what is the exact value of cosC​

let's firstly convert the mixed fractions to improper fractions and then get their product.

[tex]\stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} ~\hfill \stackrel{mixed}{1\frac{3}{7}}\implies \cfrac{1\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{10}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{2}\cdot \cfrac{10}{7}\implies \cfrac{7}{7}\cdot \cfrac{10}{2}\implies 1\cdot 5\implies 5[/tex]

The third graph from the figure represents the exponential function f(x) = 3ˣ, since the function contains the point (x, y) = (5, 243) on the cartesian plane.

In this question we must compare a given exponential function with a set formed by four functions. As the function is crescent and monotonous, then  we can choose the correct graph by a evaluating the function for a given x-value and find the graph that matches with such finding:

f(5) = 3⁵

f(5) = 243

The third graph from the figure represents the exponential function f(x) = 3ˣ, since the function contains the point (x, y) = (5, 243) on the cartesian plane.

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Answer:

7

Step-by-step explanation:

21 = 3 x 7

35 = 7 x 5

70 = 2 x 5 x 7

The greatest common factor of 21, 35 and 70 is 7.

Note : -

The greatest common factor ( GCF ) of a set of numbers is the largest factor that all the numbers share.

[tex](3^{-2})^4 = 3^{-2 \times 4} = 3^{-8} = \dfrac 1{3^8}\\\\\text{Hence the answer is D.}[/tex]

Answer:

1/3^8

Step-by-step explanation:

[tex]\hookrightarrow (3^{-2} )^{4} \\[/tex]

As,

x⁻²=1/x²

Then,

[tex]\hookrightarrow (\frac{1}{3^{2} } )^{4} \\\\\hookrightarrow (\frac{1}{9} )^{4} \\\\\hookrightarrow ((\frac{1}{3} )^{2})^{4} \\\\\hookrightarrow (\frac{1}{3})^{8}[/tex]

Answer:

-3.21538461538

Step-by-step explanation:

[tex]\mathrm{Equation\;Given:}\; 5+5x=\frac{12x-\frac{12}{5}\cdot \:7}{5}[/tex]

[tex]\mathrm{Multiply\;both\;sides\;by\;5}:[/tex]   [tex]5\cdot \:5+5x\cdot \:5=\frac{12x-\frac{12}{5}\cdot \:7}{5}\cdot \:5[/tex]

[tex]\mathrm{Now\;we\;have\;}:[/tex]  [tex]25+25x=12x-\frac{84}{5}[/tex]

[tex]\mathrm{Subtract\;by\;sides\;by\;25}:[/tex]   [tex]25+25x-25=12x-\frac{84}{5}-25[/tex]

[tex]\mathrm{Thus\;we\;have}:[/tex]  [tex]25x=12x-\frac{209}{5}[/tex]

[tex]\mathrm{Subtracting\;12x\;from\;both\;sides}:[/tex]  [tex]25x-12x=12x-\frac{209}{5}-12x[/tex]

[tex]\mathrm{So\;then\;we\;have:}[/tex] [tex]13x=-\frac{209}{5}[/tex]

[tex]\mathrm{Now\;divide\;both\;sides\;by\;13}:[/tex]  [tex]\frac{13x}{13}=\frac{-\frac{209}{5}}{13}[/tex]

[tex]\mathrm{Hence\;we\;have}:\;\;x=-\frac{209}{65}[/tex]

[tex]\mathrm{Decimal\;form}:-3.21538461538[/tex]

Kavinsky

Answer:

y = 2x - 1

Step-by-step explanation:

y - 2x + 2 = 1

6x - 3y = 3​

[tex]y - 2x + 2 = 1 \\ +2x - 2 +2x - 2\\y = 2x - 1[/tex]

Plug in for y:

6x - 3(2x - 1) = 3​

6x - 6x + 3 = 3

Simplified, 3 = 3

Answer: this solution has infinite solutions

Step-by-step explanation:

original system:

y-2x+2 = 1

6x-3y = 3

Move 2 to right side of equation

y    -2x = -1

-3y+6x = 3

solve for y in first equation

⇒ y = 2x - 1

insert y into second equation

⇒ -3(2x-1) + 6x = 3

simplify

⇒ -6x+3+6x = 3

simplify once more

⇒ 3 = 3

this solution has infinite solutions

Step-by-step explanation:

in this condition we are given simple interest time and rate

so principal is missing so we should use the formula of principal that is

P=I×100/T×R

but we should convert that month in to years and we convert it by dividing it by 12.

10yx⁵w⁴ - w³v⁵ - 5x¹¹ - 6

Degree = biggest exponent = 11

Answer:

66.9 ft

Step-by-step explanation:

Kite string forms a right triangle with the horizontal 3.5 feet off of the ground

sin 25  = opp / hyp  = height / 150

sin 25 = height / 150

150 sin25 = height      but it is 3.5 feet off of the ground...add that in

3.5  + 150 sin25 = true height = ~ 66.9 ft

answer:

x = 4

y = -3

steps :

x = 10 + 2y

x + y = 1

2y = x - 10 -> y = 1/2x - 5

x + y = 1 -> y = 1 - x

since theyre both equal to y they are equal to each other

1/2x - 5 = 1 - x

3/2x = 6

x = 4

plug 4 back where x is

y = 1 - 4

y = -3

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The area of the composite shape in the image given is calculated as: 316 yd²

To find the area of a composite shape, find the area of each of the shape that makes up the figure, then add their areas together.

The area of the composite shape = area of big rectangle + area of small rectangle + area of big triangle + area of small triangle

Area of big rectangle = (length)(width) = (5 + 4)(8) = 72 yd²

Area of small rectangle = (length)(width) = (5)(4) = 20 yd²

Area of big triangle = 1/2(base)(height) = 1/2(12)(4+5+4+7) = 120 yd²

Area of small triangle = 1/2(base)(height) = 1/2(8+5)(16) = 104 yd²

The area of the composite shape = 72 + 20 + 120 + 104 = 316 yd²

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brainly.com/question/27661391 yo im begging some one to help

Step-by-step explanation:

Find the volume of the candle:

3^2 x 3.14 x 4= 113.04cubic inches.

now divide total wax used by volume of a candle.

3278.16 / 113.04 = 29 candles.

Answer:

34.98

Simply add the 27.99 with 25%

= 34.98

Answer: 4:7

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

Given :

Solving :

Evaluating the expression :

Answer:

  3

Step-by-step explanation:

To evaluate an expression with a particular value of the variable, put that value where the variable is and do the arithmetic.

__

  1/3(-6) +5 = -2 +5 = 3

For x = -6, the value of the expression is 3.

Answer:

Surface area of rectangular prism

=P×h

=2(l+w)×h

=2(3+9)×2

=48mm²

[tex] \boxed{ \frak{Answer}}[/tex]

Given,

Length (l) = 9 mm

Breadth (b) = 3 mm

Height (h) = 2 mm

To find: The surface of it.

We, know that

Surface area of a cuboid = 2(lb + bh + lh)

By using the formula,

= 2(lb + bh + lh)

= 2(9*3 + 3*2 + 9*2)

= 2( 27 + 6 + 18)

= 2(51)

= 102 mm²

[tex] \boxed{ \frak{Keep \: Learning }}[/tex]

The sum of the first thirteen terms of the geometric series is -7971615.

This is the sum of an infinite number of terms that has a constant ratio between successive terms.

To calculate the sum of the first thirteen terms of the geometric series, we use the formula below.

Formula:

Where:

Given:

Substitute these values into equation 1

Hence, the sum of the first thirteen terms of the geometric series is -7971615.

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Answer:

20

Step-by-step explanation:

85% of 24 is 20

1.  The percent of cats between 24.16 and 35.84 is 95%

2. The percent of cats who are longer than 35.84 is 2.28 %

3. The percent of cats shorter than 24.16 inches is 2.28%

The empirical rule - formula

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

Mean, u = 30 inches

Standard Deviation, s = 2.92 inches

Formula for z-score = (x-u)/s

1. We have to find the percent of cats between 24.16 and 35.84 inches.

24.16, z-score = -2

35.84, z-score = 2

According to the empirical rule,

95% of the data values are within 2 standard deviations of the mean.

So, 95% of the cats are between 24.16 and 35.84 inches.

2. Here, x = 35.84

   z=(35.84-30)/2.92

   z= 2

According to the Empirical Rule,

95% of the values lie within 2 standard deviations of the mean.

So, the percent of cats who are longer than 35.84

100 - 97.72 = 2.28%

3. Now, x = 36.22

Using the formula mentioned above, we get:

z= 24.16-30/2.92

z=-2

According to empirical rule,

68% of the values lie within 1 standard deviation of the mean.

i.e., remaining 32% are outside the 1 standard deviation and  half of the values i.e. 16% are below 1 standard deviation.

The percent of cats shorter than 24.16 inches is 2.28%

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Given

Find z-scores for x = 24.16 and x = 35.84

Use formula

Find the corresponding percentage from z-score table

The percent of cats between 24.16 and 35.84

The percent of cats who are longer than 35.84

The percent of cats shorter than 24.16 inches

Answer:

  (E) 90°

Step-by-step explanation:

The diagonals of a parallelogram are equal in length if and only if the parallelogram is a rectangle.

Any angle of a rectangle is 90°.

_____

Adjacent angles of a parallelogram are supplementary. If the diagonals are the same length, the triangles formed by either diagonal are congruent with the triangles formed by the other diagonal. This means adjacent angles are congruent. Congruent supplementary angles are 90°.

Answer: Circle d

Step-by-step explanation:

Question 1 ) A ray has one endpoint and continues forever in the opposite direction

Question 2)

⇒

IG

Question3)

⇒

DC

Hope this helps!

Answer:

14.14

Step-by-step explanation:

Answer:

The length of the diagonal of the square is about 14.142 feet

Step-by-step explanation:

Step 1:  Determine the length

[tex]P = 4(l)[/tex]

[tex]40\ ft = 4(l)[/tex]

[tex]\frac{40\ ft}{4}=\frac{4(l)}{4}[/tex]

[tex]10\ ft = l[/tex]

Step 2:  Determine the diagonal length

Pythagorean theorem → [tex]a^2 + b^2 = c^2[/tex]

a and b are going to be the sides of the square which are both 10 ft so we just plug those in and solve for c

[tex](10)^2 +(10)^2 =c^2[/tex]

[tex]100+100=c^2[/tex]

[tex]\sqrt{200}=\sqrt{c^2}[/tex]

[tex]14.142=c[/tex]

Answer:  The length of the diagonal of the square is about 14.142 feet

Answer:

4 and 5

Step-by-step explanation:

Assuming your 2nd sentence should be: "The sum of the squares of the two numbers is 41"

X + Y = 9   {equation 1}

X² + Y² = 41  {equation 2}

from equation 1:  y = 9-x

Substitute that into equation 2

x² + (9-x)² = 41

x² + 81 - 18x + x²= 41

2x² - 18x + 40 = 0

We can factor out a 2

x² - 9x + 20 = 0

(x-5)(x-4) = 0

x = 5 or 4

checking

Your two numbers are 4 and 5

4² + 5² 

= 16 + 25

= 41

Answer:

8640

Step-by-step explanation:

1) Volume of the lower prism:

V1 = 27*20*12 = 6480

2) Volume of the higher prism:

V2 = 9*20*12 = 2160

3) Volume of the podium: V1 + V2 = 8640

Answer:

B. g(x) = (x + 2)²

Step-by-step explanation:

We got the graph of g by translating the graph of the parent function

f(x) = x² two units to the left

Therefore the equation of the graph of g is (x + 2)²

Answer:

The origin is where x,y lines meet. I put a cirlce there with no label there. Sorry it's messy

Step-by-step explanation:

I'm only a 6th grader. No hate, please. I only did what I learned from my teacher.

The answer to this is:

0.34

The probability that a person with an iron deficiency is 20 years or older will be 0.34. Then the correct option is B.

Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of occurrences.

The table is given below.

Then the probability that a person with an iron deficiency is 20 years or older will be

P = 102 / 300

P = 0.34

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For part 5 the total value is $1845, for part 6 the total net worth is $3200, and for part 7 the debt to assets value is 0.433.

It is defined as the amount one party needs to pay to another party as the first party borrowed an amount that will be credited by the second party. Debt occurs when one party cannot be able to purchase something under normal circumstances.

5)

Total value = 20×30 + 18×40 + 35×15 = $1845

6)

Net worth = (3500 + 300 + 600) - (1000+200) = $3200

7)

Total debt value = 2000+3200 = $5200

Total assets value = 10000+1300+700 = $12000

Debt to assets value = 5200/12000 = 0.433

Similarly, we can find any debt to assets value by using the formula:

Debt to assets value = Total debt/Total assets

Thus, for part 5 the total value is $1845, for part 6 the total net worth is $3200, and for part 7 the debt to assets value is 0.433.

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4.5, 4.316, 4.32, 4.312

= 4.500, 4.316, 4.320, 4.312

Look at the thousandths and hundreths place in the decimal section.

Least to greatest = 4.312 < 4.316 < 4.32 < 4.5