Thus coordiante of point H is(4,6)
The Midpoint Formula: The midpoint of two points,
(x1,y1) and (x2,y2) is the point
M=(x1+x2)/2 and (y1+y2)/2
(2+x2)/2=3
(6+y2)/2=6
solving above equation
x2=4
y2=6
Thus coordiante of point H is(4,6)
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Which of the following expressions is equivalent to 32x − 3?
the quantity 9 to the power of x end quantity over 27
the quantity 6 to the power of x end quantity over 9
the quantity 2 to the power of x end quantity over 3
the quantity 1 to the power of x end quantity over 9
The expressions which is equivalent to the given expression; 3^(2x -3) is; the quantity 9 to the power of x end quantity over 27.
Equivalent expressionIt follows from the task content that the equivalent expression as in the task content can be determined by the laws of Indices as follows;
3^(2x -3)
= 3^(2x) × 3-³
= (3²)^x × 1/3³
= 9^(x) × 1/27
= 9^(x)/27.
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The expression that is equivalent to 3^(2x - 3) is; Option A: the quantity 9 to the power of x end quantity over 27.
How to use Law of Indices?Laws of indices provide us with rules for simplifying calculations or expressions involving powers of the same base.
Now, we are given the expression as 3^(2x - 3). This can be broken down into; 3^(2x) × 3⁻³
Now, according to laws of indices;
3^(2x) = (3²)ˣ
Thus, we now have;
= ((3²)ˣ)/3³
= 9ˣ/3³
= 9ˣ/27
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On one day at a local minigolf course, there were 365 customers who paid a total of $3,100. If the cost for a child is $8 per game and the cost for an adult is $11 per
game, write a system of equations to model this scenario, where x represents the number of children and y represents the number of adults who played that day.
11x + 8y = 365
x+y = 3100
O11x+8y=3100
x+y = 365
O8x + 11y = 365
x+y=3100
O 8x + 11y = 3100
x+y = 365
The equations for modelling the scenario is 8x + 11y = 3100
x + y = 365 (option d)
Given,
Total number of customers at a local mini golf house = 365
Total amount paid by a customer = 3100
The cost for a child per game is = $8
The cost for an adult per game is = $11
So,
First equation will be:
x represents the number of children
y represents the number of adults
x + y = 365
Second equation is :
x represents the number of children
y represents the number of adults
Total amount paid by a customer = 3100
The cost for a child per game is = $8
The cost for an adult per game is = $11
8x + 11y = 3100
The equation of the given statement:
8x + 11y = 3100
x + y = 365
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Answer:
option D
Step-by-step explanation: the answer d
0.5 to the 11 power simplify
after finishing her shift, a waitress wrote 2.5 under “hours worked” on her time card. How long did she work?
Answer:
if it says 2.5 that mean 2 hours and 5 minutes
Answer:
Two hours and 30minutes
Step-by-step explanation:
find an equation, or a set of equations, to describe the set of points that are equidistant from the points p(−8, 0, 0) and q(−2, 0, 0).
The plane is defined by the equation, x = -3.
What do we mean by equations?A mathematical statement made up of 2 expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value for the variable x as x = 7 after solving this equation.To find the equation:
The distance from p(-9, 0, 0) seems to be:
d = sqrt((x+9)² + y² + z²)The separation from q(3,0,0) would be:
d = sqrt((x-3)² + y² + z²)Let's make them the same size as follows;
sqrt((x+9)² + y² + z² ) = sqrt((x-3)² + y² + z² )Square both sides before simplifying:
(x+9)² + y² + z² = (x-3)² + y² + z² x² + 18x + 81 + y^2 + z^2 = x^2 - 6x + 9 + y² + z² 18x + 81 = - 6x + 9 24x + 81 = 9 24x = -72 x = -3Therefore, the plane is defined by the equation, x = -3.
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The complete question is given below;
Find an equation, or a set of equations, to describe the set of points that are equidistant from the points p(−9, 0, 0) and q(3, 0, 0). (enter your answers as a comma-separated list of equations.)
How to find the size of angle x
Answer:
x = 50°
Step-by-step explanation:
draw a line through B parallel to the 2 given parallel lines , then
the upper angle at B and 150° are same- side interior angles and sum to 180°
upper angle = 180° - 150° = 30°
the lower angle at B and 160° are same- side interior angles and sum to 180°
lower angle = 180° - 160° = 20°
Then
x = upper angle + lower angle = 30° + 20° = 50°
A recent survey by the American Automobile Association showed that a family of 2 adults and 2 children on vacation in the United States will pay an average of $247 per day for food and lodging with a standard deviation of $60 per day. Assuming the data are normally distributed,find the nearest hundredth, the Z-scores for each of the following vacation expense amounts. If the data are normally distributed, find the
percentage of families who spent:
a. Less than $167 per day.
b. Less than $367 per day.
c. More than $247 per day.
d. More than $350 per day.
e. Less than $67 per day.
f. Between $200 and $300 per day.
g. Between $360 and $400 per day.
h. More than the median.
i. Less than the mean.
Using the normal distribution, the percentages are given as follows:
a. 9.18%.
b. 97.72%.
c. 50%.
d. 4.27%.
e. 0.13%.
f. 59.29%.
g. 2.46%.
h. 50%.
i. 50%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 247, \sigma = 60[/tex]
For item a, the proportion is the p-value of Z when X = 167, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (167 - 247)/60
Z = -1.33.
Z = -1.33 has a p-value of 0.0918.
Hence the percentage is of 9.18%.
For item b, the proportion is the p-value of Z when X = 367, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (367 - 247)/60
Z = 2.
Z = 2 has a p-value of 0.9772.
Hence the percentage is of 97.72%.
For item c, the proportion is one subtracted by the p-value of Z when X = 247, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (247 - 247)/60
Z = 0.
Z = 0 has a p-value of 0.5.
1 - 0.5 = 0.5.
Hence the percentage is of 50%.
For item d, the proportion is one subtracted by the p-value of Z when X = 350, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (350 - 247)/60
Z = 1.72
Z = 1.72 has a p-value of 0.9573.
1 - 0.9573 = 0.0427.
Hence the percentage is of 4.27%.
For item e, the proportion is the p-value of Z when X = 67, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (67 - 247)/60
Z = -3.
Z = -3 has a p-value of 0.0013.
Hence the percentage is of 0.13%.
For item f, the proportion is the p-value of Z when X = 300 subtracted by the p-value of Z when X = 200, hence:
X = 300:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (300 - 247)/60
Z = 0.88.
Z = 0.88 has a p-value of 0.8106.
X = 200:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (200 - 247)/60
Z = -0.78.
Z = -0.78 has a p-value of 0.2177.
0.8106 - 0.2177 = 0.5929.
Hence the percentage is of 59.29%.
For item g, the proportion is the p-value of Z when X = 400 subtracted by the p-value of Z when X = 360, hence:
X = 400:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (400 - 247)/60
Z = 2.55.
Z = 2.55 has a p-value of 0.9946.
X = 360:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (360 - 247)/60
Z = 1.88.
Z = 1.88 has a p-value of 0.97.
0.9946 - 0.97 = 0.0246.
Hence the percentage is of 2.46%.
For items h and i, the distribution is symmetric and the mean and the median are equal, hence both percentages are 50%.
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Topic #2: Distance & Midpoint
9. Find ST if S(-3, 10) and T(-2, 3).
Answer:
ST = 7.07 units
Step-by-step explanation:
(4x² – 11x³ – 13x² +96x
+52) ÷ (4x + 9)
The remainder of the given equation:
(4x² – 11x³ – 13x² +96x+52) ÷ (4x + 9)
= - 5393/64
Polynomial long division:Long-division polynomials are algorithms that divide polynomials by polynomials of the same or lower degree. As with the long division method of numbers, the divisor, quotient, dividend, and remainder are all part of the long division of polynomials.
what are the four steps in polynomial long division?When a divisor has more than one term or is a polynomial with more than one term, the four stages used to divide whole numbers (divide, multiply, subtract, bring down the next term) comprise the repeated operation for polynomial long division.
According to the given data:(4x² – 11x³ – 13x² +96x+52) ÷ (4x + 9) given.
Simplifying the equation:
(4x² – 11x³ – 13x² +96x+52)
(-11x³ - 9x² + 96x + 52)
Applying Polynomial long division:
(-11x³ - 9x² + 96x + 52)÷ (4x + 9)
[tex]$-\frac{11}{4} x^2+\frac{63}{16} x+\frac{969}{64}$[/tex]
(4x + 9)√(-11x³ - 9x² + 96x + 52)
-11x³ -(99/4)x²
-------------------------------------
(63/4)x² + 96x
(63/4)x² + (567/16)x
----------------------------------
(969/16)x + 52
(969/16)x - 8721/64
-------------------------------------------
- 5393/64
The remainder of the given equation:
(4x² – 11x³ – 13x² +96x+52) ÷ (4x + 9)
= - 5393/64
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Solve the inequality for x and identify the graph for its solution |x+3|>2
Answer:
Inequality Form:
x<−5 or x>−1
Interval Notation:
(−∞,−5)∪(−1,∞)
Step-by-step explanation:
Which technique most clearly minimizes the likelihood that any outcome differences between the experimental and control conditions can be attributed to age or personality differences in research participants?.
The technique that most clearly minimizes the likelihood that any outcome differences between the experimental and control groups is e. random assignment.
What is random assignment?A methodology used to divide research participants into two groups—the treatment group, also known as the experimental group, and the control group—by randomization is known as random assignment, also known as random placement.
Every research volunteer has an equal chance of being assigned to any of the groups thanks to this randomization mechanism.
In studies, random assignment is a method used to divide participants into different research groups with similar characteristics so that the groups are equal at the start of the investigation.
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Which technique most clearly minimizes the likelihood that any outcome differences between the experimental and control groups can be attributed to age or personality differences in research participants?
a. the double-blind procedure
b. statistical measurement
c. replication
d. operational definitions
e. random assignment
leila is buying a dinosaur model. the price of the model is x dollars, and she also has to pay a 7%7\%7%7, percent tax.
This problem is associated with linear equations. The total price will be 1.07x dollars.
What is a linear equation?There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.
Given,
Leila is buying a replica of a dinosaur.
The model is priced at x dollars, plus she must pay a 7% tax.
7% is shown in decimal form.
= 0.07
Tax price = 0.07 times the model's cost
= 0.07x
Total cost Leila pays for the model by adding the tax price to the model's cost.
Combining the values in the aforementioned
Leila pays the model a total of 0.07x + x.
= 1.07 in currency
As a result, Leila pays a total of 1.07 for the model.
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What is the image of the point
(
0
,
4
)
(0,4) after a rotation of
18
0
∘
180
∘
counterclockwise about the origin?
The image of point (1,-4) after a rotation of 180° counter clockwise about the origin is: (-1,4).
According to the statement
We have to find that the coordinates after the rotation.
So, For this purpose, we know that the
Rotation means a degree is being moved in clockwise or counterclockwise direction with some angle.
From the given information:
The point is a (0,4)
The rotation is drained 90, 180, 270 degrees.
Given point is:(0,4)
When some extent (x,y) is rotated 180° counter clockwise its coordinates become (-x,-y) the negative of original point.
So for the given point the coordinates will become (-0,-4)
Then,The image of point (1,-4) after a rotation of 180° counter clockwise about the origin is: (-1,4)
So, The image of point (1,-4) after a rotation of 180° counter clockwise about the origin is: (-1,4)
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Does the figure above appear to have rotational symmetry?if yes, select the angles of rotation less than 360°
(4x-1)(3x^2+3x-5) (4x−1)(3x 2 +3x−5)
Hi.
Answer:
[tex]\left(4x-1\right)^2\left(3x^2+3x-5\right)^2[/tex]
Step-by-step explanation:
[tex](aa=a^2) \left(4x-1\right)\left(4x-1\right)=\left(4x-1\right)^2\\=\left(4x-1\right)^2\left(3x^2+3x-5\right)\left(3x^2+3x-5\right)\\\left(3x^2+3x-5\right)\left(3x^2+3x-5\right)=\left(3x^2+3x-5\right)^2\\=\left(4x-1\right)^2\left(3x^2+3x-5\right)^2[/tex]
On a number line, point A is located at 9 and point B is located at -5. What is AB?
Answer:
14
Step-by-step explanation:
Im pretty sure its 14
so point A is at -5 which is here
-5 -4 -3. -2. -1. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9
A
and point B is located here
-5 -4 -3. -2. -1. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9
A B
the distance would be:
-5+5= 0 ( the bold numbers are the ones you add together)
then
0+9=9
so 5+9= 14
What is 0.57 as a fraction?
*57 REPEATING*
*IN THE SIMPLEST FORM*
WHOEVER GETS IT RIGHT GETS 5 STARS AND THE BRAIN COWN THING
Answer:
19/33
Step-by-step explanation:
57 repeating = 0.57
1. x = 0.57
2. mutiply each side by 10² = 100
100x = 57.57...
3. subtract
x = 0.57 from 100x = 57.57...
and get 99x = 57.
4. solve for x
x = 57/99
5. find the GCF of 57 and 99
57 ÷ 3 = 19
---- --- ----
99 ÷ 3 = 33
6. x = 19/33
A teacher can spend as much as $140.00 to take students to a movie. A movie
theater charges a $15.00 group fee and $7.25 per ticket.
о Set uр аn Едиation:
How many students can
teacher
the
take to the movie?
Answer:
17 students
Step-by-step explanation:
140-15=125
125/7.25=17.2....
rounded to 17
The bar graph displays data on the numbers of babies born each day of the week in the United States in a recent week.
All data in the graph are approximate.
Which of the following choices gives the most complete description of the information presented in the bar graph?
Births occurred with similar frequencies on the week days (Monday through Friday), but with noticeably smaller frequencies on the weekend days (Saturday and Sunday).
Births occurred with similar frequencies, regardless of the day of the week.
Births occurred with the lowest frequency on Sundays.
The minimum number of births appears to be approximately 7000, which occurred on Sunday. The maximum number of births appears to be approximately 13,000, which occurred on Tuesday.
Week day births seem to be twice as common as weekend births.
The correct statements regarding the given bar graph are given as follows:
Births occurred with similar frequencies on the week days (Monday through Friday), but with noticeably smaller frequencies on the weekend days (Saturday and Sunday).Births occurred with the lowest frequency on Sundays.The minimum number of births appears to be approximately 7000, which occurred on Sunday. The maximum number of births appears to be approximately 13,000, which occurred on Tuesday.What does a bar graph show?A bar graph shows the number of times that each observation appears in the data-set.
Hence, from this bar graph, we have that the average number of births per day, from Sunday to Saturday.
Births are more common during weekdays, the close to 7000 on Sunday, the maximum is close to 13000 on Tuesdays, hence the correct statements are given as follows:
Births occurred with similar frequencies on the week days (Monday through Friday), but with noticeably smaller frequencies on the weekend days (Saturday and Sunday).Births occurred with the lowest frequency on Sundays.The minimum number of births appears to be approximately 7000, which occurred on Sunday. The maximum number of births appears to be approximately 13,000, which occurred on Tuesday.From the bar graph, the biggest ratio is of 13/7 < 2, hence week day births are not quite twice as common.
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Amanda buys 2 nachos and 3 drinks from the concession stand for $12.50. Julio purchases 2 candy bars and 1 drink for $5.50. Ben buys 1 nacho and 1 candy bar for $5.00. Write a system of equations and solve it to determine the cost of each item.
Answer: 12.50= 2x + 3y,
5.50= 2x+y,
5=x+Y
Step-by-step explanation: Use a graphing calculator bro
Can someone please help me.
Answer:
you what do u need help with?
Can someone help me with this
Answer:
LM + MN=LN
Therefore (2x-16)+(x-9)=11
2x-16+x-9=11
2x+x-16-9=11
3x-25=11
3x=11+25
3x=36
x=36/3
x=12
Therefore MN=(12-9)=3
MN=3
HELP ASAP!! I'm rlly confused
Answer:
0=4
2=16
10=64
15=94
Step-by-step explanation:
hfufugihigfhydydtsyeurur
HELP 50 PTS AND BRAINLY!!!
Answer:
The sum will be close to 1/2
Step-by-step explanation:
1/4+2/7=15/28
The common denominator of 1/4 and 2/7 is 28.
1/4 -> 7/28
2/7 -> 8/28
7/28+8/28=15/28
turn that into a decimal and it will round to 0.5257
1/2=0.5
so the answer will be closer to 1/2
Answer:The sum would be close to 1/2
Step-by-step explanation:
Reflect ABC over the y-axis and then translate by
(2, -3).
Answer:
just flip it
Step-by-step explanation:
Given 33.8 × 2.5, find the product.
84.5
Step-by-step explanation:Multiply 338 ✖ 25The answer is 2450.Jump the decimal two times from one's placeThe answer will be 84.5Slope please help algreab 1
Answer:
1/2x-2
Step-by-step explanation:
sise over run and then graph on desmos
Answer:
y = [tex]\frac{1}{2}[/tex] x - 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (6, 1 ) and (x₂, y₂ ) = (- 6, - 5 )
m = [tex]\frac{-5-1}{-6-6}[/tex] = [tex]\frac{-6}{-12}[/tex] = [tex]\frac{1}{2}[/tex] , then
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (6, 1 )
1 = 3 + c ⇒ c = 1 - 3 = - 2
y = [tex]\frac{1}{2}[/tex] x - 2 ← equation of line
It takes Evan 9 minutes to complete each word search. How many word searches can Evan complete in 126 minutes?
Answer:
14 word searches
Step-by-step explanation:
126÷9=14
Step-by-step explanation:
126÷9= 14
This is becuse u want to see how many times 9 can go into 126
to check u can do 9×14 and the answer will be 126
Which statement about the product is true?
5.643 x 4.6
O The product is irrational.
The product is neither rational nor irrational.
O The nature of the product cannot be determined.
O The product is rational.
Answer:
Product is rational
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal.
Answer:
the product is rational
The ratio of cars to trucks in a parking lot is 5 cars to 3 trucks. there are 30 cars in the parking lot. how many trucks are in the parking lot
If the ratio of cars to truck in a parking lot is 5:3 and the total number of cars is 30, then the total number of truck in the parking lot is 18
Given,
The ratio of cars to truck in the parking lot = 5:3
Total number of cars in the parking lot =30
Then, the equation will be
5x=30
x=6
Then, the number of tucks in the parking lot =3x
3×6=18
Hence, if the ratio of cars to truck in a parking lot is 5:3 and the total number of cars is 30, then the total number of truck in the parking lot is 18
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