After solving the equation the value of F = (3GR -G - 8S) / 5S
Define Algebraic Expression
In mathematics, an expression that includes variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.)
Given expression is,
5F + 8 / G = 3R - 1 / S
Multiply both side by G
( 5F + 8 / G ) * G= (3R - 1 / S) * G
Simplify it,
5F + 8 = G(3R - 1) / S
Now, solve for F
5F = (3GR - G / S )- 8
5F = 3GR - G - 8S / S
F = 3GR - G - 8S / 5S
Hence, After solving the equation the value of F = (3GR -G - 8S) / 5S
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I need help pls someone I’ll give brainliest and tons of points
Answer: rotation 90 degrees counterclockwise about the origin I believe. lmk
Step-by-step explanation: counterclockwise is the key word. im jus using common sense cuz counterclock wise is from the left, and there is a rotation. lmk if it wrong tho
Being called a failure help
Determine the value of h in the equation one seventh plus h equals nine sevenths.
eight over forty nine
ten over forty nine
eight sevenths
ten sevenths
The value of h in the statement one-seventh plus h equals nine sevenths
is 8/7.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
The main concept of numerical expression is to interpret the data and convert it into numbers and their operations.
The given statement one seventh plus h equals nine sevenths can be numerically expressed as (1/7) + h = (9/7).
h = 9/7 - 1/7.
h = (9 - 1)/7.
h = 8/7.
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8) Micaela and Sumalee each improved their yards by planting hostas and shrubs. They bought their
supplies from the same store. Micaela spent $33 on 3 hostas and 6 shrubs. Sumalee spent $42 on 6
hostas and 6 shrubs. What is the cost of one hosta and the cost of one shrub?
Cost of shrub is $4 and Cost of hosta is $3. Cost is the value of money that was spent on producing or providing a service and is therefore no longer available for use.
How to calculate cost ?The term "cost" can refer to the amount of money or other resources that are required to produce, acquire, or obtain something. In business and economics, cost is often used to refer to the total expense associated with a product or service, including materials, labor, and other expenses.
Micaela spent a total of $33 on 3 hostas and 6 shrubs. Since the cost of the hostas is H x 3 and the cost of the shrubs is S x 6, we can write the following equation:
H * 3 + S * 6 = 33
Similarly, Sumalee spent a total of $42 on 6 hostas and 6 shrubs, so we can write the following equation:
H * 6 + S * 6 = 42
cost 3 hostas and 6 shrubs = $33
cost 6 hostas and 6 shrubs = $42
Cost difference 33 - 42 = 9
So, cost of 3 hostas = $9
Cost of one hosta = $9/3 = $3
$9 + cost of 6 shrubs = $33
cost of 6 shrubs = $33- $9 = $24
Cost of one shrub = $24/6 = $4
Cost of shrub is $4 and Cost of hosta is $3.
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Two systems of equations are given below.
For each system, choose the best description of its solution.
If applicable, give the solution.
System A
x+3y=9
-x-3y=9
System B
-x-3y=-3
x+3y=3
O The system has no solution.
O The system has a unique solution:
(x, y) = (
O The system has infinitely many solutions.
They must satisfy the following equation:
y = 0
O The system has no solution.
O The system has a unique solution:
(x, y) = (D)
O The system has infinitely many solutions.
They must satisfy the following equation:
y=0
The system A has no solution.
The system B has the solution y=( 3-x )/3
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
System A:
x+3y=9..........(1)
-x-3y=9 ..........(2)
(1) => x=9-3y........(3)
Substitute (3) into (2)
(2) = > - ( 9-3y ) - 3y = 9
-9 + 3y - 3y = 9
-9 =9
This is false.
So, the system has no solution.
System B:
-x-3y=-3..........(1)
x+3y=3..........(2)
(2) => x=3-3y........(3)
Substitute (3) into (1)
-(3-3y)-3y=-3
-3+3y-3y= -3
-3=-3
This is true,
So, the solution is:
x=3-3y
=> 3y= 3-x
=> y=( 3-x )/3
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Express the radical using the imaginary unit, i.
Express your answer in simplified form.
±√-27 = ±
Answer:
±3i√3
= -3i√3 or 3i√3
Step-by-step explanation:
Simplify the complex radical
Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The equation that is a quadratic is 2(x + 5)4 + 2x² + 5 = 0
Option C is the correct answer.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
A quadratic equation is an equation with a second degree in x.
Now,
[tex]x^4[/tex] – 6x² – 27 = 0
This is not second-degree in x.
3[tex]x^4[/tex] = 2x
3x³ = 2
This is not the second degree in z.
2(x + 5)4 + 2x² + 5 = 0
8x + 40 + 2x² + 5 = 0
2x² + 8x + 45 = 0
This is in the second degree in x.
6(2x + 4)2 = (2x + 4) + 2
24x + 48 = 2x + 4 + 2
22x + 42 = 0
This is not in the second degree of x.
6[tex]x^4[/tex] = -x² + 5
This is not in the second degree of x.
8[tex]x^4[/tex] + 2x² – 4x = 0
This is not in the second degree of x.
Thus,
The quadratic equation is 2(x + 5)4 + 2x² + 5 = 0
Option C is the correct answer.
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5. Determine if a triangle with the following measurements is a right triangle. a=14, b=16, c=18
Explain why or why not.
No. 14+16 does not equal 18
Yes. 14²+16^2=18²
Yes. The longest side is c, which is 18.
No. 14²+16² does not equal 18²
The given measurement not forming the right triangle. So the option D is correct.
In the given question, we have to determine if a triangle with the following measurements is a right triangle.
The given measurement is:
a=14, b=16, c=18
We have to explain why or why not the given statement is correct or not.
The given options are:
(a) No. 14+16 does not equal 18
(b) Yes. 14^2+16^2=18^2
(c) Yes. The longest side is c, which is 18.
(d) No. 14^2+16^2 does not equal 18^2
As we know that the given measurement form right triangle we he follows the Pythagorean Theorem.
To prove the right triangle, the square of largest value is equal to the sum of square of other two values. So;
18^2 = 14^2+16^2
324 = 196 + 256
324 = 452(False)
So, the given measurement not forming the right triangle. So the option D is correct.
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Larissa sold 50 items at the state fair and made $450. She sold compact mittors and small pouches. Each mirror is $7 and each pouch is $12.
Write and solve a system of equations to represent the given scenario.
What does the solution to the system of equations represent in the context of the problem? Explain.
The equations are x+y=50 and 7x + 12y = 450
x = the number of mirrors = 30
y = the number of pouches = 20
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Let x be the number of mirrors
Let y be the number of pouches
x+y=50......(1)
Each mirror is $7
cost of x mirrors = 7x
Each pouch is $12.
cost of y pouches = 12y
7x + 12y = 450 .........(2)
(1) => x=50-y ...........(3)
Substitute (3) into (2)
(2) => 7(50-y) + 12y = 450
350 - 7y + 12y = 450
5y = 450 - 350 = 100
y= 100/5 = 20
(1) => x = 50 - 20 = 30
Thus, x = the number of mirrors = 30
y = the number of pouches = 20
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in the figure below measaure of angle 1 is 36. find angle 2,3, and 4
Zachary recorded the grade-level and instrument of everyone in the middle school
School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar
Bass
Drums
Keyboard
7
14
15
9
Eighth Grade Students
Instrument # of Students
Guitar
Bass
Drums
Keyboard
2
15
2
11
Based on these results, express the probability that an eighth grader chosen at
random will play the drums as a percent to the nearest whole number.
Percent to the nearest whole number = 7%
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Probability = (Number of possible outcomes)/(Total number of outcomes)
Total number of outcomes = 2 + 15 + 2 + 11 = 30
Number of possible outcomes = 2
Probability = 2/30 = 1/15 = 0.0666
Percent to the nearest whole number = 0.0666 *100 = 7%
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Answer:7
Step-by-step explanation:
Solve the inequality 4x≥60. Then describe how the graph of the solution would look on a number line.
The inequality of the solution is x > 15.
How to solve inequality?Make use of the following procedures to solve an inequality:
Step 1: Remove fractions by multiplying all terms by the fractions' lowest common denominator.Step 2 Combine like terms on both sides of the inequality to simplify.Step 3 Obtain the unknown on one side and the integers on the other by adding or subtracting amounts.We need to eliminate the coefficient that multiplies the variable in this linear inequality in order to isolate it.
By dividing both sides by 4, this may be done.
The inequality of the solution is
4x≥60.
=[tex]\frac{4x}{4} \geq\frac{60}{4} \\\\= \frac{x}{1} \geq 15\\\\x\geq 15[/tex]
The inequality of the solution is x > 15.
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explain how to solve the equation 16 + 7/x = 24
Answer:
x=8/7
Step-by-step explanation:
16+7/x=24
Subtract 16 on each side
7/x=8
multiply 1/7 on each side
x=8/7
1. Find x Round to the nearest tenths place.
12.2
24.5
11.8
8.4
The value of x is 11.8. So the option c is correct.
In the given question, we have to find the value of x.
The given options are:
(a) 12.2
(b) 24.5
(c) 11.8
(d) 8.4
To find the value of x we use the trigonometry ratio.
As we know that cosine is the ration of adjacent side and hypotenuse.
From the given diagram
Cos(46) = x/17
Now simplifying
0.695=x/17
Multiply by 17 on both side, we get;
x = 11.8
Hence, the value of x is 11.8. So the option c is correct.
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I have finished half of this problem but i am still unsure on how to finish.
Answer:
Triangle PQR maps onto triangle KLM. This is possible because △PQR ≅ △KLM by ASA, and one congruent figure can be mapped onto another using rigid motions.
Step-by-step explanation:
For the first blank, we are given congruence statements for 1 side on each triangle and their two adjacent angles. This means we can use the Angle-Side-Angle theorem to declare △PQR and △KLM congruent.
For the second blank, we know that rigid transformations do not change the figure, they simply move its position on a plane, so this is the correct answer; had the △PQR and △KLM not been congruent, a non-rigid transformation would have to have occured, but this is not the case here.
Answer:
ASArigidStep-by-step explanation:
Given triangles PQR and KLM with QR ≅ LM, ∠Q ≅ ∠L, and ∠R ≅ ∠M, you want to know the applicable congruence postulate and whether the triangles are mapped to each other by rigid or non-rigid motion.
Sides and anglesThe segment QR has angle Q at one end and angle R at the other end. That means the side lies between the two angles. Likewise, segment LM lies between angles L and M.
When claiming congruence of these triangles, the appropriate postulate is the one that refers to the geometry with the congruent side between the congruent angles: ASA.
Motion"Rigid" motion is motion that preserves angle and length measures. By contrast, "non-rigid" motion may involve stretching or compression in one or more directions. It may or may not preserve angles or lengths.
Congruence is about showing that angles and lengths are the same from one figure to another. If you want to map congruent figures to each other, you must do so using rigid motion.
__
Additional comment
The rigid motions include ...
translationrotationreflection.<95141404393>
What is the constant of proportionality, k, for the data in the table above? Enter answer
Enter just the numeric answer.
Answer:
you really just click on peoples questions and just be like sorry im just here for the points so im doing it to you
Step-by-step explanation:
Planning to finance her education helps people prepare for their financial future because it teaches them about
loans and interest.
savings accounts.
filing taxes
short-term goals.
Simplify the expression 3x(-2x + 5).
O 6x + 5
O 6x + 15
O-6x² +5
O -6x² + 15x
Step-by-step explanation:
3x(-2x + 5) = 3×-2×x×x + 3×5×x =
= -6x² + 15x
so, the 4th answer option is correct.
decide whether you can use the given information to prove that $\triangle abc\cong\triangle def$ . explain your reasoning. $\angle c\cong\angle f,\ \overline{ab}\cong\overline{de},\ \overline{bc}\cong\overline{ef}$
According to SAS congruent the △abc congruent △def. Thus using the given information, it can be prove.
What is congruent?
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
There are four rules to prove congruency. They are SAS, AA, ASA, and SSS.
Given that ∠c ≅ ∠f
ab ≅ de
bc ≅ ef.
According to SAS rule, if two sides and one angle of a triangle is equal to two sides and one angle of another triangle, they the triangle are congruent.
Here two sides and one angle of △abc is congruent of two sides and one angle of △def.
Therefore △abc congruent △def.
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X/5= -2 in one step?
Answer:
To solve the equation X/5 = -2 in one step, we can multiply both sides of the equation by 5 to isolate the variable X. This gives us the equation X = -2 * 5 = -10. Therefore, the value of X that satisfies the equation X/5 = -2 is X = -10.
Step-by-step explanation:
Approximate √/46 to the tenths place.
Answer:
To approximate the square root of 46 to the tenths place, we need to find the two-digit number that is closest to the square root of 46. Since the square root of 46 is between 6 and 7, we can estimate that it is about 6.5. We can check this estimate by finding the square of 6.5, which is 42.25. This is close to 46, but it is still a little bit lower than 46, so we can estimate that the square root of 46 is slightly larger than 6.5. Therefore, an approximation of the square root of 46 to the tenths place is 6.6.
Step-by-step explanation:
The table shows the total amount D in dollars that Dave charges to clean windows in r rooms he charges the same amount per room to clean windows complete the table to show the amount that each person charges to clean our rooms
The individual charges of Nikki and Dave are mentioned in the table -
Nikki Dave
$20 $12.5
$40 $25
$60 $37.5
$80 $50
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.The complete question is shown in the image attached in the end.
For Nikki, the charge function is given as -
n = 20r
We can write the charge function for Dave as follows.
We have the following points -
(1, 12.50) and (4, 50)
The charge function is equivalent to -
n = {(50 - 12.5)/(4 - 1)}r
n = (37.5/3)r
n = 12.5r
We can write the table for both Nikki and Dave as -
Nikki Dave
$20 $12.5
$40 $25
$60 $37.5
$80 $50
Therefore, the complete table representing the individual charges of Nikki and Dave are -
Nikki Dave
$20 $12.5
$40 $25
$60 $37.5
$80 $50
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which relation is a function
Answer:
top right :)
Step-by-step explanation:
you can use the ruler trick! if you drag a ruler across the math problem and it crosses two lines at the same time then it's not a function. same goes for points. and as you can see if I were to drag a ruler across this one you won't pass two points at once!
The assets and liabilities of a doctor are listed below.
Home Value $475,732
Mortgage $105,678
Credit Card Balance $7,264
Owned Work Equipment $45,798
Car Value $50,761
Investments $75,283
Personal Loan $32,187
What is the total value of the doctor's capital assets?
$45,798
$50,761
$572,291
$647,574
Answer: $647,574
Step-by-step explanation:
Capital assets are significant pieces of property such as homes, cars, investment properties, stocks, bonds, and collectibles or art. For businesses, a capital asset is an asset with a useful life longer than a year that is not intended for sale in the regular course of the business's operation.
The capital asset is recorded as its value regardless of any loan that may have been used to purchase it.
Capital assets here are: Home value, work equipment, car, and investments.
All other items are liabilliabilities.
The total value of the doctor's capital assets will be $647,574. Then the correct option is D.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
Significant pieces of property including houses, automobiles, rental properties, stocks, bonds, and collectibles or works of art are referred to as capital assets. An asset having a useful life longer than a year that is not intended for sale during normal company operations is referred to as a capital asset for enterprises.
The assets and liabilities of a doctor are listed below.
Home Value $475,732
Mortgage $105,678
Credit Card Balance $7,264
Owned Work Equipment $45,798
Car Value $50,761
Investments $75,283
Personal Loan $32,187
The total value of the doctor's capital assets will be given as,
⇒ $475,732 + $45,798 + $50,761 + $75,283
⇒ $647,574
The total value of the doctor's capital assets will be $647,574. Then the correct option is D.
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Mr. Johnson predicted the average score on the vocabulary test he gave would be 85 points.
His prediction was 8% lower than the actual average score. What was the actual average
score on the vocabulary test?
Round your answer to the nearest tenth.
The actual average score on the vocabulary test is 91.8.
How to calculate the score?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Here, Mr. Johnson predicted the average score on the vocabulary test he gave would be 85 points and his prediction was 8% lower than the actual average score.
The actual score will be:
= 85 + (8% × 85)
= 85 + 6.8
= 91.8
The actual score is 91.8.
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special Right triangles I just need the values of x,z, and y
Answer:
x = 17√3 ; y = 34√2 ; z = 34
Step-by-step explanation:
angle 30° = hypotenuse double of leg
hypotenuse = 17 · 2 = 34
x = 17 · √3 = 17√3
Angle of 45 degrees = two equal legs
z = 34
For the Pythagorean theorem
y = [tex]\sqrt{34^2 + 34^2} = \sqrt{2 (34)^2} = 34\sqrt{2}[/tex]
Answer:
Your answer is: x = 17√3 ; y = 34√2 ; z = 34. Hope it helps.
Step-by-step explanation:
How does the graph of g(x) = −(x + 3)^4 compare to the parent function of f(x) = x^4?
The 9th term of an arithmetic sequence is -5 and the 15th term is 31 find an expression for the nth term explicitly in term of n
The expression for the nth term is aₙ = 37+6n
What is an arithmetic sequence?An arithmetic sequence is a type of sequence in which the difference between the successive and preceding term is constant.
Given that, The 9th term of an arithmetic sequence is -5 and the 15th term is 31
The formula for nth term is given by;
aₙ = a+(n-1)xd
Where, a is the first term
n = number of terms
d = common difference
a₉ = a+(9-1)xd
a+8d = -5.......(i)
And
a₁₅ = a+(15-1)xd
a+14d = 31........(ii)
Solving the equation, we get,
d = 6
Putting, d = 6 in eq(i)
a+8x6 = -5
a = -5+48
a = 43
Now solving for nth term,
aₙ = 43+(n-1)x6
aₙ = 43+6n-6
aₙ = 37+6n
Hence, the nth term is (37+6n)
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What fraction is equal to 100 % ?
5/5
10/100
2/1
100
Answer:5/5
Step-by-step explanation:
5 divided by 5 is 1
A car repair company charges a $15 fee for an evaluation plus an hourly rate for any services required. What is the hourly charge for services? (Hint: the hourly charge is the slope)
If the fixed cost is $15, it is able to be removed from the two-hour charge to give the charge of ONLY the two hours, which is $150.
This means the hourly charge is $150÷2, which is $75
What is the percent error when an exact distance of 15 meters is approximated at 14.75 meters?
Answer:
98.3% or 98% if your doing sig. figs.
Step-by-step explanation:
you take 14.75 (the approximated) and divide it by the actual 15