Answer:
The answer is y = x
The equation for the line of reflection can be found by using the midpoint formula and the slope formula. The equation for the line of reflection for the given points (6, 3.7) and (3.7, 6) is y = -x + 9.7.
Explanation:The equation for the line of reflection can be found by using the midpoint formula and the slope formula. The midpoint of each corresponding pair of points can be calculated to find the coordinates of the image points. Then, the slope of the original line and the slope of the reflected line can be calculated. Using the midpoint and slope, the equation of the line of reflection can be determined.
For example, to find the equation for the line of reflection for points (6, 3.7) and (3.7, 6), we can calculate the midpoint: ( (6 + 3.7) / 2, (3.7 + 6) / 2 ) = (4.85, 4.85).
Next, we can calculate the slope of the original line using the points (6, 3.7) and (5.4, 2) using the slope formula: (2 - 3.7) / (5.4 - 6) = -1.7 / -0.6 = 2.83.
Finally, we can calculate the slope of the reflected line using the points (4.85, 4.85) and (3.7, 6) using the slope formula: (6 - 4.85) / (3.7 - 4.85) = 1.15 / -1.15 = -1.
So, the equation for the line of reflection is y = -x + b. To find b, we can use the point (4.85, 4.85). Substituting the values into the equation, we get 4.85 = -(4.85) + b, which simplifies to b = 9.7.
Therefore, the equation for the line of reflection is y = -x + 9.7.
What is the percent decrease in the number of students enrolled in the photography club
Answer:
The percent of decrease is [tex]30\%[/tex]
Step-by-step explanation:
Assuming the number of students enrolled in the photography club decrease from 50 to 35.
Then the change in student enrollment is 35-50=-15.
The percent of change is given by:
[tex]\frac{Change\:in\:enrollment}{Original\:number}\times 100\%[/tex]
[tex]\frac{-15}{50}\times 100\%[/tex]
[tex]-15*2\%=-30\%[/tex]
Answer: 30
Step-by-step explanation:
i got it right
What is the answer to -12=4+c
Answer:
c=-16
Step-by-step explanation:
We want to solve for c in the equation:
-12=4+c
We add the additive inverse of 4 to both sides of the equation to obtain:
[tex] - 12 + - 4 = 4 + - 4 + c[/tex]
We simplify to obtain:
[tex] - 12 - 4 = 4 - 4 + c[/tex]
We simplify further to get:
[tex] - 16= 0 + c[/tex]
Therefore
[tex] - 16 = c[/tex]
Or
[tex]c = - 16[/tex]
What is the slope of the line described by the equation below?
у= 5x - 22
оооо
Explanation: Linear equations can be written in the form y = mx + b where the multiplier, m, or the coefficient of the x term represents the slope of the line and b represents the y-intercept of the line.
The linear equation y = 5x - 22 has a slope equal to 5
and a y-intercept equal to -22.
Paulina gets on an elevator. At the first stop, 4 people get off and 3 get on.At the second stop, 5 people get off and 1 gets on. At the third stop, Paulina gets off. If 4 people are still in the elevator when Paulina gets off, how many people were on the elevator when she got on?
Answer:
There were 8 people on the bus when Paulina got on.
Step-by-step explanation:
Solve the equation below for x.
log2x + log(2x - 1) = log3x
Answer:
x = 5/4
Step-by-step explanation:
1. cancel x for log 3x and 2x
2. multiply log 2x-1 by log 2
3.simplify to log 4x-2 = log3
4.logs will cancel out and leave you with 4x-2 = 3
5. solve and get 5/4
Answer:
x = 5/4
Step-by-step explanation:
Solve for t
-7/4=2/5t
Answer:
Step-by-step explanation:
-7/4 = 2/5t
*5 *5
-35/4 = 2t
-8.75 = 2t
-4. 37
Use a Pythagorean Triple to find x.
