Answer: The correct option is D.
Step-by-step explanation: We are given a linear equation:
[tex]m\times 5=30[/tex]
To calculate the value of , we need to separate m from the constant '5' which is done when 5 goes to the other side of the equation and gets divided there:
[tex]m=\frac{30}{5}\\\\m=6[/tex]
Conclusion: Hence, the value of m is 6 for the given equation.
For a school drama performance, student tickets cost $5 each and adult tickets cost $10 each. The sellers collected $3,570 from 512 tickets sold. If c is the number of student tickets sold, which equation can be used to find the amount of tickets sold of each type?
10(512 – c) + 5c = 512
10(512 – c) + 5c = 3,570
5(512 – c) + 10c = 3,570
5(512 – c) + 10c 512
Answer: [tex]10(512 – c) + 5c = 3,570[/tex]
Step-by-step explanation:
Given : The number of student tickets sold is represented by c.
For a school drama performance, student tickets cost $5 each and adult tickets cost $10 each.
The sellers collected $3,570 from 512 tickets sold.
Since , the total tickets sold = 512
Therefore , the number of adults ticket = [tex]512-c[/tex]
Now, cost of total child tickets : [tex]5c[/tex]
Cost of total adult tickets = [tex]10(512 – c)[/tex]
Now, according to the cost of the tickets , we have the following equation :-
[tex]10(512 – c) + 5c = 3,570[/tex]
Simplify: -0.8b + 4.1c -(-3.2b) - 0.1c
How much will you save per lb, by buying the least expensive? Round to the nearest cent. 2.5 lbs for $8.75 or 3 pounds for $9.75.
Answer:
$0.25 per pound.
Step-by-step explanation:
Let us find unit rate for both quantities.
[tex]\text{Price per pound}=\frac{8.75\text{ dollars}}{2.5\text{ pound}}[/tex]
[tex]\text{Price per pound}=3.5\frac{\text{ dollars}}{\text{ pound}}[/tex]
Therefore, cost of per pound for first given rate is $3.5.
Now let us find unit rate for second quantity.
[tex]\text{Price per pound}=\frac{9.75\text{ dollars}}{3\text{ pound}}[/tex]
[tex]\text{Price per pound}=3.25\frac{\text{ dollars}}{\text{ pound}}[/tex]
We can see that price for second quantity is less than 1st. To find the savings per pound we will subtract 3.25 from 3.5.
[tex]\text{Savings per pound}=3.50-3.25[/tex]
[tex]\text{Savings per pound}=0.25[/tex]
Therefore, we will save $0.25 per pound by buying the least expensive.
Answer:
0.25
Step-by-step explanation:
Which letter on the number line represents the solution to -2.5r = -20? A) Point P B) Point Q Eliminate C) Point R D) Point S
Answer:
Point R = 8
Step-by-step explanation:
-2.5 r = -20
The solution to this equation is represented by a number line
In the given equation we have only the variable 'r'
We will get the value of 'r' while solving the above equation
That 'r' value is the solution point R on number line
[tex]-2.5r = -20[/tex]
divide by -2.5 on both sides
[tex]r=\frac{-20}{-2.5}[/tex]
r= 8 is our solution
The length of a rectangular is 5 centimeters less then it width. The perimeter of the rectangle is 26
Answer: length = 7 c, and width = 6 cm
Step-by-step explanation:
Two polygons are similar. The perimeter of the larger polygon is 85 meters and the ratio of the corresponding side lengths is [tex]\frac{2}{5}[/tex]. Find the perimeter of the other polygon.
Suppose the polygons have 3 sides, [tex]s_1,s_2,s_3[/tex]. In the smaller polygon, the corresponding sides would have lengths [tex]\dfrac25s_1,\dfrac25s_2,\dfrac25s_3[/tex].
So if the perimeter of the larger polygon is
[tex]s_1+s_2+s_3=85[/tex]
then the perimeter of the smaller polygon would be
[tex]\dfrac25(s_1+s_2+s_3)=\dfrac25\cdot85[/tex]
so its perimeter would be 34 meters.
Final answer:
The perimeter of the smaller similar polygon is 34 meters, calculated by setting up and solving the proportion 2/5 = P/85.
Explanation:
When dealing with similar polygons, the ratio of their corresponding side lengths is the same as the ratio of their perimeters. Given that the ratio of the sides is 2 to 5, and the perimeter of the larger polygon is 85 meters, we can set up a proportion to find the perimeter of the smaller polygon.
