Answer
[tex]y = -3x^2-4x+3[/tex]
Explanation
The standard form of a parabola is
[tex]y = ax^2 + bx + c,[/tex]
where [tex]a \ne 0[/tex], and [tex]a,b,c[/tex] are real numbers.
If it passes through (0,3) then when x = 0, y = 3 so this means that
[tex]3 = a(0)^2 + b(0) + c \implies c = 3[/tex]
so [tex]y = ax^2 + bx + 3[/tex].
If it passes through (1,-4), then when x = 1, y = -4 so
[tex]\begin{aligned}-4 &= a(1)^2 + b(1) + 3 \\a+b+3 &= -4 \\a+b &= -7 && \text{(I).}\end{aligned}[/tex]
If it passes through (-1,4) then when x = -1, y = 4 so
[tex]\begin{aligned}4 &= a(-1)^2 + b(-1) + 3 \\a-b+3 &= 4 \\a-b &= 1 && \text{(II).}\end{aligned}[/tex]
Because both (I) and (II) need to be satisfied, we have the system of equations,
[tex]\begin{cases}a+b &= -7\qquad\text{(I)}\\a-b &= 1\qquad\text{(II)}\end{cases}[/tex]
which we can easily solve by adding the two equations up to get
[tex]\begin{aligned}(a+a) + (b-b) &= -7 + 1 \\ 2a&= -6 \\a &= -3.\end{aligned}[/tex]
Then we take any of the previous equations to solve for b:
[tex]\begin{aligned}a+b &= -7\\-3 + b &= -7 \\ b &= -4\end{aligned}[/tex]
Thus the parabola in standard form is
[tex]y = -3x^2-4x+3.[/tex]
So with the three points that are given to us, we will plug them into the standard form formula that I had mentioned earlier. Firstly, plug (0,3) into the equation since the 0 will cancel out the a and b variable:
[tex]3=a*0^2+b*0+c\\3=c[/tex]
Now we know that the value of c is 3.
Next, plug (1,-4) into the standard form formula and simplify (Remember to plug 3 into the c variable):
[tex]-4=a*1^2+1*b+3\\-4=a+b+3\\-7=a+b[/tex]
Next, plug (-1,4) into the standard form formula and simplify:
[tex]4=a*(-1)^2+b*(-1)+3\\4=a-b+3\\1=a-b[/tex]
With the last two simplified equations, we will create a system of equations:
[tex]-7=a+b\\1=a-b[/tex]
With this, I will be using the elimination method. Add the two equations together, and the following equation is the result:
[tex]-6=2a[/tex]
From here we can solve for a. For this, just divide both sides by 2:
[tex]-3=a[/tex]
Now that we have the value of a, plug it into either equation to solve for b:
[tex]-7=-3+b\\-4=b\\\\1=-3-b\\4=-b\\-4=b[/tex]
AnswerNow, plug the obtained values in our standard form equation and your final answer will be:
[tex]y=-3x^2-4x+3[/tex]
hello
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plz see attachmentss below
Problem 1
Answer: Choice C) sample is appropriately large; margin of error is plus/minus 0.187
-----------------------------
Explanation:
At 90% confidence, the z critical value is roughly z = 1.645 (this is found using a table in the back of your textbook)
n = 250 is the sample size, which is appropriately large (it's over n = 30)
s = 1.8 is the standard deviation
The margin of error E is found by the formula below
E = z*s/sqrt(n)
E = 1.645*1.8/sqrt(250)
E = 0.18727008303518
E = 0.187
note: the sample mean is not used at all in the computation of the margin of error.
===========================================
Problem 2
Answer: Choice D) both are effective; however, Intensity program is more effective compare to Q30X program
-----------------------------
Explanation:
There's not much to say here other than your teacher really wrote a lot to set up this problem. There's a lot of extra filler that you need to toss out and ignore. Basically the short of it is that Brant wants to run faster so he tests two programs. He finds that both are effective (since they both yield roughly the same percent decrease in run times) but the Intensity program is better by two percentage points. It's not much, but it's something. So this is why the answer is choice D.
===========================================
Problem 3
Answer: Choice A) appropriately large; margin of error is plus/minus 0.079
-----------------------------
Explanation:
n = 150 is the sample size. It is appropriately large as it is over n = 30
At 95% confidence, using a stats table (in the back of your book) you should find the critical value is z = 1.960
p = 0.56 is the decimal version of 56%, this is the proportion of those who use public transportation
We'll use a slightly different margin of error formula. This time it's to measure the error for proportions (rather than means)
E = z*sqrt(p*(1-p)/n)
E = 1.960*sqrt(0.56*(1-0.56)/150)
E = 0.07943845584267
E = 0.079
In a right triangle one acute angle measures 48 more than 2 times the other. If the sum of the measure of the two acute angles must equal 90 find the measure is the acute angles
A)14,76 B)16,74 C)15,78. D)13,77
A given angle measures 90°.. Then, note that the total measurement of the triangle is 180°... Subtract 180° by 90°, and the other angles must add up to 90°!
Good luck!
There are 100 sophomores at the school. 85% of them are good students. What would be the percent of good students at school if (rounding the answer to the nearest whole number): b ten "A" students were to join this school
Answer:
86%
Step-by-step explanation:
77% students are good students after 10 students join the school.
What is percentage?Percentage is a part of the whole number. It is denoted by % sign.
1 %= 1/100.
Given that,
The number of sophomores in the school = 100
Also, the percentage of good students = 85%
So, number of good students = 100x85/100 = 85
If 10 students join the group,
Then total number of students = 100+10 =110
Percentage of good students = 85 x 100/110
= 77.181
= 77%(round to whole number)
The percentage of good students is 77% in school.
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Given that the lines are parallel, what angles are congruent to angle 1?
Angle 2
Angle 5
All of the above
None of the above
Answer:
All of the above
Step-by-step explanation:
<1 = <2 Alternate interior angles
<1 = <5 Corresponding angles
How are the absolut value of an imaginery number is related distance betweem two point related to another
Answer:
the absolute value of a imaginary number is somewhat similar to a distance between the two points.
Step-by-step explanation:
by absolute value of an imaginary number a+i b we mean the distance of the origin (0, 0) and the point (a,b) in the complex plane
i.e. [tex]\sqrt{a^{2} +b^{2} }[/tex]
whereas distance between two points ([tex]x_{1}[/tex],[tex]x_{2}[/tex]) and ([tex]y_{1}[/tex],[tex]y_{2}[/tex]) is given by [tex]\sqrt{(x_{1}-y_{1} )^2+( x_{2}-y_{2})^2}[/tex]
if ( [tex]y_{1}[/tex],[tex]y_{2}[/tex])=(0,0) then it is similar to the absolute value of a complex number of the type x+i y.
The balance of Susu’s savings account can be represented by the variable b. The inequality describing her balance is b > $30. Which could be a solution to the inequality?
$15
$20
$30
$35
Answer: 35
Step-by-step explanation: This answer, wants a number just greater than 30 not equal to. The symbol > means just greater than, however the symbol ≥ means greater than or equal to.
Answer:
$35
Step-by-step explanation:
Any value of b greater than $30 would be a solution. Only one of the four listed possible answers satisfies that: $35.
At 55 mph it will take you approximately _____ feet to stop the car. A. 5 feet B. 100 feet C. 228 feet
Answer:
The correct answer is option C, 228 feet
Step-by-step explanation:
As per Newton’s third law of motion:
V2 – U2 = 2 x a x S
Where V = final velocity
U = Initial Vlocity
a = acceleration (-ve)
S= distance travelled
V= 0 mph
U= 55 mph = 80.6667 ft /sec
0 – (80.6667 ft /sec)2 = 2 x (-g/2) x S
S = (80.6667 ft /sec)2 /(32.2 feet per second per second x0.5)
S = 202.1 feet
So the most nearest option is option C
ABC is a straight line. the length of AB is four times the length of BC. AC = 75cm. work out the length of AB.
Answer:
AB = 60 cm
Step-by-step explanation:
AB + BC = AC
let the length of BC = x then AB = 4x, hence
4x + x = 75
5x = 75 ( divide both sides by 5 )
x = 15
AB = 4x = 4 × 15 = 60 cm
Given to us,
ABC is a straight line,
the length of AB is four times the length of BC,
AC = 75cm.
Equation 1As given to us, the length of AB is four times the length of BC. therefore, we can write it as, AB = 4(BC), which is equation 1 for us.
Equation 2Also, the length of the ABC will be constant. therefore, 75 cm. and the line AB and BC will together form the line ABC(AC). thus, we can write it as,
AB + BC = AC
Line BC
substituting the value of AB from equation 1 we get in equation 2,
4(BC) + BC = AC
5(BC) = AC
5(BC) = 75
[tex]\bold{(BC)=\dfrac{75}{5}}[/tex]
BC = 15 cm.
