The graph below represents which system of inequalities? graph of two infinite lines that intersect at a point. One line is solid and goes through the points 0, 2, negative 2, 0 and is shaded in below the line. The other line is dashed, and goes through the points 0, 6, 3, 0 and is shaded in below the line. y < −2x + 6 y ≤ x + 2 y ≤ −2x + 6 y < x + 2 y < 2 over 3x − 2 y ≥ 2x + 2 None of the above
To solve the problem we should know about the Equation of a line and slope of a line.
The equations are (y≤ x+2) and (y< -2x+6).
Given to us
One line is solid and goes through the points (0, 2), and (-2, 0) and is shaded below the line.The other line is dashed, goes through the points (0, 6) and (3, 0), and is shaded below the line. For the first line,Given the points (0, 2), and (-2, 0), therefore,
[tex]x_2=0\\y_2=2\\x_1=-2\\y_2=0[/tex]
Substituting the values in the formula of the slope,
[tex]m=\dfrac{(y_2-y_1)}{(x_2-x_1)}[/tex]
[tex]m=\dfrac{2-0}{0-(-2)} = \dfrac{2}{2} = 1[/tex]
Substitute the value of slope and a point in the formula of line,
[tex]y = mx+c\\y_2 = mx_2+c\\2 = (1)0 +c\\c = 2[/tex]
Thus, the equation of the line is y=x+2, but as given the line is solid and is shaded below the line. therefore,
y≤ x+2
For the Second line,Given the points (0, 6) and (3, 0), therefore,
[tex]x_2=0\\y_2=6\\x_1=3\\y_2=0[/tex]
Substituting the values in the formula of the slope,
[tex]m=\dfrac{(y_2-y_1)}{(x_2-x_1)}[/tex]
[tex]m=\dfrac{6-0}{0-3} = \dfrac{6}{-3} = -2[/tex]
Substitute the value of slope and a point in the formula of line,
[tex]y = mx+c\\y_2 = mx_2+c\\6 = (-2)0 +c\\c = 6[/tex]
Thus, the equation of the line is y=-2x+6, but as given the line is shaded below the line. therefore,
y< -2x+6
Hence, the equations are (y≤ x+2) and (y< -2x+6).
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17. For the parallelogram find the value of the variables. Show your work.
18. What is the length of the second base of a trapezoid is the length of one base is 24 and the length of the midsegment is 19? Show your work
Is the following expression shown the exact answer? 144π - 216√3
true or false
Chase makes 2 gallons of soup for a dinner party. He serves 10 cups of soup to his guests. How many cups of soup will be have left over?
write a numerical sentence that illustrates the commutative property of multiplication
From a deck of 52 cards, one card is drawn at random. Match the following subsets with their correct probabilities.
1. P(face card)
2. P(seven of hearts)
3. P(no black)
4. P(king)
5. P(diamond)
Answer:
P(face card)=3/13 P(seven of hearts)=1/52P(no black)=1/2P(king)=1/13P(diamond)=1/4Step-by-step explanation:
We know that there are a total 52 cards out of which:
There are 12 face cards ( 4 kings,4 queen and 4 jack)
There are 4 pack:
13- spades 13- club 13-heart 13-diamond.
Out of which there are 26 black cards( 13 spade and 13 club)
There are 26 red cards( 13 heart and 13 diamond)
Now , we are asked to find the probability of each of the following,
1)
P(face card)
Since there are total 12 face cards out of 52 playing cards.
Hence,
P(face card)=12/52=3/13
2)
P( seven of hearts)
As there is just 1 seven of heart out pf 52 cards.
Hence, P(seven of hearts)=1/52
3)
P(no black)
This means we are asked to find the probability of red card.
As there are 26 red card.
Hence P(no black)=26/52=1/2
4)
P(king)
As there are 4 kings out of 52 cards.
Hence, P(king)=4/52=1/13
5)
P(diamond)
As there are total 13 cards of diamond.
Hence,
P(diamond)=13/52=1/4
Find the probability of drawing a king from a standard deck of cards and then drawing a queen after the first card is replaced in the deck. None of the above 1/26 1/13 1/2704 2/13
52 cards in a deck
4 kings
4 queens
King = 4/52 reduces to 1/13
Queen = 4/52 reduces to 1/13
1/13 *1/13 = 1/169
so none of the above
Graph y=-1/2x^2-1. Identify the vertex of the graph. tell whether it is a minimum or maximum. (To clarify, 1/2 is a fraction *x^2)
1. (-1,0);minimum
2.(-1,0);maximum
3.(0,1);maximum
4.(0,-1);minimum
The equation y = -1/2x^2 - 1 represents a downward opening parabola with the vertex at (0, -1), making it a maximum point.
Graph: The given equation is y = -1/2x^2 - 1. This represents a downward opening parabola.
Vertex: The vertex of the parabola is at (0, -1), making it a maximum point.
Conclusion: The correct answer is option 4: (0, -1); minimum.
Eighty seven decreased by three times a number is greater than one hundred sixty five
87-3x>165
-3x> (165-85)
-3x>80
80/-3 = -26.666
check;
87-3*(-26)=165
so x < -26
If h(x)=6-x, what is the value of (h o h)(10)
Bradley is returning home from a place that is 2 kilometers away. The function y = 2,000 − 90x represents Bradley's distance from home in meters, y, in relation to the number of minutes he walks, x. Which statements about this function are true?
Final answer:
The function y = 2,000 - 90x shows Bradley's distance from home decreases by 90 meters for every minute walked, starting from 2,000 meters away. The graph of this equation is a straight line with a negative slope, indicating constant speed.
Explanation:
The equation y = 2,000 - 90x represents Bradley's distance from home in meters, y, as a function of the time x in minutes that he walks. This equation is a linear function where the initial value 2,000 meters represents the distance from home at the start, and -90 meters/minute is the rate at which this distance decreases as Bradley walks home. As time increases by 1 minute, the distance from home decreases by 90 meters. This relationship shows that Bradley travels at a constant speed since the slope of the line representing the equation (which is the rate of change of distance with respect to time) is constant.
If we graph this function, we would get a straight line that starts at 2,000 meters on the y-axis when t=0 and has a negative slope of 90. Therefore, the graph shows that as time passes, Bradley gets closer to home at a steady pace. This also reflects that the total distance Bradley would walk is 2,000 meters, and the time it would take for him to return home can be found by setting the function equal to zero and solving for x.
You are interviewing an applicant for a sales agent position in your company. Based on the company’s record, almost every company sales agent makes a total revenue of 150x-x² pesos for selling x products in a week. If the applicant confidently assures you that he/she can easily make ₱10,000 weekly revenue, how many products should he/she sell to meet this quota?
Kenya plans to make a down payment plus monthly payments in order to buy a motorcycle. At one dealer she would pay $2,500 down and $150 each month. At another dealer, she would pay $3,000 down and $125 each month. After how many months would the total amount paid be the same for both dealers? What would that amount be?
Let us say that the total amount paid in the first dealer is P1 and the total amount paid to the second dealer is P2. So that:
P1 = 2500 + 150 t
P2 = 3000 + 125 t
Where t is the total number of months
Now we are asked when the total amount paid would be equal for the two dealers, this means P1 = P2, therefore equating the two:
2500 + 150 t = 3000 + 125 t
25 t = 500
t = 20 months
Therefore the total amount paid for both dealers would be equal after 20 months.
Perform Gauss-Jordan elimination on the augmented matrix shown.
Could someone please help me figure this out.
A lawn mower manufacturer incurs a total of $34,816 in overhead costs and $388 per lawn mower in production costs. How many lawn mowers were manufactured if the average cost of production is $660?
Answer:
128 lawn mowers
Step-by-step explanation:
Given,
The overhead cost = $ 34,816,
The cost for one lawn mower = $ 388,
Let x be the number of lawn mowers manufactured,
So, the total cost of x lawn mowers = 34816 + 388x,
Now, if the average cost of x mowers = $ 660,
So, the total cost = 660x
[tex]\implies 660x = 34816 + 388x[/tex]
[tex]660x - 388x = 34816[/tex]
[tex]272x= 34816[/tex]
[tex]\implies x = \frac{34816}{272}=128[/tex]
Hence, 128 lawn mowers were manufactured.
what is the value of the fourth term in a geometric sequence for which a1=15 and r=1/3
express your answer as a fraction
Answer: The required fourth term in the given geometric sequence is [tex]\dfrac{5}{9}.[/tex]
Step-by-step explanation: We are given to find the fourth term of a geometric sequence with the following first term and common ratio :
[tex]a=15,~~r=\dfrac{1}{3}.[/tex]
We know that
the nth term of a geometric sequence with first term a and common ratio r is given by
[tex]a_n=ar^{n-1}.[/tex]
Therefore, the forth term of the given geometric sequence is
[tex]a_4=ar^{4-1}=ar^3=15\times\left(\dfrac{1}{3}\right)^3=15\times\dfrac{1}{27}=\dfrac{5}{9}.[/tex]
Thus, the required fourth term in the given geometric sequence is [tex]\dfrac{5}{9}.[/tex]
How could you find the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,-12)
Tim enlarged a picture with a width of 5.5 inches and a length of 8 inches by a scale factor of 3. What are the dimensions of the enlargement?
a. width: 24 in.; length: 16.5 in.b. width: 16.5 in.; length: 24 in.c. width: 14.5 in.; length: 22 in.d. width: 19.5 in.; length: 25 in.
Answer:
Option b. width = 16.5 inches and length = 24 inches
Step-by-step explanation:
Tim enlarged a picture wit a width of 5.5 inches and a length of 8 inches.
He enlarged the picture by a scale factor of 3.
We have to find the new dimensions of the picture.
Since, New dimension of the picture = Scale factor × dimensions before enlargement
So new width = 3×5.5 = 16.5 inches
new length = 3×8 = 24 inches
Therefore, option b. is the answer.
Four times the sum of a number and 15 is at least 120. Find all possible solutions for x
Find the domain of the following piecewise function
EF=5x+15, FG=53 And EG=143 find the value of x
And can you please tell me how to do it?
Two cars leave the same location at the same time but one car is heading north and the other is heading south. After 3 hours, the cars are 360 miles apart. If the car heading north is traveling 10 miles per hour slower than the car heading south, what are the two speeds of the cars?
SHOW THE EQUATION
3x +3(x-10) = 360
3x +3x-30 =360
6x-30 =360
6x=390
X = 390/6 = 65
65-10 =55
One car was driving 65 mph
The other was 55 mph
10 employees in an office were absent. Of these absentees constitutes 25% of the employees, what is the total number of employees?
2(-4^2) - 2(2^4) + 3^2 - -4^2 + 2^4 = ? Please explain, I got 41 but I highly doubt I'm right.
If a train travels one mile (5,280 feet) while climbing a hill at an angle of five degrees, approximately how many vertical feet has the train climbed?
to calculate the vertical height multiply the hypotenuse ( 5280) by the sin of the angle (5)
5280 x sin(5) = 460.1823
round off to 460 feet
Which of the following rational functions is graphed below?
The solution is, Option A. is correct.
F(x) = 1/ (x-1)(x+4)
What is rational fraction?A rational fraction is an algebraic fraction such that both the numerator and denominator are polynomials.
Here, we have,
a graph is given .
We need to find which of the given rational functions is graphed in image.
On x-axis, 1 unit = 2 units
Clearly, we can see the graph is not defined at point x = - 4 and at x = 1.
Corresponding to x = - 4, factor is (x+4) .
Corresponding to x = 1, factor is (x-1) .
So, this graph is of the rational fraction
F(x) = 1/ (x-1)(x+4)
Hence, Option A. is correct.
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Find the simple interest paid for 8 years on a $850 loan at 7.5% per year.
The simple interest paid for 8 years on a $850 loan at a 7.5% annual interest rate is $510.
To calculate simple interest, you can use the formula:
Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)
Where:
- Principal (P) is the initial amount of the loan.
- Rate (R) is the annual interest rate (in decimal form).
- Time (T) is the number of years.
In this case:
- Principal (P) = $850
- Rate (R) = 7.5% = 0.075 (decimal form)
- Time (T) = 8 years
Now, plug these values into the formula:
SI = $850 × 0.075 × 8
SI = $510
The simple interest paid for 8 years on a $850 loan at a 7.5% annual interest rate is $510.
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Find the lateral area for the prism. L.A. =
Find the total area for the prism. T.A. =
Answer:
Part 1) [tex]LA=(80+16\sqrt{13})\ in^{2}[/tex]
Part 2) [tex]TA=(104+16\sqrt{13})\ in^{2}[/tex]
Step-by-step explanation:
Part 1) Find the lateral area of the prism
we know that
The lateral area of the prism is equal to
[tex]LA=Ph[/tex]
where
P is the perimeter of the base
h is the height of the prism
Applying the Pythagoras Theorem
Find the hypotenuse of the triangle
[tex]c^{2}=4^{2}+6^{2}\\ \\c^{2}=52\\ \\c=2\sqrt{13}\ in[/tex]
Find the perimeter of triangle
[tex]P=4+6+2\sqrt{13}=(10+2\sqrt{13})\ in[/tex]
Find the lateral area
[tex]LA=Ph[/tex]
we have
[tex]P=(10+2\sqrt{13})\ in[/tex]
[tex]h=8\ in[/tex]
substitutes
[tex]LA=(10+2\sqrt{13})*8=(80+16\sqrt{13})\ in^{2}[/tex]
Part 2) Find the total area of the prism
we know that
The total area of the prism is equal to
[tex]TA=LA+2B[/tex]
where
LA is the lateral area of the prism
B is the area of the base of the prism
Find the area of the base B
The area of the base is equal to the area of the triangle
[tex]B=\frac{1}{2}bh[/tex]
substitute
[tex]B=\frac{1}{2}(6)(4)=12\ in^{2}[/tex]
Find the total area of the prism
[tex]TA=LA+2B[/tex]
we have
[tex]B=12\ in^{2}[/tex]
[tex]LA=(80+16\sqrt{13})\ in^{2}[/tex]
substitute
[tex]TA=(80+16\sqrt{13})+2(12)=(104+16\sqrt{13})\ in^{2}[/tex]
On a number line, the directed line segment from Q to S has endpoints Q at –14 and S at 2. Point R partitions the directed line segment from Q to S in a 3:5 ratio. Which expression correctly uses the formula to find the location of point R?
To find the location of point R on the number line, you can use the formula for finding a point on a line segment given the endpoints and the ratio. In this case, the ratio is 3:5 and the endpoints are -14 and 2.
Explanation:To find the location of point R, you can use the formula for finding a point on a line segment given the endpoints and the ratio. In this case, the formula is:
R = Q + r(QS)
where Q is the starting point, S is the ending point, r is the ratio between Q and S, and QS is the displacement vector from Q to S. In this problem, Q is -14, S is 2, and the ratio is 3:5. So we can substitute these values into the formula and solve:
R = -14 + (3/8)(2 - (-14)) = -14 + (3/8)(16) = -14 + 6 = -8
Therefore, the location of point R is -8 on the number line.
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The location of point R is -8. The correct answer is option a. [tex]\frac{3}{3+5}(2-(-14))+(-14)[/tex]
To find the location of point R which partitions the directed line segment from Q to S in a 3:5 ratio, we use the section formula. The formula is:
[tex]R =\frac{m}{m+n}(x_2-x_1)+x_1[/tex]
Here, m = 3 and n = 5, while Q is at [tex]x_1 =[/tex] -14 and S is at [tex]x_2 =[/tex] 2.
Plugging in the values, we have:
[tex]R =\frac{3}{3+5}(2-(-14))+(-14)[/tex][tex]R = \frac{3}{8}(2+14)-14[/tex][tex]R = \frac{3}{8} (16)-14[/tex][tex]R = \frac{48}{8}-14[/tex][tex]R = 6-14[/tex]R = -8Therefore, the location of point R is at -8 on the number line and it is calculated by the expression [tex]R =\frac{3}{3+5}(2-(-14))+(-14)[/tex].
The complete question is:
On a number line, the directed line segment from Q to S has endpoints Q at –14 and S at 2. Point R partitions the directed line segment from Q to S in a 3:5 ratio. Which expression correctly uses the formula [tex]R =\frac{m}{m+n}(x_2-x_1)+x_1[/tex] to find the location of point R?
a. [tex](\frac{3}{3+5})(2-(-14))+(-14)[/tex]
b. [tex](\frac{3}{3+5})(-14-2)+2[/tex]
c. [tex](\frac{3}{3+5})(2-14)+14[/tex]
d. [tex](\frac{3}{3+5})(-14-2)-2[/tex]
WILL GIVE A BRAINLIEST IF THE ANSWER IS CORRECT!!! PLEASE HELP ASAP!!
Find the value of x in the expression (2a^4b^2)^x=4a^8b^4.
A.
x = 2
B.
x = 3
C.
x = 4
D.
x = 5