Let the perimeter of the smaller polygon be P. The proportion will be 2/5 = P/85. To find P, we cross-multiply and get: 2 * 85 = 5 * P. Simplifying, we find that P equals 34 meters. Hence, the perimeter of the smaller polygon is 34 meters.
98 points please help with math:
What is the equation of a line that is parallel to y=5/6x − 10 and passes through (12, 8) ?
Answer:
[tex] \displaystyle y _{ \text{parallel}} = \frac{5}{6} x- 2[/tex]
Step-by-step explanation:
we are given a equation of line
[tex] \displaystyle y = \frac{5}{6} x - 10[/tex]
we want to figure out the line Parallel to the given line and passes through (12,8)
to figure out the parallel line we need to figure out two things one is the Slope of the parallel line another is the y-intercept of the parallel line
figuring out the slope of the parallel line is easy because we know that parallel lines have the same slope therefore,
[tex] \displaystyle m _{ \text{parallel}} = \frac{5}{6} [/tex]
now we need to figure out the y-intercept and the equation to do so we can consider the following formula:
[tex] \displaystyle y - y_{1} = m(x - x_{1})[/tex]
we the point where the parallel line passes i.e [tex](x_1,y_1)=(12,8)[/tex] and we already got that the slope is ⅚ thus substitute:
[tex] \displaystyle y - 8= \frac{5}{6} (x- 12)[/tex]
we can figure out the equation by simplifying the above equation to slope-intercept form in order to do so
distribute:
[tex] \displaystyle y - 8= \frac{5}{6} x- \frac{5}{6} \times 12[/tex]
reduce fraction:
[tex] \displaystyle y - 8= \frac{5}{6} x- 5 \times 2[/tex]
simplify multiplication:
[tex] \displaystyle y - 8= \frac{5}{6} x- 10[/tex]
add 8 to both sides:
[tex] \displaystyle y = \frac{5}{6} x- 2[/tex]
and we are done!
What is the graph of the function f(x) = the quantity of x squared plus 3 x minus 4, all over x plus 4?
Answer:
Given the function:
f(x) = the quantity of x squared plus 3x minus 4 , all over x plus 4
i,e
[tex]f(x) = \frac{x^2+3x-4}{x+4}[/tex]
or
[tex]f(x) = \frac{x^2+4x-x-4}{x+4}[/tex]
or
[tex]f(x) = \frac{x(x+4)-1(x+4)}{x+4}[/tex]
or
[tex]f(x) = \frac{(x+4)(x-1)}{x+4}[/tex]
⇒y= f(x) = x -1 ......[1]
Find the x-intercepts and y-intercepts for the equation [1] ;
y-intercepts defined as the graph crosses the y-axis;
substitute x =0 to solve for y;
y = 0-1 = -1
y = -1
x-intercepts defined as the graph crosses the x-axis;
substitute y =0 to solve for x;
0 = x-1
or
x = 1
Plot these points (0 , -1) and (1, 0) on the graph for the given function as shown below.
Claudia works as a manufacturer of decorative jewelry boxes. A customer would like her to create some boxes with the following conditions:
The sum of the length and width must be 30 centimeters.
The height must be 3 centimeters less than the length.
The box should have the greatest possible volume.
Let's do some math to see if we can decide what size boxes Claudia needs to make, and show what we know about polynomials in the process. Remember: One formula we can use to find the volume of a box is Length * Width * Height.
Answer:
l = 20.5 cm
h = 17.5 cm
w = 9.5 cm
Step-by-step explanation:
Conditions
l+w =30 Solving for w 30 - l = w
h = l-3
V = l*w*h
Substituting in
V = l * (30-l) * (l-3)
= (30l-l^2) (l-3)
= 30 l^2 - l^3 - 90l + 3l^2
Combining like terms
Step-by-step solution
-l^3 + 33 l^2 - 90 l
To find the maximum we need to take the first derivative and then set it equal to zero
-3l^2 + 66l -90 = 0
Factor out a -3
-3 (l^2 -22l +30) =0
Using my calculator and the quadratic formula
l = 11 - sqrt(91)
l = 11 + sqrt(91)
l = 1.5 or 20.5 approximately
If l = 1. then
h= l-3 would be negative so
l = 20.5
h = l-3
h = 17.5 approximately
w = 30-l = 9.5 approximately
Drew delivers packages in city.He makes 30$ for working an 8-hour day.He also makes $4.25 for each package he delivers. If X represents the number of packages he delivers, which equation describes his daily income?
