(Irrational Numbers MC)
Approximate -17 √√60 to the nearest tenth.
O-9.3
-7.7
7.7
9.3
Question 6(Multiple Choice Worth 2 points)
(Multiplying and Dividing with Scientific Notation MC)

The solution of the equation is x=3 or x=-5.

Given that the equation is (x+2)²-2(x-+2)-15=0 and use u substitution method to solve.

Let's assume that the (x+2)=u.

The given equation is rewritten as u²-2u-15=0.

Factorize the quadratic equation by adding or subtracting two number that gives the sum of -2u and product 15u² as

u²-5u+3u-15=0

u(u-5)+3(u-5)=0

Taking out (u-5) as common and get

(u-5)(u+3)=0

Compare each equation with 0 and get

u-5=0 or u+3=0

u=5 or u=-3

Performing back substitution by substituting the values of u in x+2

when u=5 then x is

x+2=5

x=3

And when u=-3 then x is

x+2=-3

x=-5

Hence, the solutions of the (x+2)²-2(x-+2)-15=0 is x=3 and x=-5.

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Answer:X=-5 and X=3

Step-by-step explanation:

The distance from the sun to the other focus is 5.01 × 10⁹ m.

(a) The distance from the center of an ellipse to a focus is an where a is the semi major axis and e is the eccentricity. Thus, the separation of the foci ( in the case of Earth's orbit ) is;

2ae = 2(1.50 × 10¹¹)(0.0167) = 5.01 × 10⁹ m.

(b) To express this in terms of solar radii, we set up a ratio;

(5.01 × 10⁹)/(6.96 × 10⁸) = 7.2

Thus, we can conclude that the distance from the sun to the other focus is 5.01 × 10⁹ m.

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Complete question is;

The Sun's center is at one focus of Earth's orbit. How far from this focus is the other focus, (a) in meters and (b) in terms of the solar radius, 6.96 × 10⁸ m? The eccentricity is 0.0167, and the semimajor axis is 1.50 × 10¹¹ m.

Answer:

4(x+3)²+4

Step-by-step explanation:

4x²+24x+40=0

using the equation above

a:4 b:24 c:40

4(x+(24÷2x4))² + (40-(24²÷4x4))

4(x+3)²+(40-36)

4(x+3)²+4

Answer:

2.625

Step-by-step explanation:

258=2.625

Solution by Separating the Parts

258=2+58

We know that

58

is the same as

5÷8

Therefore:

258=2+(5÷8)

Then using

Long Division for 5 divided by 8

we have

=2+0.625=2.625

Rounded to a Max of 3 Decimal Places.

Solution by Converting to Improper Fraction

258=2+58

=21+58

=(21×88)+58

=168+58=218

We know that

218

is the same as

21÷8

Answer:

Your answer is D 2 and 82/100

Answer:15x3 /=divide 5 = 9

Step-by-step explanation:

because if you do 15x3 it is 45 then you divide it by 5 and get 9 as your answer!

The slope of the line containing the points A(-8,6) and B(11,2) is given as follows:

m = -0.2105.

The angle of the line is given as follows:

θ = -11.89º.

The two points on the line are given as follows:

A(-8,6) and B(11,2).

Given two points, the slope is obtained by the division of the change in y by the change in x, hence:

m = (2 - 6)/(11 + 8)

m = -0.2105.

The slope represents the tangent of the angle, hence the angle is the arc tangent of the slope, thus:

θ = arctan(-0.2105)

θ = -11.89º.

The problem asks for the slope and for the angle of the line containing points A and B.

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Answer:

I believe its 1,200 pounds.

Step-by-step explanation:

9 × 4 = 36 so youd multiply 300 by 4 as well. I'm not sure but I think this is correct.

Answer:

No, subtraction is NOT associative in rational numbers.

Step-by-step explanation:

Step-by-step explanation: We are asked to state whether subtraction is associative in rational numbers or not. To explain with an example. The subtraction is NOT associative in rational numbers.

To find the function f(x) whose derivative is f'(x) = 3 cos²x and satisfies f(0) = 2, we can integrate f'(x) with respect to x.

∫f'(x) dx = ∫3 cos²x dx

Using the trigonometric identity cos²x = (1 + cos2x)/2, we can rewrite the integral as:

∫f'(x) dx = ∫3 (1 + cos2x)/2 dx

Splitting the integral and integrating term by term, we get:

∫f'(x) dx = ∫(3/2) dx + ∫(3/2) cos2x dx

Integrating, we have:

f(x) = (3/2)x + (3/4)sin2x + C

where C is the constant of integration.

To determine the value of C and satisfy the initial condition f(0) = 2, we substitute x = 0 into the equation:

f(0) = (3/2)(0) + (3/4)sin(2 * 0) + C

2 = 0 + 0 + C

C = 2

Therefore, the function f(x) is given by:

f(x) = (3/2)x + (3/4)sin2x + 2

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it's true...........

