A triangle has sides which are consecutive odd integers and an
angle of 120°. What is the perimeter of the triangle?

Answers

Answer 1

Answer:

Perimeter = 15

Step-by-step explanation:

We are told that the length of each of the 3 sides of the triangle are consecutive odd integers.

Thus means that we can write the 3 terms as;

(x - 2), x, (x + 2)

Thus, perimeter is;

P = (x - 2) + x + (x + 2)

P = 3x

If an angle is 120°, it means that the corresponding side that is directly opposite the angle is the largest side of the triangle.

Thus, this side is (x + 2)

Using cosine rule, we have;

(x + 2)² = x² + (x - 2)² - 2(x(x - 2))cos 120

Expanding, we have;

x² + 4x + 4 = x² + x² - 4x + 4 - (2x² + 4x)(-½)

This reduces to;

4x = x² - 4x + x² - 2x

2x² = 10x

2x = 10

x = 10/2

x = 5

Thus, other sides are;

(x - 2) = 5 - 2 = 3

And (x + 2) = 5 + 2 = 7

So,perimeter is;

P = 3x = 3 × 5 = 15


Related Questions

What's greater -5/7 or -2/7

Answers

I think -2/7.

-2/7 is closer to 0 which is neither positive nor negative.

-5/7 is closer to a whole negative number.

I need help with this one

Answers

Answer:

22%of 2346 is 516.12 which would be 516 persons

For the function f defined by f(x) = x - 2, what is the value of f(7)? А 2 B 5 C 7 D 9​

Answers

Answer:

f(7) =5

Step-by-step explanation:

f(x) = x - 2

f(7) means let x = 7

f(7) = 7-2

f(7) =5

Answer:

B. 5

Step-by-step explanation:

f(x) = x - 2 when x = 7

f(7) = 7 - 2

f(7) = 5

Best of Luck!

A certain lottery requires players to select 7 different numbers, in any order, from 1 to 51 inclusive. How many different sets of 7 numbers can be chosen?

Answers

Answer:

[tex]Selection = 345025251[/tex]

Step-by-step explanation:

Given

[tex]Total = 51[/tex]

[tex]Numbers = 7[/tex]

Required

Determine number of selection

It's important that

- The first number can be any of the 51 numbers

- The second number can be any of the 51 numbers

- The third number can be any of the 51 numbers

- The fourth number can be any of the 51 numbers

And so on

Hence, number of selections is:

[tex]Selection = 51 * 51 * 51 * 51 * 51[/tex]

[tex]Selection = 51^5[/tex]

[tex]Selection = 345025251[/tex] ways

Please answer this question!!

Answers

Answer:

12.25

Step-by-step explanation:

It is easy to notice that:

QA=QB=QC

As per triangle congruence theorem (two congruent sides and a right angle)

Since:

QB = x + 9 and QC = 5x - 4

We have

x + 9 = 5x - 45x - x = 9 + 44x = 13x = 13/4x = 3.25

QA = QB = QC = 3.25 + 9 = 12.25

A local sorority sold hot dogs and bratwursts at the spring fling picnics. The first day they sold 8 dozen hotdogs and 13 dozen bratwursts for $330.00. The second day they sold 10 dozen hot dogs and 15 dozen bratwursts for a total of $390.00 how much did each cost?

Answers

Answer:

Hotdogs are $12.00 for the dozen or $1.00 each

Bratwursts are $18.00 for the dozen or $1.50 each

Step-by-step explanation:

Luke was given a gift card for a coffee shop each morning Luke uses the card to buy one cup of coffee the original amount of money on the gift card was $30 and after buying 6 cups of coffee the card had $12 remaining balance write and equation for a in terms of X representing the amount of money remaining on the card after buying X cups of coffee​

Answers

Answer:

30-6x=12

Step-by-step explanation:

30 (was the original)-6(the amount of coffee)x(the price of each coffee)=12(the remaining amount after those 6 cups)

hope this helps!!

A) write an explicit formula for the sequence 12, 16, 20, 24 B) Find the 11th term of the sequence *

Answers

Answer:

[tex]T_n = 8+ 4n[/tex]

[tex]T_{11} = 52[/tex]

Step-by-step explanation:

Given

[tex]Sequence: 12, 16, 20, 24[/tex]

Solving (a): Write a formula

The above sequence shows an arithmetic progression

Hence:

The formula can be calculated using:

[tex]T_n = a + (n - 1) d[/tex]

In this case:

[tex]a = First\ Term = 12[/tex]

Difference (d) is difference of 2 successive terms

So:

[tex]d = 16 - 12 = 20 - 16 = 24 - 20[/tex]

[tex]d = 4[/tex]

Substitute 4 for d and 12 for a in [tex]T_n = a + (n - 1) d[/tex]

[tex]T_n = 12 + (n - 1) * 4[/tex]

Open Bracket

[tex]T_n = 12 + 4n - 4[/tex]

Collect Like Terms

[tex]T_n = 12 - 4+ 4n[/tex]

[tex]T_n = 8+ 4n[/tex]

Hence, the explicit formula is: [tex]T_n = 8+ 4n[/tex]

Solving (b): 11th term

This implies that n = 11

Substitute 11 for n in: [tex]T_n = 8+ 4n[/tex]

[tex]T_{11} = 8+ 4 * 11[/tex]

[tex]T_{11} = 8+ 44[/tex]

[tex]T_{11} = 52[/tex]

Answer:

A) The explicit formula for the sequence is [tex]f(n) = 12+4\cdot n[/tex], [tex]n \in \mathbb{N}_{O}[/tex].

B) The 11th term of the sequence is 62.

Step-by-step explanation:

A) Let [tex]f(0) = 12[/tex], we notice that sequence observes an arithmetic progression, in which there is a difference of 4 between two consecutive elements. The formula for arithmetic progression is:

[tex]f(n) = f(0) +r\cdot n[/tex] (1)

Where:

[tex]f(0)[/tex] - First value of the sequence, dimensionless.

[tex]r[/tex] - Arithmetic increase rate, dimensionless.

[tex]n[/tex] - Term of the value in the sequence, dimensionless.

If we know that [tex]f(0) = 12[/tex] and [tex]r = 4[/tex], then the explicit formula for the sequence is:

[tex]f(n) = 12+4\cdot n[/tex], [tex]n \in \mathbb{N}_{O}[/tex]

B) If we know that [tex]f(n) = 12+4\cdot n[/tex] and [tex]n = 10[/tex], the 11th term of the sequence is:

[tex]f(10) = 12+4\cdot (10)[/tex]

[tex]f(10) = 62[/tex]

The 11th term of the sequence is 62.

Keith receives $25000 salary for working as a account. If keith spends 40% of his salary on expenses each year, then how much money does Keith have to spend on expenses? Round your answer to the nearest whole number if necessary.

Answers

Answer:

$25000 * 40% = 100.000

Step-by-step explanation:


10,000 on expenses. 25000X.40=10,000

What is 5 and 3/4 times 7 in fractions

Answers

Answer:[tex]\frac{161}{4}[/tex]

Step-by-step explanation:

George the Pigeon travels the same distance of 72 miles
in 4 hours against the wind as he does traveling 3 hours
with the wind in the local skies. What is the speed of
George the Pigeon in still air and the speed of the wind?

Answers

Answer:

The speed of George the Pigeon in still air = 21 miles/hr

The speed of air = 3 miles/hr

Step-by-step explanation:

Let the speed of George the Pigeon in still air = [tex]u[/tex] miles/hr

Let the speed of air = [tex]v[/tex] miles/hr

Distance traveled = 72 miles

Relative speed against the wind = [tex](u-v)[/tex] miles/hr

Time taken against the wind = 4 hours

Relative speed with the wind = [tex](u+v)[/tex] miles/hr

Time taken against the wind = 3 hours

Using the formula:

[tex]Speed = \dfrac{Distance}{Time}[/tex]

[tex]u-v=\dfrac{72}{4}\\\Rightarrow u-v=18 ..... (1)[/tex]

[tex]u+v=\dfrac{72}{3}\\\Rightarrow u+v=24 ..... (2)[/tex]

Adding (1) and (2):

[tex]2u=42\\\Rightarrow u = 21\ miles/hr[/tex]

By equation (1):

[tex]v = 21-18\\\Rightarrow v = 3\ miles/hr[/tex]

Therefore, the answer is:

The speed of George the Pigeon in still air = 21 miles/hr

The speed of air = 3 miles/hr

the ratio of potatoes to turnips is 1:1.if there are 473 potatoes how many turnips are there.

Answers

Answer:

473

Step-by-step explanation:

1:1

473:x

Cross Multiply

1x=473

Divide both sides by 1

x=473

A triangle has a base of 4 inches and a height of 12 inches. What is the area of the triangle?

Answers

Answer:

48

Step-by-step explanation:

u just multiply 12x4=48

Answer:

The area of the triangle is 24.

whats 10000x1? Im an ideot,

Answers

Answer:

10000

Step-by-step explanation:

LOL its ok :)

Answer:

10000

Step-by-step explanation:

When we multiply two numbers, the answer we get is called 'product'. The number of objects in each group is called 'multiplicand,' and the number of such equal groups is called 'multiplier'. In math, to multiply means to add equal groups. ... The two factors and the product are parts of a multiplication problem. In the multiplication problem, 6 × 9 = 54, the numbers 6 and 9 are the factors, while the number 54 is the product. The four basic mathematical operations--addition, subtraction, multiplication, and division--have application even in the most advanced mathematical theories. Thus, mastering them is one of the keys to progressing in an understanding of math and, specifically, of algebra.

:D

Brainliest?

A waterfall has a height of 1700 feet. A pebble is thrown upward from the top of the falls with an initial velocity of  feet per second. The height of the pebble h in feet after t seconds is given by the equation h=-16t^2+24t+1700 . How long after the pebble is thrown will it hit the​ ground?


PLEASE HELPPPPP

Answers

Answer:

[tex]t = 11.085[/tex]

Step-by-step explanation:

The expression is given as:

[tex]h=-16t^2+24t+1700[/tex]

Required

Determine how long it will hit the ground

When the pebble is on the ground, this implies that h = 0

So, we have that:

[tex]h=-16t^2+24t+1700[/tex] becomes

[tex]0=-16t^2+24t+1700[/tex]

Reorder

[tex]-16t^2+24t+1700 = 0[/tex]

Multiply through by -1

[tex]16t^2-24t-1700 = 0[/tex]

Solve using quadratic formula [tex]ax^2 + bx + c = 0[/tex]:

[tex]t = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

Where

[tex]a = 16[/tex]   [tex]b = -24[/tex]    [tex]c = -1700[/tex]

So, we have:

[tex]t = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

[tex]t = \frac{-(-24) \± \sqrt{(-24)^2 - 4*16*(-1700)}}{2*16}[/tex]

[tex]t = \frac{24 \± \sqrt{576 + 108800}}{32}[/tex]

[tex]t = \frac{24 \± \sqrt{109376}}{32}[/tex]

[tex]t = \frac{24 \± 330.72}{32}[/tex]

[tex]t = \frac{24 + 330.72}{32}[/tex] or [tex]t = \frac{24 - 330.72}{32}[/tex]

[tex]t = \frac{354.72}{32}[/tex] or [tex]t = \frac{-306.72}{32}[/tex]

[tex]t = 11.085[/tex] or [tex]t = -9.585[/tex]

But time can't be negative.

So: [tex]t = 11.085[/tex]

Hence, it will take 11.085 seconds to hit the ground

PLEASE HELP ME OUT FASTTTTT

Answers

Answer:

1 more slice

Step-by-step explanation:

1/2 of the pizza would be 4 since (8÷2=4)

So since we need 4 pizza slices to be gone in order to make 1/2 of the pizza...

and since we know that there are three slices missing....

the equation for this is 8-3=5 and we can't have 5 we need 4 so we need 1 more slice to be eaten

Does the ratio 15/12 and 5/4 form a proportion?

The answer is yes

Answers

Answer:

answer is c, I know because I took the test on edginuity

A rancher has 1000 feet of fencing in which to construct adjacent, equally sized rectangular pens. What dimensions should these pens have to maximize the enclosed area?

Answers

Answer:

The dimensions that will maximize the enclosed area of the pen is 250 ft by 250 ft

Step-by-step explanation:

we have the perimeter as 1000

So the sum of the lengths will be

1000/2 = 500

The dimensions that will maximize these pens will be such that they will have equal values

Mathematically, that will be 500/2 = 250 by 250

Question 10 of 10
Rewrite the following linear equation in slope-intercept form. Write your answer with no spaces. y+2=4(x-3).​

Answers

Answer:

y=4x−14

Step-by-step explanation:

solve for y.

y+2=4(x−3)

distribute 4

y+2=4x-12

subtract 2 from both sides

y+2+−2=4x−12+−2

y=4x−14

Answer:

y=4x−14

George purchases a sack of apples, a bunch of bananas, a cantaloupe, and a carton of dates for $20. If a carton of dates costs twice as much as a sack of apples and the price of a cantaloupe is equal to the price of a sack of apples minus a bunch of bananas, how much would it cost George to purchase a bunch of bananas and a cantaloupe?

Answers

9514 1404 393

Answer:

  $5

Step-by-step explanation:

Let the variables A, B, C, D represent a sack of apples, a bunch of bananas, a cantaloupe, and a carton of dates, respectively. Then the problem statement gives rise to 3 equations:

  A +B +C +D = 20

  D = 2A

  C = A -B

Substituting the last two equations into the first gives ...

  A +B + (A -B) +2A = 20

  4A = 20 . . . simplify

  A = 5 . . . . . divide by 4

Substituting this into the last equation, we have ...

  C = 5 -B

  B + C = 5 . . . . add B

The cost to purchase a bunch of bananas and a cantaloupe is $5.

A teacher keeps track of the number of students that participate at least three times in an optional study session each year. He models the attendance over the last nine years with this function. n(t) = 3.53t^2 - 33.04t + 117.56 Which graph would most likely be associated with the given model?

Answers

Answer:

its B

Step-by-step explanation:

The graph that would most likely be associated with the given model is an option(b).

What is a graph?

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

The regression equation is:

n(t) = 3.53t^2 - 33.04t + 117.56

The above regression equation is a quadratic function and non-linear.

thus, the graph must represent a non-linear relationship.

From the graphs, the only graph of the option (b) represents a quadratic function.

Other given options are either linear models or exponential.

Hence, the graph that would most likely be associated with the given model is an option(b).

Read more about regression models at:

https://brainly.com/question/18469538

#SPJ2

Robert bought some gifts that were each worth $25.90 at a store. He also bought one treat for himself that cost $4.00.
If Robert bought three gifts, which equation shows how to calculate the total amount of money he spent at the store?
A.3 x 25.90 +4= 89.70
B. O 3 x 25.90 +4= 81.70
C.3 x (25.90 + 4) = 89. 70
D.O3 (25.90 + 4) = 81. 70

Answers

A bc he bought three of the $25.90 then he bought only one for himself (the $4)

Answer:

A

Step-by-step explanation:

Since Roberto bought 3 gifts, which are each $25.90, that would mean it would be 3×25.90. Plus, he bought himself a treat would would be a +4.

Ninety-nine is what percent of 150?

Answers

Answer:

66

Step-by-step explanation:

Answer:

66

Step-by-step explanation:

I need help with this!

Answers

Answer:

9/20

Step-by-step explanation:

3/8 - 4/5 - 3/8 + 5/4

-16/20 + 25/20

-16 + 25/20

9/20

Answer: The answer is 9/20.

Step-by-step explanation:

Which equation represents the graph?

Answers

Answer:

The answer is A) y+4 =3(x+3)

Step-by-step explanation:

The slope is the rate of change, which you can see from the graph is m = 3/1 = 3.

Your options are given in point-slope form:

y-y1=m(x-x1)

Pick a point from the graph. I used;

(-3, -4). Now plug this into your point slope form equation.

y-(-4) = 3(x-(-3))

y+4=3(x+3)

I need help please sorry it’s like that a camera and a screen don’t work good together

Answers

Answer:

The value of x = 20.05

Step-by-step explanation:

As we know that the sum of the angles in a triangle is 180°.

From the diagram, we can say that the sum of the angles A, B, and C must be 180°.

so the equation of the sum of the angles of a triangle will be:

[tex]A+B+C=180^{\circ }[/tex]

As

[tex]A=43\frac{1}{4}^{\circ }[/tex]

[tex]B=5x^{\circ }[/tex]

[tex]C^{\circ }=36.5^{\circ }[/tex]

Substituting the values in the equation of the sum of the angles of a triangle to find the value of x.

[tex]A+B+C=180^{\circ }[/tex]

[tex]43\frac{1}{4}+5x+36.5=180[/tex]

[tex]\frac{173}{4}+5x+36.5=180[/tex]             ∵ [tex]43\frac{1}{4}=\frac{173}{4}[/tex]

Subtract [tex]\frac{173}{4}+36.5[/tex] from both sides

[tex]\frac{173}{4}+5x+36.5-\left(\frac{173}{4}+36.5\right)=180-\left(\frac{173}{4}+36.5\right)[/tex]

[tex]5x=100.25[/tex]

[tex]\frac{5x}{5}=\frac{100.25}{5}[/tex]

[tex]x=20.05[/tex]

Therefore, the value of x = 20.05

VERIFICATION:

[tex]A+B+C=180^{\circ }[/tex]

[tex]43\frac{1}{4}+5x+36.5=180[/tex]

[tex]43\frac{1}{4}+5\left(20.05\right)+36.5=180[/tex]

[tex]180=180[/tex]

Christina scored 2,065 points by collecting 7 coins. After collecting a total of 8 coins, how many points will Christina have scored in all?

Answers

Answer:

2065 ÷ 7 = 295

295 × 8 = 2360

Christina will have scored 2,360 points.

Need help with homework

Answers

Answer: A is (8.5,4) B is (2.5,1.5)

Step-by-step explanation:

Find the slope of the line that passes through the given points.(-4, 7) and (-2, 8)

Answers

Answer:

[tex]m=\frac{1}{2}[/tex]

General Formulas and Concepts:

Pre-Alg

Order of Operations: BPEMDAS

Algebra I

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step-by-step explanation:

Step 1: Define

Point (-4, 7)

Point (-2, 8)

Step 2: Find slope m

Substitute:                    [tex]m=\frac{8-7}{-2+4}[/tex]Subtract/Add:               [tex]m=\frac{1}{2}[/tex]

What is the perimeter of a rectangle whose short sides are4 and long sides are3?

Answers

Answer:

Permimeter=14

Step-by-step explanation:

4+4=8. 3+3=6. 8+6=14. Perimeter equals 14.

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