Answer:
(-16,24)
Step-by-step explanation:
In this problem, we have segment PR, where the endpoins have coordinates
P (-22, 32)
R (5, -4)
We want to find point Q along the segment such that
PQ : QR = 2 : 7 (1)
We can write the coordinates of point Q as
[tex]Q(x_P,y_P)[/tex]
So we can now rewrite eq(1) for both the x- and y- variable:
[tex]\frac{x_Q-x_P}{x_R-x_Q}=\frac{2}{7}[/tex] (2)
[tex]\frac{y_Q-y_P}{y_R-y_Q}=\frac{2}{7}[/tex] (3)
We start by solving eq(2) to find the coordinate x of point Q:
[tex]7(x_Q-x_P) = 2(x_R-x_Q)\\7x_Q-7x_P=2x_R-2x_Q\\9x_Q=2x_R+7x_P\\x_Q=\frac{2x_R+7x_P}{9}=\frac{2(5)+7(-22)}{9}=-16[/tex]
While for the y-coordinate:
[tex]7(y_Q-y_P) = 2(y_R-y_Q)\\7y_Q-7y_P=2y_R-2y_Q\\9y_Q=2y_R+7y_P\\y_Q=\frac{2y_R+7y_P}{9}=\frac{2(-4)+7(32)}{9}=24[/tex]
So the coordinates of Q are (-16,24).
The coordinate of Q is [tex]Q=(-16,4)[/tex]
To understand more, check below explanation.
Section formula:To find the coordinate of Q, we use section formula,
[tex]Q=(\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}},\frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}} )[/tex]
It is given that,
[tex](x_{1},y_{1})=(-22,32),(x_{2},y_{2})=(5,-4), m_{1}=2,m_{2}=7[/tex]
Substitute above values in above section formula,
[tex]Q=(\frac{(2*5)+(7*-22)}{2+7}, \frac{(2*32)+(7*-4)}{2+7})\\\\Q=(-\frac{144}{9} ,\frac{36}{9} )\\\\Q=(-16,4)[/tex]
Therefore, the coordinate of Q is [tex]Q=(-16,4)[/tex]
Learn more about the section formula here:
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To factor a trinomial you must find the product of "a" and "b" and find the sum of "c"
True
False
Answer:
true
Step-by-step explanation:
What is the value of cosθ given that (−2, −3) is a point on the terminal side of θ ?
Answer:
-0.555
Step-by-step explanation:
The terminal point of the vector in this problem is
(-2,-3)
So, it is in the 3rd quadrant.
We want to find the angle [tex]\theta[/tex] that gives the direction of this vector.
We can write the components of the vector along the x- and y- direction as:
[tex]v_x = -2\\v_y = -3[/tex]
The tangent of the angle will be equal to the ratio between the y-component and the x-component, so:
[tex]tan \theta = \frac{v_y}{v_x}=\frac{-3}{-2}=1.5\\\theta=tan^{-1}(1.5)=56.3^{\circ}[/tex]
However, since we are in the 3rd quadrant, the actual angle is:
[tex]\theta=180^{\circ} + 56.3^{\circ} = 236.3^{\circ}[/tex]
So now we can find the cosine of the angle, which will be negative:
[tex]cos \theta = cos(236.3^{\circ})=-0.555[/tex]
Plz help! Question is in the picture! 10 point reward!
Answer:
1, 8.4
Unit rate: 8.4 feet per second
Step-by-step explanation:
To find the unit rate you divide the time by the distance, therefore with 8.4 it's easy to find the unit rate! :) Hope this helps! If it did, rate brainliest
A 3 cm x 10 cm rectangle sits inside a circle with radius of 12 cm.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
Answer:
422.389 cm
Step-by-step explanation:
First you have to find the area of the circle then subtract it by the area of the rectangle. To find the area of the circle you have to square the radius then multiply it by 3.14.(12×12=144, 144× 3.14=452.389) Therefore 452.389 cm is the area of the circle. Area of the rectangle 30cm.
452.389 -30=422.389
True or false: y=x3−4 is a linear equation. A true B false
false because it is formed wrong
Final answer:
The equation y = x^3 - 4 is not a linear equation because it contains a cubic term (x^3), which means the graph is a curve, not a straight line. Therefore, the correct answer is false.
Explanation:
The equation y = x3 − 4 is not a linear equation. A linear equation is one in which every term is either a constant or the product of a constant and the first power of a variable. In the given equation, the term x3 indicates that it is a cubic term because the value of x is raised to the power of three, suggesting that the graph of this equation would be a curve, not a straight line. Therefore, the correct answer is false.
Linear equations have the general form y = mx + b, where 'm' is the slope and 'b' is the y-intercept. Examples of linear equations include y = −3x, y = 0.2 + 0.74x, and y = −9.4 − 2x, which can all be graphed as straight lines. In contrast, an equation like y = x3 − 4 does not fit this form and therefore is not considered linear.
Help me! 17 points to help me
Answer:
this is to much work for me to do.
Step-by-step explanation:
Ortega is trying to fill three bags equally with sand. He wants the bags to weigh the same. If the bags currently weigh 55 pounds, 51 pounds, and 48 pounds. Can Ortega get each bag to weigh the same by moving the weight around?
Answer:
yes
Step-by-step explanation:
The average weight of the three bags is ...
(55 +51 +48)/3 = 154/3 = 51 1/3 . . . pounds
By removing 3 2/3 pounds of sand from the heaviest bag, adding 1/3 pound to the middle-weight bag, and the remaining 3 1/3 pounds to the lightest bag, Ortega can make all of the bags weigh the same: 51 1/3 pounds.
I need help graphing on this number line
Answer:
1 is c
2 is b
3 is d
4 is a
Step-by-step explanation:
Open circle is 'less than' or 'greater than'.
Closed (shaded) circle is 'less than or equal to' or 'greater than or equal to'.
Tickets to the school dance cost $3.00 in advance or $5.00 at the
door. There were a total of 184 tickets sold, raising $688. How many tickets
were sold at the door?
Answer:
68 tickets
Step-by-step explanation:
This is a problem that involves a system of equations, the first step is to define your variables and write equations to represent the situation.
x = number of advance tickets
y = number of door tickets
x + y = 184
3x + 5y = 688
Next, you need to solve for one variable, based on how these equations are written, the best method would be to solve by multiplication.
-3(x + y = 184) (multiply equation by -3)
-3x - 3y = -552
Now we need to combine the two equations together
3x + 5y = 688
-3x - 3y = -552
From here we can eliminate the x variable when subtracting the equations, this results in:
2 y = 136
y = 68
Therefore, 68 tickets were sold at the door.
Which type(s) of equation can have infinite solutions?
A. linear-linear
B. linear-quadratic
C. quadratic-quadratic
Answer:
A and C
Step-by-step explanation:
I did the assignment
Suppose you drop a ball from a height of 10 feet. After the ball hits the floor, it rebounds to a height defined by the recursive formula an = 0.85an – 1. What is a1?
Answer:
10 feet
Step-by-step explanation:
The height of the ball after it hits the floor and rebound is defined by the recursive formula:
[tex]a_n = 0.85a_{n-1}[/tex]
This is an example of a geometric sequence in which the next term is gotten by multiplication of the previous term by 0.85.
If the ball is dropped from a height of 10 feet, the first term is 10.
Its Initial height, [tex]a_1=10 \:feet[/tex]
Harry Potter is at Ollivanders Wand Shop. As we all know, the wand must choose the wizard, so Harry cannot make the choice himself. He interprets the wand selection as a random process so he can determine the probabilities of different outcomes.
The wood types available are holly, elm, maple, and wenge. The core materials on offer are phoenix feather, unicorn hair, dragon scale, raven feather, and thestral tail.
Let A be the event that Harry is chosen by a wand made of holly and B be the event that he is chosen by a wand with a dragon scale core.
Answer: The probability of being chosen by a wand made of holly or a wand made of dragon scale core is 0.4 or 40%
Step-by-step explanation: What we have are probabilities of two events. The first is the probability that Harry Potter is chosen by a wand made of Holly which is P(A). The other event is the probability that Harry is chosen by a wand with a dragon scale which is P(B).
In other to calculate P(A), there is a total of four possibilities, (that is holly, elm, maple and wenge). Therefore, the probability is derived as;
P(A) = Number of required outcomes/Number of all possible outcomes
P(A) = 1/4 or (0.25)
To calculate P(B), there is a total of five possibilities (that is phoenix feather, unicorn hair, dragon scale, raven feather and thestral tail). Therefore the probability is derived as;
P(B) = Number of required outcomes/Number of all possible outcomes
P(B) = 1/5 or (0.20)
However, the question requires the probability of P(A or B).
First we derive the probability of being chosen by a wand made of holly AND one made of a dragon scale core. In other words we shall calculate the probability of P(A and B) which is derived as;
P(A and B) = P(A) x P(B)
P(A and ) = 1/4 x 1/5
P(A and B) = 1/20 (0.05)
The probability of P(A or B) can now be calculated as follows;
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = (0.25 +0.20) - 0.05
P(A or B) = 0.45 - 0.05
P(A or B) = 0.40
Therefore the probability that Harry Potter is chosen by a wand made of Holly or a wand with Dragon scale core is 0.4 or 40%
Answer: P( A or B) = 2/5
Step-by-step explanation:
what is 4p−5(p+6) simplified
Answer:
-p - 30
Step-by-step explanation:
4p−5(p+6)
Distribute:
=4p+(−5)(p)+(−5)(6)
=4p+−5p+−30
Combine Like Terms
=4p+−5p+−30
=(4p+−5p)+(−30)
=−p+−30
=−p−30
Write the number 7.748 x 10-5 in standard form.
OA. 0.0007748
OB. 774,800
OC. 0.000007748
D. 0.00007748
If the mean of the data set is
4 bubbles, find the number of bubbles Hannah blew. khan academy
Answer: Hannah blew 1 bubble
Step-by-step explanation:
Mean * number of gum chewers= total bubbles
4*4=16
Let’s add up the numbers of bubbles that we do know.
4+5+6=15
16-15=1
Hannah blew 1 bubble
The number of bubbles Hannah blew can be expressed as 1
How can the number of bubbles Hannah blew be calculated?The study of variables and the formula manipulation principles is known as algebra. Its roots lie in the computation methods of ancient Babylonia, but now it is a mode of thinking that permeates practically all branches of mathematics.
Let number of bubbles Hannah blew =x
Then we can set up the equation as
[tex]\frac{1}{4} (4+5+6+x)=4[/tex]
15+x=16
x=16-15
x=1
Learn more about number at
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Find: P (Red and Small)
Answer:
3/10
Step-by-step explanation:
In a computer catalog, a computer monitor is listed as being 27 inches. This distance is
the diagonal distance across the screen. If the screen measures 15 inches in height, what
is the actual width of the screen to the nearest inch?
The width of the computer monitor is 22 inches
What is a Rectangle?
In a Rectangle
It is a four sided shape where every angle is a right angleThe alternative sides are equalTwo axes of symmetry bisect each otherDiagonals are equal in lengthThe diagonal equals the square root of the width squared plus the height squared
Given data ,
Let the Width of the rectangle be W
Diagonal of the rectangle = 27 inches
Height of the rectangle = 15 inches
D² = L² + W²
W² = D² - L²
W² = ( 27 )² - ( 15 )²
= 729 - 225
= 504
Therefore , Width W = √504
≈ 22.45 inches
≈ 22 inches
Hence , the width of the computer monitor is 22 inches
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PLEASE HELP ITS URGENT
There are 4 blueberry, 6 raisins, and 2 plain bagels in a bag. Mike randomly selects two bagels without replacing the first bagel. Find the probability that he selects a raisin bagel and then a plain bagel
Answer:
The probability that he selects a raisin bagel and then a plain bagel is [tex]\frac1{11}[/tex].
Step-by-step explanation:
Probability:
The ratio of the number of outcomes of favorable event to total number of all possible outcomes is called probability of the favorable event.
[tex]Probability=\frac{\textrm{The number of favorable outcomes}}{\textrm{Total number of all possible}}[/tex]
Given that, there are 4 blueberry, 6 raisins and 2 plain bangles in a bag.
Total number of bangles= (4+6+2)
= 12
The probability that he selects a raisin
[tex]=\frac{\textrm{Number of raisin bangles}}{\textrm{Total number of bangles}}[/tex]
[tex]=\frac{6}{12}[/tex]
[tex]=\frac12[/tex]
Total number of remaining bagels is =(12-1)=11
After selecting a raisin bagel,the probability that he selects a plain bangle is
[tex]=\frac{\textrm{Number of plain bangles}}{\textrm{Total number of bangles}}[/tex]
[tex]=\frac{2}{11}[/tex]
Selecting of a raisin bangle and a plain bangle are both independent event.
The probability that he selects a raisin bagel and then a plain bagel is
[tex]=\frac{1}2\times\frac{2}{11}[/tex]
[tex]=\frac1{11}[/tex]
A pet store makes a 60% profit on sales. The manager wants the store to make over $6,000 in profit each month. Describe the inequality and the graph of the solution to find the minimum amount of sales the store must have each month to reach the goal.
The inequality is .
The graph of the solution is .
The inequality is : 0.6x > 6000. The graph of the solution is : open circle at 10,000; arrow right
Thats the right answer it told me
Answer:
The inequality is
✔ 0.6x > 6000
.
The graph of the solution is
✔ open circle at 10,000; arrow right
Step-by-step explanation:
Only 3 years late ;)
Can someone pls help me
Answer:
behaviour
Step-by-step explanation:
Please help me now please
Answer:
0.4444444
Step-by-step explanation:
2/3 x 2/3 = 0.4444 repeating!
Hope this helps!
The local newspaper has letters to the editor from
60
60 people. If this number represents
2
2% of all of the newspaper's readers, how many readers does the newspaper have?
Answer:
300 readers
Step-by-step explanation:
60/2=30
30X100=300
The total number of readers of a newspaper based on the percentage of people who wrote letters to the editor are 3000.
The number of readers the newspaper has is:
Number of readers = (60 / 0.02) = 3000 readers
Therefore, the newspaper has 3000 readers.
How are ridge transformations are congruent figures related ?
Answer:
uh im not in that grade yet so ye
Step-by-step explanation:
Takumi started studying how the number of branches on his tree changes over time.
The relationship between the elapsed time, t, in years, since Takumi started studying his tree, and the total
number of its branches, N(t), is modeled by the following function:
N(t) = 63. 2
Complete the following sentence about the yearly rate of change in the number of branches.
Every year, the number of branches
grows/shrinks
by a factor of
Answer:
Grows, Factor of 2
Step-by-step explanation:
The relationship between the elapsed time, t, in years, since Takumi started studying his tree, and the total number of its branches, N(t), is modeled by the function:
[tex]N(t) = 63. 2^t[/tex]
For illustration, let us take the growth for the first three years after he started studying the number of branches.
[tex]When \:t=1, N(1) = 63. 2^1=126\\When \:t=2, N(2) = 63. 2^2=252\\When \:t=3, N(3) = 63. 2^3=504\\504\div 252=252\div 126=2[/tex]
We notice that for each subsequent year, the number of branches doubles.
Therefore:
Every year, the number of branches grows by a factor of 2.
Which three statements are true as they relate to supply and demand? As supply rises, prices generally decrease. As demand decreases, costs generally increase. As supply decreases, prices increase. The average rate of change describes how much a quantity changes as price increases. As demand rises, the price of the product decreases.
As supply rises, prices decrease.
And The average rate of change describes how much a quantity changes as prices increases
As supply decreases, prices increase. It seems logical but I'm not 100% positive on the last one. I know the first 2 are right.
The statements that are true as they relate to supply and demand are: as supply rises, prices generally decrease; as demand decreases, prices generally increase; as supply decreases, prices increase.
Explanation:Supply and demand are fundamental concepts in economics. The law of supply states that as supply increases, prices generally decrease. This is because when there is a higher quantity supplied, producers compete to sell their products, leading to lower prices. On the other hand, the law of demand states that as demand decreases, prices generally decrease. When there is lower demand for a product, sellers may lower prices to attract more buyers.
Additionally, the statement that as supply decreases, prices increase is also true. When the quantity supplied decreases, the scarcity of the product can drive up prices as buyers are willing to pay more for limited supply. The average rate of change refers to how much a quantity changes as the price increases. It is not directly related to supply and demand dynamics, but rather focuses on the relationship between quantity and price. As demand rises, the price of a product generally increases. This is because as more people want to buy a product, sellers can charge higher prices since there is higher demand.
In a scale drawing of a law office, 1/4 inch represents 4 1/2 feet. If the actual length of the conference room is 30 3 5 feet, what is the length of the conference room, in inches, on the scale drawing?
Answer:
tbh im not sure but i think the answer is 30 ft
Step-by-step explanation:
A shipping clerk will ship an order of 200 batteries so long as three randomly selected batteries work. Past data has shown that five out of 200 batteries are defective. What is the probability that the clerk will ship the order?
Answer:
0.9264999239
Step-by-step explanation:
chance that first battery that is being checked works is 195/200
chance that second battery that is being checked works is 194/199
chance that third battery that is being checked works is 193/198
propabilty that the clerk ships the order is (195/200)×(194/199)×(193/198)
=0.9264999239
It took a skydiver 5 seconds to drop 400 feet. What is the
rate (in feet per/second) of the skydiver's drop?
80 feet per second
Step-by-step explanation:
just divide the amount he fell by the amount of time it took so you would take 400/5 and get the answer
Answer:
80
Step-by-step explanation:
If it took him 5 seconds to drop 400 feet then you have to divide it by 5 to determine the rate he can drop a certain amount of feet per second.
Mr. Ishimoto needs to replace the grass in the section of his lawn that is shown below.
A grass section can be broken into 2 rectangles. 1 rectangle has a base of 7 feet and height of 3 feet. The other rectangle has a base of 2 feet and height of 7 feet.
If the new grass costs $0.40 per square foot, how much will the grass cost Mr. Ishimoto?
$14.00
$16.40
$35.00
$41.00
Answer:
The replacing the grass will cost Mr. Ishimoto $14.00.
Step-by-step explanation:
The area of a rectangular field is:
[tex]\text{Area}=\text{height}\times \text{base}[/tex]
It is provided that Mr. Ishimoto needs to replace the grass in the section of his lawn.
The grass section can be broken into 2 rectangles.
First rectangle: Base = 7 feet and Height = 3 feet.
Second rectangle: Base = 2 feet and Height = 7 feet.
Compute the area of both the rectangles as follows:
[tex]\text{Area}_{1}=\text{height}_{1}\times \text{base}_{1}\\=3\times 7\\=21[/tex] [tex]\text{Area}_{2}=\text{height}_{2}\times \text{base}_{2}\\=7\times 2\\=14[/tex]
Now the cost of the new grass is $0.40 per square foot.
Compute the cost of replacing the grass in the first rectangular section as follows:
[tex]\text{Cost of new grass for section 1}=\text{Area}_{1} \times\$0.40\\[/tex]
[tex]=21\times \$0.40\\=\$8.40[/tex]
Compute the cost of replacing the grass in the second rectangular section as follows:
[tex]\text{Cost of new grass for section 2}=\text{Area}_{2} \times\$0.40\\[/tex]
[tex]=14\times \$0.40\\=\$5.60[/tex]
The total cost of replacing the grass is:
[tex]\text{Total cost}=\text{Cost of new grass for section 1}+\text{Cost of new grass for section 2}[/tex]
[tex]=\$8.40+\$5.60\\=\$14.00[/tex]
Thus, the replacing the grass will cost Mr. Ishimoto $14.00.
Answer
14.00
Step-by-step explanation: