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3 years ago

What is the measure of <4?

Mathematics

1 answer:

qaws [65]3 years ago

5 0

Answer:

90°

Step-by-step explanation:

Two lines intersect each other at a right angle, making them perpendicular. Thus, the resulting angles will all be 90°, making ∠4 = 90°.

Alternatively, we can use the supplementary angles equation.

Let's call the right angle marked in the picture ∠5.

∠4 + ∠5 = 180°, since the line is also a straight angle which measures 180°.

∠4 + 90° = 180°

∠4 = 90°

Either way, ∠4 = 90°

Hope this helps!

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Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1. (2 points)

love history [14]

The focus is above the directrix, so the parabola opens upward—its vertical scale factor is positive (+1/12). The line of symmetry is x=-5, so the vertex form of the equation will have the factor (x -(-5))² = (x+5)². The choice that meets both these requirements is
D. f(x) = (1/12)(x + 5)² + 2

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2 years ago

Write a polynomial function of least degree with integral coefficients that has the

frutty [35]

A polynomial function of least degree with integral coefficients that has the

given zeros $f(x)=x^4+x^3+9x^2+9x$

Given

Given zeros are 3i, -1 and 0

complex zeros occurs in pairs. 3i is one of the zero

-3i is the other zero

So zeros are 3i, -3i, 0 and -1

Now we write the zeros in factor form

If 'a' is a zero then (x-a) is a factor

the factor form of given zeros

$\:\left(x-3i\right)\left(x-\left(-3i\right)\right)\left(x-0\right)\left(x-\left(-1\right)\right)\\\left(x-3i\right)\left(x+3i\right)\left(x-0\right)\left(x+1\right)$

Now we multiply it to get the polynomial

$x\left(x-3i\right)\left(x+3i\right)\left(x+1\right)\\x\left(x^2+9\right)\left(x+1\right)\\x\left(x^3+x^2+9x+9\right)\\x^4+x^3+9x^2+9x$

polynomial function of least degree with integral coefficients that has the

given zeros $f(x)=x^4+x^3+9x^2+9x$

Learn more : brainly.com/question/7619478

6 0

2 years ago

What is decimals -4.8(5.3)

bearhunter [10]

Answer:

-25.44

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

A report by the US Geological Survey indicates that glaciers in Glacier National Park, Montana, are shrinking. Recent estimates

postnew [5]

Answer

a) C

b) B

c) C, E

d) 15.5

e) 0.7

f) 67.7

Step-by-step explanation

a) A linear equation can be written as $y=mx+c$ where $m$ is the slope and $c$ is the intercept on the $y$ -axis. The slope describes how $y$ changes when $x$ changes. A negative value means the it is a decreasing change. In our case, $y$ is $A$ and $x$ is $t$ . Thus, the slope of the equation is $m=-0.062$ . This means that the area of glacier is decreasing by $0.062 \text{km}{}^2 = 62000 \text{m}{}^2$ every year since 2000.

b) The $A$ -intercept (= 16.2 $\text{km}{}^2$ ) represents the area covered when $t=0$ . But $t=0$ starting from year 2000. This intercept then represents the area covered by glacier in the year 2000. Therefore, the area covered by glacier in 2000 was 16.2 $\text{km}{}^2$ .

c) $A=f(t)$ means the area covered after year 2000. Setting it to 12 means the area covered after $t$ years is 12 $\text{km}{}^2$ ). $t$ is therefore the number of years since 2000 that the total area covered will be 12 $\text{km}{}^2$ ).

d) $f(12)=16.2−0.062\times12 =16.2-0.744 = =15.456 15.5 \text{km}{}^2$ to 1 decimal place.

e) The term involving $t$ represents the disappearing area. In 12 years, the disappeared area is $0.062\times12=0.744 =0.7 \text{km}{}^2$ to 1 decimal place.

f) $f(t)=16.2−0.062t =12$

$0.062t = 16.2-12 = 4.2$

$t = \dfrac{4.2}{0.062}=67.7419\ldots =67.7$ years to 1 decimal place.

8 0

2 years ago

Which of the following geometric series converges?

Artist 52 [7]

All three series converge, so the answer is D.

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Consider a geometric sequence with the first term a and common ratio |r| < 1. Then the n-th partial sum (the sum of the first n terms) of the sequence is

$S_n=a+ar+ar^2+\cdots+ar^{n-2}+ar^{n-1}$