The measure of an angle is 9°. what is the measure of a complementary angle?

Final answer:

The simplified expression is 7.992 × 10³.

Explanation:

To simplify the expression 111,000 × 0.072 using scientific notation, follow these steps:

The expression simplified in scientific notation is 7.992 × 10³.

The lowest grade is 48.

The substitution method is the algebraic method to solve simultaneous linear equations. In this method, the value of one variable from one equation is substituted in the other equation.

Let the lowest grade be x and highest grade be y.

According to the given question.

[tex]y = 42 + x[/tex]

Also,

[tex]x + y= 138[/tex]

For finding the points of lowest grade and highest grade substitute

y = 42 + x in x + y = 38.

[tex]x + ( 42 + x ) = 138[/tex]

⇒ [tex]2x + 42 = 138[/tex]

⇒ [tex]x + 21 = 69[/tex]

⇒[tex]x = 69 -21[/tex]

⇒[tex]x = 48[/tex]

Therefore,

[tex]y = 48 + 42 =90[/tex]

Hence, the lowest grade is 48.

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The average speed in miles per hour for the entire trip of Emily is 38 miles per hour.

The correct answer is Option D.

Given data:

To find Emily's average speed during her entire trip, calculate the total time she spent traveling on both the highway and local roads.

To determine the speed on the highway.

On the highway, she traveled 30 miles faster than on the local roads, and her speed on the local roads is 20 miles per hour.

Speed on the highway = Speed on the local roads + 30 miles per hour

Speed on the highway = 20 miles per hour + 30 miles per hour

Speed on the highway = 50 miles per hour

Now, calculate the time spent on each segment of the trip:

Time spent on the highway = Distance on the highway / Speed on the highway

Time spent on the highway = 60 miles / 50 miles per hour

Time spent on the highway = 1.2 hours

Time spent on local roads = Distance on local roads / Speed on local roads

Time spent on local roads = 16 miles / 20 miles per hour

Time spent on local roads = 0.8 hours

Now, add the times for both segments to get the total time:

Total time = Time spent on the highway + Time spent on local roads

Total time = 1.2 hours + 0.8 hours

Total time = 2 hours

So, the average speed is determined as:

Average speed = Total distance / Total time

Average speed = (60 miles + 16 miles) / 2 hours

Average speed = 76 miles / 2 hours

Average speed = 38 miles per hour

Hence, Emily's average speed during her entire trip was 38 miles per hour.

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Answer:

  16.9

Step-by-step explanation:

The distance formula can be used to find the lengths of individual segments. It tells you ...

 d = √((Δx)² +(Δy)²)

where Δx and Δy are the differences between x- and y-coordinates of the segment end points.

Since the value is squared, the sign of the difference doesn't matter. It can be easier to write it as always positive, so in some cases it may be Δx = x₂-x₁ and in other cases it might be Δx = x₁-x₂, for example.

If the segments are labeled A, B, C, D, E in order, the distances are ...

 AB = √(5²+1²) = √26 ≈ 5.099

 BC = √(1²+3²) = √10 ≈ 3.162

 CD = Δx = 3

 DE = √(3²+2²) = √13 ≈ 3.606

 EA = Δy = 2

Then the perimeter is ...

 P = AB +BC +CD +DE +EA = 5.099 +3.162 +3 +3.606 +2 = 16.867

 P ≈ 16.9

To find the probability of choosing a red marble, then a green marble without replacement, multiply the probabilities of the individual events which is  7/76.

To find the probability that Alicia will choose red, then green marbles, we need to calculate the probability of drawing a red marble and then a green marble without replacement.

Given that there are 8 blue marbles, 5 green marbles, and 7 red marbles in the bag, the probability of drawing a red marble first is 7/20.

After removing the red marble, there are 19 marbles left in the bag, including 5 green marbles. Therefore, the probability of drawing a green marble second is 5/19.

To find the combined probability, we multiply the probabilities of the individual events:

P(Red, then Green) = P(Red) * P(Green | Red) = (7/20) * (5/19) = 35/380 = 7/76.

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we know that

the distance's formula between two points is equal to

[tex]d=\left|xB-xA\right|[/tex]

substitute

[tex]d=\left|1-(-5)\right|[/tex]

[tex]d=6\ units[/tex]

therefore

the answer is

[tex]6\ units[/tex]

The distance between two point [tex]A{\text{ and }}B[/tex] is [tex]\boxed{{\mathbf{6 units}}}[/tex].

Further explanation:  

The distance between two points is the modulus of difference of the given two points.

The distance between two points can be found by the distance formula as,

[tex]\left| {B - A} \right|[/tex]  

Here, [tex]A{\text{ and }}B[/tex] are the points on the number line.

The distance cannot be negative therefore modulus is applied in the formula.

Step by step explanation:

Step 1:

First we determine the points from the given number line.

It can be observed from the given number line that there are two points one is on the left side of the origin and the second is right side of the origin.

The point [tex]A[/tex] is [tex]- 5[/tex] and the point [tex]B[/tex] is 1.

Step 2:

Now use the distance formula to obtain the distance between the two points  [tex]A{\text{ and }}B[/tex].

Here, the value of A is [tex]-5[/tex] and B is 1.

Substitute the value of [tex]A{\text{ and }}B[/tex] to obtain the distance as,

[tex]\begin{aligned}d&= \left| {B - A} \right| \\&= \left| {1 - \left( { - 5} \right)} \right|\\&= 6{\text{ units}}\\\end{aligned}[/tex]  

Therefore, the distance between two point [tex]A{\text{ and }}B[/tex] is [tex]6{\text{ units}}[/tex].

Learn more:  

Answer details:

Grade: Junior school

Subject: Mathematics

Chapter: Number line

Keywords: Integers, distance, point, number line, units, measurement, origin, negative numbers, positive numbers, right side, left side, difference.

Final answer:

[tex]\[ h(2) = 55, \quad h(-1) = 3 \][/tex]

Explanation:

To evaluate [tex]\(h(x)\)[/tex] at the given values using synthetic division, we start with the coefficients of the polynomial [tex]\(x^6 - 4x^4 + 5x^2 + 1\).[/tex]

1. For [tex]\(h(2)\):[/tex]

  - Write down the coefficients: 1, 0, -4, 0, 5, 0, 1.

  - Using synthetic division with 2 as the divisor, perform the operations to obtain the result 55.

2. For [tex]\(h(-1)\):[/tex]

  - Repeat the process with -1 as the divisor, using the coefficients: 1, 0, -4, 0, 5, 0, 1.

  - After the calculations, the result is 3.

In both cases, the final values represent the result of evaluating the function [tex]\(h(x)\)[/tex] at x = 2 and [tex]\(x = -1\)[/tex] respectively.

Two step algebraic equations are relatively quick and easy -- after all, they should only take two steps. To solve a two step algebraic equation, all you have to do is isolate the variable by using either addition, subtraction, multiplication, or division. If you want to know how to solve two step algebraic equations in a variety of ways, just follow these steps.

1. Write the problem. The first step to solving a two step algebraic equation is just to write the problem so you can start to visualize the solution. Let's say we're working with the following problem: -4x + 7 = 15.

2. Decide whether to use addition or subtraction to isolate the variable term. The next step is to find a way to keep "-4x" on one side and to keep the constants (whole numbers) on the other side. To do this, you'll have to do the "Additive Inverse," finding the opposite of +7, which is -7. Subtract 7 from both sides of the equation so that the "+7" on the same side as the variable term is canceled out. Just write "-7" below the 7 on one side and below the 15 on the other so the equation remains balanced. Remember the Golden Rule of Algebra. Whatever you do to one side of an equation must be done to the other side to maintain the balance. That is why 7 is subtracted from the 15 as well. We only need to subtract 7 once per side, which is why the 7 is not subtracted from the -4x as well.

To solve two-variable equations, identify unknowns, find related equations, substitute known values, and solve for one variable before finding the other. Use substitution or elimination methods in case of a system of equations.

To solve equations with 2 variables, follow these steps:

Regarding a 2x2 system (two equations with two unknowns), you can either use substitution—solving one equation for one variable and then substituting into the other—or elimination—adding or subtracting equations to cancel one of the variables. If an equation has more than one unknown, additional equations are necessary to solve the system.

For instance, consider a pair of equations:
1) x + y = 10
2) x - y = 6

By adding these two equations, y is eliminated, and we can solve for x quickly. Then, we can substitute the value of x into either equation to solve for y.

put 7.6*10^-1 into the equation to get:

10log(1/7.6*10^-4) = 31.19

Answer:

h(x), f(x) , g(x)

Step-by-step explanation:

[tex]f(x) = 2x^2 - 8x[/tex]

Axis of symmetry at [tex]x=\frac{-b}{2a}[/tex], a=2, b=-8

[tex]x=\frac{-b}{2a}[/tex]

[tex]x=\frac{-(-8)}{2(2)}=2[/tex]

[tex]g(x) = x^2 - 6x + 1[/tex], a= 1, b=-6

[tex]x=\frac{-b}{2a}[/tex]

[tex]x=\frac{-(-6)}{2(1)}=3[/tex]

[tex]h(x) = -2x^2[/tex], a=-2, b=0

[tex]x=\frac{-b}{2a}[/tex]

[tex]x=\frac{-(0)}{2(-2)}=0[/tex]

Now rank the function based on their axis of symmetry

h(x), f(x) , g(x)

Answer:

-6 :))))))))))))))))))

Step-by-step explanation:

By setting up the proportion [tex]\(\frac{15}{x} = \frac{x}{135}\)[/tex] and solving for [tex]\( x \)[/tex], we find that [tex]\( x = 45 \).[/tex]

To find the value of [tex]\( x \)[/tex] when the terms 15, [tex]\( x \)[/tex], and 135 are in proportion, we set up the proportion:

[tex]\[\frac{15}{x} = \frac{x}{135}\][/tex]

This represents the relationship where the first ratio is equal to the second ratio. Cross-multiplying, we get:

[tex]\[15 \times 135 = x \times x\][/tex]

[tex]\[2025 = x^2\][/tex]

Taking the square root of both sides, we find:

[tex]\[x = \sqrt{2025}\][/tex]

[tex]\[x = \pm 45\][/tex]

However, since 15,  x , and 135 are in proportion, the value of  x  must be positive. Therefore,  x = 45 .

The question probable maybe:

If the three terms 15, x and135 are in proportion then what is the value of x