Answer:
first step is to put the (x-9)^2 into a standard form which is y=x^2−18x+81 then choose two integers larger than the x-value of the vertex point.next choose two integers smaller than the x-value of the vertex point. lastly substitute these values in place of "x" in the equation and solve for "y".
Step-by-step explanation:
x | y
7 | 4
8 | 1
9 | 0
10 | 1
11 | 4
4=(11-9)^2
1=(10-9)^2
0=(9-9)^2
1=(8-9)^2
4=(7-9)^2
The rectangle below has an area of x^2-7x+10x square meters and a width of x-5x meters. What expression represents the length of the rectangle?
Answer:
The area of a rectangle is:
\sf A=lw
Plug in what we know:
\sf x^2-7x+10=l(x-5)
Factor the left side:
\sf (x-2)(x-5)=l(x-5)
Divide (x - 5) to both sides:
\sf l=\boxed{\sf x-2}
So the length is x - 2 meters.
Step-by-step explanation:
Terrence and Lee were selling magazines for a charity. In the first week, Terrance sold 30% more than Lee. In the
second week, Terrance sold 8 magazines, but Lee did not sell any. If Terrance sold 50% more than Lee by the end of the
second week, how many magazines did Lee sell?
Choose any model to solve the problem. Show your work to justify your answer.
Please explain I don’t understand how to solve this problem.
Lee sold 40 magazines
Step-by-step explanation:
Equation Model:
Let m be the number of magazines Lee sold.
150%-130%=20%, so if 0.2m=8 then m=40
Let me show another way: In the image above 20% is equal to 8 so if we use 8 and 20% and try to reach our way up to 100% (How much Lee sold in total) then we will get our answer.
20%=8
40%=16
60%=24
80%=32
100%=40
Therefore Lee sold 40 magazines.
Hope that makes sense! If you have any more questions or need further clarification then please comment down below or message me! Good luck!
The surface area of a cone is 396π square inches. If the radius is 12 inches, find the slant height of the cone.
Answer:
Slant height = 33 inches
Step-by-step explanation:
r = 12 inches
Lateral Surface Area of cone = 396π square inches
πrl = 396π
π * 12 * l = 396π
[tex]l=\frac{396\pi }{12*\pi }\\[/tex]
l = 33 inches
de
considerando AB =PQ. Na figura abaixo, para que os triângulos ABC e PQR sejam congruentes, os
valores de xe y devem ser
Y-3
2x + 1
Q
R
A) x = 2 e y = 12
B) x = 4 e y = 8
C) x = 5 e y = 2
D) x = 6 e y = 8
Answer:
The answer might be d.
what does "cross the line, change the sign" means.
Answer: i believe its like with fractions if you have to cross the line to add or subtract it means that
Step-by-step explanation:
are you working with fractions
Hilda is taking out an $11,000 personal loan that she will repay in 5 years. If she receives a 10% interest rate, her monthly payments will be $233.72. If she receives and 18% interest rate her monthly payments will be $279.33. How much less interest will Hilda pay if she qualifies for the lower interest rate? *
Answer:
Hilda would pay $ 2,736.60 less interest
Step-by-step explanation:
The total interest payment is the total repayments for 5 years less the initial loan amount
If the interest rate is 10% Hilda repays $233.72 for 5 years multiplied by 12 months:
total repayment=$233.72*5*12=$ 14,023.20
Interest =$14,023.20-$11,000.00=$3.023.20
If the interest rate is 18% Hilda repays $279.33 for 5 years multiplied by 12 months:
total repayment=$279.33*5*12=$ 16,759.80
Interest =$16,759.80 -$11,000.00=$5759.8
Difference in interest payments=$5759.8 0-3.023.20=$ 2,736.60
simplify (2x+1) (x+3)
ACT scores are normally distributed and from 2015 to 2017, the mean was 20.9 with a standard deviation of 5.6. A perfect score is 36. What percentage of the testers scored a perfect score?
Question 4 options:
0.46%
0.35%
99.65%
99.64%
Using the normal distribution, it is found that 0.35% of the testers scored a perfect score.
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.In this problem, the mean and the standard deviation are given, respectively, by:
[tex]\mu = 20.9, \sigma = 5.6[/tex]
The proportion of scores above 36(perfect scores) is given by one subtracted by the p-value of Z when X = 36, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{36 - 20.9}{5.6}[/tex]
Z = 2.7
Z = 2.7 has a p-value of 0.9965.
1 - 0.9965 = 0.0035 = 0.35.%.
Hence, 0.35% of the testers scored a perfect score.
More can be learned about the normal distribution at https://brainly.com/question/24663213
#SPJ1
what is -2x+6y=-18 in slope intercept form?
Answer:
y = 1/3x - 3
Step-by-step explanation:
Subtract 2x on both sides
6y = 2x - 18
Isolate y by dividing 6 on both sides
y = 2/6x - 3
Simplify.
y = 1/3x - 3
Hope this helps!
Eva is 29 years old and has 2 children, ages 3 and 5. She makes 48,500 a year. Eva decides to buy a 400,000 10-year term policy then renew the policy for another ten years afterwards. To renew the policy the insurance company charges an extra 40% to her premium rate.
Answer:
Eva would have been better off selecting the 20-year term policy.
Step-by-step explanation:
Base on the scenario been described in the question, Eva would have been better off selecting the 20-year term policy. This reason is because assuming Eva bought the 20-year term policy, she wont be paying the new charge of extra 40% to her premium rate, compared to when she bought the 10-year term policy then renew the policy for another ten years.
Eva's best option would be to buy on a 20-year policy. This is better because she is able to evade the additional, 40% to her premium rate.
Insurance Premium;Premiums are percentages of the cost value charged by the insurance company for their services and benefits.
If she pays, 400,000 in ten years, this means she pays 40,000 each year.Upon renewal, she'll have to 40% more and her new premium will be; 56,000.Read more on insurance premium;
https://brainly.com/question/9696972
Which set of measurements could be the lengths of the sides of a right
triangle?
А
1, 2, 3
с
5, 12, 13
9, 13, 15
10, 20, 30
D
Answer:
5, 12, 13
Step-by-step explanation:
because if you use the pythagorean theorem, you will get 13 as the hypotenuse if you take the two shorter sides.
Y=78(0.54)^t Identify the initial amount a and the rate of growth r (as a percent) of the exponential function. Evaluate the function when t=5. Round your answer to the nearest tenth.
Answer:
[tex] y = 78(0.54)^t[/tex]
And for this case we want to identify the initial amount and for this case would be 78. And the growth rate can be obtained from the term inside of the parenthesis.
The general model is given by this model:
[tex] y = a (1+r)^t[/tex]
And then [tex] 1+r = 0.54[/tex] and [tex] r = 0.54 -1= -0.46[/tex]
And then we want to find the of the function at t=5 and we got:
[tex] y(5) = 78(0.54)^5 = 3.58 \approx 3.6[/tex]
Step-by-step explanation:
For this case we have the following function given:
[tex] y = 78(0.54)^t[/tex]
And for this case we want to identify the initial amount and for this case would be 78. And the growth rate can be obtained from the term inside of the parenthesis.
The general model is given by this model:
[tex] y = a (1+r)^t[/tex]
And then [tex] 1+r = 0.54[/tex] and [tex] r = 0.54 -1= -0.46[/tex]
And then we want to find the of the function at t=5 and we got:
[tex] y(5) = 78(0.54)^5 = 3.58 \approx 3.6[/tex]
Answer:
Initial amount = 78
Rate of growth = -46%
Y(t=5) = 3.6
Step-by-step explanation:
The general form of an exponential function is:
[tex]Y(t) = Y_0*(1+r)^t[/tex]
The initial value (Y0) is the value of Y(t) when t = 0:
[tex]Y(0) = 78*0.54^0=78[/tex]
Comparing the given function to the general form of the exponential function, the rate of growth 'r' is determined as:
[tex]Y(t) = Y_0*(1+r)^t = 78*(0.54)^t\\78*(1+r)^t = 78*(0.54)^t\\1+r=0.54\\r=-0.46=-46\%[/tex]
At t=5, the value of Y(t) is:
[tex]Y(5)=78(0.54)^5\\Y=3.6[/tex]
Which complex number has a distance of the square root of 17 from the origin on the complex plane?
Hey there! I'm happy to help! :D
-------------------------------------------------------------------
OVERVIEW
A complex number is a real number combined with an imaginary number (such as i, a number that will equal -1 when squared).
The complex plane is an interesting thing we use to graph complex numbers. The horizontal axis is where you plot the real part of the complex number, and the y-axis is where you plot the coefficient of the imaginary number.
For example, if I had the complex number 4+3i, I would plot the point (4,3) on the complex plane.
-------------------------------------------------------------------
MODULI
The modulus (plural is moduli) is the distance of a complex number from the origin on the complex plane. To find the modulus, you take the real number and the coefficient (basically the points of your graph), square them, add the results, and then you find the square root of that! Here's a little checklist so that you can always find the modulus of any complex number!
STEPS TO FIND MODULUS GIVEN COMPLEX NUMBER
STEP 1: PLOT THE COMPLEX NUMBER
Let's use our complex number 4+3i. If we plot it, the point will be (4,3)
STEP 2: TAKE YOUR VALUES OF X AND Y AND SQUARE THEM
4²=16
3²=9
STEP 3: ADD THESE SQUARES
16+9=25
STEP 4: SQUARE ROOT IT
√25=5
Therefore, the modulus (distance from the origin on the complex plane) of 4+3i is 5.
-------------------------------------------------------------------
SOLVING THE PROBLEM
In our case, we are given a modulus but not a point on the line. Our modulus is the square root of seventeen. We are going to have to the steps to find the modulus backwards to find our points. I will put the steps for finding a complex number given the modulus below.
STEPS TO FIND COMPLEX NUMBER GIVEN MODULUS
STEP 1: SQUARE THE MODULUS
√17²=17
STEP 2: FIND THE SQUARES THAT MAKE UP THE NUMBER
Before, we could just add things we found. Now, we have to find the things that were added! How do we know what things were added to find 17? Well, we know that we added two squares to find the modulus, so we will subtract a square of some sort and hopefully come up with another square.
Let's see what squares exist that are less than seventeen.
1, 4, 9, 16
(Note that one is 1², 4 is 2², 9 is 3², and 16 is 4²)
Which of these can we add to get 17?
Well, we can do 1 and 16, so this is our result so far.
STEP 3: SQUARE ROOT THE RESULTS
Now, we just find the square roots of what we found in the last problem!
√1=1
√16=4
STEP 4: PLOT THE GIVEN NUMBERS ON THE PLANE AND FIND THE COMPLEX NUMBER
We can plot these either way because the modulus of 1+4i will be the same distance from the origin as 4+i because we only use the commutative property (adding order doesn't matter) when looking for the modulus. You can also have the negative version of either number because you immediately square it, so it can also be -4+i or 4-i! You can also rearrange the equation in tons of ways to figure it out. You could also have both be negative, flip the coefficient placement, etc.!
-------------------------------------------------------------------
SOLUTION
Therefore, the complex numbers that have a distance of √17 from the origin on the complex plane are ±4±i and ±1±4i. So, why did I write all of these funny plus and minus signs? Well, it's so that I didn't have to write all of the possible equations. I believe those equations actually represent 8 possible points we can create with the solution we got.
4+i
-4+i
4-i
-4-i
1+4i
-1+4i
1-4i
-1-4i
You can plug these complex numbers back in and find the modulus with my instructions to find the modulus given a complex number. Now, you will be able to deal with moduli and complex numbers for the rest of your life!
I hope that this helps! Have a wonderful day! :)
A spinner has 8 equal-sized sections. Six of the sections are orange.
Answer:
6 put of 8, 3/4, or 75%
Step-by-step explanation:
Hope this helps ! :) good luck
The perpendicular bisector of chord AB is y=-2x+8, and the perpendicular bisector of chord BC is y= 3x-2. Recall the properties of chords. How can these equations be used to find the center of the circle that represents the whole plate
Answer:
We equate the two expressions since they both pass through the center of the circle.
The coordinate of the center of the circle is (2,4)
Step-by-step explanation:
From circle theorem, we know that the perpendicular bisector of a chord passes through the center of the circle.
Since both equations would pass through the center of the circle, we equate them.
So, -2x+8 = 3x-2
Solving for x, we have
3x + 2x = 8 + 2
5x = 10
x = 10/5
x = 2
Substituting x = 2 into any of the equations, we find the y- coordinate of the center of the circle.
y = -2x + 8 = -2(2) + 8 = -4 + 8 = 4
So, the coordinate of the center of the circle is (2,4)
Personal Answer:
The perpendicular bisector of a chord passes through the center of the circle/plate, meaning that both expressions can contribute to the finding the center. By solving for x and y, one can find the coordinates of the center of the circle.
Plato Sample Answer:
Because the perpendicular bisector of any chord of a circle passes though the center of the circle, these two perpendicular bisectors intersect at that point. You can set up a system of equations and solve to find the coordinates of the center.
I hope this helps!
Find the distance between the two points rounding to the nearest tenth (if necessary).
(5,3) and (3,6)
Answer:
1.5
Step-by-step explanation:
Plug in numbers into the distance formula.
y2-y1
____
x2-x1
6 - 3. 3
____. ___
3 - 5. -2
3/-2=-1.5
Answer:
3.6 or Sqrt(13)
Step-by-step explanation:
plug into distance formula
(3-5)^2 + (6-3)^2
4 + 9
Sqrt(13)
Sqrt(13) is equal to 3.6055127546
^ is rounded up to 3.6
Mr. Whittaker’s science class uses tide gauges to measure annual variations in water levels at different parts of a river, and then compares those variations to the average annual trend. Matea recorded that the water level in one part of the river fell 1.05 millimeters per year for 2.48 years. This data will be compared to the average annual trend, which shows the water level rising 1.8 mm/year. Which number represents the rate at which the water level fell? Which number should the rate be multiplied by to find the total variation in water level?
This question is not complete because is lacks the options for each question.
Complete question
mr. whittaker’s science class uses tide gauges to measure annual variations in water levels at different parts of a river, and then compares those variations to the average annual trend. matea recorded that the water level in one part of the river fell 1.05 millimeters per year for 2.48 years. this data will be compared to the average annual trend, which shows the water level rising 1.8 mm/year.
1) Which number represents the rate at which the water level fell?
a. -1.05 mm/year
b. -1.8 mm/year
c. -2.48 years
d. -2.48 mm/year
2) Which number should the rate be multiplied by to find the total variation in water level?
a. 1.05 mm/year
b. 1.8 mm/year
c. 2.48 years
d. 2.48 mm/year
Answer:
1) Which number represents the rate at which the water level fell?
a. -1.05 mm/year
2) Which number should the rate be multiplied by to find the total variation in water level?
c. 2.48 years
Step-by-step explanation:
Total Variation in the water level is calculated by multiplying the rate at which the water level and number or years at which the rate of the water level fell
From the question, we can see that the rate at which the water level fell is -1.05 mm/year and number of years at which the water level fell is 2.48mm
Hence,Total Variation in the water level is calculated as
-1.05 mm/year × 2.48 years
Total variation in the water level = -2.604mm
Answer:
Which number represents the rate at which the water level fell?
-1.05 mm/year
Which number should the rate be multiplied by to find the total variation in water level?
2.48 years
Step-by-step explanation:
What does it mean for points to be colinear?
Answer:
Three or more points that lie on the same line are collinear points .
Step-by-step explanation:
Michelle went shopping for some clothes and found a pair of slacks that cost
twice as much as a shirt that she liked. If the total, before tax, for the pair of
slacks and the shirt was $22.50, how much was the shirt, before tax?
Answer:
The sirt cost $7.5 before tax.
Step-by-step explanation:
Since the pair of slacks cost twice as much as the shirt, we have:
slacks = 2*shirt
And the total purchase was $22.5, so we have:
slacks + shirt = 22.5
We can create a system of equations such as:
slacks = 2*shirt
slacks + shirt = 22.5
If we apply the first formula on the second we can solve for the value of the shirt, we have:
2*shirt + shirt = 22.5
3*shirt = 22.5
shirt = 22.5/3 = 7.5
So the slacks cost:
slacks = 2*7.5 = 15
A and B are vertical angles. If m A = (4x + 14) and m B = (5x – 5)º,
then find the measure of A
Vertical angles are equal/congruent
4x+14=5x-5
X=19
4(19)+14= 90
Angle A= 90
Can someone help me!!
ASAP
Answer:
It would be 30
Step-by-step explanation:
6*5=30
A farmer picks 242 apples on monday and 118 apples on tuesday on wednesday she sells 109 of the apples at the market. Which equation can be used to find a, the number of apples the farmer has left?
Answer:
Step-by-step explanation:
The apples picked on Monday and Tuesday = 242 + 118 = 360
Apples sold on Wednesday = 360 - 109 = 521
Number of apples left = 251
Equation used: (242 + 118) - 109
A sports shop buys tents for $260 less 25% for buying more than 30 tents. The store operates on a markup of 30% of the sale price and advertises that all items are sold at a discount of 20% of the regular price. What is the regular price of the tents?
Answer: $253.50
Step-by-step explanation:
Markup = 30% of sale price
Store purchase price = (100% - 25%) × 260
Store purchase price = 75% × 260
Store purchase price = 0.75 × 260
Store purchase price = $195
Regular selling price = markup × purchase price
Markup = 30% of purchase price (100+30)%
Regular selling price :
1.30 × $195 = $253.50
7h=-(2h-18)7h=−(2h−18) solve for h please asap
Answer:
H=2
Step-by-step explanation:
I promissse
Be safe hope this helps
Answer: h is 4
Step-by-step explanation:
Clara slept for a total of 126 hours over the cousrve of two weeks.If she sleeps for the same amount of each time each night,how many hours does she sleep per night?
Answer:
9
Step-by-step explanation:
Answer:
9 hours per night
Step-by-step explanation:
Assuming a week is 7 days
7 * 12 = 14 days
126/14=9
She slept 9 hours per night
Read the word problem below. Jill had $90. She bought a skirt that normally costs $42 but was on sale for half price. She also bought a T-shirt that was $8 off its regular price. Before sales tax, the total cost of the clothes was $31. What was the regular price of the T-shirt? What question is being asked in this word problem? What is the regular price of the skirt? How much money does Jill have left? How much does the T-shirt normally cost? What is the amount Jill pays in sales tax?
Answer:
What was the regular price of the T-shirt?
$18What question is being asked in this word problem?
what is the regular cost of the t-shirt purchased by Jill.What is the regular price of the skirt?
$42How much money does Jill have left?
without considering sales tax, Jill has $90 - $31 = $59 left.If I use the sales tax from where I live, the sales tax = $1.86, so the money that Jill will have left = $59 - $1.86 = $57.14How much does the T-shirt normally cost?
$18 (same as question 1)What is the amount Jill pays in sales tax?
since you do not include the sales tax % in the question, I will simply use the sales tax from where I live = $31 x 6% = $1.86Step-by-step explanation:
skirt $21
t-shirt = p - $8
before sales tax, total cost was $31
$21 + p - $8 = $31
p = $18
At 7:00 A.M., Alicia pours a cup of tea whose temperature is 200°F. The tea starts to cool to room temperature (72°F). At 7:02 A.M. the temperature of the tea is 197°F. At 7:15 A.M. the temperature of the tea is 180°F. Alicia will drink the tea when its temperature is 172°F.
Part A
Which of the following shows an exponential cooling equation that models the temperature of the tea?
A. y = 72(0.989)x + 128
B. y = 128(0.989)x + 72
C. y = 200(0.989)x + 72
D. y = 128(0.989)x + 200
Part B
When can Ella drink the tea?
Ella can drink the tea after
7:22
7:18
Answer:
Part A
The most correct option is;
b. y = 128(0.989)x + 72
Part B
Ella can drink the tea after 7:22
Step-by-step explanation:
Here we have the temperature variation with time given in an exponential equation as follows;
Let the temperature at time x (in minutes) = y
Therefore, y = a × mˣ + b
Where:
b = Shift of the curve or the limit value of the decreasing exponential function as x → ∞
When y = 200, x = 0
Therefore. 200 = a × m⁰ + c = a + c
We note that c is the shift of the graph, the value upon which temperature increases = final temperature = 72°F
Hence a = 200 - 72 = 128°F
When y = 197, x = 2 minutes
Therefore, 197 = 128·m² + 72 =
m² = (197 - 72)/128 = 125/128
m = √(125/128) = 0.98821
Hence the exponential equation of cooling is presented in the following equation;
y = 128 × (0.98821)ˣ + 72
Therefore, the most correct option is b. y = 128(0.989)x + 72
Part B
When the temperature is 172°F we have;
172 = 128 × (0.989)ˣ + 72
∴ (0.989)ˣ = (172 - 72)/128 = 100/128 = 25/32
log(0.989)ˣ = log(25/32)
x·log(0.989) = log(25/32)
x = log(25/32)/log(0.989) = 22.32 minutes
Hence Ella can drink the tea after 7:22.
Simplify the expression. Assume that all variables are positive. Exponents in simplified form should all be positive
Answer:
5
Step-by-step explanation:
We know that a^b^c = a^ (b*c)
1/25 ^(-2/3* 3/4)
1/25^ (-2/4)
1/25 ^ -1/2
Rewriting 1/25 as 5^-2
5^-2 ^-1/2
Again a^b^c = a^ (b*c)
5^(-2*-1/2)
5 ^ 1
5
If the probability of rain is 0.75, the probability of fog is 0.25, and the probability of rain and fog is 0.25, what is the probability of rain or fog?
Answer:
[tex]P(A \cup B) = 0.75[/tex]
Step-by-step explanation:
There are two scenarios:
A - Rain
B - Fog.
The probability of rain or fog is determined by the Addition Rule, given that A and B are not mutually excluyent:
[tex]P(A\cup B) = P(A) + P(B) - P(A\cap B)[/tex]
[tex]P (A\cup B) = 0.75 + 0.25 - 0.25[/tex]
[tex]P(A \cup B) = 0.75[/tex]
If f(x) X/2 -3 and g(x) = 4X^2 + X - 4
Answer:
.im fully loaded
Step-by-step explanation:
