Isaac's birthday party costs $3 for every guest he invites. How many guests can there be,
at most, if Isaac can afford to spend a total of $18 on his birthday party?

Answer:

a. ΔABC is an isosceles triangle

b. ΔABC is a right triangle

c. The perimeter of ΔABC is approximately 10.8

Step-by-step explanation:

The given vertices of the polygon, are;

A(1, 4), B(4, 5), C(5, 2)

By observation of the differences of the coordinates of the given points, the points are non-linear, as the rate of increase in the y-values, for a given increase in the x-value, is not constant

The length of segments of the triangle ΔABC are found using the formula for finding the distance, 'd', between points given their coordinates, (x₁, y₁), (x₂, y₂), as follows;

[tex]d = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]

The length of segment, [tex]\overline {AB}[/tex] = √((5 - 4)² + (4 - 1)²) = √10

The length of segment, [tex]\overline {AC}[/tex] = √((2 - 4)² + (5 - 1)²) = √20

The length of segment, [tex]\overline {BC}[/tex] = √((2 - 5)² + (5 - 4)² = √10

The length of segment, [tex]\overline {AB}[/tex] = The length of segment, [tex]\overline {BC}[/tex], therefore, ΔABC is an isosceles triangle by definition of an isosceles triangle which is a triangle that have two sides of equal length

ΔABC is an isosceles triangle

b. According to Pythagoras' theorem, the sum of the squares of the two shorter sides (the legs) of a right triangle = The square of the length of the longest side

In if triangle ΔABC is a right triangle, we should have;

[tex]\overline {AB}[/tex]² + [tex]\overline {BC}[/tex]² = [tex]\overline {AC}[/tex]²

Checking gives;

(√10)² + (√10)² = 10 + 10 = 20 = (√20)²

Whereby [tex]\overline {AB}[/tex]² (= (√10)²) + [tex]\overline {BC}[/tex]² (= (√10)²) = (√20)² = [tex]\overline {AC}[/tex]², ΔABC is a right triangle

ΔABC is a right triangle

c. The perimeter of ΔABC = The length of segment, [tex]\overline {AB}[/tex] + The length of segment, [tex]\overline {AC}[/tex] + The length of segment, [tex]\overline {BC}[/tex]

∴ The perimeter of ΔABC = √10 + √10 + √20 ≈ 10.7966912753

By rounding off to the nearest tenth, the perimeter of ΔABC ≈ 10.8.

The circumference of a circle is equal to C=2πr

From the question, we have 615.44.

Assume that pi is equal to 3.14

Substitute and solve for r

615.44= 2(3.14)r

r= 615.44/ 6.28

r=98.4704

r=98

Therefore, the radius is about 98 units.

To check:

C=2πr

C=2 x 3.14 x 98

C=6.28 x98

C=615.44

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:

state

your answer

Answer:

4200

Step-by-step explanation:

Just add them all together

Hope this is the answer you were looking for

Answer:

The answer is b

Step-by-step explanation:

Answer:

Step-by-step explanation:

cot(theta) = cos(theta)/sin(theta)

sec(theta) = 1/ cos(theta)

sin(theta) * (cos(theta) ) / sin(theta) ) * 1/cos(theta)

The sin(theta)s and the cos(theta)s are on opposite sides of the division sign. So you are left with a bunch of ones.

The identity is proved.

Answer:

See below for explanation

Step-by-step explanation:

sinθcotθsecθ

sinθ(cosθ/sinθ)(1/cosθ)

sinθ(cosθ/sinθcosθ)

sinθ(1/sinθ)

sinθ/sinθ

1

Therefore, the identity is proven.

Answer:

D)  x = -3

Step-by-step explanation:

Answer:

44

Step-by-step explanation:

Split up the one complex shapes into two rectangles. Find the area of each rectangle and add them together.

Answer:

44 square meters

Step-by-step explanation:

split the figure into 2 easy shapes

the first shape 8*4 32

the second shape is 6*2 12

add 32 and 12

44

this is a bad explanation lol

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).

To learn more about the slope intercept form visit:

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Answer:

63 pounds

Step-by-step explanation:

Given data

Quantity of meat= 18 pounds

TIme taken= 2 hours

Rate= Quantity/Time taken

Rate= 18/2

Rate= 9 pounds per hour

Now time= 7 hours

Rate= 9 pounds per hour

Quantity= Rate*Time

Quantity= 9*7

Quantity= 63 pounds

Answer:

the answer to this is "21"

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]

Answer:

0.35

Step-by-step explanation:

j.g susghe yo s9ss9sssisjwus

Answer: D) 385.2

What you give me in the comments 1,540.7......789.4.....1,155.5.....385. I think that was the choice for me to put what kind of answer you want!

Step-by-step explanation: Hope this help :D

Answer:

cos θ = -5/13

Step-by-step explanation:

when in quadrant II with sin θ = 12/13

The trigonometric function gives the ratio of different sides of a right-angle triangle. The value of cos(0) is 5/13.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite the 90° angle.

Given the value of Sin(0) is (12/13). Therefore, the perpendicular is 12, while the hypotenuse is 13. Therefore, the base will be,

13² = 12² + Base²

Base = 5

The value of Cos(0) will be,

Cos(0) = 5/13

Hence, the value of cos(0) is 5/13.

Learn more about Trigonometric functions:

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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:

Step 2

Step-by-step explanation:

Step 1: Find the total points needed to score in six games: 96 times 6 = 576.

Step 2: Find the total points scored: 92 + 110 + 85 + 78 = 365.

WRONG

Step 1: Find the total points needed to score in six games: 96 times 6 = 576.

Step 2: Find the total points scored: 92 + 110 + 85 + 78 + 96 = 461

Step 3: Subtract the total points scored from the total points needed: 576 minus 461 = 115

Step 4: State the answer: Brenda needs to score 115 in her next game.

Therefore,

Brenda make her first mistake in step 2

Answer:

the answer is Step 2

Step-by-step explanation:

the answer is Step 2

Answer:

24

Step-by-step explanation:

41-17=24

Answer:

The number of sunny days this year = 0.75x

where,  x is the sunny days in last years.

Step-by-step explanation:

Given - This year there was 25% fewer sunny days than last year.

To find - What is the number of sunny days this year?

Proof -

Let us assume that,

The total number of sunny days last year = x

Given that,

This year there was 25% fewer sunny days than last year.

i.e this year total sunny days = 100 - 25 = 75 %

So,

we get

If there were x sunny days last year,

Then,

This year Total sunny days = 0.75x

Answer:

rectangle only has 4 sides , a rectangular prism has 6 sides

Answer:

simplify to get the answer i think it would be 0.2

Step-by-step explanation:

Answer:

⏩12°

Step-by-step explanation:

4x + 7° + 35° = 90° {being complementary angles }

4x + 42° = 90°

4x = 90° - 42°

4x = 48°

x = 48° / 4

x = 12°

Hope it will help :)❤

Step-by-step explanation:

35°+4x+7°=90°

or,42°+4x=90°

or,4x=90°/42°

or,x=2.14/4

or,x=0.53

hope this helps

Answer:

4

Step-by-step explanation:

Please mark brainliest

Answer:23

Step-by-step explanation:

Answer:

300,000 x (1.05)^2

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{20}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 20[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 10[tex]\sqrt{3}[/tex] → B

Answer:

[tex]\frac{135 - 5x}{2}= 45\\\\135 - 5x = 90 \\\\5x = 90-135\\\\5x = 45\\ x= 9[/tex]

Option B

Answer:

X= -20

Step-by-step explanation: