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3 years ago

Find an ordered pair that is a solution to the equation. 3x - y = 8

Mathematics

1 answer:

mojhsa [17]3 years ago

8 0

Answer:

Step-by-step explanation:

There are so many order pairs that can solve this equation.

To solve this problem, we choose any value of x and find y;

Given expression;

3x - y = 8

if x = 0,

3(0) - y = 8

-y = 8

y = -8;

(0,-8) is a solution

ii.

if x = 1,

3(1) - y = 8

- y = 8 - 3

y = -5

(1, -5) is a solution

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What is the solution to the equation 8 - 2b = -2/3(12b + 6)?

Delvig [45]

<span>8 - 2b = -2/3(12b + 6)
8 - 2b = -8b -4
8 + 4 = -8b + 2b
12 = -6b
b = -12/6
b = -2

So, your final answer is b = -2</span>

8 0

3 years ago

In the given diagram if AB || CD, ∠ABO = 118° , ∠BOD = 152° , then find the value of ∠ODC.

GaryK [48]

Answer:

90°

Step-by-step explanation:

Through point O draw a ray on left side of O which is || to AB & CD and take any point P on it.

Therefore,

∠ABO + ∠BOP = 180° (by interior angle Postulate)

118° + ∠BOP = 180°

∠BOP = 180° - 118°

∠BOP = 62°.... (1)

Since, ∠BOP + ∠POD = ∠BOD

Therefore, 62° + ∠POD = 152°

∠POD = 152° - 62°

∠POD = 90°.....(2)

∠POD + ∠ODC = 180° (by interior angle Postulate)

90° + ∠ODC = 180°

∠ODC = 180° - 90°

$\huge\red {\boxed {m\angle ODC = 90°}}$

6 0

3 years ago

Which of the following is a line segment in the drawing that connects two parallel lines?

charle [14.2K]

Answer:

line segment BE

Step-by-step explanation:

Parallel lines are lines that never cross. In this case, the two parallel lines are AC and DF. A line segment is part of a line that has a point at either end. The only segment which crosses lines AC and DF is segment BE.

Also, if you look at the answer choices, the first two indicate a line ↔ above the letters, which represents a line that doesn't end, while the other two choices just have a line to indicate a segment.

8 0

3 years ago

Describe how you would use the rules of exponents to simplify (7x?yz) 3. You may indicate an exponent in your answer with ^. For

SVETLANKA909090 [29]

Answer:

343x^6y^3z^3

Step-by-step explanation:

One of the rules of exponents demands:

$(abc)^m=a^mb^mc^m$

where a, b, c and m are coefficients.

Furthermore, you use the following rule for exponents of variables that already have an exponent:

$(a^n)^m=a^{m*n}$

Thus, you can apply this rules in the following way:

$(7x^2yz)^3=(7)^3(x^2)^3(y)^3(z)^3=7*7*7x^{2*3}y^3z^3=343x^6y^3z^3$

hence, the answer is 343x^6y^3z^3

5 0

3 years ago

A study was performed to investigate whether teens and adults had different habits when it comes to consuming meat-free meals. I

Elden [556K]

Answer:

H₀ should be rejected at CI 95% .

Then the proportion of adults with 95 % CI is bigger than the proportion of teen

Step-by-step explanation:

From adult sample:

n₂ = 2323

x₂ = 1601

p₂ = 1601 / 2323 p₂ = 0,689 or p₂ = 68,9%

From teen sample:

n₁ = 875

x₁ = 555

p₁ = 555/ 875 p₁ = 0,634 or p₁ = 63,4

Values of p₁ and p₂ suggest that the proportion of adults consuming at least one meat free meal per week is bigger than teen proportion.

To either prove or reject the above statement we have to develop a difference of proportion test according to:

Hypothesis test:

Null Hypothesis H₀ p₁ = p₂

Alternative Hypothesis Hₐ p₂ > p₁

So is a one-tail test to the right

We can establish a confidence interval of 95 % then α = 5 %

or α = 0,05

As the samples are big enough we will develop a z test

Then z(c) for α = 0,05 from z table is z(c) = 1,64

To calculate z(s)

z(s) = ( p₂ - p₁ ) / √p*q* ( 1/n₁ + 1/n₂ )

where p = ( x₁ + x₂ ) / n₁ + n₂ p = 555 + 1601 / 875 + 2323

p = 2156/3198 p = 0,674

and q = 1 - 0,674 q = 0,326

z(s) = ( 0,689 - 0,634 ) / √0,674*0,326 ( 1/875 + 1 / 2323

z(s) = 0,055/ √ 0,2197 ( 0,00114 + 0,00043)

z(s) = 0,055/ √0,2197* 0,00157

z(s) = 0,055/ √ 3,45*10⁻⁴

z(s) = 0,055 / 1,85*10⁻²

z(s) = 5,5/1,85

z(s) = 2,97

Comparing z(s) and z(c) z(s) > z(c)

Then z(s) is in the rejection region we reject H₀.

We can claim that the proportion of adult eating at least one meat-free meal is bigger than the proportion of teen

6 0

3 years ago