Identify the pair of alternate exterior angles.



A.
∠3 and ∠5

B.
∠2 and ∠8

C.
∠2 and ∠7

D.
∠1 and ∠8

i think B

Answer:

The value of y is 7.

Step-by-step explanation:

The given equation is

[tex]log_{11}(y+8)+log_{11}4=log_{11}60[/tex]

[tex]log_{11}[(y+8)4]=log_{11}60[/tex]               [tex][\because log_ax+log_ay=log_axy][/tex]

[tex]log_{11}(4y+32)=log_{11}60[/tex]

Equating both sides.

[tex]4y+32=60[/tex]

[tex]4y=60-32[/tex]

[tex]4y=28[/tex]

Divide both sides by 4.

[tex]y=7[/tex]

Therefore the value of y is 7.

Answer:

Malia's unit rate is greater than Bill's by $0.05.

Step-by-step explanation:

Consider the provided information.

The total amount she earns can be found using the equation y = 8.1x, where x is the number of hours she works and y is the total amount she earns in dollars.

The unit rate, when written as a fraction, has a denominator equal to one.

The unit price of Malia is $8.1

For Bill works:

Number of hours   Total amount earned

             18                          $144.90

             28                         $225.40

             35                         $281.75

Unit price would be:

[tex]\dfrac{144.90}{18}=\dfrac{y}{x}\\\\8.05=\dfrac{y}{x}\\\\y=8.05x[/tex]

Hence, unit price of Bill is $8.05

Malia's unit rate is 8.1 whereas Bill's unit rate is 8.05,

Thus, Malia's unit rate is greater than Bill's by 8.10-8.05=0.05.

Answer:

[tex]\frac{1}{1} \times \frac{3}{5}[/tex]

Step-by-step explanation:

The complete question is

Yen calculates the product 5/8 x 24/25. before he multiplies, he simplifies all the factors. what does the problem look like after he simplifies the factors?

The given product is

[tex]\frac{5}{8} \times \frac{24}{25}[/tex]

Then, Yen simplifies and the problem looks like

[tex]\frac{1}{1} \times \frac{3}{5}[/tex]

Because, we simplified 5 with 25 and 8 with 24.

Therefore, the result of the product is

[tex]\frac{3}{5}[/tex]

Answer:

BC≅AC

Step-by-step explanation:

From the given figure, triangle ABC is such that ∠CAB=∠CBA=70°, therefore the sides of the triangle that are AC and BC will be congruent to each other as if two angles of the same triangle are equal then the sides opposite to those angles are also equal  to each other, therefore

BC is congruent to AC that is BC≅AC.

An equation is equivalent to 2x + 4a = 10 will be D. x=5-2a.

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

In all answers we are solving for x. That means x needs to be by itself.

2x + 4a = 10

Subtract 4a;

2x = 10 - 4a

Divide by 2;

x = 5 - 2a

D. x=5-2a

Therefore, an equation is equivalent to 2x + 4a = 10 will be D. x=5-2a.

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Answer: D is the answer

As per linear equation, the half of 9(1/2) inches is 4(3/4) inches or 4.75 inches.

A linear equation is an equation that has one or multiple variables with the highest power of the variable is 1.

The given measurement is 9(1/2) inches.

Therefore, the half of the given measurement is

= [9(1/2) ÷ 2] inches

= [19/2 ÷ 2] inches

= 19/4 inches

= 4(3/4) inches

= 4.75 inches

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The polynomial with rational coefficients and roots -5 and 3i will be [tex]p(x)=x^3+5x^2+9x+45=0[/tex].

Polynomial p(x)=0 has the roots: -5 and 3i

It is required to write a polynomial with rational coefficient and the given roots.

The polynomial has a complex root 0+3i. So, there will be one more root of the polynomial which is 0-3i.

Now, the roots of the polynomial are

[tex]\alpha =-5\\\beta=0+3i\\\gamma=0-3i[/tex]

So, the required polynomial can be written as,

[tex](x-\alpha)(x-\beta)(x-\gamma)=(x-(-5))(x-(0+3i))(x-(0-3i))\\=(x+5)(x-3i)(x+3i)\\=(x+5)(x^2-(3i)^2)\\=(x+5)(x^2+9)\\=x(x^2+9)+5(x^2+9)\\=x^3+5x^2+9x+45[/tex]

Therefore, the polynomial with rational coefficients and roots -5 and 3i will be [tex]p(x)=x^3+5x^2+9x+45=0[/tex].

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Answer:

Step-by-step explanation:

The given equation is

[tex]y=41-3x[/tex]

Where [tex]x[/tex] is the height above the surface and [tex]y[/tex] is the temperature in degrees Celsius.

Now, the temperature on the surface can be find when the height above the surface is zero, that is [tex]x=0[/tex]. So, we replace this value and solve for [tex]y[/tex]

[tex]y=41-3x=41-3(0)\\y=41[/tex]

Therefore, the temperature on the surface of the planet is 41 °C.

The second question is about the constant rate of change of the given relation, which is also the slope of the linear expression. That constant rate of change is always the coefficient of variable [tex]x[/tex]. Therefore, the ratio of change is   [tex]r=-3[/tex]. Which means the tempearture decreases 3 °C when the height increases 1 km.

The decreasing behaviour is deduct from the ratio of change, when it's negative, that means the function decreases, like in this case.

Answer:

the answer is b) 70.7 feet

Step-by-step explanation:

thank you for amazing answers on the board.

The probability that the payroll for one week contained overtime wages or temporary help is [tex]\boxed{\frac{10}{13}}[/tex].

Further explanation:

It is given that during a [tex]52[/tex] week period, a company paid overtime wages for [tex]19[/tex] weeks and hired temporary help for [tex]11[/tex] weeks.

During [tex]5[/tex] weeks, the company paid overtime and hired temporary help.

Calculation:

A company paid overtime wages for [tex]19[/tex] weeks and [tex]5[/tex] weeks during the [tex]52[/tex] week period.

Therefore, the probability of overtime wages [tex]P(O)[/tex] is calculated as follows:

[tex]\begin{aligned}P(O)&=\dfrac{19}{52}+\dfrac{5}{52}\\&=\dfrac{19+5}{52}\\&=\dfrac{24}{52}\end{aligned}[/tex]

The probability of overtime wages is [tex]\frac{24}{52}[/tex].  

The same company hired temporary help for [tex]11[/tex] weeks and [tex]5[/tex] weeks during the [tex]52[/tex] week period.

Therefore, the probability of temporary help [tex]P(H)[/tex] is calculated as follows:

[tex]\begin{aligned}P(H)&=\dfrac{11}{52}+\dfrac{5}{52}\\&=\dfrac{11+5}{52}\\&=\dfrac{16}{52}\end{aligned}[/tex]  

The probability of temporary help is [tex]\frac{16}{52}[/tex].  

Now, the combined probability [tex]P[/tex] that the payroll for one week contained overtime wages or temporary help is calculated by adding the probabilities of overtime wages and temporary help as follows:

[tex]\begin{aligned}P&=\dfrac{24}{52}+\dfrac{16}{52}\\&=\dfrac{24+16}{52}\\&=\dfrac{40}{52}\\&=\dfrac{10}{13}\end{aligned}[/tex]

The probability that the payroll for one week contained overtime wages or temporary help is [tex]\boxed{\dfrac{10}{13}}[/tex].

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Probability

Keywords: Probability, events, outcome, sample, experiment, equally likely, random, complementary events, joint probability, independent events, mutually exclusive events, conditional probability.

The probability that a lot containing exactly two defective electronic baseball games manufactured by Tempco will still be shipped is approximately 0.821 or 82.1%. This problem is solved using the concept of hypergeometric distribution in probability theory.

This problem is a case of hypergeometric distribution in probability theory. In the given situation, the total number of games in the lot is 36, of which 34 are okay and two are defective. The inspector selects eight games out of these 36. We must calculate the probability that neither of the two defective games is in the selected 8.

This can be calculated as follows: The probability of selecting a good game first is 34/36. After we choose a good one, we now have 33 good games left in a set of 35 games, so the probability of choosing another good one is 33/35. We continue this way until we have selected all eight games. Thus, the probability that all eight games selected will be good, and therefore the lot will be shipped, is (34/36) * (33/35) * (32/34) * (31/33) * (30/32) * (29/31) * (28/30) * (27/29) = 0.821. So, the probability that a lot containing exactly two defective electronic baseball games manufactured by Tempco will still be shipped is approximately 0.821, or 82.1%, when expressed as a percentage.

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Driver A and Driver B will charge the same amount after 3 hours of service.

The subject of this question is a problem involving linear equations, a topic in mathematics. Specifically, it pertains to the intersection point of two linear functions, representing the costs charged by the two drivers over time. Let's denote the driving time as 't' (in hours) and the total cost as 'C' to solve it.

Driver A's cost function could be formulated as C = 200 + 80t, while Driver B's as C = 230 + 70t.

To find out when both drivers will charge the same amount, set these two equations equal to each other:

200 + 80t = 230 + 70t

This simplifies to 10t = 30 after subtracting 200 from both sides and 70t from both sides. Finally, dividing by 10 gives us t = 3.

Therefore, both drivers would charge the same amount after 3 hours of service.

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The solution to the inequality 3t < –15 is t < –5, attained by dividing both sides by 3.

The student's question involves solving an inequality, specifically 3t < –15. To solve for t, we need to isolate t on one side of the inequality. This can be done by dividing both sides of the inequality by 3. The solution to the inequality is:

Therefore, the correct answer to the inequality 3t < –15 is t < –5. The other options such as t > –5, t < –45, and t > –45 are incorrect.  

Division is not associative, as if you look at one of the operands to a nest of divisions, the result will vary either in proportion to it or inversely to it depending on whether it's to the right of an odd or even number of divisions. And the basic associative law changes the number of operations the rightmost operand is to the right of by 1.