Answer:
[tex]y = 181.75xz^2[/tex]
Step-by-step explanation:
Given
y jointly varies to x and z^2
Required
Find the equation
We start by writing out the variation;
[tex]y\ \alpha\ xz^2[/tex]
Write as equation
[tex]y = kxz^2[/tex]
Substitute values of x,y and z
[tex]70 = k * 21 * 25^2[/tex]
[tex]70 = k * 21 * 25 * 25[/tex]
[tex]70 = k * 13125[/tex]
Divide both sides by 7
[tex]\frac{70}{13125} = \frac{k * 131251}{13125}[/tex]
[tex]\frac{70}{13125} = k[/tex]
[tex]187.5 = k[/tex]
[tex]k = 181.75[/tex]
Substitute k in [tex]y = kxz^2[/tex]
[tex]y = 181.75xz^2[/tex]
Write an equation in slope-intercept form for the line that satisfies the following condition.
passes through (29,8), perpendicular to the graph of y= 5x +17.
Select one:
a. y = 385x + 1
b.y = -132 +385
c. Y = 12 +385
d.y= -132 + (-13)
Answer:
y = - x + 69
Step-by-step explanation:
Given the following :
Point on graph : (29, 8)
Equation of line ; y= 5x +17.
From the equation slope of line = 5
Intercept = 17
Slope of perpendicular line = - 1/5 ( negative reciprocal)
Using the equation :
y - y1 = m(x - x1)
From the Point given:
x1 = 29, y1 = 8
y - 8 = (- 1/5)(x - 29)
y - 8 = -1/5x + 29/5
y = -1/5x + 29/5 + 8
Multiply through by 5
y = - x + 29 +40
y = - x + 69
WILL MARK BRAINLIEST Give a real world example of an equation which the constant of proportionality is 15. What would the graph look like?
Answer:
Let's say someone is selling lemonade at a lemonade stand. The more cups of lemonade this person sells, the more money they get. If 1 cup= $1, then he would get $2 for 2 cups.
Step-by-step explanation:
The price of the lemonade cup and the lemonade cup are a constant of proportionality. They are proportional to each other. The more lemonade you sell, the more money you get.
The graph would be a straight diagonal line. The y would be the money, and the x would be the amount of lemonade sold. Since they are the same and proportional, they would go in a straight line.
What is the range of the function for the given domain? y = 2x − 5 D: {-2, 0, 2, 4}
Answer:
Range of Function : { - 9, - 5, - 1, 4 }
Step-by-step explanation:
We know that y = 2x - 5 provided the domain ( x - values ) { - 2, 0, 2, 4 }. Let us substitute each element in this set of domain as x in the equation "y = 2x - 5" as to solve for the y - values, otherwise known as the range of the function.
{ - 2, 0, 2, 4 }
y = 2( - 2 ) - 5 = - 9,
y = 2( 0 ) - 5 = - 5,
y = 2( 2 ) - 5 = - 1,
y = 2( 4 ) - 5 = 4
We have the set of y - values as { - 9, - 5, - 1, 4 }. This is the range of our function.
A. Y=-5/2x+2
B. Y=2/5x+2
C. Y=-2/5x+2
D. Y=5/2x+2
Answer:
B) y=2/5x+2
Step-by-step explanation:
Slope is rise over run. Since the line is increasing it’s positive. It goes up two and then five to the right, so it’s a positive 2/5.
Therefore the answer is B) y=2/5x+2
What is the graph of the solution to the following compound inequality? –6x – 1 < –25 or 3x + 4 ≤ –5
Answer:
[tex]x>4[/tex] or [tex]x \leq -3[/tex]
Step-by-step explanation:
Given :[tex]-6x -1 < -25[/tex] or[tex]3x + 4 \leq -5[/tex]
Solving first inequality :
[tex]-6x-1<-25[/tex]
Add 1 to both sides
[tex]\Rightarrow -6x-1+1<-25+1\\\Rightarrow -6x<-24\\\Rightarrow 6x>24[/tex]
Divide both sides by 6
[tex]\Rightarrow \frac{6}{6}x>\frac{24}{6}\\\Rightarrow x>4[/tex]
Solving second inequality:
[tex]3x + 4 \leq -5[/tex]
Subtract 4 from both sides
[tex]\Rightarrow 3x+4-4 \leq -5-4\\\Rightarrow 3x \leq -9[/tex]
Divide both sides by 3
[tex]\Rightarrow \frac{3}{3}x \leq \frac{-9}{3}[/tex]
[tex]\Rightarrow x \leq -3[/tex]
So, [tex]x>4[/tex] or [tex]x \leq -3[/tex]
Refer the attached graph
One number is seven less than a second number. Five times the first is 2 more than 6 times the second. Find the numbers. The value of the first number is _____.
