A distance travaled by train in three hours with a constant speed of r miles per hour

There are 120 five digit numbers that can be created

The digits are given as:

2, 3, 5, 7 and 8

Since there are no conditions, and the digits cannot be repeated.

Then the number of digits is:

Digits = 5!

Expand

Digits = 5 * 4 * 3 * 2 * 1

Evaluate

Digits = 120

Hence, there are 120 five digit numbers that can be created

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The correct answer is option A which is ZA = 3 cm

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

The triangle is shown below.

From the triangle, A is the concurrency point of angle bisectors of all vertices.

Consider ΔAYD,

Using the Pythagorean theorem,

AD² = AY² + YD²

5² = AY² + 4²

25 = AY² + 16

AY² = 25 - 16

AY² = 9

AY = √9 = 3 cm

Consider triangles ADY and ADZ.

∠AYD ≅∠AZD=90

∠ADY≅∠ADZ ( Angle bisector)

AD ≡ AD (common side)

The two triangles are congruent by the AAS postulate.

Therefore, by CPCTE, AY=ZA=3 cm

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Answer: 3cm

Step-by-step explanation: Trust Me! Answer is correct on Edge quiz!

Good Luck! :)

ZA= 3cm

The two real values that are not in the domain of the composition are x = 2 and x = -2.

Here we have:

f(x) = 1/x

g(x) = x^2 - 4

The composition is:

f°g = f(g(x)) = 1/(x^2 - 4)

The two values that are not in the domain are the values of x such that g(x) = 0, because we can't divide by zero.

g(x) = 0 = x^2 - 4

4 = x^2

±√4 = x

±2 = x

So g(x) = 0 when x = 2 or x = -2, so these are the two real values that are not in the domain of f°g.

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Answer:

147

Step-by-step explanation:

Angles in a triangle add up to 180:

x + 23 + 10 = 180

x = 147

The equivalent expression to2-1/y/3+1/y is [tex]\mathbf{=\dfrac{(2y-1)}{(3y+1)}}[/tex]

Equivalent expressions are expressions does not look the same but when a value is being replaced with their variable, they end up giving the same result.

From the information given:

We have are to determine the equivalent expression to:

[tex]\mathbf{=\dfrac{(2-\dfrac{1}{y})}{(3+ \dfrac{1}{y})}}[/tex]

So if we multiply both the numerator and the denominator with 1/y, we have:

[tex]\mathbf{=\dfrac{(2y-1)}{(3y+1)}}[/tex]

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Answer:

[tex]y=\frac{3}{4}x+2[/tex]

Step-by-step explanation:

So when you express a linear function in slope-intercept form it's given in the form of y=mx+b, where m is the slope, and b is the y-intercept. This is because as x increases by 1, the y-value will increase by m (because multiplication), and since the slope is defined as rise/run, the rise will be m, and run will be 1, giving you a slope of m/1 or m. The reason b is the y-intercept, is because whenever the linear function crosses the y-axis, the x-value will always be 0. Meaning that mx will be 0 because m * 0 will equal 0... and that leaves b by it self, so b will determine the y-intercept.

So if you look at the graph, the linear function crosses the y-axis as (0, 2) so the value of b will be 2. This gives you the equation y=mx+2.

Now to calculate the slope, we can take any two points and see how much the rise was and how much the run was. It can also be more formally defined in the equation: [tex]y=\frac{y_2-y_1}{x_2-x_1}[/tex]. So let's take the points (0, 2) and (8, 8). As you can see the x-value increases by 8 or "ran" by 8, and the y-value increased by 6. So the rise over run in this case is 6/8 which can simplified as 3/4. That is the slope. This gives you the complete equation of: [tex]y=\frac{3}{4}x+2[/tex]

The value of P(A and C) is 0.18

From the tree diagram, we have the following probability values:

P(A) = 0.6

P(C) = 0.3

The probability P(A and C) is then calculated as:

P(A and C) = 0.6 * 0.3

Evaluate

P(A and C) = 0.18

Hence, the value of P(A and C) is 0.18

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Answer:

39

Step-by-step explanation:

37 = 96 %

x  = 100%

[tex]x =\frac{37(100)}{96} =38.54= 39[/tex]

[tex]\huge\boxed{39\ \text{students}}[/tex]

Note: The numbers in this problem are a little weird and don't work out perfectly. I'll demonstrate at the end of this answer how something seems a little off in the problem, but we'll get as close as possible.

We know from the problem that 37 students are equal to 96% of the class.

Let's write this as an equation:

[tex]37=0.96x[/tex]

Divide both sides of the equation by [tex]0.96[/tex] to isolate [tex]x[/tex].

[tex]38.54\approx x[/tex]

We'll round this to [tex]39[/tex] as the final answer.

It's important to note that you can't have partial students, only whole numbers.

If we do the math here, 37 out of 39 students is about 95%.
Also, 37 out of 38 is about 97%.

I'm not sure how the original writer of the question got 96%, but I suppose 39 is the best answer with what's been given.

Answer:

well the value of x is 2 and the value of y is 1##

Step-by-step explanation:

I hope it will help you

Answer:

211.68 miles

Step-by-step explanation:

21.6 x 9.8

The equation which is equivalent to -i among the answer choices is; i^(15), option A

It follows from the concept of complex numbers that the representation -i stands for √-1 and on this note, it follows that;

i² = -1

i³ = -i

i⁴ = 1

Hence, it follows that;

i^(15) = i⁴ × i⁴ × i⁴ × i³ = 1 × 1 × 1 × -i = -i.

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Answer:

h(x) = 2^(x) - 1.

Step-by-step explanation:

Let's look at each equation:

f(x) = -3x +7, Well as x increases, since it's multiplication, there are "going to be more" -3's, so it's going to be decreasing.

g(x) = -4(2^x). While 2^x is increasing, because "there are going to be more 2's multiplied by each other" as x increases, it's being multiplied by a negative number, so it's actually going to be decrasing

h(x) = 2^(x) - 1. Here's it's going to be increases as x goes towards infinity because "there are going to be more 2's multiplied by each other", and there isn't any negative sign, while there is a negative 1, it's constant, so the overall value will be increasing

Using the given information, the percent error is 52%

From the question, we are to calculate the percentage error

From the given information,

Prediction = 23 people

Actual = 48 people

Using the formula,

[tex]Percent \ error = \frac{|Prediction - Actual|}{|Actual|}\times 100\%[/tex]

[tex]Percent \ error = \frac{|23 - 48|}{|48|}\times 100\%[/tex]

[tex]Percent \ error = \frac{|-25|}{|48|}\times 100\%[/tex]

[tex]Percent \ error = \frac{25}{48}\times 100\%[/tex]

Percent error = 52.083%

Percent error ≈ 52%

Hence, the percent error is 52%

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Answer:

x = 1

y = -2

Step-by-step explanation:

x = 19 + 9y

3x- 3y = 9

________

3(19+9y)-3y=9

y=-2

x=19+9(-2)

x=1

(1,-2)

Answer:

[tex] - x = - 1 - 9y \\ \frac{ - x}{ - 1} = \frac{ - 1}{ - 1} - \frac{9}{ - 1} \\ x = 1 + 9y...(3) \\ 3(1 + 9y) - 3y = 9 \\ 3 + 27y - 3y = 9 \\ 3 + 24y = 9 \\ 24y = 9 - 3 \\ 24y = 6 \\ \frac{24y}{24} = \frac{6}{24} \\ y = \frac{1}{4} \\ \\ \\ \\ x = 9( \frac{1}{4} ) + 1 \\ x = \frac{9}{4} + 1 \\ x = \frac{13}{4} [/tex]

Step-by-step explanation:

ATTACHED IS THE SOLUTION!

Answer:

your question is wrong, it's not an expression but a quadratic equation. if so your answer will be x=8±2√7

Step-by-step explanation:

by using, completing the square method

x²-16x-4=0

x²-16x=4

x²-16x+(-16×0.5)²=4+(16×0.5)²

x²-16x-8²=4+8²

(x-8)²=68

x-8=√68

x-8=±2√7

so x=8±2√7

please next time write the correct question

Answer:

x = 4

Step-by-step explanation:

Since they are parallel, we use the formula  

[tex]\frac{part}{part} = \frac{part}{part}[/tex]

[tex]\frac{14}{x} =\frac{7}{2}[/tex]

7x = 28

x = 4

Answer: Option 2

Step-by-step explanation:

The vertex must have a y-coordinate of 5, so eliminate options 3 and 4.

Also, since there must be a maximum, the coefficient of [tex]x^2[/tex] must be negative. So, eliminate option 1.

This leaves us with option 2.

Answer:

cos=24/25

tan=7/24

Step-by-step explanation:

sin=opposite/hypotenuse

therefore 7 is the opposite and 25 is the hypotenuse.

using pythagorean theorem we can find the adjacent. i.e hypotenuse squared= sum of adjacent squared and opposite squared.

h^2= a^2+ O^2

25 squared - 7 squared= 576

which is equal to 24 squared.

therefore adjacent=24

cos=adjacent/hypotenuse

cos=24/25

tan=opposite/adjacent

tan=7/24.

Answer:

[tex]\cos(\theta)= \dfrac{24}{25}[/tex]

[tex]\tan(\theta)=\dfrac{7}{24}[/tex]

Step-by-step explanation:

Definitions of primary trig functions

For a given acute angle in a right triangle :

...where the hypotenuse is the side across from the right angle, the opposite side is the side not touching the angle theta, and the adjacent side is the side touching the angle theta (but that isn't the hypotenuse).

We are already given the ratio for the Sine function, so we need to find the Cosine and Tangent function ratios.  It will be helpful to visualize what this triangle looks like.

The given equation states [tex]\sin(\theta)=\frac{7}{25}[/tex], so there is some right triangle, with a specific angle theta, that has a ratio of sides (opposite to hypotenuse) of 7 to 25.  For ease, we'll consider the triangle that has actual side lengths of 7 and 25 for those sides.  (See attached diagram)

Given that information, we can identify that the unknown side length is the adjacent side length.  Since the triangle is a right triangle, this value can be found through the Pythagorean Theorem.

The Pythagorean Theorem states that for any right triangle, [tex]a^2+b^2=c^2[/tex] where "c" is the length of the hypotenuse of the triangle, and "a" and "b" are the lengths of the other two sides of the triangle (often called "legs").  It does not matter which leg is chosen to be side "a" or side "b" due to the commutative property of addition, but "c" must be the hypotenuse.

[tex]a^2+b^2=c^2[/tex]

Substituting known values, and simplifying...

[tex]a^2+(7)^2=(25)^2[/tex]

[tex]a^2+49=625[/tex]

Subtracting 49 from both sides to begin to isolate "a", and simplifying...

[tex](a^2+49)-49=(625)-49[/tex]

[tex]a^2=576[/tex]

Applying the square root property to isolate "a", and simplifying/calculating...

[tex]\sqrt{a^2}=\pm \sqrt{576}[/tex]

[tex]a=\pm 24[/tex]

[tex]a=24[/tex]  or  [tex]a=-24[/tex]

Under the assumption that the triangle is an acute triangle, the adjacent side length is a positive value, so we reject the negative solution, deducing that the adjacent side length must be 24.

Side note:  If there is more information in the context of the question that suggests that theta may be larger than 90°, then other factors will need to be taken into account.

Returning to the trig ratio definitions, we can identify the requested cosine and tangent ratios

[tex]\cos(\theta)=\dfrac{\bold{adjacent} \text{ side length}} {\bold{hypotenuse} \text{ length}} = \dfrac{24}{25}[/tex]

[tex]\tan(\theta)=\dfrac{\bold{opposite} \text{ side length}} {\bold{adjacent} \text{ side length}}=\dfrac{7}{24}[/tex]

Answer:

A. Scalene

E. Obtuse

Step-by-step explanation:

Obtuse are angles that are greater than 90°

Scalene is not congruent sides.

The conditional probability illustrates that's there's a 2/8 that the event A occurs.

It should be noted that probability simply means the likelihood of the occurence of an event.

In this case, it can be delivered that P(AID) and P(DIA) aren't equal.

Hence, P(D|A) has event A as its given event, resulting in 2/8 for a probability.

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The expected number of pairs of adjacent cards which are both black is  650 / 51

For each pair of cards, the probability that they are both black is 26/52 * 25/ 51 = 25 / 102,

So since there are 52 pairs in the circle, the expected number of pairs which are both black is

25 / 102 * 52 = 650 / 51

Probability is genuinely how probable something is to happen. Every time we're unsure about the final results of an occasion, we can speak approximately the chances of sure results—how probably they're.

The evaluation of occasions governed by chance is referred to as statistics.

A sequence of movements where the outcomes are constantly unsure. The tossing of a coin, deciding on a card from a deck of playing cards, throwing a cube. It's far a single final results of an experiment. Getting a Heads even as tossing a coin is an event.

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Answer:

Hence the expression [tex]$(y+7)(y+4)=y^{2}+11 y+28$[/tex]

Step-by-step explanation:

- The given expression is (y+7)(y+4).

- We have to multiply the given expression.

- Multiply the (y+7) by 4 , multiply the (y+7) by y then add like terms.

[tex]\begin{array}{r}y+7 \\\underline {\times \quad y+28} \\4 y+28 \\\underline {y^{2}+7 y }\\y^{2}+11 y+28\end{array}[/tex]

Using proportions, the percentage change in the cost of manufacturing the kitchen cabinet was a increase of 5.5%.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The standard cost is given as follows:

S = 250 + 120 + 60 = $430.

After the increases, the price will be given as follows:

S = 250 x 1.1 + 120 x 1.08 + 60 x 0.82 = $453.8.

The price increased. The percent change, given by the change divided by the initial value, is:

P = 23.8/430 x 100% = 5.5%.

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Answer:

awnser D is the only function

The range of the function is f(x) <= 4

The attached graph is the missing piece in the question

The function f(x) is given as:

The above means that, the value of the function do not exceed y = 4

Hence, the range of the function is f(x) <= 4

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Answer: This really depends on how long you have to reach this goal.

Let’s say you want to make this amount in one month.

There is about 4 weeks in a month so you’ll need to divide 2112.24 by 4.

That would be 528.06 per week.

To find an amount per day you’ll need to divide 528.06 by 7.

That would be about 75.5 per day.

Please let me know if this doesn’t help.

The set of real numbers for the equation x – 2 = √(2x – 1) will be 5.

The solution of the equation means the value of the unknown or variable.

The equation is given below.

x – 2 = √(2x – 1)

Square on both side, then we have

               (x – 2)² = 2x – 1

         x² – 4x + 4 = 2x – 1

         x² – 6x + 5 = 0

   x² – 5x – x + 5 = 0

x(x – 5) – 1(x – 5) = 0

       (x – 5)(x – 1) = 0

                         x = 1, 5

The set of real numbers for the equation x – 2 = √(2x – 1) will be 5.

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Answer:

It's either 16 or -16

Step-by-step explanation:

Subtract 41 and 57 and you get one of those two.

My bet is 16 due to you not being able to have a negative amount of bills in your wallet in real life.

Answer:

x = 2

Step-by-step explanation:

The left side would be (3x - 12)
The right side would be (-4x+2)

In an equation, 3x - 12 = -4x+2

Combine all the letters on the left and plain numbers on the right,

3x + 4x = 12 + 2

Note: When you transfer to the other side of the equal sign, the number will change its sign.

Simplify the 3x + 4x = 12 + 2,

                     7x = 14

                      [tex]x=\frac{14}{7}[/tex]

                      x = 2

⊱________________________________________________________⊰

Answer:

Step-by-step explanation:

[tex]\large\begin{gathered} \sf{Simplify \ using \ the \ distributive \ property:} \\ \sf{3(x-4)=2(-2x+1)} \\ \ \sf{3x-12=-4x+2} \\ \rm{Move \ 12 \ to \ the \ right, \ with \ the \ opposite \ sign} \\ \ \sf{ 3x=-4x+2+12} \\ \rm{Move \ -4x \ to \ the \ left, \ wth \ the \ opposite \ sign.} \\ \sf{3x+4x=14} \\ \rm{Collect \ the \ like \ terms} \\ \sf{7x=14} \\ \rm{Divide \ the \ entire \ equation \ by 7.} \\ \sf{\dfrac{7x}{7}=\dfrac{14}{7} \\ \sf{x=2} \ \bigstar \end{gathered}[/tex]

Done!!

⊱______________________________________________________⊰

Answer:

Please review the equation format.  I made an assumption (below) for this answer.

-0.57

Step-by-step explanation:

5x2 45x 24 = 0 is not a quadratic formula,

5x^2 + 45x + 24 = 0 is, however.  Also, it gives -.8.43 as one solution.  The other is −0.569351, or -0.57 to the nearest hundredth.

The other solution of the given quadratic equation would be -0.57

Quadratic Equation

An algebraic equation of the second degree in x is known as a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

The given quadratic equation is,

5x² + 45x + 24 = 0

Here,

a = 5

b = 45

c = 24

Applying the Quadratic Formula

The quadratic formula for the two roots of a quadratic equation is given as,

[tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]       ........... (1)

and [tex]x=\frac{-b+\sqrt{b^{2}+4ac } }{2a}[/tex]   ............ (2)

Substituting the values of a, b, and c in equation (1), we get,

x = -8.43

Calculating the Second Root

Now, the other solution can be found by substituting the values of a, b, and c in the equation (2),

[tex]x=\frac{-45+\sqrt{45^{2}+4(5)(24) } }{2(5)}[/tex]

[tex]x=\frac{-45+\sqrt{(2505) } }{10}[/tex]

[tex]x=-0.57[/tex]

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