Answer:
The vertex is (3,4)
Step-by-step explanation:
f (x) = x^2 - 6 x + 13
Completing the square
-6/2 = -3 and squaring it = 9
= x^2 -6x +9 +4
= ( x-3) ^2 +4
The equation is now in vertex form
a( x-h) ^2 +k
where the vertex is ( h,k)
The vertex is (3,4)
Answer:
C on edge
Step-by-step explanation:
Maurice needs 45 exam review books for the students in his math class. The local bookseller will sell him the books at $3 each. He can also purchase them over the internet for $2 each plus $35 for postage. How much does he save by accepting the better offer?
Answer: he will save $42.50
Step-by-step explanation:
45÷3=15
45÷2+35=57.50
57.50-15= $42.50
An airplane leaves an airport and flies due west 150 miles and then 170 miles in the direction S 49.17°W. How far is the plane from the airport (round to the nearest mile)? (2 points) PLEASE HELP ASAP 30 POINTS!!!!!!! need full explanation and work
Answer:
299.99 miles
Step-by-step explanation:
Since the plane traveled due west,
The total angle is 49.17 + 90
Represent that with θ
θ = 49.17 + 90
θ = 139.17.
Represent the sides as
A = 170
B = 150
C = unknown
Since, θ is opposite side C, side C can be calculated using cosine formula as;
C² = A² + B² - 2ABCosθ
Substitute values for A, B and θ
C² = 150² + 170² - 2 * 150 * 170 * Cos 139.17
C² = 22500 + 28900 - 51000 * Cos 139.17
C² = 51400 - 51000 (−0.7567)
C² = 51400 + 38,591.7
C² = 89,991.7
Take Square Root of both sides
C = 299.9861663477167
C = 299.99 miles (Approximated)
Hence, the distance between the plane and the airport is 299.99 miles
it has rained on the 6th of january twice in the last 20 years calculate the probability that it will rain on the 6th january next year
21. Which of the following is an identity? a) sin (a) cos (a) = (1/2) sin(2 a) b) sin a + cos a = 1 c) sin(-a) = sin a d) tan a = cos a / sin a
Answer:
A
Step-by-step explanation:
[tex] \sin(2 \alpha ) = 2 \sin( \alpha ) \cos( \alpha ) [/tex]
[tex] \sin( \alpha ) \cos( \alpha) = \frac{1}{2} \sin( 2\alpha ) [/tex]
What is the constant term for 4x-2y+3
Answer:
Step-by-step explanation:
3 is the constant term.
Constant term is the term without any variables
Answer:
3
Step-by-step explanation:
The constant number is the number that has no variable and just a number.
Which expressions are equivalent to -2y-8+4y−2y−8+4yminus, 2, y, minus, 8, plus, 4, y ? Choose all answers that apply: Choose all answers that apply: (Choice A) A -2(y+4)+4y−2(y+4)+4yminus, 2, left parenthesis, y, plus, 4, right parenthesis, plus, 4, y (Choice B) B 4(-2+y)-2y4(−2+y)−2y4, left parenthesis, minus, 2, plus, y, right parenthesis, minus, 2, y (Choice C) C None of the above
Answer:
C. None of the above. The correct expression is 2(y-4)Step-by-step explanation:
Given the expression -2y-8+4y, we are to find the equivalent expressed is which other expression is similar to it. This can be expressed as shown below;
Step 1: Collect the like terms of the expression
= -2y-8+4y
= (-2y+4y)-8
Step 2: Sum up the terms in parenthesis:
= (-2y+4y)-8
= 2y-8
Step 3: factor out the common terms
= 2y-8
= 2(y-4)
Hence the equivalent expression is 2(y-4).
Answer:
A and B
Step-by-step explanation:
On Khan Academy its right.
What is the domain of the function shown on the graph?
This is another way of saying "the set of all real numbers". This is because there are no restrictions we must place on x. The graph extends infinitely in both left and right directions as the arrows indicate. Any x value can be plugged in to get some y output.
In interval notation, the domain would be written as [tex](-\infty, \infty)[/tex]
Emily's family loves to work together in the garden.They have a slight preference for flowers, as 60\%60%60, percent of their plants are flowers and 40\%40%40, percent are vegetables. They have 505050 plants growing in the garden. How many vegetable plants do they have?
50 plants total, 40% are vegetables
40% = 40/100 = 0.40
40% of 50 = 0.40*50 = 20
Answer: There are 20 vegetable plantsTo make a net from a container, you start by cutting one of the seams along the edge where the two sides meet. If you wanted to make a different net for the container, what would you do differently?
Answer:
I would not separate the same edges when making a second net. Also, I would make sure that the result cannot be rotated or flipped so that it is the same as the first.
Step-by-step explanation:
3/4a−16=2/3a+14 PLEASE I NEED THIS QUICK and if you explain the steps that would be geat:) Thank youuuuuuu
Answer:
360
Step-by-step explanation:
3/4a - 16 = 2/3a + 14 ⇒ collect like terms 3/4a - 2/3a = 14 + 16 ⇒ bring the fractions to same denominator9/12a - 8/12a = 30 ⇒ simplify fraction1/12a = 30 ⇒ multiply both sides by 12a = 30*12a = 360 ⇒ answerwhat is this equation in simplest form? 9x + 26 + 7x - 17 = 2x + (-3x) + 5x
Answer:
4x+3=0 or x=-3/4
Step-by-step explanation:
9x+26+7x-17=2x-3x+5x
arrange all numbers with coefficient x at one side let's say the left hand side and constant or real numbers at the right hand side in doing that we get
9x+7x-2x+3x-5x=17-26
12x=-9
(12x)/3=-9/3
4x=-3
x=-3/4
1A-MATH
Diviwuetalls
2 Exercise 7:
Your ansv
Type you
The three angles in a triangle are labeled A, B and C.
A = 2x
B= 3x
C=4x
Private coi
1) calculate X
2) find the actual angle of B
3) find the exterior angle to B
Answer:
Value of x = 20°
Angle B = 60°
Exterior angle to B = 300°
Step-by-step explanation:
Given:
Angles of triangle.
A = 2x
B = 3x
C = 4x
We know that,
A + B + C = 180°
2x + 3x + 4x = 180°
9x = 180°
x = 20°
Value of x = 20°
Angle B = 3x
Angle B = 3(20°)
Angle B = 60°
Exterior angle to B = 360° - 60°
Exterior angle to B = 300°
Please help i need help answering these math problems i listed below
Answer:
Step-by-step explanation:
1) (-13)* .......(-13) for 35 times = (-13)³⁵
2) (2/3) * ...... * (2/3) for 4 times = (2/3)⁴
3)(-3.1)* ......(-3.1) for 4 times = (-3.1)⁴ = 92.2531
Write an absolute value equation to satisfy the given solution set shown on a number line.
Answer:
Step-by-step explanation:
|x-a|≤b
-b≤x-a≤b
add a
a-b≤x≤a+b
put a-b=-8
a+b=-4
add
2a=-12
a=-12/2=-6
-6+b=-4
b=-4+6=2
so |x+6|≤2
a man bought a car for 8500 GH cedis and he later sold it at for 9500. find his percentage gain
Answer:
11.7647059 % gain
Step-by-step explanation:
To find the gain, take the new amount and subtract the original amount
9500-8500 = 1000
Divide by the original amount
1000/8500=.117647059
Multiply by 100% to get in percent form
11.7647059 % gain
Shape 1 and shape 2 are plotted on a coordinate plane which statement about the shapes is true?
DA Shape 1 and shape 2 are not congruent.
B A translation will prove that shape 2 is congruent to shape 1.
