You can jog around your block twice and the park once in 10 minutes. You can jog around your block twice and the park 3 times in 22 minutes.
a. Write a system of linear equations that represents this situation.
Let x represent the number of minutes it takes you to jog around your block and y represent the number of minutes it takes you to jog around the park.
What is the system of equations?
LetterD: is 120 minutes
Since p = 60 we can plug 60 into the equation.
so instead of (p / 20) x 4 it's (60 / 20) x 4 which equals 12 minutes.
Hope this helped!
What must be added to x^2+20x to complete the square
Answer:
(x+10)^2-100
Step-by-step explanation:
Use the formula (b/2)^2 in order to create a new term to complete the square. Hope this helps :)
What percent of the students are part-time students?
Answer:
The % is 33.3%
Step-by-step explanation:
Due to:
If 600 is the 100%, then 200 what % is?
600 ---> 100%
200 ---> %?
% = [(200)*(100)]/[600]
% = 33.3%
Best regards
Which statement is false?
A. No integers are irrational numbers.
B. All whole numbers are integers.
C. No real numbers are rational numbers.
D. All integers greater than or equal to 0 are whole numbers.
Irrational numbers just means that it isn’t rational so this means that A is true. If you look up a chart with irrational,rational,real, and integer it will show that all whole numbers are integers so this means B is true. C is false. Same thing about B proves that D is true. SHORT ANSWER: C is false. I hope this helps.
In the given statement D is false.
What is Rational number ?
In mathematics, a rational number is any number that can be written as a fraction, in which the numerator (the top number) and the denominator (the bottom number) are both integers, and in which the numerator is not equal to zero. In other words which can be written in p/q form.
It is rational to consider integers as rational numbers, not as irrational, because all integers, whether positive or negative, or zero can be written as p/q, for example, 2, 3 and 5 are rational because they can be written as 2/1, 3/1 and 5/1 respectively.
Due to the fact that the rational numbers as well as the irrational numbers can be added together, we can derive real numbers. This means that all real numbers are not rational numbers, since they contain irrational numbers as well.
Hence, the given statement D is false.
Read more about Rational number here :
https://brainly.com/question/24398433
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PLEASE HELP ME, im offering 20 points!
Answer:
this is a whole math test which question do you need help with
Step-by-step explanation:
3 plus two times blank equals 17 what is the blank?
simplify -5x^4(-3x^2+4x-2)
Answer:
The correct answer is 15x⁶ - 20x⁵ + 10x⁴
Step-by-step explanation:
The given expression is -5x⁴ (-3x² + 4x - 2)
Points to remember:
xᵃ * x ᵇ = xᵃ⁺ᵇ
To find the simplified expression
-5x⁴ (-3x² + 4x - 2) = (-5x⁴ * -3x²) + (-5x⁴ * 4x ) - (-5x⁴ * 2)
= 15x⁴ ⁺² - 20x⁴ ⁺ ¹ + 10x⁴
= 15x⁶ - 20x⁵ + 10x⁴
Therefore -5x⁴ (-3x² + 4x - 2) = 15x⁶ - 20x⁵ + 10x⁴
Answer:
15x⁶-20x⁵+10x⁴ is the simplification of this expression.
Step-by-step explanation:
We have given the expression:
-5x⁴(-3x²+4x-2)
We have to simplify this expression.
-5x⁴(-3x²+4x-2)
-5x⁴(-3x²)+(-5x⁴)(4x)+(-5x⁴)(-2)
15x⁴⁺²-20x⁴⁺¹+10x⁴
15x⁶-20x⁵+10x⁴
15x⁶-20x⁵+10x⁴ is the answer.
What is the slope of the line described by the equation 6X + 4y= 8
Answer:
[tex]\large\boxed{\text{The slope}\ m=-\dfrac{3}{2}}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation of a line in the standard form:
[tex]6x+4y=8[/tex]
Convert to the slope-intercept form:
[tex]6x+4y=8[/tex] subtract 6x from both sides
[tex]4y=-6x+8[/tex] divide both sides by 4
[tex]y=-\dfrac{6}{4}x+\dfrac{8}{4}[/tex]
[tex]y=-\dfrac{3}{2}x+2[/tex]
John wants to deposit $1000 as a principle amount, with an interest of 4% compounded quarterly. Cayden wants to deposit $1000 as the principle amount, with an interest of 3% compounded monthly. Explain which method results in more money after 5 years. Show all work.
Answer:
John = $1220.19
Cayden = 1161.62
Step-by-step explanation:
To find how much they'll both get, we can use the formula:
[tex]A=P(1+\dfrac{r}{n})^{nt}[/tex]
First let's start with John.
P = 1000
r = 4% or 0.04
t = 5
n = 4 (Quarterly)
[tex]A=1000(1+\dfrac{0.04}{4})^{4(5)}[/tex]
[tex]A=1000(1+0.01)^{20}[/tex]
[tex]A=1000(1.01)^{20}[/tex]
[tex]A=1220.19[/tex]
Now let's compute for Cayden's.
P = 1000
r = 3% or 0.03
t = 5
n = 12 (Monthly)
[tex]A=1000(1+\dfrac{0.03}{12})^{12(5)}[/tex]
[tex]A=1000(1+0.0025)^{60}[/tex]
[tex]A=1000(1.00.25)^{60}[/tex]
[tex]A=1161.62[/tex]
The monthly compounding gets more yield compared to the quarterly compounding due to the number of times the amount of times it increases per year.
What is the answer to 7/5 = 10.5/b
Answer: b=14.7
Step-by-step explanation:
Answer: b=7.5
Step 1: Cross-multiply.
7/5 = 10.5/b
7*b=(10.5)*(5)
7b=52.5
Step 2: Divide both sides by 7.
7b/7 = 52.5/7
Therefore:
b=7.5
Please give me a brainlist :)
The owner of Cardo Reef Tours found when the price for a tour was $9 US dollars per person
the average number of customers was 1000 per month. When he reduced his price to $7 US dollars
per person the average number of customers increased to 1500 per month. Assuming that his
demand curve was linear, what price should he charge to obtain the largest monthly revenue?
b. If f(x) = 2x
3 − 24x, find the minimum and maximum values of f in the interval [−3,5].
Answer:
The answers for your two question problem are:
a. He should charge $7 dollars
b. Maximum value : f(5) = 130
Minimum value : f(2) = -32
Step-by-step explanation:
First problem
*When he charges $9 , the numbers of customers are an average of 1000
This means the revenue is
1000*$9 = $9000
*When he charges $7 , the numbers of customers are an average of 1500
This means the revenue is
1500*$7 = $10500
Since
$10500 > $9000
The owner should charge $7, to attract more customers and get higher revenue.
Second problem
f(x) = 2x^3 − 24x
To easily solve this problem, we can graph the equation using a calculator or any plotting tool.
Please, see attached picture
The highest point of the graph, in the interval [-3,5] corresponds to
f(5) = 130
and the lowest point :
f(2) = -32
Gabe charges $30 to mow a lawn. Nate
charges $25 to mow a lawn. Their total
combined revenue one summer was $2020.
Nate mowed 6 more lawns than Gabe.
Write a system of equations to represent
this situation. Then solve the system of
equations by substitution. Explain what the
solution means.
g mowed 5 lawns and earned $150
Nate mowed 40 lawns and Gabe mowed 34 lawns for the equal earn of money. The value of x is 34.
What is the linear system?It is a system of an equation in which the highest power of the variable is always 1. It is a combination of infinite points side by side.
Given
Gabe charges $30 to mow a lawn.
Nate charges $25 to mow a lawn.
Their total combined revenue one summer was $2020.
Nate mowed 6 more lawns than Gabe.
Let the number of lawns mowed by Gabe be [tex]\rm x[/tex].
Then the number of lawns mowed by Nate be [tex]\rm x + 6[/tex].
Then the equation will be
[tex]\rm 30x + 25(x+ 6) = 2020[/tex]
On simplifying, we have
[tex]\begin{aligned} \rm 30x + 25x + 150 &= 2020\\\\\rm 55x &= 1870\\\\\rm x &= 34\end{aligned}[/tex]
Thus, Nate mowed 40 lawns and Gabe mowed 34 lawns for the equal earn of money. The value of x is 34.
More about the linear system link is given below.
https://brainly.com/question/20379472
Tom throws a ball into the air. The ball travels on a parabolic path represented by the equation h = -8t 2 + 40t, where h represents the height of the ball above the ground and t represents the time in seconds. The maximum value achieved by the function is represented by the vertex. Use factoring to answer the following:
How many seconds does it take the ball to reach its highest point?
What ordered pair represents the highest point that the ball reaches as it travels through the air?
Hint: because parabolas are symmetric, the vertex of a parabola is halfway between the zeroes of the quadratic.
Answer:
Time to highest point: 5/2, or 2.5 seconds
Ordered pair: (5/2, 50)
Step-by-step explanation:
Find the vertex of h(t). This will be the highest point of the ball
Find the x coordinate of the vertex with the formula: x = -b/(2a)
x = -40/[2(-8)] = -40/-16 = 5/2
to find the y value, plug 5/2 into the equation and solve
h(5/2) = -8(5/2)² + 40(5/2)
h(5/2) = -8(25/4) + 200/2
h(5/2) = -200/4 + 100
h(5/2) = 50
So the ball reached a maximum height of 50 feet
Final answer:
It takes 2.5 seconds for the ball to reach its highest point. The ordered pair representing the highest point is (2.5, 50), where the ball reaches a height of 50 meters.
Explanation:
The equation h = -8t^2 + 40t describes the height of a ball thrown into the air over time, where h is the height above the ground and t is time in seconds. To find how many seconds it takes for the ball to reach the highest point, we find the time at which the vertex of the parabola occurs since the vertex represents the maximum height.
We know that the ball will reach its highest point halfway between the times when it is at ground level (i.e., when h = 0). Factoring the quadratic equation 0 = -8t^2 + 40t gives us:
0 = t(-8t + 40)
0 = t(0, -8t + 40)
Setting each factor equal to zero gives us two values of t:
t = 0 s (when the ball is first thrown)
-8t + 40 = 0 => t = 5 s (when the ball hits the ground again)
Thus, the time to reach the highest point is halfway between 0 s and 5 s, which is 2.5 seconds.
The ordered pair representing the highest point is found by substituting t = 2.5 s into the original equation:
H = -8(2.5)^2 + 40(2.5)
H = -50 + 100
H = 50 meters.
Therefore, the ordered pair representing the highest point the ball reaches is (2.5, 50).
Which method is the most efficient method to use to solve x^2+6x-7=0?
A) Using the quadratic formula
B) Factoring
C) Isolating the x^2 term and finding the square root of both sides
D) All three methods would be efficient
Answer:
A
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
In my opinion factoring is the better approach here
Given
x² + 6x - 7 = 0 ← in standard form
Consider the factors of the constant term (- 7) which sum to give the coefficient of the x- term (+ 6)
The factors are + 7 and - 1, since
7 × - 1 = - 7 and + 7 - 1 = 6, hence
(x + 7)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 7 = 0 ⇒ x = - 7
x - 1 = 0 ⇒ x = 1
a school club needs 350 feet of rope for a project. they have the amounts of rope listed below.
4 pieces of rope that are each 14 yards in length
1 piece of rope that is 10.5 yards in length
1 piece of rope that is 101.25 feet in length. how much additional rope , in feet, does the school club need in order to have enough rope for their project?
Answer:
They need 57.5 more feet of rope
Step-by-step explanation:
Add all the lengths of rope together in feet ( so convert the yards to feet; 1 yd= 3 ft) and then subtract that number from 350!
Hope this helped! <3
I think this is correct
Answer:
The school club needs additional 49.25 feet of rope.
Step-by-step explanation:
Total length of rope needed = 350 feet
Available lengths are :
4 pieces of rope that are each 14 yards in length. Total length = [tex]4\times14=56[/tex] yards
1 piece of rope that is 10.5 yards in length.
Total yards = [tex]56+10.5=66.5[/tex] yards
Now converting yards to feet as the final answer will be in feet.
1 yard = 3 feet
So, 66.5 yards = [tex]3\times66.5=199.5[/tex] feet
1 piece of rope that is 101.25 feet in length.
Total rope in feet = [tex]199.5+101.25=300.75[/tex] feet
As 350 feet of rope is needed, the club needs more rope of 350-[tex]300.75=49.25[/tex] feet
Therefore, the school club needs additional 49.25 feet of rope.
H/6-1=-3 solve for H
Add 1 to both sides
h/6 = -3 + 1
Simplify -3 + 1 to -2
h/6 = -2
Multiply both sides by 6
h = -2 * 6
Simplify 2 * 6 to 12
h = -12
which expression is equivalent to 24x + 12?
You can factor 12 from both terms to get
[tex]24x+12 = 12(2x+1)[/tex]
Multiply: (−4x + 3)(−2x2 − 8x + 2) A) 8x3 − 26x2 − 32x + 6 B) 8x3 + 38x2 + 32x + 6 C) 8x3 + 26x2 − 32x + 6 D) 8x3 − 38x2 + 16x + 6
Answer:
Your answer is 8x3 + 26x2 − 32x + 6
So it's (c)
Answer: A) 8 x 3 + 26 x 2 − 32 x + 6
Step-by-step explanation:
Last summer bills lawn mowing service made a $4,500 profit. This summer his profit was $5,220. What percent increase was this?
20 points
Will mark brainliest
Show work
Answer:
The percent increase was [tex]16\%[/tex]
Step-by-step explanation:
we know that
Using proportion
Let
x------> the percent increase
[tex]\frac{100\%}{\$4,500}=\frac{x\%}{\$5,220-\$4,500} \\ \\x= 720*100\%/4,500\\ \\x=16\%[/tex]
The profit from Bill's lawn mowing service increased from $4,500 to $5,220, which is a 16 percent increase.
To calculate the percent increase in Bill's lawn mowing service profit, we would subtract the original profit from the new profit and then divide by the original profit. Finally, we multiply by 100 to get the percentage.
Original Profit = $4,500
New Profit = $5,220
Profit Increase = New Profit - Original Profit = $5,220 - $4,500 = $720
Percent Increase = (Profit Increase / Original Profit) x 100
Percent Increase = [tex]\frac{720}{4500}[/tex] x 100
Percent Increase = 0.16 x 100
Percent Increase = 16%
Therefore, the profit increased by 16 percent.
A company produces items in small batches. The machinery needs to warm up before the items can be produced. The scatterplot show the time needed to produce batches of different number of items.
Answer:
C.
Step-by-step explanation:
The answer is C since the y intercept is 20.
Answer:
Statement C is true.
Step-by-step explanation:
In this question we will go through each statement.
(A). The equipment starts producing items after about 25 minutes of warning up - False
Because machine takes 20 minutes to produce the items.
(B). Each item requires about 12 minutes of production time - False
(C). The equipment starts producing items after about 20 minutes of warming up - True
(D) Each item requires about 3 minutes of production time. - False
Which of the following best describes the solution to the system of equations below?
3x + 5y = 9
3x + 5y = 15
Answer: Option D
Step-by-step explanation:
The equation of the line in slope intercept form is:
[tex]y=mx+b[/tex]
Where m is the slope and b the y-intercept.
Solve for y from both equations:
[tex]5y=-3x+9\\y=\frac{-3}{5}x+\frac{9}{5}[/tex]
[tex]5y=-3x+15\\y=\frac{-3}{5}x+3[/tex]
As you can see, the slopes of the lines are equal, therefore, they are parallel.
If the lines are parallel then the system of equtions has no solution.
Answer:
Choice D is correct answer.
Step-by-step explanation:
We have given a system of equations.
3x + 5y = 9 eq(1)
3x + 5y = 15 eq(2)
We have to find the description of the solution of equations.
y = mx+c is the slope-intercept of equation of line where m is slope and c is y-intercept.
Eq(1) can be written as:
y = -3/5x + 3 where slope is -3/5.
Eq(2) can be written as:
y = -3/5x+5 where slope is -3/5.
Equations with equal slopes are of parallel lines and parallel lines have no solution.Hence, system has no solutions.
Choice D is correct answer.
need help with this math problem
Answer:
x = 6
Step-by-step explanation:
Complementary angles = angles that add up to 90 degrees.
Therefore 8x - 30 + 5x + 42 = 90
13x + 12 = 90
Subtract 12 from both sides and then divide each side by 13.
x = 6
What is the surface area of the cylinder?
answer is
= 1.312.53 ft²
Sandy mixed 9 ml of an acidic solution with 8 ml of a 42% acidic solution, to make a 45% acidic solution. Find the percent acid concentration of the first solution.
Answer:
47.67%
Step-by-step explanation:
Amount of 1st solution = 9 ml
Let the percentage acid concentration of 1st solution is x%
Amount of 2nd solution = 8 ml
Percentage acid concentration of 2nd solution = 42%
Percentage acid concentration of the mixture = 45%
Amount of the mixture = 8 + 9 = 17 ml
1st Solution + 2nd Solution = Mixture
x% of 9 ml + 42% of 8 ml = 45% of 17 ml
[tex]0.09x + 3.36 = 7.65\\\\ 0.09x = 7.65 - 3.36\\\\ 0.09x = 4.29\\\\ x = \frac{4.29}{0.09}\\\\ x = 47.67[/tex]
Thus, the percent acid concentration of first solution is 47.67%
Find the slope of a line perpendicular to y = 3x + 7
Answer:
-1/3
Step-by-step explanation:
The slope of the line has the form y = mx + b where m is the slope. Here the slope is m = 3. A line perpendicular to it will have a negative reciprocal slope. The negative reciprocal of 3 is -1/3.
please help me my queston is the photo
10.54cm2
This is the senseAnswer:
the answer is 10.54 cm2
Step-by-step explanation:
Mrs. Jackson is covering her bulletin board with new paper. What formula should she use to figure out how much paper to buy?
Answer: A = L x W
Step-by-step explanation:. Mrs. Jackson should use the formula to calculate area in order to figure out how much paper to buy. The formula is Area = Length x Width. This will tell her exactly how much paper she will need to cover the bulletin board.
Answer:
Step-by-step explanation:
Something of this size could be measured in either ft² or in².
Area of a rectangle is determined by multiplying the width by the height. In this case the bulletin board will be installed vertically, so let's say that
Area of board = (width)(height)
If, for example, the width were 6 feet and the height 3.5 feet, the area of this board would be (6 ft)(3.5 ft) = 21 ft²
Since 1 ft = 12 in, this 6 foot by 3.5 foot board would be 72 inches by 42 inches.
BEST ANSWER GETS BRAINLIEST For the expression 6 − y + 3, determine the coefficient for the variable term
−1
0
3
6
What is the value of 4 + 5x when x = 3? =
11
12
17
19
1. The answer would be -1 because the variable term is -y which can also be written as -1y and the coefficient is the number before the variable.
2. The answer would be 19. If you plug 3 into the equation for x you would get 4 + 5(3). Five times three is 15, and 15 plus 4 is 19.
Plz Help me 50 points to who ever answers firstt
Answer:
[tex]\boxed{\bold{57 \ Ft.}}[/tex]
Step-by-step explanation:
Assignment: Find area of rectangle without triangleArea of whole rectangle including triangle: 66 Feet
(6 * 11 = 66)
Area of Triangle: [tex]\bold{\frac{1}{2}Base \ \cdot \ Height }[/tex]
Height: 3
Base: 6 (Solved by using this: (11 - 2 + 3))
Half of base: 3
3 * 3 = 9
66 - 9 = 57