Which equation could be used to find the perimeter of a rectangle that has a width of 12 cm and a length of 16 cm? a. P = 2 · 12 + 2 · 16 b. P = 2 · 12 + 16 c. P = 12 · 16 d. P = 12 + 16

QUESTION POSTED AT 05/12/2019 - 12:06 PM

Answered by admin AT 05/12/2019 - 12:06 PM

It would be a. because a rectangle has 2 pairs of congruent sides so since the width is 12 and there are 2 sides with that measurement it would be 2(12) and the same goes for the length, and then you add them together.
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Related questions

Two sides of a triangle have lengths 10 and 15. What must be true about the length of the third side? less than 25 / less than or equal to 25 /equal to 25/ more than 25

Answer:

A. Less than 25.

Step-by-step explanation:

Let x represent 3rd side of triangle.

We have been given hat two sides of a triangle have lengths 10 and 15.

We will use triangle inequality theorem to find the 3rd side of the triangle. Triangle inequality theorem states that 3rd side of a triangle must be less than the sum of other two sides of triangle.

Using triangle inequality theorem, we can set following inequalities:

x+10>15

x+10-10>15-10

x>5

Therefore, the length of third side should be greater than 5.

10+15>x

25>x

x<25

Therefore, the length of third side should be less than 25 and option A is the correct choice.

ANSWERED AT 20/01/2020 - 01:47 PM


QUESTION POSTED AT 20/01/2020 - 01:47 PM

Find the integral of 1/sqrt(x^2-9)

Let x = 3secβ, then dx = 3secβtanβ

∫dx/√(x²-9) = ∫[(3secβtanβ)/(3tanβ)]dβ
                 = ∫secβdβ
                 = ln |tanβ - secβ| + c
                 = ln |√(x² - 9)/3 - x/3| + C
                 = ln |√(x² - 9)/x| + C

ANSWERED AT 20/01/2020 - 01:46 PM


QUESTION POSTED AT 20/01/2020 - 01:46 PM

Find the coordinates of the other endpoint when you are given the midpoint (point M) and one of the endpoints (point P). P = (3, 5) and M =(-2, 0)

I'll try to explain. The trouble is that I do not know English :)
About Points
S = (x,y)        searched point (it will be in the third quadrant )
M = (-2,0)      Midpoint | SP |
P = (3,5)        one end of the segment | SP |

You have to draw Cartesian.

 
we set in a point M and P. We both points by a simple and we extend it for the third quarter of the system. Compass measure the distance from the point M to the point P. From the point M we set a compass point S. Figure attached. Received point S = ( -7 , -5 ) . It sought a point that calculate .

We use the information that | SM | = | MP |

 x_{S}  -  x_{M} =  x_{M} -  x_{P}  \\  \\  x_{S} - (-2) = -2 - 3 \\  \\  x_{S} +2 = -5 \\  \\  x_{S} = -5 - 2 = -7

 y_{S} - y_{M}  =  y_{M}  -  y_{P}  \\  \\  y_{S}  - 0 = 0 - 5 \\  \\  y_{S}  = -5

Answer : S = (-7,-5)

as soon as I had a good range will add drawing


ANSWERED AT 20/01/2020 - 01:45 PM


QUESTION POSTED AT 20/01/2020 - 01:45 PM

The sum of the measures of two complementary angles exceeds the difference of their measures by 72°. Find the measure of the smaller angle. A. 18° B. 36° C. 54° D. 58°

First we need to define our conditions. Since the angles are complimentary, the sum of the angles must be equal to 90 degrees.

let x = first angle
y = second angle

x + y = 90

from the second condition in the problem 

x + y =72 + x -y
solving for x

x= 54

therefore the shorter side is 90 - 54 = y

y = 36 degree, the shorter side

ANSWERED AT 20/01/2020 - 01:44 PM


QUESTION POSTED AT 20/01/2020 - 01:44 PM

As the marketing designer for Burger King, you are given a 4 in by 6 in logo and have been told to create an advertisement with sides six times larger. What is the area of your advertisement (in feet)? [12 inches = 1 ft]

The area would be 144 square inches. Solution:

Area of logo
Area = L x W
Area = 4 x 6
Area = 24 square inches

Area of Ads
Area = 6 x Logo
Area = 6 x 24
Area = 144 square inches

ANSWERED AT 20/01/2020 - 01:44 PM


QUESTION POSTED AT 20/01/2020 - 01:44 PM

The length of a rectangle is 12 in. more than its width. The perimeter is 64 in. Calculate the length of the rectangle in inches.

Let x = width
x+12 = length

Perimeter of a rectangle, P = 2x+2(x+12) = 64
2x+2x+24=64
4x = 40
x=10
x+12 = 22

therefore, length is 22 in.

ANSWERED AT 20/01/2020 - 01:41 PM


QUESTION POSTED AT 20/01/2020 - 01:41 PM

What is the equation, in standard form, of a parabola that models the values in the table? x~ -2 , 0 , 4 f(x)~ 1 , 5 , -59

The equation can be obtained using microsoft excel, using manual substitution or using the statistics function of the calculator (I recommend Casio Fx 991-ES)

the equation that you will get from this method is initially 

f(x) = y = -3x^2 - 4x + 5

converting this equation to the standard form, we obtain

Standard form: (x-h)^2 = -4a(y-k)

by completing the square

we can obtain

(x + 2/3)^2 = (-1/3)(y - 19/3)

you can recheck your answers by substituing the values

ANSWERED AT 20/01/2020 - 01:40 PM


QUESTION POSTED AT 20/01/2020 - 01:40 PM

Which sentence fully illustrates that polygon ABCD is congruent to polygon PQRS? A. Corresponding pairs of angles on ABCD and PQRS are equal in measure. / B. Corresponding pairs of sides on ABCD and PQRS are equal in length./ C. Polygon ABCD maps to polygon PQRS through a reflection only. / D. Polygon ABCD maps to polygon PQRS through a translation only.

Two figures are said to be congruent when they have the same shape and size or if one object is a mirror image of the other object. I think, from the choices given, the best answer to illustrate that ABCD is congruent with PQRS is option B. Corresponding pairs of sides on ABCD and PQRS are equal in length.

ANSWERED AT 20/01/2020 - 01:38 PM


QUESTION POSTED AT 20/01/2020 - 01:38 PM

The perimeter of a rectangle is 146 cm. The width is 10 cm longer than twice the length. Find the width

Perimeter of a rectangle = 2L + 2W = 146

"width is 10 longer than twice the length"
translates to
W = 2L + 10
this can be rearranged to be
2L = W - 10

we can plug that into the first equation and get
(W - 10) + 2W = 146

add like terms
3W - 10 = 146

add 10 to both sides
3W = 156

divide both sides by 3
W = 52

therefore the width is 52 cm

ANSWERED AT 20/01/2020 - 01:36 PM


QUESTION POSTED AT 20/01/2020 - 01:36 PM

Let theta be an angle in quadrant III such that cos theta=-3/5 . Find the exact values of csc theta and tan theta .

Answer:

cosec\theta=-\frac{5}{4}

tan\theta=\frac{4}{3}.

Step-by-step explanation:

Given, let \theta  be the angle in the III quadrant .

cos\theta=-\frac{3}{5}......    (given)

In III quadrant cosec\theta is negative  and tan\theta is positive .

because , cosec\theta=reciprocal of sin\theta

it means , cosec\theta=\frac{1}{sin\theta}

Therefore,  first we find value of sin\theta

 We know that

sin^2\theta=1-cos^2\theta

sin\theta=\sqrt{1-cos^2\theta}

sin\theta=\sqrt{1-(\frac{-3}{5} )^2

sin\theta=\sqrt{1-\frac{9}{25}}

sin\theta=\sqrt{\frac{16} {25}

sin\theta=\frac{-4}{5}

Because sin\theta lies in III quadrant and in III quadrant it is negative.

Now, we know that

tan\theta=\sqrt{sec^2\theta-1}

therefore,  first we find sec\theta

sec\theta=\frac{1}{cos\theta}

sec\theta=-\frac{5}{3}

tan\theta=\sqrt{(\frac{5}{3})^2-1

tan\theta=\sqrt{\frac{25} {9}-1

tan\theta=\frac{4}{3}

Because it lies in III quadrant, therefore it take positive.

Hence,cosec\theta=-\frac{5}{4} and tan\theta=\frac{4}{3}

ANSWERED AT 20/01/2020 - 01:33 PM


QUESTION POSTED AT 20/01/2020 - 01:33 PM

Sean began jogging to live a healthier lifestyle. On his first run, he ran one-half mile. He increased his workouts by adding two miles a month to his run. He wrote the equation f(x)= 0.5 + 2x to model his progress. The variable x represents the number of a. miles he runs. b. months he runs. c. miles he ran the first day. d. calories he burns.

B. Months he runs. f(x) is the total number of miles he runs during each month. He starts with 0.5 miles and adds (+) 2 miles each month. Therefore, x must be the number of months. For example, month 1 (x) he runs 2.5 miles: 2.5 = 0.5 + 2(1); x=1.

ANSWERED AT 20/01/2020 - 01:33 PM


QUESTION POSTED AT 20/01/2020 - 01:33 PM

Write the equation 2x - 3y = 6 in slope-intercept form. A. y = 3/2x + 3 / B. y = 2/3x + 3/ C. y = 2/3x - 2

C.
2x-3y=6
-3y=6-2x
y=6/-3 -2/-3x
y= -2 + 2/3x

y=2/3x - 2

ANSWERED AT 20/01/2020 - 01:31 PM


QUESTION POSTED AT 20/01/2020 - 01:31 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

A guy wire is attached to the top of a radio antenna and to a point on horizontal ground that is 40.0 meters from the base of the antenna. If the wire makes an angle of 55° with the ground, approximate the length l of the wire. (Round your answer to the nearest tenth.)

It is useful to start by drawing a picture to visualize this problem. 

In this case we are going to use the trigonometric function cosine, which is Cos(theta) = adjacent / hypotenuse. 

Cos(55) = 40 / x 

After simplifying we reach the equation: X = 40 /  cos(55)

which would then make the length of the wire 69.7 meters long. 

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

Factor Completely: x2 + 16

Use ^ to show exponents, example, 4^2 to show 4 to the power of 2

square root both sides

√x² + √16

x+4  is fully factored

ANSWERED AT 20/01/2020 - 01:25 PM


QUESTION POSTED AT 20/01/2020 - 01:25 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

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

The motion of a simple spring hanging from the ceiling can be modeled with a cosine function. The bottom of the spring has a maximum height of 7 feet 4 inches and a minimum height of 6 feet 2 inches from the floor. It takes 2 seconds for the spring to expand from its minimum length to its maximum length. What is a cosine function that models the spring’s length in inches above and below its average, resting position? Express the model as a function of time in seconds

To get the average resting position of the spring, we must subtract the minimum from the maximum height of the spring with respect to the floor.
So,
7 + (4/12) - [ 6 + (2/12) ] = 1.5 ft

Half of this is where the resting position of the spring is located with respect to the minimum height. If the resting position of the spring is set at 0, then the amplitude of the wave is:
A = 1.5 / 2 = 0.75

Since it takes 2 seconds for the spring to expand from minimum to maximum,
Period = 2 = 2π / n
n = π

The cosine function is:
 y = A cos nt

where y is the distance from the resting position and t is the time in seconds.
y = 0.75 cos πt

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

What is the solution of the equation? 6x – 3 = 5x – 5 A. –4 B. –2 C. 0 D. –1

The answer would be -2. It is computed as follows:
6x - 3 = 5x - 5
6x - 5x = -5 + 3
x = -2

ANSWERED AT 20/01/2020 - 01:17 PM


QUESTION POSTED AT 20/01/2020 - 01:17 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
-5x+2y=-9



the equations are
3x+6y=12
-5x+2y=-9

ANSWERED AT 20/01/2020 - 01:17 PM


QUESTION POSTED AT 20/01/2020 - 01:17 PM

A researcher finds that 15% of all commuters in a metropolitan area take the train to work. The researcher polls 250 people in the area and asks them whether they take the train to work. What is the number of trials for this binomial experiment?

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

Find a number that is between 7/11 and 0.75 . A. 25/44 B. 77/99 C.23/33 D.76/99

Hello,

Answer C
23/33=0.69 69 69 .....
7/11=0.63 63 63 ....

ANSWERED AT 20/01/2020 - 01:15 PM


QUESTION POSTED AT 20/01/2020 - 01:15 PM