Answer:
x = - 2, y = 3
Step-by-step explanation:
Given
22 + yi = 20 - x + 3i
Compare the coefficients of like terms on both sides, that is
22 = 20 - x ( subtract 20 from both sides )
2 = - x ( multiply both sides by - 1 )
x = - 2
And
yi = 3i , hence y = 3
The point Q lies on the segment PR.
Find the coordinates of Q so that the ratio of PQ to QR is 2:7
P(-22, 32)
R (5, -4)
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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A walffle cone has a height of 7 inches and a diameter of 3 inches. What is the volume of ice cram that can be contained within the cone. Use 3.14 for pi. Round to the nearest hundreth
Answer:
16.49 cubic inches.
Step-by-step explanation:
Given:
A waffle cone has a height of 7 inches and a diameter of 3 inches.
Question asked:
What is the volume of ice cram that can be contained within the cone?
Solution:
First of we will find the radius ;-
Diameter = 3 inches
Radius, r = [tex]\frac{Diameter}{2} =\frac{3}{2} =1.5\ inches[/tex]
As we know:
[tex]Volume\ of\ cone=\frac{1}{3} \pi r^{2} h[/tex]
[tex]=\frac{1}{3} \times3.14\times1.5\times1.5\times7\\ \\ =\frac{49.455}{3} \\ \\ =16.485[/tex]
Thus, volume of ice cream will be 16.49 cubic inches.
I need to know what rule represents the enlargement of a figure
Answer:
The correct option is;
(x, y) → (215·x, 215·y)
Step-by-step explanation:
An enlargement is a form of transformation involving an alteration of the size of the shape. When a shape is to be enlarged, the center of the shape is noted and the enlargement of the dimensions of the shape from that center is by multiplication of each point by the factor of the enlargement or the scale factor.
Therefore, based on the requirement for enlargement, and given the dimension of the point from the center as (x, y) the enlargement then is (215·x, 215·y), where 215 is the scale factor.
Answer:
A. (x, y) → (215x, 215y)
Step-by-step explanation:
Enlargement of a figure is the process of increasing the size of a given figure by the use of a scale. It requires the use of a scale factor that is greater than 1 to form an image. This is called dilation in transformation.
Transformation is the process of manipulating the size or orientation of a figure. To enlarge a shape, a center of enlargement is required.
Thus, the rule that signifies enlargement of a figure is ;
(x, y) → (215x, 215y)
This implies multiplying the initial coordinate x and y by a factor of 215 to produce a required size of an image.
PLEASE HELP QUICKLY
In the terms of (a + b ) n : The exponents of a start at _ and increase or _decrease_ until they reach _ . The exponents of b start at _ and increase or decrease until they reach _
Answer:
The exponents of a start at n and decrease until they reach 0 . The exponents of b start at 0 and increase until they reach n
Step-by-step explanation:
The general formula for [tex](a+b)^n[/tex] is:
[tex]a^n + C_1a^{n-1}b + C_2a^{n-2}b^2 + ... + C_{n-1}a^2b^{n-2} + C_nab^{n-1} + b^n[/tex]
Therefore, the exponents of a start at n and decrease until they reach 0 . The exponents of b start at 0 and increase until they reach n
what number increased by 20% of itself equals 18?
Answer:15
15 divided by 100 then multiplied by 20 equals 3
and 3+15 equals 18
Monarch butterflies travel about 30 miles per day. How many miles does a monarch butterfly travel per hour?
Answer:
1.25 miles
Step-by-step explanation:
one day= 30 miles
one day=24 hours
so we can divide 30 to 24 to get miles travelling per hour.
1.25 miles
Which expression is equivalent to 3 7/8 - 6 1/4?
Answer:
3 42/48 + 6 12/48
Step-by-step explanation:
Final answer:
To find the equivalent expression, convert the mixed numbers to improper fractions, subtract the fractions, and then convert the result back to a mixed number.
Explanation:
The expression equivalent to 3 7/8 - 6 1/4 is:
Step 1: Convert the mixed numbers to improper fractions: 3 7/8 = 31/8 and 6 1/4 = 25/4.
Step 2: Subtract the fractions: 31/8 - 25/4 = 31/8 - 50/8 = -19/8.
Step 3: Convert the result back to a mixed number: -19/8 = -2 3/8.
Can 12,35,37 be a right triangle
Answer:
Yes
Step-by-step explanation:
If it could be a right triangle, then 12^2 + 35^2 would have to equal 37^2
12^2 = 144
35^2 = 1225
37^2 = 1369
1225 + 144 = 1369, which is 1369.
That means that it CAN form a right triangle
Answer:
yes
Step-by-step explanation:
Use the drop down to answer the question about converting 0.ModifyingAbove 64 with bar to a fraction.
How many repeating digits are in 0.ModifyingAbove 64 with bar?
What value is multiplied on both sides of the equals sign?
What fraction represents 0.ModifyingAbove 64 with bar?
Answer:
How many repeating digits are in 0.ModifyingAbove 64 with bar?
2
What value is multiplied on both sides of the equals sign?
100
What fraction represents 0.ModifyingAbove 64 with bar?
64/99
Step-by-step explanation:
i got it right. :))
There are 2 repeating digits are in 0 when modifying above 64 with bar.
100 is multiplied on both sides of the equals sign.
64/99 represents 0.
Given that,
The question about converting 0. Modifying above 64 with the bar to a fraction.
We have to determine,
How many repeating digits are in 0? Modifying above 64 with bar?
What value is multiplied on both sides of the equals sign?
What fraction represents 0?
According to the question,
The question about converting 0. Modifying above 64 with the bar to a fraction.
Converting the 64 bar into a fraction,
[tex]\bar{64} = 0.64646464[/tex]
Therefore,
[tex]\rm 0. \bar{64}=\dfrac{3}{x}\\\\ 100 \times \dfrac{\bar{64}}{100}= \dfrac{3}{x}\times 100\\\\= \dfrac{64}{100} \times {\dfrac{1}{99}}=\dfrac{300}{x}\\\\ x = \dfrac{300 \times 9900}{64}\\\\x =\dfrac {2970000}{64}[/tex]
Hence, There are 2 repeating digits are in 0 when modifying above 64 with bar.
100 is multiplied on both sides of the equals sign.
64/99 represents 0.
For more details refer to the link given below.
https://brainly.com/question/18198700
Plz help on these two.
5)x= 67° and y= 32°
(x-15)°=52°(vertically opposite angles)
=>x= 52+15° = 67°
Similarly, 4y= 128°(vertically opposite angles)
=>y=128/4= 32°
6) x= 5° , y= 22°
12x+15=75°(vertically opposite angles)
12x=75-15°
12x=60°
x= 5°
6y-27°=105°
6y= 105+27°
6y= 132°
y= 22°
Anyone help me wiv this question please
Answer:
A: 8x-12
B: 5(n+3)
Step-by-step explanation:
A) Distribute 4 to the numbers inside the parenthesis.
4 x 2x= 8x
4 x -3= -12
8x-12
B) 5 is divisible to 15, so you can divide it with both numbers.
5/5=1
15/5=5
5(n+3)
Answer:
first one is 4×2x-4×3 while the second is 5(n+3)
Step-by-step explanation:
you needed to expand letter a. and simplify letter b.
a wave has a maximum of 5. if it’s midline is at y=2, what is it’s minimum?
Answer:
-1
Step-by-step explanation:
The midline is the middle point
Subtract the midline from the maximum
5-2 = 3
Then we need to subtract this number from the midline to get to the minimum
2-3 = -1
The minimum is at -1
Answer:
-1
Step-by-step explanation:
Mean line is between min and max
2 = (5 + min)/2
4 = 5 + min
min = -1
I just need the awnser please
Answer:
The surface area is 294 ft^2 (please give branliest)
Step-by-step explanation:
area of one side 49
multiply by 6 sides
The surface area of the cube is equal to 294 square inches.
How to calculate the surface area of the cube
In this problem we find the representation of a cube, whose surface area, that is, the sum of the areas of all faces of the cube, must be computed in accordance with this formula:
A = 6 · l²
Where:
A - Surface area, in square inches.l - Side length, in inches.If we know that l = 7 in, then the surface area of the cube is equal to:
A = 6 · (7 in)²
A = 6 · 49 in²
A = 294 in²
The cube has a surface area of 294 square inches.
Rodrick worked at Jack-In-The-Box for 37.5 hours last week. His pay for the
week, before taxes was deducted, was $346.88. How much did he earn per hour?
Answer:
He earned $9.25
Step-by-step explanation:
First, you have to create an equation.
346.88= 37.5h
Then divide 346.88 by 37.5
You get 9.25=h
Rodrick earned $9.25 per hour.
Rodrick earned approximately $9.25 per hour.
Explanation:To find out how much Rodrick earns per hour, we need to divide his total pay by the number of hours worked. In this case, Rodrick worked for 37.5 hours and earned $346.88. So, to find his earnings per hour, we divide $346.88 by 37.5:
Earnings per hour = Total pay / Number of hours
Earnings per hour = $346.88 / 37.5
Earnings per hour ≈ $9.25
Therefore, Rodrick earned approximately $9.25 per hour.
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Use the graph that shows the solution to f(x)=g(x) . f(x) = 1/x−2 g(x)=x−2
What is the solution to f(x)=g(x) ?
Select each correct answer.
A −1
B 1
C 2
D 3
If you must solve this problem graphically, you have to draw the graph of the two functions and see where they meet.
Look at the attached image to see the two graphs.
You can see that they intersect twice, when x=1 and when x=3
Compute the amount in an account after 8 yr if $6500 is invested at an annual interest rate of 5.25% compounded quarterly. Round to two decimal places.
Answer:
$9865.76¢
Step-by-step explanation:
Please kindly check the attached file for explanation.
Using compound interest, it is found that the amount in the account is of $9,865.76.
Compound interest:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.In this problem:
$6500 is invested, thus [tex]P = 6500[/tex]8 years, thus [tex]t = 8[/tex]Interest rate of 5.25%, thus [tex]r = 0.0525[/tex].Compounded quarterly, thus [tex]n = 4[/tex].The amount in the equation is:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(8) = 6500(1 + \frac{0.0525}{4})^{32}[/tex]
[tex]A(8) = 9865.76[/tex]
The amount is of $9,865.76.
A similar problem is given at https://brainly.com/question/24507395
a cinema has three screens.
last Saturday there were 500 visitors.
40% went to screen 1
25% went to screen 2
the rest went to screen 3
workout how many visitors attended each screen
Answer:
200 are on screen 1
125 are on screen 2
175 went to screen 3
Step-by-step explanation:
10% is 50 so 50 x 4 =200
25% of 500 is 12, divide 500 by 4
35% is 25% + 10% = 125 + 50 = 175
WILL GIVE BRAINLIST PLZ HELP SOMEONE!!!
Martha is braiding a necklace for her friend. The graph below shows the length of the necklace with respect to the length of time Martha has spent braiding.
Select the equation that represents the proportional relationship shown on the above graph.
A. L = 10t
B. L = 1/10t
C. 20t
D. 1/20t
Step-by-step explanation:
L = 20t
Step-by-step explanation:
The length increases by 20 millimeters per minute
Answer: L=20t
Step-by-step explanation:
So I am doing Zero and Negative Exponents in geometry and I am confused on whether (5.5)^0 is undefined or equal to 1. How do I know which one it is when doing the math for this problem?
Anything to the power of zero should always equal 1.
There shouldn't be any reason why it will be undefined.
Determine the solutions of the equation. What solution
makes sense for the situation?
A rectangle has a length that is 5 inches greater than its
width, and its area is 104 square inches. The equation (x
+5)x = 104 represents the situation, where x represents
the width of the rectangle.
(x + 5)x = 104
x2 + 5x - 104 = 0
What are the dimensions of the rectangle?
width=
inches
length =
inches
5) Intro
Answer: x=8
Width=8 inches
Length=13 inches
Final answer:
The width of the rectangle is 8 inches and the length is 13 inches, as determined by solving the quadratic equation representing the area of the rectangle.
Explanation:
To solve for the dimensions of the rectangle, we need to find the value of x, which represents the width of the rectangle. The quadratic equation we have is x² + 5x - 104 = 0.
Factoring this equation, we are looking for two numbers that multiply to -104 and add to 5.
These numbers are 13 and -8, so the equation factors to (x + 13)(x - 8) = 0. Setting each factor equal to zero gives us two possible solutions for x: x = -13 or x = 8.
Since a width cannot be negative, the only sensible solution for this problem is x = 8 inches. Given that the length is 5 inches more than the width, the length will be 8 inches + 5 inches = 13 inches.
Dimensions of the rectangle:
Width = 8 inches
Length = 13 inches
I need help answering this
Answer: AB=5.66, AC=4
Step-by-step explanation:
So this triangle is a 45-45-90 triangle, meaning it has one 90 degree angle and two 45 degree angles.
If you remember from geometry, the sides that have the same angle have the same length, and seeing as angle A is 45 degrees and side BC is 4, we can know for certain that angle B is 45 degrees and side AC is also 4.
This is because angle C is already marked as the 90 degree angle due to the square symbol in it.
Now to find side AB, we would use our friend the Pythagorean Theorem, which states that [tex]a^2+b^2=c^2[/tex].
Let a = side BC and b = side AC, meaning c = side AB.
Now plug in the values and solve:
[tex]4^2+4^2=c^2[/tex]
[tex]32=c^2[/tex]
[tex]\sqrt{32} =\sqrt{c^2}[/tex]
[tex]5.65685=c[/tex]
what is the vertex of h(x)=-2x^2+8x
Answer: (2,8)
Step-by-step explanation:
Answer:
deeznuts
Step-by-step explanation:
Paula weeded 40% of her garden in 8 minutes. How many minutes will it take her to weed all of her garden? Part A Let m = the number of minutes it will take Paula to weed all of the garden. Choose the equation that can be used to find the solution to the problem.
Answer:
20 minutes
Step-by-step explanation:
40% = 8 minutes
40% x 2.5 = 100%
8 minutes x 2.5 = 20 minutes
Answer:
8m = 0.4
Step-by-step explanation:
I think thats the equation you are looking for. or i may be late to answer this question.
Based on the diagram above, a student determined the hypotenuse of the triangle to be 6√3 Determine if the student's answer is correct. If it is not correct, find the correct length.
Answer:
The student answer is wrong. The correct length of the hypotenuse is 12
Step-by-step explanation:
The question is incomplete without diagram. Find the diagram attached below.
The longest side of the right angled triangle is the hypotenuse.
The side facing the angle 30° is the opposite side of the triangle.
To find the hypotenuse, we will use the SOH CAH TOA method in trigonometry identity.
According to SOH:
Sin30° = Opposite/Hypoenuse
Sin30° = 6/Hypotenuse
Hypotenuse = 6/sin30°
Hypotenuse = 6/0.5
Hypotenuse = 6×2
Hypotenuse = 12
The student answer is wrong. The correct length of the hypotenuse is 12
Given g(x) = -x – 4, solve for x when g(x) = 9.
To solve for x when g(x) = 9 given the function g(x) = -x – 4, set the equations equal to each other. Rearrange the equation and solve for x, which gives x = -13
Explanation:The question asked for the value of x when g(x) = 9 given the function g(x) = -x – 4. We can start by setting the two equations equal to each other. This gives us -x - 4 = 9. Next, we rearrange the equation to solve for x by adding 4 to each side, which gives us -x = 9 + 4 or -x = 13. To get x on its own, we divide each side by -1. This gives us x = -13. Therefore, when g(x) = 9, x is equal to -13.
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round to 3 decimal places for the final answer
All possible outcomes for flipping a coin three times are listed below: (H = heads up, T = tails up) {HHH, THH, HTH, HHT, TTH, THT, HTT, TTT} What is the probability of obtaining at least 1 heads?
Answer:
7 out of 8
Step-by-step explanation:
Need this quick!!
Find the sum.
7х+ 15х=
A. 21x
B. 21x^2
C. 22x
D. 22x^2
Answer:
C. 22x
Step-by-step explanation:
7x+15x=22x
Answer:
C. 22x
Step-by-step explanation:
7x + 15x = 22x
You simply need to add 7 and 15 and you get 22x.
A soccer ball is kicked in the air and follow the path h(x)=2x2+1x+6, where x is the time in seconds and h is the height of the soccer ball. At what time will the soccer ball hit the ground?
Answer:
You can either factor or use quadratic formula to find where h(x)=0
Step-by-step explanation:
Remember that the ball is on the ground when h(x)=0 since that is the height. There will be two zeros, one is a negative number so would be before you kicked the ball, the other one will be when the ball comes back down.
Cruz is training to compete in a triathlon. He left his house at 6 : 00 and ran until 7 : 30 . Then he rode his bike until 9 : 45 . He covered a total distance of 51 miles. His speed when biking was 1.6 times his speed when running. Find Cruz's biking and running speeds
Final answer:
Cruz's running speed is 10 mph, and his biking speed is 16 mph, which we found by setting up an equation representing the total distance he covered and the time spent on each activity at their respective speeds.
Explanation:
To determine Cruz's biking and running speeds, we can use the information given about the total distance and the ratio of his speeds. The information tells us that Cruz ran for 1.5 hours (from 6:00 to 7:30) and biked for 2.25 hours (from 7:30 to 9:45). If we let r represent his running speed, then his biking speed would be 1.6r because it's said to be 1.6 times his running speed.
Cruz's total running distance would then be r × 1.5 hours, and his biking distance would be 1.6r × 2.25 hours. We know that the total distance covered is 51 miles, so we can set up the following equation:
1.5r + 1.6r × 2.25 = 51
Now, solve for r:
1.5r + 3.6r = 51
5.1r = 51
r = 51 / 5.1
r = 10 miles per hour
Therefore, Cruz's running speed is 10 mph, and his biking speed is:
1.6 × 10 mph = 16 mph
Cruz's running speed is 10 mph, and his biking speed is 16 mph.