Write 42 as a product of primes use index notation
The graph of $y = ax^2 + bx + c$ is shown below. Find $a \cdot b \cdot c$. (The distance between the grid lines is one unit.)
Answer:
[tex]a\cdot b\cdot c=\frac{15}{4}[/tex]
Step-by-step explanation:
Vertex is the minimum or maximum point of parabola
Vertex of parabola is (h,k)
Therefore, from given graph (-3,-2) is the lowest point.
Vertex of parabola is at (-3,-2).
Standard equation of parabola
[tex]y-k=a(x-h)^2[/tex]
Substitute the values
[tex]y-(-2)=a(x-(-3))^2=a(x+3)^2[/tex]
[tex]y+2=a(x+3)^2[/tex]
(-1,0) lies on the parabola.
Therefore, it satisfied the equation of parabola.
[tex]0+2=a(-1+3)^2=4a[/tex]
[tex]a=2/4=1/2[/tex]
Now, using the value of a
[tex]y+2=1/2(x+3)^2=1/2(x^2+6x+9)[/tex]
[tex]y+2=\frac{1}{2}x^2+3x+\frac{9}{2}[/tex]
[tex]y=\frac{1}{2}x^2+3x+\frac{9}{2}-2[/tex]
[tex]y=\frac{1}{2}x^2+3x+\frac{9-4}{2}[/tex]
[tex]y=\frac{1}{2}x^2+3x+\frac{5}{2}[/tex]
By comparing with
[tex]y=ax^2+bx+c[/tex]
We get
[tex]a=\frac{1}{2}, b=3, c=5/2[/tex]
[tex]a\cdot b\cdot c=\frac{1}{2}\times 3\times \frac{5}{2}[/tex]
[tex]a\cdot b\cdot c=\frac{15}{4}[/tex]
Trucker's Heaven Diner uses hundreds of plates, glasses, and cups each day. The dishwashers start a new load of dishes every 1 1/4 hours. If the dishwashers work for 10 hours . How many loads off dishes do they wash in that time?
A: 1/2
B: 8
C: 8 3/4
D: 12 1/3
Answer:
B: 8
Step-by-step explanation:
we are given two numbers which we can use to help solve this problem
A: the number of hours the dishwasher is being used
B: how long it takes the dishwasher to do each load
using this info we can find how many loads were washed in 10 hours by dividing the time it takes for each load by how many hours were spent.
10 / 1.25 = 8
What is the following product?
Answer:
D
Step-by-step explanation:
(5√2 - 4√3)^2 =
50 + 48 - 40√6 = 98 - 40√6
A camera has a list price of $ 869.99 before tax. If the sales tax rate is 9.5 % , find the total cost of the camera with sales tax included. Round your answer to the nearest cent, as necessary
Instructions: Find the measure of the indicated angle to the nearest
degree.
12
?
36
?
=
To find the indicated angle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking from the angle, we know the adjacent side and the hypotenuse. Therefore, we should use cosine to solve.
cos(x) = 12/36
x = cos^-1(12/36)
x = 71 degrees
Hope this helps!
Can anyone help me ? I just need the numbers
Answer:
(-6, 0) and (0, 1.5)
Step-by-step explanation:
The equation of the line in pint slope form is expressed as;
y-y0= m(x-x0)
m is the slope
(x0, y0) is the point on the line
Given
m = 1/4
(x0, y0) = (6,3)
Substitute into the formula;
y - 3 = 1/4(x-6)
4(y-3) = x - 6
4y - 12 = x-6
4y - x = -6+12
4y - x = 6
x = 4y - 6
To get the points to plot, we will find the x and y-intercept of the resulting expression.
For the x-intercept,
at y = 0
x = 4(0) - 6
x = -6
Hence the x-intercept is at (-6, 0)
For the y-intercept,
at x = 0
0 = 4y - 6
4y = 6
y = 6/4
y = 3/2
y = 1.5
Hence the y-intercept is at (0, 1.5)
Hence the required points to plot to get the required line are (-6, 0) and (0, 1.5)
342225 square root by division method pls give the steps
Answer:
185 is the square root of 34225
Step-by-step explanation:
hope you understood!!
A student measures the length of a football field and reports it to be 294 feet long. The actual length of the field is 300 feet. What is the percentage error in the student's measurement
Answer:
Percentage error in the student measurement = 2%
Step-by-step explanation:
Percentage error = (change in length) / actual length × 100
Approximate length =294 feet
Actual length = 300 feet
Percentage error = (change in length) / actual length × 100
= (300 feet - 294 feet) / 300 feet × 100
= 6/300 × 100
= 0.02 × 100
= 2%
Percentage error in the student measurement = 2%
Calculate the axis of symmetry in the equation Y = (x+1) (x-4)
Come on anyone please helppppppp.
Answer:
Every parabola has a turning point called the axis of symmetry,so for this question you just have to find the turning points
x turning point= -b/2a,and the y turning point is gotten by replacing the value of x in the equation
y=(x+1)(x-4)
=x^2-3x-4
a is 1,b is -3 and c is -4
x= -(-3)/2(1)
=1.5
and y=x^2-3x-4
=1.5^2-3(1.5)-4
= -6.25
therefore the axis of symmetry is (1.5,-6.25)
I hope this helps
Given TVW,MZV = 90°, TV = 14, and VW= 9,
which of the following choices is used to find mZW?
here's the answer to your question
Instructions: Find the measure of the indicated angle to the nearest
degree.
?
?
3
7
?
Answer:
x = 23
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan ? = 3/7
Taking the inverse tan of each side
tan ^-1 ( tan ?) = tan ^-1 (3/7)
?=23.19859
To the nearest degree
x = 23
Which angles are supplementary to each other?
• Angle 7 and Angle 3
• Angle 9 and Angle 12
• Angle 6 and Angle 12
• Angle 12 and Angle 10
Answer:
∠9 and ∠12
Step-by-step explanation:
Supplementary angles are two angles that add up to 180. Looking at all the answer choices, A, C, and D have either Big-Big angle or Small-Small angle. What we need is Big-Small angle that is next to eachother, which is ∠9 and ∠12.
Hope this helped.
(Also sorry!)
Which of the following statements is false?
A and B
I hoped it helped you
Five students are asked to randomly select and name a polygon from the group shown below. what is the probability that the first two student choose the triangle and quadrilateral, in that order
Answer:
is it 2/5 I could be wrong
13 A cylindrical iron rod 8 cm high and 6 cm in diameter stands in a cylindrical tin 12 cm in diameter. See Fig. 15.22. Water is poured into the tin until its depth is 8 cm. How far would the level drop when the rod is removed?
Answer:
2cm
Step-by-step explanation:
The volume of water displaced by the rod is
v = πr^2 h = π * 3^2 * 8 = 72π cm^3
The drop in water level is the rod volume divided by the cross-section area of the tin, or
72π/(π*6^2) = 2 cm
Help ASAP please Nd thanks
Answer:
D
Step-by-step explanation:
(4x)²=x+15
A bag of M&M's contained 13 red, 15 yellow,
44 brown, 12 orange, and 9 green candies.
What percent of the M&M's were yellow?
Answer:
16%
Step-by-step explanation:
Use the percentage formula:
P × V1 = V2
Example:
EX: P × 30 = 1.5
P =
1.5
30
= 0.05 × 100 = 5%
HELP PLEASE HURRY
THANKS
Answer:
Step-by-step explanation:
Which of the following functions represent exponential decay?
An exponential decay function goes down to the right, like in the picture attached.
An exponential function follows this format: [tex]y=ab^x[/tex], where b is less than 1 and more than 0. b is more than 0 but less than 1 in function A.
Pl ease H e l p I'm literally desperate-
If f(x) = 4x - 5 and g(x) = 7x -3, Show all steps & work. Find:
(f + g) (x)
and
(f * g) (x)
Answer:
f+g = 11x-8
f*g = 28x^2 - 47x+15
Step-by-step explanation:
f(x) = 4x - 5 and g(x) = 7x -3
(f+g)(x) = 4x - 5 + 7x -3
Combine like terms
= 4x+7x -5-3
= 11x-8
(f * g) (x) = ( 4x - 5) (7x -3)
FOIL
= 4x*7x + 4x(-3) + (-5)(7x) + (-5)(-3)
=28x^2 -12x-35x+15
Combine like terms
=28x^2 - 47x+15
Step-by-step explanation:
Step 1: Find (f + g)(x)
The definition of (f + g)(x) is f(x) + g(x). Basically add the two functions together.
[tex]f(x) + g(x)[/tex]
[tex](4x - 5) + (7x - 3)[/tex]
[tex]11x - 8[/tex]
Answer: [tex]11x - 8[/tex]
Step 2: Find (f * g)(x)
The definition of (f * g)(x) is f(x) * g(x). Basically multiply the two functions together.
[tex]f(x) * g(x)[/tex]
[tex](4x - 5) * (7x - 3)[/tex]
[tex](4x * 7x) + (4x * -3) + (-5 * 7x) + (-5 * -3)[/tex]
[tex](28x^{2}) + (-12x) + (-35x) + (15)[/tex]
[tex]28x^{2} - 47x + 15[/tex]
Answer: [tex]28x^{2} - 47x + 15[/tex]
What is the rate of change of the amount earned with respect to hours worked for this function?
A) 1/13 hours per dollar
B) 2/5 hours per dollar
C) 3 dollars per hour
D) 13 dollars per hour
The rate of change of the amount earned with respect to hours worked for this function is D. 13 dollars per hour.
What is rate of change?The rate of change for the point defined on the graph can be deduced by calculating the ratio of the difference between the two coordinate points given, similar to calculating the gradient or slope :
Point a = (5, 65) = (x₂, y₂)
Point b = (2, 26) = (x₁, y₁)
Calculating the gradient or slope :
Rate of change = (y₂ - y₁) / (x₂ - x₁)
Rate of change = (65 - 26) / (5 - 2)
Rate of change = 39 / 3
Rate= 13 dollars per hour
Learn more about rate of change on:
https://brainly.com/question/8728504
#SPJ1
Complete question
The graph shows the amount of money Miguel earns after working x hours. What is the rate of change of the amount earned with respect to hours worked for this function? hours per dollar hours per dollar 3 dollars per hour 13 dollars per hour
what is the sum of the first 5 terms of a geometric series with a sub 1 = 10 and r = 1/5?
Answer:
12.496
Step-by-step explanation:
a=10 (first term)
r= 1/5 (common ratio)
sum of first five terms
[tex] s_{5} = \frac{a( 1 - {r}^{n} ) }{1- r} [/tex]
=10{1-⅕⁵} ÷ 1-⅕
=10{1 - 1/3125} ÷ 4/5
=10{3124/3125} ÷ 4/5
=9.9968÷0.8
=12.496.
OR
a+ar+ar²+ar³+ar⁴
=10+(10x⅕)+(10x⅕²)+(10x⅕³)+(10x⅕⁴)
=10+2+0.4+0.08+0.016
=12+0.48+0.016
=12.496
How to find the measure of n
Answer:
6[tex]\sqrt{3}[/tex]
Step-by-step explanation:
we use Euclidian theorem to find n
n^2 = 6*18
n^2 = 108
n = 6[tex]\sqrt{3}[/tex]
Complete the similarity for the two triangles shown.
Triangle ABC
Answer:
triangle EFD
Step-by-step explanation:
How much water should be added to 90ml of 45 percent acid solution to dilute it to 25 percent acid solution
Answer:
72 ml
Step-by-step explanation:
Let
x = amount of water that should be added
45% acid solution = 45/100 = 0.45
25% acid solution = 25/100 = 0.25
The equation is
90(0.45) = 0.25(x + 90)
40.5 = 0.25x + 22.5
40.5 - 22.5 = 0.25x
18 = 0.25x
Divide both sides by 0.25
x = 18/0.25
= 72
x = 72 ml
What is the axis of symmetry for the graph of y – 4x = 7 – x2 ?
the axis of symmetry is x=2
A civil servant had a salary of Rs 9600. Tax up to Rs 85000 per year would be exempted. If he paid Rs 4530 as a tax, how much percent of tax was imposed?
Answer:
4%
Step-by-step explanation:
Yearly salary = 9600 * 12 = Rs. 115200
Tax = Rs . 4530
[tex]Tax \ percent = \frac{4530}{115200}*100[/tex]
= 3.93 = 4%
Which of the following are not Polynomials?
Answer:
E. is not a polynomial
Step-by-step explanation:
Because the degree of x is 2/5 which is not a polynomial.
Answer:
hmmm....
I don't think any of them are ????
[tex]\sqrt{2} = 2 ^{1/2}[/tex] that is a exponent that is a fraction ......
it appears that all the answers have fractional exponents, negative exponents, or divide by a variable??
Step-by-step explanation:
Polynomials cannot contain division by a variable.
For example, 2y2+7x/4 is a polynomial because 4 is not a variable. However, 2y2+7x/(1+x) is not a polynomial as it contains division by a variable.
Polynomials cannot contain negative exponents.
You cannot have 2y-2+7x-4. Negative exponents are a form of division by a variable (to make the negative exponent positive, you have to divide.) For example, x-3 is the same thing as 1/x3.
Polynomials cannot contain fractional exponents.
Terms containing fractional exponents (such as 3x+2y1/2-1) are not considered polynomials.
The difference in hour between full-time and part-time who work 5 hours a day is 2 working hours. How many hours per day do full-timers work?
Answer:
7
Step-by-step explanation:
The part timer works 5 hours a day
the difference between the part timer and fill time is 2
5+2=7
