Answer:
y = -2x + 31
Step-by-step explanation:
Vertex form a parabola refers to a place or a point where it turns. It takes the form of;
y = mx + c
From our question, we are supposed to convert the equation y-7 = (12-x)2 into vertex form.
To begin, open the brackets on the RHS;
y - 7 = 24 - 2x.
Then move -7 to the RHS which becomes the positive.
Y = 24 - 2x + 7
= 31 - 2x
Convert it to the form y = mx + c.
y = -2x + 31
This is the vertex form, y = -2x + 31.
Note:
For a standard form/quadratic, the equation has to be in the form ax² + bx + c = yCedrick is going to meet his mother for dinner at a restaurant halfway between his house and hers. On a coordinate grip map, Cedrick’s house is at (–51, –26) and his mom lives at (2, –4).
Where is the best restaurant for them to meet?
Greek restaurant at (–25, –15)
French restaurant at (–27, –11)
Mediterranean restaurant at (–28, –12)
Thai restaurant at (–38, –1)
Using the mid-point concept, the best restaurant for them to meet is given by:
Greek restaurant at (–25, –15).
What is the midpoint concept?The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.
For the midpoint between his house and his mom's, the coordinates are given as follows:
x = (-51 + 2)/2 = -49/2 = -24.5.y = (-26 - 4)/2 = -30/2 = -15.Hence the Greek restaurant is the best option, as it is closest.
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Which equation could be used to find the length of the hypotenuse
Answer:
first equation
Step-by-step explanation:
If f(x) = 3x + 2, what is f(5)?
Answer:
17
Step-by-step explanation:
f(5) means replacing any x in the equation with 5, so that would give you 3*5 + 2
in order of operations, 3*5 = 15 + 2 = 17
hope this helped! :)
Here's the work I've done. Is it right?
V=πr^2h
π(0.375)^2(0.80)
=0.4m^3 (smallest cylinder)
π(0.625)^2(0.80)
=1.0m^3 (middle cylinder)
0.70+0.80
=1.5m (height for big cylinder)
π(1.5)^2(1.5)
=10.6m^3
10.6m^3+0.4m^3+1.0m^3
=12.0m^3
The spa will fit 12.0m^3 of water
Answer: [tex]6.67m^3[/tex]
Step-by-step explanation:
For hemisphere...
diameter (d1) = 3m
radius (r1) = (3/2)m
The total volume of the hemisphere
[tex]v1=\frac{2}{3} \pi (r1)^3[/tex]
[tex]=\frac{2}{3} \pi (\frac{3}{2} )^3[/tex]
[tex]=\frac{9}{4} \pi[/tex]
-----------------------------------------------------------------------
For smaller cylinder
diameter (d2) = 0.75
radius (r2) = 0.75/2m
height (h2) = 0.80m
Volume of smaller cylinder
(V2) = [tex]\frac{1}{3} \pi (r2)^2h2[/tex]
[tex]=\frac{1}{3} \pi (\frac{0.75}{2} )^2*0.80[/tex]
[tex]=\frac{3}{80} \pi[/tex]
------------------------------------------------------------------------
For bigger cylinder
Volume of bigger cylinder =
[tex]V3=\frac{1}{3} \pi (\frac{1.25}{2} )^2*0.70[/tex]
[tex]=\frac{35}{384} \pi[/tex]
-----------------------------------------------------------------------
Volume of water = [tex](v1 - v2 - v3) =\frac{9}{4} \pi -\frac{3}{80} \pi -\frac{35}{384} \pi = 6.67 m^3[/tex]
The length, l call my a rectangular room is four less than the width, W, of the room. Which expression represents the area of the room.
(I have no options)
Answer: Either [tex]w(w-4)[/tex] or [tex]w^2 - 4w[/tex]
==================================================
Explanation:
w = width
w-4 = length since it is 4 less than the width
Multiply the length and width to get the area of the rectangle.
area = length*width
area = [tex](w-4)w[/tex]
area = [tex]w(w-4)[/tex]
area = [tex]w^2-4w[/tex]
In the last step, I used the distributive property.
Either expression mentioned above is valid for the area. If you had to pick only one, I'd go for [tex]w^2-4w[/tex]
What is the slope of a line parallel to the line whose equation is3x−4y=8?
−43
−34
34
43
Answer:
The parallel slope for this equation is going to be [tex]\frac{3}{4}[/tex] hope that helps and can you mark me as brainlist please.
#280 at the
Nader plans to buy a car. He can afford to pay
end of each month for 3 years. The best interest rate
he can find is 9.8% la, compounded monthly.
for this interest rate, the most he could spend on a car
is $8702.85,
Determine the amount he could spend on the
purchase of the car if the interest rate is 9.8%.la,
Compounded annually.
Based on the amount that Nader can pay per month, and the interest rate as well as the period, the amount he could spend if the rate was annual is $8,385.33.
How much could Nader spend on the car?If Nader can pay $280 per month, the amount he can pay per year i:
= 280 x 12
= $3,360
The amount that he can spend on the car is the present value of these yearly payments:
= 3,360 x (1 - (1 + 9.8%)⁻³) / 9.8%
= 3,360 x 2.49563439768461
= $8,385.33
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Write −1.2 as a ratio of two integers.
Answer: (-6:5)
Step-by-step explanation:
6/5 = 1.2
-1 * 6 = -6
-6/5 = -1.2
thus...
Ratio = (-6:5)
6. Construct the Truth Table and Determine whether each of the following compound
proposition is a Tautology, Contradiction or Contingency.
The first expression is Contingency.
The second expression is Tautology.
The third expression is Contingency.
What is Truth table?A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra.
What is Contingency?A sentence is called a contingency if its truth table contains at least one 'T' and at least one 'F. '
What is Contradiction?A statement is called a contradiction if the final column in its truth table contains only 0's.
What is Tautology?A tautology is a statement that is always true.
The first expression is Contingency.
The second expression is Tautology.
The third expression is Contingency.
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5. Ellie's street address is a prime number greater than 10 and less than 19. Which of the following could be Ellie's street address?
We want to find a prime number greater than 10 and less than 19.
* What is a prime number?
Prime number is a number that cannot be divided by any number other than 1 and itself
There are so many possibilities:
Ellie's street address could be 11, 13 or 17
Hope it helps!
Question 11
Points 2
Mary has four T-shirts-T₁, T2, T3, and T4, and
three pairs of jeans-J1, J2, and J3. The number
of possible ways she can choose her outfit is:
O 12
The computation shows that the number of possible ways will be 12.
How to calculate the value?From the information given, Mary has four t-shirts-T₁, T2, T3, and T4, and three pairs of jeans-J1, J2, and J3.
Therefore, the number of possible ways that she can choose her outfit will be:
= 4 × 3 = 12
In conclusion, the correct option is 12.
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Find the value(s) of x in the function f(x) = |-2x – 3| when f(x) = 5. (Separate multiple answers with a comma.)
Answer:
x = -4, 1
Step-by-step explanation:
Since we have a absolute value function here, we can tell there is goning to be multiple values.
First we will find x with the original function since we know |5| = 5.
Given f(x) = 5 = -2x-3,
[tex]2x-3 = 5 \\
-2x-3+3 = 5 + 3 \\
-2x = 8 \\
x = \frac{8}{ - 2} \\ = - 4[/tex]
Now we also know that |-5| = 5 as well (absolute value)
Given |-2x-3| = |-5|,
[tex] - 2x - 3 = - 5 \\ - 2x - 3 + 3 = - 5 + 3\\ - 2x = - 2 \\ x = \frac{ - 2}{ - 2} \\ = 1[/tex]
You can verifiy these 2 values by substituting them into the equation.
f(-4) = |-2(-4)-3|
= |8-3|
= |5|
= 5
f(1) = |-2(1)-3|
= |-2-3|
= |-5|
= 5
A modulus function is defined as a function that gives positive value for either a negative or positive argument. The values of x for given condition are -4 and 1.
What is a Modulus function?A function in the form of f(x) = |x| is known as a modulus function. The graph of a modulus function is symmetric about y-axis.
The function is given as,
f(x) = |-2x-3|
which implies that f(x) = -2x - 3 for x > 0 and f(x) = -(-2x - 3 )for x < 0
As per the question ,
Substitute the value of f(x) = 5, for both the cases to get the value of x as,
-2x - 3 = 5 and -(-2x - 3 ) = 5
=> x = -4 and x = 1.
Hence, the values of x obtained for the given condition are x =-4 and x = 1.
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Consider a population that grows according to the recursive rule
P
n
=
P
n
−
1
+
25
, with initial population
P
0
=
30
.
Then:
P
1
=
P
2
=
Find an explicit formula for the population. Your formula should involve
n
(use lowercase n)
P
n
=
Use your explicit formula to find
P
100
P
100
=
The explicit formula for the arithmetic sequence is: [tex]P_n = 30 + 25n[/tex]
Using the formula, we have that [tex]P_{100} = 2530[/tex].
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
From the recursive formula, we have that:
[tex]a_1 = 30 + 25 = 55, d = 25[/tex]
Hence the explicit formula is:
[tex]P_n = 55 + 25(n-1)[/tex]
[tex]P_n = 30 + 25n[/tex]
Then, when n = 100:
[tex]P_{100} = 30 + 25(100) = 2530[/tex]
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Use clustering estimation to find the approximate total in the following question.
What is the estimated total of 674, 692, 724, and 739?
ill make you brainliest
The estimated total of 674, 692, 724, and 739 is: 2800.
Clustering estimation techniqueTo find the sum using clustering estimation technique first step is to round each number to the nearest 10s.
674 into 670
692 into 690
724 into 720
739 into 740
Second step is to add
Addition=670+690+720+740
Addition=2820
2820 to the nearest 100s is 2800.
Therefore the estimated total of 674, 692, 724, and 739 is: 2800.
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Which system of equations has a solution of (0,1,2),
A.) 3x - y = -1
2y - z = 4
X- y + z = -1
B.) 2x + 4y = 4
y - 5z = 9
x+y+z=2
C.) -2x + 2y = 2
y + 7z = 13
1-y-z=0
D.) I + 3y - z = 1
4x + 2y = 2
5y - 2z = 1
Answer:
D
Step-by-step explanation:
well, you can simply put the arguments where belong and if you check choice D
5(1)–2(2)=1
so that will be the answer
Write the equation of the line that is parallel to the line y=−74x−2 through the point (4,-2).
Parallel lines have the same slope, so since the slope of the given line is -74, the slope of the line we want to find is also -74.
Substituting into point-slope form,
[tex]y+2=-74(x-4)\\\\y+2=-74x+296\\\\\boxed{y=-74x+294}[/tex]
The height "h" of a ball thrown straight up with a velocity of 88 ft/s is given by h = -16t^2 + 88t where "t" is the time it is in the air. For how many seconds the ball is in the air before it hits the ground?
Answer:
t=5.5
Step-by-step explanation:
The ball hits the ground when h = 0.
[tex]-16t^2 + 88t = 0 \\ \\ 2t^2 - 11t =0 \\ \\ t(2t-11)=0 \\ \\ t=0, 5.5[/tex]
However, as the answer must be positive, t=5.5
Please help!
P(A) = 1/3
P(B) = 2/9
P(A U B) = 4/9
Find P(A ∩ B).
A. 1
B. 1/3
C. 1/9
D. 20/18
Answer:
[tex]\sf C. \quad \dfrac{1}{9}[/tex]
Step-by-step explanation:
Addition Law for Probability
[tex]\sf P(A \cup B)=P(A)+P(B)-P(A \cap B)[/tex]
Given:
[tex]\sf P(A)=\dfrac{1}{3}=\dfrac{3}{9}[/tex]
[tex]\sf P(B)=\dfrac{2}{9}[/tex]
[tex]\sf P(A \cup B)=\dfrac{4}{9}[/tex]
Substitute the given values into the formula and solve for P(A ∩ B):
[tex]\implies \sf P(A \cup B) = P(A)+P(B)-P(A \cap B)[/tex]
[tex]\implies \sf \dfrac{4}{9} = \sf \dfrac{3}{9}+\dfrac{2}{9}-P(A \cap B)[/tex]
[tex]\implies \sf P(A \cap B) = \sf \dfrac{3}{9}+\dfrac{2}{9}-\dfrac{4}{9}[/tex]
[tex]\implies \sf P(A \cap B) = \sf \dfrac{3+2-4}{9}[/tex]
[tex]\implies \sf P(A \cap B) = \sf \dfrac{1}{9}[/tex]
[tex]\\ \rm\leadsto P(A\cap B)=P(A)+P(B)-P(A\cup B)[/tex]
[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{1}{3}+\dfrac{2}{9}-\dfrac{4}{9}[/tex]
[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{3+2-4}{9}[/tex]
[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{1}{9}[/tex]
A survey found that women's heights are normally distributed with mean 62.7 in, and standard deviation 2.8 in. The survey also found that men's heights are normally distributed with mean
69.3 in. and standard deviation 3.9 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 55 in, and a maximum of 62 in. Complete
parts (a) and (b) below.
a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement park?
The percentage of men who meet the height requirement is %.
(Round to two decimal places as needed)
Using the normal distribution, we have that:
The percentage of men who meet the height requirement is 3.06%. This suggests that the majority of employees at the park are females.
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 of men's heights are given as follows:
[tex]\mu = 69.3, \sigma = 3.9[/tex].
The proportion of men who meet the height requirement is is the p-value of Z when X = 62 subtracted by the p-value of Z when X = 55, hence:
X = 62:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{62 - 69.3}{3.9}[/tex]
Z = -1.87
Z = -1.87 has a p-value of 0.0307.
X = 55:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55 - 69.3}{3.9}[/tex]
Z = -3.67
Z = -3.67 has a p-value of 0.0001.
0.0307 - 0.0001 = 0.0306 = 3.06%.
The percentage of men who meet the height requirement is 3.06%. This suggests that the majority of employees at the park are females.
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The two dot plots represent a sample of the number of people in households in two towns. Which statements are true about the data sets?
The true statement ae:
Both have the same number of data points.
Both means are between 3 and 4.
Westwood has less variability than Middleton.
What are the true statements?A dot plot is made up of dots which represents the frequency of the values in the data set and a numberline.
The total number of data points for both dot plots is 20.
The range of Middleton is : 9 -1 = 8
The range of Westwood is: 6 - 2 = 4
Middleton has more variability than Westwood.
Mean sum of numbers / total numbers
Middleton = (1+ 2+ 2 + 2 + 2 + 3 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 4 + 5 + 5 + 5, 5 + 6 + 9) / 20 = 3.75
Westwood = ( 2 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 5 + 6 + 6 + 6) / 20 = 3.85
Here is the complete question:
The two dot plots represent a sample of the number of people in households in two towns. Which statements are true about the data sets?
Check all that apply.
Both have the same number of data points.
Both means are between 3 and 4.
Both have the same median.
Both have the same range.
Westwood has less variability than Middleton.
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use venn diagram to find the elements in each set A'
Based on the Venn diagram, the elements in set A can be found to be 2, 3 ,5, 7,and 9.
What are the elements in set A?The elements in set A would be those which are in A alone and in set B as well.
The numbers in set A alone are:
7, 3, 5, 9
The number in set B and A is 2.
The elements in set A is therefore:
2, 3 , 5, 7,and 9
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The product of w and 6
Answer:
w x 6
Because W is a variable and we don't know what W so it the equation is gonna be a open sentance
Which is not a method for solving a system of equations?
A. Graphing
B. Substitution
C. Fundamental Theorem of Arithmetic
D. Linear combination
Fundamental Theorem of Arithmetic is not a method for solving a system of equations.
What are system of equation?A system of equations is a collection of two or more equations with a same set of unknowns.
The system of equation can be solved using the following method.
Graphing methodSubstitution methodLinear combinationThe graphing involves using graph to find the intersection of the system of equation.
Substitution method involves substituting one variable to another.
Therefore, Fundamental Theorem of Arithmetic is not a method for solving a system of equations
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In major league baseball, a no-hitter is a game in which a pitcher, or pitchers, doesn't give up any hits throughout the game. No-hitters occur at a rate of about three per season. Assume that the duration of time between no-hitters is exponential. What is the probability that an entire season elapses with a single no-hitter? If an entire season elapses without any no-hitters, what is the probability that there are no no-hitters in the following season? What is the probability that there are more than 3 no-hitters in a single season?
Using the Poisson distribution, it is found that:
There is a 0.0498 = 4.98% probability that an entire season elapses with a single no-hitter.If an entire season elapses without any no-hitters, there is a 0.0498 = 4.98% probability that there are no no-hitters in the following season.There is a 0.3528 = 35.28% probability that there are more than 3 no-hitters in a single season.What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.The average rate is of 3 no-hitters per season, hence:
[tex]\mu = 3[/tex].
The probability that an entire season elapses with a single no-hitter is P(X = 0), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}3^{0}}{(0)!} = 0.0498[/tex]
There is a 0.0498 = 4.98% probability that an entire season elapses with a single no-hitter.
Seasons are independent, hence:
If an entire season elapses without any no-hitters, there is a 0.0498 = 4.98% probability that there are no no-hitters in the following season.
The probability that there are more than 3 no-hitters in a single season is P(X > 3) given as follows:
[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]
In which:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Then:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}3^{0}}{(0)!} = 0.0498[/tex]
[tex]P(X = 1) = \frac{e^{-3}3^{1}}{(1)!} = 0.1494[/tex]
[tex]P(X = 2) = \frac{e^{-3}3^{2}}{(2)!} = 0.2240[/tex]
[tex]P(X = 3) = \frac{e^{-3}3^{3}}{(3)!} = 0.2240[/tex]
Then:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0498 + 0.1494 + 0.2240 + 0.2240 = 0.6472[/tex]
[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.6472 = 0.3528[/tex]
There is a 0.3528 = 35.28% probability that there are more than 3 no-hitters in a single season.
