Answer:
[tex]x=\frac{5t^2-a}{6-5t}[/tex]
Step-by-step explanation:
Given equation is
[tex]6x+a=5t(x+t)[/tex]
We have to make [tex]x[/tex] the subject of formula. That means we have to isolate [tex]x[/tex].
[tex]6x+a=5t(x+t)[/tex]
Distribute [tex]5t[/tex]
[tex]6x+a=5tx+5t^2[/tex]
Subtract [tex]a[/tex] both side we get,
[tex]6x+a-a=5xt+5t^2-a[/tex]
[tex]6x=5xt+5t^2-a[/tex]
Subtract [tex]5xt[/tex] both side we get,
[tex]6x-5xt=5xt-5xt+5t^2-a\\6x-5xt=5t^2-a[/tex]
Now, take [tex]x[/tex] common from left side of equation
[tex]x(6-5t)=5t^2-a[/tex]
Divide [tex]6-5t[/tex] both side,
[tex]\frac{x(6-5t)}{6-5t}=\frac{5t^2-a}{6-5t}\\\\x=\frac{5t^2-a}{6-5t}[/tex]
What is the radius of my circle if it has a circumference of 154 cm give your answer to the nearest whole number
Answer: r ~= 24.50986
Step-by-step explanation:
This question is done by simply looking at the circumference formula for a circle (2pi r)
154= 2*pi*r
154/(2*pi) = r
r ~= 24.50986
Answer:
Step-by-step explanation:
[tex]circumference=2\pi*r\\\\2\pi*r=154\\\\2*\frac{22}{7}*r=154\\\\r=\frac{154*7}{2*22}\\\\r=\frac{49}{2}=24.5 cm[/tex]
20x^2+8x divided by 2
Answer:
[tex]10 {x}^{2} + 4x[/tex]
Step-by-step explanation:
[tex] \frac{20 {x}^{2} + 8x }{2} = \frac{20x}{2} + \frac{8x}{2} = 10 {x }^{2} + 4x[/tex]
This diagram shows the dimensions of a metal piece used in a machine.
What is the volume of the metal piece?
Enter your answer in the box.
____mm³
Answer:
Volume of metal piece = 3680 mm³
Step-by-step explanation:
volume of horizontal cuboid:
V = l * b * h
= 30 * 8 * 8 = 1920 mm³
Volume of vertical cuboid:
breadth = 10 mm
Length = 14+8 = 22 mm
Height = 8 mm
V = 22 * 10 * 8
= 1760 mm³
Volume of metal piece = 1920 + 1760
= 3680 mm³
Answer:
3680
i got 100 on test
Determine the intercepts of the line.
-5x+9y=-18
y intersept-(0,_)
x intercept- (_,0)
The x intercept is [tex](\frac{18}{5} , 0)[/tex]
The y intercept is (0, -2)
Solution:
Given equation is:
-5x + 9y = -18
We have to find the y intercept and x intercept
The x-intercept is the point at which the line crosses the x-axis. At this point, the y-coordinate is zero.
The y-intercept is the point at which the line crosses the y-axis. At this point, the x-coordinate is zero
Finding x - intercept:To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'.
Substitute y = 0 in given equation
[tex]-5x + 9(0) = -18\\\\-5x = -18\\\\x = \frac{18}{5}[/tex]
[tex]\text{Thus the x - intercept is } (\frac{18}{5}, 0)[/tex]
Finding y - intercept:To find the y-intercept, plug 0 in for 'x' and solve for 'y'
Substitute x = 0 in given equation
[tex]-5(0) + 9y = -18\\\\9y = -18\\\\y = -2[/tex]
Thus the y intercept is (0, -2)
To shift the graph of an equation a certain number of units __you need to
add that number to the function's equation.
O
A. down
O
B. up
SUBMIT
Answer:
Up
Step-by-step explanation:
Shifting a graph a number of units up is a vertical translation. So, in a vertical translation, we shift the graph up by adding a constant at the end of the function.
In any function [tex]f(x)[/tex]. If we add the constant [tex]d[/tex] at the end of the function, then this will shift graph of the function [tex]d[/tex] units up.
a square has an area of 25^2 what’s the length of each side??
Answer:
25
Step-by-step explanation:
Area is the square of the side length, so
s^2 = 25^2
Matching parts of this expression, we see ...
s = 25
The length of each side is 25.
