x^2-12x+36-144=0
x^2-12x-108=0
(x-18)(x+6)
X=18,-6
The ages of undergraduate students in a state in a particular year approximately follows a normal distribution, with a mean
age of 20.6 years and a standard deviation of 1.3 years.
If the total number of undergraduate students in the state is 430,000, how many students are aged 19 years or more?
A)
123,000
B)
223,000
C)
313,000
D)
383,000
find the surface area of each figure (spheres and hemispheres)
Answer:
7. 1520.53 cm²
8. 232.35 ft²
9. 706.86 m²
10. 4,156.32 mm²
11. 780.46 m²
12. 1,847.25 mi²
Step-by-step explanation:
Recall:
Surface area of sphere = 4πr²
Surface area of hemisphere = 2πr² + πr²
7. r = 11 cm
Plug in the value into the appropriate formula
Surface area of the sphere = 4*π*11² = 1520.53 cm² (nearest tenth)
8. r = ½(8.6) = 4.3 ft
Plug in the value into the appropriate formula
Surface area of the sphere = 4*π*4.3² = 232.35 ft² (nearest tenth)
9. r = ½(15) = 7.5 m
Surface area of the sphere = 4*π*7.5² = 706.86 m² (nearest tenth)
10. r = ½(42) = 21 mm
Plug in the value into the formula
Surface area of hemisphere = 2*π*21² + π*21² = 2,770.88 + 1,385.44
= 4,156.32 mm²
11. r = 9.1 m
Plug in the value into the formula
Surface area of hemisphere = 2*π*9.1² + π*9.1² = 520.31 + 260.15
= 780.46 m²
12. r = 14 mi
Plug in the value into the formula
Surface area of hemisphere = 2*π*14² + π*14² = 1,231.50 + 615.75
= 1,847.25 mi²
Keisha had $54 when she went to a bookstore. She
had $12 left after buying some books. Which
equation can be used to find a, the amount Keisha
spent on books?
54 - a = 12
B
a - 54 = 12
a +54 = 12
12 + 54 = a
Shreman drew a shape with these properties: •Four sides •Four right angles •Two sides have different lengths
Answer: the shape is a rectangle
Step-by-step explanation:
Answer:
Rectangle :)
Step-by-step explanation:
2.) Combine like terms and simplify the expression: 2x +
5y+ 7x
Your answer
Answer:
9x + 5y
Step-by-step explanation:
Here, in 2x + 5y+ 7x, the 'like terms' are 2x and 7x, and the sum of these terms is 9x. Thus, 2x + 5y+ 7x becomes 9x + 5y.
Find two numbers a and b whose sum a+b is -3 and whose difference a−b is -5
Answer:
A=-4, b=1
Step-by-step explanation:
add those two function together u will got:
a+b+(a-b)=-3+(-5)
2a=-8
A=-4
-4+b=-3
B=1
Given the definitions of f (x) and g(x) below, find the value of f(g(-6)).
f(x) = x² – 2x +9
g(x) = -3x – 14
Answer:
17
Step-by-step explanation:
How many tryouts weighed MORE THAN 450 grams?
Answer:
11
Step-by-step explanation:
Basically count each doubt that is on the number line with a value greater than 450
Answer:
11 trouts
Step-by-step explanation:
Count the dots that are after the 450-gram mark.
Trouts that weigh 452 = 5
Trouts that weigh 454 = 2
Trouts that weigh 456 = 2
Trouts that weigh 458 = 1
Trouts that weigh 460 = 1
Then, add everything up.
5 + 2 + 2 + 1 + 1 = 11
So, 11 trouts weigh more than 450 grams.
Have a wonderful day!
The original price of a pair of shoes is $60. The sale price is 25% off the original price. What is the amount off of
the original price?
Bella invested $8,400 in an account paying an interest rate of 1.9% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $9890?
Answer:
8.6 years
Step-by-step explanation:
Item 1
Use the figure to find the measures of the numbered angles.
Parallel lines a and b are intersected by a transversal t. Angle 1 and angle 99 degrees are supplementary angles. Angle 1 and angle 3 are vertical angles. Angle 2 and angle 99 degrees are vertical angles. Angle 99 degrees and angle 4 degrees are corresponding angles on the same side of the transversal. Angle 1 and angle 5 are corresponding angles on the other side of the transversal. Angle 5 and angle 7 are vertical angles. Angle 6 and angle 4 are vertical angles.
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Answer:
∠1 = ∠3 = ∠5 = ∠7 = 81°
∠2 = ∠4 = ∠6 = 99°
Step-by-step explanation:
Vertical and corresponding angles are congruent. Angles 1 and 99° are supplementary, so ...
∠1 = 180° -99° = 81°
Then we have ...
∠1 = ∠3 = ∠5 = ∠7 = 81°
∠2 = ∠4 = ∠6 = 99°
HELPPPPPPP SUMMMMBODYYY
B or A. I'm not sure, because i learned this 5 years ago, but it is a or b. the only reason i dont know which one is because i forgot what a filled in dot, versus a circle means. on point 3 on your number line, there's a circle, and there's a dot on answer A and answer B respectively. if memory serves, it should be B
Click on picture to see
Answer:
none of above
Step-by-step explanation:
Ryan bought a new phone case that was originally $80, it is now on sale for $60. What was the percentage change?
Answer: 25% decrease
Step-by-step explanation:
80 - 60
----------- = 20/80 = 1/4 OR 25%
80
Hope this helped :)
part 1. Use side ratios to determine if the triangles in each pair of similar. If so complete the similarity statement. NO LINKS!!!
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Answer:
4) ΔEFG ~ ΔECD
6) Not Similar
Step-by-step explanation:
4) Shortest to longest sides are ...
EF : FG : GE = 14 : 16 : 20 = 7 : 8 : 10 (reduced)
EC : CD : DE = 7 : 8 : 10
The triangles have the same side length ratios, so are similar.
ΔEFT ~ ΔECD
__
6) Shortest to longest, the given sides have ratios ...
UT : TV = 71 : 84 (reduced)
GT : TH = 60 : 72 = 5 : 6 (reduced)
The side ratios are different, so the triangles are NOT SIMILAR.
Answer:
part 1. Use side ratios to determine if the triangles in each pair of similar. If so complete the similarity statement. NO LINKS!!!
h(x) = x^2+ 2x- 6
what’s the answer
It equals this graph expression. it's a little cropped, but I'm Sure you know about the y & x axis.
Find the area of the shape below
No links, docs, files, drives etc
I will mark the correct answer brainlyest
You earn many points
Answer: 2200
Step-by-step explanation:
First we will find the area of the triangle, the formula for that is bh/2
(base multiplied by height divided by 2) then we input the numbers into our formula, 30 is the height of the triangle and 40 is the length of the base. So we have to solve 40*30/2 which is 600, then we solve for the square on the bottom which is b*h ( base multiplied by height) so it is 40*40, so we would get 1600, then we add 600 and 1600 together and get 2200.
Last year the depth of the river was 4.2 feet deep.
This year it dropped 5%.
Find the depth of the river this year to cross it.
Answer:
3.15 ツ
Step-by-step explanation:
Consider point P(4, 2) and line l with equation −3x+4y=6 .
The equation of the line that passes through P and is parallel to l
Step-by-step explanation:
all working is above
hope that helps
Nolan wants to buy carpet to cover his whole living room, except for the tiled floor. The tiled floor is 4 5\6 ft by 2 1\3 ft. Find the area the carpet needs to cover.
Answer:
11 5/18 ft squared
Step-by-step explanation:
because the floor is probably a rectangle, we can use the area formula to find the area of the carpet. the formula is
A = Length × Width
so now we plug in the numbers.
A = (4 5/6) × (2 1/3)
I'm going to simplify the numbers into an improper fraction because the numbers are in a mixed fraction format and I simply dislike it.
A = (29/6) × (7/3)
A = 203/18 ft squared
In the answer section, the numbers look different because I converted my 203/18 into a mixed number.
A = 203/18 = 11 5/18 ft squared
Which of the following ratios is not 2:5
A. 40:100
B. 10:20
C. 16:40
D. 6:15
Answer:
Step-by-step explanation:
Option B is the correct answer
10 : 20
In its simplest form
1 : 2
1) Simplify the product using the distributive property.
(x-2)(x+4)
Please help me answer this question
The sides of a square are all increased by 2 inches. The area of the NEW square is 49
inches squared. What is the length of a side of the original square?
A: 4.5 inches
B: 9 inches
C: 5 inches
D: 2 inches
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Answer:
C: 5 inches
Step-by-step explanation:
The length of the sides of the new square is the square root of the area:
s = √A = √49 = 7
The original square had sides 2 inches shorter, so they were ...
7 in -2 in = 5 in . . . . side length of original square
please help, will award brainliest
Answer:
First one
Step-by-step explanation:
Will you need to show that all of the parts of one triangle are congruent to all of the parts of the other triangle to prove they are congruent? Explain.
Answer:
will be sufficient to prove triangles congruent. If three sides of a triangle are congruent to three sides of another triangle, the triangles are congruent. If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
Kilgore's Deli is a small delicatessen located near a major university. Kilgore does a large walk-in carry-out lunch business. The deli offers three luncheon chili specials, Wimpy, Dial 911, Fire Bowl. At the beginning of the day, Kilgore needs to decide how much of each special to make (he always sells out of whatever he makes).
The profit on one serving of Wimpy is $0.6, on one serving of Dial 911 is $0.55, and on one serving of Fire Bowl is $0.65.
The following table shows the required ingredients to make one serving of each chili special, and the available amount of each ingredient for today :
Ingredient Required ingredient for each serving of Wimpy Required ingredient for each serving of Dial 911 Required ingredient for each serving of Fire Bowl Available Amount
Beef (lbs) 1 1 1.5 15
Onions (cup) 2 2 2 20
Special Sauce (oz) 5 2 3 90
Hot Sauce (oz) 0 5 6 60
Based on the historical sales data, Kilgore's Deli has the following considerations:
the number of servings for Fire Bowl must be at least 10% of the total number of servings for all three luncheon chili specials.
the number of servings for Fire Bowl, however, cannot exceed the number of Dial 911 by more than 3.
the available number of servings for Dial 911 must be at least 2.
(1.1) Develop the linear programming model to help determine the number of servings of Wimpy, Dial 911, and Fire Bowl to make in order to maximize his profit today. Type your algebraic formulation in the specified area in Q1 tab of the Excel template. Note you will not get full credits without including the algebraic formulation.
(1.2) Solve your LP model in Excel and fill in the following blanks (show your work in Q1 tab):
The optimal number of servings of Wimpy is
The optimal number of servings of Dial 911 is
The optimal number of servings of Fire Bowl is
The maximum possible profit is
Is there any leftover of ingredients as a result of this optimal solution? if yes, enter the amount. Otherwise, just type 0.
Amount of beef leftover
Amount of onion leftover
Amount of special sauce leftover
Amount of hot sauce leftover
Answer:
z (max) = 6.15
x₁ = 1 x₂ = 3 x₃ = 6
Amount of beef leftover 2 lb
Amount of onions leftover 0
Amount of Special Sauce leftover 61
Amount of Hot Sauce leftover 9
Step-by-step explanation:
Ingredients Beef Onions Special S Hot S Profit
Wimpy (x₁) 1 2 5 0 0.6
Dial 911 (x₂) 1 2 2 5 0.55
Fire Bowl (x₃) 1.5 2 3 6 0.65
Available 15 20 90 60
Objective Function z:
z = 0.6*x₁ + 0.55*x₂ + 0.65*x₃ to maximize
Subject to:
1) Quantity of beef : 15
x₁ + x₂ + 1.5*x₃ ≤ 15
2) Quantity of onions: 20
2*x₁ + 2*x₂ + 2*x₃ ≤ 20
3) Quantity of Special sauce: 90
5*x₁ + 2*x₂ + 3*x₃ ≤ 90
4) Quantity of hot sauce: 60
0*x₁ + 5*x₂ + 6*x₃ ≤ 60
5) Condition: The number of servings for Fire Bowl must be at least 10% of the total number of servings for all three luncheon chili specials.
x₃ ≥ 0.1 ( x₁ + x₂ + x₃ ) or x₃ ≥ 0.1*x₁ + 0.1 *x₂ + 0.1*x₃
x₃ - 0.1*x₁ - 0.1 *x₂ - 0.1*x₃ ≥ 0
- 0.1*x₁ - 0.1 *x₂ + 0.9 *x₃ ≥ 0
6)Condition: The number of servings for Fire Bowl, however, cannot exceed the number of Dial 911 by more than 3.
x₃ - x₂ ≤ 3
7)the available number of servings for Dial 911 must be at least 2.
x₂ ≥ 2
General constraints:
x₁ ≥ 0 x₃ ≥ 0 all integers
With on-line solver solution is:
z (max) = 6.15
x₁ = 1 x₂ = 3 x₃ = 6
By sbstitution on the constraints
1) x₁ + x₂ + 1.5*x₃ ≤ 15 1 + 3 + 9 = 13
Amount of beef leftover 2 lb
2) 2*x₁ + 2*x₂ + 2*x₃ ≤ 20 2 + 6 + 12 = 20
Amount of onions leftover 0
3) 5*x₁ + 2*x₂ + 3*x₃ ≤ 90 5 + 6 + 18 = 29
Amount of Special Sauce leftover 61
4)0*x₁ + 5*x₂ + 6*x₃ ≤ 60 15 + 36 = 51
Amount of Hot Sauce leftover 9
Please Help Me!
*Question Is Below Here*
Answer:
21
Step-by-step explanation:
2^3=8
7x6=42
42x8=336
336/ (10.6+5.4)
336/ 16= 21
Answer 21
Express tan(-310°) as a function of a positive acute angle in
terms of tan x
guessing
360 - 310 = 50
-tan(50)
Find the slope of the line that passes through the points (-6,-2) and (-7,2)
Answer:
-4
Step-by-step explanation:
the steps are in the pic above
The sum of two numbers is 27. The larger of the two numbers is 7 less than triple the smaller number. Indicate the two numbers below.
Answer: 69
Step-by-step explanation: EZ