The height of a triangle is 4 inches. Greater than twice it's base. The area of the triangle is no more than 168 in.². Which any quality can be used to find the possible lengths, x, of the base of the triangle

Answers

Answer 1

Step-by-step explanation:

this problem seeks to test our knowledge on word problems and algebra

Solution

let the base be x, and

the height h = 2x+4

We know that area of a triangle is given as

[tex]A= \frac{1}{2} b*h[/tex]

substituting our given values we have

[tex]168= \frac{1}{2} x*(2x+4)\\\\168= \frac{2x^2+4x}{2} \\\\168= x^2+2x\\\\[/tex]

re-arranging we have

[tex]x^2+2x-168=0\\\\[/tex]

we can now find two factors that will add up to give 2 and multiply to give -168

they are 14 and -12

[tex]x^2-14x+12x-168=0\\\\x(x-14)+12(x- 14)=0\\\\x+12=0\\\\x=-12\\\\x-14=0\\\\x=14[/tex]

The possible base of the triangle is 14 in

and the height is

[tex]h= 2x+4\\\\h=2(14)+4\\\\h= 28+4\\\\\h= 32 in[/tex]


Related Questions

Least to greatest 2.71,2 3/4,5,5/2

Answers

Answer:

3/4<5/2<2.71

Step-by-step explanation:

3/4<5/2<2.71

Answer:

5/2, 2.71, 2 3/4, 5/2

Step-by-step explanation:

This is because (5/2) is equal to 2.5

and 2.71 is equal to 2.71

then (2 3/4) is equal to 3.75

and finally 5 is just 5, so then you put them in order (Least to Greatest) and then you revert them back to their original form.

hope this helps.

A marathon race is 26.2 miles. While running the marathon, Maxwell stops every 3.25 miles for water. If he has already stopped for water 5 times, how many more miles does Maxwell have to run? PLEASE HELP I WILL MARK YOU BRAINLIEST AND PLEASE EXPLAIN

Answers

Answer:

Hey there!

If he has already stopped five times for water, he has run 5(3.25), or 16.25 miles.

He has 26.2-16.25, or 9.95 more miles to run.

Let me know if this helps :)

Answer:

9.95 miles

Step-by-step explanation:

How many times he stopped × number of miles before break = total miles that has been run.

3.25 × 5 = 16.25

26.2 - 16.25 = 9.95 miles.

The parallelogram shown below has an area of 15 squared. Find the missing height. h=? units

Answers

Answer:

5 units

Step-by-step explanation:

The area of a parallelogram is given by the formula:

[tex]A=bh[/tex]

Where b is the base and h is the height.

So we know that the area is 15. We can also see that the base is 3. Thus:

[tex]15=3h[/tex]

Divide both sides by 3:

[tex]h=5[/tex]

So, the height is 5 units.

Answer:

h=3 units

Step-by-step explanation:

Equation for finding the area of a parallelogram:

b·h=area

Equation for this answer:

3·h=15

So divide 15 by 3 and you will get your answer.

15÷3=5

So the answer is:

3·5=15

Solve the following equations below by showing all the steps.
- 1. 9(4 - 2x) – 3 = 4 - 6(3x – 5)

Answers

Answer:

No  real solution

Step-by-step explanation:

First off I'm assuming that the 1 or -1 at the begging is just the problem number:

First you distribute on both sides

36 - 18x - 3 = 4 - 18x + 30

Then combine like terms

33 - 18x = 34 - 18x

Then rearrange the terms by adding 18x to both sides and subtracting both sides by 33. You should get:

0 = 1

When you add positive 18x it cancels the -18x out. And 34 - 33 is 1. Obviously, zero cannot equal 1 so there is no real solution

Rewrite the expression in the form o
[tex] {a}^{n} [/tex]

Answers

Answer:

a^ (5/2)

Step-by-step explanation:

a^5 ÷ a ^ (5/2)

We know that x^b ÷ x^c = x^ ( b-c)

a^ ( 5 - 5/2)

a^ ( 10/2 - 5/2)

a^ (5/2)

Answer:

[tex]a^{\frac{5}{2} }[/tex]

Step-by-step explanation:

Using exponent rules, if we have [tex]a^x \div a^y[/tex] then the result can simplify to [tex]a^{x-y}[/tex]

So [tex]a^5 \div a^{\frac{5}{2}}[/tex] is the same as [tex]a^{5 - \frac{5}{2}}[/tex].

[tex]\frac{5}{1} - \frac{5}{2} = \frac{10}{2} - \frac {5}{2} = \frac {5}{2}[/tex]

So [tex]a^{\frac{5}{2}}[/tex].

Hope this helped!

A shop buys a pair of shoes for $50. They sell them for $60. What is the mark–up on the shoes?

Answers

Answer:

The markup for the shoes is 20 percent.

Step-by-step explanation:

the markup would be 20% for the shoes

please help me to prove this..​

Answers

Answer:  see proof below

Step-by-step explanation:

Use the following Sum to Product Identities:

[tex]\sin x+\sin y=2\sin\bigg(\dfrac{x+y}{2}\bigg)\cos \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x-\cos y=-2\sin\bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)[/tex]

Proof LHS →  RHS

[tex]\text{LHS:}\qquad \qquad \qquad \qquad \dfrac{\sin \theta-\sin 3\theta+\sin 5\theta -\sin 7\theta}{\cos \theta -\cos 3\theta -\cos 5\theta +\cos 7\theta}[/tex]

[tex]\text{Regroup:}\qquad \qquad \qquad \dfrac{(\sin 5\theta+\sin \theta)-(\sin 7\theta +\sin 3\theta)}{-(\cos 5\theta -\cos \theta) +(\cos 7\theta -\cos 3\theta)}[/tex]

[tex]\text{Sum to Product:}\quad \dfrac{2\sin\bigg(\dfrac{5\theta +\theta}{2}\bigg)\cos \bigg(\dfrac{5\theta -\theta}{2}\bigg)-2\sin \bigg(\dfrac{7\theta + 3\theta}{2}\bigg)\cos \bigg(\dfrac{7\theta - 3\theta}{2}\bigg)}{2\sin\bigg(\dfrac{5\theta +\theta}{2}\bigg)\sin \bigg(\dfrac{5\theta -\theta}{2}\bigg)-2\sin \bigg(\dfrac{7\theta + 3\theta}{2}\bigg)\sin \bigg(\dfrac{7\theta - 3\theta}{2}\bigg)}[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{2\sin 3\theta \cos 2\theta-2\sin 5\theta \cos 2\theta}{2\sin 3\theta \sin 2\theta-2\sin 5\theta \cos 2\theta}[/tex]

[tex]\text{Factor:}\qquad \qquad \dfrac{\cos 2\theta(2\sin 3\theta -2\sin 5\theta \cos 2\theta)}{\sin 2\theta(2\sin 3\theta -2\sin 5\theta \cos 2\theta)}[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{\cos 2\theta}{\sin 2\theta}\\\\.\qquad \qquad \qquad =\cot 2\theta[/tex]

LHS = RHS:  cot 2Ф = cot 2Ф   [tex]\checkmark[/tex]

please help i need y intercept and slope

Answers

Answer:

slope:  1 /8

y-intercept:  ( 0 , − 1 /4 )

It should be y = mx + b

You hungrily remove frozen meat from the fridge. Its temperature is 28
degrees Fahrenheit. Its temperature is increasing by 3 degrees Fahrenheit
every five minutes. What will its temperature be after 30 minutes?

Answers

46 degrees Fahrenheit
You know it increased every five minutes so 30 divided by 5 is 6. That’s 6 times it has increased. 6 multiplied by 3 which is how many degree it’s increased each increment gives you 18. That’s the told it’s increased by 30 minutes. Then add the original temperature which was 28 to 18 which gives you 46.

What is the range of h?

Answers

The range of h is 10.

The range is the difference between the highest and lowest y-values for each point on the graph.
The y-values for this graph are {-4,-2,2,4,6}
To find the range you have to solve for the difference between the highest(6) and lowest(-4) numbers.

To find the difference, count how many spaces are between the numbers -4 and 6 on the graph, and you should count 10.

I hope this helped! If you have any questions about anything I mentioned above please feel free to comment on my answer with your questions and I’ll try to get back to you!

what is the square root of 415

Answers

hey the square root is 20

Answer:

20.37

Step-by-step explanation: caculated!!

2. Evaluate 3(6 – 5) + 4

Answers

Answer:

7

Step-by-step explanation:

We first start by simplifying the bracket.

(6 - 5) = 1,

Now we have

3(1) + 4

3 + 4 = 7

also, if you expand instead of simplifying, you get.

(3*6 - 3*5) + 4

(18 - 15) + 4

3 + 4 = 7

Irrespective, the answer is 7

If the trip from Paris, France, to Geneva, Switzerland, takes 5 hours, and the train travels at 130 miles per hour, how many miles from Paris is Geneva?

Answers

Answer:  650 miles

Step-by-step explanation:

If it takes 5 hours to go from Paris to Geneva and a train is travelling at 130 miles per hour then multiply the total number of miles per hour by 5 to find how many miles you will have to travel from Paris to Geneva.

130 * 5 =  650

Over a period of a week, the 4 people in Group C ran a total of 27 miles, while the
6 people in Group D ran a total of 39 miles. On average, who ran more miles-an
individual in Group C or an individual in Group D?

Answers

Group C ran more miles an individual.

Explanation: To find the number of miles per individual, you must subtract the total number of miles by the total number of people who ran those miles. Which ever answer is larger, tells us which group ran more miles an individual.

Here are the calculations-

Group C: 27/4=6.75
Group D: 39/6=6.5

As you can see, Group C ran more miles an individual than Group D.

Hope this Helped!

Simplify 16 + 5.6 + 0.681​

Answers

Answer:

16+5.6..to solve it yiu will have to put it like this...

16.0+5.6=21.6.

21.6+0.681=22.281.

On simplifying we get the answer as 22.281

What is the BODMAS rule?

According to the BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEMDAS rule is followed to solve it.

Given here, the expression is 16 + 5.6 + 0.681​ =22.281

Hence, on simplifying we get the answer as 22.281

Learn more about the BODMAS rule here:

https://brainly.com/question/29795897

#SPJ2

Ralph Chase plans to sell a piece of property for ​$170000. He wants the money to be paid off in two waysa ​short-term note at ​12% interest and a​ long-term note at ​9% interest. Find the amount of each note if the total annual interest paid is ​$18000.

Answers

Answer: $90,000 at 12%

and $80,000 at 9%

Step-by-step explanation:

given data:

cost of property = $170,000.

short term = 12%.

long term = 9%.

total interest paid = $18,000.

Step 1

= 0.12x + 0.09 (170,000-x) = 18,000

collect like terms

= 0.12x +  15300 – 0.09x = 18,000

divide both Sides by 0.03

0.03x = 2700

x = $90,000 at 12%

and $80,000 at 9%

The sum of two consecutive integers

Answers

Are they any given ones ?

Plot the approximate location of √6 on the number line JUST ANSWER IT

Answers

Answer:

Step-by-step explanation

That's the answer

The position of the √6 on the number line is slightly right of the 2.4.

We need to determine the approximate location of √6 on the number line.

What is a number line?

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,

In the general conclusion,

√4< √6 < √9

2 < √6 < 3

So, the value of the √6 lies between 2 and 3.

√6 = 2.445

So the position of the √6 on the number line is slightly right of the 2.4.

Thus, the position of the √6 on the number line is slightly right of the 2.4.

Learn more about number line here:

brainly.com/question/17683084

#SPJ2

Peter invests $1000 at 4% compounded annually for 10 years and Jose invests $900 compounded annually at 5% for 11 years. Who ends up with more money? And how much more money?

Answers

Answer:

Jose ends up with more money with $59 more than Peter.

Step-by-step explanation:

To determine the amount they will have, you have to use the formula to calculate the future value:

FV=PV(1+r)^n

FV= future value

PV= present value

r= rate of interest

n= number of periods of time

-Peter:

FV=1,000*(1+0.04)^10

FV=1,000*1.48

FV=1,480

-Jose:

FV=900*(1+0.05)^11

FV=900*1.71

FV=1,539

Difference: $1,539-$1,480=$59

According to this, the answer is that Jose ends up with more money with $59 more than Peter.

Consider the equation 3p – 7 + p = 13. What is the resulting equation after the first step in the solution?

p – 7 = 13 – 3p
2p – 7 = 13
3p – 7 = 13 – p
4p – 7 = 13

Answers

Answer:

4p - 7 = 13

Step-by-step explanation:

The first step of the solution should be to simplify the left side by combining like terms. In this case, 3p and p are the like terms and 3p + p = 4p so the answer is 4p - 7 = 13.

Answer:

4p - 7 = 13

Step-by-step explanation:

What is the difference between two measurements of
the same object with values of 3.4 and 3.42?

Answers

Answer:

The percentage difference between 3.4 and 3.42 is 0.58651% or 0.02.

Step-by-step explanation:

Find the absolute difference between two numbers: |20 - 30| = |-10| = 10

Find the average of those two numbers: (20 + 30) / 2 = 50 / 2 = 25

Divide the difference by the average: 10 / 25 = 0.4

Express it as percentages: 0.4 * 100 = 40%

in this case, it would be 3.4 and 3.42

Answer: 0.02

Step-by-step explanation: 3.42 is bigger than 3.4 and they are asking for the difference between the two measurements. So, you subtract the 3.4 from the 3.42

Please help me with this question It’s due is in 5 min plzzz help I will beg ur legs

Answers

Answer:

[tex]\frac{s}{2t}[/tex]

Step-by-step explanation:

When you have exponents above a like term and they are being multiplied together, you add them.

For example:

[tex]a^{x} *a^{y} = a^{x + y}[/tex]

So let's group like terms in the numerator:

[tex]4r^{3} r^{-5} s^{-2} s^{-1}t[/tex]   We can add terms like in the example.

[tex]4 r^{-2} s^{-3} t[/tex]

Let's rearrange the denominator.

[tex]8r^{-2} s^{-4} t^{2}[/tex]

Now we have:

[tex]\frac{4r^{-2} s^{-3}t}{8 r^{-2} s^{-4} t^{2} }[/tex]  Cancel like terms

4/8 = 1/2    

[tex]r^{-2} /r^{-2}[/tex] = 1  So it cancels

[tex]s^{-3} / s^{-4} = s^{-1}[/tex] = s Since s is raised to the -1 it goes on top and becomes s.

[tex]t / t^{2} = 1/t[/tex]

Now we combine everything back together:

[tex]\frac{s}{2t}[/tex]

The local humane society is restocking on cat food to prepare for kitten season. Very young kittens need kitten formula which costs 3.99 per bottle. Older kittens need wet cat food which costs 1.5 per can.

Answers

Part A.) Let z be the variable denoted for the total cost of alIl kitten supplies. Then, let x be the number of bottles and let y be the number of cans. The equation would be: z = 3.99x + 1.50y The coefficients are 1 for z, 3.99 for x and 1.50 for y. There are no constants. The variables are z, x and y. Part B.) Substitute x=30 and y=120 to the equation in part A to determine z. z = 3.99(30) + 1.50(120) z = $299.7 Part C. Sales tax would be 7% of the total cost. This would be added as a constant. The expression would be: z = (3.99x + 1.50y)(1+0.07) Substituting x=30 and y=120, z = (3.99*30 + 1.50*120)(1+0.07) z = $320.679

Answer:

Step-by-step explanation:

A.) Let z be the variable denoted for the total cost of all kitten supplies. Then, let x be the number of bottles and let y be the number of cans. The equation would be:

z = 3.99x + 1.50y

The coefficients are 1 for z, 3.99 for x and 1.50 for y.

There are no constants.

The variables are z, x and y.

Part B.) Substitute x=30 and y=120 to the equation in part A to determine z.

z = 3.99(30) + 1.50(120)

z = $299.7

Part C.

Sales tax would be 7% of the total cost. This would be added as a constant. The expression would be:

z = (3.99x + 1.50y)(1+0.07)

Substituting x=30 and y=120,

z = (3.99*30 + 1.50*120)(1+0.07)

z = $320.679

The value of 1.999... in the form p/qwhere p and q are integers and q not
equal to 0 is​

Answers

Answer:

Step-by-step explanation:

1999/1000

Answer:

1999/1000

please mark me a brainlist

Which of the following is rational?
1) 3xPi

2) 2/3+9.26

3) \/45+\/26

4) 14.3+5.7876239...

BTW this ( \/ ) means the squared sybol. i did it like that because iididn't know how to do the squared symobl on a keyboard.

_
And the 3 in 14.3 is a repeating 3

Answers

I really don’t know sorry

Factorise 2xy-2x+6-6y

Answers

Answer:

2(y−1)(x−3)

Step-by-step explanation:

Factor 2xy−2x+6−6y

2xy−2x−6y+6

=2(y−1)(x−3)

If a bullet travels at 827.0 m/s , what is its speed in miles per hour?

Answers

Answer: 2,977,200 miles per hour

Step-by-step explanation: This is true because taking that that is miles per second there is 60 seconds in a minute so times that by 60 and there are 60 minutes in an hour so times that last answer by 60 again which gives you the answer

Evaluate 8r
rs when r
6 and s = 5.

Answers

Answer:

18

Step-by-step explanation:

I am assuming you meant 8r-rs, in this case:

Plug in r=6 and s=5:

8(6)-(6)(5)

8*6 = 48 and -6*5= -30

Thus,

48-30= 18

Answer  78

Step-by-step explanation:

Substitute the value of x back into the equation x + 3 – 2x = negative 2 x equals negative StartFraction one-fourth EndFraction plus StartFraction one-half EndFraction x plus 5. + x + 5 to justify the solution. What value of x is the solution?

Answers

Answer:

first one is -1 and the second question that comes up is 1, 2, and 6

Step-by-step explanation:

edge 2020

HELP !! it’s due soon

Answers

Answer:

108

Step-by-step explanation:

they are supplemntary meaning the sum of the equals 180

180 - 72 = 108

Answer:

<7= 108

Step-by-step explanation:

Angle 6 and angle 7 form a straight line. A straight line always equals to 180, so you subtract 180 from 72. 180-72=108

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