Answer:
If one number is x, the other is (96 - x)...since if you add those two together, you will get 96..and the product is x(96 - x) = 96x - x^2
Since this is a quadratic function (x to the power of 2), it is a parabola. More specifically, it is a parabola opening downwards, because there is a negative in front of the x squared. Because it downward facing the maximum value of x is going to be where the vertex is. The x value of the vertex can be found by taking the negative of b (which is the number in front of teh x) over a squared (which is the number in front of the x squared which in this case is 1)
So x = -96 / 2(-1) = -96/-2 = 48
Since as we first stated one number is x, the first number is 48
The second number will be 48, because we stated the second number to be 96-x
Therefore 48 times 48 will give you the maximum product 2304.
Hope This Helps!!!!!!!!!!!!!!
Answer:
3,600
Step-by-step explanation:
x + y = 120
y = 120 - x
Product "P"
P = x × y = x(120-x) = 120x - x²
P = -(x² - 20x)
= -(x² - 2(x)(60) + 60² - 60²)
= -(x - 60)² + 3600
Max value is 3,600
how can you find the differnt between points
Answer:
subtract one from the other
Step-by-step explanation:
You find the difference between points the same way you find any difference: you subtract one from the other.
Points are generally described by an ordered pair. When you subtract one point from the other, you subtract corresponding parts of the ordered pair:
(a, b) - (c, d) = (a-c, b-d)
__
Sometimes, when you're interested in finding the difference between points (x, y), you want to do something different with the y-difference than you do with the x-difference.
For example, the slope of a line is calculated as the ratio of the y-difference to the x-difference. The length of a line segment is the root of the sum of the squares of the differences.
Kate bought $23.40 worth of two types of bird seed. Thistle bird seed sells for $1.60 per pound
and wild bird seed sells for $0.95 per pound. If she bought 12 pounds of wild bird seed, write
and solve a linear equation to find the amount of thistle bird seed she purchased
Answer:
The amount of thistle bird seed she purchased was 7.5 pounds
Step-by-step explanation:
Let
x ----> the amount in pounds of thistle bird seed she purchased
x ----> the amount in pounds of wild bird seed she purchased
we know that
Kate bought $23.40 worth of two types of bird seed.
so
[tex]1.60x+0.95y=23.40[/tex] ----> equation A
She bought 12 pounds of wild bird seed
so
[tex]y=12\ pounds[/tex]
substitute the value of y in the equation A
[tex]1.60x+0.95(12)=23.40[/tex]
solve for x
[tex]1.60x=23.40-11.40\\1.60x=12\\x=7.5\ pounds[/tex]
therefore
The amount of thistle bird seed she purchased was 7.5 pounds
Kate bought 7.5 pounds of thistle bird seed.
Since Kate bought $ 23.40 worth of two types of bird seed, thistle bird seed sells for $ 1.60 per pound and wild bird seed sells for $ 0.95 per pound, if she bought 12 pounds of wild bird seed, to find the amount of thistle bird seed she purchased, the following calculation must be performed, through a linear function:
(12 x 0.95) + 1.60X = 23.40 11.40 + 1.60X = 23.40 1.60X = 23.4 - 11.4 X = 12 / 1.60 X = 7.5
Therefore, Kate bought 7.5 pounds of thistle bird seed.
Learn more in https://brainly.com/question/3400735
Complete the equation of the line through (3,-8) and (6,-4).
Use exact numbers.
Answer:
y = 4/3x - 12
Step-by-step explanation:
Use Point Slope Form: (y - y1) = m(x - x1)
Step 1: Find the slope
m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
m = [tex]\frac{-4 - (-8)}{6 - 3}[/tex]
m = [tex]\frac{-4 + 8}{3}[/tex]
m = [tex]\frac{4}{3}[/tex]
Step 2: Plug into point slope form
(y - (-4)) = 4/3(x - 6)
y + 4 = 4/3x - 24/3
y + 4 - 4 = 4/3x - 8 - 4
y = 4/3x - 12
Answer: y = 4/3x - 12
Janet researcher compares the math placement scores of college applicants who have, or have not taken a special college preparation program.
Independent Variable (IV):
How will you describe the IV?:
Dependent variables (DV): ]
How will you measure the DV?:
Hypothesis:
Answer:
Step-by-step explanation:
Independent Variable (IV): Special college preparation program
How will you describe the IV: Independent variable or known as manipulated variable is a variable where the researcher purposely manipulate the variable to see how it affect the results of the experiment.
Dependent variables (DV): Math placement scores of college applicants
How will you measure the DV: DV can be measured by recording the math placement scores of each applicants who have or have not taken the special college preparation program.
Explanation: In this case, the researcher wants to see how taking special college preparation program (IV) can affect the math placement scores of the applicants (DV). Explanation: In this case, the researcher wants to see how taking special college preparation program (IV) can affect the math placement scores of the applicants (DV).
Hypothesis:
If the applicants take the special college preparation program, the applicants will have higher math placement scores compared to the one who have do not take the program.
Final answer:
The independent variable in the study is whether college applicants have taken a special college preparation program or not, with the dependent variable being the math placement scores. A potential hypothesis could be that applicants who took the program will achieve higher math scores.
Explanation:
Independent Variable (IV): The independent variable in this study is whether college applicants have taken a special college preparation program or not.
Dependent Variable (DV): The dependent variable is the math placement scores of the college applicants.
Hypothesis: A possible hypothesis could be 'College applicants who have taken a special college preparation program will have higher math placement scores compared to those who have not taken the program.'
Write an equation in slope intercept form for the line that has a slope of 12 and passes through the point (3,20)
Answer:
y= 12x-16
Step-by-step explanation:
Given that you have a slope of 12 and a point of (3, 20), you are most obligated to using the Slope-Intercept form, or y=mx+b.
What this allows you to find is the y-intercept if your line has one. You take your point, (3,20), and you insert the values at the appropriate places. You should now have 20=12(3)+b. You will then solve for b by multiplying 12 and 3 to get 36 and subtract that from both sides of the equal sign. You should have 20-36=b. 20-36 is -16, which is your y-intercept.
Now you know all your needed values, you would write the Slope-Intercept form without the values for y and x, to represent your equation.
Since 12 is your slope, it will be 'm' and -16 will be 'b'.
You will end with y = 12x - 16.
Given:
Line passing through,
[tex](x_1,y_1) = (3, 20)[/tex]Slope,
[tex]m = 12[/tex]The equation will be:
→ [tex]y - y_1 = m(x-x_1)[/tex]
By substituting the values,
→ [tex]y-20=12(x-3)[/tex]
→ [tex]y-20=12x-36[/tex]
[tex]y = 12x-16[/tex]
Thus the above answer is right.
Learn more about intercept here:
https://brainly.com/question/21614609
The difference of a number and five is negative one. Find the number.
Answer:
The number is 4
Step-by-step explanation:
Write algebraically:
n-5=-1
n=4
The number is 4
To find the number when the difference of a number and five is negative one, substitute the given values into an equation and solve for the unknown variable.
Explanation:To solve the problem, let's assign a variable to the unknown number. Let's call it 'x'. The difference of a number and five can be represented as 'x - 5'. According to the problem, this expression is equal to -1. So, we can write the equation x - 5 = -1. To find x, we need to isolate it on one side of the equation. Adding 5 to both sides, we get x = 4. Therefore, the number is 4.
Learn more about number difference here:https://brainly.com/question/18757471
#SPJ2
The first layer of a rectangle prism is packed with 25 unit cubes. There are no spaces or gaps between the cubes. The prism is 7 unit cubes tall. Which expression represents the volume of the rectangular prism?
Answer:
So, the answer is 175 but in an expression it is 25x where x would be the height in this situation it is 7.
Step-by-step explanation:
So basicly if there is 25 units and there are 7 layers of that 25 units you would multiply 7 by 25 to get 175.
Hence, in an expression it would be 25x where x would be 7
Angie has saved $2.50 of her allowance every week for the past 12 weeks. If she continues saving the same amount each week, how many more weeks will it take her to save a total of $50
Answer:
20
Step-by-step explanation:
$2.50 x 12 equals 30
2.50 x 20 equals 50
x10= 2.50 x 20 =$50
last question promise
Answer:
80°
Step-by-step explanation:
A triangle = 180° total.
Because it is a parallelogram, 40° is also the measure of BCE.
180° - 60° - 40° = 80°
BEC = 80°
The difference of a number p and -9 is 12
Answer: 3
Step-by-step explanation: Your equation is p- (-9)=12. A negative plus a negative is a positive. So the equation is basically p+9=12. 12 minus 9 is 3 and that's the answer!
=
Write an equation in slope-intercept form for the line with y-intercept 5 and slope -1/4
Equation is y = -1/4x + 5
Step-by-step explanation:
Step 1: Given slope, m = -1/4 and y-intercept, b = 5. Write the equation in slope intercept form which is y = mx + b⇒ y = -1/4x + 5
I WILL GIVE BRAINLIEST
Part A:
A garden is in the shape of a circle with a radius of 10 feet. Edging is placed around the garden
How much edging, in feet, is needed to go around the garden? Round to the nearest whole number?
Part B:
Another garden is in the shape of a semicircle with a radius of 25 feet. Edging is placed around this garden.
How much edging, in feet, is needed to go around this garden? Round to the nearest whole number.
Answer:
Part A = 64 feet
Part B = 79 feet
Step-by-step explanation:
Part A
10 × 2 = 20 = Diameter
Formula is C = π × diameter
20 × π = 62.8318530718 feet = 64 feet
Part B
25 × 2 = 50
Same formula
50 × π = 157.079632679 feet
157.079632679 ÷ 2 = 78.5398163395 feet = 79 feet
divide by 2 because it is a semi circle
Hope his helped :)
For the circular garden with a radius of 10 feet, 63 feet of edging is required. For the semicircular garden with a radius of 25 feet, 129 feet of edging is needed. These figures are obtained by calculating the circumference of a circle and a semicircle, then rounding to the nearest whole number.
Explanation:To find out how much edging is needed for the gardens, we need to calculate the circumference of the circles.
Part A
The formula for the circumference of a circle (which is the distance around the edge) is 2πr, where π (pi) is approximately 3.14, and r is the radius. For a circle with a radius of 10 feet, the circumference is:
2 × 3.14 × 10 feet = 62.8 feet
Rounded to the nearest whole number, we need 63 feet of edging for the garden.
Part B
For a semicircle with a radius of 25 feet, the circumference is half that of a whole circle, plus the diameter (which is 2 × radius). So, first calculate the circumference of the whole circle and then divide by 2 and add the diameter:
(2 × 3.14 × 25 feet) / 2 + 2 × 25 feet = 78.5 feet + 50 feet = 128.5 feet
Rounded to the nearest whole number, we need 129 feet of edging for the semicircular garden.
A line that comes closest to data in the coordinate plane is called the line of
That would be the line of best fit.
The line of best fit is a straight line that best represents the data on a scatter plot.
Hope that helps, :)
There are twelve inches in 1 foot. Convert 3 feet to inches.
Answer:
36 inches
Step-by-step explanation:
since there are 12 inches in one foot, just do 12 x 3 which equals 36.
Question 1 (Mandatory) (1 point)
Which method is best used to prove that a figure has a right angle?
a) Using slope formula to show two segments have opposite reciprocal slopes.
Ub Using slope formula to show two segments have the same slope.
C) Using distance formula to show two segments are congruent.
od) Using the midpoint formula to show two segments have the same midpoint.
Answer:
A
Step-by-step explanation:
Right angle means that the two sides that meet to create right angle are "perpendicular".
Two perpendicular lines meet to form the angle of 90 degrees.
In coordinate geometry, how do we prove that two lines are perpendicular??
We show that their slopes are negative reciprocals of each other.
This also tells us that the angle between the two lines are "right angle".
So, we can use slope formula to show two segments have opposite reciprocal slopes, that will tell us that it is a right angle between the two segments.
Option A is right.