Answer:
[tex]\Large \boxed{\sf \ \ 40 \ \ }[/tex]
Step-by-step explanation:
Hello,
Let's not a and b the two numbers.
One number is seven less than a second number.
(1) b = a - 7
Five times the first is 2 more than 6 times the second.
(2) 5a = 2 + 6b
(2)+5*(1) gives
5a + 5b = 2 + 6b + 5a - 35
b = 35 - 2 = 33
a = 40
The value of the first number is [tex]\large \boxed{\sf \ \ 40 \ \ }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Match each equation with the operation you can use to solve for the variable. Subtract 10. Divide by 10. Divide by 5. Subtract 18. Multiply by 10. Add 18. Add 10. Multiply by 5. 5 = 10p p + 10 = 18 p + 18 = 5 5p = 10
Answer: 5=10 p (divide by 10) p+10=18 (subtract 10) p+18=5 (subtract 18) 5p=10 (divide by 5)
Step-by-step explanation:
You want to get p or the variable alone
Brooke solved the equation below: 6r = 72 6r − 6 = 72 − 6 r = 66 Is Brooke’s solution correct? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation.
Answer:
see below
Step-by-step explanation:
6r = 72
We need to divide each side by 6, not subtract 6 from each side
6r/6 = 72/6
r = 12
Answer:
Brooke's solution is incorrect
Divide both sides by 6
r=12
Step-by-step explanation:
The equation is:
6r=72
Brooke solved the equation like so:
6r-6=72-6
r=66
Brooke's solution is incorrect. She subtracted 6 from both sides of the equation.
Here is how the equation should be solved:
6r=72
We want to solve for r, so we have to get r by itself. 6 and r are being multiplied (6*r=6r). The inverse of multiplication is division, so we must divide both sides by 6 (not subtract 6 from both sides).
6r/6=72/6
r=72/6
r=12
Brooke's solution is incorrect. She subtracted 6 instead of dividing by 6. The correct solution is r=12.
confused on this one
1. Assume that m26 = 60°. What must be true about 26 and 23 for the
lines to be parallel? Name the postulate or theorem that you used in
this justification
Answer:
The other measurement has to be 120 degrees. In other words, the two angles have to add up to 180 degrees. The method for that is same side interior.
Step-by-step explanation:
In same side interior angles, the sum of the two angles has to be 180 degrees. So we know that one of the angles is 60 degrees so we do 180-60=120.
The initial count of a certain type of bacteria in a culture is 350. If the bacteria grows at the rate of 20% per hour, which
function models the number of bacteria after t hours?
Answer:
70
Step-by-step explanation:
[tex]\frac{20}{100}*350=70[/tex]
What is the value of x in the equation ( x +
({ x + 12) = {(x +
4x + 14) – 3?
-24
-6
2
0
Answer:
3
Step-by-step explanation:
(x+(×+12)=(×+4×+14)-3
×+×+12=×+4×+14-3
2×+12=5×-2×
+12-11=5×-2×
-1=3×
A company is building a new park in the shape of a circle with a 25 ft diameter. Portions of the new park will be covered with grass. A diagram of the park is given below, with the shaded region representing the areas that will be covered in grass. Use 3.14 for. Note: image is not drawn to scale. The area of the regions covered by grass is approximately sq ft.
Answer: The area of the regions covered by grass is approximately 313.375 sq ft.
Step-by-step explanation:
Given: A company is building a new park in the shape of a circle with a 25 ft diameter.
Then radius = [tex]\dfrac{25}{2}=12.5\ ft[/tex]
Required area = Area of circle - Area of rectangle + Area of triangle
Formula: Area of circle = [tex]\pi r^2[/tex]
Area of rectangle = length x width
Area of triangle = 0.5 x base x height
Area of circle = [tex](3.14)(12.5)^2=490.625\ \text{ft}^2[/tex]
Area of rectangle = 20 ft x 10ft = 200 ft²
Area of triangle = 0.5 x 7 x 6.5 = 22.75 ft²
Required area = 490.625 -200+22.75 = 313.375 ft²
Hence, The area of the regions covered by grass is approximately 313.375 sq ft.
how do you solve this question?
Answer:
[tex]\large \boxed{\sf \ \ \ 2x-ln(1-x) \ \ \ }[/tex]
Step-by-step explanation:
Hello,
for any real x different from 1
[tex]\dfrac{3-2x}{1-x}=\dfrac{2-2x+1}{1-x}\\\\=\dfrac{2(1-x)+1}{1-x}\\\\=2\dfrac{1-x}{1-x}+\dfrac{1}{1-x}\\\\=2+\dfrac{1}{1-x}[/tex]
if f(x)=2x
f'(x)=2
if g(x)=-ln(1-x)
[tex]g'(x)=\dfrac{-1*-1}{1-x}=\dfrac{1}{1-x}[/tex]
So antiderivative of
[tex]\dfrac{3-2x}{1-x}=2+\dfrac{1}{1-x}[/tex]
Is
2x-ln(1-x)
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
can you please answer and show your work! thank you so much :)
Answer:
1: -7
2: -7
3:-7
4: 8
5: 8
6: 8
Step-by-step explanation:
for the first one, you do 6-1=5 and then times that by 2 and then simplify that to get -7. for the second one, you do [tex]2^{3}[/tex] which is 8+4=12, and divide 24 by that to get 2 and minus nine to get -7. for the 3rd one, you do [tex]4^{2}[/tex]+9 first (16+9)= 25, and subtract 39 from that to get 14, then do 4-5=-1 *2=-2, which gets you -7. for 4 , you do 81-25= 56 over 10+8-11=7 which gets you 8. for 5, you do 36-20=16 in parentheses first and then divide 48 by that to get 3 and subtract that to get 8. last, for 6, you do 22-14 to get you 8
A computer technician charges a fixed amount for a repair, plus an additional amount per hour. The equation below describes y, the total amount the technician charges, in dollars, for a repair that takes x hours.
y=45x+75
What is the meaning of the y-intercept of the equation?
A.It means the technician charges a fixed amount of $45 for the repair
B.It means the technician charges a fixed amount of $75 for the repair.
C. It means the technician charges $45 per hour for the repair.
D.It means the technician charges $75 per hour for the repair.
Answer:B
Step-by-step explanation:
The x next to the 45 represents that if we were to put this in a graph the line would start at 45 meaning that the 45 could be the fee for looking at whats broken and the $75 is the payment for fixing it giving us the Y-intercept(out total payment)
In the given equation y=45x+75, the y intercept 75 represents the technician charges $45 per hour for the repair. Option C is correct.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
Given,
A computer technician charges a fixed amount for a repair, plus an additional amount per hour
y=45x+75
y equal to forty five x plus seventy five
In the given equation the x represents number of hours and 75 represents fixed amount.
45 represents the additional amount per hour.
In the equation y=45x+75
45 is the slope and 75 is the y intercept.
75 represents the technician charges a fixed amount of $75 for the repair.
Hence option C is correct, the technician charges $45 per hour for the repair.
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Please help! You will get 17 points!
What is the volume of the following cylinder with a diameter of 12 yds and a height of 15 yds? Do not round your answer.
(Use 3.14 for pi)
Volume = __ yds squared.
Answer:
1695.6 is the volume.
Step-by-step explanation:
3.14 * 6^2 * 15 = 1695.6
Answer:
1695.6 yds^ 3
Step-by-step explanation:
If the diameter is 12 yds then the radius is 6 yds. The height is 15 yds. Thus the volume of this cylinder is
V = πr²h = 3.14(6 yd)^2·(15 yds) = 1695.6 yds^ 3
oops i did something wrong last question cuz it accidentally showed my email
Answer:
A, D and E
Step-by-step explanation:
Option B is an inequality while Option C is an Equation. However, Rest of the options are expressions because they don't have any equality (=) sign or any inequality (<,>,≥,≤). So, they are expressions.
Juan is making a model out of rhombi. Each rhombus will be connected to the one before it. Each rhombus will be 6 inches tall and 4 inches wide.
Which are the roots of the quadratic function f(q) = q? - 125? Select two options.
Oq=515
Oq=-575
Oq=3/5
Oq=-375
Oq=25/5
Answer:
A and C
Step-by-step explanation:
The roots of the quadratic function f(q) = q² - 125 are q = 5 and q = -5.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The quadratic function f(q) = q² - 125 can be factored as (q - 5)(q + 5).
Now,
To find the roots, we set the function equal to zero and solve for q:
So,
q² - 125 = 0
(q - 5)(q + 5) = 0
q - 5 = 0 or q + 5 = 0
q = 5 or q = -5
Therefore,
The roots of the quadratic function f(q) = q² - 125 are q = 5 and q = -5.
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Which of the following cross sections cannot be produced by slicing a right rectangular prism? A. pentagon B. circle C. rectangle D. trapezoid
Answer:
The answer is option B.
Step-by-step explanation:
Since it's a rectangular prism slicing will produce either a rectangle or trapezoid and not or a circle since it's round
Hope this helps you
Answer: B. Circle
Step-by-step explanation:
Since the base is a rectangle and the faces are rectangular, there is no way to slice the prism to get a a circle.
The trapezoid ? Maybe. A diagonal slice starting on a corner will create a quadrilateral with uneven sides.
Pentagon? Imagine starting on the top near a corner-- but not on the corner-- with a diagonal line, slicing down towards the opposite corner. You should be able to get an irregular pentagon.
A rectangle is easy!
No circles!
Enjoy! I hope this helps you.
PLEASE HELP 13 INSTEAD OF FIVE POINTS!!!! I REALLY NEED HELP
Answer:
y = 3/7 x - 3
Step-by-step explanation:
The first number should be positive because the dots are slowly going up, not down. The first number also cannot be 7/3 because the slope of that would be over 2, and in this graph, the slope isn't even more than one. The last answer we have to eliminate is y = 3/7x + 3 because the +3 is the y-intercept, and in the graph, it doesn't touch the positive 3. So the answer is y = 3/7x - 3.
Pls solve and explain
Answer:
4950 potholes in 6 weeks, estimated is 4800.
Step-by-step explanation:
To estimate, let's round 825 to the nearest 100th - 800.
Now we multiply 800 times 6 to find our estimate.
[tex]800\cdot 6 = 4800[/tex]
If we know that the road repair crew can fix 825 potholes PER WEEK, we can set up a proportion to find how many they can do in 6 weeks.
[tex]\frac{825}{1} = \frac{x}{6}[/tex]
Let's cross multiply to find the value of x.
[tex]825\cdot6=4950\\4950\div1=4950[/tex]
So the repair crew can fix 4950 potholes in 6 weeks.
4950 is pretty close to 4800, so our exact answer should be correct.
Hope this helped!
Answer:
the answer is 4950
Step-by-step explanation:
Because the ratio would be 825:1 and if you times the 1 by 6. it would give you 6 and do the same to the other side with 825 that would give you 4950. hope you like my answer.
The formula for calculating simple interest is I = prt. Which is the equivalent equation solved for r? StartFraction I Over p t EndFraction = r StartFraction p t Over I EndFraction = r I minus p t = r I + p t = r
Answer: r = I/pt
Step-by-step explanation:
Interest divided by the principal × time gives the rate. It's usually expressed as a percentage per year.
The equivalent equation for r is r=I/pt which is option a.
What is equation?Equation is relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It is of many types like linear equation, quadratic equation, cubic equation, etc.
How to find equation?We have been given an equation I=prt and we have to find the equivalent equation which is solved for r.
I=prt
In this p is principal, r is rate of interest and t is time period.
Divide both sides by pt.
I/pt=prt/pt
I/pt=r
Hence the equation equivalent to I=prt is r=I/pt which is option a.
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Which is the factorization of x3 + 8? (x + 2)(x2 – 2x + 4) (x – 2)(x2 + 2x + 4) (x + 2)(x2 – 2x + 8) (x – 2)(x2 + 2x + 8)
Answer:
here the answer is down below
Step-by-step explanation:
Answer:
A (x+2)(x^2-2x+4)
Step-by-step explanation:
just took test
A machining company needs to manufacture more than 20 fixtures in a day. The company uses five identical machines to make the fixtures. If each machine produces x fixtures, which inequality represents this situation? A. 5x > 20 B. 5x 20 + 5 D. 5x < 20 + 5
Answer:
A. 5x>20
Step-by-step explanation:
Because the company has to produce more than 20 fixtures you need greater than 20 and you have 5 machines time the number they produce.
Hope this helps, if it does please mark brainliest!!
Answer:
5x > 20
Step-by-step explanation:
I got a 100
Find the mean absolute deviation (MAD) of the data in the bar chart below.
Mean absolute deviation of the given data is 1.5
What is Mean absolute deviation?The average absolute deviation of a data set is the average of the absolute deviations from a central point.
What is Mean?The arithmetic mean, also known as arithmetic average, is a measure of central tendency of a finite set of numbers
From the given bar chart
Mean = Sum of the terms / Number of terms
Mean = [tex]\frac{4+5+6+1}{4}=4[/tex]
Mean absolute deviation = [tex]\frac{1}{n}[/tex]∑ | mean- x|
MAD = [tex]\frac{|4-4|+|4-5|+|4-6|+|4-1|}{4} =\frac{0+1+2+3}{4}=1.5[/tex]
Hence, Mean absolute deviation of the given data is 1.5
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Answer:
1.5
Step-by-step explanation:
Which expression is equivalent to *picture attached*
Answer:
[tex]\sum_{n=3}^{20}(n(n+1))=\sum _{n=3}^{20} n^2+ \sum _{n=3}^{20} n[/tex]
Step-by-step explanation:
Given expression : [tex]\sum_{n=3}^{20}(n(n+1))[/tex]
Solving further :
[tex]\Rightarrow \sum_{n=3}^{20}(n^2+n)[/tex]
[tex]\Rightarrow \sum _{n=3}^{20} n^2+ \sum _{n=3}^{20} n[/tex]
So, [tex]\sum_{n=3}^{20}(n(n+1))=\sum _{n=3}^{20} n^2+ \sum _{n=3}^{20} n[/tex]
So, The given expression is equivalent to Option A
So, Option A is the answer
Solve for x: 4x - 2 > 6x + 8. (5 points)
x<-5
x>5
x<5
x>-5
Answer:
x<-5 is the correct answer
Answer:
x<-5 is the answer
Step-by-step explanation:
What properties must a quadrilateral possess in order for the quadrilateral to be classified as a.. trapezoid isosceles trapezoid
Answer:
Step-by-step explanation:
The typical isosceles trapezoid will have a uniform width, measured vertically, but two ends that are not square (not perpendicular to the x-axis. The two sloping ends are congruent (their slopes have exactly the same slope.
The same could be said of an isosceles trapezoid that is vertical; the sloping ends have the same slope.
Answer:
2 parallel sides
2 non-parallel, congruent sides
Step-by-step explanation:
As any other quadrilateral, an isosceles trapezoid has 4 sides. 2 sides must be parallel. The other two sides cannot be parallel but must be congruent.
How many solutions does this system have? 2 x - 3 y = 10. -4 x + 6 y = - 20.
A) One
B) Two
C) An infinite number
D) No solution
Answer: The correct answer is: [D]: " No solution " .
______________________________________
Step-by-step explanation:
We are given the following system of equations:
2x − 3y = 10 ;
-4x + 6y = -20 ;
_______________________________________
Let us take the second equation:
-4x + 6y = -20 ;
and multiply each side by "-1 " ; to get rid of the "negative numbers" ; and to rewrite the equation without the "negative numbers" :
- 1 * { - 4x + 6y } = -1 * (-20} ;
to get:
4x − 6y = -20 ;
Now, let us simply this equation further; by divide each side of the equation by "2" ;
(4x − 6y) / 2 = (-20) / 2 ;
→ [ (4x) / 2 ] − [ (6y) / 2 ] = -10 ;
to get: 2x − 3y = -10 ;
Then we have: 2x − 3y = 10 ;
Note: 10 ≠ -10 .
_______________________________________
So the answer is: [D]: " No solution."
_______________________________________
Hope this explanation helps you! Best wishes!
_______________________________________