Janelle and her family are traveling around Europe by train. Their trip will begin in Madrid, Spain, and will end in Rome, Italy. The first part of their train journey, from Madrid, Spain, to Barcelona, Spain, took 3 hours. Use this information to solve the problems below. Part A If the train went 390 miles in 3 hours, what was the speed of the train in miles per hour?

Answer:

AB = 20 ft

AC = 40 ft

Step-by-step explanation:

==>Given:

Rectangular window ABCD, where,

side AB = ½ of side AC

Perimeter = 120ft

==>Required:

Length of side AB and side AC

==>Solution:

Let AB = x

If x = ½ of AC

AC = 2x

Perimeter = 2(AB + AC)

Thus,

120 = 2(x+2x)

120 = 2(3x)

120 = 6x

Divide both sides by 6 to solve for x

120/6 = x

20 = x

AB = x = 20 ft

AC = 2x = 2(20) = 40ft

The polynomials that have (x+2) as a factor are [tex]\rm A(x) = x^3-3x^2-10x[/tex] and [tex]\rm C(x) = x^3-2x^2-13x-10[/tex] and this can be determined by using the factorization method.

Check all the options in order to determine the polynomials that have (x+2) as a factor.

A)

[tex]\rm A(x) = x^3-3x^2-10x[/tex]

Factorize the above equation.

[tex]\rm A(x) = x(x^2-3x-10)[/tex]

[tex]\rm A(x) = x(x^2-5x+2x-10)[/tex]

[tex]\rm A(x) = x(x(x-5)+2(x-5))[/tex]

[tex]\rm A(x) = (x)(x+2)(x-5)[/tex]

This polynomial has a factor (x+2). Therefore, this option is correct.

B)

[tex]\rm B(x) = x^3+5x^2+4x[/tex]

Factorize the above equation.

[tex]\rm B(x) = x(x^2+5x+4)[/tex]

[tex]\rm B(x) = x(x^2+4x+x+4)[/tex]

[tex]\rm B(x) = x(x(x+4)+1(x+4))[/tex]

[tex]\rm B(x) = (x)(x+1)(x+4)[/tex]

Therefore, this option is incorrect.

C)

[tex]\rm C(x) = x^3-2x^2-13x-10[/tex]

Factorize the above equation.  

[tex]\rm C(x) = x^3+2x^2-4x^2-8x-5x-10[/tex]

[tex]\rm C(x) = x^2(x+2)-4x(x+2)-5(x+2)[/tex]

[tex]\rm C(x) = (x^2-4x-5)(x+2)[/tex]

This polynomial has a factor (x+2). Therefore, this option is correct.

D)

[tex]\rm D(x) = x^3-6x^2+11x-6[/tex]

Factorize the above equation.  

[tex]\rm D(x) = x^3+2x^2-8x^2-16x+27x+54-60[/tex]

In the above polynomial (x+2) is not the factor. Therefore, this option is incorrect.

For more information, refer to the link given below:

https://brainly.com/question/6810544

Answer:

Step-by-step explanation:

Given the expression [tex]log_81000 = log_210[/tex], to prove this expression is true using the properties of logarithm, we will follow the following steps.

Starting from the Left Hand Side:

Answer:

It is a 9/10 chance of having at least one boy. The probability is also high enough for the couple to be very confident in having at least one boy in 9 children.

Step-by-step explanation:

I listed all of the possible combinations below

GGGGGGGGG           BGGGGGGGG

BBGGGGGGG           BBBGGGGGG

BBBBGGGGG           BBBBBGGGG

BBBBBBGGG            BBBBBBBGG

BBBBBBBBG             BBBBBBBBB

Total number of combinations with at least one boy is 9/10

This is a very high percentage, which means the couple is very likely to have at least one boy.

Answer:

9π or 28.3 units²

Step-by-step explanation:

A = πr²

A = π(3)²

A = 9π

or

A= 28.3 units²

Hope this helps. :)

Answer:

B) It is irrational and equal to [tex] = 4\sqrt{2} [/tex]

Step-by-step explanation:

The expression, [tex] \sqrt{18} + \sqrt{2} [/tex] , is an irrational expression because it contains two irrational numbers, [tex] \sqrt{18} [/tex] and [tex] \sqrt{2} [/tex] . Both number are not perfect square. there is no whole number that would be squared that will give you 18 nor 2.

The expression can be equals the following:

[tex] \sqrt{18} + \sqrt{2} [/tex]

[tex] = \sqrt{9*2} + \sqrt{2} [/tex]

[tex] = \sqrt{9}*\sqrt{2} + \sqrt{2} [/tex]

[tex] = 3\sqrt{2} + \sqrt{2} [/tex]

[tex] = 4\sqrt{2} [/tex]

Answer:

4 root 2

Step-by-step explanation:

Step-by-step explanation:

Net $103.92 [$25.98 ÷ 20%]

List. $129.90 [ $103.92 + $25.98]

Answer:

Step-by-step explanation:

22x + 1 = 8

Send 1 to the right side of the equation

22x = 8 - 1

22x = 7

Divide both sides by 22

x = 7/22

Hope this helps you

Answer:

B.

Step-by-step explanation:

The double cone is a cone on top of another cone. The bottom cone has the circular base on the bottom and the tip on top. The upper cone is upside down, and the two tips touch. Since the vertical plane goes through the tips of both cones, the cross section must have a shape that  gets to a point at the middle of the height.

Answer: B. One triangle with the tip on top and an inverted triangle above it with the tips touching.

Answer:

B.

Step-by-step explanation:

answer: B. one triangle tip on top and invert above it with the top touching

Answer:

The following combination describes a regression line that is a good fit for the data

a. Larger R-sq and small Se

Step-by-step explanation:

In regression analysis, we measure the goodness of fit in terms of two parameters.

1. R² ( R-squared or also called the coefficient of determination)

2. SE ( Standard Error)

1. R-squared

The R-squared indicates the relative measure of the percentage of the variance with respect to the dependent variable.

R-squared is measured in percentage so it doesn't have any unit.

The greater the R-squared percentage, the better is the goodness of fit.

2. Standard Error

The SE basically indicates that on average how far the data points are from the regression line.

The unit of the standard error is the same as the dependent variable.

The lower the SE, the better is the goodness of fit.

Therefore, the correct option is (a)

a. Larger R-sq and small Se

Answer:

7/8

Step-by-step explanation:

The numbers that are not 3 are 1, 2, 4, 5, 6, 7, and 8.

7 out of 8 numbers.

P(not 3) = 7/8

Answer:

7/8

Step-by-step explanation:

There are a total of 8 cards, and one of the cards is 3.

Their cards that are not 3 are 1,2,4,5,6,7,8. Therefore, there is a total of 7 cards that are not 3.

Now, let’s find the probability of drawing a card that is not 3.

P(not 3)= numbers that are not 3 / total numbers

There are 7 numbers that are not 3 and 8 total number cards.

P(not 3)= 7/8

Answer:

The equation that shows the profit: P = 2x + 3y

Step-by-step explanation:

The number of sneaker = x

The number of sandals = y

Cost of sneaker = 8 dollars.

Cost of sandals = 14 dollars.

Selling price of sneaker = $10

Selling price of sandals = $17

Total revenue = $10x + $17y

Total cost  = $8x + $14y

Profit (P)  =  Total revenue  - Total cost.

Profit = ($10x + $17y) – ($8x + $14y)

P = 10x +17y – 8x – 14y

P = 2x + 3y

Answer:

Step-by-step explanation:

Factors of 12

2, 3 , 6 , 4, 1, 12

Answer:

Step-by-step explanation:

Given the encoded message defined by the function f(x) = x³-1,  the inverse function that the decoder would need when the message is received can be expressed as thus:

let the inverse of the function be represented as y such that y = x³-1.

Making x the subject of the formula from the equation above;

x³ = y+1

Taking the cube root of both sides:

∛x³ = ∛(y+1)

x = ∛(y+1)

replacing y with x:

y = ∛(x+1)

f⁻¹(x) = ∛(x+1)

The encoded message is the inverse function ∛(x+1)

Answer:

Where is the table because I dont see it up here?

Answer:

D.

Step-by-step explanation:

The function is an absolute value. That just means that all the y-values (in this case) will be positive, but there is nothing that limits the x-values. So, D. {x | x = all real numbers}.

Hope this helps!

Step-by-step explanation:

[tex] \frac{2}{ \sqrt{9} } [/tex]

[tex] \frac{2 \times \sqrt{9} }{ \sqrt{9} \times \sqrt{9} } [/tex]

[tex] \frac{2 \sqrt{9} }{9} [/tex]

Answer:

[tex]\frac{2\sqrt{9} }{9}[/tex]

Step-by-step explanation:

[tex]\frac{2}{\sqrt{9} } \\[/tex]

[tex]\frac{2}{\sqrt{9} } * \frac{\sqrt{9} }{\sqrt{9} }[/tex]

[tex]\frac{\sqrt{9} }{\sqrt{9} }[/tex]  is equal to 1, so it doesn't change the value, just helps us simplify.

[tex]\frac{2\sqrt{9} }{9}[/tex]

There are no common factors between 2 and root 9, so we are done

Answer:

B

Step-by-step explanation:

Answer:

Measure of angle 2 = 82°

Step-by-step explanation:

m∠1 = (10 x + 8)°

m∠3 = (12 x - 10)°

2 lines are said to intersect to form 4 angles. And the labelling of the angles was done starting from top left, clockwise: the angles are 1, 2, 3, 4.

Find attached the diagram obtained from the given information.

Vertical angles are angles opposite each other when two lines intersect. As such, they are equal to each other.

Considering our diagram

m∠1 = m∠3

m∠2 = m∠4

Sum of all four angles firmed = 360° (sum of angles at a point)

m∠1 +m∠2 + m∠3 + m∠4 = 360°

m∠1 = m∠3

(10 x + 8)°= (12 x - 10)°

10x-12x = -10-8

-2x = -18

x= 9°

Also m∠2 = m∠4, let each equal to y

(10 x + 8)°+ y + (12 x - 10)° + y = 360

10x + 12x - 10 +8 +2y = 360

Insert value of x

22(9) -2 + 2y = 360

2y = 360-196

2y = 164

y = 82°

m∠2 = m∠4 = y = 82°

Measure of angle 2 = 82°

Answer:

2 = 82°

Step-by-step explanation:

Answer:

E = { x l x is a perfect square <36}

And we can rewrite it taking in count the list of all the perfect squares less than 36 and we have:

1= 1*1

4= 2*2

9 = 3*3

16 =4*4

25= 5*5

And we can rewrite the set on this way:

E= {1,4,9,16,25}

Step-by-step explanation:

For this problem we have the following set:

E = { x l x is a perfect square <36}

And we can rewrite it taking in count the list of all the perfect squares less than 36 and we have:

1= 1*1

4= 2*2

9 = 3*3

16 =4*4

25= 5*5

And we can rewrite the set on this way:

E= {1,4,9,16,25}

Answer:

-5, -3, -1 , 1 , 3

Step-by-step explanation:

Answer:

2009.6

Step-by-step explanation:

As we know, volume of a right cylinder is πr²h.

here, diameter is mentioned, which gives that the radius is half of the diameter.

r= 1/2*16=8 feet

height= 10 feet

π=3.14

volume= 3.14*8²*10

          = 3.14*64*10

            =3.14*640

             = 2009.6

so, that much water is needed to fill the tank

Answer:

2,010.6192982

Step-by-step explanation:

Answer:

Function

Step-by-step explanation:

A function is a relation where each x-value has only one y-value. In this problem, all the x-values have a y-value of 3. It is a function because even though they all share the same y-value, they don't have more than one y-value. It would be a relation but not a function if one x-value had two y-values.

Hope this helps. :)

Step-by-step explanation:

O D. F(X) = 3W-3 the answer is D

The function that represents the situation is F(x) = -x² - 3.

The correct option is A.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph. It's a common type of problem in algebra, specifically the modification of algebraic equations.

here, we have,

Let the functions f(x) and g(x) be two real functions.

And g (x) = f (x) + k, where k is real numbers.

The function can be sketched by shifting f (x), k units vertically.

The value of k can find the direction of shift:

if k > 0, the base graph shifts k units up, and

if k < 0, the base graph shifts k units down.

Given that ,

the parent function is g(x) = x².

To find the transformed function F(x):

The function's diagram is in the opposite direction.

That means the function is -x².

And the function is shifted 3 units down vertically.

From the definition the required function is,

F(x) = -x² - 3.

Therefore, F(x) = -x² - 3.

To learn more about the transformation on the graphs;

brainly.com/question/19040905

#SPJ7

complete question:

The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has been changed somewhat. Which of the following could be the equation of F(x)?

A.

F(x) = –x2 – 3

B.

F(x) = x2 – 3

C.

F(x) = –(x + 3)2

D.

F(x) = –(x – 3)2

where is the table that represents the quadratic function

Answer:

B. 35%

Step-by-step explanation:

P(winning $1.00)=40%

P(winning $5.00)=20%

P(winning $10.00)=5%

In a probability distribution, the sum of the probability must always be equal to 1.

Therefore:

P(winning $0.00)=1-(40%+20%+5%)

=1-(0.4+0.2+0.05)

=1-0.65

=0.35

The probability of winning nothing at all is 35%.

Answer:

Her temperature is 97.27ºF.

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]\mu = 98.2, \sigma = 0.62[/tex]

Z = -1.5. What is her​ temperature?

Her temperature is X when Z = -1.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.5 = \frac{X - 98.2}{0.62}[/tex]

[tex]X - 98.2 = -1.5*0.62[/tex]

[tex]X = 97.27[/tex]

Her temperature is 97.27ºF.

Answer:

The height of the ball is less than 17 feet for t > 2 seconds.

Step-by-step explanation:

The height of the ball after t seconds is given by the following equation:

[tex]h(t) = -16t^{2} + 81[/tex]

For which interval of the time is the height of the ball less than 17 feet

This is t for which:

[tex]h(t) < 17[/tex]

So

[tex]-16t^{2} + 81 < 17[/tex]

[tex]16t^{2} < -64[/tex]

Multiplying by -1

[tex]16t^{2} > 64[/tex]

[tex]t^{2} > \frac{64}{16}[/tex]

[tex]t^{2} > 4[/tex]

[tex]t > \sqrt{4}[/tex]

[tex]t > 2[/tex]

The height of the ball is less than 17 feet for t > 2 seconds.

━━━━━━━☆☆━━━━━━━

▹ Answer

#3. 1.89/100

▹ Step-by-Step Explanation

1.89 → hundreths place so..

1.89/100 is the correct answer

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

Step-by-step explanation:

[tex]x/a=1+x/b \\Make- x -subject- of- formula\\Multiply -both-sides-by ; ab\\bx =ab+ax\\bx-ax=ab\\x(b-a) =1ab\\\frac{x(b-a)}{(b-a)} = \frac{ab}{(b-a)} \\x = \frac{ab}{(b-a)}[/tex]

[tex]x/a=1+x/b\\Make ; b -subject-of-formula\\\frac{x}{a} -1=\frac{x}{b} \\Multiply-both-sides-by ; b\\\\b(\frac{x}{a} -1) = x\\\frac{b(\frac{x}{a} -1)}{(\frac{x}{a} -1)} = \frac{x}{(\frac{x}{a} -1)} \\\\b = \frac{x}{(\frac{x}{a} -1) }[/tex]

Step-by-step explanation:

x÷a = 1 + x÷b

To make x subject of the formula

x÷a = 1 + x÷b

x/a - x/b = 1

(xb - xa)/ab = 1

xb - xa = ab

x(b - a) = ab

x = ab/(b-a)

To make b subject of the formula

x÷a = 1 + x÷b

x/a - 1 = x/b

(x - a)/a = x/b

b(x-a) = ax

b = ax/(x-a)