To find the duration of workout plans A and B offered by Shen, we set up a system of linear equations and solved them. Both plans last 1.25 hours each.
Explanation:Let us denote the duration of workout Plan A as A hours and Plan B as B hours. We can use the provided information to set up a system of linear equations representing the total training time on each day. On Friday, 3 clients did Plan A and 5 did Plan B for a total of 10 hours, leading to the equation 3A + 5B = 10. On Saturday, 6 clients did Plan A and 2 did Plan B for a total of 10 hours, resulting in the equation 6A + 2B = 10.
To solve this system of equations, we can use substitution or elimination. Multiplying the first equation by 2 gives us 6A + 10B = 20. Then we can subtract the Saturday equation from this to find the value of B:
(6A + 10B) - (6A + 2B) = 20 - 108B = 10B = 1.25 hoursNow that we know the duration of Plan B, we can plug this into either of our original equations to find the duration of Plan A. Let's use the Friday equation for this purpose:
3A + 5(1.25) = 103A + 6.25 = 103A = 3.75A = 1.25 hoursAs it turns out, both workout plans last the same amount of time, 1.25 hours each.
5 1⁄5 decimeters = centimeters
Answer:
[tex]\large\boxed{5\dfrac{1}{5}\ decimeters=52\ centimeters}[/tex]
Step-by-step explanation:
[tex]1\ dm=10\ cm\qquad\text{(1 decimeters = 10 centimeters)}\\\\\text{Therefore}\\\\5\dfrac{1}{5}\ dm=\dfrac{5\cdot5+1}{5}\ dm=\dfrac{26}{5}\ dm=\dfrac{26}{5}\cdot10\ cm=\dfrac{260}{5}\ cm=52\ cm[/tex]
To convert 5 1/5 decimeters to centimeters, you can multiply 5 by 10 and add the result to the centimeters part (1/5).
Explanation:To convert decimeters to centimeters, we need to know that there are 10 centimeters in 1 decimeter. So, to convert 5 1/5 decimeters to centimeters, we can multiply 5 by 10 and add the result to the centimeters part (1/5). Converting 1/5 to centimeters gives us 2 centimeters. Therefore, 5 1/5 decimeters is equal to 51 centimeters.
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PLEASE HELP!!!!!!!!!!!!!!!!!!!
Answer:
The top cable is 115.52 feet long
The bottom cable is 110.86 feet long
Step-by-step explanation:
The ground anchor #2, the tower, ground level, and both cables form a figure made of two right triangles as shown in the figure below
We are required to compute L1 and L2 which are the hypotenuses of both triangles from which we have both legs
We'll apply the Pythagoras's theorem. If a and b are the legs of a right triangle and c its hypotenuse, then
[tex]c^2=a^2+b^2[/tex]
For the bottom ground support cable, a=41, b=103
[tex]L2^2=41^2+103^2[/tex]=110.86\ feet
For the top ground support cable, a=41, b=108
[tex]L1^2=41^2+108^2[/tex]=115.52\ feet
The top cable is 115.52 feet long
The bottom cable is 110.86 feet long
How do you divide 3 1/4 and 3?
First we're going to change the 3 1/4 into an improper fraction.
3 1/4 is the same as 13/4
When dividing fractions, it's the same thing as multiplying by the reciprocal.
What this means is we're going to flip the second fraction.
So the original problem is this:
13/4 divided by 3/1
It now looks like this:
13/4 multiplied by 1/3
Then, simply multiply the top numbers together and then multiply the bottom numbers together.
13*1=13
4*3=12
your answer is 13/12
Which graph represents the function f(x)=x4+8x3+6x2−40x+25?
Answer:
Graphic A. (Upper left graphic)
Step-by-step explanation:
The roots of the fourth-order polynomial are, that is the values of x which make polynomial equal to zero:
[tex]x = 1[/tex] and [tex]x = -5[/tex]
By comparing the results with each graphic, it is evident that option A corresponds with the function. (Upper left graphic)
To graph the function f(x)=x4+8x3+6x2−40x+25, choose values of x, find corresponding y-values, and plot the points to form a curve.
To graph the function f(x) = x4 + 8x3 + 6x2 - 40x + 25, we need to plot points on a coordinate plane and connect them to form a graph. Here are the steps:
Choose a few values of x, such as -2, -1, 0, 1, and 2.Plug each value of x into the equation to find the corresponding y-values. For example, when x=-2, y=(-2)4+8(-2)3+6(-2)2-40(-2)+25.Plot the points on the coordinate plane (x,y) and connect them to form a smooth curve.The resulting graph should be a curve that goes through the plotted points.
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PLEASE HELP!I'M NEWW
Answer:
I think its 90°, since it l00ks like a right angle
5. Suppose you buy a $1999 LCD TV on layaway. If you pay 5% down and make $50 payments
every week, how many weeks will it be before you pay off the TV?
Answer:
38 Weeks
Step-by-step explanation:
1999$ x .05% = 99.95 Down Payment
Remaining Balance = 1899.05
1899.05$ / 50$ = 37.98100
It would approximately take a total of 38 weeks to pay it off!
Answer: 38 weeks
Step-by-step explanation:
$1999 * 0.05 = $99.95
1999 - 99.95 = 1899.05
1899.05/50 = 37.981
38 weeks
Consider the equations: y = 2x − 4 and y = x − 2. Solve the system of equations by completing the table of values to find an ordered pair that satisfies both equations.
Answer:
The order pair is (2,0)
Step-by-step explanation:
On the picture
Answer:
(2,6)
Step-by-step explanation:
Cory is paid $567.20 biweekly.
What is his annual salary?
O
$6,806.40
$13,612.80
o
$14,747.20
$29,494.40
Answer:
14,747.20
There are 52 weeks in a year being paid bi-weekly means being paid every other week or 26 times a year. So 567.20 * 26 is 14747.20.
a line with a slope of 5/3 passes through the point (10, -5). what is its equation in point slope
The equation of line in point-slope form with slope 5/3 passing through the point (10-5) is:
[tex]y+5 = \frac{5}{3}(x-10)[/tex]
Step-by-step explanation:
Given
Slope = m = 5/3
Point = (x1,y1) = (10, -5)
Point-slope form is:
[tex]y-y_1 = m(x-x_1)[/tex]
As the slope and point is already given, we only have to put the values in the equation to get the equation of required line:
[tex]y-(-5) = \frac{5}{3}(x-10)\\y+5 = \frac{5}{3}(x-10)[/tex]
Hence,
The equation of line in point-slope form with slope 5/3 passing through the point (10-5) is:
[tex]y+5 = \frac{5}{3}(x-10)[/tex]
Keywords: equation of line, point-slope form
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Jose burns 8 calories per minute. Does Jose burn more than 500 calories per hour?
Answer: No, he burns 480
Step-by-step explanation: you multiply 8 by 60, the amount of minutes in an hour
What is the solution to the equation below? square root of 4-3x divided by square root of 3x equals 2
Possible answers: x=4/9 x=4/15 x= 7/9 x=7/15
Answer:
B.[tex]x=\frac{4}{15}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt{4-3x}}{\sqrt{3x} } =2[/tex]can be simplify by doing some algebra.Particulary, in this case, [tex]\frac{\sqrt{4-3x}}{\sqrt{3x} } =\sqrt{\frac{4-3x}{3x} }[/tex], because of the distributive property with respect to division and multiplication.Then, by dividing numerator and denominator by 3x inside the power we get [tex]\sqrt{\frac{\frac{4}{3x}-1}{1}}=\sqrt{\frac{4}{3x}-1} =2[/tex].To dispose of the squared root, we raise to power 2 both sides of the equation, to obtain the following expression: [tex]\frac{4}{3x}-1=4[/tex].Finally, we just have to clear out the value of x from this expression, by addding 1 both sides of the equation: [tex]\frac{4}{3x}=5[/tex], and then by multiplying both sides by 3x, and then dividing the result by 15. This yields [tex]x=\frac{4}{15}[/tex]Answer:4/15
Step-by-step explanation:
Catskill is 15 miles from Saugerties. What would the
distance on the map be?
Answer:
6 inches
Step-by-step explanation:
the map is equal to
1/2.5 inch / miles
by proportion :
1/2.5 inch/miles = x inches / 15 miles
x = 15/2.5
x=6 inches!!
I hope this helped you!! :)
c)
100x5
Simplify radical
Answer:
500
Step-by-step explanation:
100 X 5 = 5 + 5 + 5 + 5...100 times = 100 + 100 + 100 + 100 + 100 = 500
Answer:
500
Step-by-step explanation:
yes
Which medicinal product is made using animal products?
A. Flu vaccine
O
B. Aspirin
C. Rose oil
O
D. Morphine
SUBM
Answer:
C. Rose oil
Step-by-step explanation:
Which medicinal product is made using animal products?
A. Flu vaccine
O
B. Aspirin
C. Rose oil
O
D. Morphine
SUBM
Answer:A. Flu vaccine
Step-by-step explanation:
Jina spent $27 on fruit at the grocery store. She spent a total of $60 at the store. What percentage of the total did she spend on fruit?
Answer:
45%
Step-by-step explanation:
27/60 = .45
First, divide.
27 / 60 = 0.45
Multiply by 100%.
0.45 * 100% = 45%
______
Jina spent 45% of her total on fruits.
______
Best Regards,
Wolfyy :)
what is 23,234+12,346?
For this case we must solve the following sum:
23,234
+ 12,346
---------------
35,580
We place the addends one below the other so that the units coincide in the same column. We add each digit, we get the expression:
[tex]35,580[/tex]
ANswer:
[tex]35,580[/tex]
Find the slopes of lines AB and CD. Show your work. Line AB goes through points A(3,4) and B(7,7). Line CD goes through points C (0,0) and D (-6,8).
Slope formula: y2-y1/x2-x1
Line AB:
= 7-4/7-3
= 3/4
Line CD:
= 8-0/-6-0
= 8/-6
= -4\3
______
Best Regards,
Wolfyy :)
Which expression is equivalent to 4(7 + 8)?
A) 11+8
B) 11+12
C) 28+12
D) 28+32
Answer:
D) 28+32
Step-by-step explanation:
4(7+8)=4(15)=60
PLZZZ HELP ASAP!!!
Two angles are a linear pair. One third of the measure of the first plus 12 is equal to the measure of the second. what are the measures of both angles?
Answer:
Step-by-step explanation:
Let's angle be x and y
Then......
⅓x+12=y......eqn(I)
Since are linear
x+y=180
y=180-x.....eqn(ii)
Substitute the eqns
You get x=126°
From eqn (iii)
You get y=54°
Those are angles
The measures of both angles are 126° and 54°.
What are Linear Pair of Angles?Linear pair of angles are the pair of angles formed when two lines are intersected at a point forming on a line.
Sum of the measures of angles of linear pair is supplementary.
Given that,
Two angles are a linear pair.
Let x and y be the measures of two angles.
We have,
y = 1/3 x + 12
Sum of the angles is supplementary.
x + y = 180
x + 1/3 x + 12 = 180
4/3 x = 168
x = 126°
y = 180 - 126 = 54°
Hence the angles are 126° and 54°.
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9. Wade has 126 inches of 1-inch wide bias tape for a border
on a rectangular banner. If the banner needs to be 48
inches long, what is the maximum width it could be?
Answer:
Let 'x' represent the width.
2*48 + 2x = 126
x = 15 in
The maximum width could be 15 inches.
Final answer:
To find the maximum width of the rectangular banner, calculate the total length of bias tape used, subtract it from the available bias tape, and divide the remaining inches by 2. The maximum width of the banner is 15 inches.
Explanation:
Maximum Width Calculation:
Calculate the total length of bias tape used: 48 inches x 2 sides = 96 inches.
Subtract the total length from the available bias tape: 126 - 96 = 30 inches.
Divide the remaining inches by 2 (since there are 2 widths): 30 / 2 = 15 inches.
what is the common difference of 31, -169, -369, -569?
Answer:
31 is a positive number, while -169, -369, and -569 is negative.
Step-by-step explanation:
Negative numbers, are numbers less then 0 and include a negative sign that looks like this "-".
Positive numbers are numbers above 0 and don't include a negative sign.
-169, -369, and -569 is negative because they have a negative symbol and the number is below 0, while 31 is positive because it's above 0 and doesn't include a negative sign.
what is the answer if 2.4 x 5.8
Answer: 13.92
Step-by-step explanation: 8x4 then 8x2
zero the hero
5x4 then 5x2
lastly add
Answer:
13.92
Step-by-step explanation:
So the explanation is on the picture lol
8 km + 2300 m +12,000 cm = ?
Answer:
The result is 10.42 kilometers, or 10,420 meters or 1'042,000 centimeters.
Step-by-step explanation:
1. Let's review the information given to us for solving the question:
8 kilometers plus 2,300 meters plus 12,000 centimeters
2. Let's do the conversions to find the result either in kilometers, meters or even centimeters.
A. In kilometers:
8 kilometers
2,300 meters = 2.3 kilometers
12,000 centimeters = 120 meters = 0.12 kilometers
10.42 kilometers
B. In meters
8 kilometers = 8,000 meters
2,300 meters
12,000 centimeters = 120 meters
10,420 meters
C. In centimeters
8 kilometers = 8,000 meters = 800,000 centimeters
2,300 meters = 230,000 centimeters
12,000 centimeters
1'042,000 centimeters
The final sum is 10,420 meters.
To solve the mathematical problem of adding different units of measurement, we first need to convert everything to the same unit. In this case, let's convert all measurements to meters (m).
Convert 8 kilometers (km) to meters. Since 1 km = 1000 m => 8 km = 8 x 1000 => 8000 m.Convert 2300 meters (m) to meters. This is already in meters, so no conversion is needed and it remains 2300 m.Convert 12,000 centimeters (cm) to meters. Since 1 m = 100 cm, 12,000 cm = 12,000 / 100 = 120 m.Now, add these values together:
8000 m + 2300 m + 120 m = 10,420 meters
fire work a travels at the speed 300 ft/s firework b travels 240 ft/s. firework b is launched 0.25s before firework a. how many seconds after firework b launches will both fireworks explode?
Answer:
Both fireworks will explode after 1 seconds after firework b launches.
Step-by-step explanation:
Given:
Speed of fire work A= 300 ft/s
Speed of Firework B=240 ft/s
Time before which fire work b is launched =0.25s
To Find:
How many seconds after firework b launches will both fireworks explode=?
Solution:
Let t be the time(seconds) after which both the fireworks explode.
By the time the firework a has been launched, Firework B has been launch 0.25 s, So we can treat them as two separate equation
Firework A= 330(t)
Firework B=240(t)+240(0.25)
Since we need to know the same time after which they explode, we can equate both the equations
330(t) = 240(t)+240(0.25)
300(t)= 240(t)+60
300(t)-240(t)= 60
60(t)=60
[tex]t=\frac{60}{60}[/tex]
t=1
Final answer:
By setting the distance traveled by both fireworks equal, we find that both Firework A and B will explode 1.25 seconds after Firework B is launched.
Explanation:
To solve the problem of when both fireworks will explode, we can use the constant speed equation distance = speed × time. Firework A travels at 300 ft/s, and Firework B travels at 240 ft/s. Firework B is given a 0.25s head start. We need to find the time when they have traveled the same distance.
Let's call the time after Firework B launches when both explode as t. Since Firework A launches 0.25s after B, it will have traveled for t - 0.25s when they explode together. The equations for the distances traveled by both fireworks until that point will be:
Distance Firework A: 300 (t - 0.25)Distance Firework B: 240 tSetting these distances equal to each other:
300 (t - 0.25) = 240 t
Solving for t:
300t - 75 = 240t
60t = 75
t = 1.25s
Therefore, both fireworks will explode 1.25 seconds after Firework B launches.
Given ^MNO = ^PQR,
MN = 6 +2y, MO = 2x + 1,
PO = 3y + 4, and PR = 10 - X.
Find the lengths of PQ and PR.
Answer:
Part 1) [tex]PQ=10\ units[/tex]
Part 2) [tex]PR=7\ units[/tex]
Step-by-step explanation:
The correct question is
The triangles MNO and PQR are congruent. (MNO≅PQR)
Find the lengths of PQ and PR.
we know that
If two figures are congruent, then its corresponding sides are congruent
In this problem
MN and PQ are corresponding sides
MO and PR are corresponding sides
NO and QR are corresponding sides
therefore
MN≅PQ
MO≅PR
NO≅QR
step 1
Find the value of y
we have
[tex]MN = 6 +2y\\ PQ = 3y + 4[/tex]
equate the equations
[tex]3y + 4=6 +2y[/tex]
solve for y
[tex]3y-2y=6-4[/tex]
[tex]y=2[/tex]
step 2
Find the length of PQ
[tex]PQ = 3y + 4[/tex]
substitute the value of y
[tex]PQ = 3(2) + 4=10\ units[/tex]
step 3
Find the value of x
we have
[tex]MO = 2x + 1\\PR = 10 - x[/tex]
equate the equations
[tex]2x+1=10-x[/tex]
solve for x
[tex]2x+x=10-1[/tex]
[tex]3x=9[/tex]
[tex]x=3[/tex]
step 4
Find the length of PR
[tex]PR = 10 - x[/tex]
substitute the value of x
[tex]PR = 10-3=7\ units[/tex]
the temperature is -2 if the temperature rises by 15 what is the new temperature
2. A parking lot holds 40 cars. There are 20 cars in the lot already. Which inequality can be solved to show all the
numbers of cars c that can still park in the lot?
a. 20+C < 40
C. 60
b. 20+C = 40
d. 60 SC
Kevin weighed 200 pounds when he started his diet and lost 26 pounds. What percent of his original weight did Kevin lose?
A
8%
B
12%
C
13%
D
16%
Answer:
C = 13%
Step-by-step explanation:
Diego has 48 chocolate chip cookies, 64 vanilla cookies, and 100 raisin cookies for a bake sale. He wants to make bags that have all three cookie flavors and the same number of each flavor per bag.
How many bags can he make without having any cookies left over?
The number of bags he can make without having any cookies left over is 4 bags.
Number of chocolate chips = 48Number of vanilla cookies = 64Number of raisin cookies = 100How to find highest common factor48 = 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
64 = 1, 2, 4, 8, 16, 32 and 64
100 = 1, 2, 4, 5, 10, 20, 25, 50, and 100.
The highest common factor of 48, 64 and 100 is 4
Therefore, the number of bags he can make without having any cookies left over is 4 bags
Each bag has:
chocolates cookies = 48/4
= 12 each
Vanilla cookies = 64/4
= 16 each
Raisin cookies = 100/4
= 25 each
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Diego can make 12 bags without having any cookies left over, ensuring each bag contains an equal number of each flavor.
To determine how many bags Diego can make without having any cookies left over, we need to find the greatest common divisor (GCD) of the quantities of each type of cookie.
Step 1:
Find the GCD of the quantities of each type of cookie:
GCD(48, 64, 100) = 4
Step 2:
Calculate the number of bags Diego can make:
Each bag will contain 4 cookies of each flavor, as determined by the GCD.
For chocolate chip cookies: 48 cookies ÷ 4 cookies/bag = 12 bags
For vanilla cookies: 64 cookies ÷ 4 cookies/bag = 16 bags
For raisin cookies: 100 cookies ÷ 4 cookies/bag = 25 bags
Step 3:
Determine the minimum number of bags Diego can make without any cookies left over:
The minimum number of bags is determined by the smallest number of bags he can make for any type of cookie, which is 12 bags for chocolate chip cookies.
Therefore, Diego can make 12 bags without having any cookies left over.
A fence around the school football field is
1,666 feet long. Seven teams of students
will paint the fence. Each team will paint
an equal length of the fence. What length
of the fence will each team paint?
Each team will paint 238 ft of the fence.
Step-by-step explanation:
Length of fence = 1666 ft
Number of students teams = 7
Let x be the length covered by each team, therefore,
7x=1666
Dividing both sides by 7;
[tex]\frac{7x}{7}=\frac{1666}{7}\\x=238\ ft[/tex]
Each team will paint 238 ft of the fence.
Keywords: length, division
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