Answers
Given:
[tex]\begin{bmatrix}{x} & {7y} \\ {z} & {20}\end{bmatrix}=\begin{bmatrix}{4} & {21} \\ {4} & {20}\end{bmatrix}[/tex]Let's find the values of the variables so that the matrices are equal.
To find the values of the variables, divide the values of the result by the corresponding values of the main matrix.
We have:
• x = 4
• 7y = 21
Divide both sides by 7:
7y/7 = 21/7
y = 3
• z = 4
[tex]\begin{gathered} \begin{bmatrix}{x=4} & {7y=21} \\ {z=4} & {20}\end{bmatrix} \\ \\ \begin{bmatrix}{4} & {7(3)} \\ {4} & {20}\end{bmatrix} \end{gathered}[/tex]Therefore, we have:
• x = 4
,• y = 3
,• z = 4
ANSWER:
• x = 4
,• y = 3
,• z = 4
Related Questions
what is the ratios of 29:1, and the math eqation.
Answers
The ratio of 29: 1 is 29
The mathematical equation is 29/1
A ratio can simply be defined as an ordered pair of numbers, say x and y, written in the form x / y where of the denominator is note equivalent to zero.
It is known to explain how many times a given number contains another number in a proportion.
It is seen as the comparison of two numbers , elements or quantities having the same units and moving further to explain how much of one of the element or quantity is present in the another one.
This is achieved based on their magnitude or sizes.
A proportion is a mathematical equation with which two ratios are set equivalent to each other.
A ratio is expressed mathematically as;
x/y
Given the ratio;
29: 1
The equation is = 29/1 = 29
Hence, the ratio is 29
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2. Solve the following addition problem. Remember to carry as necessary.
6 cu yd 9 cu ft
134 cu in
+ 1 cu yd 12 cu ft
200 cu in
Answers
The solution to the given addition problem is 150.6 ft^9.
Converting everything to the same unit is the simplest solution to this problem.
The conversions are:
1 cubic yard = (27 cubic feet)
1 cubic inch = (0.000578704 cubic feet)
The addition can be performed as,
(6 cu yd × 9 cu ft × 134 cu in) + (1 cu yd × 12 cu ft × 200 cu in)
= [6(27 cu ft) × 9 cu ft × 134(0.000578704 cu ft)] + [1(27 cu ft) × 12 cu ft × 200(0.000578704 cu ft)]
= 150.6 ft^9
The result of the addition is 150.6 ft^9.
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NO LINKS!!! Part 2 Please help me with this Similarity Practice
Answers
Answer:
C' = (15, 7)
Dilation by a scale factor of 3 with the origin (0, 0) as the center of dilation, followed by a translation of 1 unit up.
Step-by-step explanation:
If two triangles are said to be similar, their corresponding angles are congruent and their corresponding sides are in the same ratio.
Given vertices of triangle ABC:
A = (0, 0)B = (1, 4)C = (5, 2)To maintain similarity (and thus keep the corresponding angles of both triangles the same) but not maintain congruence, dilate triangle ABC.
Given:
B' = (3, 13)If ΔABC is dilated by a scale factor of 3, with the origin as the center of dilation, B' = (3, 12). If the triangle is then translated 1 unit up, B' = (3, 13), which matches the given coordinate of point B'.
Therefore, the series of transformations is:
Dilation by a scale factor of 3 with the origin (0, 0) as the center of dilation.Translation of 1 unit up.Mapping Rule: (x, y) → (3x, 3y + 1)
Therefore, the coordinates of point C' are:
⇒ C' = (3(5), 3(2) + 1) = (15, 7)
A company manufactures calculators and sells them at $50 each. The fixed costs are $4000 per month and the variable costs per unit are $32. Calculate the number of units that need to be manufactured and sold per month to break even.
Answers
The number of units that is needed to be manufactured and sold per month by the company to break even is 222 units
How to calculate the number of units needed to break even ?The first step is to write out the parameters given in the question
The sales price per unit is $50
The fixed cost per month is $4000
The variable cost per unit is $32
The formula for calculating the units needed to break even can be expressed as follows
Fixed Costs ÷ (Sales price per unit – Variable costs per unit)
4000/(50-32)
= 4000/18
= 222.2
Hence 222 units are needed to be manufactured per month
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A sales representative receive a monthly salary of $1600 plus a commission of 3% of the total monthly sales. write a linear model that relates total monthly wages W to sales S
Answers
Answer:
The equation is W = 1600 + .03S
Consider the graph of the function f(x) = 2^x Which statements describe key features of function g if g(x) = f(x + 2)?
Answers
The statements that describe key features of function g if g(x) = f(x + 2) are;
a. y-intercept at (0,4)
b. domain of {x|-∞ < x < ∞}
c. horizontal asymptote of y = 0
What are the features of the Function?We are given the function f(x) = 2^(x)
We want to find the features of the function g if;
g(x) = f(x + 2)
Let us first find f(x + 2);
g(x) = f(x + 2) = 2^(x + 2)
The y-intercept is when x = 0;
g(0) = 2^(0 + 2)
g(0) = 4
Some features in a function that limit the x values are: roots, fractions, etc.
g(x) = 2^(x + 2) does not have any restricting value of x.
This means the value of x ranges from negative infinity to positive infinity.
Hence, the domain is: (-∞, ∞)
Next, calculate the horizontal asymptote.
To do this, we plot the graph of g(x) --> see attachment
Then we trace a horizontal line from the horizontal part of the curve of g(x) till it gets to the y-axis.
From the attached graph of g(x), the line touches the y-axis at y = 0
So, the horizontal asymptote is: y = 0
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The missing options are;
a. y-intercept at (0,4)
b. domain of {x|-∞ < x < ∞}
c. horizontal asymptote of y = 0
d. horizontal asymptote of y=2
e. y-intercept at (0,1)
Answer:
see photo
Step-by-step explanation:
Plato/Edmentum
Help me pls with this fast!
Answers
Answer:
Step-by-step explanation:
...
Answer:
2x+9=7
Step-by-step explanation:
"Sum" means addition
"2 times a number" since the number is unknown we use a letter, since its a letter we usually don't need parentheses
"and" is usually used ror addition so another clue
"is" just means equals
Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels 12 miles per hour slower than the westbound train. If the two trains are 300 miles apart after 2 hours, what is the rate of the westbound train?
Answers
Answer:
81 mph
Step-by-step explanation:
2x+2(x-12) = 300
Find the savings plan balance after 6 months with an APR of 8% and monthly payments of $200
Answers
The savings account balance after six months with an 8% annual percentage rate and $200 monthly contributions is $202.6.
What does a savings plan formula serve?Savings Plan Formula
The future worth of a savings or investment account in which you make regular deposits can be calculated using the formula below.
EXAMPLE 1 Assume you put $100 into a savings account each month that pays 7.3% interest that is compounded monthly.
To determine the saving plan balance after 6 month
First of all we have to calculate the growth factor
Growth factor =(1+(0.08/6)) per month
Growth factor= 1.013
Now let calculate the savings plan balance after 6 month
Saving plan balance after 6
Months =$200.00x1.0133
= $202.6
From conclusion the saving plan balance after 6 month is=$202.6
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which of the following is the rational algebric expression of the verbal phrase below? the ratio of the sum of 2x and 4y and the difference of 8x and 10y.
Answers
638x636y73637zy
Answer:
Because first multiple and divide and Again Multiple and ans
A friend lends you $720, which you agree to repay with 4% interest. How much will you have to repay? How much was the interest?
Answers
Answer: $16081.60
Step-by-step explanation:
1)
FV=3000(1.03)=$3090
2)
240*1.04=$249.60
3)
FV=14000(1.02)^7
FV=14000(1.1487)
FV=$16081.60
go quick if you have a good brain
see attachment beloww.
Answers
Answer:y=21°
x=8°
Step-by-step explanation:
3y+27=90
3y=63
y=21°
x+90°+8x+18°=180°
9x+108°=180°
9x=72°
x=8°
Find a smart way to compute.1 8/11 x 5/12 + 5/12 x 3/11
Answers
On simplifying the given equation, the answer is [tex]\frac{5}{6}[/tex]
How an equation can be simplified?The fundamental guidelines and procedures to simplify any statement are as follows:
By multiplying factors, remove any grouping symbols like brackets and parenthesis.
If the words contain exponents, use the exponent rule to eliminate grouping.
Add or subtract like terms to combine them.
Add the constants together.
Given,
1 8/11 x 5/12 + 5/12 x 3/11
[tex]\frac{19}{11}[/tex] × [tex]\frac{5}{12}[/tex] + [tex]\frac{5}{12}[/tex] × [tex]\frac{3}{11}[/tex]
Taking [tex]\frac{5}{11 * 12}[/tex] as a common factor,
⇒ [tex]\frac{5}{11 * 12}[/tex] ( [tex]19 + 3[/tex])
⇒ [tex]\frac{5}{11 * 12}[/tex] × 22
On simplifying,
⇒ [tex]\frac{5}{6}[/tex]
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On Monday, your English teacher gives you a list of twenty-five vocabulary terms to be memorized. You memorize all of them Monday night and do not look at the list again. Because you do not study again, you forget 6% of the list each day.a. Does this problem represent exponential growth or decay? How do you know?b. Which exponential formula below will you use for this problem? Why?(Your choices are f(x) = a (1 + r) or f(x) = a (1-ry')c. Write the formula for this specific problem. Explain how you know where each number goes in the formula.d. How many terms will you remember seven days later for the test? Show all your work and explain your computations.
Answers
Answer:
a. Exponential decay
b. f(x) = a (1 - r)^x
c. f(x) = 25(1 - 0.06)^x
d. 16 terms
Explanation:
a. Does this problem represent exponential growth or decay? How do you know?
Each day the number of terms that you know is less than the day before, so there is a decrease in the vocabulary terms memorized. It means that the problem represents exponential decay.
b. Which exponential formula below will you use for this problem? Why?
The formula for the exponential decay is:
[tex]f(x)=a(1-r)^x[/tex]Where a is the initial value and r is the rate of decay.
So, the formula that you will use is f(x) = a (1 - r)^x
c. Write the formula for this specific problem. Explain how you know where each number goes in the formula.
The initial value is 25 terms and the decay rate is 6%, so the specific equation is:
[tex]f(x)=25(1-0.06)^x[/tex]d. How many terms will you remember seven days later for the test? Show all your work and explain your computations.
Now, we need to replace the value of x by 7, so:
[tex]\begin{gathered} f(7)=25(1-0.06)^7 \\ f(7)=25(0.94)^7 \\ f(7)=25(0.6485) \\ f(7)=16.21 \end{gathered}[/tex]Therefore, you will remember 16 terms seven days later.
Molly grows corn on her farm to sell for pig feed. one of her fields produced 176.4 bushels of corn this year . if corn is currently selling 3.75 per bushel, how much will molly earn from this field
Answers
This year, one of her fields yielded 176.4 bushels of corn. $661.5 will Molly make from this field if corn is now selling for $3.75 per bushel.
Given that,
On her farm, Molly raises corn that she sells for pig food. This year, one of her fields yielded 176.4 bushels of corn.
We have to find how much will Molly make from this field if corn is now selling for $3.75 per bushel.
We have to multiply
=176.4×3.75
=661.5
Therefore, $661.5 will Molly make from this field if corn is now selling for $3.75 per bushel.
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QUESTION DOWN BELOW! PLEASE HELP WILL GET 100 POINTS IM STUCK PLEASE HELP EXPLAIN ITS DUE SOON!!
many thanks!!!
ITS DUE SOON!
Answers
1) given
2) base angles theorem
3) PN=QN
4) [tex]\angle 3=\angle 4[/tex]
5) MP=OQ
7) PQ, QP
8) MQ=PO
9) ASA
I need help with question #8
Answers
Hope this helps!!
Let f(x)=x+1 and g(x)=x^2-x. Find and simplify the expression. (f+g)(-5)
Answers
Answer:
26
Step-by-step explanation:
(f+g)(-5)=
f(-5)+g(-5)=
-5+1+(-5)^2-(-5)=
-4+25+5=
-4+30=
30-4=26
ALGEBRA 1 HW!! PLEASE HELP WILL GIVE BRAINLYEST please only answer b
Answers
Answer:
20
Step-by-step explanation:
Every 1 hour it cost $20
You can find this by using the equation y2-y1 divided by x2-x1
y2 is 40 y1 is 20
x2 is 2 and x1 is 1
40-20 divided by 2-1 equals 20
The slope of a line is
Answers
Answer:
-2
Step-by-step explanation:
You have to use rise over run. For example, to go from (-1,0) to (-2,2), you have to go up 2 squares and go left 1. That gives you 2/-1, which is -2. Hope this helps!
I need the answer to this with an explanation. This is ratio.
Answers
Given that 2500 students entered the Teacher Education Program.
[tex]\text{Number of male students + Number of female students = 2500}[/tex]20% of the students are male. Thus,
[tex]\begin{gathered} \text{Number of male students = 20\% of 2500} \\ \Rightarrow\frac{20}{100}\times2500 \\ \text{Number of male students = 500} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \text{Number of male students + Number of female students = 2500} \\ 500\text{ + Number of female students =2500} \\ \Rightarrow Number\text{ of female students = 2500 -500 = 2000 } \end{gathered}[/tex]Thus, the ratio of the number of males to the number of females is evaluated as
[tex]\begin{gathered} \text{Number of female : Number of male} \\ 2000\text{ : 500} \\ reducing\text{ to the lowest term gives} \\ 4\colon1 \end{gathered}[/tex]Hence, the ratio of the number of females to the number of males is thus 4:1
divide and round to the nearest hundredths place. 4.05 divided 0.07
Answers
We have the next operation
[tex]\frac{4.05}{0.07}=57.857=57.86[/tex]the result of this operation rounded to nearest hundredths place is 57.86
Solve: (6x2 + 5x + 1) ÷ (x + 2).
A.) 6x - 7
B.) 6x - 7 - x/15 + 2
C.) 6x + 8
D.) 6x - 7 + 15/ x+ 2
Answers
Answer:
d
Step-by-step explanation:
Divide
6x2+5x+1
x+2
=6x−7+
15
x+2
In 25 minutes Shiloh can In 10 laps around the track. Determine the number of
laps he can run
per minute.
A.
Find the constant of proportionality in this situation.
Answer:
B. Write an equation to represent the relationship.
Answer:
Answers
Shiloh can run 04 laps per minute if in 25 minutes Shiloh can run in 10 laps around the track and it is Laps per minute is simply division.
What is constant of proportionality?The ratio that is connecting two given numbers is what is known as the exact proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names that can be given for the constant of proportionality.
To represent the equation in laps per min,
L/m = 10/25
= 2/5
= 0.4 laps per minute
The constant of proportionality in this situation
10/25 = 0.4
The equation to represent the relationship.
y = 0.4x
How do you determine the proportionality constant?Identifying the same x and y variables is the first step in determining the proportionality constant. X will be the weight and Y will be the number of butter sticks in order to calculate the exact weight to stick ratio.
Then to determine the proportionality constant, we can use the constant equation k = y x.
Why is K the proportionality constant?When two variables are directly or indirectly proportional to one another, their relationship can be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used.
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2x-5>3 and -4x+7<-25
whats the compound inequality and how would it be graphed
Answers
Answer:
8 < x
see attached for the graph
Step-by-step explanation:
You want the compound inequality and the graph that represents the solution to the system ...
2x-5>3 and -4x+7<-25
SolutionThe first inequality has the solution ...
2x -5 > 3 . . . . . given
2x > 8 . . . . . . . add 5
x > 4 . . . . . . . divide by 2
The second inequality has the solution ...
-4x +7 < -25
-4x < -32 . . . . . . subtract 7
x > 8 . . . . . . . . divide by -4
The solution is the intersection of these solution spaces:
4 < x and 8 < x
The intersection is ...
8 < x . . . . . solution to the compound inequality
The graph is attached.
ASAP!! The Brown family baked 3 pies for Thanksgiving. They made a pumpkin pie, an apple pie, and a cherry pie. They ate 0.75 of the pumpkin pie, 0.5 of the apple pie, and 0.6 of the cherry pie How many pies did the Brown family eat in all? Record your answer as a decimal number.
Answers
Answer: The Brown family ate 1.85 pies in all
Step-by-step explanation: If you think about it all you have to do is 0.75+0.5= 1.25 and then you do 1.25+ 0.6 and then get 1.85 so they ate 1.85 pies in all
Hope this helped!!!!
What’s the correct answer answer asap
Answers
the answers is a. bones to bones
What is the value of x that makes this equation true?4x+5=x+14
Answers
Explanation:
To solve for x first we have to put all terms that contain x together:
[tex]4x+5=x+14[/tex]Substract x from both sides:
[tex]\begin{gathered} 4x-x+5=x-x+14 \\ 3x+5=14 \end{gathered}[/tex]Now substract 5 from both sides:
[tex]\begin{gathered} 3x+5-5=14-5 \\ 3x=9 \end{gathered}[/tex]And finally divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{9}{3} \\ x=3 \end{gathered}[/tex]Answer:
x = 3
Solve for x.
(x - 2)² = 2
Answers
The value of x is 4 and 0
What is basic algebra ?Algebra is a branch of mathematics that helps translate real-world problems or situations into mathematical formulas. Mathematical operations like addition, subtraction, multiplication, and division as well as variables like x, y, and z are needed to construct a valid mathematical expression. Coordinate geometry, calculus, and trigonometry are just a few of the mathematics topics that involve algebra. A simple algebraic equation is 2x + 4 = 8. Algebraic expressions are the result of performing operations on variables and constants, such as addition, subtraction, multiplication, division, etc. Consider that James and Natalie came up with the notion to arrange matchsticks into numerical patterns when they were fiddling with them.
Given that : [tex](x-2)^{2} = 2[/tex]
[tex](x-2)^{2} = 2[/tex]
(x-2)=±2
x= 4
x=0
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Increase 10kg by 20%
I'm genuinely tonta right now please help
Answers
When 10kg is increased by 20%, the number becomes 24%
What is the result of the percentage increase?
Percentage is a measure of frequency that is used to express a quantity as a number out of 100. The sign that is used to represent percentages is %. In order to convert a number to a percentage, multiply the number by 100.
The new increased number = (100% + percentage increase) x initial number
(100 + 20%) x 20%
120% x 20%
1.20 x 20% = 24%
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