Answer:
767
Step-by-step explanation:
A right triangle has legs that measure 7 cm and 6 cm. What is the length of the hypotenuse in meters?
Answer:
[tex]\sqrt{85} or 9.22[/tex]
Step-by-step explanation:
You need to remember the following equation:
[tex]a^{2} + b^{2} = c^{2}[/tex]
Where a and b is the lengths of the two sides and c is the hypotenuse.
So simply plug these values into this:
[tex]6^{2} + 7^{2} = h^{2}[/tex]
36 + 49 = h^2
36 + 49 = 85
So the hypotenuse is the square root of 85:
[tex]\sqrt{85} = 9.22[/tex]
Select the correct graph for the system of inequalities from the list of graphs. Indicate which graph represents the system, and list three possible solutions in the form of (x, y).
y greater or equal than minus 5 x plus 1 y greater than minus 4 x minus 2 y greater or equal than minus 2
Choose a graph from the list of graph, like in the picture.
Solve the system of linear equations by substituting. Check your solution
I WILL MARK YOU BRAINLYEST
4# y=5x-7
-3x-2y=-12
5# -4x+y=6
-5x-y=21
6# -7x-2y=-13
x-2y=-13
HELPPP PLEASEEE!!! Find the perimeter of ΔTAP with vertices T(1, 4), A(4,4), and P(3,0) to the nearest tenth unit.
Answer: 11.6 units.
Step-by-step explanation:
1. Plot the points as you can see in the graph attached.
2. As you can see, the lenght TA is 3 units.
3. Apply the formula for calculate the distance between two points, to calculate the length TP and TA. The formula is:
[tex]d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]
4. Therefore, you have:
[tex]TP=\sqrt{(1-3)^{2}+(4-0)^{2}}=4.47units[/tex]
[tex]AP=\sqrt{(4-3)^{2}+(4-0)^{2}}=4.12units[/tex]
5. The perimeter is the sum of the the lenght of each side, therefore:
[tex]Perimeter=3units+4.47units+4.12units\\Perimeter=11.59units[/tex]
6. To the nearest tenth unit:
[tex]Perimeter=11.6units[/tex]
Amy paid ?$69.77 for a pair of running shoes during a 25 ?%-off sale. What was the regular? price?
Answer:
The regular price was $93.03
Step-by-step explanation:
In order to find the regular price, divide the amount spent by the percentage of which she paid for it. Since it was 25% off, she paid 75% of the overall price.
$69.77/75% = $93.03
7) Days People 1 26 2 30 3 34 4 38 5 42 6 46 The chart shows how many people have signed up to go on a field trip each day. 62 students are allowed to go on the field trip. On which day would you expect that number to be reached? A) 8 B) 9 C) 10 D)
Answer:The answer is mostly C) 10
Step-by-step explanation:
It's C because when you go to day 9, you count after 58 by adding 4 more, which equals 62 and then, since day 10) is 68 people that means that the answer is C.
Answer: c 10
Step-by-step explanation:
Since each day 4 more people sign up, on day 7, 50 will have signed up; on day 8, 54 people; day 9, 58 people; and day 10, 62 people
The parent function is f(x)=2^x−6+3 and the new function is g(x)=2^x − 3+2 .
How does the graph change from f(x) to g(x) ?
Select each correct answer.
The graph is shifted 3 units right.
The graph is shifted 1 unit up.
The graph is shifted 1 unit down.
The graph is shifted 3 units left.
Answer:
left 3 units
down 1 unit
Step-by-step explanation:
The required transformation is obtained by shifting of 3 units left and 1 unit down. The correct options are (c) and (d).
How to transform a graph of the function?The graph of a function can be transformed by either shifting it in the right, left, up or down.
When the transformation is rightwards, the function becomes as f(x - a).
The given functions are as below,
f(x) = [tex]2^{x - 6} + 3[/tex]
And, g(x) = [tex]2^{x - 3} + 2[/tex]
It can be rewritten as,
g(x) = [tex]2^{x - 3} + 2[/tex] = [tex]2^{x - 6 + 3} + 3 - 1[/tex]
It clearly shows as per the rule of transformation, f(x) is shifted 3 units left and 1 unit down to get g(x).
Hence, the parent function f(x) is shifted 3 units left and 1 unit down.
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A family purchased tickets for a concert. They paid a total of $90 for 7 adult tickets and 12 child tickets. The price of a child ticket was two-thirds the price of an adult ticket.How much was the price of an adult ticket
Answer: 7 + 2/3(12) = 15
90/15 = $6 for adult tickets
Shawn is coasting down a 500 cm long ramp on his inline skates. The wheels on his inline skates are 32 cm in circumference. How many rotations does each wheel make while Shawn is coasting down the ramp? Plz help
Answer:
16 rotations.
Step-by-step explanation:
We have been given that Shawn is coasting down a 500 cm long ramp on his inline skates. The wheels on his inline skates are 32 cm in circumference.
To find the number of rotations we will divide length of ramp by 32 as distance covered by wheels in one rotation will be equal to 32 cm.
[tex]\text{Number of rotations}=\frac{\text{Total distance}}{\text{Circumference of wheel}}[/tex]
[tex]\text{Number of rotations}=\frac{500}{32}[/tex]
[tex]\text{Number of rotations}=15.625\approx 16[/tex]
Therefore, each wheel must make 16 rotations while Shawn is coasting down the ramp.
What is an advantage that experimental probability has over theoretical probability?
a.
Experimental probability is more rigorously tested than theoretical probability.
b.
Experimental probability provides unique results, while theoretical probability only provides generic results which may not fit the situation.
c.
It is not always possible to calculate theoretical probability in complex situations, but experimental probability can be calculated any time experiments can be run.
d.
Experimental probability changes over time, while theoretical probability remains constant.
C. It is not always possible to calculate theoretical probability in complex situations, but experimental probability can be calculated any time experiments can be run.
The advantage of experimental probability over theoretical probability is that option C. It is not always possible to calculate theoretical probability in complex situations, but experimental probability can be calculated any time experiments can be run.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Experimental probability is the probability where the probability of something is found by real experiments.
This is not computed by assuming or calculation.
Theoretical probability is the probability where the probability of something is found theoretically.
The probability is found using formulas and calculation.
So, it is not always possible to calculate theoretical probability in complex situations.
But experimental probability can be found in any case using experiments.
Hence the correct option is C.
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Consider the functions. How do the graphs of these function compare to one another? (In picture)
Answer: True, False, True
Step-by-step explanation:
To determine steepness, compare the coefficients of each function:
f(x) = 4x² coefficient is: 4
g(x) = [tex]\dfrac{15}{4}x^2[/tex] coefficient is: 4.75
h(x) = [tex]\dfrac{4}{15}x^2[/tex] coefficient is: 0.27
f(x) ??? h(x)
4 > 0.27
f(x) is steeper than h(x)
h(x) ??? g(x)
0.27 < 4.75
h(x) is LESS steep than g(x)
g(x) ??? f(x)
4.75 > 4
g(x) is steeper than f(x)
Solve the equation:
9 (x − 9)−3 = −4 (2x + 4)
4
-4
100
68
Answer:
Step-by-step explanation:
Applying BODMAS here;
We first solve what is in the brackets:
9x - 81 -3 = -8x - 16
We then put the like terms together:
9x + 8x = -16 + 81 + 3
We then do the addition:
17x = -16 + 84
We then do the subtraction:
17x = 68
Simplifying this gives:
x = [tex]\frac{68}{17}[/tex] = 4
(02.03)A bicyclist rides 14 miles in 112 minutes. If she continues at this speed, how long will it take her to travel 35 miles?
Answer:
280 minutes
Step-by-step explanation:
First, you must find the miles per minute:
112/14 = 8
Then you must multiply the miles per minute by the amount of miles:
35 * 8 = 280
A wildlife preservation group records the number of squirrels in a city park. The first count recorded is 30 squirrels. A second count of 60 squirrels is recorded six months later, and 120 squirrels are counted at the end of one year. Assuming that no squirrel dies and the growth rate remains the same, which function represents the number of squirrels after x years? A) f(x) = 30x B) f(x) = 302x C) f(x) = 30(2)x D) f(x) = 30(2)2x
Answer:
A F(x)=30x
Step-by-step explanation:
just plug number in to the equations to see which one matches
Answer: [tex]f(x)=30\cdot2^{2x}[/tex]
Step-by-step explanation:
Given: A wildlife preservation group records the number of squirrels in a city park.
The first count recorded = 30 squirrels.
A second count of 60 squirrels is recorded six months later, and 120 squirrels are counted at the end of one year.
The growth rate of squirrel=[tex]\frac{120}{30}=4=2^2[/tex]
The exponential growth equation is given by :-
[tex]y=Ab^n[/tex], where A is the initial amount , b is the growth rate and n is the time period.
If the growth rate remains constant, then the function represents the number of squirrels after x years is given by :-
[tex]f(x)=30\cdot(2^2)^x=30\cdot2^{2x}[/tex]
F the measures, in degrees, of the three angles of a triangle are x,x+10, and 2x-6 the triangle must be
Answer: The triangle mentioned here is an acute angled triangle.
Step-by-step explanation: x+x+10+2x-6=180°(angle sum prop. of triangles)
= 4x+4=180°
= 4x=174°
= x=44°
therefore, x=44°
,x+10=44+10=54°
,2x-6=2(44)-6=82°
If gasoline costs 2.14 per gallon and you drive 500 miles in a car that gets 30 mpg, what is the cost of gasoline
Answer:
35.7
Step-by-step explanation:
First, you would calculate how many gallons of gasoline the car gets. To do this, divide your total mileage of 500 miles by the mpg (30). Now you know how many gallons of gasoline will be used by the car. After calculating, you get 16.67. Multiply this by how much it costs per gallon of gasoline, and you get an answer of $35.7.
A person who weighs 120 pounds on Earth weighs 20 pounds on the Moon. How much does a 93-pound person weigh on the Moon? A person who weighs 120 pounds on Earth weighs 20 pounds on the Moon. How much does a 93-pound person weigh on the Moon? Item 22 A person who weighs 120 pounds on Earth weighs 20 pounds on the Moon. How much does a 93-pound person weigh on the Moon?
The relationship between the weight of a person on Earth and the
person's weight on the Moon is a proportional relationship.
The weight of a 93 pounds person on the Moon is 15.5 pounds.Reasons:
The weight of the person on Earth = 120 pounds
Weight of the person on the Moon = 20 pounds
Required:
The weight of a person that weighs 93 pounds on Earth on the Moon
Solution:
Let x represent the factor (acceleration due to gravity) on Earth, let y
represent the factor on the Moon, and let m, represent the mass of the
person, we have;
x·m = 120
y·m = 20
Therefore;
[tex]\displaystyle \mathbf{\frac{x \cdot m}{y \cdot m}} = \mathrm{\frac{x}{y} } = \frac{120}{20} = 6[/tex]
For the person that weighs 93 pounds on Earth, we have;
[tex]\displaystyle \mathrm{\frac{x}{y} } = \mathbf{\frac{93}{Weight \ on \ the \ Moon}} = 6[/tex]
Which gives;
[tex]\displaystyle Weight \ of\ the \ person\ on \ the\ Moon = \frac{93}{6} = 15.5[/tex]
The weight of the person on the Moon = 15.5 pounds
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As Jupiter revolves around the sun, it travels at a speed of approximately 8 miles per second. Convert this speed to miles per minute. At this speed, how many miles will Jupiter travel in 6 minutes? Do not round your answers.
speed: __ miles/minutes ?
distance traveled in 6 minutes: __ miles ?
Answer:
Thus; Jupiter travels at 480 miles/m and in 6 minutes, it will travel 2880 miles.
Step-by-step explanation:
First to convert it you need to multiply 8 miles per second by 60 seconds because there are 60 seconds in a minute:
8 miles x 60 s
1 second 1 min
The unit of seconds will cancel out so you will get 480 miles/ min
To get how far it travels in 6 min you need to multiply the speed by 6 minutes
480 miles x 6 min = 2880
1 min
The unit of minutes will cancel out to get 2880 miles
I NEED HELP
Manny and Emma are both competing in a long jump competition at there school. Manny can jump three fifths of the distance that Emma can jump. Manny can jump 21 inches how far can Emma jump.
21.6
20.4
35
12.6
I hope this helps, sorry for my messy handwriting. If you have any questions feel free to ask me!
Erica has 1 over 3 of a watermelon to share equally with 3 friends. How much will each person get
Answer:
1/9
Step-by-step explanation:
1/3 ÷ 3 is the set-up for the problem we are trying to solve.
Remember when we divide fractions we multiply by the reciprocal. So we have:
1/3 × 1/3 since the reciprocal of 3/1 is 1/3
Multiplying 1/3 x 1/3 we find the product is 1/9
Therefore, each person would receive 1/9 of the watermelon