The table shows the times of the top six swimmers in the women’s 100 meter butterfly at the 2012 Olympic Games. A 2-column table with 6 rows. Column 1 is labeled Place with entries 1, 2, 3, 4, 5, 6. Column 2 is labeled Time (seconds) with entries 55.98, 56.87, 56.94, 57.17, 57.27, 57.35. Between which two places is the difference in finishing times the shortest? What is the difference in those times?
Answer:
The difference in finishing time between the 2nd and 3rd places is the shortest and it is 0.07 seconds.
Step-by-step explanation:
The first positioned swimmer took 55.98 seconds and the second positioned swimmer took 56.87 seconds to complete the race.
So, the difference is (56.87 - 55.98) = 0.89 seconds.
The second positioned swimmer took 56.87 seconds and the third positioned swimmer took 56.94 seconds to complete the race.
So, the difference is (56.94 - 56.87) = 0.07 seconds.
The third positioned swimmer took 56.94 seconds and the fourth positioned swimmer took 57.17 seconds to complete the race.
So, the difference is (57.17 - 56.94) = 0.23 seconds.
The fourth positioned swimmer took 57.17 seconds and the fifth positioned swimmer took 57.27 seconds to complete the race.
So, the difference is (57.27 - 57.17) = 0.10 seconds.
The fifth positioned swimmer took 57.27 seconds and the sixth positioned swimmer took 57.35 seconds to complete the race.
So, the difference is (57.27 - 57.35) = 0.08 seconds.
Therefore, the difference in finishing time between the 2nd and 3rd places is the shortest and it is 0.07 seconds. (Answer)
Answer:
Between which two places is the difference in finishing times the shortest?
2 & 3
What is the difference in those times?
0.07
Step-by-step explanation:
i do
List the numerical coefficient of each term in the expression.
6.9x343 -0.55x?y +2.65
6.9 for X and -0.55 for X and 1 for Y
Step-by-step explanation:
The numerical Coefficient is said to be the fixed number that is in multiple with the variable. If the number is not with the variable then it is not taken into account.
STEP 1:
6.9 is the coefficient for X
STEP 2:
-0.55 is the coefficient for x
STEP 3:
1 is the coefficient for y
STEP 4:
343 a 2.65 not considered as the don't have the variables.
Can someone please help me with this question
Answer:
B, E
Step-by-step explanation:
It can be helpful to factor the first two terms:
f(x) = x^2(x -7) +36
This can make it easier to evaluate the function for different values of x.
The answer choices suggest you need to know whether f(5) and f(-14) match the values given here.
f(5) = 5^2(5 -7) +36 = -50 +36 = -14 . . . . matches choice B (and E)
f(-14) = (-14)^2(-14-7) +36 = -21(196) +36 . . . . does not match choice A (or D)
__
The one remaining answer choice we need to consider is C. If we look at f(0) for this equation, we find it is (-5)(-10) +14 = 64, which does not match f(0) = 36 for the function given in the problem statement.
The only true answer choices are B and E.
_____
The remainder theorem tells you that f(a) = the remainder from f(x)/(x -a).
42% of what number is 0.21?
Answer: 0.5
Step-by-step explanation:
Let the number be x , then
42% of x = 0.21
0.42x = 0.21
divide through by 0.42
x = 0.21/0.42
x = 0.5
Therefore : 42% of 0.5 = 0.21
Answer:
.5
Step-by-step explanation:
.42/1 * x = .21
x = .21/.42
x = .5 or 1/2
I need help please and thank you
Answer:30
Step-by-step explanation:
Answer:
I think the correct answer is
A- 40
B- 40
How many points need to be removed from this graph so
that it will be a function?
1 point
2 points
3points
4 points
Answer:
OPtion 3 points
Step-by-step explanation:
See the attached figure.
As shown, we can notice that the coordinates of all the points are (-3,2), (-3,3), (1,4), (1,-4), (2,-2), (2,-4).
The figure will be a function if for each value of x there exist a unique value of y.
In the figure, for each value of x we have two values of y. So it is not a function. We need to remove any of ordered pairs that have same input values.
From (-3,2) and (-3,3), we need to remove one point.
From (1,4) and (1,-4), we need to remove one point.
From (2,-2) and (2,-4), we need to remove one point.
It means total we need to remove 3 points from this graph so that it will be a function.
So, the correct option is 3 points.
A circle has a diameter of 3.6cm.
What is it’s radius?
Answer:
1.3
Step-by-step explanation:
Radius is half of a diameter so you just need to divide 3.6 by 2
Answer:
1.8
Step-by-step explanation:
The formula for diameter and radius is 2r = d, if we solve this equation we get 2r = 3.6 So, divide 3.6 by 2 and you got your answer!
A power regression equation for this data is: t = a^
Answer:
1.5
Step-by-step explanation:
Answer:
The person above is right.
Its: T = A^ 1.5
Step-by-step explanation:
Graph the planet data, shown right, using the regression calculator. When you are done, click “Resize window to fit data.”
Mercury and Venus are
✔ closer to
the sun than Earth is.
So, their orbital periods are
✔ shorter
than Earth's orbit.
The further a planet is from the sun, the
✔ longer
its orbit is.
A power regression equation for this data is:
T = A^
1.5
I took it and got it right.
Arianna is saving money for college so she invests $1,000 into a savings account that earns interest every year. If the amount in the savings account is represented by the function
9x2+50x+1000, where x is the number of years. How much money does Arianna have in her account after 6 years?
Answer: $1,624
Step-by-step explanation:
The amount after x-years is given as :
9[tex]x^{2}[/tex] + 50x + 1000
Since x represents number of years , this means that after 6 years , the amount will be :
9([tex]6^{2}[/tex] ) + 50(6) + 1000
⇒9(36) + 300 + 1000
⇒324 + 300 + 1000 =
Therefore, the amount after 6 years will be $1,624
Sneha is planning a 5-night vacation. It will cost $50 for transportation, $290 for food, and $95 per night for a hotel room. She has $143 in savings and can earn $48 per driveway shoveling driveways. How many driveways must she shovel to have enough money to pay for the trip?
Answer:
Step-by-step explanation:
Total cost for trip = 290 + 50 + 95*5 =290+50+ 475 = $ 815
Savings = $143
Money needed = 815 - 143 = $ 672
No. of driveways = 672/48 = 14
14 driveways must she shovel to have enough money to pay for the trip.
Sneha needs to calculate the total cost of her vacation which is $815. After taking into account her savings, she requires an additional $672. As she earns $48 shoveling each driveway, she would need to shovel 15 driveways.
Explanation:This is a question of basic algebra and problem solving. Sneha needs to calculate the total cost of her vacation first. She will spend $50 on transportation, $290 on food, and $95 per night for the hotel for 5 nights, or $475 ($95 x 5) for the hotel total.
Adding these amounts together, Sneha's vacation will cost $815 ($50 + $290 + $475). She currently has $143 in savings, meaning she needs $672 more dollars ($815 - $143).
As Sneha earns $48 for each driveway she shovels, we divide the total she needs by the earning for each driveway. That gives us 14 driveways. As Sneha can't shovel a fraction of a driveway, she will need to shovel 15 driveways in total.
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Abby can buy an 8-pound bag of dog food for $7.40 or a 4-pound bag of the same dog food for $5.38 . Which is the better buy
Answer:
the eight pound bag is better because you would have to pay $10.76 if you buy two of the 4 pound bags so you are saving $3.36
Step-by-step explanation:
Answer:
the 8 pound buy
Step-by-step explanation:
The weight of an object on a particular scale is 145.2 lbs. The measured
weight may vary from the actual weight by at most 0.3 lbs. What is the range
of actual weights of the object?
Answer:
(144.9;145.5) so from 144.9 to 145.5lbs
1. What is the difference between a median of a triangle and an altitude?
Answer:
The difference between a median and altitude of a triangle is given below :
Altitude is the perpendicular line drawn from a vertex of a triangle to its opposite side .But a median of a triangle is a segment connecting a vertex to the midpoint of its opposite side.
Step-by-step explanation:
The difference between a median and altitude of a triangle is given below :
Altitude is the perpendicular line drawn from a vertex of a triangle to its opposite side .But a median of a triangle is a segment connecting a vertex to the midpoint of its opposite side.
10x — 12y = 6
5х – бу=3
Answer:
The equations system has multiple solutions for x, y.
Step-by-step explanation:
Let's solve for x and y this equations system:
We can observe that the second equation is a simplification of the first (divided by 2) and therefore, the system has multiple solutions for x and this way:
x y
-27/5 -5
-21/5 -4
-3 -3
-9/5 -2
-3/5 -1
3/5 0
9/5 1
3 2
21/5 3
27/5 4
33/5 5
How many gallons of 90% antifreeze must be mixed with 60 gallons of 15% antifreeze to get a mixture that is 80%?
390 gallons of 90 % antifreeze must be mixed with 60 gallons of 15% antifreeze to get a mixture that is 80%
Solution:
Let "x" be the gallons of 90 % antifreeze
60 gallons of 15 % antifreeze
Then, (x + 60) is the gallons present in final mixture that is 80 %
Therefore, x gallons of 90 % antifreeze is mixed with 60 gallons of 15 % antifreeze to get a mixture that is (x + 60) gallons of 80 %
Thus, a equation is framed:
90 % of x + 15 % of 60 = 80 % of (x + 60)
Solve the above equation for "x"
[tex]90 \% \times x + 15 \% \times 60 = 80 \% \times (x+60)\\\\\frac{90}{100} \times x + \frac{15}{100} \times 60 = \frac{80}{100} \times (x+60)\\\\0.9x + 0.15 \times 60 = 0.8(x + 60)\\\\0.9x + 9 = 0.8x + 48\\\\0.9x - 0.8x = 48 - 9\\\\0.1x = 39\\\\ x = 390[/tex]
Thus 390 gallons of 90 % antifreeze must be mixed
Solve the below system of equations using the linear combination method. Show all your work, explaining each step in solving the system using the linear combination method.
2x + 3y = 1
y = -2x - 9
The solution of the system of equations is (-7 , 5)
Step-by-step explanation:
The steps of the linear combination method are:
Make the coefficients of one variable in the two equations same in values and different in signsAdd the two equations to eliminate that variable and make one equation of the other variableSolve the equation to find the other variableSubstitute its value in any one of the two equations to find the variable that eliminate before∵ 2x + 3y = 1 ⇒ (1)
∵ y = -2x - 9
- Add 2x to both sides
∴ 2x + y = -9 ⇒ (2)
Multiply equation (2) by -1 to make the coefficients of x opposites
∴ -2x - y = 9 ⇒ (3)
Add equations (1) and (3) to eliminate x
∴ 2y = 10
Divide both sides by 2
∴ y = 5
Substitute the value of y in equation (1) or (2) to find x
∵ 2x + 5 = -9
- Subtract 5 from both sides
∴ 2x = -14
- Divide both sides by 2
∴ x = -7
The solution of the system of equations is (-7 , 5)
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2x+y=1
9x + 3y = -3
The x-coordinate of the point of intersection is
-2
0
5
Answer:
The x-coordinate of the point of intersection is -2
Step-by-step explanation:
Here we have a typical system of linear equations whose solution will give us both the x- and the y- coordinates (i.e. the intersection point).
Let us solve the system and find which matches the available options, as follow. Given:
[tex]2x+y=1\\9x+3y=-3[/tex]
Taking the first expression and re arranging to solve for [tex]x[/tex] we have:
[tex]2x+y=1\\2x=1-y\\x=\frac{1-y}{2}[/tex] Eqn.(1)
Plugging in it, in the second expression we then have
[tex]9(\frac{1-y}{2} )+3y=-3\\\\\frac{9}{2}-\frac{9y}{2}+3y=-3\\ \\\frac{9}{2}-\frac{9y}{2}+\frac{6y}{2}=-\frac{6}{2}\\ \\-\frac{9y}{2}+\frac{6y}{2}=-\frac{6}{2}-\frac{9}{2}\\-3y=-15\\y=\frac{-15}{-3}\\ y=5[/tex]
So finally plugging in the y value in Eqn.(1) we have
[tex]x=\frac{1-5}{2} \\x=\frac{-4}{2}\\ x=-2[/tex]
The x-coordinate of the point of intersection is -2
John’s dog weighed 7 pounds when he got him. The dogs weight tripled each year for two years. How many ounces did John’s dog now weigh?
Answer:
Step-by-step explanation:
1st year- 7*3=21
2nd year- 21*3=63
Find the sum 45+46+47+48...+135+136
Answer:
457
Step-by-step explanation:
I add all the numbers I could see and got 457.... i need more information hope this helps
The three-dimensional figure below is a solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it. Find the volume of the solid in cubic millimeters.
A.60
B.300
C.540
D.780
Answer:
540
Step-by-step explanation:
4×4×15×6×6=540
Explanation:
hope it helps
The volume of the solid rectangular prism with a hole is 444 mm³.
