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3 years ago

8

Which method(s) can be used to solve a system of equations? Select all that apply. distributing graphing substitution formulas a

ddition modeling

1 answer:

katovenus [111]3 years ago

6 0

Distributing, formulas, and addition

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Which of the following are necessary when proving that the opposite angles of a parallelogram are congruent? Check all that appl

erma4kov [3.2K]

A. Corresponding parts of congruent triangles are congruent.

4 0

3 years ago

Read 2 more answers

I need help please I have to finish this

4vir4ik [10]

Answer: x=4

Step-by-step explanation:

We know that line segment AC= AB + BC

we also know that AB= 3x+8 and BC= 2x-5

by substituting these, we get AC= (3x+8)+(2x-5)

AC is given as being 23, so we know that

23= (3x+8)+(2x-5)

by combining like terms, we get that

5x+3=23

simplify this to get that x=4

6 0

3 years ago

The heights (in inches) and pulse rates (in beats per minute) for a sample of 40 women were measured. Using technology with the

Viktor [21]

Answer:

There is not sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of women

Step-by-step explanation:

The correlation coefficient between the variables h(height in inches) and pulse rates (in beats per minute) is 0.202

Sample size n=40

Level of significane alpha = 0.01

Create null and alternate hypothesis as:

H0: r=0

Ha: r not equal 0

(Two tailed test at 1% significance level)

Sample r = 0.202

r difference = 0.202

test statistic t = $\frac{r\sqrt{n-2} }{\sqrt{1-r^2} } \\=\frac{0.202(\sqrt{38} )}{\sqrt{0.9592} } \\=\frac{1.25}{0.9794} \\=1.271$

df =n-2 =38

t critical value for 0.01 and df =38 is 2.704

Since our test statistic lies below 2.704, we accept null hypothesis

There is not sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of women

7 0

3 years ago

What is the correct answer?

egoroff_w [7]

X⁴ - 81 = x⁴ - 9² (Difference of 2 squares, then we an write it:

(x²-3)(x²+3) =0, → then (x²-3) = 0 and (x²+3)=0

(x²-3) = 0 → x² = 3 → x = +√3 and x = -√3
(x²+3) =0 → x² = -3 → x = +√-3 and x = -√3→ or i√3 AND x = -i√3

A{ -3 , +3 , -i√3 , i√3}

4 0

3 years ago

In each part, decide if the statement is true. If it is true, prove it. If it is not true, give an explicit counterexample and d

svet-max [94.6K]

Answer: Hello!

ok, remember that "if and only if" implies that you need to prove the statement in both ways, this is represented with the ⇔ usually.

a) For any sets A, B and C, A ∩ B ⊆ C if and only if either A ⊆ C or B ⊆ C.

In this type of problems, i find very useful start looking for some counterexample.

In this case, suppose that A = {1,2,3,4,5} , B = {3,4,5,6,7} and C = {3,4,5,6}

then is easy to see that A ⊄ C and B ⊄C.

And A∩B = {3,4,5}

then A∩B ⊂ C

then the statement is false (because one of the ways is false, remember that this is an "if and only if" statement)

b) For any sets A, B and C, A ⊆ B ∩ C if and only if both A ⊆ B and A ⊆ C.

the first way is true; because if A ⊆ B ∩ C. then all the elements of A are in the intersection of B and C (which are common elements for B and C) and then all the elements of A are in the set B and in the set C, and this means that A ⊆ B and A ⊆ C.

But let's see the other way now, suppose that A ⊆ B and A ⊆ C, now we want to know if A ⊆ B ∩ C.

if A ⊆ B and A ⊆ C, means that all the elements of A are in B, and all the elements of A are in C, then all the elements of A are common elements between B and C, this means that B ∩ C is at least equal to A (at least, because we know that all the elements of A are common elements between B and C, but there could be more common elements that don belong to A)

then A ⊆ B ∩ C.

4 0

3 years ago