The square and the triangle have equal perimeters. (There is a picture of a square with one side shown as x-5 and there is a picture of a triangle with one side shown as 12 and the other two sides as x) A. Find the value of x B. Find the perimeter

QUESTION POSTED AT 05/12/2019 - 09:20 AM

Answered by admin AT 05/12/2019 - 09:20 AM

A.
4(x-5) = 12 + x + x
4x - 20 = 12 + 2x
4x - 2x = 12 + 20
2x = 32
x = 16

B.
square's p = 4(x-5) = 4(16-5) = 4(11) = 44

triangle's p = 12+2x = 12+2(16) = 12+32 = 44

square's p = triangle's p ( correct )

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QUESTION POSTED AT 20/01/2020 - 01:32 PM

Find cos(sin-1(3/5))

Sin-1 (3/5) = 36.869
cos 3/5 = 0.999

ANSWERED AT 20/01/2020 - 01:30 PM


QUESTION POSTED AT 20/01/2020 - 01:30 PM

Which function below has the smallest slope? A Graph with a line going through -5 on the Y Axis and Postive 2 and a half on the X axis. f(x) f(x) = 2x - 3 h(x) x h(x) -1 3 1 7 3 11

For the first line:
m = (-5 - 0) / (0 - 2.5) = 2

For the second line:
From the given equation,
m = 2

For the third, using the given coordinates (-1,3) (1,7)
m = (7 - 3) / (1 - (-1)) = 2

Therefore, all the slopes of the lines are 2 and none of them have the smallest slope compared to the others.

ANSWERED AT 20/01/2020 - 01:28 PM


QUESTION POSTED AT 20/01/2020 - 01:28 PM

Find the exact value of sec(5pi/ 3) and and sin(7pi/6)

I know the equation is 1/cos
but is it negative sqrt(3)/2 or positive?
or is it negative 1/2 or positive?
This makes the reference angle π/6 or 30º which gives cos 30º=√3/2 or a sec value of 2/√3=2√3/3
sec(-5pi/6)=-2√3/3

ANSWERED AT 20/01/2020 - 01:27 PM


QUESTION POSTED AT 20/01/2020 - 01:27 PM

If the value of sinx=0.42, what is cos x?

From the relation of 
sin(x)^2 + cos(x)^2 = 1 
(0.42)^2 + cos(x)^2 = 1 
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cos(x) = √(1-(0.42)^2)
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ANSWERED AT 20/01/2020 - 01:26 PM


QUESTION POSTED AT 20/01/2020 - 01:26 PM

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.

Hello,

a(2)=-6
a(3)=-6*r
a(4)=-6*r²
a(5)=-6*r^3=162
a(5)/a(2)=r^3=162/(-6)=-27==>r=-3

a(1)=-6/(-3)=2
a(2)=2*(-3)
a(3)=2*(-3)²
a(4)=2*(-3)^3
a(5)=2*(-3)^4

a(n)=2*(-3)^(n-1)




Answer

ANSWERED AT 20/01/2020 - 01:24 PM


QUESTION POSTED AT 20/01/2020 - 01:24 PM

Find an integer, x, such that 5, 10, and x represent the lengths of the sides of an obtuse triangle. A. 4 B. 5 C. 6 D. 11

Hello,

5<10+x ==> -5<x realized
10<5+x ==> x>5
x<5+10 ==> x<15
==> 5<x<15
==>x=6 or x=11 but for x=11 angle none obtus
==> 1solution x=6 (angle = 130.5416...°)




ANSWERED AT 20/01/2020 - 01:23 PM


QUESTION POSTED AT 20/01/2020 - 01:23 PM

A student factors 3x2 – 12 to the following. 3(x2 – 4) Which statement about 3(x2 – 4) is true? A. The expression is equivalent, and it is completely factored. / B.The expression is equivalent, but it is not completely factored./ C. The expression is not equivalent, but it is completely factored./ D.The expression is not equivalent, and it is not completely factored.

Answer:

Option B is correct that is the expression is equivalent, but it is not completely  factored.

Step-by-step explanation:

We have given an expression

3x^2-12

when we take the common factor out which is 3 from the expression we will get

3(x^2-4)

This expression is equivalent but is not completely factored because the term

(x^2-4)\text{can be further factored as}(x-2)\text{and}(x+2)\text{from the formula}a^2-b^2=(a+b)(a-b)

Hence, Option B is correct.

Option C and D are discarded because given factor is equivalent  

Option A is discarded  because expression is not completely factored.

 

ANSWERED AT 20/01/2020 - 01:22 PM


QUESTION POSTED AT 20/01/2020 - 01:22 PM

The graph of a certain quadratic function does not cross the x-axis. Which of the following are possible values for the discriminant?a) 18 b) 0 c) -25 d) -7

As the function is quadratic, it must be positive or equal 0. 
Therefore B and D are possible values.

ANSWERED AT 20/01/2020 - 01:22 PM


QUESTION POSTED AT 20/01/2020 - 01:22 PM

4x^2-x-3=0 solve by completing the square x= ??

Hello,

4x²-x-3=0
==>(2x)²-2*1/2*x+1/4-3-1/4=0
==>(2x-1/2)²-13/4=0
==>(4x-1)²-13=0
==>(4x-1-√13)(4x-1+√13)=0
==> x=(1+√13)/4 or x=(1-√13)/4



ANSWERED AT 20/01/2020 - 01:22 PM


QUESTION POSTED AT 20/01/2020 - 01:22 PM

f(x)=x2-3x-7 find f(-3) a- -7 b- 8 c- 11 d- 22

Hello,

f(-3)=(-3)²-3*(-3)-7=9+9-7=11
Answer C

ANSWERED AT 20/01/2020 - 01:21 PM


QUESTION POSTED AT 20/01/2020 - 01:21 PM

What is the axis of symmetry for the function? y = x2 + 3x - 4 y = -2 x = -2 x = -1.5 y = -1.5 What is the vertex for the function? y = x2 - 4x - 3 (-1, 2) (0, -3) (1, -6) (2, -7) The vertex of y = 9 - 8x - x2 is (-4, 25) False True

Axis of symmetry is a line passing through the vertex which divides the curge into two parts such tha each part looks the same.
For y= x^{2} +3x-4, the 'x' part is squared and the coefficient of x^{2} is positive. Hence, the curve will be a parabola facing up which means that the axis of symmetry will be a vertical line. i.e. x = m.
Investigating, f(-1) == (-1)^{2} +3(-1)-4=1-3-4=-6
f(-1.5) = = (-1.5)^{2} +3(-1.5)-4=2.25-4.5-4=-6.25
f(-2) = = (-2)^{2} +3(-2)-4=4-6-4=-6
From these, the curve has a vertex at point (-1.5, -6)
Therefore the axis of symmetry is line x = -1.5 (i.e. the third option)

ANSWERED AT 20/01/2020 - 01:21 PM


QUESTION POSTED AT 20/01/2020 - 01:21 PM

Find functions f and g so that h(x) = (f ∘ g)(x). h(x) = (6x - 14)^8 A. f(x) = 6x - 14, g(x) = x^8 B. f(x) = 6x^8 - 14, g(x) = -14 C. f(x) = x^8, g(x) = 6x - 14 D. f(x) = (6x)^8, g(x) = -14

Hello,

Answer C

Be carefull

A: is (gof)(x)=g(f(x))=g(x^8)=6x^8-14

C: fog(x)=f((g(x))=f(6x-14)=(6x-14)^8

ANSWERED AT 20/01/2020 - 01:19 PM


QUESTION POSTED AT 20/01/2020 - 01:19 PM

Help me understand please ;-; Which shows the equation in standard form? 6y - 12 = -3x Which shows the equation in standard form? 10 - 2(x - y) = 3x + 1

Standard form for first one is
ax+by=c

6y-12=-3x
add 3x both sides
3x+6y-12=0
add 12
3x+6y=12


second one
distribute (don't forget double negative y)
10-2x+2y=3x+1
minus 3x both sides
10-5x+2y=1
minus 10 both sides
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the equations are
3x+6y=12
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Answer:

Number of trials are 250.

Step-by-step explanation:

A researcher finds 15% of all commuters in a metropolitan area take the train to work.

The researcher polls 250 people in the area to ask them whether they take the train to work or not.

We have tell the number of trials for this binomial experiment.

Researcher will do 250 trials to confirm whether they take the train work and this irrespective of their response.

ANSWERED AT 20/01/2020 - 01:16 PM


QUESTION POSTED AT 20/01/2020 - 01:16 PM

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Hello,

Answer C
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ANSWERED AT 20/01/2020 - 01:14 PM


QUESTION POSTED AT 20/01/2020 - 01:14 PM

Find the value of cos(sin-1(3/5))

cos( sin^{-1}  \frac{3}{5} ) \\ =cos(sin^{-1} 0.6) \\ =cos36.87 \\ =0.8

ANSWERED AT 20/01/2020 - 01:14 PM


QUESTION POSTED AT 20/01/2020 - 01:14 PM

Every Saturday, Heather goes mountain biking. It takes Heather 32 minutes to bike 6 miles. The distance is a function of the time. Which is a reasonable range in the context of the problem? 1. 0 ≤ f(t) ≤ 6 2. 0 ≤ f(t) ≤ 32 3. 6 ≤ f(t) ≤ 32 4. 12 ≤ f(t) ≤ 24

Since distance is a function of time, then the range must be the possible time that Heather could spend with her mountain bike.

Given that she can travel for period 32 minutes and that there can be no negative time. The answer is:
2. 0 ≤ f(t) ≤ 32

ANSWERED AT 20/01/2020 - 01:14 PM


QUESTION POSTED AT 20/01/2020 - 01:14 PM

How many pairs of parallel sides does a trapezoid have? none/ one/ three/ two

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QUESTION POSTED AT 20/01/2020 - 01:13 PM

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1. The reason for statement 2 is
Distributive Property

2. The reason for statement 2 is
Commutative Property

3. The reason for statement 3 is
Associative Property

4. The reason for statement 5 is
Commutative Property

5. The reason for statement 1 is
Associative Property
The reason for statement 3 is
Addition

ANSWERED AT 20/01/2020 - 01:12 PM


QUESTION POSTED AT 20/01/2020 - 01:12 PM

Solve the quadratic equation by completing the square. x2 + 6x + 7 = 0

Hello,

x²+2*3x+3²+7-9=0
==>(x+3)²-2=0
==>(x+3-√2)(x+3+√2)=0
==> x=-3+√2 or x=-3-√2

ANSWERED AT 20/01/2020 - 01:12 PM


QUESTION POSTED AT 20/01/2020 - 01:12 PM

List L consists of numbers 1, square root of 2, x, and x^2 , where x>0, and the range of the numbers in list L is 4. Which quantity is larger? A. x B. 2

If the range of the numbers in the list L is 4, then x can't be 4 since there is an element in the list that is x^2. Therefore,
0 ≤ x^2 ≤ 4 so that it would be the highest number and
0 ≤x ≤ 2

So, the value of x can be equal to 2 but not higher. So, 2 is always greater or equal to x.

ANSWERED AT 20/01/2020 - 01:11 PM


QUESTION POSTED AT 20/01/2020 - 01:11 PM

If cos Θ = negative two over five and tan Θ > 0, what is the value of sin Θ? negative square root / 21 negative square root / 21 over 5 square root / 21 over 5 square root of 21 over 2

Answer:  The correct option is (B) negative square root 21 over 5.

Step-by-step explanation:  Given that for an angle \theta,

\cos \theta=-\dfrac{2}{5},~~~\tan \theta>0.

We are to find the value of \sin \theta.

We know that

Cosine is negative in Quadrant II and Quadrant III.

Tangent is positive in Quadrant 1 and Quadrant III.

So, the given angle \theta lies in the Quadrant III.

We will be using the following trigonometric identity:

\cos^2\theta+\sin^2\theta=1.

We have

\cos \theta=-\dfrac{2}{5}\\\\\\\Rightarrow \sqrt{1-\sin^2\theta}=-\dfrac{2}{5}\\\\\\\Rightarrow 1-\sin^2\theta=\dfrac{4}{25}\\\\\\\Rightarrow \sin^2\theta=1-\dfrac{4}{25}\\\\\\\Rightarrow \sin^2\theta=\dfrac{21}{25}\\\\\\\Rightarrow \sin \theta=\pm\dfrac{\sqrt{21}}{5}.

Since the angle \theta lies in Quadrant III and sine is negative in that quadrant, so

\sin\theta=-\dfrac{\sqrt{21}}{5}.

Thus, option (B) is correct.

ANSWERED AT 20/01/2020 - 01:11 PM


QUESTION POSTED AT 20/01/2020 - 01:11 PM

What will the last payment be to pay off a $1,250 computer plus 8% sales tax with monthly payments of $120? $10 $11 $12 $20 $30

The last payment would be $30. This is computed by solving first the total amount of computer including 8% tax, so 1,250 times 8% is equal to 100, then 100 plus 1,250 is 1,350. Then 1,350 will be divided by 120, which is equal to 11.25. Getting the 0.25, from 11.25, multiply be 120 (0.25 times 120), is equal to $30.

ANSWERED AT 20/01/2020 - 01:11 PM


QUESTION POSTED AT 20/01/2020 - 01:11 PM

Transversal t cuts parallel lines a and b as shown in the diagram. Which equation is necessarily true? a) m<1=m<2 b)m<4=m<6 c) m<3+m<5=90 degrees d)m<7=m<8

If the numbering of the angles is similar to this:
1 | 2
-----
3 | 4
5 | 6
----
7 | 8

Then none of the the choices are necessarily true.

The equations would have been:
1 = 4 = 5 = 8
2 = 3 = 6 = 7
3 + 5 = 4 + 6 = 180


ANSWERED AT 20/01/2020 - 01:11 PM


QUESTION POSTED AT 20/01/2020 - 01:11 PM

Given right triangle SIP such that i = 54 and s = 19, which of the following statements are true? Round to the nearest hundredth.

Answer:

 (D)   p = 50.55 (Round to the nearest hundredth).

Step-by-step explanation:

Given: Right triangle SIP such that i = 54 and s = 19.

To find: Which of the following statements are true,  round to the nearest hundredth.

Solution: We have given that Right triangle SIP , i = 54 and s = 19.

By the Pythagoras theorem (IP)²+(SI)² = (SP)².

Plugging the values

                                 (19)²+(p)² = (54)².

                                  361+(p)² =2916

  On subtracting both side by 361.

                     (p)²+ 361 - 361 =2916 -361

                      (p)² = 2555

Taking square root both sides .

                    √(p)² = \sqrt{2555}.

                       p = 50.547

p = 50.55 (Round to the nearest hundredth).

Therefore,   (D)   p = 50.55 (Round to the nearest hundredth).

ANSWERED AT 20/01/2020 - 01:09 PM


QUESTION POSTED AT 20/01/2020 - 01:09 PM