The correct answer is option A.
To find the volume of the solid rectangular prism with a hole, we calculate the volume of the outer rectangular prism and subtract the volume of the inner rectangular prism.
Volume of the Outer Rectangular Prism:
The outer rectangular prism has dimensions 15 mm (length) × 6 mm (width) × 6 mm (height). The volume (V_outer) is given by:
Volume_outer = length × width × height = 15 × 6 × 6 = 540 mm³.
Volume of the Inner Rectangular Prism:
The inner rectangular prism has dimensions 4 mm (length) × 4 mm (width) × the height of the outer prism (6 mm). The volume (V_inner) is given by:
Volume_inner = length × width × height = 4 × 4 × 6 = 96 mm³.
Volume of the Solid Rectangular Prism with Hole:
Subtracting the volume of the inner prism from the volume of the outer prism gives the volume of the solid:
Volume_solid = V_outer - V_inner = 540 - 96 = 444 mm³.
Therefore, the correct volume of the solid rectangular prism with a hole is 444 mm³.
The question probable may be:
The three-dimensional figure below is a solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it. Find the volume of the solid in cubic millimeters.
A. 444
B.300
C.540
D.780
Write 1/10 and 1/10 as decimals to complete the expression.
Answer:0.2
Step-by-step explanation: 1/10 and 1/10
Simply means this in maths
1/10+1/10
0.1+0.1= 0.2
Does anyone know this??
Answer:
z = 65°
y= 105°
Step-by-step explanation:
angle z is adjacent to 115° on a straight line, hence they are supplementary angles, i.e they add up to 180°
hence,
z + 115° = 180°
z = 180° - 115° = 65°
recall that the sum of angles inside a convex quadrilateral always adds up to 360°
i.e z + y + 102° + 88° = 360° (we know z from above)
65 + y +102+88=360
y = 360 -65-102-88 = 105°
Given the two linear equations 4r - 5 = 17 and 12 - 2s = 2, what is the product of r and s?
[tex]\text{You're solving the equations:}\\\\4r - 5 = 17\\ 12 - 2s = 2\\\\\text{Solve for r:}\\\\4r-5=17\\\\\text{add 5 to both sides}\\\\4r=22\\\\\text{Divide both sides by 4}\\\\\boxed{r=5.5}\\\\\text{Solve for s:}\\\\12 - 2s = 2\\\\\text{Subtract 12 from both sides}\\\\-2s=-10\\\\\text{Divide both sides by -2}\\\\[/tex]
[tex]\boxed{s=5}[/tex]
An equation is formed when two equal expressions. The product of r and s is 27.5.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation 4r - 5 = 17 can be solved for r as shown below,
4r - 5 = 17
Add 5 on both the sides of the equation,
4r - 5 + 5 = 17 + 5
4r = 22
Divide both the sides of the equation by 4,
4r / 4 = 22 / 4
r = 11/2
r = 5.5
The given equation 12 - 2s = 2 can be solved for s as shown below,
12 - 2s = 2
Subtract 12 from both the sides of the equation,
12 - 2s - 12 = 2 - 12
-2s = -10
Divide both the sides of the equation by -2,
-2s/-2 = -10/-2
s = 5
Now, the product of r and s can be written as,
r × s
= 5.5 × 5
= 27.5
Hence, the product of r and s is 27.5.
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A train goes past you in 10 seconds and goes past a 100 meter long bridge in 30 seconds. What is the length (in meters) and the speed (in m/s) of the train?
To find the length of the train and its speed, we can use the formula Length = Speed x Time. By setting up and solving equations, we can find that the length of the train is 200 meters and the speed of the train is 20 m/s.
Explanation:To find the length of the train, we can use the formula:
Length = Speed x Time
Given that the train takes 10 seconds to pass you and 30 seconds to pass the bridge, we can calculate:
Length of train = Speed of train x Time taken to pass you = Speed x 10
Length of train + Length of bridge = Speed of train x Time taken to pass the bridge = Speed x 30
Substituting the values, we have:
Speed x 10 + 100 = Speed x 30
Simplifying the equation, we get:
Speed = 400/20 = 20 m/s
Substituting the value of speed back into the first equation, we have:
Length of train = 20 x 10 = 200 meters
Therefore, the length of the train is 200 meters and the speed of the train is 20 m/s.