Line ABSubstituting the value of BC in equation 1, we get,
AB = 4(BC)
AB = 4 x 15
AB = 60 cm
Hence, the length of line AB is 60 cms.
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Meghan paid $7 dollars for a book. This price included a 20% discount. What was the original price of the book?
To find the original price of the book after a 20% discount, multiply the price paid by 0.2 and subtract the result from the price paid.
Explanation:To find the original price of the book, we need to determine the amount of the 20% discount and subtract it from the price Meghan paid. First, let's calculate the discount amount by multiplying $7 by 20% (or 0.2), which gives us $1.40.
Next, subtract the discount amount from the price Meghan paid: $7 - $1.40 = $5.60. The question asks us to find the original price of a book before a 20% discount which Meghan paid $7 for post-discount.
Therefore, the original price of the book was $5.60.
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Kong took 15%fewer secounds than Nolan took to complete his test.Kong took 85 secounds. How many secounds did Nolan take
Answer:
100sec
Step-by-step explanation:
100-15=85%
85%/85s = 100%/x
Crisscross method
x=8500/85
x=100s
DEFG is a parallelogram. Segment DH = 2y + 6, segment HF = 4x + 1, segment HE = 3x + 2 and segment GH = 20. Find the value of x
Answer:
6
Step-by-step explanation:
If GH equals 20 so does HE so 3x6+2=20
Answer:
x=6
Step-by-step explanation:
given that DEFG is a parallelogram and the diagonals bisect at H.
Since diagonals bisect each other in a parallelogram, we have
DH = HF and EH = HG.
GH=20 is given. i.e. 3x+2 = 20
Subtract 2
3x = 18
Divide by 3
x =6
so answer is x =6.
We can find value of y also. DH =HF=4x+1
i.e. 2y+6 = 25
y = 9.5
Pine Bluff Middle School is having its annual Spring Fling dance, which will cost \$400$400. The student treasurer reported that the dance fund has \$75$75 left over from last year. Each ticket to the dance costs \$4$4.
The table shows the value of an account x years after the account was opened. Based on the exponential regression model, which is the best estimate of the value of the account 12 years after it was opened? $8,910 $8,980 $13,660 $16,040
Answer:
Correct choice is B
Step-by-step explanation:
The exponential regression model can be written as exponential function
[tex]y=a\cdot b^x.[/tex]
Then
[tex]5,000=a\cdot b^0=a,\\ \\5,510=a\cdot b^2\Rightarrow 5,510=5,000\cdot b^2,\\ \\b^2=\dfrac{5,510}{5,000}=\dfrac{551}{500}\Rightarrow b\approx 1.05.[/tex]
Thus,
[tex]y=5,000\cdot (1.05)^x.[/tex]
When [tex]x=12,[/tex] you get
[tex]y(12)=5,000\cdot (1.05)^{12}\approx \$8,980.[/tex]
Factor x^3-4x^2-3x+18=0 given that 3 is a zero.
A) (x+2)(x-3)^2=0
B) (x-2)(x-3)^2=0
C) (x-2)(x-3)(x+3)=0
D) (x+2)(x-\sqrt{3})(x+\sqrt{3})=0
Answer:
B: (x + 2)(x - 3)^2
Step-by-step explanation:
This is only going to have 3 roots. One of them is (x - 3)
D does not look right. So let's solve it using synthetic division.
3 || 1 - 4 -3 18
3 -3 -18
========================
1 -1 -6 0
So what you have is a quadratic
x^2 - x - 6 = 0 which will factor(x - 3)(x + 2) = 0x - 3 = 0x = 3x + 2 =0x = - 2(x - 3)(x - 3)(x + 2 ) = 0The answer is B
Point E is located at (−2, 4) and point F is located at (5, 10) . What are the coordinates of the point that partitions the directed line segment EF¯¯¯¯¯ in a 7:3 ratio?
Answer:
(2.9, 8.2)
Step-by-step explanation:
Formula used for finding the coordinates of the point that partitions the directed line segment EF
[tex](\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})[/tex]
Point E is located at (−2, 4) and point F is located at (5, 10)
(x1,y1) is (-2,4) and (x2,y2) is (5,10) , m=7, n= 3
Plug in the values in the formula
[tex](\frac{7(5)+3(-2)}{7+3}, \frac{7(10)+3(4)}{7+3})[/tex]
[tex](\frac{29}{10}, \frac{82}{10})[/tex]
(2.9, 8.2)
Answer:
(2.9, 8.2)
Step-by-step explanation:
I took the test
Hailey is starting a new exercise program. The first day she will spend 30 minutes on a treadmill. She will increase her time on the treadmill by 5 minutes each day for two weeks. Which function T(d), time in minutes, can be used to determine how many minutes Hailey will spend on the treadmill on any specific day.
