2(-4^2) - 2(2^4) + 3^2 - -4^2 + 2^4 = ? Please explain, I got 41 but I highly doubt I'm right.
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]
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.
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
Four times the sum of a number and 15 is at least 120. Find all possible solutions for x
What numbesr can be multiplied and added to equal the same number?
2
2x2 = 4
2+2 =4
0
0x0=0
0+0=0
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?
How could you find the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,-12)
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
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.
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]
Perform Gauss-Jordan elimination on the augmented matrix shown.
Could someone please help me figure this out.
write a numerical sentence that illustrates the commutative property of multiplication
EF=5x+15, FG=53 And EG=143 find the value of x
And can you please tell me how to do it?
If h(x)=6-x, what is the value of (h o h)(10)
angle ABD and angle DBC are supplementary. Find the value of x.
A. 6
B. 8
C. 4
D. 10
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
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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HELP!!!!!!! I GIVE BRAINLEST AND THANKS!!!!!! + 5 POINTS!!!!
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.
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.
Find the domain of the following piecewise function
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
WILL GIVE BRAINLIST!!!!!!!!!!!!!! A group of students were surveyed to find out if they like working as a camp counselor and/or as a lifeguard during summer break. The results of the survey are shown below:
32 students like working as a camp counselor
8 students like working as a camp counselor but do not like working as a lifeguard
29 students like working as a lifeguard
8 students do not like working as a lifeguard or a camp counselor
Four students created the tables below to represent the data. CC represents camp counselor and LG represents lifeguard.
Which student's table is correct?
Answer:
I think Table C - Corralle
Answer:
c
Step-by-step explanation:
10 employees in an office were absent. Of these absentees constitutes 25% of the employees, what is the total number of employees?
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?
Sherita’s club is selling grapefruit to raise money. For every box they sell, they get $1.35 profit. They have sold 84 boxes already. How many more boxes must they sell to raise 270 dollars
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]
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