Enter an equation that passes through the point (12, 7) and forms a system of linear equations with no solution when combined with the equation y=−3/4x+8.
Answers
To answer this question, we need to know that two linear equation that does not have solutions must not cross to each other, that is, they do not have a common point. For this case, both lines must be parallel lines. So in the question, we need to find a parallel line to the given line. Two parallel lines have the same slope.
Then, we have that the line must pass through (12, 7), and, because it is parallel to y = -3/4x + 8, and the slope for this line is m = -3/4, then, the line equation is, applying the point-slope form of the line:
[tex]y-y_1=m(x-x_1)[/tex]And
x1 = 12
y1 = 7
m = -3/4
Then
[tex]y-7=-\frac{3}{4}(x-12)\Rightarrow y-7=-\frac{3}{4}x+\frac{3}{4}\cdot12\Rightarrow y-7=-\frac{3}{4}x+\frac{36}{4}[/tex][tex]y-7=-\frac{3}{4}x+9\Rightarrow y=-\frac{3}{4}x+9+7\Rightarrow y=-\frac{3}{4}x+16[/tex]Then, the line equation is y = -3/4 x + 16.
We can check this if we use the elimination method as follows:
This is a FALSE result, and we do not have solutions for this system. Therefore, the line equation is y = -3/4 x + 16.
Related Questions
Which 3 pairs of side lengths are possible measurements for the triangle?
Answers
SOLUTION
From the right triangle with two interior angles of 45 degrees, the two legs are equal in length, that is AB = BC
And from Pythagoras, the square of the hypotenuse (AC) is equal to the square of the other two legs or sides (AB and AC)
So this means
[tex]\begin{gathered} |AC|^2=|AB|^2+|BC|^2 \\ since\text{ AB = BC} \\ |AC|^2=2|AB|^2,\text{ also } \\ |AC|^2=2|BC|^2 \end{gathered}[/tex]So from the first option
[tex]\begin{gathered} BC=10,AC=10\sqrt{2} \\ |AC|^2=(10\sqrt{2})^2=100\times2=200 \\ 2|BC|^2=2\times10^2=2\times100=200 \end{gathered}[/tex]Hence the 1st option is correct, so its possible
The second option
[tex]\begin{gathered} AB=9,AC=18 \\ |AC|^2=18^2=324 \\ 2|AB|^2=2\times9^2=2\times81=162 \\ 324\ne162 \end{gathered}[/tex]Hence the 2nd option is wrong, hence not possible
The 3rd option
[tex]\begin{gathered} BC=10\sqrt{3},AC=20 \\ |AC|^2=20^2=400 \\ 2|BC|^2=2\times(10\sqrt{3})^2=2\times100\times3=600 \\ 400\ne600 \end{gathered}[/tex]Hence the 3rd option is wrong, not possible
The 4th option
[tex]\begin{gathered} AB=9\sqrt{2},AC=18 \\ |AC|^2=18^2=324 \\ 2|AB|^2=2\times(9\sqrt{2})^2=2\times81\times2=324 \\ 324=324 \end{gathered}[/tex]Hence the 4th option is correct, it is possible
The 5th option
AB = BC
This is correct, and its possible
The last option
[tex]\begin{gathered} AB=7,BC=7\sqrt{3} \\ 7\ne7\sqrt{3} \end{gathered}[/tex]This is wrong and not possible because AB should be equal to BC
Hence the correct options are the options bolded, which are
1st, 4th and 5th
Solve and graph on a number line. 2(x-1) 4 or 2 (x-1)>4
Answers
The given inequality is:
2 (x - 1
In the scoring for a game, points can be negative and positive. There were - 3.25 points scored 4 times, -2.75 points scored 5 times, 3 points scored 2 times, and 5.5 points scored 4 times. How many more times would 5.5 points need to be scored to have a total gain greater than 15 points?
A. 1
C. 3
B. 2
D. 4
Answers
The number of times that 5.5 points is need to be scored to have a total gain greater than 15 points is A. 1
How to calculate the value?From the information, it was stated that there were - 3.25 points scored 4 times, -2.75 points scored 5 times, 3 points scored 2 times, and 5.5 points scored 4 times.
In this case, the entire score will be:
= (-3.25 × 4) + (-2.75 × 5) + (3 × 2) + (5.5 ×4)
= -13 - 13.75 + 6 + 22
= 11.25
Therefore, the times that 5.5 points is needed to be scored to have a total gain greater than 15 will be 1 time since 11.25 + 5.5 = 16.75. This is more than 15.
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I thought of a number. from ²/₇ parts of that number I subtracted 0,4 and got ⅗. The number is: A: ²⁄₇ B: ⅖ C: 3,5D: 4,5
Answers
Note : The use of comma as number separator represent point in this solution
Step 1: Let the number be x, thus, 2/7 parts of the number means
[tex]\frac{2}{7}x[/tex]Step 2: Subtract 0,4 from 2/7 parts of x
[tex]\frac{2}{7}x-0,4\Rightarrow\frac{2}{7}x-\frac{4}{10}[/tex]Step 3: Equate the expression above to 3/5
[tex]\frac{2}{7}x-\frac{4}{10}=\frac{3}{5}[/tex]Step 4: Simplify the equation above
[tex]\begin{gathered} \frac{2}{7}x-\frac{4}{10}=\frac{3}{5} \\ \frac{20x-28}{70}=\frac{3}{5}(\text{cross multiply)} \\ 5(20x-28)=70(3) \\ 100x-140=210 \\ 100x=210+140 \\ 100x=350 \\ \frac{100x}{100}=\frac{350}{100}(\text{Divide both side by 100)} \\ x=3,5 \end{gathered}[/tex]Hence, the number is 3,5
Option C is correct
Find an equation of the line. Write the equation using function notation.
Through (4, -1); perpendicular to 4y=x-8
The equation of the line is f(x) =
Answers
The equation of line perpendicular to 4y = x-8 passing through (4,-1) is:
[tex]y = -4x+15[/tex].
What is a equation of line?These lines are written in the form y = mx + b, where m is the slope and b is the y-intercept. We know from the question that our slope is 3 and our y-intercept is –5, so plugging these values in we get the equation of our line to be y = 3x – 5.
Given equation of line is:
4y=x-8
We have to convert the given line in slope-intercept form to find the slope of the line
Dividing both sides by 4.
[tex]y = \frac{1}{4}x-2[/tex]
Let [tex]m_{1}[/tex] be the slope of given line
Then,
[tex]m_{1}[/tex] = [tex]\frac{1}{4}[/tex]
Let [tex]m_{2}[/tex] be the slope of line perpendicular to given line
As we know that product of slopes of two perpendicular lines is -1.
[tex]m_{1}*m_{2} = -1\\\frac{1}{4}*m_{2}=-1\\ m_{2} = -4[/tex]
The slope intercept form of line is given by
[tex]y = m_{2}x+c[/tex]
[tex]y = -4x+c[/tex]
to find the value of c, putting (4,-1) in equation
[tex]-1 = -4*4+c\\-1+16 = c\\c = 15[/tex]
Putting the value of c in the equation
[tex]y=-4x+15[/tex]
Hence, The equation of line perpendicular to 4y = x-8 passing through (4,-1) is [tex]y = -4x+15[/tex].
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Determine the angle relationship. Drag the correct answer to the blank. what is the angle relationship of < 3 & <7
Answers
we have that
between m<3 and m<7 -----> no relationship (because q and p are not parallel)
Part 2
the relationship between m<12 and m<10
is
vertical angles
m<12=m<10 ------> by vertical angles
The linear regressionequation andcorrelation coefficientfrom the above datawas calculated to be:Predicted y = 16.2+2.45(x) with r = 0.98What is the coefficientof determination?Answer Choices:A. Coefficient of determination = 0.98B. Coefficient of determination = 0.96C. Coefficient of determination = 0.99D. Coefficient of determination cannot be determined with only the given information.
Answers
Given:
[tex]\text{ coefficient of correlation \lparen r\rparen = 0.98}[/tex]To find:
Coefficient of determination
Explanation:
The coefficient of determination is also known as the R squared value, which is the output of the regression analysis method.
If the value of R square is zero, the dependent variable cannot be predicted from the independent variable.
So, here the required coefficient of determination is:
[tex]r^2=(0.98)^2=0.9604\approx0.96[/tex]Final answer:
Hence, the required coefficient of determination is (B) 0.96.
The product two consequences positive even numbers is 728. Find the smaller of the two numbers. The smaller number is
Answers
Let the first number = n
So second number = n+2
the product of number is 728.
That mean:
[tex]n(n+2)=728[/tex]Solve the equation:
[tex]\begin{gathered} n(n+2)=728 \\ n^2+2n=728 \\ n^2+2n-728=0 \end{gathered}[/tex][tex]\begin{gathered} n^2+2n-728=0 \\ n^2+28n-26n-728=0 \\ n(n+28)-26(n+28)=0 \\ (n+28)(n-26)=0 \\ n=-28;n=26 \end{gathered}[/tex]For positive number is n=26.
scond number is:
[tex]\begin{gathered} =n+2 \\ =26+2 \\ =28 \end{gathered}[/tex]So smaller number is 26.
Which of these would not produce a representative sample that determines the favoritesport of the students at the local high school?ask every tenth student from a list of names in the student directoryask every tenth student who arrives at school on Wednesdayask ten students wearing football jerseys each day for a weekask five students from each classroom chosen by picking numbersMy Progress >
Answers
Answer: ask ten students wearing football jerseys each day for a week
This sample wouldn't b representative because, the use of a footblla
C) 1) if Z1 and 22 are complementary angles, and mZ1 = 74°; find m22.
Answers
Answer:
16
Explanation:
The angles ∠1 and ∠2 are complementary, meaning
[tex]\angle1+\angle2=90^o[/tex]Visually,
Now, ∠1 = 74; therefore,
[tex]74^o+\angle2=90^o[/tex]subtracting 74 from both sides gives
[tex]\angle2=90^o-74^o[/tex][tex]\angle2=16^o[/tex]which is our answer!
The graph of function f is shown. The graph of an exponential function passes through (minus 0.25, 10), (0, 6), (5, minus 2) also intercepts the x-axis at 1 unit. Function g is represented by the table. x -1 0 1 2 3 g(x) 15 3 0 - 3 4 - 15 16 Which statement correctly compares the two functions? A. They have the same y-intercept and the same end behavior as x approaches ∞. B. They have the same x-intercept but different end behavior as x approaches ∞. C. They have the same x- and y-intercepts. D. They have different x- and y-intercepts but the same end behavior as x approaches ∞.
Answers
The given data points from the graph of the exponential function, f, and the, values from the table of the function g, gives the statement that correctly compares the two functions as the option;
B. They have the same x–intercept but different end behaviours as x approaches ∞What is the end behaviour of a graph?The end behaviour of a function is the description of how the function behaves towards the boundaries of the x–axis.
The given points on the exponential function, f, are;
(-0.25, 10), (0, 6), (5, -2) and also the x–intercept (1, 0)
The points on the function g, obtained from the table of the values for g(x), expressed as ordered pairs are;
(-1, 15), (0, 3), (1, 0), (2, -34), (3, -16)
The coordinates of the x–intercept is given by the point where the y–value is zero.
The x–intercept for the exponential function, f, is therefore (1, 0)
Similarly, the x–intercept for the function, g, is (1, 0)
Therefore, both functions have the same x–intercept
However, the end behaviour of the function, f, as the x approaches infinity is that f(x) approaches negative infinity, while the end behaviour of the function, g, as the the value of x approaches infinity is g(x) is increasing towards positive infinity.
The correct option is therefore;
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21. Juanita is packing a box that is 18 inches long and 9 inches high. The total volume of the box.1,944 cubic inches. Use the formula V = lwh to find the width of the box. Show your work
Answers
The width of the box is 12 inches
Explanations:
The formula for calculating the volume of a rectangular box is expressed as:
[tex]V=\text{lwh}[/tex]where:
• l is the ,length ,of the box
,• w is the ,width, of the box
,• h is the ,height ,of the box
Given the following parameters
• length = 18 inches
,• heigh = 9 inches
,• volume = 1,944 cubic inches
Substitute the given parameters into the formula to calculate the width of the box as shown:
[tex]\begin{gathered} 1944=18\times w\times9 \\ 1944=162w \end{gathered}[/tex]Divide both sides by 162 to have:
[tex]\begin{gathered} 162w=1944 \\ \frac{\cancel{162}w}{\cancel{162}}=\frac{1944}{162} \\ w=12\text{inches} \end{gathered}[/tex]Hence the width of the box is 12 inches
Write the decimal as a quotient of two integers in reduced form.
0.513
Answers
The given decimal can be written as a quotient of 513/1000.
What is quotient?
In maths, the result of dividing a number by any divisor is known as the quotient. It refers to how many times the dividend contains the divisor. The statement of division, which identifies the dividend, quotient, and divisor, is shown in the accompanying figure. The dividend 12 contains the divisor 2 six times. The quotient is always less than the dividend, whether it is larger or smaller than the divisor.
we can write the decimal given 0.513 as a answer of of 513 divided by 1000.
I.e.
[tex]0.513 = \frac{513}{1000}[/tex]
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What is the value of 3-(-2) how can I solve this questions
Answers
Explanation:
[tex]\text{Given: }3-\mleft(-2\mright)[/tex]To find the value od 3-(-2), we will multiply the sign at the outer with the inner
[tex]undefined[/tex]An equation that can be used to determine the total
Answers
The equation that we have to build has the following form:
[tex]y=mx+b[/tex]• The fixed cost of the phone is $88, which will be represented by ,b,.
,• The variable cost per month is $116.43, which will be represented by ,m,.
,• y ,is the dependent variable that we want to know (, C(t) ,)
,• x ,is the independent variable, in our case, ,t,.
Replacing the values given in the problem we get:
[tex]C(t)=116.93t+88[/tex]The cost for 22 months will be:
[tex]C(22)=116.93\cdot22+88[/tex][tex]C(22)=2660.46[/tex]Answer:
• Equation
[tex]C(t)=116.93t+88[/tex]• Cost in 22 months: $2660.46
Determine the common ratio for each of the following geometric series and determine which one(s) have an infinite sum.
I. 4+5+25/4+…
II. -7+7/4-7/9+…
III. 1/2-1+2…
IV. 4- ++...
A. III only
B. II, IV only
C. I, Ill only
D. I, II, IV only
Answers
The correct answer is Option A ( III Only). I . -16 sum cannot be negative, II. Not a G.P, III. Sum = 1/4, and IV. Not a G.P.
Solution:Given geometric series,
I. 4 +5 +25 /4 ….
The common ratio(r) is (5/1)/(4/1) = 5/4.
S∞ = a / ( 1 - r)
= 4 / ( 1 - 5/4)
= 4 / -1/4
S∞ = -16.
Since sum cannot be negative.
II . -7 + 7/3 - 7/9+ ....
Here common ratio = -7 / (7/3) = -1/3
but - 7/9 / 7 /3 = 7/9
Here there is no common ratio so this not a G.P.
iii. 1/2 -1 + 2.....
Common ratio = -1 / (1/2) = -2
S∞ = a / ( 1 - r)
= 1/2 / (1 -(-2))
S∞ = 1/4.
iv 4 - 8/5 +16/5.....
Here there is no common ratio.
So this is not a G.P.
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The data shows the total number of employee medical leave days taken for on-the-job accidents in the first six months of the year: 12, 6, 15, 9, 28, 12. Use the data for the exercise. Find the standard deviation.
Answers
ANSWER:
The standard deviation is 7
STEP-BY-STEP EXPLANATION:
The standard deviation formula is as follows
[tex]\sigma=\sqrt[]{\frac{\sum^N_i(x_i-\mu)^2_{}}{N}}[/tex]The first thing is to calculate the average of the sample like this:
[tex]\begin{gathered} \mu=\frac{12+6+15+9+28+12}{6} \\ \mu=\frac{82}{6}=13.67 \end{gathered}[/tex]Replacing and calculate the standard deviation:
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{(12_{}-13.67)^2_{}+(6_{}-13.67)^2_{}+(15_{}-13.67)^2_{}+(9_{}-13.67)^2_{}+(28-13.67)^2_{}+(12_{}-13.67)^2_{}}{6}} \\ \sigma=\sqrt[]{\frac{293.33}{6}} \\ \sigma=6.99\cong7 \end{gathered}[/tex]Use the Binomial Theorem to expand the expression.(x +6)^3
Answers
ok
[tex]\begin{gathered} (x+6)^3=^{}x^3+3(x)^2(6)+3(x)(6)^2+6^3 \\ \text{ = x}^3+18x^2\text{ + 3(36)x + 216} \\ \text{ = x}^3+18x^2\text{ + 108x + 216} \end{gathered}[/tex][tex]\begin{gathered} (a+b)^3\text{ } \\ first\text{ term = a} \\ \text{second term = b} \\ \text{theorem } \\ (a+b)^3=a^3+3a^2b+3ab^2+b^3 \end{gathered}[/tex]that is the rule
just identify a and b in your problem
a = x
b = 6
Substitute in the theorem, and simplify
help meeeeeeeeee pleaseee !!!!!
Answers
Because x is continuous, we should use interval notation, the domain is:
D: [1, ∞)
How to find the domain?For a function y = f(x), we define the domain as the set of possible inputs of the function (possible values of x).
To identify the domain, we need to look at the horizontal axis. The minimum value is the one we can see in the left side, and the maximum is the one we could see on the right side.
There we can see that the domain starts at x = 1 and extends to the left, so the notation we can use for the domain is:
D: x ≥ 1
We know that the value x =1 belongs because there is a closed dot there.
The correct option is A, because the domain is continuous (as we can see in the graph), we should use interval notation. In this case the domain can be written as:
D: [1, ∞)
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The function f(x) = 40(0.9)^x represents the deer population in a forest x years after it was first studied. What was the deer population when it was first studied?a. 44b.40c. 36d.49
Answers
We are given the function that models a deer population:
[tex]f(x)=40(0.9)^x[/tex]Where x is the years since the study started. If we want to know the initial population, we want to find the population at x = 0 years.
Thus:
[tex]f(0)=40(0.9)^0=40\cdot1=40[/tex]The correct answer is option b. 40
Let f(x) = 2x-1 and g(x) = x2 - 1. Find (f o g)(-7).
Answers
Answer: (f o g)(-7) = 95
Step by step solution:
We have the two functions:
[tex]\begin{gathered} f(x)=2x-1 \\ g(x)=x^2-1 \end{gathered}[/tex]We need to find (f o g)(-7) or f(g(-7)), first we evaluate g(-7):
[tex](f\circ g)(-7)=f(g(-7))[/tex][tex]g(-7)=-7^2-1=49-1=48[/tex]Now we evaluate f(48):
[tex]f(48)=2\cdot48-1=96-1=95[/tex]Consider the function f(x)= square root 5x-10 for the domain [2, +infinity). find f^-1(x), where f^-1 is the inverse of f. also state the domain of f^-1 in interval notation.edit: PLEASE DOUBLE CHECK ANSWERS.
Answers
let f(x) = y
To find the inverse of f(x), we would interchange x and y:
[tex]\begin{gathered} y\text{ = }\sqrt[]{5x\text{ - 10}} \\ \text{Interchanging:} \\ x\text{ = }\sqrt[]{5y\text{ - 10}} \end{gathered}[/tex]Then we would make the subject of formula:
[tex]\begin{gathered} \text{square both sides:} \\ x^2\text{ = (}\sqrt[]{5y-10)^2} \\ x^2\text{ = 5y - 10} \end{gathered}[/tex][tex]\begin{gathered} \text{Add 5 to both sides:} \\ x^2+10\text{ = 5y} \\ y\text{ = }\frac{x^2+10}{5} \\ \text{The result above is }f^{\mleft\{-1\mright\}}\mleft(x\mright) \end{gathered}[/tex][tex]\begin{gathered} f^{\mleft\{-1\mright\}}\mleft(x\mright)\text{ = }\frac{x^2+10}{5} \\ The\text{ domain of the inverse is all real numbers} \\ \text{That is from negative infinity to positive infinity} \end{gathered}[/tex]In interval notation:
[tex]\begin{gathered} \text{Domain = (-}\infty,\text{ }\infty) \\ f^{\{-1\}}(x)\text{ = }\frac{x^2+10}{5}\text{for domain (-}\infty,\text{ }\infty) \end{gathered}[/tex]One ton (2,000 pounds) is equivalent to 907 kilograms. A baby elephant weighs about 91 kilograms atbirth. Approximately how many pounds (lbs.) is this?A 200 lbs.B 400 lbs.C 600 lbs.D 1,000 lbs.
Answers
Since 2000 pounds = 907 kilograms, use the conversion factor:
[tex]\frac{2000\text{ pounds}}{907\operatorname{kg}}[/tex]To find out what 91 kg are equal to, measured in pounds:
[tex]91\operatorname{kg}=\frac{2000\text{ pounds}}{907\operatorname{kg}}=\frac{91\cdot2000}{907}\text{ pounds =200.66 pounds}[/tex]Therefore, a baby elephant weighs about 200 lbs.
Pour subtracted from the product of 10 and a number is at most-20,
Answers
we have
four subtracted from the product of 10 and a number is at most-20
Let
n ----> the number
so
[tex]10n-4\leq-20[/tex]solve for n
[tex]\begin{gathered} 10n\leq-20+4 \\ 10n\leq-16 \\ n\leq-1.6 \end{gathered}[/tex]the solution for n is the interval (-infinite, -1.6]
All real numbers less than or equal to negative 1.6
I need a math tutor asap .
Answers
For this exercise you need to remember that a Cube is a solid whose volume can be calculated using the following formula:
[tex]V=s^3[/tex]Where "V" is the volume of the cube and "s" is the length of any edge of the cube (because all the edges of a cube have the same length).
For example, if you have a cube and you know that:
[tex]s=5\operatorname{cm}[/tex]You can substitute this value into the formula and then evaluate, in order to find the volume of the cube. This would be:
[tex]\begin{gathered} V=(5\operatorname{cm})^3 \\ V=125\operatorname{cm}^3 \end{gathered}[/tex]The answer is:
You can find it using the formula
[tex]V=s^3[/tex]Where "s" is the length of any edge of the cube
name the three congruent parts shown by the marks on each drawing
Answers
In this case the aswer is very simple. .
The congruent parts are the equal parts in the 2 triangles.
Therefore, the congruent parts would be:
1. side AB and side XY
2. ∠ A and ∠ X
3. side AC and side XZ
That is the solution. .
there are approximately 1.2 x 10^8 households in the U.S. If the average household uses 400 gallons of water each day what is the total number of gallons of water used by households in the US each day ? Please Answer this im scientific notation
Answers
According to the given data we have the following:
total households in the US=1.2*10^8. hence:
[tex]1.2*10^8=120000000[/tex]average household uses 400 gallons of water each day
let x=total number of gallons of water used by households in the US each day
Therefore x=total households in the US*average gallons of water households uses each day
x=120,000,000*400
x=48,000,000,000
The total number of gallons of water used by households in the US each day is 48,000,000,000
The House of Pizza say that their pizzas are 14 inches wide, but when you measured it, the pizza was 12 inches. What is your percent error? Make sure to include your percent sign! (Round to 2 decimals)
Answers
The percent error of the house of the pizza would be 2.
The difference between the estimated and actual values in comparison to the actual value is expressed as a percentage. In other words, the relative error multiplied by 100 equals the percent error.
How to calculate the percent error?Percent errors indicate the magnitude of our errors when measuring something in an analysis process. Lower percentage errors indicate that we are getting close to the accepted or original value.
Suppose the actual value and the estimated values after the measurement are obtained. Then we have:
Error = Actual value - Estimated value
To determine the percent error, we will measure how much percent of the actual value, the error is, in the estimated value.
We have been given that House of Pizza says that their pizzas are 14 inches wide, but when measured, the pizza was 12 inches.
WE know that Error = Actual value - Estimated value
Then Error = 14 - 12 = 2
Therefore, the percent error would be 2.
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Plot Points & Graph Function (Table Given)
Answers
We have the next function
[tex]y=-\sqrt[]{x}+3[/tex]We need to calculate some points
x y
0 3
1 2
4 1
9 0
Let's plot the points and then we connect them in order to obtain the graph
The following distribution represents the number of credit cards that customers of a bank have. Find the mean number of credit cards.Number of cards X01234Probability P(X)0.140.40.210.160.09
Answers
To solve this problem we have a formula at hand: the mean (m) number of credits cards is
[tex]m=\sum ^{}_XX\cdot P(X)[/tex]Then,
[tex]m=0\cdot0.14+1\cdot0.4+2\cdot0.21+3\cdot0.16+4\cdot0.09=1.66[/tex]