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2 years ago

What is the sum of all the interior, exterior, and central angles in a convex hexagon?

1 answer:

5 0

<span>What is the sum of all the interior, exterior, and central angles in a convex hexagon?
INTERIOR=180
EXTERIOR=360
CENTRAL=360</span>

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If a polynomial function f(x) has roots 1+square root of 2 and-3, what must be a factor of f(x)?

nevsk [136]

To find the factor a a polynomial from its roots, we are going to seat each one of the roots equal to $x$ , and then we are going to factor backwards.

We know for our problem that one of the roots of our polynomial is -3, so lets set -3 equal to $x$ and factor backwards:
$x=-3$
$x+3=0$
$(x+3)$ is a factor of our polynomial.

We also know that another root of our polynomial is $1+ \sqrt{2}$ , so lets set $1+ \sqrt{2}$ equal to $x$ and factor backwards:
$x=1+ \sqrt{2}$
$x-1= \sqrt{2}$
$x-1- \sqrt{2}=0$
$(x-(1+ \sqrt{2})=0$
( $(x-(1+ \sqrt{2} ))$ is a factor of our polynomial.

We can conclude that there is no correct answer in your given choices.

8 0

3 years ago

Classify the triangle as acute, right, or obtuse based on the side lengths of 8, 11, and 14.

ratelena [41]

Answer:

Obtuse

Step-by-step explanation:

$8^2+11^2=14^2\\64+121=196\\185=196$

Since the hypotenuse is bigger, the triangle is obtuse

8 0

2 years ago

Read 2 more answers

Calculate the value of x to one decimal place. a0inches

gtnhenbr [62]

Answer:

Step-by-step eNow examine the right triangle on the left in the figure.

x%2F10=sin%2850%29, in reference to the 50 degree angle, hypotenuse is that slanted segment of 10 units, and "x" is the opposite side from the 50 degree angle.

7 0

2 years ago

Criterion: Identify IV, DV, and hypotheses and evaluate the null hypothesis for an independent samples t test. Data: Use the inf

Papessa [141]

The table is missing in the question. The table is provided here :

Group 1 Group 2

34.86 64.14 mean

21.99 20.46 standard deviation

7 7 n

Solution :

a). The IV or independent variable = Group 1

The DV or the dependent variable = Group 2

b).

$H_0: \mu_1 = \mu_2$

$H_a:\mu_1 < \mu_2$

Therefore, $t = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{S_2^2}{n_2}}}$

$t = \frac{34.86 - 64.14}{\sqrt{\frac{21.99^2}{7}+\frac{20.46^2}{7}}}$

t = -2.579143

Now, $df = min(n_1 - 1, n_2 - 1)$

df = 7 - 1

= 6

Therefore the value of p :

$=T.DIST(-2.579143,6,TRUE)$

= 0.020908803

The p value is 0.0209

$p< 0.05$

So we reject the null hypothesis and conclude that $\mu_1 < \mu_2$

7 0

2 years ago

The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5

notsponge [240]

<h2> Question # 1</h2>

Answer:

25 is the factor which grows by between x = 5 and x = 7.

Step-by-step explanation:

Considering the exponential function

$f\left(x\right)\:=\:3\left(5\right)^x$

The growth factor between $x=1$ and $x=3$ is given by:

$\left[3\left(5\right)^3\right]\div \left[3\left(5\right)^1\right]$

$\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^3\right]\::\quad 375$

$\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^1\right]\::\quad 15$

So,

= $375\div \:15$

= $25$

Similarly, growth factor between $x=5$ and $x=7$ is given by:

$\left[3\left(5\right)^7\right]\div \left[3\left(5\right)^5\right]$

= $\frac{3\cdot \:5^7}{3\cdot \:5^5}$

$\mathrm{Divide\:the\:numbers:}\:\frac{3}{3}=1$

= $\frac{5^7}{5^5}$

$\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}$

$\frac{5^7}{5^5}=5^{7-5}$

= $5^{7-5}$

= $5^2$

= $25$

Therefore, 25 is the factor which grows by between x = 5 and x = 7.

<h2> Question # 2</h2>

Answer:

The population be in 24 years will be 27000.

Also, the population growth modeled by an exponential function as $y=A\cdot \left(b\right)^t$ is an exponential function.

The graph for $y=A\cdot \left(b\right)^t$ is also shown in attached figure.

Step-by-step explanation:

If a city that currently has a population of 1000 triples in size every 8 years.
what will the population be in 24 years?
Is the population growth modeled by a linear function or an exponential function?

As the city that currently has a population of 1000 triples in size every 8 years.

So, for this case

$y=A\cdot \left(b\right)^t$

where

$A$ = Initial population amount

$b$ = growth rate

$t$ = time

Substituting the values in the function

$y=A\cdot \left(b\right)^t$

$y=1000\cdot \:\:3^{\frac{1}{8}t}$

So, the population be in 24 years

$y=1000\cdot \:\:3^{\frac{1}{8}24}$

$3^{\frac{1}{8}\cdot \:24}=3^3$

$\:y=3^3\cdot 1000$

$y=1000\cdot \:\:27$

$y=27000$

Therefore, the population be in 24 years will be 27000.

Also, the population growth modeled by an exponential function as $y=A\cdot \left(b\right)^t$ is an exponential function.

<h2 /><h2> Question # 3</h2>

Answer:

the graph of the function will translate horizontally 3/5 units right.

Step-by-step explanation:

We have to find the effect on the graph of the function $f(x)=2x$ when it is replaced by f(x- 3/5).

We already have an idea that rule for horizontal translation:

Given a function $f(x)$ , and a constant c > 0, the function $g(x) = f(x - a)$ represents a horizontal shift c units to the right from f(x). The function $h(x) = f(x + a)$ represents a horizontal shift c units to the left.

As 3/5 > 0, so the graph of the function will translate horizontally 3/5 units right.

Therefore, the graph of the function will translate horizontally 3/5 units right.

Keywords: exponential function, translation function, growth factor

Learn more about exponential function and growth factor form brainly.com/question/10147339

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6 0

3 years ago