After evaluation we get the values as a = 8 + -0.4285714286b
Given, the expression is (7a ₊ 10)/(3b ₊ 6) = 72
Simplifying
(7a ₊ 10) ₊ (3b ₊ 6) = 72
Reorder the terms:
(10 ₊ 7a) ₊ (3b ₊ 6) = 72
Remove parenthesis around (10 ₊ 7a)
10 ₊ 7a ₊ (3b ₊ 6) = 72
Reorder the terms:
10 + 7a + (6 + 3b) = 72
Remove parenthesis around (6 + 3b)
10 + 7a + 6 + 3b = 72
Reorder the terms:
10 + 6 + 7a + 3b = 72
Combine like terms: 10 + 6 = 16
16 + 7a + 3b = 72
Solving
16 + 7a + 3b = 72
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-16' to each side of the equation.
16 + 7a + -16 + 3b = 72 + -16
Reorder the terms:
16 + -16 + 7a + 3b = 72 + -16
Combine like terms: 16 + -16 = 0
0 + 7a + 3b = 72 + -16
7a + 3b = 72 + -16
Combine like terms: 72 + -16 = 56
7a + 3b = 56
Add '-3b' to each side of the equation.
7a + 3b + -3b = 56 + -3b
Combine like terms: 3b + -3b = 0
7a + 0 = 56 + -3b
7a = 56 + -3b
Divide each side by '7'.
a = 8 + -0.4285714286b
Simplifying
a = 8 + -0.4285714286b
hence we get the solution of the equation.
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How we use scientific calculator
Answer:
I'll answer the question in the picture first.
log(6) = 1.788
log(8) = 2.079
ln(6) = 1.792
ln(8)= 2.08
How to use a scientific calculator?
There are many different types of scientific calculators, so it is difficult to give a single answer to this question. However, most scientific calculators have a variety of buttons that perform different functions. Typically, there are buttons for the four basic operations ( addition, subtraction, multiplication, and division), as well as buttons for more complex functions such as square roots and exponential operations. To use a scientific calculator, simply press the buttons corresponding to the operations you want to perform.
Step-by-step explanation:
how should i find the volume of the sphere?
Answer:
Volume of sphere = 4.187x³
Step-by-step explanation:
[tex]\textsf {Volume of a sphere = $\dfrac{4}{3} \pi {r^2 }$}[/tex]
Here r = x
[tex]\textsf {Volume = $\dfrac{4}{3} \pi {x^2 }$}[/tex]
[tex]\textsf {Volume of cuboid = $4x^3$}\\[/tex]
[tex]\textsf {volume of sphere = $\dfrac{4}{3}\pi \cdot x^3$}[/tex]
[tex]\textsf {Since $\pi \approx 3.14$, this is} \approx \dfrac{4\cdot (3.14)}{3} x= 4.187x[/tex]
So volume of sphere of radius x = 4.187x³ is greater than cuboid volume of 4x³
a bucket holds c liters of water but a jar holds d liters more how much water do they hold together
The bucket and the jar together will hold (c + d) litres of water.
What is defined as linear equation on two variables?A linear function does have a positive relationship, so increasing one variable (input variable) causes a rise in the second variable (output variable), implying that the variables have always been directly proportional. As a result, the graph of such a linear function is a straight line with a constant slope.Correspondingly, a linear equation is a first-order algebraic equation with two variables and terms with exponents of one.A linear equation in 2 variables [x and y] is any equation with the form:
ax + by = c and at least one of a or b being non-zero.
This is known as the equation's General Form.
For the given question;
The water hold by bucket = c litres.
The water hold by jar = d litres.
Thus, the water hold by both bucket and jar is is linear equation with two variable c and d.
Total water = c + d
By, varying any value the total amount of the water will also get change.
Thus, total water hold by jar and bucket is (c + d) litres.
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A certain state uses the following progressive
tax rate for calculating individual income tax:
Income
Progressive
Range ($)
Tax Rate
0 - 3000
2%
3001 - 5000
3%
5001 - 17,000
5%
17,001 and up
5.75%
Calculate the state income tax owed on an $80,000
per year salary.
tax = $[?]
Round your answer to the nearest whole dollar amount..
Enter
Answer:
4600
Step-by-step explanation:
80000 is in 17001 and up category so the tax will be 5.75%. 80000/100 *5.75 = 4600
Line A passes through (0, -3) and (5, -1). Find the equation of Line A.
Answer:
[tex]y=\frac{2}{5}x-3[/tex]
or
[tex]y+3=\frac{2}{5} (x-0)[/tex]
Step-by-step explanation:
Finding the Equation of a Line Given Two Points:In order to find the equation of a line, we must identify point (x,y) and slope (m). Slope formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Point-slope formula: [tex]y-y_1=m(x-x_1)[/tex]Slope-intercept formula: [tex]y=mx+b[/tex]We are given two points on Line A: (0,-3) and (5,-1). We can assign each integer to a variable in the slope formula (see above):
[tex]x_1=0[/tex]
[tex]y_1=-3[/tex]
[tex]x_2=5[/tex]
[tex]y_2=-1[/tex]
As we have identified point, we can now work to identify slope by substituting our points into the slope formula:
[tex]m=\frac{-1-(-3)}{5-0}=\frac{2}{5}[/tex]
Now that we have identified both point and slope for Line A, we can format these values in point-slope form. Substitute values into the formula:
[tex]y-(-3)=\frac{2}{5} (x-0)=y+3=\frac{2}{5}x[/tex]
Solve for [tex]y[/tex] to achieve an answer in slope-intercept form ([tex]y=mx+b)[/tex]:
[tex]y=\frac{2}{5} x-3[/tex]
Please explain how to do this, I have no clue!!!! Literally will give 50 points! Maybe even brainliest, just explain how to do it!!!
Solve the following equation. x/6 + 4 = 20 Then place the correct number in the box provided.
Answer:
x = 96
Step-by-step explanation:
[tex]\frac{x}{6} +4=20[/tex]
1. Isolate the variable 'x'.
1a. Subtract 4 so the equation becomes [tex]\frac{x}{6} =16[/tex]
2a. Multiply both sides by 6 to turn the fraction into a normal number, which becomes x=96.
Answer:
[tex] \sf \large \: x=96[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
x/6+4=20
Step 1: Simplify both sides of the equation.
1/6x+4=20
Step 2: Subtract 4 from both sides.
1/6x+4−4=20−4
1/6x=16
Step 3: Multiply both sides by 6.
6*(1/6x)=(6)*(16)
x=96
The following tables represent a function and its inverse. Compare the functions.
h(x)
h–1(x)
Which statements describe the functions? Check all that apply.
The domain of h–1(x) is the range of h(x).
The range of h–1(x) is the range of h(x).
The x-intercept of h–1(x) is the x-intercept of h(x).
The x-coordinate of the x-intercept of h–1(x) is the y-coordinate of the y-intercept of h(x).
The maximum of h(x) is the largest x-value of
h–1(x).
the 3 correct statements are:
The domain of h⁻¹(x) is the range of h(x).The maximum of h(x) is the largest x-value of h⁻¹(x).The x-coordinate of the x-intercept of h⁻¹(x) is the y-coordinate of the y-intercept of h(x).Which statements describe the functions?For a function f(x), we define the inverse function f⁻¹(x):
This means that, if for a given value of x = x₀ we have:
f(x₀) = y₀
Then:
f⁻¹(y₀) = x₀
From this, we can conclude that the domain of f(x) is the range of the inverse, and the range of f(x) is the domain of the inverse.
Then the statements that are correct are:
The domain of h⁻¹(x) is the range of h(x).The maximum of h(x) is the largest x-value of h⁻¹(x).The x-coordinate of the x-intercept of h⁻¹(x) is the y-coordinate of the y-intercept of h(x).These 3 are the 3 correct statements.
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Given the following values, find the perimeter of the figure shown below:
AB = 8 cm, BC = 3 cm, CD = 1 cm, DE = 2 cm, EF = 3 cm, and FG = 1 cm.
Do not include "cm" with your response.
The perimeter of the given figure for the given values is equal to 24units.
As given in the question,
Given values of the figure,
AB = 8 cm, BC = 3 cm, CD = 1 cm, DE = 2 cm, EF = 3 cm, and FG = 1 cm
HG = AB - (EF + CD)
= 8- (3 +1)
= 4 units
AH = (BC-DE)+FG
= (3-2)+1
=2units
Perimeter of the given figure
= AB + BC+ CD+ DE+ EF+ FG+ GH+ HA
= 8+ 3+ 1+ 2+ 3+ 1+ 4+ 2
=24 units
Therefore, the perimeter of the given figure for the given values is equal to 24units.
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Find last year's salary if, after 2% pay raise, this year's salary is 37,740
The last year's salary is found as 33078.43.
How do you calculate the percentage of a number?Divide the value by the total value as well as multiply the result by 100 to get the percentage. (amount/total amount), the formula for determining the percentage is 100%.
A percentage is defined as a portion of the whole expressed in the form of 100. There are two ways to calculate a percentage:
The unitary method is implemented.By changing the denominator of the fraction to 100.As per the given question;
The salary for the current year is given as 37,740.
There is the increase in 2%.
Let the last year's salary be x.
Then 2% of x will be;
x + 2%of x = 37,740
x + 2x/100 = 37,740
x + 0.02x = 37,740
1.02x = 37,740
x = 37,740/1.02
x = 33500
Therefore, the value of last year's salary is was 33,500.
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Select the Correct answer: Josh rents a kayak at a nearby state park. He pays a flat rate of $12.99 plus $3.75 for each hour that he spends in the water. How much did Josh spend if he was on the river for 4 1/2 hours? $16.88, $29.87, $16.74, $28.74
Answer:12.99+ 3.75x= total. therefore, 12.99+3.75(4)= 27.99
Step-by-step explanation:
tho
For a ride on a rental scooter, Jose paid a $6 fee to start the scooter plus 8 cents per minute of the ride. The total bill for Jose's ride was $16.48 . For how many minutes did Jose ride the scooter?
Answer:
40
Step-by-step explanation:
Answer:
6+8x=
16.8
x=
Step-by-step explanation:
A football team lost 5 yards on each of four plays what was their overall change in position
Answer: -20 yards
Step-by-step explanation:
Loss in 5 yards ==> -5 yards
-5*4=-20 yards
What is 5 1/4 hours after 7:00 p.m
Answer:
12:15 or a quarter past 12
Step-by-step explanation:
Math.
The correct answer is: " 12:15 a.m."
Step-by-step explanation:
1 hour = 60 minutes {"exact equivalent."}
⇒ p.m. = afternoon or evening;
{Note: "p.m." stands for: post meridiem —in Latin terminology.}.
____
7 hours + 5 hours = 12 hours; 12 hours + [tex]\frac{1}{4}[/tex] hours = 12[tex]\frac{1}{4}[/tex] hours.
____
1) 1st hour: 7 pm - 8 pm
2) 2nd hour: 8 pm - 9 pm
3) 3rd hour: 9 pm - 10 pm
4) 4th hour: 10 pm - 11 pm
5) 5th hour: 11 pm - 12 am ;
Note: After 5 [five] hours past 7:00 pm;
The determined time, at this stage of solving this problem, is: 12am ; {commonly known as midnight ; based on the "am/pm" time schedule.
{Note: "a.m." stands for: ante meridiem— in Latin terminology.}
Then: we add: " [tex]\frac{1}{4}[/tex] " hour to: 12 am.
____
[tex]\frac{1}{4}[/tex] hr = 0.25 hr.
{ [tex](\frac{1}{4} hr )* \frac{60minutes}{hr} =?[/tex] } ;
→ The units of "hr" [for: "hour(s)"]; cancel out ; since: "[ (hr ÷ hr) = 1 ] ".
and we have: [tex]\frac{1}{4}* 60= 60/4 =[/tex] [tex]15 min.[/tex]
____
So: 12am + 15 minutes; which is: 12:15 a.m. → the correct answer.
Hope this is helpful to you!
Best wishes in your academic endeavors!
____
4.
STEM In 10 minutes, a heart can beat 700 times. At this rate,
in how many minutes will a heart beat 140 times? At what rate.
can a heart beat? (Example 4)
According to the average rate, Heart can beat 140 times in = 2 minutes and Rate of heart beat= 70 beat per minute .
According to the statement
We have to find that the rate of the heart beat.
So, For this purpose, we know that the
Average rate is a measure of how much the function changed per unit, on average, over that interval.
From the given information:
In 10 minutes, a heart can beat 700 times. At this rate,in how many minutes will a heart beat 140 times?
Then
Heart can beat 700 times in = 10 minutes .
Heart can beat 140 times in = 10*140/700 minutes .
Heart can beat 140 times in = 1400/700 minutes .
Heart can beat 140 times in = 2 minutes .
Rate of heart beat : 140/2 beat per minute.
Rate of heart beat= 70 beat per minute .
Therefore, According to the average rate, Heart can beat 140 times in is 2 minutes and Rate of heart beat is 70 beat per minute.
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Lauren was trying to approximate the solution to n² = 115. She said that it lies
between √100 and √121. Therefore, it lies between 4 and 5, however a little closer
to 5. She approximated it to be about 4.7. Do you agree or disagree with her
reasoning? Explain.
What she approximated as 4.7 is not correct because the nearest perfect squares are 10 and 11 which are different from what she got.
How to find the square root of a number?We are told that Lauren is trying to approximate the solution to n² = 115.
Now, she has figured out that it lies between √100 and √121..
Now, √100 = 10 and √121 = 11. Thus, we can say that if she says it is between 4 and 5, then she is wrong because the nearest perfect squares are 10 and 11 which are different from what she got.
Thus, what she approximated as 4.7 is not correct.
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find the measure of the indicated angle that makes lines u and v parallel
To make lines u and v parallel, the indicated angle must be 108°.
What are angles?An angle is a figure in Plane Geometry formed by two rays or lines that share a common endpoint. "Angle" comes from the Latin word "angulus," which means "corner." The two rays are referred to as the sides of an angle, and the common endpoint is referred to as the vertex.So, if two parallel lines n and m intersect, then all the angles generated in line m must be exactly the same as the angles generated in line n.
At the intersection of two lines, two adjacent angles must add up to 180°.According to the first criterion, the missing angle denoted by a "?" must have the same measure as the angle just below the 72° angle.According to the second (and previously used) criterion, we must have:
? + 72° = 180°When we solve that, we get:
? = 180° - 72° = 108°Therefore, to make lines u and v parallel, the indicated angle must be 108°.
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A rectangular cardboard has dimensions as shown. The length of the cardboard can be found by dividing its area by its width. What is the length of the cardboard in inches?
Rectangle with width labeled on the right, width equals 3 and 1 over 4 inches. Below the rectangle, it says, length equals question mark. Inside the rectangle, it says, area equals 21 and 2 over 3 square inches. answers: 5 and 1 over 12
6 and 2 over 3
18 and 5 over 12
56 and 1 over 3
The Length of the rectangle is: B. 6 2/3.
How to Find the Length of a Rectangle?The area of a rectangle is calculated as: Area = (length)(width). Therefore, if we known the area of a rectangle and its width, we can find the length of the rectangle using:
Length of rectangle = area of rectangle / width of rectangle.
Given the following:
Area of a rectangle = 21 and 2 over 3 square inches
Width = 3 and 1 over 4 inches
Length of the rectangle = 21 2/3 ÷ 3 1/4
Length of the rectangle = 65/3 ÷ 13/4
Length of the rectangle = 65/3 × 4/13
Length of the rectangle = 260/39 = 6 2/3.
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A clothing store sells 300 skirts in January of the number of skirt it sells in February is 40% higher how many skirts will it sell
In February, it will sell 420 skirts.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
A clothing store sells 300 skirts in January.
The number of skirts it sells in February is 40%,
that means,
the number of skirts,
= 300 x 1.4
= 420 skirts.
Therefore, It will sell 420 skirts.
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how do i d+2 in words
Answer:
9
Step-by-step explanation:
what is 0.2 writen as a %
i (x)=x² +3
j (x)=4x-3
Find (ij) (-1)
Delcie is asked to rewrite the expression 500 using an exponent. How should Delcie
correctly rewrite the expression?
Graph the inequality.
y < −x + 3
The graph is attached below.
The given inequality is:y < -x + 3On rearranging,x + y < 3To graph the inequality, first of all, we need to draw the corresponding equation of line on the graph.The corresponding equation of a line for an inequality can be found by replacing the less than or greater than sign with an equal to sign.The corresponding equation for the given inequality is:x + y = 3The two points which satisfy the above equation of line are (0, 3) and (3, 0).Plot the line on the graph.Now, put the coordinates of the origin into the inequality.If the inequality holds true, then shade the area from the line towards the origin and vice versa.Thus, the graph of the inequality is obtained.To learn more about equations, visit :
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The sum of an integer and 7 times the next consecutive odd integer is 6. Find the value of the greater integer.
The value of the greatest integer is equal to 1.
We are given that:
The sum of an integer and 7 times the next consecutive odd integer is 6
Consecutive numbers are the numbers that follow each other continuously in the order from smallest to largest. For example 34 and 35.
Let the first number be x.
Second number = x + 2 ( as we need an odd integer)
ATQ:
x + 7( x + 2) = 6
x + 7 x + 14 = 6
8 x = 6 - 14
8 x = - 8
x = - 1
x + 2 = - 1 + 2
= 1
Therefore, the value of the greatest integer is equal to 1.
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the answer is 1.
i just did this question on delta
Solve the following pair of simultaneous equations by drawing a graph.
y – 2x = 1 and 2y – x = 8
Answer:
[tex]x = 2[/tex]
[tex]y = 5[/tex]
Step-by-step explanation:
The graph is in the attached image above
Answer:
(2, 5)=======================
Given equations:
y - 2x = 1 and2y - x = 8Solve by graphing, graph each line and find the point the lines intersect, this point is the solution.
See the attached, the solution is (2, 5)
True or False : If a collection has two sets of values that appear the same amount of time and more than any other number in the set , it is considered bimodal .
Answer:
Step-by-step explanation
it is true
ynthia Besch wants to buy a rug for a room that is 20 ft wide and 26 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 280 square feet of carpeting. What dimensions should the rug have?
Answer:
Step-by-step
For which value of x is line l parallel to line m?
(Click document to see image.)
Answer:
x = 30°
Step-by-step explanation:
If l and m are parallel lines, then corresponding angles should be congruent.
3x - 20 = 2x + 10
Add 20 to both sides,
3x = 2x + 10 + 20
3x = 2x + 30
Subtract 2x from both sides,
3x - 2x = 30
x = 30
what property is
-2(x-y)=-2x+2y
Answer:
Distributive.
Step-by-step explanation:
This is the distributive property. :)
What does it mean when an answer has the positive and negative sign at the same time?