C. A rotation and a translation will prove that shape 2 is congruent to shape 1
OD. A reflection a rotation, and a translation will prove that shape 2 is congruent to shape 1
Answer:
The answer is D. A reflection, a rotation and a translation will prove that shape 2 is congruent to shape 1.
35.
What is the equation of the line that is
parallel to y = 4x + 3 and passes through
the point (2,6)?
HELP! answer if you can!
Hi there! :)
Answer:
[tex]\huge\boxed{y = 4x - 2}[/tex]
Given line with an equation of y = 4x + 3
Parallel lines contain equivalent slopes, so a parallel line to the given equation would contain a slope of m = 4.
Plug in the coordinates of the point given, along with the slope into the equation y = mx + b where:
m = slope
y = y-coordinate of point
x = x-coordinate of point
Solve for the 'b' value, or y-intercept:
y = mx + b
6 = 4(2) + b
6 = 8 + b
b = -2
Rewrite the equation as slope-intercept form:
y = 4x - 2
Answer:
When you see the word "parallel", you know the new line will have the same slope.
parallel to y = 4x + 3
So, the new line will have a slope of 4
"Indicate the region where y≥ 4x + 3
Plot y= 4x + 3 by finding the points that make it true. For example, (y = 0, x = 3/4), (y = 2, x = 2) and so on.
y = 4x + b
b is the y intercept ( point y when x = 0)
Insert new coefficients:
+2 = 4(0) + b
b = +2
y = 4 + 2
[tex] \: [/tex]
Anna is planting in her garden the package says she needs to use 4 punds od fertilizer for 120 sqft the area of annas yard is 180 how much fertilizer is needed for the 180 sqft garden
Answer:
6 pounds
Step-by-step explanation:
The area of Anna's garden = 180 square feet
From the question, we know that:
120 square ft = 4 pounds of fertilizer
180 square ft = y
Cross Multiply
120 × y = 4 × 180
y = 4 × 180/120
y = 720/120
y = 6 pounds
Therefore, the amount of fertilizer that is needed for Anna's 180 square feet garden is 6 pounds.
Barry has been watching the geese that live in his neighborhood. The number of geese changes each week. n f(n) 1 56 2 28 3 14 4 7 Which function best shows the relationship between n and f(n)? f(n) = 28(0.5)n f(n) = 56(0.5)n−1 f(n) = 56(0.5)n f(n) = 112(0.5)n−1
Answer:
B. f(n) = 56(0.5)^n-1
Step-by-step explanation:
First, You have to find out the starting population, if you look at the problem you see the population starts at 56
f(x) = 56
Second, you know that the population goes down 50% each week so it has a decay of 0.5
f(x) = 56(0.5)
Third, you need to add the exponent of n to make it exponential. But, if you just add n then the the population would be 28 on week 1 which is incorrect. To fix that you make the exponent n-1 so when you are on week 1 it doesn't become 28 but it stays on 56, and on week 2 it's 28, ect
f(x) = 56(0.5)^n-1
Each lap around a park is 1 1⁄5 miles. Kellyn plans to jog at least 7 1⁄2 miles at the park without doing partial laps. How many laps must Kellyn jog to meet her goal?
Answer:
She needs to jog 7 laps to make sure she covers at least 7.5 miles
Step-by-step explanation:
Kelly's goal is to complete 7 1/2 miles which in decimal form is: 7.5 miles.
Each lap around the park is 1 1/5 miles, which in decimal form is written as: 1.2 miles
Then, to find how many laps she needs to complete we do the quotient:
7.5/1.2 = 6.25
which means that she needs a quarter of a lap more than 6 laps, so she needs to go for 7 laps to meet the goal
Find the measure of b
Answer:
b = 76°
Step-by-step explanation:
According to the inscribed angles proposition, the measure of an inscribed angle in a semicircle is said to be 90°.
Therefore, in the figure given, m<a = 90°
b = 180° - (90° + 14°) => sum of angles in a triangle.
b = 180° - 104°
b = 76°
16. Acme car rental agency charges a fee of $29 per day plus $0.15 per
mile. Travel Ease car rental agency charges $20 per day plus $0.25 per
mile. For a one-day trip, what mileage would make the two rates equal?
Answer:
90 miles
Step-by-step explanation:
0.15x + 29 = y ---- acme car agency
0.25 x + 20 = y ---- travel ease agency
0.15x + 29 = 0.25x + 20
9 = 0.1x
x = 90
If we did not write the equation 5x=21, instead we wrote it 21=5x,
we would get a different solution.
O True
O False
Answer:
Step-by-step explanation:
5x = 21 and 21 = 5x are identical relationships, and so the solution would be the same in both cases. (Commutative Property: order of addition/subtraction is immaterial)
Solve for y
4x + 7y +5
Ahmad has some files.
He gave 3/5 of the files and had 14 files left.
How many files did he have at first?
Answer:
The answer is 35Step-by-step explanation:
Let the number of files he had be x
He gave 3/5 of the files
That's
3/5x
After that he still had 14 files left which means when we subtract 14 from the original files we should get 3/5 of the original files
So we subtract 14 from the original number of files
That's
x - 14
We equate the two statements
that's
[tex] \frac{3}{5} x = x - 14[/tex]
Multiply through by 5
[tex]5 \times \frac{3}{5} x = 5x - 70[/tex]
We have
3x = 5x - 70
3x - 5x = 70
-2x = - 70
Divide both sides by -2
We have the final answer as
x = 35Therefore he had 35 files at first
Hope this helps you
Answer:
35 files
Step-by-step explanation:
gave=3/5
left=2/5 = 14f
had= 5/5
2/5=14
5/5
5×14÷2 = 35
what is -7 + 11 - 14 + 3 + 12
Answer:
5
Step-by-step explanation:
Answer:
5 (Follow PEMDAS left—>right)
what is the range and domian of y=(x-4)
Sofia ordered sushi for a company meeting. They change plans and increase how many people will be at the
meeting, so they need at least 100 pieces of sushi in total.
Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi. The sushi
comes in rolls, and each roll contains 12 pieces and costs $8.
Let R represent the number of additional rolls that Sofia orders.
1) Which inequality describes this scenario?
Choose 1 answer:
Answer:
The answer is given below
Step-by-step explanation:
The options are not given but I would list the inequalities needed to solve this problem.
As a result of increase in people to attend meeting, the number of sushi needed to be ordered is 100 pieces. Sofia has already ordered 24 pieces. If R is the number of additional rolls that Sofia orders.
The number of additional rolls that Sofia orders (R) must be greater than or equal to the difference between the number of Sushi needed to be ordered and the number of Sushi that has already being ordered. It is given by the inequality:
R ≥ 100 - 24
R ≥ 76
If each roll contains 12 pieces, the number of rolls needed (n) is given by:
n ≥ R/12
n ≥ 76/12
n ≥ 6.33
n ≥ 7
If each roll cost $8, the money needed to buy the sushi is given as:
Cost ≥ 8(7) ≥ $56
A taxi cab company charges a flat rate of $2.00 per trip plus $0.25 per mile of the trip. If m is the number of miles traveled on a particular trip, interpret the following expressions: a) 0.25m b) 2.00 + 0.25m
Answer:
b) 2.00 + 0.25m
Step-by-step explanation:
2.00per trip and $0.25 per mile = 2.00 + 0.25m
Answer:
see below
Step-by-step explanation:
a) 0.25m
This is the cost of the mileage alone
The cost is 25 cents per mile times m miles
b) 2.00 + 0.25m
This is the total cost of the trip
There is a 2 dollar flat rate fee plus the cost of the miles
2 dollars plus m miles at 25 cents per mile
I NEED HELP PLEASE :(
Answer:
7/8
Step-by-step explanation:
power of 1/2 is the same as square root.
√(49/64) = 7/8 since 7/8 * 7/8 = 7*7/8*8 = 49/64
