If the width of the painting is w, then its length is 2w. Then, since the frame is 2 inches thick on each side of the painting, its width is w+4 and its length is 2w+4. So the area of the rectangle bounded by the frame (which includes both the area of the frame and the area of the painting) is (w+4)(2w+4).
The area of the painting is w×2w=2w2, and the area of the frame is 196 square inches, so the area of the two combined is 2w2+196. However, that is the same area as the other one I described, so we can then equate the two, i.e. (w+4)(2w+4)=2w2+196. You can then solve that equation for w, and hence find all of the relevant dimensions.
The sum of x and its square is equal to y times z.
Answer:
x + [tex]x^{2}[/tex] = yz
Step-by-step explanation:
Consider a circle whose size can vary. The circumference of the circle is always
2
π
times as large as its radius. Let
r
represent the radius of the circle (in feet) and let
C
represent the circumference of the circle (in feet).
Answer:
The circumference of the circle is always 2π times as large as its radius. Let r represent the radius of the circle (in feet) and let C represent the circumference of the circle (in feet).
Step-by-step explanation:
hopes this helps
answer 2
π
times as large as its radius.
Given f(x) = x^2 - 3x + 5, what is f(-2)?
A. f(-2) = 3
B. f(-2) = -5
C. (-2) = 15
Directions: “Write out an equation that will go with the following problem and then solve it.”
“A restaurant is full. There are some four-person tables and 8 tables with couples. If there are 56 people here, how many four-person tables are there?”
Answer:
Incomplete question
Forgot to add how many tables
Step-by-step explanation:
Let's solve the equation step by step,
Step: Let's make an equation to find how many four person table are there
Let x represent for four person table and y for 8 person table,
4x + 8y = 56,
x+y=z
Let f(x) = -10x-18 and g(x) = -3x, find (f-g)(x).
Answer:
[tex]{ \tt{f(x) = - 10x - 18}} \\ { \tt{g(x) = - 3x}} \\ \\ { \tt{(f - g)(x) = ( - 10x - 18) -( - 3x) }} \\ \\ { \tt{(f - g)(x) = ( - 10x + 3) - 18}} \\ \\ { \tt{(f - g)(x) = - 7x + (3 - 18)}} \\ \\ { \tt{(f - g)(x) = - 7x - 15}}[/tex]
Using the ratio 49N:5kg calculate the force needed to lift an object that is 365 kg
The force needed to lift an object that is 365 kg is calculated as; 3577 N
How to solve ratio problems?
We are given the ratio as;
49N : 5 kg
This ratio means that 49 newtons of force represents 5 kg of mass. Now, we want to find the force required to lift an object with a mass of 365 kg.
Using the given ratio, we can say that the force that can lift a mass of 365 kg is calculated as;
(365 * 49)/5 = 3577 N
Thus, we conclude that the force needed to lift an object that is 365 kg is calculated as 3577 N.
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in the system of equations below, a and b are constants and x and y are variables. If the system
of equations below has no solution, what is the value of a b?
ax - y = 0
x - by = 1
The value of ab = 1 in the two given equations with no solutions.
What do we mean by equations with no solutions?When the two lines are parallel, a system of two linear equations in two variables has no solution. In terms of algebra, this means that when we solve the system, we get a false equation. On a graph, the lines never intersect because they have the same slope but different y-intercepts. There will be no solution if (a₁/a₂) = (b₁/b₂) (c₁/c₂). This is referred to as an inconsistent pair of linear equations.So, it is said that the two equations (ax - y = 0) and (x - by = 1) have no solutions.
Then,
a/1 = 1/b = 0Cross multiply:
ab = 1Therefore, the value of ab = 1 in the two given equations with no solutions.
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Which system of equations is represented by the matrix below?
[2 3| 2]
[12 0| -24]
System of equations is represented by the matrix below is 2x + 3y = 2 and 12x = -24
[2 3 2]
[12 0 -24]
This means 2x + 3y = 2 and 12x = -24
How matrix is used to solve system of equation?
The matrix can be used to solve system of equation. it can be 3 by 3 matrix or 2 by 2 matrices.
The first rows of the matrix above represent the coefficient of the first equation and second row represents the second equation of the system of equations.
Matrices is the plural form of matrix, which is a rectangular array or table with rows and columns of numbers or elements. They can have as many columns and rows as they want. Matrix operations include addition, scalar multiplication, multiplication, transposition, and others.
Matrices, the plural form of matrix, are the arrangements of numbers, variables, symbols, or expressions in a rectangular table with varying rows and columns. They are rectangular arrays with defined operations such as addition, multiplication, and transposition. The elements of the matrix are the numbers or entries in it. The horizontal entries of matrices are referred to as rows, while the vertical entries are referred to as columns.
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656 divded by 9 and 3.6 divded by 17
Answer: 72.8 and 0.21
Answer:
72.8888888889
and
0.5142857143
Question content area top Part 1 Zachary purchased a computer for $1,500 on a payment plan. Five months after he purchased the computer, his balance was $975. Ten months after he purchased the computer, his balance was $450. What is an equation that models the balance y after x months?
The equation that models the balance y after x months is given by y = 1500 -150x,
Apparently, we have to assume that the balance is a linear function of the number of months that the payment is boing made.
We are given 3 points:
(0, 1500), (6, 600) and (8, 300)
Any two of these can be used to write the equation of the line :
y = (y₂ - y₁) / (x₂ - x₁) (x - x₁) + y₁
y = (600 - 1500) / (6 - 0) (x - 0) + 1500
y = - 900 / 6 x + 1500
y = 1500 - 150 x
where x is the number of months.
Therefore, the equation that models the balance y after x months is given by y = 1500 -150x,
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What is the difference when 54.89 is subtracted from 235.987?
29.0877
1,810.97
290.877
181.097
ill brainlist the right answer
[tex]{ \blue{ \tt{option(d)}}} \: { \boxed{ \red{ \sf{181.097}}}}[/tex]
Step-by-step explanation:
[tex] \: \: \: \: 235.987[/tex]
[tex] - \: \: \: 54.89[/tex]
_______________
[tex]{ \boxed{ \red{ \sf{= 181.097}}}}[/tex]
When simplifying --7(3)(-10) + (-4), can you multiply 3 and -10 first and get the same result as multiplying - 7 and 3 first?
Explain.
Answer:
See explanation
Step-by-step explanation:
Yes
-7(3)(-10) + (-4) =
-7(-30) + (-4)= ==> multiply 3 and -10
210 - 4=206
-7(3)(-10) + (-4) =
-21(-10) + (-4)= ==> multiply -7 and 3
210 - 4=206
206=206 √
Graph the line y-5x=-3
Answer:(0,-3)
Step-by-step explanation:
It's quite simple once you understand. First plug in values
if x=0 then y= -3, if x =1 then y=2. Plug in values based on the equation.
Since my first substitution is 0,-3, that is the one I will plot on a graph.
Hope it helps!!
Answer:
y = 5x - 3
Points: (0, -3) and (1, 2)
Step-by-step explanation:
y - 5x = -3
+5x +5x
y = 5x - 3
The starting point is at (0, -3)
Count up five then right 1
rise
-------
run
I hope this helps!
which of the following 5-digit numbers can be rounded to 20,000?
If a 12-gram serving of pasta contains 3 g of protein, how many grams of protein are in a 1,362-gram box of the pasta?
There are 340.5g of protein in 1,362 gram box of pasta
How to calculate the number of grams of protein ?12 gram serving of pasta contains 3g of protein
The number of protein in 1362 gram box of pasta can be calculated as follows
3/12 = x/1362
cross multiply
12x= 3×1362
12x= 4086
x= 4086/12
= 340.5
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The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 14 HCF of water is $32.62 , and the cost for using 48 HCF is $78.52 . What is the cost for using 40 HCF of water?
The cost for using 40 HCF of water is $67.72
What is the cost for using 40 HCF of water?To solve this question, we use the following representations
x represents HCFy represents the amountUsing the above representations, we have the following points
(x, y) = (14, 32.62), (48, 78.52)
For 40 HCF of water, we have
(x, y) = (40, y)
The slope of a linear equation is calculated using
m = (y2 - y1)/(x2 - x1)
So, we have
m = (78.52 - 32.62)/(48 - 14) = 1.35
m = (78.52 - y)/(48 - 40)
Substitute m = 1.35 in m = (78.52 - y)/(48 - 40)
So, we have:
1.35 = (78.52 - y)/(48 - 40)
Evaluate the difference
1.35 = (78.52 - y)/8
Multiply both sides by 8
10.8 = 78.52 - y
This gives
y = 78.52 - 10.8
Evaluate the difference
y = 67.72
Hence, the cost for using 40 HCF of water is $67.72
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“Some friends ordered two cinnamon sugar pizzas cut into 12 pieces each for dessert. Each person had 2 slices and there were four slices leftover. How many friends were at the dinner?
Write out an equation that will go with the problem and then solve it.”
Answer: 4 People were at the dinner.
Equation: 2x + 4 = 12
Step-by-step explanation: We know that there are 4 pieces left. So we can just take away 4 from 12. When that's done, we're left with 8 eaten slices. Then divide the 8 slices by the number of pieces per person. Therefore, 8/2 gives us 4.
I took algebra last year and loved it! I hope this helps!
On Olga's 16th birthday, her uncle invested $2,000 in an account that was locked into a 1.75% interest rate, compounded monthly. How much will Olga have in the account when she turns 18? Round to the nearest cent.
Answer is NOT $2,071.19
I can't figure it out, the only answer I get when putting the numbers into the formula is $2,071. I feel like the trick is the "locked" part. Although that seems normal. 16-17 is 1 year, and 17-18, is another, so 2 years. I'm not sure why the answer is wrong.
61% of 407
rounding pls <3
Answer:
Step-by-step explanation:
61.407
Answer:
248.3
Step-by-step explanation:
61% of 407
61% = 0.61
0.61 * 407 = 248.27
248.27 = 248.3
248.3
what is -11 + l-5l - l-15l
Answer: -21
Step-by-step explanation: abs(-5) and abs (-15) just makes it positive, so the equation becomes -11 + (5) - (15), which equals -21.
Find the value of x.
130°
(2x)
Answer:
Step-by-step explanation:
Vertical opposite angles are equal to each other so
2x = 130
x = 65 (divide both sides by 2)
Write algebraic expressions for two numbers with a sum of -17. Let one of the number be represented by x.
The algebraic expression is x + y = -17
Given,
The sum of two numbers = -17
One number = x
We have to write an algebraic expression for the above condition:
Algebraic expression
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.).
You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.
So, let’s find the algebraic expression:
Given that one number is x. We can take other number as y.
So, the expression will be like:
x + y = -17
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The sum of the measures of two complementary angles is 90°. If one angle measures
15° more than twice the measure of the other, find the measure of the smaller angle.
The smaller angle measures: ?
Answer: 75°
Step-by-step explanation:
Solution;
Here:. let, one angle be x
From the question ,
x+15=90(Being sum of complementary angle)
x=90-15
x=75
A pole that is 3.5m tall casts a shadow that is 1.26 m long. At the same time, a nearby building casts a shadow that is 35.75m long. How tall is the building? Round your answer to the nearest meter.
The height of the building is 99 meters.
How to find the height of the building?The pole is 3.5m tall and cast a shadow of 1.26 metres long.
At the same time a nearby building casts a shadow that is 35.75m long.
Therefore, this will form a ratio.
The height of the building can be found as follows:
Establishing the ratio,
where
x = height of the building
3.5 / x = 1.26 / 35.75
cross multiply
35.75 × 3.5 = 1.26 × x
125.125 = 1.26x
divide both sides by 1.26
125.125 / 1.26 = 1.26x / 1.26
x = 125.125 / 1.26
x = 99.3055555556
x = 99 meters
Therefore, the height of the building is 99 meters.
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The points I, J, K and L all lie on the same line segment, in that order, such that the ratio IJ:JK:KL is equal to 2:5:5 IfIL=60, find KL.
The length of KL with the given ratio is 25 units
How to determine the length of KL?The given parameters are:
IJ : JK : KL is equal to 2 : 5 : 5
IL = 60
Rewrite properly as:
IJ : JK : KL = 2 : 5 : 5
This means that the length of KL
KL = KL ratio/Sum of ratios * IL
So, we have
KL = 5/(2 + 5 + 5) * 60
Evaluate the sum
KL = 5/12* 60
Divide 60 by 12
So, we have
KL = 5 * 5
Evaluate the product
KL = 25
Hence, the length of KL with the given ratio is 25 units
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Your company will generate $71,000 in annual revenue each year for the next seven years from a new information database. If the appropriate interest rate is 8.75 percent, what is the present value?
The present value of the annual revenue of $71,000 for seven years at 8.75% is $360,357.02
What is the present value?The present value represents the discounted value of future cash flows over a period.
The present value can be computed using the PV table, formula, or an online finance calculator, as follows:
Data and Calculations:N (# of periods) = 7 years
I/Y (Interest per year) = 8.75%
PMT (Periodic Payment) = $71,000
FV (Future Value) = $633,642.98 ($497,000 + $136,642.98)
Results:
Present Value (PV) = $360,357.02
Sum of all periodic payments = $497,000 ($71,000 x 7)
Total Interest $136,642.98
Thus, the present value of the annual revenue of $71,000 for seven years at 8.75% is $360,357.02
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K(2, 7), L(6, 12), M(13, 13), N(9.8) (Slope Formula) is it a parallelogram?
angles and sides opposite one another on a parallelogram are congruent, we can say this is a parallelogram because there are congruent.
What in mathematics is a parallelogram?
A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.Slope Formula: y2-y1/x2-x1
KL: 12-7/6-2 = 5/4
LM; 13-12/13-6 = 1/7
MN: 8-13/9-13 = 5/4
KN: 7-8/9-2 = 1/7
Since angles and sides opposite one another on a parallelogram are congruent, we can say this is a parallelogram because there are congruent.
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The table below shows the assets and liabilities of the Tanner family.
Assets and Liabilities Amount
Checking account $17,532
Car (paid off) $12,225
Retirement Savings $43,675
Credit Card Debt $7,876
Home Loan Balance $65,225
What is the net worth of the Tanner family?
If checking account has $17,532,car (paid off) is $12,225,retirement savings are $43,675,credit card debt is $7,876,home loan balance has $65,225, the the net worth of the Tanner family is $331.
Given that checking account has $17,532,car (paid off) is $12,225, retirement savings are $43,675,Credit Card Debt is $7,876,Home Loan Balance has $65,225.
We are required to find the net worth of the Tanner family.
Net worth is basically the value of the assets a person or corporation owns, minus the liabilities they owe.
Net worth=Checking account+Car +Retirement savings-credit card debt-Home loan balance
=17532+12225+43675-7876-65225
=$331
Hence if checking account has $17,532,Car (paid off) is $12,225 ,retirement Savings are $43,675,credit card debt is $7,876,home loan balance has $65,225, the the net worth of the Tanner family is $331.
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please help
please hury
the one you highlighted is right!
Answer:
The highlighted one is correct!
ln(3) - ln(2) + ln(1/x) =
A. 3 / (2x)
B. 3x/2
C. 1 + 1/x
D. 3/2 - 1/x
The required simplified solution for the given logarithm expression is y = 3 / 2x.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
To simplify the given expression,
ln(3) - ln(2) + ln(1/x) = ln (y)
ln(3) + ln(1/x) = ln(2) + ln(y)
By the property of logarithm,
3/x = 2y
y = 3 / 2x
Thus, the required simplified solution for the given logarithm expression is y = 3 / 2x
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