1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Rasek [7]
3 years ago
9

The height of a triangle is 4 in. greater than twice its base. The area of the triangle is no more than 168 in.2. Which inequali

ty can be used to find the possible lengths, x, of the base of the triangle?
Mathematics
2 answers:
Jet001 [13]3 years ago
8 0
Recall that A = 1/2bh. We are given that h = 4+2b So, putting it all together: 168 = 1/2 b(4+2b) 168 = 1/2(4b + 2b^2) 168 = 2b + b^2 b^2 + 2b - 168 = 0. Something that multiplies to -168 and adds to 2? There's a trick to this. Notice 13^2 = 169. So, it's more than likely in the middle of the two numbers we're trying to find. So let's try 12 and 14. Yep. 12 x 14 = 168. So this factors into (b+14)(b-12) So b = -14 or b =12. Is it possible to have a negative length on a base? No. So 12 must be our answer. Let's check this. If 12 is our base, then according to our problem, 2*12 + 4 would be our height... or 28. so what is 12 * 28 /2? 196. Check. Hope this helped!
den301095 [7]3 years ago
8 0
X=base 
(2x+4)=height
Area of a triangle=(base x height)/2
We can suggest this inequality:

x(2x+4)/2<168
x(2x+4)<336
2x²+4x<336
2x²+4x-336<0
x²+2x-168<0

1) we change the inequality sign of inequality by equality sign.
x²+2x-168=0
x=[-2⁺₋√(4+672)] / 2
x=(-2⁺₋√676)/2
we have two solutions:
x₁=(-2-√676)/2=-14
x₂=(-2⁺√676)/2=12

2) we make intervals with these values.
(-∞, -14<span> )
</span><span>(-14,12)
</span>(12, +∞)

3) we check  it out if these intervals work
(-∞,-14), For instead; if x=-15⇒ (-15)²+2(-15)-168=27>0. this solution interval don´t work.

(-14,12), For example; if x=1 ⇒(-1)²+2(1)-168=-168<0 this solution interval works.
but the solutions have to be always positive numbers, therefore, the solution is:  (0,12).

(12,+∞) , For example, if x=13 ⇒ (13)²+2(13)-168=27>0, this solution  interval don´t work.

Answer: the inequality is : <span>x(2x+4)/2<168, and the interval solution is (0,12) for the values of the base. </span>

You might be interested in
In the diagram below, P is circumscribed about quadrilateral ABCD. What is the value of x?
alexira [117]
We know that
In any quadrilateral where the vertices are on the circumference of a circle, the opposite angles add up to 180 degrees. 

So,
 in this problem
(x+20) + 110 = 180 \\ x+130=180 \\ x=180-130 \\ x=50degrees

therefore

the answer is
x=50degrees
7 0
3 years ago
Read 2 more answers
CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars
velikii [3]

Answer:

P(939.6 < X < 972.5) = 0.6469

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars.

This means that \mu = 965, \sigma = 113

Sample of 57:

This means that n = 57, s = \frac{113}{\sqrt{57}} = 14.97

Find the probability that a single randomly selected policy has a mean value between 939.6 and 972.5 dollars.

This is the pvalue of Z when X = 972.5 subtracted by the pvalue of Z when X = 939.6. So

X = 972.5

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{972.5 - 965}{14.97}

Z = 0.5

Z = 0.5 has a pvalue of 0.6915

X = 939.6

Z = \frac{X - \mu}{s}

Z = \frac{939.6 - 965}{14.97}

Z = -1.7

Z = -1.7 has a pvalue of 0.0446

0.6915 - 0.0446 = 0.6469

So

P(939.6 < X < 972.5) = 0.6469

3 0
2 years ago
A bike path is 3 miles long. there are distance markers every path one fourth mile to the end of the path. which number line cor
Fynjy0 [20]

Given :

A bike path is 3 miles long. there are distance markers every path one fourth mile to the end of the path.

To Find :

Which number line correctly models this situation and the total number of distance markers.

Solution :

It is given that their are markers every 1/4 part of mile.

So, their are 4 markers per mile.

Numbers of markers in 3 miles long path is :

n = 3\times 4\\\\n = 12

Therefore, the total number of distance markers in 3 mile path is 12.

Hence, this is the required solution.

5 0
3 years ago
Allison bought 15 donuts and 12 cupcakes at the bakery. Of these items, 2/3 of the donuts were glazed, and 4/6 of the cupcakes w
Mariulka [41]

Answer: 7

Step-by-step explanation: I had this question before

8 0
3 years ago
Read 2 more answers
Log10 (2x + 1) - logio(3x - 2) = 1​
Pavlova-9 [17]

Answer: x=3/4

Step-by-step explanation:

To solve, first express the left side as one logarithm. To do so, apply the quotient rule which is log_bM/N=log_bM-log_bN .

log((2x+1)/(3x-2))=1

Then, express the equation to its equivalent exponential form to eliminate the logarithm.

Note that the exponential form of log_b M=a is M=b^a .

Since the base of the logarithm in the given equation is not written, it indicates that its base is 10.

So re-writing the equation, it becomes:

log_10((2x+1)/(3x-2))=1

And its exponential form is:

(2x+1)/(3x-2)=10^1

(2x+1)/(3x-2)=10

Now that the equation has no more logarithm, the next step is to remove the x in the denominator.

To do so, multiply both sides by 3x-2.

(3x-2)*(2x+1)/(3x-2)=10*(3x-2)

2x+1=30x-20

Next, combine like terms.

To combine 30x and 2x, bring them together on one side of the equation. So, move 2x to the right side by subtracting both sides by 2x.

2x-2x+1=30x-2x-20

1=28x-20

To combine 20 and 1, bring them together on the side opposite the term with x. So, add both sides by 20.

1+20=28x-20+20

21=28x

And, divide both sides by 28 to have x only at the right side.

21/28=(28x)/28

3/4=x

Hence, the solution to the given equation is x=3/4 .

3 0
3 years ago
Other questions:
  • Which of the following polynomials is a binomial
    13·2 answers
  • AD = DB and AE = EC. BC = 22 and EF = 9.<br><br> DE = [?]
    6·1 answer
  • . In 2018, there is an average of 45.6 people per 3 square kilometers in the United States. How many people live in 1 square kil
    9·1 answer
  • Thomas has $6.35 in dimes and quarters. The number of dimes is three more than three times the number of quarters.
    13·1 answer
  • 0.034 is 1/10 of 0.0034
    9·1 answer
  • Which of the following statements is always true of similar polygons?
    6·2 answers
  • Which hill described in the table is the steepest and why?
    8·1 answer
  • Find an<br> expression which represents the sum of (8x - 7) and (10x + 3) in<br> simplest terms.
    8·1 answer
  • What would you divide the numerator and denominator by to put 16 over 24 in simplest form?
    7·2 answers
  • Multiply and divide rational expressions and simplify the answer
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!