Let's try so solve this equation:
[tex]\begin{gathered} -4k+4k=0 \\ 0=0 \end{gathered}[/tex]When you have a result of 0 = 0, that means the equation has infinite solutions, that is, any value of k we use would satisfy the equation.
So the equation has infinitely many solutions.
8. Here is a graph of the equation 3x - 2y = 12.
Select all coordinate pairs that represent a solution to
the equation.
A. (2,-3)
B. (4,0)
C. (5,-1)
D. (0, -6)
E. (2,3)
Answer:
A,B,D
Step-by-step explanation:
By replacing the points in the current equation you can get true statements which are correspondent to answer A,B,D
Which statements about the opposite of −12 are true? Select each correct answer. Responses −12 and its opposite are on located on the same side of zero on a number line. negative 12, and its opposite are on located on the same side of zero on a number line. The opposite of −12 is −1/12. The opposite of , negative 12, is , negative fraction 1 over 12, . −12 and its opposite are located the same distance from zero on a number line. negative 12, and its opposite are located the same distance from zero on a number line. The opposite of the opposite of −12 is −12.
Answer:
The opposite would be +12.
Step-by-step explanation:
In math, an opposite number is the number on the other side of zero on the number line that is the same distance from zero. For example, the number 5 is five spaces from zero on the right-hand side of the number line while the opposite. So the opposite would be -5 because it is five spaces from zero on the left side of a number line.
Is 1/4 n - 16 equivalent to 4(n - 4)?
Answer:
[tex]\frac{1}{4}n-16[/tex]is not equivalent to:
[tex]4(n-4)[/tex]Explanation:
The expression
[tex]\frac{1}{4}n-16[/tex]can be written as:
[tex]\frac{1}{4}(n-64)[/tex]It is not equivalent to:
[tex]4(n-4\text{)}=4n-16[/tex]Find the slope of the lines (-3,-1) and (-6,-10)
m = rise/run = (-10 - (-1))/(-6 - (-3)) = -9/-3 = 3
the slope of the line is equal to 3.
triangle XZW ~ triangle XYV, find the perimeter of triangle XZW
176.4
Explanation
as the triangle are similar we can set a proportion
Step 1
find the YZ value
a) let
[tex]ratio1=\frac{hypotenuse}{rigth\text{ side}}[/tex]so,for triangle XZW
[tex]ratio=\frac{40+32}{28+YZ}[/tex]and for triangle XYV
[tex]ratio=\frac{40}{28}[/tex]as the ratios are equal, we can set a proportion
[tex]\frac{40+32}{28+YZ}=\frac{40}{28}[/tex]b) now,solve for YZ
[tex]\begin{gathered} \frac{40+32}{28+YZ}=\frac{40}{28} \\ \frac{72}{28+YZ}=\frac{40}{28} \\ cross\text{ multiply} \\ 72*28=40(28+YZ) \\ 2016=1120+40YZ \\ subtract\text{ 1120 in both sides} \\ 2016-1120=1120+40YZ-1120 \\ 896=40YZ \\ divide\text{ bothsides by 40} \\ \frac{896}{40}=\frac{40YZ}{40} \\ 22.4=YZ \end{gathered}[/tex]so
YZ=22.4
Step 2
find the length of the side WZ
a) let
[tex]ratio=\frac{hypotenuse\text{ }}{base}[/tex]hence
[tex]\begin{gathered} ratio_1=\frac{40+32}{WZ}=\frac{72}{WZ} \\ ratio_2=\frac{40}{30} \end{gathered}[/tex]set the proportion and solve for YZ
[tex]\begin{gathered} ratio_1=\text{ ratio}_2 \\ \frac{72}{WZ}=\frac{40}{30} \\ cross\text{ multiply} \\ 72*30=40WZ \\ 2160=40WZ \\ divide\text{ both sides by 40} \\ \frac{2160}{40}=\frac{40WZ}{40} \\ 54=WZ \end{gathered}[/tex]Step 3
finally, find the perimeter of triangle XZW
Perimeter is the distance around the edge of a shape,so
[tex]Perimeter_{\Delta XZW}=XY+YZ+ZW+WV+VX[/tex]replace and calculate
[tex]\begin{gathered} Per\imaginaryI meter_{\Delta XZW}=XY+YZ+ZW+WV+VX \\ Perimeter_{\Delta XZW}=28+22.4+54+32+40 \\ Perimeter_{\Delta XZW}=176.4 \end{gathered}[/tex]therefore, the answer is
176.4
I hope this helps you
mputing and Using a Least-Squares Regression LineVehiclesight (tons) Gas mileage (mpg)1.6291.6451.75261.952221821211822.32.5The table shows the weight and gas mileage of severalvehicles.What is the equation of the least-squares regressionline, where ŷ is the predicted gas mileage and x is theweight?ŷ=V+According to the regression equation, a car that weighs1.8 tons would have a gas mileage of aboutmiles per gallon.
From the table, we have the following points:
(x, y) ==> (1.6, 29), (1.6, 45), (1.75, 26), (1.95, 22), (2, 18), (2, 21), (2.3, 21), (2.5, 18)
Let's find the regression line.
Apply the slope-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
To find the slope, apply the formula:
[tex]m=\frac{n(\Sigma xy)-\Sigma x\Sigma y}{n(\Sigma x^2)-(\Sigma x)^2}[/tex]Where:
• ∑x = 1.6 + 1.6 + 1.75 + 1.95 + 2 + 2 + 2.3 + 2.5 = 15.7
• ∑y = 29 + 45 + 26 + 22 + 18 + 21 + 21 + 18 = 200
• ∑xy = 1.6⋅29 + 1.6⋅45 + 1.75⋅26 + 1.95⋅22 + 2⋅18 +2⋅21 +2.3⋅21 + 2.5⋅18 = 378.1
• ∑x² = 1.6² + 1.6² + 1.75² + 1.95² + 2² + 2² + 2.3² + 2.5² = 31.525
,• n is the number of data = 8
Now, plug in values into the equation and solve for m:
[tex]\begin{gathered} m=\frac{8(378.1)-15.7*200}{8(31.525)-(15.7)^2} \\ \\ m=-20.175\approx20.2 \end{gathered}[/tex]The slope, m = -20.2
To find the y-intercept, b, apply the formula:
[tex]\begin{gathered} b=\frac{(\Sigma y)(\Sigma x^2)-\Sigma x\Sigma xy}{n(\Sigma x^2)-(\Sigma x)^2} \\ \\ b=\frac{200(31.525)-15.7*200}{8(31.525)-15.7^2} \\ \\ b=64.594\approx64.6 \end{gathered}[/tex]Therefore, the regression equation is:
y = 64.6 + (-20.2)x
(b). Substitute 1.8 for x in the equation and solve for y:
y = -20.2(1.8) + 64.6
y = 28.24 = 28.
ANSWER:
(A). y = 64.6 + (-20.2)x
(B). 28
Answer:
here's your answer :)
Step-by-step explanation:
Find the indicated quantity, given u = (4, -9), v = (-4, -7).Step 4 of 4: Find (u • v)4v.
Answer:
[tex]\begin{equation*} \langle-1316,-2303\operatorname{\rangle} \end{equation*}[/tex]Explanation:
Given the vectors:
[tex]\begin{gathered} u=\langle4,-9\rangle \\ v=\langle-4,-7\rangle \end{gathered}[/tex]The dot product of u and v is calculated below:
[tex]\begin{gathered} u\cdot v=4\times-4+-9\times-7 \\ =-16+63 \\ =47 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} (u\cdot v)4v=47\times4\langle-4,-7\rangle \\ =329\langle-4,-7\rangle \\ =\langle-4\times329,-7\times329\rangle \\ =\langle-1316,-2303\operatorname{\rangle} \end{gathered}[/tex]The indicated quantity is:
[tex]\begin{equation*} \langle-1316,-2303\operatorname{\rangle} \end{equation*}[/tex]
Louis food out six different size at the picnic at the end of the picnic he noticed this about about the pies one whole apple pie was eaten and 3/4
Louis had 6 different pies. Some of them were eating and we want to know how much pie there's left. First, we have the information that one apple pie was entirely gone. From this, we know there were 5 pies remaining.
[tex]6-1=5[/tex]Then, he also noticed the other apple pie had 3/4 gone. Which means that 1/4 of this second apple pie was leftover.
[tex]1-\frac{3}{4}=\frac{1}{4}[/tex]Applying this same logic, we can deduct all the slices that were eaten from the total amount of pie we had at first to get the leftovers.
[tex]\begin{gathered} 6-1-\frac{3}{4}-\frac{1}{2}-\frac{1}{8}-\frac{5}{8}-\frac{3}{4} \\ =5-\frac{1}{2}-\frac{6}{4}-\frac{6}{8} \\ =5-2-\frac{3}{4} \\ =3-\frac{3}{4} \\ =2+\frac{1}{4} \end{gathered}[/tex]What we've done in this last equation, was taking our first amount of pies (6), subtract the whole apple pie that was eaten (1), the three quarters that were eaten from the other apple pie (3/4) and the other eaten slices from the others.
Which means, the result of this calculation is our amount of leftover slices.
We still have 2 and a quarter pies.
graph a line that is parallel to the given line. determine the slope of the given line and the one you graphed in simplest form. click and drag on the graph to draw a line. Click and drag to plot a parallel line. The line will change colors when a parallel or perpendicular line is drawn accurately.
Choosing two points of the line given ( Lg ):
• A( ,0, -4, )
,• B( -,1.5, 0, )
Procedure:
0. Finding the slope ( ,m ,) of ,Lg:
[tex]m_{Lg}=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m_{Lg}=\frac{0_{}-(-4)_{}}{-1.5_{}-0_{}}=\frac{4}{-1.5}=-\frac{8}{3}[/tex][tex]m_{Lg}=-\frac{8}{3}[/tex]Also, based on point (0, -4), we can determine the intersection in y - axis ( b = -4). Therefore, the equation of the line given is:
[tex]y=mx+b[/tex][tex]y=-\frac{8}{3}x-4[/tex]To determine the parallel slope ( mp ), we know that parallel lines have the same slope:
[tex]m_p=m_{Lg}=-\frac{8}{3}[/tex]For the new graph, you would have to choose a different parameter b, all the equation would be the same except b. Choosing b = 3 as an example:
[tex]y=-\frac{8}{3}x+3[/tex]Answer:
• Original slope: -8/3
,• Parallel slope: -8/3
use 3.14for πThe area of the circle is
The general expression for the area of circle with radius r is express as :
[tex]\text{ Area of circle = }\Pi(radius)^2,\text{ where }\Pi=3.14[/tex]In the given circle : radius is 5ft
Substitute radius = 5 ft in the expression for the area of circle :
[tex]\begin{gathered} \text{ Area of circle = }\Pi(radius)^2 \\ Area\text{ of circle=3.14}\times5\times5 \\ \text{ Area of Circle = 78.5 ft}^2 \end{gathered}[/tex]Answer : Area of circle is 78.5 square feet
perform the calculation then round to the appropriate number of significant digits
The given expression is,
[tex]\frac{308.45}{1.12}[/tex]On division we get,
[tex]\frac{308.45}{1.12}=275.4017[/tex]On rounding we get, 275.402.
Which of the following distribution belongs to discrete distribution?Even distributionOdd distributionInteger distributionReal numbers distribution
Explanation:
Discrete probability distribution:
It counts the occurrences that have countable or finite outcomes.
As the even numbers, odd numbers are countably infinite .
The real numbers are not countable.
So, the discrete distributions are Integer distribution.
Line segment AB has a midpoint C.If AC=17 and AB = 5x-6, then find the value of x
From that diagram that is drawn above, C is the midpoint of the line AB:
AC = 17
AB = 5x - 6
Since C is the midpoint of AB;
AB = 2AC = 2CB:
5x - 6 = 2(17)
5x - 6 = 34
5x = 34 + 6
5x = 40
x = 40/5
x = 8
Answer two questions about Equations A and B
A. 2r-1= 5x
B. -1 = 3x
1) How can we get Equation B from Equation A?
Choose 1 answer:
Add/subtract the same quantity to/from both sides
Add/subtract a quantity to/from only one side
Rewrite one side (or both) by combining like terms
Rewrite one side (or both) using the distributive property
In the given equation A, we can (A) subtract the same quantity from both sides.
What are equations?In a mathematical equation, the equals sign is used to express that two expressions are equal. An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. Like 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others. The three primary forms of linear equations are point-slope, standard, and slope-intercept.So, obtain equation B from equation A:
Equation A: 2x - 1 = 5xEquation B: -1 = 3xWe can subtract (2x) from both sides to get equation B as follows:
2x - 1 = 5x2x - 2x - 1 = 5x - 2x-1 = 3xTherefore, in the given equation A, we can (A) subtract the same quantity from both sides.
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Two question I want to verify my answerSolve for y in terms of x 2x =1-5yAnd Simplify the given expression Write answer with a positive exponent (X^-3/y^4)^-4
Part 1
we have
2x =1-5y
solve for y
step 1
Adds 5y both sides
2x+5y=1
step 2
subtract 2x both sides
5y=-2x+1
step 3
Divide by 5 on both sides
y=-(2/5)x+1/5
Part 2
we have the expression
[tex](\frac{x^{-3}}{y^4})^{-6}=(\frac{y^4}{x^{-3}})^6=(y^4x^3)^6=y^{(24)}x^{(18)}[/tex]For each equation in the table, give the slope of the graph.
Answer:
1. undefined
2. 0
3. -6
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = slope
b = y-intercept.
Since the equation x = -6 is a vertical line, the slope is undefined.
Since y = -6 is a horizontal line, the slope is 0.
The slope of y = -6x is -6. This is because it is the coefficient of the variable x.
Given a function described as the equation y= 4x - 4, what is y when x is 1, 2, and 3?A 2, 8, 16B 4,8, 12C 0,4,8D 0, 6, 12
Answer
C. 0, 4, 8
Explanation
Given function:
y = 4x - 4
What to find:
To find y when x = 1, 2, and 3
Step-by-step solution:
When x = 1
y = 4(1) - 4
y = 4 - 4
y = 0
When x = 2
y = 4(2) - 4
y = 8 - 4
y = 4
When x = 3
y = 4(3) - 4
y = 12 - 4
y = 8
ty received test Graves of 71%, 82%, 71%, 78% and 78%.A) what grade would he need to make on the 6th test to get a C if a C is at least 75% but less than 80%?B) is it possible for tie to get a b or better for his test average at least 80%?
As given that first 5grades are: 71%, 82%, 71%, 78% and 78%.
Let the 6th grade be C
a). Then:
[tex]75\leq\frac{71+82+71+78+78+C}{6}\leq80[/tex]Simplifying it:
[tex]\begin{gathered} 75\leq\frac{71+82+71+78+78+C}{6} \\ 75\times6\leq380+C \\ 450\leq380+C \\ 450-380\leq C \\ 70\leq C \end{gathered}[/tex]And:
[tex]\begin{gathered} \frac{380+C}{6}\leq80 \\ 380+C\leq480 \\ C\leq100 \end{gathered}[/tex]So C should be in between 70 to 100.
b). For at least 80%:
[tex]\begin{gathered} \frac{71+82+71+78+78+C}{6}\ge80 \\ 380+C\ge80\times6 \\ 380+C\ge480 \\ C\ge100 \end{gathered}[/tex]It is not possible for getting b grade as one cannot achieve more than maximum marks if the maximum marks are 100.
Margo borrows $1200, agreeing to pay it back with 4% annual interest after 17 months. How much interest will she pay?
Answer:
$68
Step-by-step explanation:
P = $1200
R = 4%
T = 17months (Convert to years; 17 months ÷ 12 months)
Formular for Interest; I = PRT
100
I = $1200 × 4 × 17
100 × 12
I = $68
In an all boys school, the heights of the student body are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. What is the probability that a randomly selected student will be taller than 71 inches tall, to the nearest thousandth?
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Answer:
0.010
Step-by-step explanation:
We solve the above question using z score formula
z = (x-μ)/σ, where
x is the raw score = 63 inches
μ is the population mean = 70 inches
σ is the population standard deviation = 3 inches
For x shorter than 63 inches = x < 63
Z score = x - μ/σ
= 63 - 70/3
= -2.33333
Probability value from Z-Table:
P(x<63) = 0.0098153
Approximately to the nearest thousandth = 0.010
Therefore, the probability that a randomly selected student will be shorter than 63 inches tall, to the nearest thousandth is 0.010.
Each of John’s notebook is 3/4 inches wide. If he has 36 inches of space remaining on his bookshelf, how many notebooks will fit? Write your answer in simplest form.
Given that:
- The width of each of John’s notebooks is:
[tex]\frac{3}{4}in[/tex]- The space remaining on his bookshelf is:
[tex]36in[/tex]Let be "x" the number of notebooks that will fit in John's bookshelf.
Knowing that:
[tex]\frac{3}{4}in=0.75in[/tex]You can set up the following proportion:
[tex]\frac{1}{0.75}=\frac{x}{36}[/tex]Now you have to solve for "x":
[tex]\begin{gathered} (\frac{1}{0.75})(36)=\frac{x}{36} \\ \\ \frac{36}{0.75}=x \end{gathered}[/tex][tex]x=48[/tex]Hence, the answer is:
[tex]48\text{ }notebooks[/tex]After every score in a sample is multiplied by 5,the mean is found to be M = 40.What was the value for the original mean?
Since each of the data value is multiplied by 5, the new mean will be 5 times the original mean.
To get the original mean, we need to divide by 5.
Therefore the original mean is given by:
[tex]\frac{40}{5}=8[/tex]Answer: 8
If you are given a rectangle, what are the degrees of its rotational symmetry? (I need all of them between but not including 0 and 360 degrees)
A rectangle is an Order 2 of symmetry because it matchs its fugure only 2 times while rotating through 360 degrees.
The degrees of symmetry can be calculated as:
[tex]\frac{360\degree}{\text{Order}}=\frac{360\degree}{2}=180\degree[/tex]We see that at 180 degrees of rotation the shape is identical to the original shape.
This does not repeat for any other angle between 0 and 360 degrees.
Answer: 180 degrees.
Suppose angles a and B are the two acute angles in a right triangle and that b < a. Apply the relationship between sine and cosine todetermine which statements are correct.sin(6x - 10) = cos(4x + 10)A)x = 9B)a = 46°a = 48°D)B = 42°E)B = 44
The right statements are: A, B and E
Sin(A)=cos(B)
then we check if using x=9 this holds true:
sin(6x-10)=cos(4x+10)
sin((6*9)-10) = sin(44º)
cos(4x+10)=cos(46)
Sin(44)=0.694=cos(46)
then a is true
Now, we know that b
Mary used the quadratic formula to find the zeros of the equation below. Select the correct zeros of the equation:3x^2 - 9x + 2 = 0Answer choices include:x = fraction numerator 9 plus-or-minus square root of 57 over denominator 6 end fractionx equals fraction numerator negative 9 plus-or-minus square root of 57 over denominator 2 end fractionx equals fraction numerator 9 plus-or-minus square root of 105 over denominator 2 end fractionx equals fraction numerator negative 9 plus-or-minus square root of 105 over denominator 6 end fraction
We have the next quadratic function given:
[tex]3x^2-9x+2=0[/tex]Mary used the next quadratic formula:
[tex]x=\frac{-b^\pm\sqrt{b^2-4ac}}{2a}[/tex]Replace using the form ax²+bx+c
Where a= 3
b=-9
c=2
Then:
[tex]\begin{gathered} x=\frac{-\lparen-9)\pm\sqrt{\left(-9\right)^2-4\left(3\right)\left(2\right)}}{2\left(3\right)} \\ x=\frac{9\pm\sqrt[]{57}}{6}\frac{}{} \end{gathered}[/tex]Therefore, the correct answer is "x = fraction numerator 9 plus-or-minus square root of 57 over denominator 6 end fraction"
Dylan’s boat can carry 40 people across a river. Last month, 2504 people road on Dylan’s boat. What is the least number of trips that Dylan could have made across that river.
The required least number of trips that Dylan would have made across the river is 62.
Given that,
Dylan’s boat can carry 40 people across a river. Last month, 2504 people rode on Dylan’s boat. What is the least number of trips that Dylan could have made across that river is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Total people road = 2504
Maximum people can road at single trip = 40
Least number of trip = 2504 / 40
Least number of trip = 62
Thus, the required least number of trips that Dylan would have made across the river is 62.
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Please help ASAP!! 31 points and brainliest!
I really need help! Please show your work so I can understand how to get the answers too!
A relation is a function if it has only One y-value for each x-value. Functions f(2/3)=2/9 for f(x)=2x²-4x+2 and f(1/4)==-21/4 for f(x)=4x²+2x-6
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is
f(x)=2x²-4x+2
Put x=2/3
f(2/3)=2(2/3)²-4(2/3)+2
=2(4/9)-8/3+2
=8/9-8/3+2
=(8-24+18)/9
f(2/3)=2/9
Now f(x)=4x²+2x-6
Put x=1/4
f(1/4)=4(1/4)²+2(1/4)-6
=4/16+2/4-6
=1/4+1/2-6
= 1+2-24/4
f(1/4)==-21/4
Hence functions f(2/3)=2/9 for f(x)=2x²-4x+2 and f(1/4)==-21/4 for f(x)=4x²+2x-6
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Find the missing quantity with the information given. Round rates to the nearest whole percent and dollar amounts to the nearest cent
Given:
Original Price $4.50
Markdown=$1.30
[tex]\begin{gathered} \text{ \% Markdown=}\frac{1.30}{4.50}\times100 \\ \text{ \% Markdown=}28.89\text{ \%} \end{gathered}[/tex]Identify the property of real numbers illustrated in the following equation.(+6) + [y? • (-4)] = [y2 • (-4)] + (-6)
Given
[tex]\mleft(+6\mright)+\mleft[y^2•(-4)\mright]=\mleft[y^2•(-4)\mright]+(-6)[/tex]Answer
Commutative property of addition
the scale of a map is 1cm: 7milesthe distance between two cities is 102.2 miles.find the distance between the two cities on the map
Ok, so:
We know that the scale given is the next one:
1cm = 7miles.
Now, let me draw something here below:
So, the cities are separated by a distance of 102.2 miles.
If 1 cm = 7 miles,
Then, we're going to convert 102.2 miles to our map scale.
102.2 miles * ( 1cm / 7 miles).
And we obtain:
14.6cm