How would I solve 5(x -2) =2x +16?
Answer: First, multiply 5 by x-2 to get 5x-10. We now have 5x-10=2x+16. Subtract 2x on both sides: 3x-10=16. Add 10 to both sides: 3x=26. Lastly, divide by 3x to isolate x: x=8.6666667
The table shows the temperature (in degrees) for eight consecutive days as well as the respective number of ice cream cones an ice cream shop sold on each of these days.
Temperature: 68, 77, 83, 85, 89, 94, 96, 99
number of cones: 403, 447, 457, 465, 489, 503, 543, 576
About how many ice cream cones woud you expect the shop to sell if the temperature one day is 106 degrees? Find a line of best fit for this data and use it to make your prediction.
A. 579
B. 585
C. 602
D. 617
Answer:
B. 585
Step-by-step explanation:
A graph of the scatter plot and line of best fit is attached.
The temperature in this problem will be the independent variable, or x. This is because we are assuming that the number of ice cream cones sold depends on the temperature; this means the number of ice cream cones will be the dependent variable, or y.
This means in our graphing calculator, we will enter temperature in the first list and the number of cones in the second.
After drawing the scatter plot, we run the linear regression; we get the values for a and b in our equation, y = ax+b:
a = 5.08
b = 46.59
This gives us the equation y = 5.08x + 46.59.
Entering our temperature, 106, in for x gives us
y = 5.08(106) + 46.59 = 585.07 ≈ 585
Answer:
B
Step-by-step explanation:
585 Just took the test. Reference above to see explanation.
what is the ratio of 36 dm to 6 m
Answer:
Step-by-step explanation:
Ratio means division. 36 dm / 6 dm = 6. Cancel out dm.
As a ratio, it would technically be 6:1
The ratio of boys and girls in a classroom is 15 to 12 what is the ratio of boys to total students
Hi There!
Answer:
15 to 27
Step-by-step explanation:
Boys: 15
Girls: 12
Total Students: 15 + 12 = 27
Boys to Total Students = 15 to 27
Hope This Helps :)
To find the ratio of boys to total students in a classroom, divide the number of boys by the total number of students. In this case, the ratio is 5/9.
Explanation:To find the ratio of boys to total students in a classroom, we need to know the total number of students in the classroom. Let's assume that there are 27 students in total.
The ratio of boys to girls is given as 15 to 12. This means that for every 15 boys, there are 12 girls. To find the ratio of boys to total students, we add up the number of boys and divide by the total number of students.
In this case, the number of boys is 15 and the total number of students is 27. So the ratio of boys to total students is 15/27. This can be simplified to 5/9.
Learn more about ratio here:https://brainly.com/question/32531170
#SPJ2
What is the probability the spinner will land on a dotted region?
A- 25%
B- 33%
C-37.5%
D- 50%
Dotted Regions Include- 25%, 12.5%, and 12.5%
Stripped Regions Include- 12.5%, and 25%
White Region Includes- 12.5%
The probability for the spinner landing on the dotted region is 1/2.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lies in the close interval of 0 and 1 [0,1].
The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.
The probability for the given case is evaluated as,
P(Spinner lands on dotted region) = Total space for dotted region/100
= (25 + 12.5 + 12.5)/100
= 50/100
= 1/2
Hence, the probability that the spinner will land on a dotted region is 1/2.
To know more about probability click on,
https://brainly.com/question/11234923
#SPJ2
A piece of steel pipe 12.5 feet long weighs 158 pounds. How much does a piece of the same steel pipe 18.75 feet long weigh?
Answer:
18.75 feet of steel pipe weighs 237 pounds
explanation:
find out how much 1 feet weighs than u can find out how much 18.75 feet.
by doing it like this
158÷ 12.5
=12.64
1 feet equals 12.64 pounds
12.64× 18.75
=237 pounds this is the answer
i do apologize if it wrong
Answer:
That new length would weight 237lbs
Step-by-step explanation:
To find this, we first need to find the weight per foot of the pipe. We can do this by taking the total weight and dividing by length.
158lbs/12.5ft = 12.64 pounds per feet.
Now we can multiply the rate by the new length.
12.64 pounds per feet * 18.75ft = 237lbs
Which of the following best describes the relationship between (x + 1) and the polynomial x2 - x - 2?
A. It is impossible to tell whether (x + 1) is a factor.
B. (x + 1) is not a factor.
C. (x + 1) is a factor.
Answer:
C
Step-by-step explanation:
to factor x² - x - 2
consider the factors of the constant term which sum to give the coefficient of the x-term.
the factors are - 2 and + 1 since - 2 × 1 = - 2 and - 2 + 1 = - 1
x² - x - 2 = (x - 2)(x + 1), hence (x + 1) is a factor
The relationship between (x + 1) and the polynomial x² - x - 2 is that ( x + 1) is a factor of x² - x - 2.
What is a polynomial?A mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a non negative integral power.
How to know whether there is any relation between (x + 1) and the polynomial x² - x - 2?The given polynomial is x² - x - 2.
Here we should try to factorise the polynomial.x² - x - 2
= x² - 2x + x - 2
= x( x - 2) + 1( x - 2)
=( x - 2) ( x + 1)
So we can see that, ( x + 1) is a factor of x² - x - 2.
So, option C is correct.
Find more about "Factorization" here : https://brainly.com/question/25829061
#SPJ2
The radius of the circle whose equation is (x + 4)² + (y - 2)² = 36 is
Answer: 6
The equation given to you is in the form (x-h)^2 + (y-k)^2 = r^2
The right hand side 36 is in the place of r^2, so r^2 = 36 leading to r = 6 after you apply the square root to both sides.
48 POINTS! PLEASE HELP!
show your work
Answer:
c. y = 1.25
Step-by-step explanation:
The equation for direct variation is
y = kx,
where k is the constant of proportionality.
We can use the given values of x and y to find k for this case.
y = kx
-10 = k * 40
k = -10/40
k = -0.25
The equation for this case is
y = -0.25x
Now we let x = -5 and solve for y.
y = -0.25x
y = -0.25(-5)
y = 1.25
Answer: c. y = 1.25
Answer:
c y = 1.25
Step-by-step explanation:
The equation for direct variation is y= kx
If we know y and x we can solve for k
-10 = k*40
Divide each side by 40
-10/40 =k
-1/4 =k
The equation for this direct variation is
y =-1/4 x
Given that x =-5
y = -1/4 *-5
y = 5/4
y = 1.25
Need help with 5-8, will give brainliest to best and most accurate answer
Answer:
#5: 80mm, #6: 50yd, #7: 36m, #8: 32ft
Step-by-step explanation:
For #5:
The ratio between the two shapes is 24/15 = 8/5, based on the corresponding sides.
So, multiplying 8/5 with the smaller shape's perimeter of 50 would give you 80mm, which is the bigger shape's perimeter.
For #6:
The ratio between the two shapes is 15/9 = 5/3, based on the corresponding sides.
So, multiplying 5/3 with the smaller shape's perimeter of 30 would give you 50yd, which is the bigger shape's perimeter.
For #7:
The ratio between the two shapes is 12/4 = 3, based on the corresponding sides (You can also check this with 15/5).
So, multiplying 3 with the smaller shape's perimeter of 12 would give you 36m, which is the bigger shape's perimeter.
For #8:
The ratio between the two shapes is 12/21 = 4/7, based on the corresponding sides.
So, multiplying 4/7 with the bigger shape's perimeter of 56 would give you 32ft, which is the smaller shape's perimeter.
Hope this helps! Have a nice day!
Help with #7 please I don’t understand
Answer:
A
Step-by-step explanation:
(2x^2 + 3x - 4) (x + 4)
FOIL.
2x^2 times x = 2x^3
3x times x is 3x^2
-4 times x = -4x
2x^2 times 4 = 8x^2
3x times 4 = 12 x
-4 times 4 = -16
Combine like terms to get 2x^3 + 11x^2 + 8x - 16.
The lunch special at Jimmy John’s costs $5.60. The math club has $50.40 in its treasury. How many lunch specials can the club buy? Write and solve an inequality. Show your work
They can afford 9. You work it out by dividing 50.40 / 5.60
The math club can buy at most 9 lunch specials from Jimmy John's with the money in its treasury.
To determine how many lunch specials the math club can buy, we need to divide the total amount of money in the treasury by the cost of one lunch special. Let's denote the number of lunch specials the club can buy as \( n \).
The cost of one lunch special is $5.60, which can be written as a fraction of dollars as[tex]\( \frac{560}{100} \)[/tex]to make the calculations easier. The total amount of money in the treasury is $50.40, which can similarly be written as [tex]\( \frac{5040}{100} \).[/tex]
Now, we set up the inequality to find the maximum number of lunch specials \( n \) that can be bought without exceeding the treasury's funds:
[tex]\[ \frac{560}{100}n \leq \frac{5040}{100} \][/tex]
To solve for \( n \), we divide both sides of the inequality by the cost of one lunch special:
[tex]\[ n \leq \frac{\frac{5040}{100}}{\frac{560}{100}} \][/tex]
[tex]\[ n \leq \frac{5040}{560} \][/tex]
[tex]\[ n \leq 9 \][/tex]
Since \( n \) must be an integer (you can't buy a fraction of a lunch special), the math club can buy 9 lunch specials at most. Any more than that, and they would not have enough money. Thus, the maximum number of lunch specials the club can buy is 9."
Cecily is comparing two checking accounts. Checking account A has a monthly fee of $16 and a per-check fee of $0.08, while checking account B has monthly fee of $14 and a per-check fee of $0.12. She want to know how many checks she would need to write per month for the accounts to charge the same amount in fees.
Part 1: If x represents the number of checks Cecily writes per month, what expression represents the monthly fee in dollars charged by checking account A?
Part 2: What equation can be set up to solve for the number of checks Cecily would need to write per month for the accounts to charge the same in fees?
Answer:
(1) 0.08x + 16
(2) 0.08x + 16=0.12x + 14
Step-by-step explanation:
Checking account A has a monthly fee of $16 and a per-check fee of $0.08
Per check fee is a constant rate that is 0.08
Let x represents the number of checks Cecily writes per month
1 check fee = 0.08
x checks fee = 0.08x
monthly fee is $16 , we add that as well
So total monthly fee charges for account A is
0.08x + 16
checking account B has monthly fee of $14 and a per-check fee of $0.12.
1 check fee = 0.12
x checks fee = 0.12x
monthly fee is $14 , we add that as well
So total monthly fee charges for account B is
0.12x + 14
(2) To find number of checks write per month for the accounts to charge the same in fees
WE set both expression , account A = account B
0.08x + 16=0.12x + 14
Subtract 0.12x on both sides
-0.04x + 16 = 14
Now subtract 16 on both sides
-0.04x = -2
Divide by -0.04 on both sides
So x= 50
What is the proportional relationship of 15 mL to 3.75 L
To find the proportional relationship of 15 mL to 3.75 L, we first convert 3.75 L to milliliters, which is 3,750 mL. Then, we set up a proportion and solve for the unknown liter value. The proportional relationship of 15 mL to 3.75 L is 0.05625 L.
Explanation:The student is asking about the proportional relationship between two different units of liquid volume: milliliters (mL) and liters (L). To establish this relationship, a conversion is needed, since 1 liter is equivalent to 1,000 milliliters.
First, we need to convert 3.75 liters to milliliters:
Now, let's express the proportion:
X varíes directly with y and z. X =1200 when y =20 and z=30 find x when y=10 and z=20
Answer:
Value of x = 400
Step-by-step explanation:
Joint variation states that describes a situation where a variable depends on two (or more) other variables, and varies directly with some of them.
Given: x varies directly with y and z.
i.e [tex]x \propto y[/tex] and [tex]x \propto z[/tex]
then we have the joint variation as;
[tex]x = k yz[/tex] ......[1] where k is the constant variation.
Substitute the value of x =1200 when y =20 and z = 30 to solve for k;
[tex]1200 = k (20)(30)[/tex]
Simplify:
[tex]1200 = 600k[/tex]
Divide both sides by 600 we get;
[tex]k = 2[/tex]
Now, substitute k =2 , y =10 and z = 20 to find x;
Using [1] we have;
[tex]x = 2 \times (10)(20) = 2 \times 200[/tex]
Therefore, the value of x is, 400
Answer:
x = 400
Step-by-step explanation:
given that x varies directly with y and z the the equation relating them is
x = kyz ← k is the constant of variation
to find k use the given condition x = 1200 when y = 20 and z = 30
k = [tex]\frac{x}{yz}[/tex] = [tex]\frac{1200}{20(30)}[/tex] = 2, thus
x = 2yz is the direct variation equation
when y = 10 and z = 20, then
x = 2 × 10 × 20 = 400
the graph shows the height of a gold ball driven from a tee box as a function of the horizontal distance that it travels
equation in intercept form
equation in vertex form
will give brainliest
Answer:
Intercept form y=-5/64 (x) (x-160)
Vertex form y = -5/64 (x-80)^2 + 500
Step-by-step explanation:
The equation for a parabola in intercept form is y =a(x-p) (x-q)
where p and q are the intercepts. We know that it intersects the x axis at 0 and 160, so we can substitute these in
y = a(x-0) (x-160)
y = a(x) (x-160)
We have to calculate the value of a.
Using the point (80, 500)
500 = a(80) (80-160)
500 = a (80) *(-80)
500 = a *-6400
Divide each side by -6400
a = -500/6400
a = -5/64
So the equation in intercept form is
y = -5/64 (x) (x-160)
The equation for a parabola in vertex form is
y = a(x-h)^2 +k
We know the vertex is (80,500)
y = a(x-80)^2 + 500
We need to pick a point to solve for a. (0,0)
0 = a(0-80)^2 + 500
Subtract 500 from each side.
-500 = a(-80)^2
-500 = a (6400)
Divide by 6400
-500/6400 = a
-5/64 = a ( Does this look familiar?)
y = -5/64 (x-80)^2 + 500
A turtle crawls 3 yards in an hour. How far will it crawl in 2 hours?
Answer:
It will crawl 6 yards in 2 hours. If you can, please mark me the brainliest :)
Step-by-step explanation:
3 yards an hour * 2 hours = 6 yards per hour.
Answer: 2hrs = 120 mins
1km = 100,000cm
120 x 38 = 4560cm
Can someone walk me through this? (Geometry - Triangle Congruence Proof using SAS Theorem)
Answer: sample
Step-by-step explanation:
Which statement about a right triangle is true? The length of each leg equals 12 of the hypotenuse.
The square of the hypotenuse is equal to the sum of the squares of the legs.
One leg is always longer than the hypotenuse.
A right triangle can have only one obtuse angle.
Answer:
I didn’t know you could have more than 2 answers that’s pretty cool
Step-by-step explanation:
The total distance around Dave's rectangular-shaped bedroom is 220 feet. The width of the room is 50 feet. What is the area of Dave's bedroom in square feet?
The area of Dave's bedroom, which is a rectangle with a length of 60 feet and a width of 50 feet, is calculated to be 3000 square feet.
Explanation:The subject of this question is Mathematics, specifically geometrical calculations related to rectangles. The question provides the perimeter and one side length of a rectangle (Dave's bedroom) and asks for the area. First, remember that the perimeter of a rectangle is calculated by the formula 2(length + width). In the given problem, the total distance around the room (or the perimeter) is 220 feet and the width of the room is 50 feet. We can use the perimeter formula to find the length: 220 = 2(length + 50), so length = (220/2) - 50, which is 60 feet.
Now, the area of a rectangle is calculated by the formula length x width. In Dave's room, the length is 60 feet and the width is 50 feet. So Area = Length x Width = 60 feet x 50 feet = 3000 square feet. Thus, the area of Dave's bedroom is 3000 square feet.
Learn more about Area of Rectangle here:https://brainly.com/question/8663941
#SPJ12
To find the area of Dave's rectangular-shaped bedroom, multiply the length by the width which is 6000 sq ft.
Explanation:To find the area of Dave's bedroom, we need to determine the length of the room.
Since the total distance around the room is 220 feet and the width is 50 feet, we can subtract twice the width from the total distance to find the length.
This gives us a length of 220 - 2(50) = 120 feet.
The area of a rectangle is found by multiplying the length by the width, so the area of Dave's bedroom is 120 * 50 = 6000 square feet.
Learn more about Area of a rectangle here:https://brainly.com/question/15218510
#SPJ12
Helppppppppppp me pleaseeeeeee
ILL GIVE BRAINLIEST ANSWER IN 5 MIN
Which of the sets of ordered pairs represents a function?
A = {(−5, 5), (−2, 2), (2, −2), (5, −5)}
B = {(4, 2), (3, −2), (9, 4), (11, −3)}
Select one:
a. Only A
b. Only B
c. Both A and B
d. Neither A nor B
Answer:
D.
Step-by-step explanation:
Function does not have duplication of a number.be
The A choice contains duplicates of both 2 and -2.
The B choice contains a duplicate of 4.
Therefor, it must be D.
==============================================
Which of the sets of ordered pairs represents a function?
A = {(−5, 5), (−2, 2), (2, −2), (5, −5)}
B = {(4, 2), (3, −2), (9, 4), (11, −3)}
Select one:
a. Only A
b. Only B
c. Both A and B
d. Neither A nor B
A calcium ion has 20 protons and 18 electrons. Each proton has a +1 charge and each electron has a -1 charge. What is the charge of the calcium ion?
Answer:
Ca^(2+) or the charge is 2 plus or just 2
Step-by-step explanation:
Charge on the calcium ion = 20*(+1) + 18*(-1) = 20 - 18 = 2
The charge on the calcium ion is +2
Help plz
Eleven students are lined up at the drinking fountain. Every other student is a boy. The first, third, fifth, and seventh students are boys. Which other ones are boys?
Answer:
The 9th and 11th students are also boys.
Step-by-step explanation:
Every other student is a boy. Since the 7th student is a boy this means the 8th student is a girl.
You can also think of it with odd numbers. Every odd numbered student is a boy.
Please help me with number 2,3,4,5,6 THANK YOU
Answer:
I will help you with question number 2.
48:
12*4
Step-by-step explanation:
12*4=48
Luke and Aiden go to the movie theater and purchase refreshments for their friends.
Luke spends a total of $30.50 on 8 bags of popcorn and 2 drinks.
Aiden spends a total of $49.00 on 7 bags of popcorn and 6 drinks.
Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink.
Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.
Answer:
30.50 = 8p +2d
49= 7p +6d
The price of a bag of popcorn is $2.50
Step-by-step explanation:
p = price of popcorn
d = price of drinks
Luke costs:
30.50 = 8p +2d
Aiden
49= 7p +6d
I will multiply Lukes equation by -3 so I can use elimination on the d variable
-3 (30.50) =-3( 8p +2d)
-91.50 = -24p -6d
Now add the modified equation to Aidens equation
49 = 7p +6d
-91.50 = -24p -6d
-------------------------
-42.5 = -17p
Divide each side by -17
-42.50/-17 = -17p/-17
2.5 = p
Each popcorn costs 2.5
A coffee maker costs $124.46. It is marked down 40%.
What is the final price of the coffee maker after it is marked down?
Hi There!
Step-by-step explanation:
40% = 0.4
124.46 * 0.4 = $49.784 (Discount)
124.46 - 49.784 = $74.676 (Sale Price)
74.676 = 74.68
Answer:
$74.676 or $74.68
Hope This Helps :)
Answer:
The cost would be $74.68
Step-by-step explanation:
To find this amount, multiply the original price by the percentage you would be paying. Since the mark down is 40%, we know that the amount paid is 60%. So multiply that by the original cost.
$124.46 * 60% = $74.68
A car salesperson earns 5.8% commision on every car sold. How much commision will the salesperson earn on the sale of a 28,400 car?
Answer:
1647.2
Step-by-step explanation:
5.8% times 28,400 = 1647.2
5.8% = 5.8/100 = .058
so .058 times 28,400 = 1647.2
Final answer:
To find the commission, convert the rate to decimal by dividing by 100 then multiply by the sale price. A salesperson earns 5.8% commission, resulting in $1,647.20 for a $28,400 car.
Explanation:
To calculate the commission a car salesperson earns on the sale of a car, you first need to understand that commission is a percentage of the sale price they receive as their payment. In this case, the salesperson earns a 5.8% commission on each car sold. To find out how much commission they would earn on a $28,400 car, the following calculation is performed:
Sale price of car = $28,400
Commission rate = 5.8%
First, convert the commission rate from a percentage to a decimal by dividing by 100:
5.8% / 100 = 0.058
Next, multiply the sale price by the decimal commission rate:
$28,400 x 0.058 = $1,647.20
Therefore, the commission earned on the $28,400 car is $1,647.20.
Write an equation of the line that is perpendicular to -x + y = 5 and passes through the point (2, -5). A) y = x - 7 B) y = x - 5 C) y = x - 3 D) y = -x - 3
Answer:
D) y = -x - 3
Step-by-step explanation:
Step 1. Find the slope (m₁) of the original line
The equation for the original line is
-x + y = 5 Add x to each side
y = x + 5
slope = m₁ = 1
Step 2. Find the slope (m₂) of the perpendicular line
m₂ = -1/m₁ Substitute the value of m₁
m₂ = -1/1
m₂ = -1
====================
Step 3. Find the equation for the perpendicular line
y = mx + b Substitute the value of m₂
y = -x + b
The line passes through (2, -5).
-5 = -2 + b Add 2 to each side
b = -3
y = -x - 3
In the image, below the graph of your original equation is the red line.
The blue line passing through (2, -5) is the perpendicular line.
Please help! 50 POINTS!!!
Answer:
f(x) = 2/3 x +3
Step-by-step explanation:
We know the y intercept ( where it crosses the y axis) is 3
We can calculate the slope from 2 points (-3,1) and (0,3)
Slope = (y2-y1)/(x2-x1)
= (3-1)/(0--3)
= (3-1)/(0+3)
= (2/3)
The slope is 2/3
Since we know the slope and the y intercept, we can use the slope intercept form
y= mx+b
y = 2/3 x+3
f(x) = 2/3 x +3