Translate the sentence into an equation.
Twice the difference of a number and 8 is 2.
Use the variable c for the unknown number.
Answers
jakajsnskshsmsjsbsb
Answer:
2×c=8 c=4
Step-by-step explanation:
Related Questions
How to solve 3.6 x 2.1? Please tell me step-by-step. Thank you!
Answers
Answer:
Multiply 36 and 21 and put point(.) after two digits
Step-by-step explanation:
7.57
Simplify -4(8) on McGraw hill
Answers
Answer:
-32
Step-by-step explanation:
A positive times a negative is a negative.
Use the quotient rule to simplify the expression. Write the expression with positive exponents.
Answers
Answer:
\(\displaystyle 4^{4}\)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Exponential Rule [Dividing]: \(\displaystyle \frac{b^m}{b^n} = b^{m - n}\)Step-by-step explanation:
Step 1: Define
\(\displaystyle \frac{4^{-4}}{4^{-8}}\)
Step 2: Rewrite
Exponential Rule [Dividing]: \(\displaystyle 4^{-4 - (-8)}\)Subtract Exponents: \(\displaystyle 4^{4}\)Quadrilateral MNPQ is rotated at 90 degrees counterclockwise about the origin and then rotated 270 degrees counterclockwise about the origin
Answers
After the double rotation, the vertices of the quadrilateral MNPQ are transformed to M'', N'', P'', and Q''. The shape of the quadrilateral may have changed, but the order of the vertices remains the same.
When a quadrilateral MNPQ is rotated counterclockwise at 90 degrees about the origin, each vertex undergoes a transformation.
The new positions of the vertices after this rotation can be denoted as M', N', P', and Q'. The order of the vertices remains the same.
Next, when the rotated quadrilateral M'N'P'Q' is further rotated counterclockwise at 270 degrees about the origin, each vertex undergoes another transformation.
The new positions of the vertices after this rotation can be denoted as M'', N'', P'', and Q''. Again, the order of the vertices remains the same.
It's important to note that a 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation.
The result of the double rotation is equivalent to a single clockwise rotation of 90 degrees.
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Please see the attached
Answers
a. Monthly payment for the bank's car loan is $407.67
b. Monthly payment for the savings and loan association's car loan is $315.99
c. Total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.
What is interest rate?The cost of borrowing money, usually expressed as a percentage of the amount borrowed, is what a lender charges a borrower to use their money. This cost is known as an interest rate.
(a) To find the monthly payment for the bank's car loan, we can use the formula for the present value of an annuity:
\(PV = PMT * \frac{1 - (1 + \frac{r}{n})^{(-n*t)}}{\frac{r}{n} }\)
putting the given values,
⇒ \(21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*5)}}{\frac{0.065}{12} }\)
Solving for PMT, we get:
PMT = $407.67
Therefore, the monthly payment for the bank's car loan is $407.67
(b) To find the monthly payment for the savings and loan association's car loan, we can use the same above formula:
where PV is still $21,000, PMT is the monthly payment, r is still 0.065, n is still 12, but t is now 7 years x 12 months/year = 84 payments.
putting the given values,
\(21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*7)}}{\frac{0.065}{12} }\)
Solving for PMT, we get:
PMT = $315.99
Therefore, the monthly payment for the savings and loan association's car loan is $315.99.
(c) Bank's car loan: $407.67 x 60 = $24,460.20
Savings and loan association's car loan: $315.99 x 84 = $26,495.16
Therefore, the bank's car loan would have the lowest total amount to pay off, by: $26,495.16 - $24,460.20 = $2,034.96
Therefore, the total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.
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find two positive numbers that satisfy the given requirements. the second number is the reciprocal of the first number and the sum is a minimum
Answers
The two positive numbers are 1 and 1, depending on the given information.
Let first number be x. So, the second number is 1/x. Now, their sum is minimum, so representing the expression for given information -
Sum (x) = x + 1/x
Rewriting the expression -
Sum (x) = x + \( {x}^{-1} \)
Finding the derivative
Sum' (x) = 1 + (-1) \( {x}^{-2} \)
Sum' (x) = 1 + (-1)/\( {x}^{-1} \)
Sum' (x) = (x² - 1)/x²
Now, to find the minimum -
x² - 1/x² = 0
Multiplying x² on Right Hand Side of the equation
x² - 1 = 0
Rewriting the equation
x = ± 1
As the numbers are positive, so x will be 1.
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Find the measure of the indicated angle in each triangle.
A)37
B)63
C)80
D)180
Answers
m∠U = 80°
total interior angle in a triangle is 180°m∠U + 37° + 63° = 180°
m∠U = 180° - 63° - 37°
m∠U = 80°
m<U be x
Apply angle sum property
\(\\ \rm\rightarrowtail x+37+63=180\)
\(\\ \rm\rightarrowtail x+100=180\)
\(\\ \rm\rightarrowtail x=80\)
-2log (6x + 1) = -6.
Answers
Given f(x)=2x^2-5x+kf(x)=2x2−5x+k, and the remainder when f(x) is divided by x-1x−1 is -22−22, then what is the value of k?
Answers
Answer:
k=20
remainder=34
Step-by-step explanation:
Solve by the quadratic formula.
a) 5
b) -1
c) 1
d) -1/2
e) 4
Answers
Answer:
I hope this helps a little bit.
Step-by-step explanation:
the answer is -1/2 or -1
Which triangle makes this statement true?
∆ABC ≅ _____
no links
Answers
Answer:
C. EFG
Step-by-step explanation:
ABC ≅ EFG
AB has the same value as EF
BC has the same value as FG
CA has the same value as GE
And one thing, even if 2 triangles are proportional like ABC and RST, if they're not congruent like ABC and EFG, then that's not the answer.
∆ABC ≅ ∆EFG (Option C) because it is congruent to ∆ABC based on the given information and the criteria for congruence between right triangles.
For the given options, triangle EFG is same as triangle ABC and is therefore congruent to triangle ABC.
To show that two triangles are congruent, we need to establish that all corresponding sides and angles are equal. We can see that all the given options is a right triangle so, we can further investigate to verify the congruence.
Now, to find the triangle congruent to ∆ABC, we need to check the options where corresponding sides and angles are equal. For congruence between two right triangles, it is sufficient to prove that:
1. Both triangles have a right angle (which we already assumed).
2. The lengths of the two legs of the right triangles are equal.
3. The lengths of the hypotenuses of the right triangles are equal.
If all three conditions are met, the right triangles will be congruent by the Side-Angle-Side (SAS) congruence rule.
It is observed that all these conditions are satisfied by ∆EFG, making the two triangles identical in shape and size. Hence, ∆ABC ≅ ∆EFG (Option C).
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What is the solution set of |-x|=-10
Answers
Answer:
No Solutions
Step-by-step explanation:
Hello!
No matter what number goes into an absolute value bracket, the number always turns into its positive form.
Since this absolute value bracket produces a negative number, there will be no solutions for any values of x.
Therefore, the solution set is No Solutions.
Ivanna is draining an aquarium. The graph shows the amount of water (in liters) in the aquarium versus time (in minutes).
(a) At what time does the amount of water in the aquarium reach 0 liters?
minutes
(b) Choose the statement that best describes how the time and amount of water are related. Then fill in the blank.
As time increases, the amount of water in the aquarium decreases.
At what rate is the amount of water decreasing?
liters per minute
As time increases, the amount of water in the aquarium increases.
At what rate is the amount of water increasing?
liters per minute
Answers
A linear function gives us the following:
a) At 0 seconds, there are 300 liters of water in the aquarium.
b) The amount of water is losing volume at a rate of 60 liters per minute as time goes on.
Given,
Linear function;-
Modeling a linear function involves:
y = ax + b
That where:
The rate of change, or a, is the slope, or how much y changes when x changes by one.B is the y-intercept, which is also known as the function's starting point and is the value of y at x = 0.The y-intercept in this problem is 300, hence 300 liters of water are present in the tank at 0 seconds.
The quantity drops by 60 liters each minute, so:
Water is losing volume at a rate of 60 liters per minute as time goes on.
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O f(x) = (x + 1)(x-2)(x - 3)
Of(x) = (x - 1)(x + 2)(x+3)
Of(x) = (x + 1)(x + 2)(x+3)
Of(x) = (x - 1)(x - 2)(x − 3)
Answers
Answer:
D) f(x) = (x - 1)(x - 2)(x - 3)-------------------------------------
The x-intercepts are the roots of the function and according to the graph the roots are:
1, 2 and 3Hence the function is:
f(x) = (x - 1)(x - 2)(x - 3)Answer:
D) f(x) = (x - 1)(x - 2)(x - 3)
Step-by-step explanation:
From inspection of the given graph, the points at which the curve intersects the x-axis are:
(1, 0)(2, 0)(3, 0)Factor Theorem
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
According to the factor theorem, as f(x) = 0 when x = 1, x = 2 and x = 3 then (x - 1) and (x - 2) and (x - 3) are factors of the polynomial.
Therefore, the equation of the function is:
f(x) = (x - 1)(x - 2)(x - 3)
imagine you and a friend are trying to rearrange the furniture in your classroom. You push on a desk with a force of 150 N to the right. Your friend pushes on the same desk with a force of 50 N to the left. What is the net force on the desk?
Answers
Answer:
100NStep-by-step explanation:
If I push on a desk with a force of 150 N to the right and my friend pushes on the same desk with a force of 50 N to the left, this means that I pushed the desk in the positive x direction and the force I applied is F1 = +150N; my friend pushes the desk in the negative x direction and the applied force will be F2 = -50N.
THe net force will the sum total of both forces acting on the desk.
Net force F = F1+F2
Given F1 = +150N and F2 = -50N
Net force F = +150N+(-50N)
Net force F = +150N-50N
Net force F = +100N
Hence the net force on the desk is 100N
I need help with this problem if do thank you a lot
Answers
The first circle have the values of x = 89° and y = 8.49. The second circle have values of x = 132° and y = 15.72. And the third circle have the value of a = 8.67.
What are circle theoremsCircle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.
For the first circle:
28° = x - 61° {secant tangent angle}
x = 28° + 61°
x = 89°
y² = 4 × 18
y = √72
y = 8.4853
For the second circle:
triangles formed by intersecting tangents are congruent so;
x = 2 × [180 - (24 + 90)]
x = 2 × 66°
x = 132°
tan 24 = 7/y {opposite/adjacent}
y = 7/tan 24
y = 15. 7223
For the third circle:
9(9 + a) = 21 × 8 {secant secant}
81 + 9a = 168
9a = 168 - 81
9a = 87
a = 87/9
a = 9.6667.
Therefore, the first circle have the values of x = 89° and y = 8.49. The second circle have values of x = 132° and y = 15.72. And the third circle have the value of a = 8.67.
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A probability distribution for various prize values is given by the following table.
Prizes Probabilities
$0.00 0.83
$100.00 0.08
$500.00 0.08
$10,000.00 0.01
Find the expected winnings. Round your answer to the nearest cent.
Answers
Answer:
$148
Step-by-step explanation:
Expected winnings = ($0.00 x 0.83) + ($100.00 x 0.08) + ($500.00 x 0.08) + ($10,000.00 x 0.01)
Expected winnings = $0.00 + $8.00 + $40.00 + $100.00
Expected winnings = $148.00
Natalie is selling fruit at the Saturday market. She has a
otal of 48 pears that she wants to sell. She makes bags of
pears and sells them for $5 per bag. In which equation
oes b represent the number of bags of pears?
Answers
If Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.
To represent the number of bags of pears, b, that Natalie sells at the Saturday market, we can use the following equation:
b = total_number_of_pears / pears_per_bag
In this equation, "total_number_of_pears" represents the total quantity of pears Natalie has, and "pears_per_bag" represents the number of pears she puts in each bag.
Given that Natalie has a total of 48 pears, we can substitute the value into the equation:
b = 48 / pears_per_bag
Now, we need to determine the number of pears she puts in each bag. The information provided states that Natalie sells bags of pears, and each bag is sold for $5. However, the specific number of pears per bag is not given. To proceed, we need this information.
Let's assume that Natalie puts 4 pears in each bag. We can substitute this value into the equation:
b = 48 / 4
Simplifying the equation gives:
b = 12
So, if Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.
It's important to note that the specific value of "pears_per_bag" will affect the final result. If Natalie puts a different number of pears in each bag, the equation will yield a different number of bags sold.
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What is the value of t that satisfies the equation below? 3(t + 4) – 2(2t + 3) = -4
Answers
Answer:
10
Step-by-step explanation:
A card is drawn from a standard deck of cards without jokers
What is the probability that the card is either black or a heart
Answers
Answer:
Step-by-step explanation:
Remark
The two black suites are
Clubs
Spades
Each of them has 13 cards so the total number of black cards is 2*13 = 26
Add to that the hearts which also has 13 cards
The total number of possible good cards is 13 + 26 = 39
Answer
P(hearts or Black) = 39/52
P(hearts or Black) = 3/4
P(hearts or Black) = 0.75
Me and my friend had an eating contest, I ate 75 biscuits with a ratio of 5:3. How many did my friend eat?
Answers
75 divided by 5 is 15.
15 times 3 is 45.
Your friend are 45 biscuits.
The people go to a restaurant. Their bill comes to $78.00. They decide to split the cost. One person pays 4.50 the next person pays 3 time that amount. How much will the their person have to pay
Answers
Answer:
13
Step-by-step explanation:
u multiply 4.50 x 3 it makes it 13.5 so they basically need to pay more .
The flu started spreading in a school. The first week after winter break, 5 students came to school sick. After each week the number of
sick students increased by 60%. Assuming the model continued for the first several weeks, what is the growth factor that would
appear in the equation for the function?
A.) 1.40
B.) 1.60
C.) 5.60
D.) 1.06
Answers
9(3.2)^2+4x-11 how to solve
Answers
The solution of the given linear equation is (103.16 + 4x).
What is meant by linear equation?Linear equations are degree 1 equations. It is the straight line equation. The standard linear equation is ax+by+c =0, where a and b are both are not zero. There are only 1 or 2 two variables in a linear equation. In a linear equation, no variable is raised to a power greater than just one or is employed as the denominator of such a fraction. When you find two values that satisfy a linear equation and plot them on a coordinate grid, each of the points fall on the same line.The given equation is;
= 9(3.2)² + 4x - 11
For finding (3.2)² = 3.2×3.2
(3.2)² = 10.24
Put the value in equation;
= 9×10.24 + 4x - 11
Multiply 9×10.24 = 92.16
Put the value;
= 92.16 + 4x + 11
Now, add the constant value
= (92.16 + 11) + 4x
= 103.16 + 4x
As, 4x is a variable part, it will not get added to the constant 103.16.
Thus, the solution of the equation is 103.16 + 4x.
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7. Which graph represents a proportional
relationship
PLEASE HELP ME
Answers
Answer:
B
Step-by-step explanation:
It's a relationship
what the answer for this area?
Answers
Answer:
the answer is 105
Step-by-step explanation:
because 5×3=15 so 15×7 =105
What is x. PLEASE HELP NEED ANSWERS NOW. M=
Answers
12x+16x+40-32=180
28x+8=180
X=180-8/28=6
I think so my calculation may be wrong )
Here is a Fill in the Gaps Question:
A prism is a three-______________ shape with the same _______________ all the way through.
Please help.
Jake :)
P.S you will get 40 pts :)
Answers
Answer:
A prism is a three-dimensional shape with the same cross-section all the way through.
Step-by-step explanation: Im not sure if i got the second right
A prism is a three-dimensional shape with the same cross-section all the way through.
A prism is a type of three-dimensional (3D) shape with flat sides. It has two ends that are the same shape and size (and look like a 2D shape).It has the same cross-section all along the shape from end to end; that means if you cut through it you would see the same 2D shape as on either end.
What is called prism?A prism has a solid shape consisting of two identical ends (such as triangle, square, rectangle, etc.), flat faces or surfaces and uniform cross-section across its length. The cross-section looks like a triangle hence called triangular prism. The shape of the prism does not have any curve.
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Which value for x makes the open sentence true?
5+4⋅x=3²+x²
a. 5
b. 4
c. 3
d. 2
Answers
Answer:
D) 2
Step-by-step explanation:
First Method: Solve for xThere are two ways to find what value of x will make this equation true. The first method is to solve for x in the equation.
The given equation is:
\(5+4*x=3^2+x^2\)Rewrite this equation by evaluating the exponent on the right side of the equation, and make 4 * x = 4x.
\(5+4x=9+x^2\)Subtract \((5+4x)\) from both sides of the equation (so we can keep the \(x^2\) positive). It's just preference.
\(0=9+x^2-5-4x\)Simplify the right side of the equation by combining like terms and rearranging terms to follow the format of \(ax^2+bx+c\).
\(0=x^2-4x+4\)Factor this quadratic by seeing what two terms multiply to \(4\) and add up to \(-4\). These two terms are \(-2\). Notice that this is a perfect square.
\(0=(x-2)(x-2)\)Solve for x by setting the expressions inside the parentheses equal to 0.
\((x-2) = 0 \\ x - 2 = 0 \\ $Add to both sides of the equation.$\\ x =2\)This means that answer choice D) 2 is correct.
Second Method: Plug in the answer choicesThe second method is to substitute the given answer choices into the equation, which works when you are given answer choices. Otherwise, the first method is ideal.
Use the form of the equation where we set all the terms equal to 0.
\(0=x^2-4x+4\)Start with answer choice A, and work your way up to D to check all of them.
A) Substitute 5 for x into the equation.
\(0=(5)^2-4(5)+4 \\ 0 = 25 - 20 + 4 \\ 0=1\)This is a false statement; 0 does not equal 1.
B) Substitute 4 for x into the equation.
\(0=(4)^2-4(4)+4 \\ 0= 16-16+4 \\ 0=4\)This is a false statement; 0 does not equal 4.
C) Substitute 3 for x into the equation.
\(0=(3)^2-4(3)+4 \\ 0=9-12+4 \\ 0=1\)This is a false statement; 0 does not equal 1.
D) Substitute 2 for x into the equation.
\(0=(2)^2-4(2)+4 \\ 0=4-8+4 \\ 0=0\)This is a TRUE statement; thus, the answer is D) 2.
Which expressions are equivalent to 24-7? Choose all the correct answers. Show your work.
Answers
The equivalent expressions to \(24^{-7}\) are given as follows:
C. \(\left(\frac{1}{24^{-7}}\right)^{-1}\)
F. \((24^3 \times 24^4)^{-1}\)
What are are equivalent expressions?Equivalent expressions are expressions that have the same value for all possible values of the variables. In other words, equivalent expressions are different ways of writing the same mathematical idea.
The exponent in the denominator can be moved to the numerator with the changed signal, hence:
\(\left(\frac{1}{24^{-7}}\right)^{-1} = (24^7)^{-1}\)
Applying the power of power rule, we multiply the powers, hence:
\((24^7)^{-1} = 24^{-7}\)
When two terms with the same base and different exponents are multiplied, we add the bases and keep the exponents, hence:
\((24^3 \times 24^4)^{-1} = (24^7)^{-1} = 24^{-7}\)
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