A rectangle has a length that is twice the width. The width is to be extended by 5 ft and the length by 3 ft, so the total area becomes 99 square feet. What was the original length?

Answer Choices:
4 ft
6 ft
8 ft
10 ft
12 ft
14 ft
16 ft

Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

[tex]\frac{3}{8}[/tex]×[tex]\frac{2}{9}[/tex]

You can cut off 3 and 9 because they have 3s there

You can also cut off 2 and 8 since they have 2s there.

[tex]\frac{1}{4}[/tex]×[tex]\frac{1}{3}[/tex]

[tex]=\frac{1}{12}[/tex]

Answer:

The triangle EFG can be constructed with the following specifications: [tex]EF = 8\,cm[/tex], [tex]FG = 7\,cm[/tex], [tex]EG = 12\,cm[/tex], [tex]E \approx 34.093^{\circ}[/tex], [tex]F \approx 106.068^{\circ}[/tex], [tex]G \approx 39.838^{\circ}[/tex].

Step-by-step explanation:

A triangle is formed by either knowing the lengths of its three sides or knowing two angles and the length of a side or knowing a angle and the lengths of two sides. By Geometry, we know that sum of internal angles in triangles equals 180°. In order to construct this triangle, we need to know the measures of angles E, F and G by means of the Law of Cosine:

Angle E

[tex]E = \cos^{-1}\left[\frac{(7\,cm)^{2}-(12\,cm)^{2}-(8\,cm)^{2}}{-2\cdot (12\,cm)\cdot (8\,cm)} \right][/tex]

[tex]E \approx 34.093^{\circ}[/tex]

Angle F

[tex]F = \cos^{-1}\left[\frac{(12\,cm)^{2} - (8\,cm)^{2} - (7\,cm)^{2}}{-2\cdot (8\,cm)\cdot (7\,cm)} \right][/tex]

[tex]F \approx 106.068^{\circ}[/tex]

Angle G

[tex]G = \cos^{-1}\left[\frac{(8\,cm)^{2}-(12\,cm)^{2}-(7\,cm)^{2}}{-2\cdot (12\,cm)\cdot (7\,cm)} \right][/tex]

[tex]G \approx 39.838^{\circ}[/tex]

The triangle EFG can be constructed with the following specifications: [tex]EF = 8\,cm[/tex], [tex]FG = 7\,cm[/tex], [tex]EG = 12\,cm[/tex], [tex]E \approx 34.093^{\circ}[/tex], [tex]F \approx 106.068^{\circ}[/tex], [tex]G \approx 39.838^{\circ}[/tex].

Answer:

b. (16 , 4)

Step-by-step explanation:

f(x):   0 -> 1 , 4 -> 16

f⁻¹(x):  1 -> 0 , 16 -> 4

Answer:

Triangle P is scaled up 3 times to become triangle Q.

Answer:

1 solution,since it cuts one time

y=2

Step-by-step explanation:

taking the equations

[tex]3x+2y=7, 4x-3y=-2\\[/tex] as equation 1 and 2 respectively,

Multipy the equation 1 by 4

Multipy the equation 2 by 3

[tex](3x+2y=7 )[/tex]×4

[tex](4x-3y=-2)[/tex]×3

[tex]12x+8y=28\\12x-9y=-6\\\\[/tex] comes as equation 3 and 4, subtract 4 from 3,

[tex]12x-12x+8y+9y=28+6\\17y=34\\y=2[/tex]

Step-by-step explanation:

m L 1 = 180°-75° = 105° ( angles in one side)

m L 2 = 75° (corresponding angles)

Vertical angles have sum 180

m<1=

m<2

Answer:

2 times 2 =4 4 times 4 =16 then you add I think

Answer: Ok so that is a fact for sure

Answer:

yup

Step-by-step explanation:

Answer:

The lateral surface area is 336 square feet

Step-by-step explanation:

Given

See attachment for storage

Required

The lateral surface area

From the attached figure, we have:

[tex]L = 14[/tex] --- Length

[tex]W = 7[/tex] --- Width

[tex]H = 8[/tex] --- Height

The lateral area is calculated as:

[tex]Area = 2 * H * (L + W)[/tex]

So, we have:

[tex]Area = 2 * 8 * (14 + 7)[/tex]

[tex]Area = 16 * (14 + 7)[/tex]

[tex]Area = 16 * 21[/tex]

[tex]Area = 336[/tex]

Answer:

there were 8 dog ears in all.

Step-by-step explanation:

Since the statement says that they saw two teachers each walking with two dogs, you have to multiply the number of teachers for the number of dogs each one had to find the total number of dogs they had:

2*2=4

Now, as the statement indicates that each dog had two ears you have to multiply the number of dogs for the number of ears each one has:

4*2=8

According to this, the answer is that there were 8 dog ears in all.

Answer: 6 Im sure

Step-by-step explanation:

By successive approximations we find that [tex]x \approx 3.3[/tex] for [tex]f(x) = g(x)[/tex].

How to find a solution of two functions by direct inspection

According to the table, the value of [tex]x[/tex] must be between 3 and 3.5. [tex]x[/tex] is the solution of [tex]f(x) = g(x)[/tex] if and only if [tex]f(x) - g(x) = 0[/tex]. Let suppose that [tex]x = 3.3[/tex], then:

[tex]3.3^{2}+13 = 3\cdot (3.3) + 14[/tex]

[tex]-0.01[/tex]

As we need only two decimals, approximation seems to be reasonable.

By successive approximations we find that [tex]x \approx 3.3[/tex] for [tex]f(x) = g(x)[/tex]. [tex]\blacksquare[/tex]

Statement is incomplete and incorrectly formatted, correct form is presented below:

Cora is using successive approximations to estimate a positive solution to [tex]f(x) = g(x)[/tex], where [tex]f(x) = x^{2}+13[/tex] and [tex]g(x) = 3\cdot x + 14[/tex]. The table shows her results for different input values of [tex]x[/tex]:

x         f(x)           g(x)

 0         13             14

 1          14             17

 2         17             20

 3         22            23

 4         29            26

3.5     25.25       24.5

To learn more on numerical methods, we kindly invite to check this verified question: https://brainly.com/question/19034634

Answer:

Clare starts with:

a*x^2 + b*x + c = 0

And she gets to:

(2*a*x + b)^2 = b^2 - 4*a*c

Now we want to show the final steps to solve the equation (isolating x)

First, we apply the square root to both sides:

[tex]\sqrt{(2*a*x + b)^2} = \sqrt{(b^2 - 4*a*c)}[/tex]

Because the square root has two solutions, (one negative and one positive), we will write:

[tex]2*a*x + b = \pm \sqrt{b^2 - 4*a*c}[/tex]

Now we subtract b in both sides:

[tex](2*a*x + b) - b = \pm \sqrt{b^2 -4*a*c} - b[/tex]

[tex]2*a*x = \pm \sqrt{b^2 -4*a*c} - b[/tex]

Now let's divide by 2*a in both sides:

[tex]2*a*x/(2*a) = \frac{\pm \sqrt{b^2 -4*a*c} - b}{2*a}[/tex]

[tex]x = \frac{\pm \sqrt{b^2 -4*a*c} - b}{2*a}[/tex]

Answer:

C

Step-by-step explanation:

1. Absolute values are in the shape of a V, so the answer is automatically C.

2. If you did not know that, you can see that the graph is a function because it passes the vertical line test. This rules out option A. By looking at the graph, you can see it passes the x-axis twice, meaning that it has 2 x-intercepts. This rules out option B. X-intercepts always have a y-coordinate of 0, so we can rule out option D. The only option left after this is C.

Answer:

$217.94

Step-by-step explanation:

Answer:

$7+$2(x-1)-y

Step-by-step explanation:

$7+$2(x-1)=y where $7 is fixed fee and $2(x-1) represents $2 more for every ADDITIONAL dog more than the first dog.

Answer:

4^-8

Step-by-step explanation:

When multiplying two exponents with the same base, in this case, 4, you need to add the two powers (-6 + -2), to get -8.

Answer:

D.) 5625 pi inches squared

Step-by-step explanation:

square root of 625 = 25

25 x 3 = 75

A= pi r(squared)

A= 75squared pi

A= 5625 pi inches squared

Answer: D

Step-by-step explanation:

Answer:

235 C D s =

8 =

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

yes

Answer:

3m+4g+6+k

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I Think I Got It Right But This Is From A LONG time ago

Answer:

B. 60

Step-by-step explanation:

I am pretty sure this is a 30-60-90 similarity right triangle. If that's the case, then the answer is 60 degrees. Have a good day! :DDD

Answer:

Sorry, but I can't see this well! I am on lapton, and it is impossible to tilt the whole thing over.

Answer: A: 145 degrees

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

The trapezoids are similar, so you need to find which sides allign with each other. It can be seen that among the paralel sides of the trapezoid, the longer ones will be similar by the factor of 2. So, 2*7=14

Answer:

14 feet

Step-by-step explanation:

Answer:

1 ramdhjajdjejjejdnsns

Answer:

-8-6

-8+6

6-(-8)

Step-by-step explanation:

Answer:

put the pointy end of the compass on the end line point then draw a circle at a measurement of 3cm 4 cm or 5 cm