A geometry teacher asked Charlene to define “acute triangle.” Charlene said that an acute triangle is a triangle whose three interior angles have measures less than 90°. Is Charlene’s definition valid?

[tex](a+4)^2 -11(a+4) -42\\\\=x^2 -11x -42~~~~~~~~~~~~~~~~~~~~~~~~;[a+4 = x]\\\\=x^2 -14x +3x -42\\\\=x(x-14) +3(x-14)\\\\=(x+3)(x-14)\\\\=(a+4+3)(a+4-14)~~~~~~~~~~~~;[\text{Substitute back}~ a+4 =x]\\\\=(a+7)(a-10)[/tex]

Answer:

(a - 10) (a + 7)

Step-by-step explanation:

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(a + 4)² - 11(a + 4) - 42

Fractorize

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So the equation will be

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[tex] \sf \large {x}^{2} - 11x - 42[/tex]

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[tex] \sf {x}^{2} - 14x + 3x - 42[/tex]

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[tex] \sf x(x - 14) + 3(x - 14)[/tex]

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[tex] \sf (x - 14)(x + 3)[/tex]

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[tex] \sf (a + 4 - 14)(a + 4 + 3) \\ \\ \boxed{ \frak{(a - 10)(a + 7)} } [/tex]

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Answer:Hello the  Answer to your math problem  is attached

Step-by-step explanation:

Step-by-step explanation:

(6+r)^2 = 81 + r^2

36 + 12r+ r^2 = 81 + r^2

12r = 81-36 = 45

r = 15/4 = 3.75

Answer:

0.33 recurring

Step-by-step explanation:

assuming alol the fractions are equal, find the total number of possibilities and assign one for each number

Answer:

If the question asks to write the answer as a power, it should be the power of 6 without the variable of Z.

Answer:

4/5

Step-by-step explanation:

Answer:

n + (n + 6) = 24.

Step-by-step explanation:

Let him have n  blue marbles, then he has n + 6 other narbles.

He has a total of 24 marbles, so:

n + (n + 6) = 24.

Answer:

B) n + (n + 6) = 24, where n is the blue marbles

Step-by-step explanation:

^^

Answer:
1) 25
2) 61
3) 20
4) 25
5) 65.46

Explanation:

1) Use the formula " (n-2)180. N = the number of sides.
(25-2)180 = 4140

2) The sum of the polygon is 900.
(7-2)180 = 900
Add up all the numbers and variables then equal them to 900.

3) To find an interior of an 18-gon is the use of this formula:
(n-2)180 = Sum of the polygon
Sum / n

(18-2)180 = 2880
2880 / 18 = 160
180 - 160 = 20 ; Because they are supplementary.

4) (25-2)180 = 4140
4140 / 25 = 165.6

5) Copy the formula for explanation #3. But instead of an 18-gon, do 11-gon.  

Answer:

The length of the field is equal to 96 m.

General Formulas and Concepts:
Algebra I

Equality Properties

Terms/Coefficients

Geometry

Perimeter Formula [Rectangle]: P = 2l + 2w

Step-by-step explanation:

Step 1: Define

Identify given.

P = 354 m

w = 81 m

Step 2: Find Length

∴ we have found the length of the field to be 96 meters.

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Topic: Geometry

A percentage is a way to describe a part of a whole. The total tax of Tegan's earnings will be £8,520(£6,400+£1,200).

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Since there is no tax for the first £11,000, therefore, the earnings which will be taxed,

£48,300 - £11,000 = £37,300

The amount of tax for the income of £11,000 to £43,000, will be,

20% of (£11,000 to £43,000)

= 20% × (£43,000 - £11,000)

= £6,400

The amount of tax for the income of £11,000 to £150,000, will be,

40% of (£43,000 to £48,300)

= 40% × (£5,300)

= £2,120

Hence, the total tax of Tegan's earnings will be £8,520(£6,400+£1,200).

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Here we go ~

It's been given that :

[tex]\qquad \sf  \dashrightarrow \: \vec{v} = - \vec{u}[/tex]

And magnitude of vector u is 6 units and with a direction 330°

And we are asked to find the magnitude and direction of vector v ~

So, let's get stated ~

As we can observe, vector v and vector u have equal magnitude because they have equal sign between them.

that is :

[tex]\qquad \sf  \dashrightarrow \: | \vec{v} | = | \vec{u}| [/tex]

[tex]\qquad \sf  \dashrightarrow \: | \vec{v}| = 6 \: units[/tex]

And the negative sign in the equation shows that the two vector have opposite directions or you can say they are anti-paralllel.

So, we can just rotate vector u by 180° to get vector v ~

[tex]\qquad \sf  \dashrightarrow \: \hat{n} = 330 \degree - 180 \degree[/tex]

[tex]\qquad \sf  \dashrightarrow \: \hat{n} = 150 \degree[/tex]

Conclusion :

Answer:

C. 5f +25

Step-by-step explanation:

Answer:

y + 5x + 8

Explanation:

Move numbers or variable:

y + 5x + 8

Additional Information:

x + y + 1

This has three terms, coefficient of 1, constant of 1

Answer:

[tex]\huge\boxed{\bf\: x + 5y + 8}[/tex]

Step-by-step explanation:

We need to make an expression using the given conditions. Let's look at them in order.

Condition 1:

If the expression has three terms then let's take the three terms as, x, y & z. Therefore, the expression uoto now = x + y + z.

Condition 2:

Now, the expression has a term with coefficient = 5. Let's put 'y' with coefficient 5 since the second term has two blanks in the question. So, expression = x + 5y + z.

Condition 3:

The expression also has a constant 8. By substituting the value of 'z' with 8 (as 'z' is not given in the options), we get the final expression as → x + 5y + 8.

[tex]\rule{150pt}{2pt}[/tex]

Answer:

68 cubic feet

Step-by-step explanation:

Split the object into 2 so you have 2 squares. Now do 2x4x6=48cbft. Then do 5x2x2=20cbft. Then just add them together! 48+20=68!

Hope this helps! ;-)

Answer:

14 gm

Step-by-step explanation:

34 minutes is TWO half lives   1/2 * 1/2 = 1/4   will be left

   1/4 * 56 = 14 gm

                    [tex]\rule{199}{1}[/tex]

Given question:-

Which inequality is equivalent to -y≥18?

Answer and how to solve:-

Divide by -1 on both sides to fully simplify the inequality, which is what we're asked to do.

So we get

y≤-18

Notice that the inequality sign changed.

The inequality sign changes when we divide both sides of an inequality by a negative number.

[tex]\rule{300}{1}[/tex]

Answer:

the answer is exponential

Step-by-step explanation:

Answer:

Hi! My guess would be exponential.

Step-by-step explanation:

stay safe, and I hope I helped I apologize if I am wrong, good luck friends

Answer:

Looking at the problem we come across one issue where we have two minus signs.  However, this issue can be fixed because for example if we multiply -1 by -1 we would just get 1.  Therefore these two minus signs cancel out and we put a plus sign so our problem becomes -7 + 13.  Now we just combine and we get 6.

Answer:

6

Step-by-step explanation:

[tex](-7)-(-13)\\(-7)+13\\13-7\\6[/tex]

Answer:

a=3/5 , b=4/5. ,.

c=5/5

c=5/5

=1

The following claims concerning hyperbola are correct:

It's worth noting that a hyperbola is essentially an open curve with two branches.

The center is at (0, 0), the vertex is at (–6, 0), and the directrices are all vertical lines.

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Answer:

1,2,5

Step-by-step explanation:

The justification of step a is common denominator and the justification of step b is multiplication property of equality

The equation is given as:

[tex]a(x + \frac{b}{2a})^2 = -c + \frac{b^2}{4a}[/tex]

Take the LCM

This gives

[tex]a(x + \frac{b}{2a})^2 = \frac{-4ac + b^2}{4a}[/tex]

The above represents a common denominator.

Multiply both sides by 4a

[tex]4a^2(x + \frac{b}{2a})^2 = -4ac + b^2[/tex]

The above represents the multiplication property

Hence, the justifications are common denominator and multiplication property of equality

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Step A: common denominator

Step B: multiplication property of equality

Answer:

6.84 hours

Step-by-step explanation:

I will have to assume  100 is fully charged and that it drains 1/9 of 100 for each hour

76 / ( 100 * 1/9) = 6.84 hrs

Answer:Don’t know I will just get points.Thx

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

10 to the second power is 10^2. Therefore, that is 10x10.

This results in 100.

Answer:

100

Step-by-step explanation:

it is 100 because first you have to get 2 10's and times 10 x 10= and that equals 100 so thats how you get 100!

Answer:

It's not possible to get 16 from 1 divided by 4 alone. It will always be 0.25

Answer:

18.33%.

Step-by-step explanation:

The total number of cars is 60

what you want is the red number (11)

You set up what you want over what you have and end up with:

11/60

turn this into decimal and you get 0.183

to turn into percent multiply by a 100

You end up with 18.33%

Answer:

18.3%

Explanation:

Red = 11, silver = 24, gray = 16 black = 9

[tex]\sf probability = \dfrac{favorable \ outcomes}{total \ possible \ outcomes}[/tex]

[tex]\rightarrow \sf \dfrac{11}{60} \ x \ 100[/tex]

[tex]\rightarrow \sf 18.3 \%[/tex]

Answer:

Probability of anything =

    (number of possible successful outcomes)

divided by

    (total possible number of outcomes) .

There are 36 total marbles in the bag, so there are 36 total

possible outcomes of one draw.

The successful outcomes are all the possible draws that are

not blue.    There are 28 of those.

So the probability of a non-blue selection is

        28/36  =  7/9  =  77.8%  (rounded)

Step-by-step explanation:

Answer:

The probability that a marble ball drawn will not be blue is

[tex] \frac{7}{9} [/tex]