The sum of two numbers is 65. The larger number is five more than three times the smaller number. What are the numbers? (Systems of Equations)

Answer:

I think its 132.

The total surface area of the triangular prism is 200 cm².

Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)

First, find the height of the prism.

Let h is the height of the prism

Use the pythagoras theorem

then

5² = (6/2)² + h²

5² = 3² + h²

25 = 9 + h²

h² = 25 - 9

h² = 16

h =4

Now apply the surface area formula

total surface area = ( 5 + 5 + 6) 11 + 6×4

                             = 16 × 11 + 24

                             = 176 +24

                             = 200 cm²

Hence the surface area is 200 cm²

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Step-by-step explanation:

Consider LHS

[tex] \cos(x) + \sin(x) \tan(x) = \sec(x) [/tex]

Apply quotient identies

[tex] \cos(x) + \sin(x) \times \frac{ \sin(x) }{ \cos(x) } = \sec(x) [/tex]

Multiply the fraction and sine.

[tex] \cos(x) + \frac{ \sin {}^{2} (x) }{ \cos(x) } = \sec(x) [/tex]

Make cos x a fraction with cos x as it denominator.

[tex] \cos(x) \times \cos(x) = \cos {}^{2} (x) [/tex]

so

[tex] \frac{ \cos {}^{2} (x) }{ \cos(x) } + \frac{ \sin {}^{2} (x) }{ \cos(x) } = \sec(x) [/tex]

Pythagorean Identity tells us sin squared and cos squared equals 1 so

[tex] \frac{1}{ \cos(x) } = \sec(x) [/tex]

Apply reciprocal identity.

[tex] \sec(x) = \sec(x) [/tex]

9514 1404 393

Answer:

  3√3 square units

Step-by-step explanation:

The area of a regular n-sided polygon with radius r is given by the formula ...

  A = (n/2)r²·sin(360°/n)

For n=3 and r=2, the area is ...

  A = (3/2)(2²)·sin(360°/3) = 6·sin(120°) = 6(√3/2)

  A = 3√3 . . . . square units

_____

Alternate solution

The center of this polygon is the centroid, which divides each median into parts with the ratio 2:1. This means the given radius is 2/3 of the height of the triangle. The base of the triangle is 2/√3 times the height, so is ...

  b = (2/√3)(3) = 2√3

The area using these dimensions is calculated as ...

  A = 1/2bh

  A = 1/2(2√3)(3) = 3√3 . . . . square units

Answer:

48 1/4 packages

Step-by-step explanation:

Answer:

D)  x = -3

Step-by-step explanation:

Answer:

 ^^

Step-by-step explanation:

Answer:

You didn't add the range. I'll use (0<x<2π)

cosx = -1/2

x=-cos-¹(1/2)

x= -60°

Cosine is negative in the second and 3rd quadrants

180-x ---- Second quadrant

x+180 ----- 3rd quadrant

So

Our answer

180-(-60)=240° or 4π/3 second quad

180+(-60) = 120° or 2π/3---- 3rd quad

Answer:

Area of a circle = πr^2 if pi here = 3

then (3 × 81) in^2 = 243 in^2

Hope it helps

Answer:

The area of circle is 254.34 in².

Step-by-step explanation:

Given :

To Find :

Using Formulas :

[tex]\star{\small{\underline{\boxed{\sf{\pink{R = \dfrac{D}{2}}}}}}}[/tex]

[tex]\star{\small{\underline{\boxed{\sf{\pink{Area_{(Circle)} = \pi{r}^{2} }}}}}}[/tex]

Solution :

Here we have given that diameter of circle is 18 in. So, finding the radius of circle :

[tex]\implies{\sf{Radius = \dfrac{D}{2}}}[/tex]

[tex]\implies{\sf{Radius = \dfrac{18}{2}}}[/tex]

[tex]\implies{\sf{Radius = \cancel{\dfrac{18}{2}}}}[/tex]

[tex]\implies{\sf{Radius = 9 \: in}}[/tex]

[tex]\star{\underline{\boxed{\sf{\red{Radius = 9 \: in}}}}}[/tex]

Hence, the radius of circle is 9 in.

[tex]\rule{200}2[/tex]

Now, we know the radius of circle is 9 in. So, finding the area of circle by substituting the values in the formula :

[tex]\implies{\sf{Area_{(Circle)} = \pi{r}^{2}}}[/tex]

[tex]\implies{\sf{Area_{(Circle)} = 3.14\times {(9)}^{2}}}[/tex]

[tex]\implies{\sf{Area_{(Circle)} = 3.14\times {(9 \times 9)}}}[/tex]

[tex]\implies{\sf{Area_{(Circle)} = 3.14\times (81)}}[/tex]

[tex]\implies{\sf{Area_{(Circle)} = \dfrac{314}{100} \times 81}}[/tex]

[tex]\implies{\sf{Area_{(Circle)} = \dfrac{314 \times 81}{100}}}[/tex]

[tex]\implies{\sf{Area_{(Circle)} = \dfrac{25434}{100}}}[/tex]

[tex]\implies{\sf{Area_{(Circle)} = 254.34 \: {in}^{2} }}[/tex]

[tex]{\star{\underline{\boxed{\sf{\red{Area_{(Circle)} = 254.34 \: {in}^{2}}}}}}}[/tex]

Hence, the area of circle is 254.34 in².

[tex]\rule{300}{1.5}[/tex]

Answer:

Step-by-step explanation:

Was the latter half of this function, -64 / 2x + 14, meant to be:

-64 / 2x              +              14, or

-64 / (2x + 14)?

In the first case the vertical asymptote is x = 0.

In the second, the vertical asymptote is the root of 2x + 14, or x = -7

Use parentheses in problems such as this one, to eliminate ambiguity.

Answer:

I don't have the right calculator but if you type sin-1(11/60) it'll give you the answer

Answer:

See the three attached images.

Step-by-step explanation:

image1 shows the intersection of b and c:  [tex]b \cap c[/tex]. (green "football")

image2 shows the complement of a (outside a):  [tex]a'[/tex]  (yellow)

image3 shows the intersection of those sets:  [tex]a'\cap (b\cap c)[/tex] (green "football with a bite out of it")   :-)

Answer:

0.6832

Step-by-step explanation:

Given :

Mean, m = 52

Standard deviation, s = 7

-1.2 standard deviation of average = 57 - 1.2(7) = 57 - 8.4 = 48.6

2 standard deviations of average = 57 + 2(7) = 57 + 14 = 71

Zscore = (48.6 - 52) / 7 = - 0.486

Zscore = (71 - 52) / 7 = 2.714

P < -0.486) = 0.31348

P < 2.714 = 0.99668

P < 2.714 - P < -0.486 = (0.99668 - 0.31348) = 0.6832

9514 1404 393

Answer:

  -12dx +15ex +9fx

Step-by-step explanation:

  - 3x * (4d - 5e - 3f) = (-3x)(4d) +(-3x)(-5e) +(-3x)(-3f)

  = -12dx +15ex +9fx

Answer:

Yes, 9^2+40^2=41^2

Step-by-step explanation:

From the Pythagoras’ theorem, the square of the hypotenuse of a right triangle equals the sum of the squares of the two other sides

From what we have , the side lengths are 9, 40 and 41

As we can see, 41 is the longest side length and that makes it the hypotenuse

The square of the two other sides is 40^2 + 9^2 = 1,681

Also, 41^2 = 1,681

As we can see, the sum of the squares equal the square of the hypotenuse

Since this follows the theorem, we can conclude that the triangle is a right triangle

Answer:

C, Yes, 92+402=412.

Step-by-step explanation:

Answer:

42.25 feet ³

Step-by-step explanation:

Volume of the box = length × width × height

Length = 6 1/2 feet = 6.5 feet

Width = 3.25 feet

Height = 2 feet

Volume of the box = length × width × height

= 6.5 feet × 3.25 feet × 2 feet

= 42.25 feet ³

Volume of the box = 42.25 cubic foot

Answer:

y is 107° and z is 36°

Step-by-step explanation:

73° and y are supplementary angles so they add up to 180°

Answer:

y = 107

z = 36

Step-by-step explanation:

We are given that line o is parallel to line m, and we can notice line k is a transversal through them both. Using same side interior angles, we can say that:

y + 73 = 180

and

y = 107

Next, using vertical angles, we can say that:

5z - 73 = y

We already have y = 107, so we can substitute that in:

5z - 73 = 107

5z = 180

z = 36

Answer:

B,E

Step-by-step explanation:

(5,0) (5=x, 0=y)

A is false because y = 0

B is true because x=5

c is false because y = 0

D is false because again y = 0

E is true because 5,0 is on the x axis

- Gage Millar, Algebra 2 tutor

Answer:[tex]h=\sqrt{96}in.[/tex]

Step-by-step explanation:

.

Answer:

answer is D I think

Step-by-step explanation:

.............

Answer:

25.13

Step-by-step explanation:

C = 2πr

C = 2π(4)

C = 25.13

Hope this helps!

Answer:

The answer is: u-3>-6

This is because 10-3=7 and 7>-6

The value of QR in the triangle is 16 units

Recall that Congruence of triangles represents the similarity of triangles. Two triangles are congruent if their corresponding sides and angles are congruent

The question states that  ΔPML≅ΔTRQ

This implies that ML/QR = PM/TR

⇒(7x-9)/2x+2  = 35/14

Cross and multiplying we have

14(7x-9) = 35(2x+2)

=98x-126 = 70x +70

98x-70x = 70+126

⇒28x = 196

Making x the subject of the formula

x= 196/28 = 7

Recall that the side QR = 2x+2

Then by substitution,

2(7) +2

14+2 =16

This therefore keeps the side QR as 16 units.

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Answer:

x=0

y= x + 8

Step-by-step explanation:

find the oblique asymptotes using long polynomial divison

Answer:

using Pythagoras theorem x=32.7

Answer:

21.7

Step-by-step explanation:

In order to solve this problem, we can use trig functions. We are given the side adjacent to the 37° given and we are looking for the hypotenuse. This means that cosine function is the most suitable. Cosine is written as:

cos(θ°) = adjacent / hypotenuse

We can substitute the values we have:

cos(37°) = 17.3 / x

And rewrite the expression:

x = 17.3 / cos(37°)

Then, use a calculator to evaluate:

x = 21.66194689

This can be rounded to 21.7

Answer:

A. x= -5

B. x= 8

Step-by-step explanation:

A. 25 - 3x = 40

-3x = 40 - 25

-3x = 15

x= 15/-3

x= -5

B. 2 (x-10) =  -4

x-10 = -4/2

x-10 = -2

x = 8

A. 25 - 3x = 40

         -3x = 40 - 25

               = 15

            -x = 15/3

             x = -5

   Checking

    25 - 3*-5 = 40

    25 + 15 = 40

            40 = 40

       LHS = RHS

B. 2(x-10) = -4

    2x - 20 = -4

            2x = -4 +20

             x = 16/2 = 8

Hope u understand

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Answer:

Step-by-step explanation:

Answer:

It would be the fourth one

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

We can substitute the point (2, 2) into the equation. So, in place of x would be 2 and in place of y would be 2 as well:

y = 6 - 2x

2 = 6 - 2(2)

2 = 6 - 4

2 = 2

Since the above is a true statement, the point (2, 2) must belong to the line y = 6 - 2x

Yes, the line y=6-2x passes through the point (2, 2).

Given that, the line y=6-2x passes through the point (2, 2).

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

Here, substitute (x, y)=(2, 2) is the given line y=6-2x, we get

2 = 6-2(2)

2 = 2

Since, LHS = RHS

Yes, the line y=6-2x passes through the point (2, 2).

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Answer:

24

Step-by-step explanation:

41-17=24

Answer: 3. 2/3 2. (Just make up a problem with the model). 1. 3/8-2/8= ____(answer)

Step-by-step explanation: