screen is 768 square inches.
Explanation:To find the width and height of an older 40 inch television with an aspect ratio of 4:3, we can use the formula:
Width = aspect ratio * height
Since the aspect ratio is 4:3, we divide the width by 4 and multiply by 3 to find the height.
Therefore, the width of the television is 32 inches and the height is 24 inches.
To find the area of the screen, we use the formula:
Area = width * height
Substituting the values, we get:
Area = 32 inches * 24 inches
Therefore, the area of the screen is 768 square inches.
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The length of a rectangle is 6 inches longer than it’s width. The perimeter is 96 inches. Find the dimensions (length and width) is the rectangle
Final answer:
To find the dimensions of the rectangle, we used the perimeter formula and set up equations to solve for the width (21 inches) and length (27 inches), given that the length is 6 inches longer than its width and the perimeter is 96 inches.
Explanation:
To solve for the dimensions of the rectangle when the length is 6 inches longer than its width and the perimeter is 96 inches, we need to set up two equations based on the perimeter formula for a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
Let w represent the width of the rectangle. Then, the length of the rectangle is w + 6 inches. By substituting these into the perimeter formula, we get:
96 = 2(w + 6) + 2w96 = 2w + 12 + 2w96 = 4w + 1284 = 4ww = 21Now that we know the width is 21 inches, we can find the length by adding 6 inches to the width:
Length = Width + 6 = 21 + 6 = 27 inchesTherefore, the dimensions of the rectangle are 27 inches in length and 21 inches in width.
Final answer:
To find the dimensions of the rectangle, we used the perimeter formula and set up equations to solve for the width (21 inches) and length (27 inches), given that the length is 6 inches longer than its width and the perimeter is 96 inches.
Explanation:
To solve for the dimensions of the rectangle when the length is 6 inches longer than its width and the perimeter is 96 inches, we need to set up two equations based on the perimeter formula for a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
Let w represent the width of the rectangle. Then, the length of the rectangle is w + 6 inches. By substituting these into the perimeter formula, we get:
96 = 2(w + 6) + 2w
96 = 2w + 12 + 2w
96 = 4w + 12
84 = 4w
w = 21
Now that we know the width is 21 inches, we can find the length by adding 6 inches to the width:
Length = Width + 6 = 21 + 6 = 27 inches
Therefore, the dimensions of the rectangle are 27 inches in length and 21 inches in width.
Zenin earns $142 per shift at his new job. During a pay period, he works 12 shifts. What would his pay be for that period?
Answer:
total pay for his work is $1704
Step-by-step explanation:
given data
Zenin earns = $142 per shift
total shifty = 12
to find out
What would his pay for 12 shift
solution
we have given per shift charge and total shift
so
total pay for his work = total shift × per shift charge ................1
put here value
total pay for his work = 12 × $142
total pay for his work = $1704
Duane can do 46 pullups in two minutes. Find the rate.
46 pullups in 2 minutes>
46/2=23
23 pullups per minute
23, 46, 69, 92 ect.
The rate of the pullups would be 23 pullups per minute.
How to measure the rate of change of something as some other value changes?Suppose that we have to measure the rate of change of y as x changes, then we have:
[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
Known that we divide by the change in the independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.
Given that Duane can do 46 pullups in two minutes.
46 pullups in 2 minutes
46/2=23
23 pullups per minute
23, 46, 69, 92 etc.
Hence, the rate of the pullups would be 23 pullups per minute.
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13822 to 1 significant figure
If you wanna round 13822 to 1 significant figure you will need to find the nearest 10k, which is 10000 in this case
10000 = 1 . 10^4
That means
13822 ≈ 1 . 10^4 = 1(overline)0000
The Significant Figures will be 5 if the number is 13822 after using the definition of the Significant Figures the answer is 5.
What are significant figures?Significant digits are the figures in a number that express the value -the size of a quantity to a specified degree of accuracy.
It is given that:
13822 to 1 significant figure
The number is 13822
Answer: 13822
Significant Figures: 5
Decimals: 0
Scientific Notation: 1.3822e+4
Thus, the Significant Figures will be 5 if the number is 13822 after using the definition of the Significant Figures the answer is 5.
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Is 2/3 and 8/12 in equivalent ratio
Answer: if your question here is if they are the same since it says equivalent then yes
Step-by-step explanation: 2/3 = 8/12
Write a rule for the linear function with the following description. The graph contains the points (-3,-2) and (3, 0).
Answer:
[tex]y = \frac{1}{3} x -1[/tex]
Step-by-step explanation:
1. find the slope that includes the points (-3,-2) and (3,0)
[tex]\frac{y2-y1}{x2-x1} =m[/tex] ->slope
0-(-2)/3-(-3) = [tex]\frac{2}{6} (simplify) = \frac{1}{3}[/tex]
2. find the y-intercept
[tex]y = mx +b[/tex] -> slope-intercept form
plug in the y-coord. and the x-coord along with the slope you found (or rather I found) and solve. It could be from either coordinate given.
[tex]0=\frac{1}{3} (3)+b[/tex]
3. solve.
[tex]0 = 1 +b[/tex]
[tex]-1 = b[/tex]
4. write the equation with the slope and y-int you found and voila!
Donna was playing a trivia game where you gained points for correct answers and lost points for incorrect answers. At the start of round 2 she was at −300 points. During round 2 she answered twelve 50 point questions correct and she answered four 50 points questions incorrect. What was her score at the end of the round 2? A) 50 B) 100 C) 200 D) 400
Step-by-step explanation:
B 100
Answer:
B
Step-by-step explanation:
What is the unit and standard form for 10 x 3 tens
Answer:
300
Step-by-step explanation:
All you do is multiply 10 by 30 [3 tens] to get three hundred.
I am joyous to assist you anytime.
The width of a rectangular park is 23.4 yards. What is the perimeter of the park if the length is 2.5 times larger than the width.
Answer:
163.8 yd
Step-by-step explanation:
The perimeter of a rectangle is twice the length added to twice the width.
The width is 23.4 yd.
The length is 2.5 times the width, so to find the length, we multiply the width by 2.5.
length = 2.5 * width = 2.5 * 23.4 yd = 58.5 yd
The length is 58.5 yd.
perimeter = 2 * length + 2 * width
perimeter = 2 * 58.5 yd + 2 * 23.4 yd
perimeter = 117 yd + 46.8 yd
perimeter = 163.8 yd
[tex]Hey![/tex]
-------------------------------------------------
[tex]\large\boxed{Perimeter~of~the~retangular~park~is~163.8~yards!}[/tex]
-------------------------------------------------
[tex]Steps To Solve:[/tex]
[tex]Find~the~length.[/tex]
[tex]23.4~*~2.5~=~58.5[/tex]
[tex]Find~the~perimeter.[/tex]
[tex]p~=~(length~*~2)~+~(width~*~2)[/tex]
[tex]p~=~(58.5~*~2)~+~(23.4~*~2)[/tex]
[tex]p~=~117~+~46.8[/tex]
[tex]p~=~163.8[/tex]
-------------------------------------------------
[tex]Hope~This~Helped!~Good~Luck![/tex]
Solve each equation for x.
8(2x+3x+2)= -4x+148
Step-by-step explanation:Step 1: Simplify both sides of the equation.
8(2x+3x+2)=−4x+148
(8)(2x)+(8)(3x)+(8)(2)=−4x+148(Distribute)
16x+24x+16=−4x+148
(16x+24x)+(16)=−4x+148(Combine Like Terms)
40x+16=−4x+148
40x+16=−4x+148
Step 2: Add 4x to both sides.
40x+16+4x=−4x+148+4x
44x+16=148
Step 3: Subtract 16 from both sides.
44x+16−16=148−16
44x=132
Step 4: Divide both sides by 44.
44x
44
=
132
44
x=3
answer: x=3
The solution to the equation 8(2x+3x+2) = -4x + 148 is x = 3.
Explanation:To solve the given equation, let's start by simplifying both sides. First, we distribute the 8 to each term within the parentheses on the left hand side of the equation: 8(2x + 3x + 2) = 16x + 24x + 16 = 40x + 16. The equation then reads:
40x + 16 = -4x + 148.
Next, let's bring all terms involving x together on one side of the equation and constants on the other. We have:
40x + 4x = 148 - 16,
which gives us:
44x = 132.
Finally, to isolate x we divide both sides of the equation by 44 and we get:
x = 3
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5. A grocer wishes to mix two kinds of nuts costing
$2.41 per pound and $3.65 per pound to make a
248 pounds of mixed nuts costing $2.51 per pound.
To determine the number of pounds of the $2.41
per pound nuts in the mixture, solve for x in the
equation 2.41x +3.65(248 - x) = 622.48. How
many pounds of the $2.41 per pound nuts should
included in the mixture?
Ans:
The solve for x:
2.41x+3.65(248-x)=622.48
2.41x+3.65×248-3.65x=622.48
2.41x-3.65x+905.2=622.48
-1.24x=622.48-905.2
-1.24x= -282.72
x= -282.72÷ -1.24
x=228
Pounds of nuts nper pound $2.41should be included:
228× $2.41
=549.48
Hope it Helps!
The grocer should include approximately 227.84 pounds of the nuts that cost $2.41 per pound.
The grocer is trying to find the right balance of two kinds of nuts to reach a desired price point for a mix. The equation provided should be solved for x, which represents the number of pounds of nuts costing $2.41 per pound. Here is a step-by-step solution:
Begin with the given equation: 2.41x + 3.65(248 - x) = 622.48.
Distribute 3.65 across the parentheses: 2.41x + 3.65 * 248 - 3.65x = 622.48.
Combine like terms: -1.24x + 904.80 = 622.48.
Subtract 904.80 from both sides of the equation: -1.24x = -282.32.
Divide both sides by -1.24 to find x: x = 227.84.
So, the grocer should include approximately 227.84 pounds of the nuts that cost $2.41 per pound.
What is the answer to -2+25x+17=-35
Your Answer is x = −2
Hope this Helps.