Answer:
A) T(d) = 5d + 30
Step-by-step explanation:
Answer:
T(d) = 5d + 30
Step-by-step explanation:
Hailey is starting a new exercise program.
The first day she will spend 30 minutes on a treadmill.
She will increase her time on treadmill by 5 minutes each day for 2 weeks.
We have to form the function modeling this situation.
The equation will be in a linear form y = md + c
where c = constant term = 30 minutes
m = rate of change = Increase in time of exercise per day = 5
d = variable representing day
y = Second variable representing total time given for exercise
y = 5d + 30 or y = 5d + 30
We can rewrite the equation in the form of a function.
T(d) = 5d + 30
Consider the diagram what is the length of segment ab
The length of segment AB is 9 units. So the answer is B) 9.
To find the length of segment AB, we can use the angle bisector theorem, which states that in a triangle, the length of the angle bisector from a vertex to the opposite side is proportional to the lengths of the two segments of that side.
Let's denote the length of AB as x.
Given that BC = 9 units and B is the midpoint of AC, AC = BC = 9 units.
Given that AD = 16 units.
Since B is the midpoint of AC, we can deduce that AB = BC = 9 units.
Therefore, the correct answer is B) 9.
Complete and correct question:
'Consider the diagram. What is the length of segment AB?
A) 7
B) 9
C) 18
D) 25
Which isn't a function?
Answer:
Step-by-step explanation:
It is the first one because a parabola cannot go sideways from a funtion because there are more than one y values for each x value
Which system of equations correspond to this matrix equation?
Question 9 options:
5x + 2x = -7
3y - 4y = -6
5x + 2y = -7
3x + 4y = -6
5x + 2y = -7
3x - 4y = -6
5x - 2y = -7
3x - 4y = -6
Answer:
5x + 2x = -7
3y - 4y = -6
Step-by-step explanation:
Given the matrix, we can multiply across the constant matrix and down the variable matrix
5x +2y = -7
3x -4y = -6
Answer: (C)
Step-by-step explanation:
When multiplying matrices:
Row 1 x Column 1 = the value in Row 1 Column 1
[tex]\left[\begin{array}{cc}5&2\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]= -7[/tex]⇒ 5(x) + 2(y) = -7⇒ 5x + 2y = -7Row 2 x Column 1 = the value in Row 2 Column 1
[tex]\left[\begin{array}{cc}3&-4\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]= -6[/tex]⇒ 3(x) + -4(y) = -6⇒ 3x - 4y = -6Combine the two equations to get:
[tex]\left \{ {{5x + 2y = -7} \atop {3x - 4y = -6}} \right[/tex]
Joshua and his four friends each have 1/2 package of crackers. HOW many packages of crackers do they have in all
Answer:
2 1/2 packages of crackers
Step-by-step explanation:
Answer:
2.5 packages of crackers
Step-by-step explanation:
multiply .5 by 5
good luck
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Which sentences highlight the protection of consumer rights? Steven and Samuel are managers in different retail stores. Steven allows customers to look at different products and verify the product details before choosing a product. Steven’s priority is satisfied customers. Samuel prefers saving time and attending to maximum number of customers in a given time. He does not allow customers to see different products and verify product details before choosing them. He insists that consumers should just trust the products in his store and directly buy the products available instead of comparing different brands.
The basic consumer right includes "Right to be informed" that states the availability of information required for weighing alternatives, and protection from false and misleading claims in advertising and labeling practices.
Hence, the sentence "Steven allows customers to look at different products and verify the product details before choosing a product. Steven’s priority is satisfied customers" - justifies the definition of consumer rights.
So, this above sentence highlights the protection of consumer rights.
The sentences that highlight the protection of consumer rights are explained in the answer.
Explanation:The sentences that highlight the protection of consumer rights are:
Steven allows customers to look at different products and verify the product details before choosing a product.Steven’s priority is satisfied customers.Samuel prefers saving time and attending to the maximum number of customers in a given time and does not allow customers to see different products and verify product details before choosing them.He insists that consumers should just trust the products in his store and directly buy the products available instead of comparing different brands.These sentences illustrate the importance of allowing customers to make informed choices and verify product details, which are fundamental consumer rights.
Find f(4) for f(x)=4x+3
I know I’m asking a lot of these but I stink at math
f(4)=4*4+3=16+3=19
What you must do is to plug in 4 as x into the function to get your answer.
Answer:
the answer is 19
Step-by-step explanation:
1. You substitute the 4 for the x.
2. Next, your do 4 times 4 to get 16 and add to the 3 to equal 19
3. Finally, f(x)=19
What is the quetient of 17.51 / 3.4?
Answer:
5.15
Step-by-step explanation:
I entered 17.5 slash 3.4 into my TI calculator
Answer:
5.15 Hope this helps!!!!!!!!!
The bike shop is having a sale. Everything in the store is 20% off. A bike is originally priced at $345.00 What is the sale of the bike? Enter your answer in the box.
To find the sale price of a bike originally priced at $345.00 with a 20% discount, calculate the discount amount ($69.00) and subtract it from the original price, resulting in a sale price of $276.00.
Explanation:The bike shop is having a sale where everything in the store is 20% off. To calculate the sale price of a bike that is originally priced at $345.00, you first need to determine the discount amount. Convert 20% to a decimal by dividing 20 by 100, which gives you 0.20. You then multiply the original price of the bike, $345.00, by 0.20 to find the discount amount.
$345.00 \times 0.20 = $69.00
Next, subtract the discount from the original price to find the sale price.
$345.00 - $69.00 = $276.00
Therefore, the sale price of the bike is $276.00.
A circle has an arc of length 48(3.14) that is intercepted by a central angle of 120°
Please please help me out!!!
Answer: 31%
Step-by-step explanation: If you divide the amount of Graduate students receiving Financial Aid by the total students receiving Financial Aid then you get 31%
A building is 190 feet tall and has a shadow that is also 190 feet. Determine the angle of elevation from the tip of the shadow to the top of the building.
A) 15°
B) 30°
C) 45°
D) 60°
Answer:
C) 45°
Step-by-step explanation:
Do you know what an isosceles right triangle looks like?
Its legs are the same length and its acute angles are 45°. Compare that to the picture.
The angle of elevation from the tip of the shadow to the top of the building is 45°
How to get 5% of 220 files
To find 5% of 220 files, convert the percentage to a decimal (5/100 = 0.05) and multiply it by 220. The result is 11, meaning 5% of 220 files is 11 files.
To calculate 5% of 220 files, you need to use the concept of percentage from basic mathematics. Here's a step-by-step explanation:
Understand that 'percent' means 'per hundred'. So, 5% can be expressed as 5/100.
Multiply the percentage (in this case, 5/100) by the total number of files (which is 220).
Perform the calculation: (5/100) times 220 = 0.05 times 220 = 11.
Therefore, 5% of 220 files is 11 files.
wanda has $640 in her checking account. she pays her landlord $75 per week for rent.
which function best models the linear relationship?
y = 640x 75
y = −75x 640
y = −75x − 640
y = 75x 640
Answer:
Option B is correct
[tex]y = -75x+640[/tex]
Step-by-step explanation:
The equation of line is given by:
[tex]y=mx+b[/tex]
where, m is the rate or slope and b is the initial amount.
As per the statement:
Wanda has $640 in her checking account.
She pays her landlord $75 per week for rent.
Assume that the number of weeks be x.
Let us assume that the y represented the money in the account after x weeks.
then;
the function becomes,
[tex]y = 640-7x[/tex]
or
[tex]y = -75x+640[/tex]
Therefore, the function best models the linear relationship is, [tex]y = -75x+640[/tex]
A wild horse runs at a rate of 8 miles per hour for 6 hours. Let yy be the distance, in miles, the horse travels for a given amount of time, xx, in hours. This situation can be modeled by a function. Which of these describe the domain of the function? Group of answer choices 0\le x\le60≤x≤6 0\le y\le60≤y≤6 0\le x\le480≤x≤48 0\le y\le480≤y≤48
Answer:
[tex]0\leq x\leq 6[/tex]
[tex]0\leq y\leq 48[/tex]
Step-by-step explanation:
we are given
speed =8 mph
time = 6 hours
so, we have
[tex]x=6[/tex]
now, we can find distance
distance = (speed)*(time)
[tex]distance=8\times 6 miles[/tex]
[tex]distance=48 miles[/tex]
so, we have
[tex]y=48 miles[/tex]
so, our range for x and y can be
[tex]0\leq x\leq 6[/tex]
[tex]0\leq y\leq 48[/tex]