The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The correct option is C.
What is the triangle inequality theorem?The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
[tex](a+b) > c\\(b+c) > a\\(c+a) > b[/tex]
Given the length of the two sides of the triangle, therefore, we can write the inequalities,
8 + 5 > x ⇒ 13 > x
8 + x > 5 ⇒ x > - 3
5 + x > 8 ⇒ x > 3
Now, as per the inequality the value of x can lie between 3 to 13, but as the side needs to be greatest, therefore, the value of x will be 12.
Hence, the correct option is C.
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Answer:
12in
Step-by-step explanation:
Which of the following statements are true?
The prime factorization of 21 is 3 x 7.
The LCM of 14 and 21 is 42.
The prime factorization of 14 is 2 x 7.
14 is a composite number.
21 is a prime number.
The GCF of 14 and 21 is 14.
Answer:
The prime factorization of 14 is 2 x 7.
Step-by-step explanation:
The prime factorization of 14 is 2 x 7.
Answer:
14 is a composite number
Step-by-step explanation:
4, 5, 5, 6, 7, 8, 8,9
What is the range?
Solve f(-4) for f(x) = 7x - 4x
f(-4)= [?]
Enter
ternational Academy of Science. All Rights Reserved.
Answer:
-12
Step-by-step explanation:
What you have to do is plug -4 into the function as a puzzle. So, replace all x with -4.
f(-4) = 7(-4) - 4(-4) = -28 + 16 = -12
f (-4) = 7x ( 1-4 ) - 4 (-4)
= -28 + 16
= -12
What is a equation example?
An equation is a mathematical statement this is made from two expressions related by an equal sign. for instance, 3x – 5 = 16 is an equation. solving this equation, we get the fee of the variable x as x = 7.
A declaration of the equality of mathematical expressions. An expression representing a chemical reaction by using chemical symbols. equation.
Conclusion: There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. We review all three in this article.
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Which is most needed in order for groupwork technology to succeed?
A music club has $187 to buy ice cream for a party. Each carton of ice cream costs $4. If the club buys as many cartons as possible, how much money will the club have left?
Answer:
They would have $3 dollars left over.
Step-by-step explanation:
If you divide 187 by 4, you get 46.75. But if you look again, you can see that the remainder is 3 and it can confirm that it is the left over money that the club has now after buying as many ice cream cartons as possible.
Evaluate the limit. lim x → 0 4ex/2 − 4 − 2x − 1 2 x2 x3
The limit of the given expression lim x → 0 [4eˣ/2 − 4 − 2x − 12x² + x³] is determined as -2.
Limit of the function
The limit of the given expression is calculated as follows;
lim x → 0 [4eˣ/2 − 4 − 2x − 12x² + x³]
= (4e⁰)/2 - 4 - 2(0) - 12(0) + (0)
= (4)/2 - 4
= 2 - 4
= - 2
Thus, the limit of the given expression lim x → 0 [4eˣ/2 − 4 − 2x − 12x² + x³] is determined as -2.
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It’s been a while since I did Math but, in most scenarios, when you solve for an equation with only 1 x variable and you substitute it back in, it should always be true and equal the answer in the original equation(?).
For this equation, the answer was x=7, but when I substitute it back in, I was unable to get the original solution back, which means it is “no solution” after all.
Why is that?
Let's replace every copy of x with 7 and simplify.
[tex]\sqrt{5x+1}+9 = 3\\\\\sqrt{5*7+1}+9 = 3\\\\\sqrt{35+1}+9 = 3\\\\\sqrt{36}+9 = 3\\\\6+9 = 3 \ \text{ .... note the 6 on the left isn't negative}\\\\15 = 3\\\\[/tex]
Which is clearly false. This is probably the set of steps you followed to get "no solution".
Why is there no solution? Well let's subtract 9 from both sides to isolate the square root
[tex]\sqrt{5x+1}+9 = 3\\\\\sqrt{5x+1}+9-9 = 3-9\\\\\sqrt{5x+1} = -6\\\\[/tex]
Recall that the result of a square root operation is never negative. The range of [tex]y = \sqrt{x}[/tex] and [tex]y = \sqrt{5x+1}[/tex] is the set of nonnegative numbers. There is no way we can have the left hand side result in -6
If there was a negative sign out front the square root and we have this instead
[tex]-\sqrt{5x+1}+9 = 3\\\\[/tex]
then the answer would be x = 7
Unfortunately, there isn't such a negative sign, so we stick with "no solutions".
Find the indefinite integral using the substitution provided.
[tex]\int\limits({\frac{14e^2^x}{e^2^x+10}) } \, dx[/tex]
[tex]u=e^2^x+10[/tex]
Answer: [tex]7\text{Ln}\left(e^{2x}+10\right)+C[/tex]
This is the same as writing 7*Ln( e^(2x) + 10) + C
=======================================================
Explanation:
Start with the equation [tex]u = e^{2x}+10[/tex]
Apply the derivative and multiply both sides by 7 like so
[tex]u = e^{2x}+10\\\\\frac{du}{dx} = 2e^{2x}\\\\7\frac{du}{dx} = 7*2e^{2x}\\\\7\frac{du}{dx} = 14e^{2x}\\\\7du = 14e^{2x}dx\\\\[/tex]
The "multiply both sides by 7" operation was done to turn the 2e^(2x) into 14e^(2x)
This way we can do the following substitutions:
[tex]\displaystyle \int \frac{14e^{2x}}{e^{2x}+10}dx\\\\\\\displaystyle \int \frac{1}{e^{2x}+10}14e^{2x}dx\\\\\\\displaystyle \int \frac{1}{u}7du\\\\\\\displaystyle 7\int \frac{1}{u}du\\\\\\[/tex]
Integrating leads to
[tex]\displaystyle 7\int \frac{1}{u}du\\\\\\7\text{Ln}\left(u\right)+C\\\\\\7\text{Ln}\left(e^{2x}+10\right)+C\\\\\\[/tex]
Be sure to replace 'u' with e^(2x)+10 since it's likely your teacher wants a function in terms of x. Also, do not forget to have the plus C at the end. This is a common mistake many students forget to do.
To verify the answer, you can apply the derivative to it and you should get back to the original integrand of [tex]\frac{14e^{2x}}{e^{2x}+10}[/tex]
A) all values at which h has a local maximum
B ) all local maximum values of h
For the given function h(x), we have:
a) at x = -2 and x = 2.
b) y = 0 and y = 3.
How to identify the maximums of function h(x)?
First, we want to get the values of x at which we have maximums. To do that, we need to see the value in the horizontal axis at where we have maximums.
By looking at the horizontal axis, we can see that the maximums are at:
x = -2 and at x = 2.
Now we want to get the maximum values, to do that, we need to look at the values in the vertical axis.
The first maximum value is at y = 0 (the one for x = -2)The second maximum is at y = 3 (the one for x = 2).If you want to learn more about maximums:
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DEF, DF = 16 and m angle F = 45
Answer: [tex]8\sqrt{2}[/tex]
================================================
Work Shown:
x = length of each leg
Use the pythagorean theorem to get...
[tex]a^2+b^2 = c^2\\\\x^2+x^2 = 16^2\\\\2x^2 = 256\\\\x^2 = 256/2\\\\x^2 = 128\\\\x = \sqrt{128}\\\\x = \sqrt{64*2}\\\\x = \sqrt{64}*\sqrt{2}\\\\x = 8\sqrt{2}\\\\[/tex]
Or as an alternative path, you can divide the hypotenuse by [tex]\sqrt{2}[/tex] and then rationalize the denominator.
Both of these methods apply to 45-45-90 triangles only.
Answer:
[tex]8\sqrt{2}[/tex]
Step-by-step explanation:
We can sum the angles in a triangle to 180°:
m<D + m<E + m<F = 180°
m<D + 90° + 45° = 180°
m<D = 45°
Therefore, the triangle is an isosceles right triangle, since the base angles, <F and <D are the same measure. Because the triangle is isosceles, the legs are congruent, meaning that
DE = EF
We can use the Pythagorean Theorem([tex]a^{2} + b^{2} = c^{2}[/tex]) and plug in 16 as c, and DE and EF as a and b:
[tex]DE^{2} + EF^{2} = 16^{2}[/tex]
Since DE is the same as EF, we can substitute it in:
[tex]DE^{2} + DE^{2} = 256\\2DE^{2} = 256\\DE^{2} = 128\\DE = \sqrt{128}[/tex]
The square root of 128 is the same as [tex]8\sqrt{2}[/tex] since 128 can be factored into 64 x 2. So [tex]8\sqrt{2}[/tex] is the answer.
If you are looking for an easier way to do this, once you are able to recognize DEF is an isosceles triangle, you can say [tex]DE \times \sqrt{2} = 16[/tex] as this applies to all isosceles right triangles. This simplifies to:
[tex]DE = \frac{16}{\sqrt{2}} \\DE = \frac{16}{\sqrt{2} } \times \frac{\sqrt{2}}{\sqrt{2} } \\DE = \frac{16\sqrt{2} }{2} \\DE = 8\sqrt{2}[/tex]
N(-2,-2) after a 90 degree counterclockwise rotation
Answer: (2,-2)
Step-by-step explanation:
Rotating 90 degrees counterclockwise (about the origin) maps (x,y) onto (-y,x), so the answer is N'(2,-2)
Select the expressions whose value is 4.
0(-2)²
02(-2)
0-4÷2
0-41
Answer: The correct answer is A, [tex](-2)^{2}[/tex].
Step-by-step explanation:
A negative multiplied with another negative is a positive. Squaring is multiplying an integer by itself. Thus, it would look like -2×-2, which is equal to 4. I hope this helps!! :)
How can you make a sum of 12
There are several ways
Let's check all
1+112+103+94+85+76+60+12NO LINKS!!
Solve the compound inequality. Write the solutions in interval notation.
x + 7 ≥ 4 and 11x - 8 ≥ 3
Answer: [1, infinity)
===========================================================
Explanation:
Let's isolate x in the first inequality mentioned.
x + 7 ≥ 4
x + 7-7 ≥ 4-7
x ≥ -3
I subtracted 7 from both sides to undo the +7.
Now isolate x in the second inequality. We first add 8 to both sides, then divide both sides by 11.
11x - 8 ≥ 3
11x - 8+8 ≥ 3+8
11x ≥ 11
11x/11 ≥ 11/11
x ≥ 1
------------------
The two solutions we found were
x ≥ -3 and x ≥ 1
Next, draw out a number line with closed circles at -3 and 1. Shade to the right of each closed circle endpoint as you see below.
Notice that the two inequalities overlap for x ≥ 1
In other words, if a number is -3 or larger AND 1 or larger, then the number is 1 or larger.
The two solutions intersect to form x ≥ 1
The inequality x ≥ 1 is the same as 1 ≤ x which is the same as 1 ≤ x < infinity
Then that turns into the interval notation of [1, infinity)
The square bracket includes the endpoint 1.
If needed, use the infinity symbol in place of the word "infinity".
Answer:
[1, ∞)
Step-by-step explanation:
To solve a compound inequality, first separate it into two inequalities and solve them separately:
Solution of Inequality 1:
x + 7 ≥ 4
⇒ x ≥ 4 - 7
⇒ x ≥ -3
Solution of Inequality 2:
11x - 8 ≥ 3
⇒ 11x ≥ 3 + 8
⇒ 11x ≥ 11
⇒ x ≥ 1
As both graphs overlap for x ≥ 1, this is the solution.
Therefore, in interval notation: [1, ∞)
Which of the following points is shown in the graph below?
Answer:
Step-by-step explanation:
Comment
Only the x is minus. You know this because if you rotate the x axis 90 degrees clockwise, the plus axis will be on your right and the minus part of the axis on your left.The other 2 (y and z) are positive.All answers give - 4 in their choices. You are not helped much by -4y is on your left right now. That is the plus direction so y = 5z is 6 units up, so it is positive.Answer (-4,5,6)
B
Sally makes $3,000 each month. What is the most she can spend on housing?
Following the 30% rule of thumb, Sally should only spend a maximum of $900 on her rent
Numbers and percentageGiven Data
Monthly Salary = $3000Percentage spent on rent = 30%Let us find 30% of $3000
= 30/100* $3000
= 0.3*$3000
= $900
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Which of the following demonstrates how the 70 is calculated using the
combination pattem?
Answer:
A because it shows that the calculations are correct as well as combination pattem
pls help! thank you!
Using the zero product property, we can set each factor equal to zero.
First Factor [tex]x^{4}+5x^{2}-36[/tex]
[tex]x^{4}+5x^{2}-36=0\\(x^{2}+9)(x^{2}-4)=0\\x^{2}+9=0, x^{2}-4=0\\x=\pm 3i, x=\pm 2[/tex]
Second Factor [tex]2x^{2}+9x+5[/tex]
Using the quadratic formula, we get [tex]x=\frac{-9 \pm \sqrt{41}}{4}[/tex].
If we changed the 3 to a 0 in the equation, what would happen to the graph?
A function assigns the values. The function will move down by 3 units.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The graph of the function is given below. Now if 3 is replaced by a 0, then the y-intercept of the function will become zero while keeping the slope the same. Therefore, the function will move down by 3 units.
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Solve 10x-4y=15 for y.
Answer:
y = 15/-4 + 2.5x
Step-by-step explanation:
10x - 4y = 15
-4y = 15 - 10x
y = 15/-4 + 2.5x
Evaluate 15÷3·(-2) + |-10|
[tex]15 \div 3( - 2) + | - 10| \\ 5( - 2) + 10 \\ - 10 + 10 \\ 0[/tex]
Hope it helps
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HELPP (NO LINKS)
The table shows the value of a townhome for 3 years after it is purchased. The values
form a geometric sequence. If the pattern continues, how much will the townhome be
worth after 7 years?
The amount that the home will be worth after 7 years is $457763.67
The geometric sequence is sometimes called the exponential sequence. The formula for calculating the nth term of an arithmetic sequence is expressed as:
Tn = ar^n-1
where
a is the first term = 120,000
r is the common ratio = 150000/120000 = 1.25
Required
7th term
Substitute
T7 = 120,000(1.25)^7-1
T7 = 120,000(1.25)^6
T7 = 120,000(3.8147)
T7 = $457763.67
Hence the amount that the home will be worth after 7 years is $457763.67
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Answer:
(c) $457,763.67
Step-by-step explanation:
hope this helps:)
Is 82296 a perfect square? If not, which number is multiplied to make it a perfect square?
No, Number 82296 is not a perfect square.
And, We multiply by 82296 in the number 82296 to amke a perfect square.
What is square root of a number?A square root of a number is a value that multiplied by itself gives the same number.
Given that;
The number is,
⇒ 82296
Now,
If the number 82296 is a perfect square number.
So, We get;
⇒ x² = 82296
⇒ x = √82296
⇒ x = 286.87
So, This number is not a perfect square number.
If we multiply by the number 82296 in the number 82296, we get;
⇒ 82296 × 82296
⇒ (82296)²
Thus, It become a perfect square number.
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Adrian's annual salary is $111,000. He is not eligible for a Roth IRA because he makes
too much money. His company offers a matching program that is 1:1 up to 3% of annual
salary. (do not include commas or dollar signs in your answers)
How much should he contribute to Roth IRAS?
If he is not eligible for Roth IRAs, then he cannot contribute to Roth IRAs. However, he can contribute $3,330 monthly under his company's Matching Program.
What is a Roth IRA?The Individual Retirement Account to which employees in the United States can contribute after-tax earnings is called the Roth IRA.
Under its governing principles, certain individuals whose annual income exceeds stipulated amounts are INELIGIBLE to contribute.
How do we arrive at $3,330?Recall that the question indicates that his company offers a matching program with a ratio 1:1 up to 3% of his annual salary.
Since his annual salary is $111, 000,
3% x 111,000 = 3,330.
This means that annually, the total matching contribution due to Adrian would be:
3,330 x 2 = 6, 660.
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PLEASE HELP The quotient of seven more than three times a number m The number 27 less than n as an algebraic expression?
The algebraic expression is (7 + 3m)/27 < n
How to determine the number?The statement is given as:
"The quotient of seven more than three times a number m and the number 27 is less than n"
The numbers are represented as n and m
Quotient means divide
So, we have:
The quotient of seven more than three times a number m and the number 27 is represented as:
(7 + 3m)/27
The result is less than n.
So, we have:
(7 + 3m)/27 < n
Hence, the algebraic expression is (7 + 3m)/27 < n
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I’LL GIVE BRAINLIST IF YOU ANSWER CORRECT:
Answer:
Step-by-step explanation:
Solution
The first step is to simplify the top of the fraction. Subtract 5.6 - 2.7
The numerator (top) and denominator(bottom) are decimal fractions. They are 2.9 for the top and 2.9 for the bottom.
The whole expression reduces down to 1, which is an integer.
Note
You have choices. If you want exact answers you will have to list those choices.
Answer: 1
Apply the indicated operations to the matrix; then choose the correct answer.
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The correct option is B.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
When the indicated operation 4R₁ → R₁ is applied then the matrix will be,
[tex]\left[\begin{array}{ccc}1&2&0\\-2&-1&3\end{array}\right] \rightarrow \left[\begin{array}{ccc}4&8&0\\-2&-1&3\end{array}\right][/tex]
Hence, the correct option is B.
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Julia is in charge of buying clothing in bulk for a sporting goods store. The table shows the unit prices of the items she intends to buy.
Unit Prices of Clothing Items for a Sporting Goods Store
Item
Unit Price
T-shirts
$7.50
Shorts
$9.00
Windbreakers
$12.25
If she will buy 35 T-shirts, 45 pairs of shorts, and 25 windbreakers, what will be her total cost?
$958.75
$973.75
$1,021.25
$1,038.75
The total cost of 35 T-shirts, 45 pairs of shorts, and 25 windbreakers is $973.75.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Cost of 1 T-shirt = $7.50
Cost of 35 T-shirts = 7.50 x 35
= 262.5
Cost of 1 Shorts = $9.00
Cost of 45 T-shirt = 9.00 x 45
= 405
Cost of 1 windbreakers = $12.25
Cost of 25 windbreakers = 12.25 x 306.25
So, The total cost of 35 T-shirts, 45 pairs of shorts, and 25 windbreakers
= 262.5+405+306.25
= $973.75
Hence Her total cost is $973.75.
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Math need help please
Two large trees, 5.5m and 6.8m tall, stand 12m apart. A bird flies directly from the top of one tree to the top of the other. How far has the bird flown?