Answers
Answer:
Option C: (2, 1, 0)
Step-by-step explanation:
We are given a system of three equations. Usually, we eliminate a variable from the equations. Solve for the remaining two equations and determine the value of the third equation later.
Here, we are given the choices. So, we can readily substitute each option in the equations. The solution should satisfy all the three equations.
Option A: (3, 1, 0)
Equation (1): 3x + 3y + 6z = 9
⇒ 3(3) + 3(1) + 6(0) = 9 + 3 ≠ 9
Option A does not satisfy the first equation. So, it is eliminated.
Option B: (0, 1, 0)
Substituting in the first equation: 3x + 3y + 6z = 9
⇒ 3(0) + 3(1) + 6(0) = 3 ≠ 9
Option B does not satisfy as well. Hence, it is eliminated.
Option C: (2, 1, 0)
Substituting in 3x + 3y + 6z = 9
⇒ 3(2) + 3(1) + 6(0) = 9
It satisfies Equation 1. For this to be a solution, it should satisfy all the three equations. So, we check for equation 2 and 3.
Equation 2: x + 3y + 2z = 5
2 + 3(1) + 2(0) = 2 + 3 = 5
Equation 3: 3x + 12y + 12z = 18
3(2) + 12(1) + 12(0) = 6 + 12 = 18
Option C satisfies all the equations. So, it is the solution to the system.
On simple substitution, Option D can be eliminated as well.
Hence, the answer.
Related Questions
Leon has 16 fewer quarters than dimes. He has 34 quarters.
Use the five-step problem-solving plan.
How many dimes does Leon have?
Enter you answer in the box.
Answers
Answer:
A grand total of 50 dimes
Step-by-step explanation:
The SAS Theorem can be used to prove that two triangles are similar.
True
False
Answers
Answer:
The answer is true.
I took the quiz! :)
There are 9 large bicycles at the store. There are 6 small bicycles at the store. How many bicycles are at the store?
Answers
Answer:15
Step-by-step explanation:9+6=15
Answer: 15
Step-by-step explanation:
9+6
1. What is the unit price of shampoo if a
15-ounce bottle costs $2.79?
A. about $0.19 per ounce
B. about $0.29 per ounce
C. about $1.90 per ounce
D. about $5.38 per ounce
Answers
Hope this helps
The dimensions of a 7-cm by 2-cm rectangle are
multiplied by 3. How is the area affected?
Answers
Answer:
Step-by-step explanation:
9
Final answer:
Multiplying the dimensions of a rectangle by 3 increases its area by a factor of 9, which is the square of 3. The area of the rectangle goes from 14 cm^2 to 126 cm^2.
Explanation:
When the dimensions of a rectangle are multiplied by a certain factor, the area of the rectangle is affected by the square of that factor. Initially, the area of a 7-cm by 2-cm rectangle is 14 cm2. When the dimensions are each multiplied by 3, the new dimensions become 21 cm by 6 cm. Therefore, the new area is 21 cm imes 6 cm = 126 cm2. The area scales in proportion to the square of the linear dimensions. If we compare the new area to the old area, we see that 126 cm2 / 14 cm2 equals 9, meaning the area has increased by a factor of 9, which is 32, since we multiplied the dimensions by 3. This principle applies generally: when a rectangle's dimensions are scaled by a factor, its area is scaled by the square of that factor.
There is 200 tickets if 18 where purchased in advanced what percentage where purchased in advanced
Answers
Answer: 9%
Step-by-step explanation:
You can just divide 200 in half which gives you 100. And divide 18 in half which gives you 9. 9/100, and since 100 is the percent’s denominator (if percent were viewed in fraction), it would be 9.
Joyce paid $98.00 for an item at the store that was 30 percent off the original price. What was the original price?
Answers
Answer:
$127.40
Step-by-step explanation:
$98-30%=$127.4
$65 dress pants 20% discount
Answers
Answer:
52
Step-by-step explanation:
65 dollar is price so it has 20 percent discount so,
65× 20% = 13
so,
65- 13
52 dollars
An architect uses a 3-D printer to create the scale model for a house that will be built. In the model the house is 53cm tall . The house will be 624 cm tall. The volume of the model is 0.8125 cubic meter. What is the volume of the house . (Note: 1 cubic meter = 1,000,000 cubic centimeters)
Answers
Answer:
The volume of the actual house is 1,324.94 cubic meters
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Height of the scale model = 53 cm
Height of the actual house = 624 cm
Scale of the model = 642/53 = 11.77
Volume of the scale model = 0.8125 cubic meters
2. What is the volume of the house?
For answering the question we have to find the width and the length of the model, then use the scale of the model for calculating the volume of the actual house, this way:
Volume of the scale model = 0.8125 cubic meters
Area of the scale model = Volume of the model/Height of the model
Area of the scale model = 0.8125/0.53
Area of the scale model = 1.533 square meters
Area of the scale model = Length * Width
Area of the scale model = 1.533 * 1
Now, we can calculate, the measurements of the house to calculate its volume:
Height of the actual house = 6.24 meters
Length of the actual house = 1.533 * 11.77 = 18.04 meters
Width of the actual house = 1 * 11.77 = 11.77 meters
Volume of the actual house = 6.24 * 18.04 * 11.77
Volume of the actual house = 1,324.94 cubic meters
Instructions:
Three of Carlos and Clarita's friends are purchasing school supplies at the bookstore. Stan buys a notebook, three packages of pencils, and two markers for $7.50. Jan buys two notebooks, six packages of pencils, and five markers for $15.50. Fran buys a notebook, two packages of pencils, and two markers for $6.25.
Question 1
Based on the information in the instructions, write a system of equations to model the situation. Let n represent the price of a notebook, p represent the price of a package of pencils, and m represent the price of a marker.
Question 2 How much does an individual notebook cost? Question 3 How much does a package of pencils cost? Question 4 How much does an individual marker cost?
Answers
Answer:
Notebook = $2.75
Pencil = $1.25
Markers = $ 0.50
Step-by-step explanation:
Stan:
n + 3p + 2m = 7.5
Jan:
2n + 6p + 5m = 15.50
Fran:
n + 2p + 2m = 6.25
Stan - Fran:
p = 1.25
Lets replace p with 1.25
n + 3(1.25) + 2m = 7.5
2n + 6(1.25) + 5m = 15.50
n + 2(1.25) + 2m = 6.25
Simplify
n + 3.75 + 2m = 7.5
2n + 7.5 + 5m = 15.50
n + 2.50 + 2m = 6.25
n + 2m = 3.75 stan
2n + 5m = 8 jan
n + 2m = 3.75 fran
stan = fran
jan - 2(stan)
m = 0.5
n = 2.75
5. How can you use the Distributive Property to
factor the expression 6x + 15?
Answers
Answer:
Divide it all by 3, then put it outside the parentheses.
3(2x+5)
Step-by-step explanation:
The requried factors of the given expression are given as 3[x + 5].
What are the factors?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
here,
The distributive property is given as,
a[b + c] = ab + bc
Now,
the given expression performing the distributive property in a way given as,
ab + bc = a[b + c]
Given expression,
= 6x + 15
= 3 × 2x + 3 × 5
= 3 [2x + 5]
Thus, the requried factors of the given expression are given as 3[x + 5].
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If f ( x ) is a linear function, f ( − 2 ) = 0 , and f ( 4 ) = − 5 , find an equation for f ( x ) . f (x)=
Answers
Answer:
f(x).f(x) [tex]=\frac{25}{36} x^2 +\frac{25}{9}x+\frac{25}{9}[/tex]
Step-by-step explanation:
Given f(x) is a linear function.
Let f(x)= ax+c
given,f(-2)=0
∴a(-2)+c=0
⇔-2a +c=0
⇔c=2a ..........(1)
Again f(4) = -5
∴a.4+c=-5
⇔4a+c=5
⇔4a +2a=5 [∵ c= 2a]
⇔6a=5
⇔[tex]a=\frac{5}{6}[/tex]
Putting the value of a in equation (1)
[tex]c=2 \times \frac{5}{6}[/tex]
[tex]\Leftrightarrow c= \frac{5}{3}[/tex]
Therefore f(x) [tex]=\frac{5}{6} x+\frac{5}{3}[/tex]
f(x).f(x)
[tex]=(\frac{5}{6} x+\frac{5}{3})(\frac{5}{6} x+\frac{5}{3})[/tex]
[tex]=(\frac{5}{6} x+\frac{5}{3})^2[/tex]
[tex]=\frac{25}{36} x^2 +\frac{25}{9}x+\frac{25}{9}[/tex]
Determine whether the statement is true of false and support your reasoning: Mr. Flores has 100 pictures in a photo album. Of these pictures, 20 show his friends, 50 show his family, and 30 show his pet dachshund, Frou-Frou. Based on this information, the probability of Mr. Flores randomly selecting a picture of Frou-Frou is greater than the probability of randomly selecting a picture of his family
Answers
So, the given statement is false.
Step-by-step explanation:
Given , Mr. Flores has 100 pictures in a photo album. Of these picture , 20 show his friends , 50 show his family and 30 show his pet dachshund.
Probability formula:
[tex]P(A)=\frac{\textrm{Number of favorable outcomes to A}}{\textrm {Total number of out comes}}[/tex]
Total number of out come = 100
Number of photo of his family = 50
Therefore the probability of Mr. Flores selecting a picture of his family is
[tex]=\frac{50}{100}[/tex] [tex]=\frac{1}{2}[/tex] [tex]= \frac{5}{10}[/tex]
The probability of Mr. Flores selecting a picture of his friend is [tex]=\frac{20}{100}[/tex] [tex]=\frac{1}{5} = \frac{2}{10}[/tex]
The probability of Mr. Flores selecting a picture of his pet dachshund [tex]=\frac{30}{100}[/tex] [tex]=\frac{3}{10}[/tex]
Since [tex]\frac{5}{10}>\frac{3}{10}>\frac{2}{10}[/tex]
Therefore the probability of Mr. Flores randomly selecting a picture of his family is greater than the probability of randomly selecting a picture Frou -Frou.
So, the given statement is false.
How do I use the cosine rule for these problems?
Answers
Answer:
see explanation
Step-by-step explanation:
Using the Cosine rule
a² = b² + c² - 2abcosA ← Rearranging for cosA gives
cosA = [tex]\frac{b^2+c^2-a^2}{2ab}[/tex]
(a)
let a = 10, b = 7, c = 8 and A = α, then
cosα = [tex]\frac{7^2+8^2-10^2}{2(7)(8)}[/tex] = [tex]\frac{49+64-100}{112}[/tex] = [tex]\frac{13}{112}[/tex], thus
α = [tex]cos^{-1}[/tex]( [tex]\frac{13}{112}[/tex] ) ≈ 83° ( to the nearest degree )
(b)
let the angle opposite side 7 be x
Using the Sine rule
[tex]\frac{10}{sin83}[/tex] = [tex]\frac{7}{sinx}[/tex] ( cross- multiply )
10sinx = 7sin83 ( divide both sides by 10 )
sinx = [tex]\frac{7sin83}{10}[/tex] , thus
x = [tex]sin^{-1}[/tex] ( [tex]\frac{7sin83}{10}[/tex] ) = 44°
The third angle can be found using the sum of angles in a triangle
third angle = 180° - (83 + 44)° = 180° - 127° = 53°
The 3 angles are 83°, 44°, 53°
Write the ratio as a fraction in simplest form.
1) 15 girls to 6 boys and question 2) 24 plays for 3 teams
Answers
Answer:
Part 1) [tex]\frac{5}{2}[/tex] or [tex]5:2[/tex]
Part 2) [tex]\frac{8}{1}[/tex] or [tex]8:1[/tex]
Step-by-step explanation:
Write the ratio as a fraction in simplest form
Part 1) 15 girls to 6 boys
we know that
To find out the ratio, divide the number of girls by the number of boys
so
[tex]\frac{15}{6}[/tex]
Simplify
Divide by 3 both numerator and denominator
[tex]\frac{5}{2}\ \frac{girls}{boys}[/tex]
Part 2) 24 plays for 3 teams
we know that
To find out the ratio, divide the number of plays by the number of teams
so
[tex]\frac{24}{3}[/tex]
Simplify
Divide by 3 both numerator and denominator
[tex]\frac{8}{1}\ \frac{plays}{team}[/tex]
Final answer:
To simplify the ratios 15 girls : 6 boys and 24 plays : 3 teams, find the greatest common factor and divide both parts of the ratio by it, resulting in the simplest forms rac{5}{2} and 8, respectively.
Explanation:
To write the ratios as fractions in simplest form for the given scenarios:
For the ratio of 15 girls to 6 boys, the fraction would be rac{15}{6}. To simplify, divide both the numerator and the denominator by their greatest common factor (GCF), which is 3. Thus, the simplest form is rac{15 \/ 3}{6 \/ 3} = rac{5}{2}.
For the ratio of 24 plays for 3 teams, the fraction is rac{24}{3}. Again, to simplify, divide both the numerator and the denominator by the GCF, which is 3 in this case. The simplest form is rac{24 \/ 3}{3 \/ 3} = rac{8}{1}, which can also be written simply as 8 since a denominator of 1 implies the value is a whole number.
What is the reflection of (8, -5) in the Y axis
Answers
Answer:
(-8, -5)
Step-by-step explanation:
I plotted the equation on a graph and looked at the reflection and got that.
The cost of some office furniture after a 20% reduction was $3520.00. What was the original price before the furniture was discounted?
Answers
Answer:
[tex]\$4,400[/tex]
Step-by-step explanation:
Let
x ----> the original price of the furniture
Remember that
[tex]100\%-20\%=80\%=80/100=0.80[/tex]
we know that
The original price multiplied by 0.80 must be equal to the cost of the furniture after a 20% reduction
so
The linear equation that represent this situation is
[tex]0.80x=3,520.00[/tex]
solve for x
Divide by 0.80 both sides
[tex]x=\$4,400[/tex]
Answer:
4.00
Step-by-step explanation:
A square wall has a surface area of 121ft? What is the length of the wall?
Answers
Ans 11ft
Step-by-step explanation:
Sq Area= length * length
Length=√area=√121=11
0 = 4x2+12x+9
Simplify the expression to solve the equation. x =
Answers
Answer:
-1.5
Step-by-step explanation:
The value of x is -3/2 or -1.5.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
4x²+12x+9 =0
Now, the solution for the expression is
4x²+12x+9 =0
4x²+6x+ 6x +9 =0
2x( 2x + 3)+ 3 (2x+ 3)= 0
(2x+ 3) (2x+ 3) = 0
x= -3/2, x= -3/2
Hence, the value of x is -3/2 or -1.5.
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PLEASE HELP TRYING TO MAKE HONOR ROLL
The sum of two numbers is 36. Their difference is 14. What are the two numbers?
A. -14 and 50
B. -11 and 47
C. 11 and 25
D. 14 and 22
Answers
Answer:
it is B. -11 and 47
Step-by-step explanation:
you have to take away 47 and 11 and it equals 36.
Elijah drinks 35 out of 40 ounces of the water in her water bottle what percentage did Elijah drink
Answers
Answer:
87.5%
Step-by-step explanation:
35/40=7/8=0.875=87.5%
it wants at least 20 characters to answer this question so whoops
A game designer must decide how to color four buildings that are in a row. Using only the colors yellow, green, red, and blue, each building must be painted with exactly one color. Any two neighboring buildings must be different colors, and the first and last buildings must be different colors. How many ways are there to paint the four buildings?
Answers
To determine how many ways to paint the buildings, we consider the choices for each building sequentially, considering the constraints. There are either 36 or 24 combinations, depending on the colors chosen for the first and last buildings. A step-by-step count confirms this range of possibilities.
A systematic approach gives us the general formula: 4 choices for the first building × 3 choices for the second building × 3 choices for the third building × (2 or 3) choices for the fourth building, depending on the first color chosen. This results in a total of 36 or 24 possible combinations, depending on the first and last color's relationship. A careful count avoiding the restrictions on the colors confirms this.
When rounded to the nearest thousand,
the number of pieces of trash collected
by the Beach Clean Up Crew was 8,000.
What numbers below could be the actual
number of pieces of trash collected?
A. 8,283
B. 8,507
C. 8,835
D. 7,582
E. 7,689
Please help me I have a fever and my brain isn't working.. If u do, I will give it as a brilliant answer.. Plus 20 points..
Answers
What If? If Taryn and Alastair want to earn an additional $735 ear
additional hours will each spend mowing lawns? Assume each
sat the rate shown in the table and charges by the hour. Explain
many additional hours wil
mows a
Jarun
and
13. Multistep Tomas makes balloon sculptures at a circus. In 180 minutes.
he uses 252 balloons to make 36 identical balloon sculptures.
a. How many minutes does it take to make one balloon
sculpture? How many balloons are used in one sculpture?
minutes
Answers
18.
