Answer:
4.5
Step-by-step explanation:
43-32+2-4= 9
9/2= 4.5
Find the vertex, axis of symmetry, y intercept of each parabola. State the number of x intercepts. Then sketch the graph of each function. f(x)=2(x-4)^2+4
Answer:
Vertex: [tex](x,y) = (4,4)[/tex], Axis of symmetry: [tex]x = 4[/tex], no x-Intercepts, y-Intercepts: [tex](x,y) = (0, 36)[/tex]. The graph is represented in the image attached below.
Step-by-step explanation:
The equation of the parabola in vertex form and whose axis of symmetry is vertical is described by this formula:
[tex]y - k = C\cdot (x-h)^{2}[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]C[/tex] - Vertex constant.
[tex]h, k[/tex] - Coordinates of the vertex.
By direct comparison, we find the following information:
[tex]h = 4[/tex], [tex]k = 4[/tex], [tex]C = 2[/tex]
Vertex
The vertex is a point of the parabola so that [tex](x,y) = (h, k)[/tex].
If we know that [tex]h = 4[/tex] and [tex]k = 4[/tex], then the coordinates of the vertex are [tex](x,y) = (4,4)[/tex].
Axis of symmetry
The axis of symmetry is a line of the form [tex]x = h[/tex].
If we know that [tex]h = 4[/tex], then the axis of symmetry is [tex]x = 4[/tex].
To find the x and y intercepts, we need to transform the equation of the parabola into its standards, which is a second grade polynomial:
[tex]y - k = C\cdot (x-h)^{2}[/tex]
[tex]y - k = C\cdot (x^{2}-2\cdot h\cdot x +h^{2})[/tex]
[tex]y = C\cdot x^{2} -2\cdot C\cdot h \cdot x + (C\cdot h^{2}+k)[/tex]
If we know that [tex]h = 4[/tex], [tex]k = 4[/tex] and [tex]C = 2[/tex], then the equation of the parabola in standard form is:
[tex]y = 2\cdot x^{2}-16\cdot x + 36[/tex]
x-Intercepts
The x-intercepts of the polynomial (if exist) can be found by the Quadratic Formula:
[tex]x_{1,2} = \frac{16\pm \sqrt{(-16)^{2}-4\cdot 2\cdot (36)}}{4}[/tex]
[tex]x_{1,2} = 4 \pm \frac{\sqrt{-32}}{4}[/tex]
[tex]x_{1,2} = 4 \pm i \,\frac{4\sqrt{2}}{4}[/tex]
[tex]x_{1,2} = 4 \pm i\,\sqrt{2}[/tex]
As both roots are conjugated complex numbers, there are no x-intercepts.
y-Intercepts
The y-intercept (if exists) can be found by evaluating the polynomial at [tex]x = 0[/tex]:
[tex]y = 2\cdot 0^{2} - 16\cdot 0 + 36[/tex]
[tex]y = 36[/tex]
The y-intercept is [tex](x,y) = (0, 36)[/tex].
Lastly, we proceed to plot the function by using graphing tools.
PLEASE HELP I NEED THE ANSWER THANK YOU
Answer:
B
Step-by-step explanation:
The members of a golf team contributed a total of $14.30 for a party to be held after their practice. Each member contributed the same amount of money in dimes only. How many members are in the team and how much money did everyone contribute? Give all possible answers.
Answer:
each teammate contributed 1.43 sorry but i do not know how many members they have because my head hurts
The wheely fast co. Makes custom skateboards for professional riders. They model their profit with the relation P=-2b^2 + 14b - 20, where b is the number of skateboards they produce(in thousands) and P is the company's profit in hundred thousands of dollars. When does wheely fast break even?
Answer:
The answer is below
Step-by-step explanation:
Breakeven point is the point of balance where their is neither a loss or a profit. At the breakeven point, the revenue gotten from the sell of goods is equal to the cost of production of the goods, hence the profit is zero.
Given the profit function:
P=-2b² + 14b - 20
At breakeven P = 0, hence:
0 = -2b² + 14b - 20
-2b² + 14b - 20 = 0
-2b² + 10b + 4b - 20 = 0
-2b (b - 5) + 4(b - 5) = 0
(b - 5)(-2b + 4) = 0
b - 5 = 0; or -2b + 4 = 0
b = 5; or b = 2
Since b is in thousands, hence the company breaks even when the number of skateboards produced is either 2000 or 5000
Is this a function? Or is it not a function ? I’ll give brainlist.
Answer:
its a function something to remember is if anything on the y line (up and down) touches its not a function otherwise it is
Step-by-step explanation:
The distance between the lines: 4x+3y-11 and 8x+6y=15 is
Answer:
The distance between the lines: 4x+3y-11 and 8x+6y=15 is [tex]\frac{7}{10}[/tex]
Step-by-step explanation:
You have two parallel and different lines. The form of the implicit equations is:
A*x + B*y + C= 0
A'*x + B'*y + C'=0
Since the two lines are parallel, the coefficients of their general equations must satisfy that the slopes are equal.
Therefore, the equations can be transformed so that the coefficients A and B are equal, multiplying or dividing one of them by a constant.
So, the distance between two lines can be expressed as follows:
[tex]d=\frac{|C-C'|}{\sqrt{A^{2} +B^{2} } }[/tex]
In this case, you have:
4x+3y-11= 0 Multiplying this equation by 2 you get: 8x +6y -22=08x+6y-15 =0Then, you have:
A= 8B=6C= -22C'= -15Replacing in the definition of distance:
[tex]d=\frac{|-22-(-15)|}{\sqrt{8^{2} +6^{2} } }[/tex]
Solving:
[tex]d=\frac{|-7|}{\sqrt{8^{2} +6^{2} } }[/tex]
[tex]d=\frac{7}{\sqrt{8^{2} +6^{2} } }[/tex]
[tex]d=\frac{7}{\sqrt{64+36 } }[/tex]
[tex]d=\frac{7}{\sqrt{100 } }[/tex]
[tex]d=\frac{7}{10}[/tex]
The distance between the lines: 4x+3y-11 and 8x+6y=15 is [tex]\frac{7}{10}[/tex]
If 5x – 3y = 1 and
x - 2y = - 4, then xy = ? .
A 5
B 4
© 6
D 8
E 9
Answer:
[tex]6[/tex]
The answer is C:6
What is the slope of the line shown below? (Enter your answer as a decimal if
necessary.)
Benjamin needs $0.75 more cents to buy a granola bar that costs $1.89. How much money does Benjamin have now? The equation that correctly models the problem is To undo what has been done to the variable on both sides of the equation. The solution of the equation is
✔ b + 0.75 = 1.89
✔ subtract 0.75
✔ b = $1.14
the person above me doesn't make since so here the answers
Benjamin presently have $1.14.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Benjamin needs $0.75 more cents to buy a granola bar that costs $1.89.
let Benjamin have the amount $b.
So, the Expression to represent the situation is:
b + 0.75 = 1.89
Now, subtract 0.75 from both side
b + 0.75 - 0.75 = 1.89 - 0.75
b = 1.14
Learn more about Equation here:
https://brainly.com/question/29657983
#SPJ6
The teacher asked her students to name a pair of supplementary angles. Ryan said <4 and <2 and the
teacher said he was wrong.
a) Explain why he is wrong, and give the name of the angle pair <4 and <2 represents.
b) Then, give 1 example of a pair of angles that are supplementary,
Answer and Step-by-step explanation:
The angles Ryan chose aren't supplementary (next to) to each other and don't add up to 180.
An angle pair that are supplementary to each other are angles 2 and 3.
#teamtrees #PAW (Plant And Water)
1. “Systems of Linear Equations”
American Airlines sold a certain number of tickets from Los Angeles to Hawaii. They charged $90
for flight x and the remaining tickets for $250 for flight y. If the airline sold 120 tickets and
collected a total of $27,600 from the sale of those tickets:
a) Set up the System of Linear Equations
b) How many tickets of each flight were sold?
c) How much money was made from each flight?
Answer:
Part A)
[tex]\begin{aligned} x+y&=120 \\ 90x+250y&=27600\end{aligned}[/tex]
Part B)
Flight X sold 15 tickets and Flight Y sold 105 tickets.
Part C)
Flight X made $1,350 and Flight Y made $26,250.
Step-by-step explanation:
Let the amount of tickets sold by Flight X be represented by x and the amount of tickets sold by Flight Y be represented by y.
Part A)
The airline sold 120 tickets in total. Hence:
[tex]x+y=120[/tex]
Each x ticket costs $90 and each y ticket costs 250. The total income was $27,600. Thus:
[tex]90x+250y=27600[/tex]
Our system of equations is:
[tex]\begin{aligned} x+y&=120 \\ 90x+250y&=27600\end{aligned}[/tex]
Part B)
Solve the system of equations. We can use substitution. From the first equation, subtract y from both sides:
[tex]x=120-y[/tex]
In the second equation, we can divide everything by 10 and substitute in x:
[tex]9(120-y)+25y=2760[/tex]
Simplify:
[tex]16y+1080=2760[/tex]
So:
[tex]y=105\text{ tickets}[/tex]
Using the equation above:
[tex]x=120-(105)=15\text{ tickets}[/tex]
Flight X sold 15 tickets and Flight Y sold 105 tickets.
Part C)
Since each ticket of Flight X sold for $90 and Flight X sold 15 tickets, Flight X made $1,350.
Then it follows that Flight Y made $26,250.
f(x) = 3x² + 7x; g(x) = 6x +3; f(x) - g(x) =
Answer:
[tex] = 3x {}^{2} + x - 3[/tex]
What is the slope-intercept form equation of the line that passes through (2, 4) and (4, 10)?
O y = -3x - 2
O y = -3x + 2
O y = 3x + 2
O y = 3x - 2
⊹˚ʚ ❑Answer︰The slope is 3!
⊹˚ʚ ❑Explanation︰use the formula y2-y1 over x2-x1
✎Daily reminder: make sure to eat food and stay hydrated, have a good day :D
Answer:
y = 3x - 2.
Step-by-step explanation:
The slope of the line (m) = (10-4)/(4-2)
= 3.
y - y1 = m(x - x1)
y - 10 = 3(x - 4)
y = 3x - 12 + 10
y = 3x - 2.
Evaluate the expression when x = 4.
6(x + 8)
Answer:
6x+48
Step-by-step explanation:
6(x+8)
=(6)(x+8)
=(6)(x)+(6)(8)
=6x+48
Answer:
72
Step-by-step explanation:
6(4+8)
6(12)
the answer is 72
Which angels are corresponding angles
Answer:
B. 5 and 7
E. 1 and 3
F. 6 and 8
Step-by-step explanation:
The angles in matching corners are called corresponding angles.
Which expression is equivalent to
Answer:
[tex] x {4}[/tex]
Step-by-step explanation:
easy math
Tracey paid $374.25 for a new iPad. What was the original cost if the iPad was on sale for 25% off
Answer:
$467.8125
Step-by-step explanation:
Percentage increase = 25% × 374.25
New value = 374.25 + Percentage increase
New value =
374.25 + Percentage increase =
374.25 + (25% × 374.25) =
374.25 + 25% × 374.25 =
(1 + 25%) × 374.25 =
(100% + 25%) × 374.25 =
125% × 374.25 =
125 ÷ 100 × 374.25 =
125 × 374.25 ÷ 100 =
46,781.25 ÷ 100 =
467.8125 ≈
467.81
The length of an original drawing is 6 inches and the scaled drawing is 9 inches. What is the scale factor as a percent?
Answer:
2/2 I'm not sure for that but its base on answer key
Answer:
[tex]66 \frac{2}{3} \%[/tex]
Step-by-step explanation:
[tex]scale \: factor = \frac{scaled \: drawing}{original \: drawing} [/tex]
[tex]∴scale \: factor = \frac{6}{9} [/tex]
Simplify the fraction by dividing both the numerator and denominator by 3:
[tex]scale \: factor = \frac{2}{3} [/tex]
As a percentage, scale factor
[tex] = \frac{2}{3} \times 100\%[/tex]
[tex] = 66 \frac{2}{3} \%[/tex]
What is the solution to the system of equations below?
CU
y=-x+6 and y=-30
A. (45, -30)
B. (-30, 30)
C. (-30, 45)
D. (30, -30)
Answer:
(36,-30)
Step-by-step explanation:
y = -30
Solve for x
y = -x+6
-30 = -x+6
Subtract 6 from each side
-36 = -x
Multiply each side by -1
x = 36
Answer:
A. (45, –30)
Step-by-step explanation:
trust me<33
SOMEONE PLEASE HELP ME ASAP
EXPLANATION = BRAINLIEST, THANK YOU
Answer:
Step-by-step explanation:
volume of a cylinder=πr^2h
=3.14*2^2*4
=3.14*4*4
=50.24 m^3
please help asap!!!! will mark brainliest
Answer:
A 9x--12 i hope this helps
Answer:
a. 9x-12
Step-by-step explanation:
Perimeter means total length of sides.
So, add (2x-7)+(5x-3)+(2x-2)
9x-12
DO IT ASAP! Thank you very much!
Answer:
a = 5
Step-by-step explanation:
According to the factor theorem, if x + 2 is a factor, then by dividing the polynomial by the binomial, we are meant not to have a remainder
In this case, the remainder would be zero
So, if we set the binomial equals zero and substitute the x-value into the polynomial, we are supposed to have 0
So we have this as;
x + 2 = 0
x = -2
-2^3 -2(-2)^2 -2(a) + 6 = 0
-8-8-2a + 6 = 0
-16 + 2a + 6 = 0
2a -10 = 0
2a = 10
a = 10/2
a = 5
Having ____ siblings is just as common as having____
Answer:
1 ; 3
Step-by-step explanation:
Hope this answer helps you :)
Have a great day
Mark brainliest
Could really use some help! i meed it bad
Answer:
b= 10
Step-by-step explanation:
h=2b, (bh/2)=100, bh=100, b^2=100, b=10
System of equations, please help.
Answer:
3.75*A + 2.50*D = 35
A + D = 12
A = 12 - D
3.75*(12-D) +2.5*D= 35
45 - 3.75D + 2.5D = 35
45 - 1.25D = 35 |-35
10 - 1.25D = 0 |+1.25D
10 = 1.25D | /1.25
8 = D
A+D=12
A+8=12 |-8
A=4
If you like it, brainliest would be cool
Someone help me please!
Answer:
y < -3x + 2
Step-by-step explanation:
The shading is below the line meaning the inequality is less than. Moreover, the line is dashed meaning there is no 'equal to'.
Therefore, the inequality is y < -3x + 2.
WILL MARK BRAINLIEST!
Bob is a barista. He worked for 6 hours and earns $12 in tips. If he made $84 by the end of the day, how much does Bob make an hour? Which equation with a variable represents this situation.
A study shows that 20% of college students pray daily in their own religious beliefs. In a group of 300 college students, find the probability that 57 to 62 of them pray daily in their own religious beliefs. Use up to 4 decimal places accuracy for
μ
ˆ
p
,
σ
ˆ
p
, and your answer.
0.2805
0.6141
0.47385
0.3336
None of the above.
Answer:
0.2805
Step-by-step explanation:
Given that p = 20% = 0.2, n = 300.
The mean (μ) = np = 0.2 * 300 = 60
The standard deviation (σ) = [tex]\sqrt{np(1-p)}=\sqrt{300*0.2(1-0.2)}=6.93[/tex]
The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma }[/tex]
For x = 57:
[tex]z=\frac{57-60}{6.93 } =-0.43[/tex]
For x = 62:
[tex]z=\frac{62-60}{6.93 } =0.29[/tex]
From the normal distribution table, P(57 < x < 62) = P(-0.43 < z < 0.29) = P(z < 0.29) - P(z < -0.43) = 0.6141 - 0.3336 = 0.2805
45-[38-{60÷3-(6-9÷3)÷3}]
45 - [ 38 - { 60/3 - ( 6 - 3 )/3} ]
45 - [ 38 - { 60/3 - 3/3 } ]
45 - [ 38 - { 20 - 1 } ]
45 - [ 38 - 19 ]
45 - 19
=26
hope this helps....
HELPP WILL GIVE BRAINLEST !!!!!!!!
Answer:
8.06
Step-by-step explanation: