Find two consecutive whole numbers that square root 86 lies between.

1. f(x)= (x+4)(x-6) 2. f(x)= (2x-4)(x-3)

devlian [24]

The intercepts and the standard form of each polynomial are listed below:

x-Intercept: x = - 4 or x = 6, Standard form: f(x) = x² - 2 · x - 24, y-Intercept: f(0) = - 24
x-Intercept: x = 1 / 4 or x = 3, Standard form: f(x) = 2 · x² - 10 · x + 12, y-Intercept: f(0) = 12

<h3>How to find the intercepts and the standard form of quadratic equations</h3>

In this case we need to find the intercepts of each quadratic equation and transform each quadratic equation into standard form. The x-intercept correspond with each of the roots of the polynomial and the y-intercept is found by evaluating the expression at x = 0.

Now we proceed to find each element:

Case 1

x-Intercept

x = - 4 or x = 6

Standard form

f(x) = (x + 4) · (x - 6)

f(x) = x² - 2 · x - 24

y-Intercept

f(0) = - 24

Case 2

x-Intercept

x = 1 / 4 or x = 3

Standard form

f(x) = (2 · x - 4) · (x - 3)

f(x) = 2 · (x - 2) · (x - 3)

f(x) = 2 · (x² - 5 · x + 6)

f(x) = 2 · x² - 10 · x + 12

y-Intercept

f(0) = 12

To learn more on quadratic equations: brainly.com/question/1863222

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6 0

1 year ago

to find the distance between a point x and an inaccessible point z, a line segment xy is constructed. measurements show that xy

marshall27 [118]

Answer:

$\approx \bold{602\ m}$

Step-by-step explanation:

Given the following dimensions:

XY=966 m

$\angle XYZ$ = 38°24', and

$\angle YZX$ = 94°6'

To find:

Distance between points X and Z.

Solution:

Let us plot the given values.

We can clearly see that it forms a triangle when we join the points X to Y, Y to Z and Z to X.

The $\triangle XYZ$ has following dimensions:

XY=966 m

$\angle XYZ$ = 38°24', and

$\angle YZX$ = 94°6'

in which we have to find the side XZ.

Kindly refer to the image attached.

Let us use the Sine rule here:

As per Sine Rule:

$\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}$

Where

a is the side opposite to $\angle A$

b is the side opposite to $\angle B$

c is the side opposite to $\angle C$

$\dfrac{XZ}{sin\angle Y} = \dfrac{XY}{sin\angle Z}\\\Rightarrow \dfrac{966}{sin94^\circ6'} = \dfrac{XZ}{sin38^\circ24'}\\\Rightarrow XZ=\dfrac{966}{sin94^\circ6'} \times sin38^\circ24'\\\Rightarrow XZ=\dfrac{966}{0.997} \times 0.621\\\Rightarrow XZ=601.69 \m \approx \bold{602\ m}$

4 0

3 years ago

A laundromat charges $1.50 to wash and $1.25 to dry a load of laundry.

djverab [1.8K]

It asked to choose all the points so ( B, C, E )

4 0

3 years ago

Read 2 more answers

Two brands of AAA batteries are tested in order to compare their voltage. The data summary can be found below.

garik1379 [7]

Answer:

The 95% confidence interval would be given by $0.281 \leq \mu_1 -\mu_2 \leq 0.529$

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".

$\bar X_1 =9.2$ represent the sample mean 1

$\bar X_2 =8.8$ represent the sample mean 2

n1=27 represent the sample 1 size

n2=30 represent the sample 2 size

$\sigma_1 =0.3$ population standard deviation for sample 1

$\sigma_2 =0.1$ population standard deviation for sample 2

$\mu_1 -\mu_2$ parameter of interest.

Solution to the problem

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm z_{\alpha/2}\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =9.2-8.8=0.4$

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: "=-NORM.INV(0.025,0,1)".And we see that $t_{\alpha/2}=1.96$