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3 years ago

What is the rectangle's height and base?

Mathematics

2 answers:

HACTEHA [7]3 years ago

6 0

Answer:

Base = 16cm

Height = 7cm

riadik2000 [5.3K]3 years ago

3 0

Answer:

base = 16 cm

height = 7 cm

Step-by-step explanation:

area of a rectangle = base (b) x height (h)

base (b) = 9 + h

area = 112 cm²

plug in values:

112 = (9 + h) * h

112 = 9h + h²

h² + 9h - 112 = 0

h can be solved using quadratic equation

-9 ± √ (9² - 4 (1) (-112))

h = --------------------------------------

-9 ± √529

h = ----------------

h = 7 ; h = -16

therefore the height of a rectangle (h) = 7 cm

solve for base (b)

base (b) = 9 + h

base (b) = 9 + 7

base (b) = 16 cm

proof:

area of a rectangle = base (b) x height (h)

112 = 16 * 7

112 = 112 ---- ok

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3 years ago

Slove the simoltanous equation by using substitution or elimination method 5x-3y=1 3x+2y=1

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By substitution method 

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3 years ago

Solve the following equation. Round solution to the tenths place. 29 = с/7.2 C =

expeople1 [14]

Answer:

c = 208.8

Step-by-step explanation:

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3 years ago

What is -15xy + 25x factored

Oksanka [162]

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<h3>Factoring equation</h3>

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2 years ago

Read 2 more answers

A random sample from a normal population is obtained, and the data are given below. Find a 90% confidence interval for . 114 157

melamori03 [73]

Answer:

$103.160 \leq \sigma \leq 187.476$

And the upper bound rounded to the nearest integer would be 187.

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 mean or variance 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.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

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Data given: 114 157 203 257 284 299 305 344 378 410 421 450 478 480 512 533 545

The confidence interval for the population variance $\sigma^2$ is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

On this case we need to find the sample standard deviation with the following formula:

$s=sqrt{\frac{\sum_{i=1}^{17} (x_i -\bar x)^2}{n-1}}$

And in order to find the sample mean we just need to use this formula:

$\bar x =\frac{\sum_{i=1}^n x_i}{n}$

The sample mean obtained on this case is $\bar x= 362.941$ and the deviation s=132.250

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Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a tabel to find the critical values.