Answers
A system of equations is consistent if the system has a solution and it is inconsistent if it has no solution.
Since the lines intersect at a point, the system has a solution and the solution is unique.
If a system has a unique solution, then the system is independent.
Therefore, the given system of equations is consistent and independent. It has a unique solution.
Related Questions
Find the mean: 16,12,15,10,7,916
Answers
You can calculate the mean by using the formula:
Mean=sum of values/number of values
Then,
[tex]undefined[/tex]A media company wants to track the results of its new marketing plan, so the video production manager recorded the number of views for one of the company's online videos. The results of the first 5 weeks are shown in this table. Write an equation to model the relationship between the number of weeks, x, and the number of views, f(x). Enter the correct answer in the box by replacing the values of a and b.
Answers
ANSWER
[tex]f(x)=5120\cdot1.25^x[/tex]EXPLANATION
We want to write an equation that models the relationship between the number of weeks (x) and the number of views, f(x).
From the table, we see that the relationship of the two terms (number of views and number of weeks) is exponential.
The general form of an exponential function is given as:
[tex]f(x)=a\cdot b^x[/tex]where a = initial value
b = exponential factor
We have to find a and b.
We do this by replacing x and f(x) in the function with values from the table.
Let us use the first set of values:
[tex]\begin{gathered} 5120=a\cdot b^0 \\ \Rightarrow5120=a\cdot1 \\ \Rightarrow a=5120 \end{gathered}[/tex]We have found the value of a, now we can find the value of b by using another set of values from the table.
That is:
[tex]\begin{gathered} 6400=5120\cdot b^1 \\ 6400=5120\cdot b \\ \text{Divide both sides by 5120:} \\ b=\frac{6400}{5120} \\ b=1.25 \end{gathered}[/tex]Now, we have found a and b.
Therefore, the equation that models the relationship between number of views and number of weeks is:
[tex]f(x)=5120\cdot1.25^x[/tex]Please help:What are the zeros of the quadratic function?f (z )= 3z^2 − 11z − 4Enter your answers, as simplified fractions if necessary, in the boxes.The zeros of f (z) are __ and __.
Answers
We need to find the zeros for the next function:
[tex]f(z)=3z^2−11z−4[/tex]We can find those zeros using the quadratic formula given by:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Use the form ax²+bx+x.
Where a=3
b= -11
c=-4
Replacing :
[tex]\begin{gathered} x=\frac{-(-11)\pm\sqrt{(-11)^2-4(3)(-4)}}{2(3)} \\ Simplify \\ x=\frac{11\pm\sqrt{169}}{2\ast3} \\ x=\frac{11\pm13}{2\ast3} \\ Therefore: \\ x_1=\frac{11-13}{6}=\frac{-2}{6}=-\frac{1}{3} \\ x_2=\frac{11+13}{6}=\frac{24}{6}=4 \end{gathered}[/tex]Therefore, the zeros of f (z) are -1/3 and 4.
true or false16. The y-intercept of the equation, = −7^2 + 11 − 12 is 12
Answers
For us to be able to determine if it is true or false, let's evaluate the given equation:
[tex]\text{ y = -7x}^2\text{ + 11x - 12}[/tex]In order to find the y-intercept of a function, we substitute x equals to 0. A y-intercept always has an x-coordinate of 0.
Thus, we get,
[tex]\text{ y = -7x}^2\text{ + 11x - 12}[/tex][tex]\text{ y = -7(0)}^2\text{ + 11(0) - 12}[/tex][tex]\text{ y = -7(0)}^{}\text{ + 0 - 12 = 0 + 0 - 12}[/tex][tex]\text{ y = -12}[/tex]The y-intercept of the given equation is -12.
Therefore, the answer is FALSE.
What is the opposite of the given number?-10.1
Answers
According to the given data we have the following number:
-10.1
Therefore, the opposite of this given number would be the number 10.1
Instead of -10.1 the opposite would always be with the contrary sign. In this case is the opposite is a positive number.
In this case is -10.1. but for example if we the have to find the opposite number of 1 that would be the -1.
All real number would have and opposite number, except for the number 0.
Please help by providing answers to these questions.
Answers
Graph of proportional relationship is given y =kx , answer of the following questions are as follow:
1. Based on the information , the constant of proportionality represents the multiplicative relationship between two quantities.
2. Variable represents the constant of proportionality is k.
3. The constant of proportionality is known as the scale factor.
4. The graph of y = kx is a line that passes through the origin.
8. y/x =7 represents the constant of proportionality.
9. Scale factor of the constant of proportionality of figure S to T is 1/4.
As given,
Graph represents proportional relationship is given by:
y = kx
⇒ k = y/x
Represents the multiplicative relationship between the variables y and x.
1. Based on the information , the constant of proportionality represents the multiplicative relationship between two quantities.
'k' is the scale factor represents the constant of proportionality.
2. Variable represents the constant of proportionality is k.
3. k is the scale factor.
4. y =kx
when x=0 ⇒ y =0 represents graph passes through origin.
8. y =kx ⇒y /x =k if k =7 then y/x =7 represents constant of proportionality.
9. 2/8 = 4.5/18= 3/12 =1.5/6 = 1/4
Scale factor of the constant of proportionality of figure S to T is 1/4.
Therefore, graph of proportional relationship is given y =kx , answer of the following questions are as follow:
1. Based on the information , the constant of proportionality represents the multiplicative relationship between two quantities.
2. Variable represents the constant of proportionality is k.
3. The constant of proportionality is known as the scale factor.
4. The graph of y = kx is a line that passes through the origin.
8. y/x =7 represents the constant of proportionality.
9. Scale factor of the constant of proportionality of figure S to T is 1/4.
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L is the midpoint of JM. K is the midpoint of JL. JL = 15. What is thelength of KM?
Answers
We can draw the situation as:
So, if L is the midpoint of JM, JL is equal to LM and JM is equal to 2 times JL
JL = LM
JL + LM = JM
JL + JL = JM
2JL = JM
We can calculate JM using JL as:
2JL = JM
2*15 = JM
30 = JM
Then, if K is the midpoint of JL, JK is equal to KL and JL is 2 times JK
JL = 2JK
Replacing JL by 15, we get:
15 = 2JK
15/2 = JK
7.5 = JK
Finally, KM can be calculated as:
KM = JM - JK
KM = 30 - 7.5
KM = 22.5
Answer: 22.5
The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set.2, 10, 15, 4. 14. 7. 14, 8, 2, 10The range is(Simplify your answer.)The population mean is(Simplify your answer. Round to the nearest tenth as needed.)The population variance is I(Simplify your answer. Round to the nearest tenth as needed.)The population standard deviation is(Simplify your answer. Round to the nearest tenth as needed)Enter your answer in each of the answer boxes.
Answers
The numbers of regular-season wins for 10 football teams in a given season are given below
[tex]2,10,15,4,14,7,14,8,2,10[/tex]We are asked to find the range, mean, variance, and standard deviation of the population data set.
Range:
The range is the difference between the maximum value and the minimum value in a data set.
From the given data set,
Maximum value = 15
Minimum value = 2
[tex]\begin{gathered} \text{Range}=\text{maximum}-\text{minimum} \\ \text{Range}=15-2 \\ \text{Range}=13 \end{gathered}[/tex]Therefore, the range is 13
Mean:
The population mean is given by
[tex]\mu=\frac{\sum^{}_{}X}{N}[/tex]Where X is the terms in the data set and N is the number of terms in the data set.
[tex]\begin{gathered} \mu=\frac{2+10+15+4+14+7+14+8+2+10}{10} \\ \mu=\frac{86}{10} \\ \mu=8.6 \end{gathered}[/tex]Therefore, the population mean is 8.6
Variance:
The population variance is given by
[tex]\sigma^2=\frac{\sum^{}_{}(X-\mu)^2}{N}[/tex]Where X is the terms in the data set, μ is the mean, and N is the number of terms in the data set.
[tex]\begin{gathered} \sigma^2=\frac{\sum^{}_{}(X-\mu)^2}{N} \\ \sigma^2=\frac{(2-8.6)^2+(10-8.6)^2+(15-8.6)^2+(4-8.6)^2+(14-8.6)^2+(7-8.6)^2+(14-8.6)^2+(8-8.6)^2++(2-8.6)^2++(10-8.6)^2}{10} \\ \sigma^2=\frac{214.4}{10} \\ \sigma^2=21.4 \end{gathered}[/tex]Therefore, the population variance is 21.4
Standard deviation:
The population standard deviation is given by
[tex]\begin{gathered} \sigma^{}=\sqrt[]{\frac{\sum^{}_{}(X-\mu)^2}{N}} \\ \sigma=\sqrt[]{\sigma^2} \end{gathered}[/tex]Since we have already find the population variance, we can simply find take the square root of variance.
[tex]\begin{gathered} \sigma=\sqrt[]{\sigma^2} \\ \sigma=\sqrt[]{21.4} \\ \sigma=4.6 \end{gathered}[/tex]Therefore, the population standard deviation is 4.6
Analyze the general equation of a linear function, y = mx. No matter what value the constant m has, which pair of numerical values (x, y) always satisfies this mathematical equation? Justify your answer.
Answers
The pair of numerical values (x,y) that always satisfies the mathematical equation of linear equation y = mx is (0,0).
A two-variable linear equation can be thought of as a linear relationship between x and y, or two variables whose values rely on one another.
The slop-intercept form of a linear equation is y = mx + b.
For y = mx, b = 0.
If we put x = 0 in y = mx, y = 0.
Therefore, y = mx line always passes through (0,0) for any value of m because (0,0) always satisfies the equation y = mx.
Hence, (x,y) = (0,0).
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five hundred twelve thousandths decimal form
Answers
The first step to answer this question is to write the fraction for the given sentences.
Five hundred twelve thousandths is:
[tex]\frac{512}{1000}[/tex]To write it as a decimal, solve the quotient:
[tex]\frac{512}{1000}=0.512[/tex]The answer is 0.512.
how do i find the sale price?if original price is $77.00markdown is 32%
Answers
The markdown price can be calculated as,
[tex]\begin{gathered} \text{Markdown price}=\frac{Markdown\text{ Percent}}{100}\times Original\text{ price} \\ \text{Markdown price}=\frac{32}{100}\times77 \\ \text{Markdown price}=24.64 \end{gathered}[/tex]Now, the sale price is,
[tex]\begin{gathered} \text{Sale price=Original price -markdown price} \\ \text{Sale price=}=77-24.64 \\ \text{Sale price=}52.36 \end{gathered}[/tex]Therefore, the sale price is $52.36.
I thought this answer was the sixth root, cubed, value of 16. But I am not sure so I need help with the question
Answers
In order to find the correct options, we need to know the following property:
[tex]a^{\frac{b}{c}}=\sqrt[c]{a^b}[/tex]So, rewriting the expression 243^(3/5), we have:
[tex]243^{\frac{3}{5}}=\sqrt[5]{243^3}[/tex]That is, 243^(3/5) is the 5th root of 243 cubed. Its value is:
[tex]\sqrt[5]{243^3}=\sqrt[5]{14348907}=27[/tex]turn 5 7/10 into a decimal and a percent
Answers
It is a mixed number:
[tex]5\frac{7}{10}[/tex]THe whole part, 5, is going to stay 5.
Now, let's work with the fractional part.
7/10 into a decimal would require for division.
7 divided by 10 is 0.7
Thus,
IN Decimal, it will be "5.7"
To find percentage from decimal, we multiply by 100 and tag along a % sign.
So,
[tex]5.7\cdot100=570[/tex]The number, in percentage, is 570%
Minnesota fell from 48 degrees to -12 degrees over a 24 hour period. what was the average temperature change per hour?
Answers
We have to calculate the average temperature change per hour.
We know that the temperature drops from 48 degrees to -12 degrees in 24 hours.
To calculate the average change, in degrees per hour, we calculate the ratio between the variation of the temperature and the interval of time.
We can expres this as:
[tex]v=\frac{\Delta T}{t}=\frac{T_f-T_i}{t}=\frac{-12-48}{24}=\frac{-60}{24}=-2.5[/tex]Answer: The average change in temperature is -2.5 degrees per hour.
Find the side length of a cube with a volume of 111 ft³ If necessary, round your answer to the nearest tenth.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
volume of a cube
V = 111 ft³
side lenght = ?
Step 02:
volume of a cube
V = s³
[tex]\begin{gathered} 111ft^{3\text{ }}=\text{ s } \\ \sqrt[3]{111ft^3}\text{ = s } \end{gathered}[/tex]4.81 ft ³ = s
The answer is:
The side length is 4.8 ft³
Samuel's family members are choosing numbers to see in what order they will choose gifts. The numbers 1 through 10 are written on pieces of paper. All numbers are equally likely to be chosen. What is the probability that the first person chooses a number less than 3? O A. 10 3 B. 10 2 C. 2 10 O D. 3 10
Answers
Answer:
[tex]\text{Probability}=\frac{2}{10}[/tex]Step-by-step explanation:
Probability is represented by the following expression:
[tex]=\frac{\text{Number of ways it can occur}}{Total\text{ number of outcomes}}[/tex]Then, since there are 2 numbers less than 3:
[tex]\text{Probability}=\frac{2}{10}[/tex]Describe 4 types of Quadrilaterals
Answers
Answer:
Parallelograms, Squares, Rectangles, and Rhombuses
Step-by-step explanation:
Which situation represents a proportional relationship?
O Renting a movie for $2 per day
O Renting a movie for $2 per day with a coupon for $0.50 off for the first day
O Renting a movie for $2 per day along with paying a $5 membership fee
O Renting a movie for $2 for the first day and $1 for each day after the first day
Answers
As they are in the right ratio, option D, "Renting a movie for $2 for the first day and $1 for each day after the first day," demonstrates a proportionate relationship.
Proportional Relationship
When two variables' ratios are equivalent, proportional relationships between them emerge. The fact that one variable is consistently equal to the constant value of the other in a proportional connection is another way to think of them. This constant is known as the "constant of proportionality."
Ratio
In mathematics, a ratio shows how frequently one number appears in another. For instance, the ratio of apples to mangos in a bowl of fruit would be nine to six if there were nine apples and six mangos. Apples make up 9:15 of the entire fruit, whereas Mangos make up 6:9 of the total fruit.
Option D, "Renting a movie for $2 for the first day and $1 for each day after the first day," illustrates a proportional relationship because the ratio is correct
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Find the rule for the following sequence. Then find the 45th term.
Answers
Answer:
[tex]a_{45}=221[/tex]Step-by-step explanation:
Arithmetic sequences are represented by the following equation;
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ where, \\ a_1=\text{ first term} \\ d=\text{ common difference} \\ n=\text{ nth term} \end{gathered}[/tex]The common difference is the difference between the consecutive terms:
[tex]\begin{gathered} d=6-1=5 \\ d=11-6=5 \\ d=16-11=5 \end{gathered}[/tex]Therefore, the equation that represents this sequence:
[tex]a_n=1+5(n-1)[/tex]Now, if we want to find the 45th term, substitute n=45:
[tex]\begin{gathered} a_{45}=1+5(45-1) \\ a_{45}=1+5*(44) \\ a_{45}=1+220 \\ a_{45}=221 \end{gathered}[/tex]Determine the slope by using the slope formula and add two points on the line check your answer by drawing a right triangle and labeling the rise and run right numbers in simplest form select undefined if Applicable
Answers
Answer:
The slope is -2
Explanation:
The slope can be calculated as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1, y1) and (x2, y2) are the coordinates of two points in the line.
Replacing (x1, y1) by ( 0, -1) and (x2, y2) by (1, -3), we get:
[tex]m=\frac{-3-(-1)}{1-0}=\frac{-3+1}{1}=\frac{-2}{1}=-2[/tex]Now, we can check the answer using the following drawing
Since rise over run is also equal to 2/(-1) = -2. We can say that the slope is -2.
Estimate. Then find the quotient. Round to the nearest thousandth.24.752:6Estimate=Quotient =
Answers
Estimate = 4.13
Quotient = 4.12533333
To the nearest thousand 4.12533
PLS HELP Rewrite the following equation in slope-intercept form.
y + 8 = –3(x + 7)
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Step by step
An equation in the slope-intercept form is written as. y=mx+b.
m is the slope of the line and b is the y-intercept.
y +8 = -3x -21
Subtract 8 from both sides to isolate y
y + 8 - 8 = -3x -21 -8
y = -3x -29
Answer:
[tex] \sf \: y = -3x - 29[/tex]
Step-by-step explanation:
Given equation,
→ y + 8 = -3(x + 7)
The slope-intercept form is,
→ y = mx + b
Let's rewrite the equation,
→ y + 8 = -3(x + 7)
→ y + 8 = -3x - 21
→ y = -3x - 21 - 8
→ [ y = -3x - 29 ]
Thus, answer is y = -3x - 29.
Please help answer the questions 1-6
Answers
The equations for each slope - intercept pair are discussed below.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept
Given are the slopes and [y] intercepts of some lines.
We can write the equation for each pair as discussed above in the general equation.
[1] → The equation of the straight line with slope [m] = -3 and y- intercept
[c] = 4 will be → y = -3x + 4.
[2] → The equation of the straight line with slope [m] = 0 and y- intercept
[c] = 0 will be → y = 0.
[3] → The equation of the straight line with slope [m] = 7/3 and y- intercept [c] = 3 will be → y = 7/3x + 3.
[4] → The equation of the straight line with slope [m] = -1/2 and y- intercept [c] = 5 will be → y = -1/2x + 5.
[5] → The equation of the straight line with slope [m] = -1/4 and y- intercept [c] = 4 will be → y = -1/4x + 4.
[6] → The equation of the straight line with slope [m] = -4/3 and y- intercept [c] = 1 will be → y = -4/3x + 1.
Therefore, the equations for each slope - intercept pair are discussed above.
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Find the equation line parallel y=(-4/5)x+12 passing through (-6,2)
Answers
So we want to find the equation of a line parallel to
[tex]y=-\frac{4}{5}x+12[/tex]Passing through the point (-6,2).
First, remember that a line is parallel to other if their slopes are the same.
Then, the slope of our parallel line will be also -4/5.
Remember that a line has the following equation:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Now, we know that the parallel line has slope = -4/5 and passes through the point (x,y) = (-6,2), so we could replace in our previous equation as follows:
[tex]\begin{gathered} 2=-\frac{4}{5}(-6)+b \\ 2=\frac{24}{5}+b \\ b=2-\frac{24}{5} \\ b=-\frac{14}{5} \end{gathered}[/tex]Therefore, the equation of the parallel line to y=(-4/5)x+12 passing through (-6,2) is:
[tex]y=-\frac{4}{5}x-\frac{14}{5}[/tex]
For scenarios of statistical studies are given below decide which study uses a sample statistic
Answers
The sample statistic is defined as any number computed from the sample data. This means that the data must be a sample and not the entire population. Looking at the options,
option D is correct
as the x increases by 1, what will the rate of change for y in this equation y=-3x+10
Answers
Answer:
Rate of change = -3
Explanation:
Given the equation:
[tex]y=-3x+10[/tex]When x=1
[tex]\begin{gathered} y=-3(1)+10 \\ =-3+10 \\ =7 \end{gathered}[/tex]When x=2
[tex]\begin{gathered} y=-3(2)+10 \\ =-6+10 \\ =4 \end{gathered}[/tex]Observe that the value of y decreases by 3 as the x increases by 1.
Thus, the rate of change is -3.
Alternate Route
Another way is to express and compare the line with the slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ y=-3x+10 \end{gathered}[/tex]The rate of change is the coefficient of x.
Coefficient of x = -3
Thus, the rate of change is -3.
4x+10=30
solve it please
Answers
Answer:
x = 5
Step-by-step explanation:
4x + 10 = 30 ( subtract 10 from both sides )
4x = 20 ( divide both sides by 4 )
x = 5
Answer:
x = 5
Step-by-step explanation:
4x + 10 = 30
Step 1:
30 - 10 = 4x
20 = 4x
Step 2:
20/4
x=5
Step 3: Prove your answer correct
4(5) + 10 = 30
20 + 10 = 30
x = 5
Question 2(Multiple Choice Worth 2 points)
(01.06 MC)
Simplify 31.
1
0-1
-1
Answers
Answer:
[tex]-i[/tex]
Step-by-step explanation:
Imaginary numbers
Since there is no real number that squares to produce -1, the number [tex]\sqrt{-1}[/tex] is called an imaginary number, and is represented using the letter [tex]i[/tex].
Given expression:
[tex]i^{31}[/tex]
Rewrite 31 as 30 + 1:
[tex]\implies i^{30+1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]
[tex]\implies i^{30} \cdot i^1[/tex]
[tex]\implies i^{30}i[/tex]
Rewrite 30 as 2 · 15:
[tex]\implies i^{(2 \cdot 15)}i[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies \left(i^2\right)^{15}i[/tex]
[tex]\textsf{Apply\:imaginary\:number\:rule}\quad \:i^2=-1:[/tex]
[tex]\implies \left(-1\right)^{15}i[/tex]
As -1 to the power of an odd number is -1:
[tex]\implies -1 \cdot i[/tex]
[tex]\implies -i[/tex]
16 ftTo the nearest tenth, what is the height of the triangle?A. 9 feetB. 14.4 feetC. 17.5 feetD. 23 feethB7 ftС
Answers
In the right triangle, there is a relation between the 2 legs of the right angle and the hypotenuse (the opposite side to the right angle)
[tex](hypotenuse)^2=(leg1)^2+(leg2)^2[/tex]From the given figure
∵ leg1 = 7 ft
∵ leg2 = h ft
∵ hypotenuse = 16 ft
→ Substitute them in the rule above to find h
[tex](16)^2=(7)^2+h^2[/tex]∵ 16^2 = 256 and 7^2 = 49
[tex]\therefore256=49+h^2[/tex]→ Subtract 49 from both sides
[tex]\begin{gathered} 256-49=49-49+h^2 \\ 207=h^2 \end{gathered}[/tex]→ Take square root for both sides to find h
[tex]\begin{gathered} \therefore\sqrt[]{207}=\sqrt[]{h^2} \\ 14.38749=h \end{gathered}[/tex]→ Round it to the nearest tenth
∴ h = 14.4 feet
The answer is B
between 1993 and 1996 there were 6545 injured during horse races find the ratio of injured per year
Answers
First, we have to calculate the years passed between 1993 and 1996:
1996-1993 = 3 years
Now divide the number of injured during horse races (6545) by the number of years (3)
6545 /3
2,182 injured per year