27
36
x
PLEASE I NEED IT FOR TEST
Answer: 45
Step-by-step explanation:
A^2 + B^2 = C^2
27^2 + 36^2 = x^2
729 + 1296 = 2025
square root of 2025 = 45
X = 45
Tim answered all the questions on his math yes but got 10 wrong. He received 4 points for every correct answer, and no penalty for wrong answers. His score was 76 points write an equation and find the total number of questions on the test
Answer: (a) 4x + 10(0) = 76
(b) 29questions
Step-by-step explanation: let the correct answer = x.
4points for correct answer each total 4xpoints
Since no penalty for wrong answers, his total points were 76points.
Equation: 4x = 76
x = 19. He scored 19 correct answers.
Total number of questions on the test = 19 correct answers + 10 wrong answers
29 questions
Ramond is putting a fence around his rectangular garden shown above. Before he can build the fence, he needs to find the perimeter of the garden. If the garden is 4 meters long by 2 meters wide, what is the perimeter of the garden?
The gardens perimeter is 12 meters.
Explanation:
The garden has a 4m length and a 2m width. The perimeter of any given rectangle is two times the sum of the length and the width of the same rectangle.Perimeter = 2 × (length of the rectange + width of the rectangle)Perimeter = 2 × (4m + 2m) = 2 × (6m) = 12 meters.
So the gardens perimeter is equal to 12 meters.Ramond needs to buy a fence for a garden whose parameter is 12 meters.The diameter of a circle is 40 m. Find the aread of the circle in terms of π
Answer:
40π
Step-by-step explanation:
Circumference Formula: C = 2πr
Step 1: Divide diameter by 2 to get the radius
40 / 2 = 20 m -> Radius
Step 2: Plug into the Circumference Formula
C = 2π(20)
C = 40π
Answer: 40π
Answer:
Step-by-step explanation:
The radius of the circle is d/2
The Area of the circle is pi*r^2
The Area of the circle is pi * (d/2)^2
The Area of the circle is A = pi * (40/2)^2
The Area of the circle is A = 400 * pi
is 20/31 closer to 66% or 75% Explain and show why
Step-by-step explanation:
We have,
[tex]\dfrac{20}{31}[/tex]
Show that [tex]\dfrac{20}{31}[/tex] is closer 66 % or 75 %.
∴ The percentage of [tex]\dfrac{20}{31}[/tex]
= [tex]\dfrac{20}{31}\times 100[/tex]
= [tex]\dfrac{2000}{31}[/tex]
= 64.516 %
≈ 66 %, shown.
Because the percentage of [tex]\dfrac{20}{31}[/tex] is 66 percent (%).
Thus, [tex]\dfrac{20}{31}[/tex] is closer 66 percent (%) , shown.
The fraction 20/31 is closer to 66%.
To determine which percentage 20/31 is closer to, we first need to convert the percentages into fractions and then compare them with 20/31.
66% can be written as a fraction as 66/100. Simplifying this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 2 in this case:
[tex]\[ \frac{66}{100} = \frac{66 \div 2}{100 \div 2} = \frac{33}{50} \][/tex]
Further simplifying by dividing both by 11, we get:
[tex]\[ \frac{33}{50} = \frac{33 \div 11}{50 \div 11} = \frac{3}{5} \][/tex]
75% as a fraction is 75/100. Simplifying this fraction by dividing both the numerator and the denominator by 25, we get:
[tex]\[ \frac{75}{100} = \frac{75 \div 25}{100 \div 25} = \frac{3}{4} \][/tex]
Now we compare the fraction 20/31 with 3/5 and 3/4. To compare these fractions, we can find a common denominator or convert them to decimal form.
Converting to decimal form:
[tex]\[ \frac{20}{31} \approx 0.645 \] \[ \frac{3}{5} = 0.6 \] \[ \frac{3}{4} = 0.75 \][/tex]
Now we can see that 0.645 is closer to 0.6 than it is to 0.75. Therefore, 20/31 is closer to 66% (or 3/5) than it is to 75% (or 3/4).
Alternatively, we could also cross-multiply to compare the fractions directly:
For 20/31 and 3/5:
[tex]\[ 20 \times 5 = 100 \] \[ 31 \times 3 = 93 \][/tex]
Since 100 is greater than 93, 20/31 is greater than 3/5, but not by much.
For 20/31 and 3/4:
[tex]\[ 20 \times 4 = 80 \] \[ 31 \times 3 = 93 \][/tex]
Since 93 is much greater than 80, 20/31 is less than 3/4 by a larger margin than its difference with 3/5.
Thus, by both methods, we conclude that 20/31 is closer to 66%.
A customer gets a 14% discount on monthly internet service. If the customer pays $51.60 a month after the discount, what is the original price of the internet service?
Answer:
60
Step-by-step explanation:
I used the guess and change method and subtracting every guessed number for 51.6. I found out that if you subtract 60 by 14%, you'll get 51.6.
Hope this helps :)
Prove that the value of the expression: (5^18–25^8)(16^4–2^13–4^5) is divisible by 30 and 44.
Answer:
See explanation
Step-by-step explanation:
Given the expression
[tex](5^{18}-25^8)(16^4-2^{13}-4^5)[/tex]
First, simplify all terms:
[tex]25^8=(5^2)^8=5^{2\cdot 8}=5^{16}\\ \\16^4=(2^4)^4=2^{4\cdot 4}=2^{16}\\ \\4^5=(2^2)^5=2^{2\cdot 5}=2^{10}[/tex]
Then the expression is
[tex](5^{18}-5^{16})(2^{16}-2^{13}-2^{10})[/tex]
Use distributive property in both factors:
[tex](5^{18}-5^{16})(2^{16}-2^{13}-2^{10})=\\ \\=(5^{16}(5^2-1))(2^{10}(2^6-2^3-1))=\\ \\=(5^{16}(25-1))(2^{10}(64-8-1))=\\ \\=5^{16}\cdot 24\cdot 2^{10}\cdot 55=\\ \\=5^{16}\cdot 4\cdot 6\cdot 2^{10}\cdot 5\cdot 11=\\ \\=5^{16}\cdot 2^{10}\cdot (4\cdot 11)\cdot (5\cdot 6)=\\ \\=5^{16}\cdot 2^{10}\cdot 44\cdot 30[/tex]
Therefore, this expression is divisible by 30 and by 44
find the values of a and b such that x^4 +ax^3 -7x^2 - 8x +b is exactly divisible by(x+2) and (x+3)
Answer:
a = 2 ; b = 12
Step-by-step explanation:
p(x)=x⁴ + ax³ - 7x² - 8x +b
p(x) is exactly divisible by (x + 2). So p(-2)=0
(-2)⁴ + a(-2)³ - 7(-2)² - 8(-2) +b = 0
16 - 8a - 7*4 +16 + b =0
16 - 8a - 28 + 16 + b =0
4 - 8a + b = 0
-8a + b = -4 -----------(i)
p(x) is exactly divisible by (x + 3). So p(-3)=0
(-3)⁴ + a(-3)³ - 7(-3)² - 8(-3) +b = 0
81 -27a - 63 + 24 + b =0
42 - 27a + b = 0
-27a + b = -42 ------------(ii)
-8a + b = -4 -----------(i)
-27a + b = -42 ------------(ii)
subtract 19a = 38
a = 38/19 = 2
a=2
Substitute a value in equation (i)
-8*2 + b= -4
-16 + b = -4
b = -4 + 16
b = 12
Which two points are on the graph of y = -x + 3
Answer:
[tex](3,0),(0,3)[/tex]
Step-by-step explanation:
y-intercept:
[tex]Substitute\ x=0\\\\y=0+3\\\\y=3\\\\Hence\ (0,3)\ is\ on\ the\ graph.[/tex]
x-intercept:
[tex]Substitute\ y=0\\\\0=-x+3\\\\x=3\\\\Hence\ graph\ passes\ through\ (3,0)[/tex]
The original scale factor for a scale drawing of a house plan is 1/80 , and the length of the original scale drawing is
12 inches. What is the length of a new scale drawing if the scale factor of the new scale drawing to actual length
of the house is 1/180?
HELP NOW PLEASE
Answer:
[tex]5\frac{1}{3}\ in[/tex]
Step-by-step explanation:
we know that
The original scale factor is 1/80
That means
1 unit in the drawing represent 80 units in the actual
or
1 inch in the drawing represent 80 inches in the actual
step 1
Find the actual length with the original scale
using proportion
[tex]\frac{1}{80}=\frac{12}{x}\\\\x=80(12)\\\\x= 960\ in[/tex]
step 2
The new scale drawing is
[tex]\frac{1}{180}[/tex]
That means
1 unit in the drawing represent 180 units in the actual
or
1 inch in the drawing represent 180 inches in the actual
step 3
Find the length of a new scale drawing
using proportion
[tex]\frac{1}{180}=\frac{x}{960}\\\\x=960/180\\\\x= 5.33\ in[/tex]
Convert to mixed number
[tex]5.33\ in=5\frac{1}{3}\ in[/tex]
The actual length of the house if the scale is 1/80 is = 5 1/3 inches
What is a scale drawing?A scale drawing is a reduced form in terms of dimensions of an original image / building / object
Scale of the drawing = dimensions of the scale drawing / dimensions of the original image.
Actual length when the scale was 1/80 = 80 x 12 = 960 inches
Actual length when the scale was 1/180 = 960 / 180 = 5 1/3 inches
To learn more about scale drawings, please check: https://brainly.com/question/26388230
A new car is purchased for 17900 dollars. The value of the car depreciates at 12.25%
per year. What will the value of the car be, to the nearest cent, after 10 years?
Answer:
Therefore the value of the car after 10 year will be = $4,845.34
Step-by-step explanation:
A new car is purchased for $17900. the value of the car depreciates at 12.25% per year.
Since the value of the car depreciates therefore the amount of the car is
[tex]A= P(1-\frac{r}{100})^n}[/tex]
[tex]=17900(1-\frac{12.25}{100})^{10}[/tex] [ p = $17900, r = 12.25% and n =10 years]
= $ 4,845.34
Therefore the value of the car after 10 year will be = $4,845.34
The value of the car be, after 10 years will be $4845.34.
Given that,
A new car is purchased for 17900 dollars.
The value of the car depreciates at 12.25% per year.
We have to determine,
What will the value of the car be, after 10 years.
According to the question,
The value of the car depreciates therefore the amount of the car is determined by the formula,
[tex]A = P (1 -\dfrac{r}{100})^n[/tex]
Where, P = $17900, r = 12.25% and n =10 years
Substitute all the values in the formula,
[tex]A = P (1 -\frac{r}{100})^n\\\\A = 17900(1 -\frac{12.25}{100})^{10}\\\\A = 17900( 1- 0.1225)^{10}\\\\A = 17900(0.8775)^{10}\\\\A = 17900 \times 0.270\\\\A = 4845.34[/tex]
Hence, The value of the car be, after 10 years will be $4845.34.
To know more about Percentage click the link given below.
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0.63 ÷ 1.638 what is ir
Answer:
[tex]0.3846154[/tex]
Step-by-step explanation:
We want to perform the following division:
0.63 ÷ 1.638
Let us convert everything to fraction to get:
[tex]\frac{63}{100}\div \frac{1638}{1000}[/tex]
We multiply by the reciprocal of the second fraction to get:
[tex]\frac{63}{100}\times \frac{1000}{1638}[/tex]
[tex]=\frac{63}{1638}*10[/tex]
[tex]=0.03846154*10=0.3846154[/tex]
Final answer:
To find the result of 0.63 divided by 1.638, you multiply both numbers by 1000 to remove the decimals and then divide, resulting in approximately 0.384612.
Explanation:
The question asks for the result of dividing 0.63 by 1.638. To solve this problem, you perform division as you would with any two numbers. The steps are as follows:
Set up the division problem: 0.63 ÷ 1.638.
To make the division simpler, you can multiply both the divisor (1.638) and the dividend (0.63) by powers of 10 to remove the decimals. In this case, multiply both by 1000 to get 630 ÷ 1638.
Perform the division: 630 divided by 1638 equals approximately 0.384612.
Thus, 0.63 ÷ 1.638 is approximately 0.384612.
The sum of 8 and a number h is 12 into an equation
Answer: 4
Step-by-step explanation:
The sum of 12 and 8 is 12 add 8 which is 20. The difference between 12 and 8 is 12 minus 8 which is 4.
I don't know if this is right but if it is not tell me plz.
:) Thx
An airplane flies 600 km in 1 hour. What is it’s average speed in kilometers per hour.
Find f(100) and show how to solve
BRAINLIEST!!!
5. Find mEG.
Answer:
24
Step-by-step explanation:
mEG = 24 units
Hope it helps
a 0.5 kg ball is kicked with a force of 40 N. what is the resulting acceleration of the ball?
Answer: The resulting acceleration of the ball is 80m/s² .
Step-by-step explanation:
Formula for force : [tex]F= ma[/tex]
,where m = mass pf object and a = the resulting acceleration of object.
As per given , we have
The mass of ball : m= 0.5 kg
Force = 40 N
Let 'a' be the resulting acceleration of the ball.
Substitute all values in formula , we get
[tex]40=(0.5)a\\\\\Rightarrow\ a=\dfrac{40}{0.5}=80\ m/s^2[/tex]
Hence, the resulting acceleration of the ball is 80m/s² .
The acceleration of the ball is 80 Newton per kg.
Given that
A 0.5 kg ball is kicked with a force of 40 N.
We have to determine
What is the resulting acceleration of the ball?
According to the question
The acceleration of the ball is determined by the following formula;
[tex]\rm Acceleration = \dfrac{Force}{Mass}[/tex]
The mass of the ball is 0.5 kg.
The force applied to the ball is 40 N.
Therefore,
The acceleration of the ball is,
[tex]\rm Acceleration = \dfrac{Force}{Mass}\\ \\ \rm Acceleration = \dfrac{40}{0.5}\\ \\ \rm Acceleration = 80 \ Newton \ per \ kg[/tex]
Hence, The acceleration of the ball is 80 Newton per kg.
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The expression LaTeX: -5t^2+40t
−
5
t
2
+
40
t
predicts the height, in meters of an object t seconds after a person launches it into the air.
It will take _ seconds for the object to hit the ground.
Answer:
8 seconds
Step-by-step explanation:
Given
h = - 5t² + 40t
When the object hits the ground then h = 0
Substitute h = 0 into the function and solve for t
- 5t² + 40t = 0 ← factor out - 5t from each term
- 5t(t - 8) = 0
Equate each factor to zero and solve for t
- 5t = 0 ⇒ t = 0
t - 8 = 0 ⇒ t = 8
t= 0 denotes the time of launch
t = 8 denotes the time it hits the ground
Which symbol makes the number sentence true?
A. <
B. >
C. =
Answer:
solution is c
Step-by-step explanation:
look at picture
The Murphy family is on a road trip. On the first day, they traveled 30% of their total distance. On the second day, they traveled another 1/4 of the total distance. What fraction of the total distance do they have left after the second day? What percent? ANSWER ASAP!
Answer:
[tex] \frac{11}{20} [/tex]
On the first day, they traveled 30 percents of the total distance. On the second day they traveled one fourth of the total distance. One fourth converted into percentage is 25 percent. Then you add 30 plus 25 because that is the to a
total distance that Murphy's family traveled for 2 days. It will be 55 percents, and you convert 55 percents into fraction will be 55/100, and you simplify it, will be 11/20.
On a coordinate plane, a line is drawn from point J to point K. Point J is at (1, negative 10) and point K is at point (7, 2). What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1? y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1 –8 –5 0 6On a coordinate plane, a line is drawn from point J to point K. Point J is at (1, negative 10) and point K is at point (7, 2). What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1? y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1 –8 –5 0 6On a coordinate plane, a line is drawn from point J to point K. Point J is at (1, negative 10) and point K is at point (7, 2). What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1? y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1 –8 –5 0 6
Lines can be divided into different segments of different lengths using ratios.
