Let f(x) = 2x + 8, g(x) = x² + 2x

Question A data set is summarized in the frequency table below. The data set contains a total of 50 data values. What is the mis

d1i1m1o1n [39]

Answer:

Missing frequency = 4

Step-by-step explanation:

Given:

Qty Number

1 5

2 6

3 5

4 6

5 □

6 5

7 8

8 4

9 4

10 3

Total 50

Find:

Missing frequency

Computation:

Missing frequency = Total frequency - Counted

Missing frequency = 50 - 46

Missing frequency = 4

3 0

3 years ago

a cuboid with a volume of 924 cm3 has dimensions 4cm (x+1)cm and (x+11)cm. show clearly that x^2 +12x-220=0. show the equation b

nikdorinn [45]

Answer:

Part 1)

The equation by factorization is

$x^{2}+12x-230=(x-(-6+\sqrt{266}))(x-(-6-\sqrt{266}))$

Both values of x are

$x1=-6+\sqrt{266}$

$x2=-6-\sqrt{266}$

Part 2) The dimensions of the cuboid are

$4\ cm$ , $(-5+\sqrt{266})\ cm$ and $(5+\sqrt{266})\ cm$

Step-by-step explanation:

step 1

we know that

The volume of the cuboid is equal to

$V=LWH$

substitute the given values

$V=4(x+1)(x+11)$

$V=924\ cm^{3}$

so

$4(x+1)(x+11)=924\\4(x^{2}+11x+x+11)=924\\ 4(x^{2}+12x+11)=924\\x^{2}+12x+11=231\\x^{2}+12x-230=0$

Complete the square

$x^{2}+12x-230=0$

$x^{2}+12x=230$

$x^{2}+12x+36=230+36$

$(x+6)^{2}=266$

square root both sides

$x+6=(+/-)\sqrt{266}$

$x=-6(+/-)\sqrt{266}$

so

$x1=-6+\sqrt{266}$

$x2=-6-\sqrt{266}$

therefore

The equation by factorization is

$x^{2}+12x-230=(x-(-6+\sqrt{266}))(x-(-6-\sqrt{266}))$

step 2

Find the dimensions of the cuboid

The dimensions are

$4\ cm$

$(x+1)\ cm -----> (-6+\sqrt{266}+1)=(-5+\sqrt{266})\ cm$

$(x+11)\ cm ----> (-6+\sqrt{266}+11)=(5+\sqrt{266})\ cm$

4 0

3 years ago

Read 2 more answers

"In ABC, mBAC = 5x + 8, mABC = 6x + 22, and mBCA = 3x  25.

strojnjashka [21]

<span>In angle ABC, the measure of angle BAC = 5x + 8, </span>measure of angle ABC = 6x + 22, and measure of angle BCA = 3x  25. You know that the sum of the angles of a triangle is 180 degrees. And since the angles BAC, ABC and BCA are the corners of the triangle then just add them and equate to 180 degrees.

5x + 8 + 6x + 22 + 3x + 25 = 180
14x + 55 = 180
14x = 125
x = 8.93

5 0

3 years ago

Read 2 more answers

Find the measure of the central angle of an arc if its length is 14pi and 12 is the radius.

professor190 [17]

$\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\[-0.5em] \hrulefill\\ s=14\pi \\ r=12 \end{cases}\implies 14\pi =12\theta \implies \cfrac{14\pi }{12}=\theta \\\\\\ \stackrel{\textit{radians}}{\cfrac{7\pi }{6}}=\theta ~\hspace{10em}\stackrel{\textit{in degrees}}{210^o}$

3 0

3 years ago

What is the area of of a circle with the circumference of 6.28

Vedmedyk [2.9K]

Circumference = $2 \pi r$
6.28 = $2 \pi r$
r = 1

Area = $\pi r^2$
Area = $\pi (1)$
Area = 3.14

Hope that helps :)

3 0

3 years ago

Read 2 more answers

Let f(x) = 2x + 8, g(x) = x² + 2x – 8, and h(x)