If z = (5)(11)(28)(38), what is the
greatest prime factor of z?
A. 5
B. 7
C. 11
D. 13
E. 19
Answers
Answer:
E. 19
Step-by-step explanation:
z = (5)(11)(2·2·7)(2·19)
z = 2³·5·7·11·19
The greatest prime factor is 19.
Select all the correct answers.
Which three of these story details can help a reader identify the theme
O
the author's background
O
repetition of ideas
the amount of dialogue
the interaction of story elements
the main conflict
Answers
Answer:
ideas and conflict and maybe elements depending on the story
Solve n÷6>2. Graph the solution. The solution is?
please help!
Answers
Answer:
n>12
Step-by-step explanation:
n/6>2
n>2*6
n>12
The Graph of the inequality is shown below.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
We have the inequality,
n÷6>2
Multiply both side by 6 we get
(n ÷ 6 ) 6 > 2 x 6
n > 12.
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what is the y-intercept, and what does it represent?
Answers
Answer:
The y-intercept is where an equation's graph hits the y-axis. It represents the constant value, when x=0, the intercept is the constant
Step-by-step explanation:
The y-intercept indicates the vertical position where the line or curve intersects the y-axis
The y-intercept refers to the point where a line or curve intersects the y-axis on a graph.
It is the value of the dependent variable (y) when the independent variable (x) is equal to zero.
In the equation of a line in slope-intercept form (y = mx + b), where m represents the slope of the line and b represents the y-intercept, the y-intercept is the constant term (b).
The y-intercept represents the value of the dependent variable (y) when the independent variable (x) is not present or equal to zero.
It is the initial value or starting point of the function or graph.
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The graph shows the solution for which inequalities
Answers
Answer:
Option 3
Step-by-step explanation:
y is less than the y values on the red line and greater than the y values on the blue line.
Equation of the red line:
y-intercept is clearly 3
using (0,3) & (-2,2)
Slope = (y2-y1)/(x2-x1)
= (3-2)/(0-(-2)) = 1/2
y = (1/2)x + 3
Equation of the blue line:
y-intercept is clearly -2
Using (0,-2) & (1,1)
Slope = (1-(-2))/(1-0) = 3/1 = 3
y = 3x - 2
y < (1/2)x + 3 & y > 3x - 2
The graph shows the solution for the following inequalities; C. y ≥ 3x - 2 and y ≤ -1/2(x) + 3.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
[tex]y - y_1 = m(x - x_1)[/tex]
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope for the red line by using these points (2, 4) and (0, 3);
[tex]Slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope (m) = (3 - 4)/(0 - 2)
Slope (m) = 1/2
At point (0, 3) and a slope of 1/2, an inequality for this line can be calculated by using the point-slope form as follows:
y - 3= 1/2(x - 0)
y = 1/2(x) + 3
y ≤ 1/2(x) + 3 (since the solid line is shaded below).
At point (0, -2) and a slope of 3, an inequality for this line can be calculated by using the point-slope form as follows:
y + 2= 1/2(x - 0)
y = 3(x) - 2
y ≥ 3x - 2 (since the solid line is shaded below).
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A 6cm section of plastic water pipe has inner diameter of 12cm and outer diameter of 15cm. find the volume of the plastic pipe not the hollow interior to the nearest hundredth
Answers
Answer:
The volume of the plastic pipe is 141 cubic centimetre
Step-by-step explanation:
Given:
The Length of the plastic water pipe = 12 cm
The inner Diameter of the plastic water pipe = 12 cm
The outer Diameter of the plastic water pipe = 15 cm
To Find:
the volume of the plastic pipe not the hollow interior to the nearest hundredth = ?
Solution:
The volume of the plastic water pipe can be found by using the volume of the cylinder formula
The Volume of the cylinder = [tex]\pi r^2 h[/tex]
Where
r is the radius
h is the height
Radius r [tex]= \frac{diameter}{2} = \frac{15}{2} = 7.5 cm[/tex]
On substituting the values
The Volume of the cylinder
= [tex]\pi (7.5) (6)[/tex]
= [tex]45 \pi[/tex]
= 141.37 cubic centimetre
= 141 cubic centimetre