The y-coordinate of the point at this ratio is 0
The coordinates of J and K are given as:
[tex]\mathbf{J = (1,-10)}[/tex]
[tex]\mathbf{K = (7,2)}[/tex]
The ratio is given as:
[tex]\mathbf{m:n =5:1}[/tex]
The y-coordinate of the point at this ratio is calculated using:
[tex]\mathbf{y_p = \frac{my_2 + ny_1}{m+n}}[/tex]
So, we have:
[tex]\mathbf{y_p = \frac{5 \times 2 + 1 \times -10}{5+1}}[/tex]
[tex]\mathbf{y_p = \frac{10 -10}{5+1}}[/tex]
Simplify the numerator, and the denominator
[tex]\mathbf{y_p = \frac{0}{6}}[/tex]
Divide the fraction
[tex]\mathbf{y_p = 0}[/tex]
Hence, the y-coordinate is 0
Read more about line segment ratios at:
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The y-coordinate of the point is 0.
The formula for the section formula is
x [tex]= \frac{mx_2 + nx_1}{m + n}[/tex]
y [tex]= \frac{my_2 + ny_1}{m + n}[/tex]
Substituting in the points, we get
x = [tex]= \frac{5(7) + 1(1)}{5 + 1} = \frac{36}{6} = 6[/tex]
y [tex]= \frac{5(2) + 1(-10)}{5 + 1} = \frac{0}{6} = 0[/tex]
Therefore, the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1 is 0.
2 times 5 with a expont of 2 minus (4+1)
Answer:
2([tex]5^{2}[/tex])-5
45
Step-by-step explanation:
Answer:
45
Step-by-step explanation:
2x5^2-(4+1)
2x25-5
50-5
45
Tina owns a florist shop. She charges 2.99 cents for each flower plus a delivery fee of 5.
y=_____________, only type what goes in the blank.
Answer:
Charges per flower delivered by Tina is, y= 2.99 (x) + 5
Step-by-step explanation:
Given:
Tina's charges per flower = 2.99 cents
Delivery charged by Tina = 5 units or 5$
We have fill the blank in terms of 'y'.
We know slope intercept form that is : y = m(x)+b
So here we have to fill numbers according to the slope intercept form.
Let the numbers of flowers sold by Tina be 'x'.
Here slope (m) will be the charge of each flower charged by the florist.
The delivery charge is the fixed rate so its the constant value and will be treated equivalent to y-intercept or b values.
Arranging our values:
[tex]m=2.99[/tex] cents , [tex]b=5\$[/tex]
Then the slope-intercept form :
⇒ [tex]y=m(x)+b[/tex]
⇒ [tex]y= 2.99(x) + 5[/tex]
We have to type only that goes in the blank and that is 2.99(x) +5.
y = 2.99(x) + 5 is our final answer.
How many teaspoons are in 1/4 cups
Answer:
12 U.S teaspoons are in 1/4 cups.
The Formula is to multiply the volume value by 48.
So Since a 1/4 us cup=0.25 we can multiply this by 48.
0.25*48=12
So our awnser is 12 teaspoons
There are 12 teaspoons in 1/4 cups.
To understand this conversion, we need to know the standard conversion factors for cups and teaspoons. There are 16 teaspoons in 1 cup. Therefore, to find out how many teaspoons are in 1/4 cup, we divide the number of teaspoons in a full cup by 4.
Here is the calculation:
1 cup = 48 teaspoons
[tex]\( \frac{1}{4} \times 48 \)[/tex] teaspoons
[tex]\( = \frac{1}{4} \times \frac{48}{1} \)[/tex]
[tex]\( = \frac{48}{4} \)[/tex]
[tex]\( = 12 \)[/tex]
Therefore, there are 12 teaspoons in 1/4 cups.