14) What is the vertex of y= x- 4x + 7?
True or false: f(x) is a function.
f(x)
Answer:
yes it is
Step-by-step explanation:
f(x) or g(x) are functions
Answer:
It is False
Step-by-step explanation:
I tried true and got it wrong
Last year, Rina's history and math classes had regular tests. Each history test had 14
questions and each math test had 11 questions. If Rina had to answer the same number of
history questions and math questions last year, what is the smallest number of each type of
question she must have answered?
Answer:
154
Step-by-step explanation:
This ones tough so im not sure but try it. I hope this helps
If a tennis ball has a diameter of 14, What is the volume of the tennis ball? Use 3.14 for pi.
Answer:
1436
Step-by-step explanation:
Which number is most likely an irrational number?
Bowser bought mushrooms
at the farmer's market. He
paid $4.32 for 6 pounds of
mushrooms. At that rate,
how much should he pay for
5 pounds of mushrooms?
Please help ty! I added extra points.
Hillary and Charlene both drove from City A to City B. At 10 a.m., Hillary left City A and drove at an average speed of 120 km/h. Charlene drove at an average speed of 144 km/h and took 50 minutes. She arrived at City B at the same time as Hillary. Find the time Charlene left City A.
Let's denote the time Charlene left City A as [tex]\( t \).[/tex]
Since Charlene took 50 minutes (or [tex]\(\frac{50}{60} = \frac{5}{6}\) hours)[/tex] to reach City B, and she arrived at the same time as Hillary, we can set up the equation based on the distances traveled by both:
For Hillary:
[tex]\[ \text{Distance}_\text{Hillary} = \text{Speed}_\text{Hillary} \times \text{Time}_\text{Hillary} \]\[ \text{Distance}_\text{Hillary} = 120 \times (t + 1) \][/tex]
For Charlene:
[tex]\[ \text{Distance}_\text{Charlene} = \text{Speed}_\text{Charlene} \times \text{Time}_\text{Charlene} \]\[ \text{Distance}_\text{Charlene} = 144 \times \left(t + \frac{5}{6}\right) \][/tex]
Since they traveled the same distance, we can equate these two expressions:
[tex]\[ 120 \times (t + 1) = 144 \times \left(t + \frac{5}{6}\right) \][/tex]
Now, solve for \( t \):
[tex]\[ 120t + 120 = 144t + 120 \]\[ 24t = 120 \]\[ t = 5 \][/tex]
So, Charlene left City A at 5:00 a.m.
A store that sells merchandise on a college campus is restocking their inventory of sweatshirts and t-shirts. They order a total of 934 items. Each sweatshirt costs $8.00 and each t-shirt costs $5.00. They spend a total of $5,933.00.
A system of equations is written to represent this scenario, where s represents the number of sweatshirts ordered and t represents the number of t-shirts ordered.
{s+t=934
{8s+5+=5933
The solution to the system is (421, 513). Interpret this solution in the context of the situation.
A. The store ordered 513 sweatshirts and 421 t-shirts.
B. The store ordered 421 sweatshirts and 513 t-shirts.
C. The store spent $513.00 on sweatshirts and $421.00 on t-shirts.
D. The store spent $421.00 on sweatshirts and $513.00 on t-shirts.
Answer:
Option B.
Step-by-step explanation:
A system of equations is written to represent this scenario, where s represents the number of sweatshirts ordered and t represents the number of t-shirts ordered.
s + t = 934
8s + 5t = 5,933
The solution to the system is (421, 513).
So, The number of sweatshirts = 421
And the number of t-shirts = 513
Because 8 * 421 + 5 * 513 = $5,933
We will check the options:
A. The store ordered 513 sweatshirts and 421 t-shirts. ⇒Wrong
B. The store ordered 421 sweatshirts and 513 t-shirts. ⇒True
C. The store spent $513.00 on sweatshirts and $421.00 on t-shirts. ⇒Wrong
Because the solution represents the number of sweatshirts and t-shirts.
D. The store spent $421.00 on sweatshirts and $513.00 on t-shirts. ⇒Wrong
Because the solution represents the number of sweatshirts and t-shirts.
So, the answer is option B.
Sarah and Kaylee go to the movie theater and purchase refreshments for their friends.
Sarah spends a total of $47.00 on 12 drinks and 1 bag of popcorn.
Kaylee spends a total of $81.75 on 3 drinks and 9 bags of popcorn.
Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn.
Using these equations, determine and state the price of a drink, to the nearest cent.
Each drink costs $3.25 and each popcorn costs $8.
Step-by-step explanation:
Step 1:
Assume each drink costs x dollars and each popcorn costs y dollars.
From the given data, we can write the following equations;
[tex]12x + y = 47[/tex], take this as equation 1,
[tex]3x+9y=81.75[/tex], take this as equation 2.
Step 2:
We multiply equation 2 with 4 so we can cancel out the variable x in both equations. By doing this we get
[tex]3x+9y = 81.75[/tex], take this as equation 3. When we subtract 3 from 1, the x variable is canceled out and y can be calculated.
[tex]-35y = -280, y = \frac{280}{35} = 8[/tex]
Step 3:
Substituting this value of y in any of the previous equations we will get x's value.
Here this value of y is substituted in equation 1.
[tex]12x+8 = 47, 12x= 39[/tex],
[tex]x=\frac{39}{12} = 3.25[/tex]
So we have x = $3.25 and y = $8. So each drink costs $3.25 and each popcorn costs $8.
Sammy opens a bag of
skittles and counts all the
green skittles. There are
13 green skittles in a bag
with 65 skittles. What is the
ratio of green to total
skittles?
Final answer:
To find the ratio of green to total skittles, divide the number of green skittles by the total number of skittles and simplify the fraction. The ratio of green to total skittles is 1:5.
Explanation:
To find the ratio of green to total skittles, we need to divide the number of green skittles by the total number of skittles and simplify the fraction.
Ratio = Number of green skittles / Total number of skittles
Ratio = 13 / 65
Since 13 and 65 are both divisible by 13, we can simplify the fraction to:
Ratio = 1 / 5
Therefore, the ratio of green to total skittles is 1:5.
Factor: 25 m 6 −16 25m6−16 (5m3 + 8)(5m3 – 8) (5m3 – 8)2 (5m3 – 4)2 (5m3 + 4)(5m3 – 4)
Answer:
(5m^3+4)(5m^3-4)
Step-by-step explanation:
(*) A^2 - B^2 =(A+B) (A-B)
25m^6-16=
(5m^3)^2 - 4^2=(*)
(5m^3+4)(5m^3-4)
If x over 5 equals 3 then what is x
Answer:
x=15
Step-by-step explanation:
x/5 =3
Multiply each side by 5
x/5 *5 = 3*5
x = 15
Which of the following equations has infinitely many solutions
Answer:
D
Step-by-step explanation:
Both equations are same
Answer:
D. 3x - 5 = -5 + 3x
Step-by-step explanation:
3x - 5 = -5 + 3x
3x = 3x
x = x (Infinitely many solutions)
solve by using distributive property: 12x - 6y = 12 and x = -2y +11
Answer:
x = [tex]\frac{1}{11}[/tex]; y = [tex]\frac{-60}{11}[/tex]
Step-by-step explanation:
x = -2y + 11 so x + 2y = 11 (1)
12x - 6y = 12 so 6x - y = 6 (2)
(1) - 2(2) ↔ (x + 2y) - 2(6x - y) = 11 - 2(6)
↔ - 11x = - 1
↔ x = [tex]\frac{1}{11}[/tex]
(2) ↔ y = 6x - 6 = 6([tex]\frac{1}{11}[/tex]) - 6 = [tex]\frac{6}{11}[/tex] - 6 = [tex]\frac{-60}{11}[/tex]
Brainliest???
A survey was conducted on 37 people so find out the colours that they like. It was found that 20 people like red, 22 people like blue and 17 people like green. It was also found that 7 people like blue and red, 12 people like blue and green, and 9 people like red and green. Assuming that x persons like three colours, find the value of x
A) 2
B) 4
C) 6
D) 8