Write as an algebraic expression and then simplify if possible The distance traveled by a train in three hours with a constant speed of r miles per hour.

For this case we have that by definition of trigonometric relations of rectangular triangles, that the cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle. Then, according to the figure we have:

[tex]Cos (A) = \frac {3} {4.24} = 0.707547169811\\Cos (B) = \frac {3} {4.24} = 0.707547169811[/tex]

So:

[tex]\frac {Cos (A)} {Cos (B)} = \frac {0,707547169811} {0,707547169811} = 1[/tex]

Answer:

[tex]\frac {Cos (A)} {Cos (B)} = 1[/tex]

Hi there! My name is Zalgo and I am here to help you out today. When you multiply (x2-5x) (2x+x-3), you will get 3x^3-18x^2+15x.

I hope that this info helps! :)

"Stay Brainly and stay proud!" - Zalgo

(By the way, can you mark me Brainliest? I'd greatly appreciate it! Thank you! XP)

Answer:

The inequality [tex]5x-3y >15[/tex] have a dashed line

Step-by-step explanation:

we have

[tex]5x-3y >15[/tex]

The solution of this inequality is the shaded area below the dashed line

The equation of the dashed line is [tex]5x-3y=15[/tex]

The slope of the dashed line is positive

The y-intercept of the dashed line is -5 ---> point (0,-5)

The x-intercept of the dashed line is x=3 ----> point (3,0)

Graph the solution

see the attached figure

Answer:

[tex]\frac{81}{3}[/tex]

Step-by-step explanation:

Given the direct variation equation

y = kx ← k is the constant of proportionality

then for

y = [tex]\frac{81}{3}[/tex] x

k = [tex]\frac{81}{3}[/tex]

Answer:

b. 128°

Step-by-step explanation:

arc LJ = 2 (26) = 52°

arc KL = 180° (half circle)

so

arc JK = 360° - (arc LJ + arc KL)

arc JK = 360° - 232°

arc JK = 128°

Answer

b. 128°

Despite different rental costs, the rental costs for company A and company B will be the same, after 50 miles.

To solve this, we need to set up an equation based on their pricing structures and solve for the number of miles.

Let m represent the number of miles driven. The cost for company A would be $40 + $0.30m, and the cost for company B would be $20 + $0.70m.

We set these two expressions equal to each other to find the breakeven point:

$40 + $0.30m = $20 + $0.70m

Subtracting $0.30m from both sides gives us:

$40 = $20 + $0.40m

Next, we subtract $20 from both sides:

$20 = $0.40m

Dividing both sides by $0.40, we get:

m = 50

Answer:

5.87

Step-by-step explanation:

29.35/x=100/20

(29.35/x)*x=(100/20)*x       - we multiply both sides of the equation by x

29.35=5*x       - we divide both sides of the equation by (5) to get x

29.35/5=x

5.87=x

x=5.87

Answer:

$5.87

Step-by-step explanation:

20% = 20/100 = 1/5

hence 20% tip,

= 20% of the total cost

= 1/5 x $29.35

= $5.87

Answer:

She used an incorrect formula. The formula should be the change in y-values with respect to the change in the x-values

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex](x2,y2)=(-7,4)[/tex]

[tex](x1,y1)=(2,-3)[/tex]

Substitute the values

[tex]m=\frac{4+3}{-7-2}[/tex]

[tex]m=\frac{7}{-9}[/tex]

[tex]m=-\frac{7}{9}[/tex]

therefore

She used an incorrect formula. The formula should be the change in y-values with respect to the change in the x-values

Answer:

C

Step-by-step explanation:

Answer:

-39/8y

Step-by-step explanation:

-4/y(2)+(-7/8y)

Answer:

20,001,030,001

For this case we must express the following phrase in numerical form:

"twenty billion, one million thirty thousand and one as a number"

twenty billion is equivalent to [tex]20,000,000,000[/tex]

one million equals [tex]1,000,000[/tex]

thirty thousand equals [tex]30,000[/tex]

one equals 1

Then, we can express:

[tex]20,001,030,001[/tex]

Answer:

20,001,030,001

Answer:

The scale factor is 2

Step-by-step explanation:

AB -->A'B' : enlargement , scale factor is greater than 1

From QA to QA' : 1.25 to 2.5 so the ratio is 1:2

The scale factor is 2

Answer:

2/3

Step-by-step explanation:

-5/12 ÷ -5/8

Copy dot flip

-5/12 * -8/5

The 5's cancel

-8/-12

Divide the top and bottom by -4

2/3

Answer:

2/3

Step-by-step explanation:

-5/12 divided by -5/8

To solve this you need to change the division sign to a multiplication sign.Then find the reciprocal of the second fraction. It should look like this.

-5/12*-8/5

Then you multiply straight across

5*8=40

5*12=60

40/60

This can be simplified to 2/3

the slope intercept form is y=mx+b

since the line intersects at (0,3) b= 3

since the slope is 0 m= 0

so the equation would be y=0x+3 or y=3

Answer:

y=3

Step-by-step explanation:

Hi there!

We are given that a line contains the point (0, 3), and has the slope 0

We want to find the equation of this line, in slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

The y intercept is the point that intersects the y axis; at this point, the value of x is 0

The point (0, 3) we were given is actually the y intercept of this line (the value of x at this point is 0!)

We can therefore, plug it into the formula.

We can just plug in the y value as b into the equation.

Here's the equation so far:

y=mx+3

Now we need to find m.

As the the slope of the line is 0, it means that if we plug 0 in as m, then we can find the equation of the line.

So substitute 0 as m

y=0x+3

This can also be written as y=3

Hope this helps!

See more on finding the equation of the line from a slope and a point here (n.b. the answer is written in a different format, but the logic is still the same): https://brainly.com/question/14358313

Answer:

a negative multiplied or divided by negative is positive. if its adding or subtracting it takes sign of the bigger number. and it dividing so the number is not going to get bigger. so its positive 7

[tex]\text{Hey there!}[/tex]

[tex]\text{Since, both of your terms (-42 and -6) are negative, we know that your answer}[/tex] [tex]\text{will most likely be a POSITIVE number}[/tex]

[tex]\text{Because. negative \& negative makes positive!}[/tex]

[tex]\text{-42}\div\text{(-6)}=\dfrac{-42}{(-6)}=42\div6=7[/tex]

[tex]\boxed{\boxed{\text{Answer: C. 7}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

S and T

Step-by-step explanation:

I put R&T, that's wrong. It's S and T.

The pair of spheres are congruent is S and T.

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

As, per the given figure,

Figure R having a radius 3.

Figure S is having a radius 4

Figure T is having radius 4

So, by considering the property of congruence figure S and T will be congruent spheres.

Learn more about congruence here:

brainly.com/question/7888063

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Answer:

(2y-cubert(15)x)(4y^2+2cubert(15)xy+cubert(15^2)x^2)

Step-by-step explanation:

It almost look like someone possibly meant to write a perfect cube there instead of 51... but we can still factorize this... it just won't be as pretty.

The formula for factoring a difference of cubes is

u^3-v^3

=(u-v)(u^2+uv+v^2).

So the answer here is

(2y)^3-(cubert(15)x)^3

=(2y-cubert(15)x)(4y^2+2cubert(15)xy+cubert(15^2)x^2)

cubert means cube root of

The thing I'm cube rooting is the thing in ( ) next to the cubert.

Make sure you actually write the symbol for cube root instead of my notation.

Answer: Its (5,-2)

Step-by-step explanation: When you reflect across the x-axis the y value changes.

Answer:

Option D. (0, 2)

Step-by-step explanation:

we have

[tex]f(x)=2(3)^{x}[/tex]

This is a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

a is the initial value

b is the base

r is the rate of change

In this problem

a=2 ---> the initial value ( value of the function when the value of x is equal to zero)

b=3

b=1+r ----> 3=1+r ----> r=2 ---> r=200%

Remember that

The initial value of the function is equal to the y-intercept

The initial value is the point (0,2)

therefore

The y-intercept is the point (0,2)

well, this is an OCTAgon, OCTA = 8.

[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\ \cline{1-1} a=30\\ p=\stackrel{8\times 12}{96} \end{cases}\implies A=\cfrac{1}{2}(30)(96)\implies A=1440[/tex]

Answer:

1 - x - 2 + 2x = 10x - 25 - x

Step-by-step explanation:

We have the expression: 1 - (x+2) + 2x = 5(2x - 5) - x

Applying the distributive property we get:

1 - x - 2 + 2x = 10x - 25 - x

So, the following equation is the result of that step: 1 - x - 2 + 2x = 10x - 25 - x

Answer:

The equation is:

[tex]1-x-2 + 2x = 10x-25-x[/tex]

Step-by-step explanation:

The distributive property says that

[tex]c(a+b) = ac + bc[/tex]

In this case we have the following equation

[tex]1-(x+2) + 2x = 5(2x-5)-x[/tex]

Then apply the distributive property as shown below

[tex]1-1*x-1*2 + 2x = 5*2x-5*5-x[/tex]

Now simplify the expression

[tex]1-x-2 + 2x = 10x-25-x[/tex]

So the equation that results after applying the distributive property is:

[tex]1-x-2 + 2x = 10x-25-x[/tex]

Answer:

k = 4.

Step-by-step explanation:

An arithmetic sequence has a common difference.

So for this to be arithmetic:

k + 3 - (k - 1) = 3k - 1 - (k + 3)

k + 3 - k + 1 = 3k - 1 - k - 3

3 + 1 = 2k - 4

4 + 4 = 2k

k = 4.

The sequence is  3, 7, 11.

Final answer:

The system of equations y = 1/4x + 2 and 3y = -3/4x - 6 represents two distinct parallel lines with the same slope but different y-intercepts, thus the system has no solution.

Explanation:

To find the solution to the system of equations y = 1/4x + 2 and 3y = -3/4x - 6, we need to check if they have a common solution, indicating the point where they intersect, or if they are parallel, which would mean they have no solution, or if they are the same line, which would translate into infinitely many solutions.

First, simplify the second equation by dividing every term by 3, which gives y = -1/4x - 2. Now we can see that the coefficients of x and the constant terms in both equations are multiples of one another but with opposite signs, which means the lines are parallel and have the same slope but different y-intercepts. Therefore, these two equations represent two distinct parallel lines that never intersect.

The correct answer is that there is no solution to this system of equations because the lines are parallel and will never meet.

Answer:

supplementary

Step-by-step explanation:

Angles 2 and 3 form a straight line.  Straight lines are supplementary

Answer:

Supplementary

Step-by-step explanation:

1 and 2 are vertical along with 3 and 4 they can't be complementary non of them form right angles but supplementary is a straight line making 180 degrees.

Answer:

C. f(x)=3(1/2)^x

Step-by-step explanation:

standard form of a function is f(x)=ab^x

a should be 3, or the y value where the x value is 0

the b value is 1/2 because that's the rate of change

x = original price, or 100%

if we take off 25% from 100% what's left is 75%, that's the discounted price.

let's then take 10% of that.

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{75\% of "x"}}{\left( \cfrac{75}{100} \right)x\implies 0.75x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{10\% of 0.75x}}{\left( \cfrac{10}{100} \right)0.75x\implies 0.075x}~\hfill \stackrel{\textit{total percent savings}}{0.75x-0.075x\implies 0.675x} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{changing that to percent format}}{0.675\cdot 100\implies 67.5\%}[/tex]

If

[tex]S=1+2+\cdots+(n-1)+n[/tex]

then it's also true that

[tex]S=n+(n-1)+\cdots+2+1[/tex]

so that

[tex]2S=(1+n)+(2+(n-1))+\cdots+((n-1)+2)+(n+1)=n(n+1)\implies S=\dfrac{n(n+1)}2[/tex]

For any integer [tex]n[/tex], [tex]n(n+1)[/tex] is even. We have [tex]5\mid S[/tex] if either [tex]5\mid n[/tex] or [tex]5\mid(n+1)[/tex]. This means [tex]n[/tex] must satisfy either [tex]n\equiv0\pmod5[/tex] or [tex]n\equiv4\pmod5[/tex], in which case we have a general solution of

[tex]n=5k[/tex]

or

[tex]n=5k-1[/tex]

where [tex]k[/tex] is any integer.

1. The given absolute value inequality is:

[tex] |x| \: > \: 5[/tex]

This implies that;

[tex] - x \: > \: 5 \: or \: x \: > \: 5[/tex]

We the first inequality by -1 and reverse the sign to get:

[tex]x \: < - \: 5 \: or \: x \: > \: 5[/tex]

The correct answer is

C. { x|x < -5 or x > 5}

2. The given inequality is:

[tex] |4x - 8| \: < \: 12[/tex]

This implies that,

[tex] - (4x - 8) \: < \: 12 \: or \: (4x - 8) \: < \: 12[/tex]

Divide through the first inequality by -1 and reverse the sign

[tex]4x - 8\: > \: - 12 \: or \: 4x - 8\: < \: 12[/tex]

Group similar terms:

[tex]4x \: > \: - 12 + 8 \: or \: 4x \: < \: 12 + 8[/tex]

Simplify:

[tex]4x \: > \: - 4\: or \: 4x \: < \: 20[/tex]

Divide both sides by 4

[tex]x \: > \: - 1\: or \: x \: < \: 5[/tex]

Answer:

[tex]P =4.83\%[/tex]

Step-by-step explanation:

First we calculate the number of possible ways to select 2 cards an ace and a card of 10 points.

There are 4 ace in the deck

There are 16 cards of 10 points in the deck

To make this calculation we use the formula of combinations

[tex]nCr=\frac{n!}{r!(n-r)!}[/tex]

Where n is the total number of letters and r are chosen from them

The number of ways to choose 1 As is:

[tex]4C1 = 4[/tex]

The number of ways to choose a 10-point letter is:

[tex]16C1 = 16[/tex]

Therefore, the number of ways to choose an Ace and a 10-point card is:

[tex]4C1 * 16C1 = 4 * 16 = 64[/tex]

Now the number of ways to choose any 2 cards from a deck of 52 cards is:

[tex]52C2 =\frac{52!}{2!(52-2)!}[/tex]

[tex]52C2 = 1326[/tex]

Therefore, the probability of obtaining an "blackjack" is:

[tex]P = \frac{4C1 * 16C1}{52C2}[/tex]

[tex]P = \frac{64}{1326}[/tex]

[tex]P = \frac{32}{663}[/tex]

[tex]P =0.0483[/tex]

[tex]P =4.83\%[/tex]

Answer:

Probability = 0.0483

Percentage = 4.83%

Step-by-step explanation:

We know that a blackjack hand played with one deck consists of:

1 of the 4 aces = [tex]\frac{4}{52}[/tex]

So 1 out of the 16 cards worth 10 points will be equal to = [tex]\frac{16}{52}[/tex]

Finding the probability of getting a blackjack hand assuming that the cards were not replaced:

P (blackjack hand) =  P(1st ace) × P(2nd 10 point card) +  P(1st 10 point card) × P(2nd ace)

P (blackjack hand) = [tex]\frac{4}{52} \times \frac{16}{51} + \frac{16}{52} \times \frac{4}{51}[/tex] = 0.04827

Percentage of getting blackjack hand = 4.83%

Answer:

6x³ - 4x² + 4x

Step-by-step explanation:

The additive inverse is the value added to make the expression equal to zero.

Given

- 6x³ + 4x² - 4x , then the additive inverse is

- ( - 6x³ + 4x² - 4x)

= 6x³ - 4x² + 4x

The additive inverse of the polynomial is 6x³ - 4x² + 4x.

Given: Polynomial

-6x³ + 4x² - 4x

Additive inverse of the polynomial is the polynomial when added to the original polynomial gives the sum zero.

Let, the additive inverse of the given polynomial be P.

⇒ P + -6x³ + 4x² - 4x = 0

⇒ P = 6x³ - 4x² + 4x

Therefore, the additive inverse of the given polynomial is 6x³ - 4x² + 4x.

Learn more about the Polynomial here: https://brainly.com/question/16306595

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