The height of a triangle is 7 ft more than its base. If the area of the triangle is 30 ft2, what is the length of the base?

2 ft


5 ft


9 ft


12 ft

Answers

Answer 1

Answer:

see below

Step-by-step explanation:  5 27  7  16

area = 1/2 bh

height of a triangle is 7 ft more than its base

base = b

height = b + 7

area = 30

area = 1/2 b(h)

30 = 1/2 b(b + 7)

30 = 0.5(b²+ 7b)

30 = 1/2 b²+ 3.5b           solve for b

1/2 b²+ 3.5b = 30        

1/2 b²+ 3.5b - 30 = 0        

b²+ 7b - 60 = 0            factor

   (b +12)(b - 5) = 0    when b = -12 or 5     base length can't be negative

b = base = 5

area = 1/2 bh     1/2×2(9)     = 9

area = 1/2 bh     1/2×5(12)     = 60

area = 1/2 bh     1/2×9(16)     = 56

area = 1/2 bh     1/2×12(19)     = 114


Related Questions

2.) Combine like terms and simplify the expression: 2x +
5y+ 7x
Your answer

Answers

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.

please help, will award brainliest

Answers

Answer:

First one

Step-by-step explanation:

h(x) = x^2+ 2x- 6
what’s the answer

Answers

It equals this graph expression. it's a little cropped, but I'm Sure you know about the y & x axis.

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

Answers

Answer:

17

Step-by-step explanation:

hello if anyone would pls help

Answers

Answer:

x = 12

Step-by-step explanation:

It is a 90° angle which means that both of the angles need to add up to 90. 90-20 =70. 6×12 = 72.

6×9= 72

72-2 = 70

It adds up.

Hope this helps.

This is (Worth 10 points)

Answers

Answer:

C. Both A and B are solutions to the equation

Step-by-step explanation:

A negative number sqaured is positive.

Answer:

D

Step-by-step explanation:

It is D because the correct awnser is X=4

Find the slope of the line that passes through the points (-6,-2) and (-7,2)

Answers

Answer:

-4

Step-by-step explanation:

the steps are in the pic above

Function Composition:
Let the function [tex]f(x)= 3x + 2[/tex] and [tex]g(x) = \frac{x+3}{2x-10}[/tex] , determine:

Answers

Answer:

Given

f(x) = 3x + 2g(x) = (x + 3) / (2x - 10)

#1

g · f(x) = g(f(x)) = (3x + 2 + 3)/ (2(3x + 2) - 10) = (3x + 5) / (6x - 6)

#2

f · g(x) = f(g(x)) = 3[(3x + 2) / (2x - 10)] + 2 = (9x + 6) / (2x - 10) + 2 = (9x + 6 + 4x - 20)/ (2x - 10) = (13x - 14) / (2x - 10)

Describe how to graph the solution of y ≤ −x2 + 2x.

Answers

Answer:

See graph and explanation

Step-by-step explanation:

Assuming you mean y ≤ −x² + 2x, you graph y = −x² + 2x and then fill in the area beneath the curve of the parabola to represent the included values. See the graph for a visual.

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

Answers

9514 1404 393

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

Which of the following ratios is not 2:5

A. 40:100

B. 10:20

C. 16:40

D. 6:15

Answers

Answer:

Step-by-step explanation:

Option B is the correct answer

10 : 20

In its simplest form

1 : 2

What is the surface area?
And an explanation too but if not it’s ok

Answers

Answer:

356 cm.

Step-by-step explanation:

Whenever you find the surface area of a rectangular prism, remember this mnemonic:

LISA WILSON LOST HER WITCH HAT TWICE.

(TWICE) 2 (LENGTH × WIDTH + LENGTH × HEIGHT + WIDTH × HEIGHT)

In this rectangular prism, the length is 8, the width is 14, and the height is 3 (the order of numbers in length, width, and height does not matter).

Now, we can just plug in the numbers.

LENGTH × WIDTH + LENGTH × HEIGHT + WIDTH × HEIGHT

[tex]2(8*14+8*3+14*3) = 356.[/tex]

Therefore, the surface area of this rectangular prism is 356 centimeters.

The answer is 356 cm :)

What is the distance between points (8,11) and (8,−2) on a coordinate plane?

Enter your answer in the box.

units.

Answers

Answer: 13 units is the distance between the points.

the cost of using broadband in a hotel is £30 per hour formula to work out this total this total cost is cost in pounds = 3× number of hours. Workout the total of using boardband for 2 hours and 5 hours​

Answers

Answer:

10

Step-by-step explanation:

-9x - 12 = -3
Step By Step Pls

Answers

Answer:

x = -1

Step-by-step explanation:

-3 +12 = 9

-9x = 9

-9(-1)=9

9 - 12 = -3

-9x-12=-3
Multiply by -1
9x+12=3
Divide by 3
3x+4=1
Subtract 4
3x=-3
Divide by 3
x=-1

Degree and Radian Measures

What is the degree equivalent of π/4?

a. 180°
b. 90°
c. 120°
d. 45°

Please select the best answer from the choices provided

Answers

Answer:

D. 45°

Step-by-step explanation:

I calculated it logically

Launch Problem
a) There are two stores selling boxes of crackers. Based on the information below, which store should Sylvio
purchase the crackers from? Explain your answer.
Store 1
ion
Numbero Boed Cachers
3
5
6
00
9
B
12
2
bl...
Store 2:
C = 1.5b
c = cost and b = boxes of crackers
...
b) Sylvio also needs to purchase lemons. If Sylvio wants to buy 3 boxes of crackers and 6 lemons and he does
not want to go to both stores, which one should he shop at? Explain your answer.
Store 1:
Number of lemons
3
6
9
12
1
Cost (in dollars)
2
3
4

Answers

my best answer is B i hope this helps

Click on picture to see

Answers

Answer:

none of above

Step-by-step explanation:

Assume a bank loan requires an interest payment of $85 per year and a principal payment of $1,000 at the end of the loan's eight-year life. What would be the present value of this loan if it carried a 10 percent interest rate?

Answers

Answer:

$919.98

Step-by-step explanation:

To solve using a financial calculator do

N=8

I/Y=10

PMT=85

FV=1000

CMPT PV get 919.98

To do by hand find the present value of the interst payments

85*(1-(1/1.1)^8)

which is 453.4687

Find the present value of the final ballon payment

1000*(1/1.1)^8

which is 466.507

take the sum

466.507+453.4678= 919.98

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

Answers

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

Practice:

Determine the coordinates of the point on the unit circle corresponding to the given central angle. If necessary, round your results to the nearest hundredth.
180°

a. (-1, 0)
b. (0, 1)
c. (0, -1)
d. (1, 0)

Please select the best answer from the choices provided

Answers

Answer:

A. (-1, 0)

Step-by-step explanation:

I calculated it logically

4a - 2b = 10
write down the value of 2b-4a

Answers

Answer:I think 11 will be the answer

PLZ HELP

19 students were surveyed on the number of hours of Netflix they watched last week.

The data from the survey is below:

{0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 10, 11}

What is the mode for this data?

Answers

Answer:

Step-by-step explanation:

Answer:

i think the answer is 4

hope this help?

Calculate (0.25) x (0.44). Show your work.

Answers

Answer:

0.11

Step-by-step explanation:

0.44/x=100/25

(0.44/x)*x=(100/25)*x

0.44=4*x

0.44/4=x

0.11=x

How much larger is the volume of a triangular prism when you double the height of the prism?

Answers

9514 1404 393

Answer:

  2 times

Step-by-step explanation:

Other things remaining the same, the volume of any prism is proportional to its height. If you double the height, it is like having two prisms of the same size. The volume doubles. The new volume is 2 times the original volume.

In the coordinate plane, you are given JKL with J(2, 3), K(10,4), and L(6, 10). Using the distance formula, classify JKL

Answers

Answer:

Perimeter of JKL = 22.55 unit (Approx.)

Step-by-step explanation:

Given:

Coordinate of J = (2,3)

Coordinate of K = (10,4)

Coordinate of L = (6,10)

Find:

Perimeter of JKL

Computation:

Distance = √(x1 - x2)² + (y1 - y2)²

Distance between JK = √(2 - 10)² + (3 - 4)²

Distance between JK = √64 + 1

Distance between JK = √65

Distance between JK = 8.06 unit

Distance between KL = √(10 - 6)² + (4 - 10)²

Distance between KL = √16 + 36

Distance between KL = √52

Distance between KL = 7.21 unit

Distance between LJ = √(6 - 2)² + (10 - 3)²

Distance between LJ = √4 + 49

Distance between LJ = √53

Distance between LJ = 7.28 unit

Perimeter of JKL = Distance between JK + Distance between KL + Distance between LJ

Perimeter of JKL = 8.06 + 7.21 + 7.28

Perimeter of JKL = 22.55 unit (Approx.)

no links or i will report
Drag each number to the box on the right so it matches the value of the expression on the left. Each number may be used once, more than once, or not at all.


33.6252768.48

Expression Value of the Expression

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4

×

(

4

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3

)

]



3


[

(

7



5

)

÷

1

2

]

×

2


(

5

.

4

+

3

)

×

(

6



2

)


[

9

÷

3

+

6

]

×

3


(

4

+

3

.

2

)

×

[

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9



2

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+

2

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Answers

Answer:

The answers go in the following order:

25

8

33.6

27

68.4

In XYZ the measure of Z=90 ZY=7, XZ=24 and YX=25 what ratio represents the cosine of X?

Answers

Answer:

24/25

Step-by-step explanation:

on delta math

The ratio of cosine of angle X is 24/25.

What is trigonometric ratio?

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled.

Given a right triangle, XYZ with angle Y equals 90° and  ZY=7, XZ=24 and YX=25

The ratio of the cosine of an angle is the ratio of the base to the hypotenuse of the right triangle,

Here, Cosine of angle X = XZ/YX

cosX = 24/25

Hence, The ratio of cosine of angle X is 24/25.

For more references on trigonometric ratios, click;

https://brainly.com/question/25122825

#SPJ2

PLS HELP I REALLY NEED HELP FAST

Answers

Answer:

1st one

Step-by-step explanation:

The Intelligence Quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 25. What is the probability we could select a sample of 80 adults and find the mean of this sample is between 95 and 105

Answers

Answer:

The probability is 0.6796

Step-by-step explanation:

Given

Population Mean - 100

Population Standard Deviation - 25

As we know

z = x-μ/σ, where:

z is the standard score

x is the raw score  

μ is the population mean

σ is the population standard deviation

Z value for mean of sample = 95

z1 = -100+95/25 = -5/25 = -0.2

P value for Z = -0.2 is 0.2912

Z2 = 100-105/25 = 0.2

P(z > 0.2 = 1 - P(z ≤ 0.2) = 1 - 0.0294 = 0.9706

P(-0.2 < z < 0.2) = 0.9706 - 0.2912= 0.6796

The probability is 0.6796

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