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matrenka [14]
2 years ago
12

Select the correct answer. Which function has the same graph as x + y = 11?

Mathematics
1 answer:
Zinaida [17]2 years ago
8 0

The function that has the same graph as x + y = 11 is f(x) = -x + 11

<h3>Graph of functions</h3>

From the question, we are to determine the function that has the same graph as the given equation

The given equation is

x + y = 11

In the above equation, y is the dependent variable.

and

Among the given equation, f(x) is the dependent variable

Thus, we can write that

x + f(x) = 11

Isolate f(x)

f(x) = -x + 11

Hence, the function that has the same graph as x + y = 11 is f(x) = -x + 11

Learn more on Graph of functions here: brainly.com/question/20388062

#SPJ1

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Use the method in the Example to find the square roots of 1 + √3i
kiruha [24]

Answer:

\sqrt{1 + \sqrt{3} i}=\pm (1.58+i 0.548)

Step-by-step explanation:

Given

z = 1 + √3 i

Let \sqrt{1+\sqrt(3) i}=p+iq

Squaring both sides

1+\sqrt(3) i=p^2-q^2+2ipq

Comparing real and imaginary part

Re(LHS)=Re(RHS)

1=p^2-q^2...........................(1)

comparing Im(LHS)=Im(RHS)

√3=2pq

q=\frac{\sqrt{3}}{2p}

Substitute q in equation (1)

1=p^2-(\frac{\sqrt{3}}{2p})^2

p^4-p^2-0.75=0

Let x=p^2

x^2-x-0.75=0

x=\dfrac{1\pm \sqrt{1^2+4\times 0.75}}{2}

x=\frac{1\pm 4}{2}

we take only Positive value because p^2=x

x=2.5  

p^2=2.5

thus p=\pm 1.58

q=\pm 0.548

thus,

\sqrt{1 + \sqrt{3} i}=\pm (1.58+i 0.548)

5 0
3 years ago
Is 4/16 equivalent to 3/5
azamat
No, as if you reduce 4/16 it is 1/4, not 3/5, therefore they are not equivalent.
7 0
3 years ago
Heather has divided ​$5400 between two​ investments, one paying 8​%, the other paying 5​%. if the return on her investment is ​$
Phantasy [73]

Answer:

$2500 at 8%.

$2900 st 5%.

Step-by-step explanation:

Let x be the amount invested at rate of 8% and y be the amount invested at the rate of 5%.

We have been given that Heather has divided ​$5400 between two​ investments. We can represent this information as:

x+y=5400...(1)

The return on her investment is ​$345.  

Earnings from the investment at 8% will be 8% of x.

Earnings from the investment at 5% will be 5% of y.

(\frac{8}{100})x+(\frac{5}{100})y=345...(2)

0.08x+0.05y=345...(2)

We will use substitution method to solve our system of equations. From equation (1) we will get,

x=5400-y

Substituting this value in equation (2) we will get,

0.08(5400-y)+0.05y=345

432-0.08y+0.05y=345

-0.08y+0.05y=345-432

-0.03y=-87

\frac{-0.03y}{-0.03}=\frac{-87}{-0.03}

y=2900  

Therefore, Heather has invested an amount of $2900 at 5%.

Let us substitute y=2900 in equation (1) to solve for x.

x+2900=5400

x+2900-2900=5400-2900

x=2500

Therefore, Heather has invested an amount of $2500 at 8%.

6 0
3 years ago
A circle with a radius of 3cm sits inside a circle with a radius of 11cm.
lozanna [386]

Answer:

Area of shaded region = 351.68 cm²

Step-by-step explanation:

Area of a circle = πr²

where r = radius = 3.14

Area of bigger circle = 3.14 × 11²

= 3.14 × 11 × 11

= 379.94cm²

Area of smaller circle = 3.14 * 3²

= 3.14 × 3 × 3

= 28.26cm²

Area of shaded region = Area of bigger circle - Area of smaller circle

= (379.94 - 28.26) cm²

= 351.68 cm²

8 0
3 years ago
Help asap please, dhebduhd
Kamila [148]
Hi there !

The answer is B. angle 4.

An alternate interior angle is diagonally across one angle on the inside of the transversal. Opposite of 5 on the inside is angle 4.

Hope this helps !
6 0
2 years ago
Read 2 more answers
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