Answers
Given
[tex]-6=-20-v[/tex]- For -72 = 9(-20 - v):
[tex]\begin{gathered} -\frac{72}{9}=\frac{9(-20-v)}{9} \\ -8=-20-v \end{gathered}[/tex]The equation is not equivalent
- For -90 = 15(-20 - v):
[tex]\begin{gathered} \frac{-90}{15}=\frac{15(-20-v)}{15} \\ -6=-20-v \end{gathered}[/tex]The equation is equivalent
- For 5 * -6 = -100 - 5v:
Common factor 5
[tex]\begin{gathered} -30=5(-20-v) \\ \frac{-30}{5}=\frac{5(-20-v)}{5} \\ -6=-20-v \end{gathered}[/tex]The equation is equivalent
- For 3 * -6 = -60 - 3v:
Common factor 3
[tex]\begin{gathered} -18=3(-20-v) \\ \frac{-18}{3}=\frac{3(-20-v)}{3} \\ -6=-20-v \end{gathered}[/tex]The equation is equivalent
Answer:
-90 = 15(-20 - v)
5 * -6 = -100 - 5v
3 * -6 = -60 - 3v
Related Questions
Write the augmented matrix for the following system of equations.
9y-5+9z = 0
7x=-3y+7+z
5x + 7y = 5
Answers
The augmented matrix of the given equations is shown (Refer to the matrix attached below.)
What is an augmented matrix?An augmented matrix in linear algebra is a matrix created by joining the columns of two given matrices, typically so that the same basic row operations can be applied to each of the given matrices individually. An augmented matrix for a system of equations is a matrix of numbers where each column represents all the coefficients for a single variable and each row represents the constants from one equation (both the coefficients and the constant on the other side of the equal sign).So, the augmented matrix will be:
Equations are,
9y-5x+9z = 07x=-3y+7+z5x + 7y = 5Rewrite them systematically as:
-5x + 9y + 9z = 07x + 3y - z = 75x + 7y + 0 = 5Now, augmented matrix:
(Refer to the matrix attached below)Therefore, the augmented matrix of the given equations is shown (Refer to the matrix attached below.)
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At 7 pm, the temperature outside was -5°C what does | - 5 | represent in this situation
Answers
means it's 5 degrees below zero
The United States is the worlds leading exporter of wheat with approximately 27.8 billion metric tons per year . Suppose turkey exports 10% of the U.S total . About how many metric tons are exported by turkey ?
Answers
Answer: 3 billion
Step-by-step explanation:
27.8 x 10% = 2.78 billion which rounds to 3
Describe how CPCTC would help you here. (8x-6) D T Students DE VOLTRON
Answers
CPCTP = Corresponding parts of congruent triangles are congruent:
That means that since both angles are congruent (equal) the sides are also congruent:
8x+6 = 3x+9
Solve for x
8x-3x = 9-6
5x= 3
x= 3/5
m³ +9n when m = 4
and n = 5
Answers
Answer:
109
Step-by-step explanation:
you first cube 4 which means 4x4x4
64
then multiply 9x5 and get 45
then add 45+64 and you get your answer
r2/r12 A. r10B. 1/r6C.1/r10D. r8E. r6
Answers
this is
[tex]\frac{r^2}{r^{12}}=r^{2-12}=r^{-10}=\frac{1}{r^{10}}[/tex]answer: C
A triangle on a coordinate plane is translated according to the rule T-8, 4(x, y). Which is another way to write this rule?
(x, y)
(x + 4, y-8)
(x-4, y-8)
O(x, y)
O (x,y) - (x-8, y + 4)
O(x, y) (x+8, y-4)
Answers
A triangle coordinate translate T-8, 4(x, y). Then we can rewrite the translation rule as :
( x, y ) → ( x - 8, y + 4).
Solution:A translation is a type of transformation in which every point in a figure moves the same distance in the same direction. Slides are another term for translations. A translation can be described using words like "moved up 3 and over 5 to the left" or with notation.The function translation / transformation rules are as follows: f (x) + b raises the function by b units. The function f (x) b is shifted downward by b units. f (x + b) moves the function to the left by b units.Here we know that according to the translation rule Ta,b( x , y) the translation of a point (x,y) by (a,b) is given by:
(x , y) → ( x + a , y + b)
The following statement is true: A triangle on a coordinate plane is translated according to the rule.
T₋₈ , ₄(x , y).
Then, another way to write this rule is:
( x , y) → (x + (-8) , y + (4))
( x, y ) → ( x - 8, y + 4).
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Prove the segments joining the midpoint if consecutive sides of an isosceles trapezoid form a rhombus.
Answers
DEFG is a rhombus by definition of rhombus (option B)
Explanation:
To prove that DEFG is a rhombus, we will find the distance between all the 4 sides of the quadrilateral. A rhombus has all 4 sides equal.
Distance formula is given as:
[tex]$$dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}$$[/tex][tex]\begin{gathered} distance\text{ DE: D}(-a-b,\text{ c})\text{ and E}(0,\text{ 2c}) \\ x_1=-a-b,y_1=c,x_2=0,y_2\text{ = 2c} \\ distance\text{ DE = }\sqrt{(0\text{ - }(-a-b))^2\text{ + }(2c\text{ - c})^2} \\ distance\text{ DE = }\sqrt{(0\text{ +}a+b)^2\text{ + c}^2}\text{ } \\ distance\text{ DE = }\sqrt{(\text{a + b})^2+c^2} \end{gathered}[/tex][tex]\begin{gathered} distance\text{ EF: E}(0,\text{ 2c})\text{ and F}(a\text{ + b, c}) \\ x_1=0,y_1=2c,x_2=a+b,y_2\text{ = c} \\ distance\text{ EF = }\sqrt{(c\text{ - 2c})^2+\text{ }(a\text{ + b - 0})^2} \\ distance\text{ EF = }\sqrt{(-c)^2+(a+b)^2}\text{ } \\ \text{distance EF = }\sqrt{c^2\text{ + }(a+b)^2} \end{gathered}[/tex][tex]\begin{gathered} distance\text{ GF: G}(0,\text{ 0})\text{ and F }(a+b,\text{ c}) \\ x_1=0,y_1=0,x_2=a+b,y_2\text{ = c} \\ distance\text{ GF = }\sqrt{(c\text{ - 0})^2+\left(a+b-0\right)^2} \\ distance\text{ GF = }\sqrt{c^2+(a+b)^2} \end{gathered}[/tex][tex]\begin{gathered} distance\text{ DG: D}(-a-b,\text{ c})\text{ and G }(0,\text{ 0}) \\ x_1=-a-b,y_1=c,x_2=0,y_2\text{ = 0} \\ distance\text{ GD = }\sqrt{(0-c)^2+(0-(-a-b))^2} \\ distance\text{ GD = }\sqrt{(-c)^2+\left(0+a+b\right)^2} \\ distance\text{ GD = }\sqrt{c^2\text{ + }(a+b)^2} \end{gathered}[/tex]From our calculation, Distance DE = Distance EF = Distance GF = Distance GD
All 4 sides are equal (congruent)
DEFG is a parallelogram with congruent sides. So DEFG is a rhombus by definition of rhombus (option B)
Fractions and Mixed Numbershogy Commercing eng yourStephan owns a landscaping compary. Today, he is mowing three lawns: one is 1/4 of an acre, one is of 1/2 an acre, and one is 1 1/3 acres. How many acres of lawn is Stephan going to nowtoday. Simplify your answer and write it as a mixed fraction if necessary25 acresSvendoseSotPassHold
Answers
We would add each of the given fraction. Thus, the number of acres that he is going to mow
Ethan's income is 4500 per month a list of some of his expenses appear below what percent of Ethan's expenses is rent
Answers
Ethan's income:4500
$975 was spent in rent
percentage of Ethan's expenses on rent:
[tex]\begin{gathered} =\frac{975}{4500}\times100 \\ =21.7 \end{gathered}[/tex]percentage of Ethan's income on rent=21.7%
Bob is spending money at a constant rate. Suppose he initially has $1000, and after 8 months, he has $200.
Which of these expresses the rate at which Bob's amount of money is changing?
Answers
The required rate at which Bob's amount of money is changing is $100 per month.
Given that,
Bob is spending money at a constant rate. Suppose he initially has $1000, and after 8 months, he has $200. The expression of the rate at which Bob's amount of money is changing is to be determined.
Here,
Initial money = $1000
Rest money = $200
Time = 8 months,
Rate = [1000 - 200] / 8
Rate = [800] / 8
Rate = $100
Thus, the required rate at which Bob's amount of money is changing is $100 per month.
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Find the percent of change from 80 kmph to 60 kmph
33.3% increase
25% increase
25% decrease
33.3% decrease
Answers
The most appropriate choice for Percentage will be given by
There is a 25 % decrease in speed
3rd option is correct
What is percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. Then that number is called percentage.
For example, 2% means [tex]\frac{2}{100}[/tex]
Original speed = 80 kmph
New speed = 60 kmph
Decrease in speed = (80 - 60) kmph
= 20 mph
Percentage decrease = [tex]\frac{20}{80} \times 100\\[/tex]
= 25 %
There is a 25% decrease in speed.