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he Golfing Emporium had a set of 10 golf clubs that were marked on sale for $780. This was a discount of 30% off the original selling price.
Step 2 of 4 : If the golf clubs cost The Golfing Emporium $620, what was their profit? Follow the problem-solving process and round your answer to the nearest cent, if necessary.
The profit for the Golfing Emporium is $160.
How to get the profit?
We know that profit is defined as the difference between the revenue and the cost.
Here, we know that on the sale, the Golfing Emporium sells the set of clubs at $780 (this is the already discounted price).
While when they buy the set, the pay $620 for it.
Then the profit is given by:
P = $780 - $620 = $160
The profit for the Golfing Emporium is $160.
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Dr. Silas studies a culture of bacteria under a microscope. The function b_1(t)=1200(1.8)^t represents the number of bacteria t hours after Dr. Silas begins her study.
The number of bacteria in a second study is modeled by the function b_2(t)=1000(1.8^t.
What does the value of 1000 represent in this situation?
What does the difference of 1200 and 1000 mean between the two studies?
The _ means the 1&2 is under the b
The value of 1000 represent the initial population of bacteria in the study and the difference of 1200 and 1000 mean difference between the initial populations in the studies.
What are exponential Function ?Exponential functions are are written as y(x) = abˣ
Here
a is the initial population
b is the rate of growth or decrease
x is the time taken
The Given exponential function is
[tex]\rm b_1(t) = 1200( 1.8 )^t\\\\b_2(t) = 1000 (1.8)^t[/tex]
From the standard equation of Exponential function
(a) a = 1200 and 1000 is the initial population of the bacteria
(b)The difference of 1200 and 1000 means the difference between the initial populations in the studies
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What is the angle of rotation for the following figure?
Answer:
Angle rotation 120 ,90,60,45
how do you solve this?
B. The standard deviation is he square root of variance. The larger the standard deviation the more variation
Answer:
this is quite an easy problem.
Step-by-step explanation:
The problem appears to be asking for the class with the greatest variability of test 1, which merely means that you are looking for the graph that has the most distributed test scores. The graph that shows the largest difference in each test score will be your answer.
Please help with this question if you can
Line AE is NOT parallel to line BD. This is because the intercepts made by the lines and the transversals are not proportional
Parallel lines theoremIn the given diagram,
If
[tex]\frac{|AB|}{|ED|} =\frac{|AC|}{|EC|}[/tex]
Then,
Line AE is parallel to line BD
From the given information,
|AB| = x = 9
|ED| = 5
|AC| = 9 + 11 = 20
|EC| =5 + 7 = 12
Thus,
[tex]\frac{9}{20}=\frac{5}{12}[/tex]
20 × 5 = 9 × 12
100 ≠ 108
∴ The lines are not parallel
Hence, line AE is NOT parallel to line BD. This is because the intercepts made by the lines and the transversals are not proportional
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Solve the equation on the
interval [0, 2π).
4(sin x)² - 2 = 0
The solutions to the equation on the given interval are;
x = π/4, 3π/4, 5π/4, 7π/4.
What is the solution to the equation on the interval?Given that;
4(sin x)² - 2 = 0Interval = [ 0, 2π )4(sin x)² - 2 = 0
Add 2 to both sides and divide both sides 4
4(sin x)² - 2 + 2 = 0 + 2
4(sin x)² = 2
(4(sin x)²)/4 = 2/4
(sin x)² = 1/2
Square both sides
√((sin x)²) = ±√(1/2)
sin x = ±√(1/2)
sin x = ±(√2)/2
Next, we solve for x
Not that 180° = π
x = sin⁻¹ ( (√2)/2 ) = 45° = 180°/4 = π/4
x = π/4
Since the sine function is positive in the first and second quadrant, we subtract the reference angle from π to find the solution in the second quadrant.
x = π - π/4
x = 3π/4
Now, we find the period of sin x
2π / |b|
We know that, the distance between a number and zero is 1
2π / 1
2π
Hence, period of sin x function is 2π, values will repeat every 2π radians in both direction.
Since sine function is negative in third and fourth quadrant,
x = 2π + π/4 + π
x = 5π/4
Now, add 2π to every negative angle to get a positive angle
x = 2π + ( - π/4 )
x = 2π×4/4 - π/4
x = ((2π × 8) - π ))/4
x = (8π - π)/4
x = 7π/4
Therefore, the solutions to the equation on the given interval are;
x = π/4, 3π/4, 5π/4, 7π/4.
Learn more on radian solutions here: https://brainly.com/question/16044749
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