Answer:h= [tex]\frac{(p/0.7-b)}{r}[/tex]
Step-by-step explanation:
1) p/0.7=rh+b
2) (p/0.7)-b=rh
3) [tex]\frac{(p/0.7-b)}{r}[/tex] =h
h= [tex]\frac{(p/0.7-b)}{r}[/tex]
The equivalent equation for isolated variable h = [tex]\frac{p-0.7b}{r}[/tex] obtained from the equation p = 0.7(rh + b).
What is meant by isolating a variable?Isolating a variable is the re-arrangement of the equation for the required variable. Even though rewriting the terms, doesn't affect the logic of the equation. It forms an equivalent equation.
Isolating the variable h from the given equation:The given equation is p = 0.7(rh + b)
Where,
p - home pay
h - working hours
r - the rate of dollars per hour
b - bonus received
Re-writing the equation for the variable h:
p = 0.7(rh + b)
⇒ p/0.7 = rh + b
⇒ p/0.7 - b = rh
⇒ h = p/0.7r -b/r
∴ h = [tex]\frac{p-0.7b}{r}[/tex]
Therefore, variable h is isolated and obtained an equivalent equation.
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what is the area of the triangle? (sorry if its sideways)
Answer:
6
Step-by-step explanation:
2 x 6 = 12/2 = 6
Answer:
A = 6 units ^2
Step-by-step explanation:
The area of a triangle is found by
A = 1/2 bh where b is the length of the base and h is the height
A = 1/2 (6) *2
A = 6 units ^2
A family is planning a wedding celebration in a gazebo. They want to know the area so that they can determine how many people can comfortably fit inside. They take some measurements and find that each side is 8 ft long and the apothem is 9.7 ft. What is the area of the enclosed gazebo?
Answer:
The area of the enclosed gazebo is [tex]310.4\ ft^{2}[/tex]
Step-by-step explanation:
I assume that is a regular octagon (eight equal aides)
we know that
The area of a regular polygon is equal to
[tex]A=\frac{1}{2}(P)(a)[/tex]
where
P is the perimeter of the polygon
a is the apothem
Find the perimeter P (the octagon has 8 sides)
[tex]P=8(8)=64\ ft[/tex]
[tex]a=9.7\ ft[/tex]
substitute
[tex]A=\frac{1}{2}(64)(9.7)[/tex]
[tex]A=310.4\ ft^{2}[/tex]
Two companies allow you to pay monthly for your food truck permits. Company A charges a one time fee of $150 and $45 per month. Company B charges a one time fee of $125 and $50 per month.
The simultaneous Equations for both total costs are;
Company A: y = 45x + 150
Company B: y = 50x + 125
Thus, both companies charge the same amount of money for food truck permits for 5 months
How to find the equation of the total charges?
We are told that;
Company A charges a one time fee of $150 and $45 per month.
Company B charges a one time fee of $125 and $50 per month.
Thus, using the concept of the equatiom of a line In slope intercept form, we have:
Company A: y = 45x + 150
Company B: y = 50x + 125
let's use the number 5 for x as an example
45(5) + 150 = 375
50(5) + 125 = 375
So both companies charge the same amount of money for food truck permits for 5 months.
Complete question is;
Two companies allow you to pay monthly for your food truck permits. Company A charges a one time fee of $150 and $45 per month. Company B charges a one time fee of $125 and $50 per month. Write an equation or a system of equations and explain what each solution tells you about the situation
What is the chance that a person randomly selected off the street was born in May
8%
12%
20%
30%
Answer: Eight percent.
Step-by-step explanation: In order to find this, we have to use the probability formula, which is:
The Event We Are Looking For/All of the Events.
In this case, plugging the numbers into the formula we get
May(1)/All the months in the year, including May (12).
Diving this, our answer will be 0.08333..., or rounded up to 0.8
However, since we are only looking for one specific event, we can take the number 100, and divide it by all the events. 12/100 is 8.333..., or rounded to 8.
Final answer:
The chance that a person randomly selected off the street was born in May is about 8%, assuming birth rates are evenly distributed throughout the year.
Explanation:
The question, "What is the chance that a person randomly selected off the street was born in May?" is one that pertains to the subject of probability in Mathematics. Since there are typically 12 equally likely months that a person could be born in, and assuming there is no significant variation in birth rates by month, the chance that someone chosen at random off the street was born in May is 1 out of 12 months.
Thus, to calculate the probability, you would divide 1 by 12, which equals approximately 0.0833. To express this as a percentage, we multiply by 100, yielding an 8.33% chance. Therefore, the closest answer among the provided options is 8%.
Find the additive inverse of 6+4i
[tex]0-(6+4i)=0-6-4i=-6-4i[/tex]
The additive inverse of the complex number 6+4i is -6-4i because it negates both the real and imaginary parts, resulting in a sum of zero when added to the original number.
The additive inverse of a complex number is a number that, when added to the original number, yields a sum of zero. For the complex number 6+4i, its additive inverse is found by changing the sign of both the real and the imaginary parts. Therefore, the additive inverse of 6+4i is -6-4i.
Please help!!!!! Thanks
Answer:
Look to the attached file
Step-by-step explanation:
what transformation was not done to the linear parent function, f(x)=x, to get the function g(x)=-3(x-4)-7
A. Reflection over the x-axis
B. Shift down 7 units
C. Shift right 4 units
D. Horizontal stretch by a factor of 3
Answer: D. Horizontal stretch by a factor of 3.
Step-by-step explanation:
Below are some transformations for a function [tex]f(x)[/tex]:
If [tex]f(x)-k[/tex], then it is shifted "k" units down.
If [tex]f(x-k)[/tex], then it is shifted rigth"k" units.
If [tex]-f(x)[/tex], then it is reflected across the x-axis.
If [tex]cf(x)[/tex] and [tex]c>1[/tex], then it is stretched vertically by a factor of "c".
If [tex]f(cx)[/tex] and [tex]0<c<1[/tex], then it is stretched horizontally by a factor of [tex]\frac{1}{c}[/tex].
Based on this, the transformations done to the function [tex]f(x)=x[/tex] to get the function [tex]g(x)=-3(x-4)-7[/tex] are:
- It is shifted 7 units down.
- It is shifted rigth 4 units.
- It is reflected over the x-axis.
- It is vertically stretched by a factor of 3.
Therefore, the transformations that was not done to the function [tex]f(x)=x[/tex] to get the function [tex]g(x)=-3(x-4)-7[/tex] is:
Horizontal stretch by a factor of 3.
5. (03.02)
If g(x) = x2 + 3, find g(4). (2 points)
16
19
8
11
Answer:
19
Step-by-step explanation:
g(x)=x^2+3
g(x)=(4^2)+3
g(x)=16+3=19
if g of x = x squared + 3, then 4 squared = 16, plus 3 = 19
Answer:
option(B) g(4) =19.
Step-by-step explanation:
Given:If g(x) = [tex]x^{2}[/tex] + 3.
To find: g(4).
Solution: We have given that
g(x) = [tex]x^{2}[/tex] + 3.
for x=4.
g(4) = [tex]4^{2}[/tex] + 3.
g(4) = 16+3
g(4) =19.
Therefore, option(B) g(4) =19.
Workers have packed 1,400 glasses in 7 boxes. If they pack 3 more boxes, how many glasses will they have packed in all?
1box = 1400/7 = 200
200×3=600
1400+600=2000
Answer:
2000
Step-by-step explanation:
Given :Workers have packed 1,400 glasses in 7 boxes.
To Find :If they pack 3 more boxes, how many glasses will they have packed in all?
Solution:
Workers packed no. of glasses in 7 boxes = 1400
Workers packed no. of glasses in 1 box = [tex]\frac{1400}{7}[/tex]
Workers packed no. of glasses in 3 boxes = [tex]\frac{1400}{7} \times 3[/tex]
= [tex]600[/tex]
So, initially they packed 1400 glasses
If they pack 3 more boxes so, the pack 600 glasses more
So, The total no. of glasses have packed by workers = 1400+600 = 2000
Hence they have packed 2000 glasses in all.
What is the point-slope form of a line with slope 2 that contains the point (1,3)?
A. y-1 = 2(x-3)
B. y+ 3 = -2(x - 2)
c. y + 3 = 2(x+1)
D. Y-3 = 2(x - 1)
The scores on a test are normally distributed with a mean of 80 and a standard deviation of 16. What is the score that is 2 standard deviationsdeviations aboveabove the mean?
The deviation from 80 of about 16 is normal.
So the lowest is usually 80 - 16 = 64 and the highest is 80 + 16 = 96
But now we have a "deviation" that is 2 standard deviations above the mean score.
So 80 + 16 + 16 = 112 is this score.
Hope this helps.
r3t40
Final answer:
To calculate the score that is 2 standard deviations above the mean of 80 with a standard deviation of 16, you add 2 times the standard deviation to the mean, resulting in a score of 112.
Explanation:
To find the score that is 2 standard deviations above the mean on a test with a mean of 80 and a standard deviation of 16, we use the formula:
Score = Mean + (Number of Standard Deviations × Standard Deviation)
So, plugging in the numbers we get:
Score = 80 + (2 × 16)
Score = 80 + 32
Score = 112
The desired score is therefore 112, which is 2 standard deviations above the mean of 80.
evaluate x -2 y 0 / x 3 y -2 when x = 2 and y = 5
Answer:
5/8
Step-by-step explanation:
first plug in for x & y, then solve. you should get 5/8
2 -2 +5 +0 / 2 +3 +5 -2
5/8
Answer:
125/32
Step-by-step explanation:
Select the correct answer from the drop-down menu.
Divide the binomial by the monomial to find the quotient.
48r4y – 725672
-12.12y
Answer:
[tex]-(4x^2)+6(x^4)y[/tex]
Step-by-step explanation:
Here apply the law of indices where ;
[tex]A^x*A^y=A^{x+y}[/tex]
Given;
You should first simplify the numerator using the denominator as a factorThen cancel the like termFollowed by further factorization[tex]\frac{48x^4y-72x^6y^2}{-12x^2y} \\\\\\\frac{-12x^2y(4x^2-6x^4y^2)}{-12x^2y} \\\\\\=-4x^2+6x^4y\\\\\\=-(4x^2)+6(x^4)y[/tex]
Three sisters went shopping for Mother’s Day. Each sister bought a gift for their mom. Maggie spent 3 times as much as Karen. Karen spent half as much as Jasmine. All together, they spent $60. Then, solve your equation to determine how much each sister spent on their gift.
Answer:
Let j = amount Jasmine spent, k = amount Karen spent, and m = amount Maggie spent.
m = 3k, k = (1/2)j
j + k + m = $60
2k + k + 3k = $60
6k = $60
k = $10, m = $30, j = $20
Jasmine spent $20, Karen spent $10, and Maggie spent $30.
Please help me this is urgent 15 points and brainiest
If m∠EQD=(5x+2)°, what is the value of x?
=====================================================
Explanation:
The angle EQD is an inscribed angle that cuts off the arc from E to D (the shortest path). Note how central angle ECD also cuts off this same arc. By the inscribed angle theorem, we know that
inscribed angle = (1/2)*(central angle)
angle EQD = (1/2)*(angle ECD)
We can multiply both sides by 2 and flip the equation to get
angle ECD = 2*(angle EQD)
Now replace "angle EQD" with 5x+2
angle ECD = 2*(5x+2)
2*(5x+2) = angle ECD
Next, replace "angle ECD" with 104 as this is the measure of this central angle.
2*(5x+2) = angle ECD
2*(5x+2) = 104
From here, we solve for x
2*(5x+2) = 104
2*5x + 2*2 = 104
10x + 4 = 104
10x+4-4 = 104-4 ..... subtracting 4 from both sides
10x = 100
10x/10 = 100/10 ...... dividing both sides by 10
x = 10
The bearing of Q from P is 150° and the bearing of P from R is 15°.if Q and R are 244metres and 324metres respectively from P.(i) represent this information on a diagram (ii) calculate the distance between Q and R correct to two decimal place(iii) find the bearing of R from Q,correct to thr nearest degree.
Pam is playing with red and black marbles. The number of red marbles she has is three more that twice the number of black marbles she has. She has 42 marbles in how. How many red marbles does Pam have?
Answer:
29 red marbles
Step-by-step explanation:
Call R the number of red marbles and B the number of black marbles.
According to the second sentence, R = 2B + 3.
According to the third sentence, R + B = 42.
Now we have 2 equations, 2 unknowns. Sub the first into the second since it already has R isolated:
2B + 3 + B = 42
3B = 39
B = 13
Now sub this into either of the original equations (I'll use the first):
R = 2(13) + 3
R = 29
A farmer wants to put a fence around a garden in the shape of a square. The fence posts are placed every 2 meters. One side of the garden is 10m long. How many posts does the farmer need?
Answer:
The farmer would need 80 posts.
Step-by-step explanation:
If one side of the garden is 10m long, and the garden is a square, we can assume that all 4 sides will be 10m. That makes it 40m in total. Times 40×2 and you get 80.
Use numerals instead of words. If necessary use/ for the fraction bar
Answer:
10
Step-by-step explanation:
Range=big-small=34-16=18
Interquartile range=big number in box-small number in box= 29-21=8
The different between the two is 18-8=10
Answer:
The difference of range and interquartile range is 10.
Step-by-step explanation:
Consider the provided information.
From the box plot we can identify:
The lowest value is 16
The first quartile is 21
The 2nd quartile or median is 26
The 3rd quartile is 29
The highest value is 34
Range is the difference of the highest value and lowest value of the data set.
Range = 34 - 16 = 18
Interquartile range is the difference of the 3rd quartile from the 1st quartile.
IQR: 29 - 21 = 8
Thus, the difference of range and interquartile range is:
18 - 8 = 10
Hence, the difference of range and interquartile range is 10.
Which of the following is a factor of 2x^4 + 20x^3 + 50x^2?
A. 2x^3
B. x^4
C. x+4
D. x+5
Answer:
D. x + 5
Step-by-step explanation:
2x^4 + 20x^3 + 50x^2
= 2x^2 (x^2 + 10x + 25)
= 2x^2 (x + 5)^2
= 2x^2 (x + 5) (x + 5)
Answer
D. x + 5
For this case we have the following expression:
[tex]2x ^ 4 + 20x ^ 3 + 50x ^ 2[/tex]
It is observed that we can extract common factor [tex]2x ^ 2[/tex], since it is common in the three terms:
[tex]2x ^ 2 (x ^ 2 + 10x + 25) =[/tex]
If we factor the expression into parentheses, we must look for two numbers that add 10 and multiply 25. These are: 5 and 5.
Rewriting the expression we have:
[tex]2x ^ 2 ((x + 5) (x + 5))[/tex]
Thus, one of the factors of the original expression is[tex]x + 5[/tex].
Answer:
Option D
What’s the value of x
Answer:
x = 25
Step-by-step explanation:
The 2 given angles form a straight angle and are supplementary, that is
2x + 2 + 5x + 3 = 180
7x + 5 = 180 ( subtract 5 from both sides )
7x = 175 ( divide both sides by 7 )
x = 25
Use the graph of f(x) to evaluate the following:
Answer:
[tex]\large\boxed{\dfrac{1}{2}}[/tex]
Step-by-step explanation:
[tex]\text{The average rate of change of function}\ f(x)\\\text{over the interval}\ a\leq x\leq b\ \text{is given by this expression:}\\\dfrac{f(b)-f(a)}{b-a}.\\\\\text{Read from graph the values of function for}\ x=3\ \text{and}\ x=5.\\(look\ at\ the\ picture)\\\\f(3)=1,\ f(5)=2\\\\\text{Substitute:}\\\\\dfrac{f(5)-f(3)}{5-3}=\dfrac{2-1}{2}=\dfrac{1}{2}[/tex]
use natural logarithms to solve the equation 5e^3x+7=21
Answer:
5e^(3x+7)=21
e^(3x+7)=4.2
(3x+7)lne=ln4.2
lne=1
3x+7=1.435
3x= -5.565
x= -1.855
To solve the equation [tex]5e^{3x}+7=21[/tex], isolate the exponential term, take the natural logarithm of both sides, and then solve for x. This results in x ≈ 0.3362.
To solve the equation [tex]5e^{3x}+7=21[/tex], follow these steps:
First, isolate the exponential term by subtracting 7 from both sides:
[tex]5e^{3x} = 14[/tex]
Next, divide both sides of the equation by 5:
[tex]e^{3x} =\frac{14}{5}[/tex]
Now, take the natural logarithm (ln) of both sides:
[tex]ln(e^{3x}) = ln(\frac{14}{5})[/tex]
Since the natural logarithm and the exponential function are inverse operations, the left side simplifies to:
[tex]{3x} = ln(\frac{14}{5})[/tex]
Finally, solve for x by dividing by 3:
[tex]x =\frac{1}{3}\times ln(\frac{14}{5})[/tex]
Using a calculator, this results in:
x ≈ 0.3362
solve for x in the equation
I need help ASAP
Answer:
D
Step-by-step explanation:
Given
2x² + 3x - 7 = x² + 5x + 39
Subtract x² + 5x + 39 from both sides
x² - 2x - 46 = 0 ← in standard form
with a = 1, b = - 2, c = - 46
Solve for x using the quadratic formula
x = (- (- 2) ±[tex]\sqrt{(-2)^2-(4(1)(-46)}[/tex] ) / 2
= ( 2 ± [tex]\sqrt{4+184}[/tex] ) / 2
= ( 2 ± [tex]\sqrt{188}[/tex] ) / 2
= ( 2 ± 2[tex]\sqrt{47}[/tex] ) / 2
= 1 ± [tex]\sqrt{47}[/tex]
Rationalize the denominator and simplify. 6 /5-3
Final answer:
To rationalize the denominator and simplify the expression 6 / (5-3), multiply the numerator and denominator by 1/2. Then, simplify the expression to get 3/1 = 3.
Explanation:
To rationalize the denominator and simplify the expression 6 / (5-3), we can start by multiplying the numerator and denominator by a skillfully chosen factor. In this case, we can choose 1/2 as the factor.
The numerator becomes 6 * 1/2 = 3, and the denominator becomes (5-3) * 1/2 = 2/2 = 1.
Therefore, the simplified expression is 3/1 = 3.
What is the solution to the inequality X squared <49
[tex]x^2<49\\x<7 \wedge x>-7\\x\in(-7,7)[/tex]
What is the point-slope form of a line that has a slope of 1/2 and passes through point (–7, 2)?
Answer:
D
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here m = [tex]\frac{1}{2}[/tex] and (a, b) = (- 7, 2), hence
y - 2 = [tex]\frac{1}{2}[/tex] (x - (- 7)) → D
y - 2 = [tex]\frac{1}{2}[/tex](x + 7)
The point-slope form of the equation will be [tex]y-2 = \dfrac{1}{2}(x-(-7))[/tex]. The correct option is D.
In mathematics, slope refers to the measure of the steepness or inclination of a line or a curve. It quantifies the rate at which one variable changes with respect to another variable. The slope is commonly denoted by the letter "m."
Given that the slope of the line is 1/2. The point through which the line is passing is (-7,2).
The general form of the equation of the line passing through the point (-7,2) and the slope is 1/2 can be written as,
[tex]y-y_1 = m(x-x_1)[/tex]
The equation of the line in point-slope form can be written as,
[tex]y - y_1 = m(x-x_1)\\y-2=\dfrac{1}{2}(x-(-7))[/tex]
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Complete the solution of the equation. Find the value of y when x equals -7.
-4x-9y=-26
Answer:
y = 6Step-by-step explanation:
Put x = -7 to the equation -4x - 9y = -26, and solve it for y:
-4(-7) - 9y = -26
28 - 9y = -26 subtract 28 from both sides
-9y = -54 divide both sides by (-9)
y = 6
Which unit of measure would be appropriate for the volume of a cylinder that is 8 meters tall and has a radius of 4 meters
Answer: cubic meters : m³
Step-by-step explanation:
Cylinder volume is the product of area of the base by height.
Area of the base is the product of π·radius² = square meters : m²
Volume = square meters·meters = m²·m = cubic meters : m³
[tex]\textit{\textbf{Spymore}}[/tex]
Sketch the graph of y = (x - 3)2 - 25, then select the graph that corresponds
to your sketch.
Answer:
Option C. Graph C
Step-by-step explanation:
we have
[tex]y=(x-3)^{2}-25[/tex]
This is the equation of a vertical parabola open upward (vertex is a minimum)
The vertex is the point (3,-25)
therefore
The graph is C
The graph in the attached figure
Answer:c
Step-by-step explanation: