All categories

2 years ago

I'm confused on how to do this question

Mathematics

1 answer:

laila [671]2 years ago

3 0

Answer:

CE = 35

Step-by-step explanation:

Based on the Triangle Proportionality Theorem, BD divides AC and CE proportionally. This implies that:

BC:AB = DC:DE

Plug in the values

(x - 5)/6 = 14/(2x + 3)

(x - 5)(2x + 3) = 14*6

x(2x + 3) -5(2x + 3) = 84

2x² + 3x - 10x - 15 = 84

2x² - 7x - 15 - 84 = 0

2x² - 7x - 99 = 0

Factorize

2x² - 18x + 11x - 99 = 0

2x(x - 9) +11(x - 9) = 0

(2x + 11)(x - 9) = 0

2x = -11

x = -11/2

x = 9

Let's take the positive value of x

Thus:

CE = 14 + 2x + 3

Plug in the value of x

CE = 14 + 2(9) + 3

CE = 14 + 18 + 3

CE = 35

You might be interested in

A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimeters on a pain sca

saul85 [17]

Answer:

The 95% confidence interval for the difference would be given by (-1.776;0.376)

We are 95% confidence that the true mean difference is between $-1.776 \leq \mu_d \leq 0.376$ . Since the confidence interval contains the value 0, we don't have enough evidence to conclude that hypnotism appear to be effective in reducing pain.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Let put some notation

x=test value before , y = test value after

x: 6.4 2.6 7.7 10.5 11.7 5.8 4.3 2.8

y: 6.7 2.4 7.4 8.1 8.6 6.4 3.9 2.7

The differences defined as $d_i = y_i -x_i$ and we got:

d: 0.3, -0.2, -0.3, -2.4, -3.1, 0.6, -0.4, -0.1

We can calculate the mean and the deviation for the sample with the following formulas:

$\bar d=\frac{\sum_{i=1}^n d_i}{n}$

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}$

$\bar d=-0.7$ represent the sample mean for the difference

$\mu_d$ population mean (variable of interest)

$s_d$ =1.32 represent the sample standard deviation

n=8 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar d \pm t_{\alpha/2} *\frac{s_d}{\sqrt{n}}$ (1)

In order to calculate the critical value t we need to find first the degrees of freedom, given by:

$df=n-1=8-1=7$

Since the Confidence is 0.95 or 95%, the value of alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,8)".And we see that $t_(\alpha/2)=2.306$

Now we have everything in order to replace into formula (1):

$-0.7-2.306\frac{1.32}{\sqrt{8}}=-1.776$

$-0.7+2.306\frac{1.32}{\sqrt{8}}=0.376$

So on this case the 95% confidence interval for the difference would be given by (-1.776;0.376)

6 0

3 years ago

Simplify -3[5 - (-8 + 6)]<br> -21<br> -9<br> 21

Aloiza [94]

Answer:

Step-by-step explanation:

Here you go mate

Step 1

-3[5-(-8+6)] Equation/Question

Step 2

-3[5-(-8+6)] Simplify

(-3)(7)

Step 3

(-3)(7) Multiply

-21

Answer

-21

Hope this helps

8 0

2 years ago

On the coordinate plane, the four corners of Alejandro's garden are located at (0,2), (4,6), (8,2), and (4,-2). Which shape most

ohaa [14]

It is the shape of a rectangle

6 0

3 years ago

Read 2 more answers

Find the sum of the odd integers between 24 and 50

morpeh [17]

Answer:

481

Step-by-step explanation:

There are several ways you can get there.

1. There are only 13 numbers, so you can write them down and add them up.

25 + 27 + 29 + ... + 47 + 49 = 481

2. You can use the formula for the sum of an arithmetic sequence. This one has a starting value of 25, an ending value of 49, and 13 terms.

Sum = ((start) + (end))/2 × (number of terms) = (25 +49)/2×13 = 481

3. You can use a formula for the terms of the series and evaluate the sum.

an = 25 +2(n -1) = 2n +23

$\sum\limits_{n=1}^{13}{(2n+23)}=2\sum\limits_{n=1}^{13}(n)+\sum\limits_{n=1}^{13}{(23)}=2\dfrac{13\cdot 14}{2}+13\cdot 23=481$

4 0

2 years ago

An eagle is flying around and its velocity vvvv as a function of time tttt is given in the graph below where rightwards is the p

mojhsa [17]

9514 1404 393

Answer:

8 units

Step-by-step explanation:

Displacement is the area under the velocity curve. The area of interest is in the shape of a trapezoid, so we can use the formula ...

A = (1/2)(b1 +b2)h

to find the area.

Here, b1=3, b2=1, h=4, so the area is ...

A = (1/2)(3 +1)(4) = 8

The displacement is 8 units in the time from t=1 to t=4.

7 0

3 years ago