Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form

cos and sec can be found

The requried simplified expression is 1 / cosØ, which is equivalent to secØ. The correct option is secØ.

Let's simplify the given expression and see which of the provided options match:

We are given the expression √(1 + tan²Ø).

Now, recall the trigonometric identity: tan²Ø = sin²Ø / cos²Ø.

Substitute this identity into the expression:

√(1 + sin²Ø / cos²Ø)

Next, find a common denominator for the fraction inside the square root:

√((cos²Ø + sin²Ø) / cos²Ø)

Since cos²Ø + sin²Ø = 1 (as per the Pythagorean trigonometric identity), the expression becomes:

√(1 / cos²Ø)

Now, we can take the square root of 1 and cos²Ø separately:

√1 / √cos²Ø

Simplify:

1 / cosØ

The simplified expression is 1 / cosØ, which is equivalent to secØ.

Therefore, the correct option is: secØ.

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Step-by-step explanation:

since we are using Pythagoras

c² = a² + b²

with c being the Hypotenuse (the baseline opposite of the 90° angle),

you want to get the expression

y² = 3² + 3²

so, you pick the ² and put it next to the y left of the "=" sign.

and to the right of the "=" sign you put 3, ², +, 3, ²

Answer:

-1/2

Step-by-step explanation:

Answer:x is -1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Expanding the right-hand side,

[tex](a-b)(a^{2}+ab+b^{2})=a^{3}+a^{2}b+ab^{2}-a^{2}b-ab^{2}-b^{3}=a^{3}-b^{3}[/tex]

Thus, the identity is true.

Answer:

A ≈ 22.2 ft²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × [tex]\frac{50}{360}[/tex]

   = π × 7.13² × [tex]\frac{5}{36}[/tex]

    = 50.8369π × [tex]\frac{5}{36}[/tex]

    ≈ 22.2 ft² ( to the nearest tenth )

Answer:

a=9

b=-6

Step-by-step explanation:

The cost to buy 18 notebooks and 12 desktop computers will be $8100.

The cost to buy n notebooks and d desktop computers will be 300n + 225d

The cost of a given material is the amount attached and to be paid for getting that material.

From the given information:

The cost to buy 18 notebooks and 12 desktop computers will be:

= 300(18) + 225(12)

= 5400 + 2700

= $8100

The cost to buy n notebooks and d desktop computers will be:

= 300(n) + 225(d)

= 300n + 225d

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Answer:

Using the concepts of Number System, we find that the sum of the largest and the smallest of the given four numbers is 4.29.

Step-by-step explanation:

The given set of numbers is 3.09, 3.9, 0.39 and 0.399.

The given numbers are related to each other as:

3.9 > 3.09 > 0.399 > 0.39

3.9 is greater than 3.09 as

3.9 > 3.09

3 + 0.9 > 3 + 0.09

0.9 > 0.09

90 > 9

0.399 is greater than 0.39 as

0.399 > 0.39

399 > 390

Now, the smallest number in the series is 0.39 and the largest number in the series is 3.9.

The sum of the largest and the smallest of the given four numbers is:

3.9 + 0.39

4.29

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Answer:

The sum of the other two numbers is 120.

Step-by-step explanation:

To find an average, you add all the numbers involved and divide it by the amount of numbers involved. in this case,

(x+y+z) ÷ 3 =50

x=30

Divide both sides by three to remove the denominator.

(30+y+z)÷ 3 (*3) = 50(*3)

(30+y+z)=150

Subtract 30 from both sides.

(30+y+z)-30= 150-30

y+z=120

a straight line make an angle of 180° ,

so 115+y=180

y=65°

for the top part of the triangle it makes an angle of 360° , so 304+y=360

y=56

sum measure of interior angles of triangle is 180° , According to this rule (n-2)180 ; where n is the no. of sides .

so

65+56+y= 180

121+y=180

y=59( the angle next to X)

X+59=180( together they make an angle of 180)

x=121°

Hope it helps

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Answer:

x=1/3

Step-by-step explanation:

first multiply both bracket to together and then you get, 9x=3

x=1/3, then sub in to other equation and get the rest answer.

hope it helpful

Answer:

[tex]a_{n} =18-8n\\a_{8} =18-8(8)=-46[/tex]

Answer:

-46

Step-by-step explanation:

(hello, I just answered your previous question--some stuff will sound similar because we are applying the same concept :)  )

We know that the nth term of the sequence is 18 - 8n

the "nth" term of a sequence means that you can plug in the term place to get the term value (ex. if the nth term is n + 2, we can plug any term in {let's say, the eighth term, 8 + 2 = 10 ; to get our term's value}  )

  18 - 8n is sequence

  18 - 8(8) is 8th term

  18 - 64 is 8th term

 -46 is the 8th term

hope this helps!! :)

Answer:

C will be your answer.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = 5/2 [/tex]

[tex] \qquad \tt \rightarrow \: y = 3/2[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: x = \cfrac{y}{3} + 2 \: \: \: \: \: \: \: \: - (1)[/tex]

[tex]\qquad \tt \rightarrow \: 7x -5 y = 10 \: \: - (2)[/tex]

[tex] \textsf{put value of x in equation 2} [/tex]

[tex]\qquad \tt \rightarrow \: 7 \bigg( \cfrac{y}{3} + 2 \bigg) - 5y = 10 [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{7y}{3} + 14 - 5y = 10 [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{7y}{3} - 5y = 10 - 14[/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{7y - 15y}{3} = - 4[/tex]

[tex]\qquad \tt \rightarrow \: - 8y = - 4(3)[/tex]

[tex]\qquad \tt \rightarrow \: y = \cfrac{ - 12}{ - 8} [/tex]

[tex]\qquad \tt \rightarrow \: y = \cfrac{ 3}{ 2} [/tex]

[tex] \textsf{put value of y in equation 1 } [/tex]

[tex]\qquad \tt \rightarrow \: x = \cfrac{y}{3} + 2[/tex]

[tex]\qquad \tt \rightarrow \: x = \bigg (\cfrac{3}{2} \sdot\cfrac{1}{3} \bigg) + 2[/tex]

[tex]\qquad \tt \rightarrow \: x = \cfrac{1}{2} + 2[/tex]

[tex]\qquad \tt \rightarrow \: x = \cfrac{1 + 4}{2} [/tex]

[tex]\qquad \tt \rightarrow \: x = \cfrac{5}{2} [/tex]

Kat should tell Kim that It's too late to change the area of this kite because the length of the diagonals of a kite determines its area.

In Mathematics, the area of a kite is equal to one-half the product of the length of its diagonals. Mathematically, the area of a kite can be calculated by using this formula:

A = ½ × d₁ × d₂

Where:

Since Kit has already cut his sticks for the diagonals, Kat should tell him that it's too late to change the area of this kite because the length of the diagonals of a kite determines its area.

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Answer:

-4n+7

Step-by-step explanation:

because you take away 4 each time and the nber that would come before 3 is 7.

Answer:

Answer x=2/3, -1
Option B

Step-by-step explanation:

Answer:

B) x =( 2/3, -1)

Step-by-step explanation:

Equation:

[tex]6x {}^{2} + 2x = 4[/tex]

Solution:

We know that,

[tex] \rm \: Quadratic \: formula (x)=\cfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

According to the problem,

Plugging them on the formulae,we obtain,

Choice B is accurate.

Fatoumata's salary after 3 years will be $58,000.

Fatoumata's salary after tt years will be $43,000 + (5,000tt).

The linear equation that can be used to determine Fatoumata's salary after the passage of time is:

Initial salary + (yearly increase x number of years)

$43,000 + 5000t

$43,000 + 5000(3) =  $58,000.

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Do long division (see the attachment).

[tex]\dfrac{1}{22}=0.04545\ldots=0.0\overline{45}[/tex]

Answer:

x = 6

Step-by-step explanation:

CT is a median, which means it divided AB into two equal parts so we can write the following equation:

7x + 9 = 5x + 21 transfer like terms to the same side of the equation

7x - 5x = 21 - 9 do the extraction

2x = 12 divide both sides by 2

x = 6

The correct answer is option C which is 5(2a − 3) = (2a − 3) ⋅ 5 showing commutative property.

If altering the operands' order has no effect on the outcome, the binary operation is commutative in mathematics.

a x b = b x a

So for the expression 5(2a − 3) = (2a − 3) ⋅ 5 suppose 5 is a and ( 2a - 3 ) is b so.

a x b = b x a

5(2a − 3) = (2a − 3) ⋅ 5

Therefore the correct answer is option C which is 5(2a − 3) = (2a − 3) ⋅ 5 showing commutative property.

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Answer:

Let consider the following linear equation systems by using the known points and second-grade polynomial:

(-1, 7)

a + b + c = 7a+b+c=7

(5, 7)

25\cdot a + 5\cdot b + c = 725⋅a+5⋅b+c=7

(6,10)

36\cdot a + 6 \cdot b + c = 1036⋅a+6⋅b+c=10

After some algebraic manipulation, the values for the polynomial coefficients are found:

a = \frac{3}{5}a= 53 , b = -\frac{18}{5}b=− 518

, c = 10c=10

The polynomial is:

y = \frac{3}{5}\cdot x^{2} - \frac{18}{5}\cdot x+10y= 53

⋅

Step-by-step explanation:

For complete solution see the above attachment!

Answer:

2.5 gallons of the 20% solution must be replaced by the 36% solution.

Step-by-step explanation:

[tex].12(20 - x) + .36x = 20(.15)[/tex]

[tex]2.4 - .12x + .36x = 3[/tex]

[tex]2.4 - .24x = 3[/tex]

[tex] - .24x = - .6[/tex]

[tex].24x = .6[/tex]

[tex]x = 2.5[/tex]

The difference of the polynomials is [tex]1.3t^{3}-0.2t^{2}-6t-8[/tex] and the additive inverse of the polynomial being subtracted is [tex]-0.6t^{2} +8+18t[/tex].

The given polynomials are [tex](1.3t^{3}+0.4t^{2} -24t )[/tex] and [tex]0.6t^{2} +8-18t[/tex].

We need to find the additive inverse of the polynomial being subtracted.

In mathematics, the additive inverse of a number a is the number that, when added to a yields zero. This number is also known as the opposite, sign change, and negation.

Now, [tex](1.3t^{3}+0.4t^{2} -24t )-(0.6t^{2} +8-18t)[/tex]

[tex]=1.3t^{3}+0.4t^{2}-0.6t^{2}-24t+18t-8[/tex]

[tex]=1.3t^{3}-0.2t^{2}-6t-8[/tex]

The additive inverse of the polynomial being subtracted is [tex]-0.6t^{2} +8+18t[/tex].

Therefore, the difference of the polynomials is [tex]1.3t^{3}-0.2t^{2}-6t-8[/tex] and the additive inverse of the polynomial being subtracted is [tex]-0.6t^{2} +8+18t[/tex].

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Answer: (3,-1)

Step-by-step explanation:

distance between R & S x values: 9

distance between R & S y values: -6

multiply each by 2/3 (the proportion)

9/1 x 2/3 = 6; -6/1 x 2/3= -4

add the answers to R x & y values:

-3 + 6= 3; 3 - 4= -1

Answer:

D

Step-by-step explanation:

using the section formula

(x₁, y₁ ) and (x₂, y₂ ) divided in the ratio m : n , then

point = ([tex]\frac{mx_{2}+nx_{1} }{m+n}[/tex] , [tex]\frac{my_{2}+ny_{1} }{m+n}[/tex] )

thus for R (- 3, 3 ) and S (6, - 3 ) in the ratio 2 : 1

Q = ( [tex]\frac{2(6)+1(-3)}{2+1}[/tex] , [tex]\frac{2(-3)+1(3)}{2+1}[/tex] )

   = ( [tex]\frac{12-3}{3}[/tex] , [tex]\frac{-6+3}{3}[/tex] )

  = ( [tex]\frac{9}{3}[/tex] , [tex]\frac{-3}{3}[/tex] )

  = (3, - 1 )

Answer:

60

Step-by-step explanation:

Total degree of triangle interior angles is 180

So x+2x+3x=180

6x=180

x=30

Measurement of angle C is 2x which is 60 degree

Answer:

Step-by-step explanation:

[tex]\bf tan\:\theta =\cfrac{opp}{adj}[/tex]

[tex]\bf tan(35^o)=\cfrac{x}{20}[/tex]

[tex]\bf 20\;tan (35^o)=x[/tex]

[tex]\bf 14ft=x[/tex]

The height of the tree:-

Answer:

19.00 ft to the nearest hundredth.

Step-by-step explanation:

tan 35 = h / 20

h = 20 tan 35

Now we add the man's height

Total height of the tree

=  20 tan 35 + 5

=  19.00 ft to the nearest hundredth.

Answer:

your questions is not clear but from my observations

let the number be x

x/7+25=34

x+175/7=34

x+175=238

x=238-175

×=63

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Answer:

  b, c

Step-by-step explanation:

A function is continuous if its graph can be drawn without lifting the pencil. It is decreasing wherever its slope is negative.

__

A graph of the function is attached. It has a "jump" discontinuity at x=0, so is not a continuous function.

The value of f(0) is 2, so the y-intercept is 2.

The given function is defined for all values of x, so its domain is all real numbers.

The function is decreasing for values of x > 0, so does not approach positive infinity for large positive x.

The function has a stationary point at x=0, so is not decreasing over its entire domain.

_____

Additional comment

The function is decreasing everywhere except at x=0. The point (0, 2) is the vertex of the quadratic portion of the function, so a tangent is horizontal there. At such horizontal tangent points, a function is neither increasing nor decreasing. It is tempting to ignore this exception, because the function is decreasing everywhere else.