3rd option is correct
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rewrite the sum in the form a(b+c) such that integers b and c have no common factor
Answers
The given format of the sum is
[tex]a(b+c)[/tex]The sum is,
24+16
The greatest common factor of 24 and 16 is 8, since,
[tex]\begin{gathered} 24=12\times2=3\times2\times2\times2 \\ 16=8\times2=4\times2\times2=2\times2\times2\times2 \end{gathered}[/tex]Therefore we can write, 24+16 as,
[tex]24+16\rightarrow8\times3+8\times2=8(3+2)[/tex]Select the graph of the piecewise function given by: ƒ(x) = 0 for 0 ≤ x < 4ƒ(x) = 3 for 4 ≤ x < 8ƒ(x) = 6 for 8 ≤ x < 12
Answers
Given,
ƒ(x) = 0 for 0 ≤ x < 4
ƒ(x) = 3 for 4 ≤ x < 8
ƒ(x) = 6 for 8 ≤ x < 12
To select the graph of the given piecewise function.
The solid circle represents the inclusion of the point. Similarly, the hollow circle represents the exclusion of the point.
Option A:
It can be observed in option A that the circles are represented properly and the function is properly shown in the respective interval.
As a result, option A is correct.
Option B:
It can be observed that option B does not follow the proper circle for denoting the endpoints of the interval.
As a result, option B is incorrect.
Option C:
A company makes pens. They sell each pen for $ 6
Answers
Answer:
a. -3,000
b. 1,750
Explanation:
We were given the following information:
A company makes pens:
Each pen is sold at $6 per unit
Revenue = 6 * x
Manufacture Cost = 2 * x
Start-up Cost = $7,000
Cost = Manufacture Cost + Start-up Cost = 2 * x + 7,000
Profit = Revenue - Cost
a) The profit is calculated for 1,000 pens as shown below:
[tex]\begin{gathered} Profit=Revenue-Cost \\ \text{For the making of 1,000 pens, it means: }x=1,000 \\ Revenue=6\cdot x=6\times1,000 \\ Revenue=\text{\$}6,000 \\ Cost=2\cdot x+7,000 \\ Cost=2\times1,000+7,000 \\ Cost=2,000+7,000 \\ Cost=\text{\$}9,000 \\ \\ Profit=6,000-9,000 \\ Profit=-\text{\$}3,000 \\ \\ \therefore Profit=-\text{\$}3,000 \end{gathered}[/tex]Hence, the profit is -3,000
b) We will calculate for the number of pens needed to be sold for the company to break even as shown below. We have:
[tex]\begin{gathered} \text{At breakeven: }Revenue=Cost \\ \Rightarrow6x=2x+7,000 \\ \text{We will calculate for the value of the variable ''x'':} \\ 6x=2x+7,000 \\ \text{Subtract ''2x'' from both sides, we have:} \\ 6x-2x=7,000 \\ 4x=7,000 \\ \text{Divide both sides by ''4'', we have:} \\ x=\frac{7,000}{4} \\ x=1,750 \\ \\ \therefore x=1,750 \end{gathered}[/tex]Hence, the breakeven occurs when the company has made 1,750 pens
The length, x (in inches), and weight, y (in ounces), for
a type of bass were measured for a random sample of
10 bass from a lake. These measurements were then
analyzed and the value for 2 was determined to be
96%.
Which of the following is the best interpretation of this
value?
4% of the variation in the bass's length is
determined by the variation in the bass's weight.
O 96% of the variation in the bass's weight is
determined by the variation in the bass's length.
96% of the variation in the bass's length is
determined by the variation in the bass's weight.
98% of the variation in the bass's weight is
determined by the variation in the bass's length.
Answers
Best interpretation of the value of 96% is that there is a strong positive linear relationship between the length and weight of the bass in the sample
What is linear equation?
A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:
y = mx + b
The value of 96% refers to a correlation coefficient, which measures the strength of the linear relationship between two variables. In this case, the two variables are length (x) and weight (y) of a type of bass. A correlation coefficient of 96% indicates a very strong positive correlation between the two variables, meaning that as the length of the bass increases, its weight tends to increase as well.
However, the value does not provide information about causality or which variable is influencing the other.
Therefore, none of the given interpretations are accurate. Instead, the best interpretation of the value of 96% is that there is a strong positive linear relationship between the length and weight of the bass in the sample, and further analysis may be needed to determine the direction and strength of causality between the two variables.
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Solve and graph 3x+1<10
Answers
The given inequality is
3x + 1 < 10
Subtracting 1 from both sides of the inequality, we have
3x + 1 - 1 < 10 - 1
3x < 9
Dividing both sides of the equation by 3, we have
3x/3 < 9/3
x < 3
The number line is shown below
The values to the left of 3 are all less than 3. The circle is not shaded because 3 is not included in the values of x.
(1/5+1/2 to the 2nd power)+3/10x5
Answers
The value of this given algebraic addition is 51/100.
The problem is in sentence format, we have to convert this to a mathematical format.
We can find the value of these given mathematical digits by following a few steps.
1/5 + ( 1/2 )^2 + 3/10×5
= 1/5 + 1/4 + 3/50 = 40/ 200 + 50/200 + 12/200
( we have multiplied both denominator and nominators with different numbers to assure that denominator of all numbers is the same )
= 102/200 ( here we have divided both with 2, to minimize the given fraction )
= 51/100.
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Find the solution to the system of equations. You can use the interactive graph below to find the solution.-2x+2y=-43x+3y=-18x=___y=___
Answers
Answer:
• x=-2
,• y=-4
Explanation:
Given the system of equations:
[tex]\begin{gathered} -2x+2y=-4 \\ 3x+3y=-18 \end{gathered}[/tex]Solve for x and y using the graphical method.
The first step is to plot each of the lines using the x and y-intercepts.
First Equation (-2x+2y=-4)
When x=0
[tex]\begin{gathered} 2y=-4 \\ y=-2 \\ \implies(0,-2) \end{gathered}[/tex]When y=0
[tex]\begin{gathered} -2x=-4 \\ x=-\frac{4}{-2} \\ x=2 \\ \implies(2,0) \end{gathered}[/tex]Join the points (0,-2) and (2,0) as shown below:
Second Equation (3x+3y=-18)
When x=0
[tex]\begin{gathered} 3y=-18 \\ y=-6 \\ \implies(0,-6) \end{gathered}[/tex]When y=0
[tex]\begin{gathered} 3x=-18 \\ x=-\frac{18}{3} \\ x=-6 \\ \implies(-6,0) \end{gathered}[/tex]Join the points (0,-6) and (-6,0) on the same graph as shown below:
The solution to the system is the point where the two lines intersect.
The point is (-2,-4).
Therefore:
• x=-2
,• y=-4
,•
What are the coordinates of the focus of the parabola?y=18x2+2x
Answers
The equation of the given parabola is
[tex]y=\frac{1}{8}x^2_{}+2x[/tex]Rewrite the equation in the vertex form
[tex]y=a(x-h)^2+k[/tex]The equation becomes
[tex]\begin{gathered} y=\frac{1}{8}x^2+2x \\ y=\frac{1}{8}(x^2+16x) \\ 8y=x^2+16x \\ 8y=x^2+6x+64-64 \\ 8y=(x+8)^2-64 \end{gathered}[/tex]Divide through the equation by 8
This gives
[tex]y=\frac{1}{8}(x+8)^2-8[/tex]Comparing the equation with the vertex form
It follows
[tex]a=\frac{1}{8},h=-8,k=-8[/tex]The focus of a parabola in vertex form is given as
[tex]F=(h,k+\frac{1}{4a})[/tex]Substitute h = -8, k = -8 and a = 1/8 into the formula for focus
This gives
[tex]F=(-8,-8+\frac{1}{4(\frac{1}{8})})[/tex]Simplify the expression
[tex]\begin{gathered} F=(-8,-8+\frac{1}{\frac{1}{2}}) \\ F=(-8,-8+2) \\ F=(-8,-6) \end{gathered}[/tex]Therefore, the focus of the parabola is at (-8, -6)
Your Aunt is having a baby. You have created a party game for a baby shower. It is called pick the gender. You put pink and blue tiles into a bag. You ask two guests to pick one tile each out of the bag without looking. You tell your guests that if they are the same color, player A wins and if they are two different colors, then player B wins.How many tiles of which colors did you put into the bag to make sure that both players have an equal chance of winning?
Answers
There have to be an equal number of pink and blue tiles in the bag make sure that both players A and B have an equal chance of winning as they events of probability.
What is probability of an event?If an event say A can occur in a-ways and fail to occur in b-ways and as well (a + b)-ways are equally likely, then the probability of A is given as P(A) = a/(a + b).
Let the probability of having a winner at the party be P(W) = 1, which is a certain event.
then addition of the probability of player A = P(A) winning and the probability of player B = P(B) winning must be equal to 1.
Hence,
P(A) + P(B) = (1/2) + (1/2)
P(A) + P(B) = 1
This implies there must be equal number of the pink and blue tiles.
Thus, there have to be equal number of pink and blue tiles so that any of the event occurring must result in the two players having equal chance of winning.
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Estimate the total cost of the following items for your dorm room round the individual cost to the nearest $10 round your answer to the nearest dollar (cents)
Answers
We will determine the approximate cost as follows:
[tex]149.67+59.58+29.56+19.79=258.60[/tex]So, the total cost would be $258.60.
E3.This table shows the times, in minutes, It took 40 sixth grade students to run 1 mile.frequency15time (minutes)4 to less than 66 to less than 88 to less than 1010 to less than 1212 to less than 1414 to less than 16131272INTLDraw a histogram for the information in the table.321
Answers
The histogram is shown below:
h(n) = -2n + 3g(n) = 4nFind (h•g)(-2)
Answers
Given:
h(n)=-2n+3
g(n)=4n
The objective is to find
[tex](h\cdot g)(-2)[/tex]Let's rewrite the required function as
[tex]\begin{gathered} (h\cdot g)=h\lbrack g(n)\rbrack \\ h\lbrack g(n)\rbrack=-2(4n)+3 \\ h\lbrack g(n)\rbrack=-8n+3 \\ (h\cdot g)(-2)=-8(-2)+3 \\ (h\cdot g)(-2)=16+3 \\ (h\cdot g)(-2)=19 \end{gathered}[/tex]Hence the value of (hog)(-2)=19
19 students reported seeing the latest blockbuster film over the summer, 76 total students were surveyed. Which fraction represents the ratio of students who saw the movie to total students surveyed?A. 1/4B. 4/15C. 2/7D. 3/7
Answers
In this case the answer is very simple. .
We must find the proportion and compare it with the options.
Step 01:
ratio of students who saw the movie
[tex]\frac{\text{students saw the movie}}{\text{total students surveyed}}\text{ = }\frac{19}{76}\text{ = }\frac{1}{4}[/tex]The answer is:
Option A.
1. How does someone find the equation of a boundary line?2. How does someone determine if the points on the boundary line are solutions to the inequality?
Answers
Answer:
D: Find the boundary line equation by replacing the inequality sign with =
Explanation:
Part 1
Given any inequality, say:
[tex]yTo find the equation of the boundary line, replace the inequality sign with the equality(=) sign. This gives the equation of the boundary line to the inequality above as:[tex]y=x+5[/tex]The correct choice is D.
Part 2
When drawing the boundary line:
• Use a solid line for the inequalities: ≤ or ≥
,• Use a broken line for the inequalities: < or >
If the boundary line is solid, the points on the boundary line are solutions to the inequality, otherwise, they are not.
Find the missing side of the triangle.A. √11 miB. 2√2 miC. 1 miD. √19 mi
Answers
Since we have a right-angled triangle, we can use the Pythagoras Theorem:
[tex]a^2+b^2=c^2[/tex]where a and b are the shorter sides of the triangle and c is the hypotenuse.
a = x; b = 3 mi; c = sqrt(10).
We substitute our values and then we solve for x:
[tex]\begin{gathered} x^2+3^2=(\sqrt[]{10})^2 \\ x^2=10-3^2 \\ x^2=1 \\ x=1 \end{gathered}[/tex]Therefore, the missing side of the triangle is 1 mi.
Which inequality symbol should be placed in the blank to make the statement true? - 12_ -8
Answers
Answer:
<
Step-by-step explanation:
Negative 12 is less than negative 8.
given the following list of axioms drawing model on a separate sheet of paper to properly represent the information describing drawing in your own words there exists by points each line contains only these Five Points there exist two lines each line contains at least two points
Answers
Five random points, 3 of them collinear:
To go through all the points with only two lines, one of the five points has to be colinear with other 2 points.
If the fifth point wasn't colinear, we would need another line to draw.
If four of the five points were colinear between them, we could have had a line that goes through this 4 points, and the other line going through the remaining point.
If the five points were colinear, we would have need only one line to go through them.
this is a practice assessment! Therefore it isn’t for a grade . I just need help solving this
Answers
We are given a quadrilateral inscribed in a circle, therefore, the sum of opposite angles is equal to 180 degrees, therefore:
[tex]\angle O+\angle M=180[/tex]Replacing the values we get:
[tex]100+x=180[/tex]Solving for "x":
[tex]\begin{gathered} x=180-100 \\ x=80 \end{gathered}[/tex]Therefore, the value of "x" is 80 degrees.