Answer:

False

Step-by-step explanation:

Verified correct with test results.

The image of Point A, after a dilation which is centered at the origin with a scale factor of 2 is ( 4, 2 )

When a dilation is centered at the origin with a scale factor of 2, the coordinates of a point are multiplied by 2.

Given a point A(2,1) , the image of point A after a dilation centered at the origin with a scale factor of 2 is:

Point X :

= 2 x 2

= 4

Point Y:

= 1 x 2

= 2

So the image of point A after the dilation is the point A' with coordinates ( 4, 2 )

It's important to note that dilation either expands or contracts the figure and the center of dilation is the fixed point around which the expansion or contraction occurs.

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The trucks arrive 10 minutes after the first call. The first and the second truck travel for 5 miles and 8 miles respectively.

In a time difference of 3 minutes, two fire trucks are called.

The average speed of the first truck is 30 miles per hour.

The average speed of the second truck is 60 miles per hour.

The trucks totally travel for 12 miles and arrive at the same time.

Let d be the number of miles the first truck drove.

Let t be the number of minutes it took the first truck to travel.

Now, Convert 30 miles per hour to a half mile per minute and 60 miles per hour to a mile per minute as we are measuring time in minutes.

For the first truck:

d = 0.5t

The second truck traveled 12 - d miles if the first truck traveled d miles. In the event where the first truck traveled for t minutes and was called 3 minutes later, the second vehicle would have gone for t - 3 minutes.

For the second truck:

12 - d = t - 3

Therefore,

12 - 0.5t = t - 3

15 = 1.5t

t = 15 / 1.5

t = 10 minutes

The trucks arrive after 10 minutes after the first call.

Then,

d = 0.5t = 0.5(10) = 5 miles

And 12 - d = 12 - 5 = 8 miles.

Hence, the first truck traveled for 5 miles and the second truck traveled for 8 miles.

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The complete question is mentioned below:

A fire truck is called to a scene. Three minutes later, a second truck is called. The first truck averages only 30 mph, but the second averages 60 mph. The trucks travel a total of 12 miles and arrive at the same time. How long from the first call did the trucks take to arrive? How far did each travel? We must first remember to change miles per hour to miles per minute.

Answer: 0.31

Step-by-step explanation:

0.3158 is closer too 0.3100 than 0.3000 or 0.3

Rounding 0.3058 to the nearest hundredth gives us 0.31.

Given that a number we need to round it to the nearest hundredth,

To round 0.3058 to the nearest hundredth, we need to look at the digit in the thousandth place (the third decimal place).

Step 1: Look at the digit in the thousandth place. In this case, the digit is 5.

Step 2: Determine if the digit is 5 or greater. If the digit is 5 or greater, we round up. If the digit is less than 5, we round down.

Since the digit in the thousandth place is 5, we round up.

Step 3: Round up the number in the hundredth place. In this case, the number in the hundredth place is 0.

Rounding up 0 to the nearest hundredth gives us 1.

Therefore, rounding 0.3058 to the nearest hundredth gives us 0.31.

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The expression represents the number of coins Arthur is x + 80 cents.

The term expression in math refers a sentence with a minimum of two numbers or variables and at least one math operation.

Here we have given that Arthur has x pennies. His father gave him 6 dimes, and his mother gave him 4 nickels.

And we need to find expression represents the number of coins Arthur has now.

From the given question, here we have to convert the pennies, dimes and nickels into same unit before adding to get the expression for the number of coins Arthur will have in total.

AS we know that one penny = 1 cent, one dime = 10 cents, one nickel = 5 cents and

Therefore, x pennies = x cents

Then 6 dimes = 60cents

Then 4 nickels = 20 cents

Therefore, the Arthur's coins in total is written as,

=> (x + 60 + 40) cents

=> (x + 80) cents.

Therefore, the resulting expression is written as (x + 80) cents.

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Answer:

12 hours

Step-by-step explanation:

First, figure out her hourly rate

Next, divide 252 by the hourly rate to figure out how many hours he will have to work

Multiply the hourly rate by number of hours worked to check your answer

At a rate of $21 per hour, he has to work for 12 hours to make $252.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Ravi made $378 for 18 hours of work.

So, Ravi's unit rate or earnings per hour is $(378/18).

= $21.

Now, In one hour he makes $21.

Therefore, To make $252 he has to work (252/21) hours.

= 12 hours.

So, Ravi has to work for 12 hours to make $252.

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The answer is s=√225 in. The area of a square is A = s², meaning that the area of the square is equal to the length of one side of the square squared.

A four-sided polygon with all sides equal in length. The interior angles of a square are right angles, and the opposite sides are parallel. The four sides of a square meet at its four vertices.

In this case, s is the side length.

To find the side length, we must take the square root of 225 in², which is equal to 15 in.

Therefore, the side length of the square is s=√225 in.

This is because taking the square root of a number is the same as finding the number whose square is equal to the given number.

In this case, the number whose square is equal to 225 in² is 15 in.

Hence, the side length of the square is s=√225 in.

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The solution to the equation and to the nearest tenth is:

x = 4.3

x = 0.3

To solve for x in this equation, we will use the quadratic formula as the equation is the quadratic type. In this equation:

\(x = -b±\sqrt{b^{2} - 4ac} /2a\\x = 9±\sqrt{-9^{2} - 4(2*2} /2*2\\x = 9±\sqrt{81 - 16}/4\\\)

So, x = 9 ± √65/4

x = 9 + 8/4

x = 17/4

x = 4.26 and approximately, 4.3 to the nearest tenth.

Also,

x =  9 - 8/4

x = 1/4

x = 0.25

x = 0.3 So, the two values of x to the nearest tenth are 4.3 and 0.3

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9 because 12 + is greater than/equal to 9+3

There are 123 different possibilities. Therefore, we can derive from the multiplication principle that there are 13(123) ways.

Probability: The branch of mathematics known as probability deals with numerical expressions of the probability that an event will occur, or the probability that a statement will be true.

The probability of an event is a number between 0 and 1, with approximately 0 meaning improbability and 1 meaning certainty.

The probability of an event occurring increases with its probability. A simple example is tossing a fair (fair) coin.

Both outcomes (heads and tails) have equal probability, the coin is fair, heads are more likely than tails, there are no other possible outcomes, and either outcome has half the probability.

According to our question:

Let n be the maximum number of subsets of 5 elements that can be chosen from the first 14 natural numbers,

where at least 2 of the 5 digits are consecutive.

We created a block of two consecutive numbers ((1,2), (2,3), (13,14), etc.).

Now you can select this block in 13 different ways. You have to choose 3 numbers from the remaining 12 numbers.

So, from the multiplication principle, we know that we have 13 × (123).

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Answer: B

Step-by-step explanation:

B) 180−m180-m180−m

The equation that best represents this relationship is y = 1/35x. The best equation that represents the relationship between the number of miles traveled x, and the number of gallons of gas used y is y = 1/35x.

This is because the table shows that as the number of miles traveled increases, the number of gallons of gas used also increases, but not at a constant rate. The ratio of miles traveled to gallons used is not constant, meaning that the relationship is not directly proportional (y = kx). Instead, the data suggests that there is a constant "efficiency" rate of 1/35 gallons per mile.  

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Answer:

8

Step-by-step explanation:

x=-4 perfectly suits x<=-1 since -4<=-1

Hence, when calculating g(-4), you need to apply the expression -x+4

Hence:

g(-4)=

-x+4=

-(-4)+4= ==>   plug in -4 for x

4 + 4 = 8   ==> Negating a negative number is equaled to taking the

                       positive number.

Answer: many solutions

Ok done. Thank to me :>

A highway superintendent states that four bridges into a city are used in the ratio 2:3:3:4 during the morning rush hour.

A highway study of an SRS of 6000 cars indicates that main answer in 40 words and explanation in 140 words.According to the question, there are four bridges into the city, and they are used in the ratio of 2:3:3:4.

That means that for every 2 cars coming from the first bridge, there are 3 cars coming from the second and the third bridges and 4 cars coming from the fourth bridge.According to the SRS of 6000 cars, the total number of cars from the first bridge is: 2/12 * 6000 = 1000

The total number of cars from the second bridge is: 3/12 * 6000 = 1500The total number of cars from the third bridge is: 3/12 * 6000 = 1500The total number of cars from the fourth bridge is: 4/12 * 6000 = 2000

Therefore, the number of cars coming from the first, second, third, and fourth bridges are 1000, 1500, 1500, and 2000, respectively, during the morning rush hour.

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Step-by-step explanation:

To find the equivalent ratio for 13/20 in terms of m/n, we can set up the proportion:

13/20 = m/n

To solve for m/n, we can cross-multiply:

13n = 20m

Then, we can divide both sides by 13 to isolate m/n:

m/n = 20/13

So, the equivalent ratio for 13/20 in terms of m/n is 20/13.

Step-by-step explanation:

so, to find the % of successful free throws out of the total number of free throws, we only need to do the division as indicated by the ratio :

13/20 = 0.65

so, 0.65 parts of of the whole 1 were successful.

as % is expressed in parts of 100, we need to multiply this statement by 100 :

65 parts of the whole 100 were successful.

so, 65% were successful.

Answer:

No, No, Yes, Yes.

Step-by-step explanation: 2 times -3 = -6. -6 times -4 = 24.

So, with that said, the first one multiples out to -24.

The second multiplies out to again -24.

12 times 2 = 24.

A negative and a negative multiply to become a positive, so -4 times -6 = 24.

Answer:

24 i belive

so you should choose

Step-by-step explanation:

(6) (-4) = no

(-3) (8) =no

(12) (2) =yes

(-4) (-6)= yes