In △ABC, ∠C = 2∠B and ∠A = 540, find the measure of ∠B.​

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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It looks like you're saying

[tex]f(x) = ax^2 + bx + c[/tex]

and you're asked to find [tex]a,b,c[/tex] given [tex]f(0)=-4[/tex], [tex]f(1)=-1[/tex], and [tex]f(-1)=-5[/tex].

Evaluate [tex]f[/tex] at the three given points:

[tex]x=0 \implies f(0) = \boxed{c = -4}[/tex]

[tex]x=1 \implies f(1) = -1 = a + b + c \implies a+b = 3[/tex]

[tex]x=-1 \implies f(-1) = -5 = a - b + c \implies a - b = -1[/tex]

[tex](a+b) + (a-b) = 3 + (-1) \implies 2a = 2 \implies \boxed{a=2}[/tex]

[tex]a-b = -1 \implies \boxed{b=3}[/tex]

and the mapping is [tex]f(x) = 2x^2 + 3x - 4[/tex].

Answer:

A) 9

Step-by-step explanation:

⇒ Circumference of a Circle = 2πr

[tex]36=2\pi r[/tex]

[tex]r=\frac{36}{2} \pi[/tex]

[tex]r=\frac{18}{\pi }[/tex]

Length of arc = rθ

θ = angle AC = [tex]90^o[/tex]

Convert [tex]90^o[/tex] to radian

= [tex]\frac{90\pi }{180}[/tex]

= [tex]\frac{\pi }{2}[/tex]

length of arc = 18/π x π/2

= 9

Answer: 1230

Step-by-step explanation:

[tex]V=\frac{1}{3}(\pi)(r^{2)h=\frac{1}{3}(\pi)(7^{2})(24) \approx \boxed{1230 \text{ cm}^{3}}[/tex]

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:

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:

-1/2

Step-by-step explanation:

Answer:x is -1

Step-by-step explanation:

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

please mark me as brainlyst

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.

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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The values of a, b, and c are needed to write the equation's general form will be a = 1; b = -3; c = 0.Option A is corect.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Given equation;

x²-3x=0

The quadratic equation in the form is;

ax² + bx + c = 0

On putting the values of the options one by one we will get the answer;

1 x²+(-3)x+0

x²-3x=0

Hence, option A is corect.

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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:

Jim:  2/9

Step-by-step explanation:

8/9-4/6

48/54-36/54          [Convert each fraction to a common denominator:  54

                              Multiply (8/9)*(6/6)=48/54;  Multiply (4/6)*(9/9) = 36/54]

 48/54-36/54 = 12/54

12/54 can be reduced to 2/9

Jim also has 2/9

Sue- 8/9-4/6=4/3 or 1 1/3:  Sue subtracted both the numerator and denominator.  This is not correct.

Jim- 8/6 - 4/6 = 48/54 - 36/54= 12/54 or 2/9:  Good Job Jim

Bob- 8/9- 4/6 = 8/54-4/54= 4/54 = 2/27:  Bob converted both denominators to 54, but did not multiply the numerators by the same numbers.  Bad Bob.

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!! :)

Option third "The original amount of the mortgage" is correct because every month that passes, the amount left to pay decreases.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}[/tex]

[tex]\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

As we know the line of best is represented by:

y = mx + c

Here m is the slope and c is the y-intercept.

A scatter plot is made to model the amount of money left to pay on a mortgage.

Every month that passes, the amount left to pay decreases.

Plug x = 0 to get the y-intercept

y = c

The y-intercept representing the original amount of the mortgage.

Thus, option third "The original amount of the mortgage" is correct because every month that passes, the amount left to pay decreases.

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Do long division (see the attachment).

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

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]

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:

70.04 cm²

Step-by-step explanation:

Area = base x height

10.3 x 6.8 = 70.04

Hope this helps :)

[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]

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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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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The fraction of the counters that Lesleay gets is 5/9.

A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. An example is 1/2.

The fraction of the counters that Lesleay gets = number of counters she gets / total number of counters

10/18 = 5/9

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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:

C will be your answer.

Please Mark as brainlist!

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

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

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:

that means that the new ones contains c-14*32/100

Hope This Helps!!!

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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