Factor the expression x2 − 14x + 45 completely.

Applying the inscribed angle theorem, the measure of arc AB that doesn't go through point C is: 100 degrees.

Based on the inscribed angle theorem, if ∅ is the inscribed angle measure, the measure of the central angle subtended by the same arc equals 2(∅).

m∠BAC = 40 degrees.

Central angle = 2(40) = 80 degrees [based on the inscribed angle theorem]

Corresponding arc BC = 80 degrees.

Arc AC through point B = 180 degrees [half circle]

Arc AB = 180 - arc BC = 180 - 80 = 100 degrees.

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Answer:

x = 4

Step-by-step explanation:

[tex]5^{9x} =25^{4x+2}[/tex]

First you need to get a common base as your number.

[tex]5^{9x} =5^{2(4x+2)}[/tex]

The second number changed because 5 squared is 25. Changing it to this form gives us the same base number of 5. Now we use the distributive property in the exponent.

[tex]5^{9x} =5^{8x+4}[/tex]

Now we can use this statement:

[tex]A^{m} =A^{n}[/tex] if [tex]m=n[/tex]

Using this we solve:

9x = 8x+4

-8x  -8x

x = 4

Hope it helps!

The answer will be x squared over 4 plus y squared over 8 equals 1.

An ellipse is an oval shape geometry having two focuses and the curve is equidistant from the focus.

The general equation of the ellipse is given as;

(x²/a²) + (y²/b²) = 1

The coordinates of a foci are: (±c, 0) where;

c² = b² - a²

However, we know that equation of directrix is; x = ±a/e

Now, Directrix is given ±4

Thus, a/e = 4

a = 4e

We also know that c = ae from ellipse foci coordinates.

Thus, ae = 2

since ae = 2, then (4e)e = 2

4e² = 2

e² = 2/4

e = 1/2

Thus;

a = 4 × 1/2

a = 2

Since c² = b² - a²;

2² = b² - 2²

4 = b² - 4

b² = 8

From (x²/a²) + (y²/b²) = 1, we can put our values to get;

x²/4 + y²/8 = 1

Hence the answer will be x squared over 4 plus y squared over 8 equals 1.

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Answer:

B (2,6,10,14)

Step-by-step explanation:

I think C and D are imposible to be the answer.

A and B are 50% to be the answer.

But I choose B.

For 90 degrees coordinate will be swapped and the position of the coordinate is in the third quadrant. Then the location of point q will be at (–4, –3).

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

A rectangle is transformed according to the rule 90º.

The rectangle has vertices located at r'(–4, 4), s'(–4, 1), p'(–3, 1), and q'(–3, 4).

Then the location of q will be

For 90 degrees coordinate will be swapped and the position of the coordinate is in the third quadrant. Then the location of point q will be at (–4, –3).

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Answer:

(4, 3) , (4, 0) , (6, 0)

Step-by-step explanation:

M (1, 4)

M ' ( 1 + 3, 4 - 1)

namely M ' (4, 3)

N (1, 1)

N ' ( 1 + 3 , 1 - 1)                       ((x, y) 3 squares right and 1 square down means

namely n" (4, 0)                         ( x + 3, y - 1))

p (3, 1)

p ' ( 3 + 3 , 1 - 1)

namely p' (6, 0)        

Step-by-step explanation:

(3,4) not that sure about the coordinates are right

If Kara rollerblades at given average speed, in 15 minutes, she will rollerblade a distance of 3.5kilometers or 3500meters.

Note that, speed is distance traveled per unit time.

Mathematically, Speed = Distance ÷ time.

Hence, Distance = Speed × time

Given that;

Distance = Speed × time

Distance = 14km/hr × 0.25hr

Distance = 3.5km or (3.5×1000)m

Distance = 3.5km or 3500m

Therefore, if Kara rollerblades at given average speed, in 15 minutes, she will rollerblade a distance of 3.5kilometers or 3500meters.

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Answer:

In the first step, there is an issue when distributing the -3 to the terms inside of the parentheses. When multiplying the -3 to the -5, you would get an answer of +15, not -15.

The full correct process is:

(4m + 9) - 3(2m - 5) = 4m + 9 - 6m + 15

                                = 4m - 6m + 9 + 15

                                = -2m + 24

"In order to meet ADA requirements, a wheelchair ramp must have an angle of elevation of no more than" the angle of elevation  is mathematically given as

∅=3.434

Generally, the equation for the angle is mathematically given as

[tex]\theta=\frac{opp}{adj}\\\\Therefore\\\\tan\theta=\frac{1.5}{25}\\\\tan\theta=\frac{1.5}{25}\\\\\theta=tan^{-1}\frac{1.5}{25}\\\\[/tex]

∅=3.434

In conclusion, the angle of elevation

∅=3.434

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The independent variable: number of pounds of fertilizer; and dependent variable: number of square feet of garden covered.

Let

Dependent variable are variables which takes its value based on other values in an equation.

Independent variable are variables which takes its value outside an equation.

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Answer:

119 4/7

Step-by-step explanation:

Add up all the sides

Hi Student!

Looking at the picture that was provided, we see that the problem statement is asking for us to determine the perimeter of the shape is.  Perimeter is the outer layer of the shape which would include the lengths of all the sides that are exposed to the outside.

In this case, we are given 7 different values which represent each of the different sides of the shape which we need to add together to get the perimeter.

Create an expression

Using the expression above, all we need to do is combine all of the values which will give us the outline on our shape.  However, since some of the values have different denominators, we will first need to combine the whole numbers and then combine those with a common denominator and finally apply a common denominator to be able to add the rest.

Combine the whole numbers

Combine those with a common denominator

Covert to mixed fraction and simplify

Find common denominator and combine

Simplify the expression

Therefore, the final answer for the perimeter of the figure that was provided would be [tex]119\frac{4}{7}[/tex] units.

Answer:

what subject of math? Anything to do with calc is a tough area but I can try.

Step-by-step explanation:

sometimes

Step-by-step explanation:

irrational numbers are numbers that cannot be expressed as a quotient of 2 numbers

rational numbers are numbers that can be expressed as a fraction.

for example let's take these examples of iirational numbers:

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

[tex]\pi \times \pi = 9.86960....[/tex]

the 1st product (2) can be written as a fraction but the second one cannot be written as a fraction

No, it does not make any sense to say that the density of helium is  0.1785 kilograms per square meter.

No, it does not make any sense to say that the density of helium is  0.1785 kilograms per square meter.

The reason why it doesn't make sense is because density of helium, and all the rest of the chemical elements are calculated as;

Density = mass/volume

where;

mass is measured in kilograms.

volume is measured in cubic meter.

Thus, the density of the helium should be expressed as 0.1785 kilograms per cubic meter.

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Answer:

45m

Step-by-step explanation:

4m+19m+14m+8m=45m

Answer:

Step-by-step explanation:

By the inscribed angle theorem, [tex]a=21, b=42[/tex]

So, since angles in a triangle add to 180 degrees, the angle vertical to c is [tex]180-21-42=117[/tex], and thus [tex]c=117[/tex]

Answer:

  65.9 ft

Step-by-step explanation:

The Law of Sines tells us the relationship between an angle and the opposite side. We are given the angle opposite the given side, but we need the angle opposite the side of interest.

__

The sum of angles in a triangle is 180°, so the measure of the angle at the balloon is ...

  angle C = 180° -75° -60° = 45°

Then the distance between Amaya and Rochelle (c) is ...

  c/sin(C) = r/sin(R)

  c = r×sin(C)/sin(R) = (90 ft)×sin(45°)/sin(75°)

  c ≈ 65.8846

Amaya and Rochelle are about 65.9 feet apart.

Answer:

2018 I believe.

Step-by-step explanation:

He'll be two times his age in 2032 which is 28 years old. Subtract 28 from 2032 and you get 2018.

Answer:

2018

Step-by-step explanation:

in 2032 he will be 28 years old because he is 2 times older than 14, 2032-14=2018, because 14 years have passed since he was 14

Part (a)

There are 3 face cards (jack, queen, king) in any given suit. We have 4 suits. That gives 3*4 = 12 face cards total.

12/52 = 3/13 is the probability of getting a face card on any random selection. This probably does not change for any future selection because we put the current card back. In other words, the deck has not changed. Contrast this with part (b) where the probabilities will change since the card counts decrease each time (since we don't put the card back).

The probability of getting 3 face cards in a row, with replacement, is:

(3/13)*(3/13)*(3/13) = 0.012289 approximately

This converts to the percentage 1.2289% after moving the decimal point two spots to the right. This is the same as multiplying by 100.

Lastly, round that to one decimal place to get 1.2%

The percent sign is already taken care of, so you'll just input the number only.

=============================================================

Part (b)

Like mentioned earlier, the probability of a face card is 12/52

I won't reduce that fraction, as you'll see why below.

After that first card is not put back, the 12 decreases to 12-1 = 11 and we have 52-1 = 51 cards left over.

11/51 is the probability of getting another face card, where we have no replacement going on.

Then 10/50 is the probability of getting a third face card. Again, with no replacement.

Therefore,

(12/52)*(11/51)*(10/50) = 0.009955

is the approximate probability of getting 3 face cards in a row with no replacement. Notice the count down 12,11,10 in the numerators. There's also the countdown 52, 51, 50 in the denominators. This nice pattern only happens if we don't reduce the reducible fractions. This is why I didn't reduce.

Anyways 0.009955 converts to 0.9955% which rounds to 1.0% or simply 1%

A triangle is a three-edged polygon with three vertices. If the triangle is rotated 180° about the cross then it will be done as shown below.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to b

If the triangle is rotated 180° about the cross then it will be done as shown below. This is because the triangle is 2 units away from the cross(dot) therefore, after rotation it will be at the same distance from the point.

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Answer:

My guess would be b or d

Step-by-step explanation:

B. The square root function is the quadratic function reflected across

the line y = x, with a limited domain.

graph y=x^2 and y=√x and y=x

graph is attached

gathmath

The given quadratic equation [tex]y = x^2 + 3x - 10[/tex] Hence, the correct option is D one real root.

Let the quadratic equation given be of the form ax^2 + bx + c = 0, then

The quantity [tex]b^2 - 4ac[/tex] is called its discriminant.

The solution contains the term [tex]\sqrt{b^2 - 4ac}[/tex] which will be:

Real and distinct if the discriminant is positive

Real and equal if the discriminant is 0

Non-real and distinct roots if the discriminant is negative

The given quadratic equation

[tex]y = x^2 + 3x - 10[/tex]

a = 1

b = 3

c = -10

The discriminant

[tex]b^2 - 4ac[/tex]

= 9 - 4(1)(-10)

= 9- 40

= - 31

Thus, Non-real and distinct roots if the discriminant is negative.

Hence, the correct option is D one real root.

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Answer:

A. -0.8

Step-by-step explanation:

The closer its absolute value to 1, the stronger the relationship is.

A. |-0.8| = 0.8

B. |-0.6| = 0.6

C. |-0.5| = 0.5

D. |-0.7| = 0.7

0.8 is closest to 1, therefore representing the strongest correlation.

Hope this helped :)

The simplified value is shown below:

Exponent refers to the number of times a number is used in a multiplication. Power can be defined as a number being multiplied by itself a specific number of times.

First,

3²*4³*[tex]2^{-1}[/tex]/(3*4)²

=9*64/144*2

= 576/288

=2

Second,

(3*2)^4 *[tex]3^{-3}[/tex]/2³*3

=1296/8*81

=1296/648

=2

Third,

[tex]3^{-3} *2^{-3} *6^{3} /(4^{0} )^{2}[/tex]

= [tex]6^{3} /(1 )^{2} *3^{3} *2^{3}[/tex]

= [tex]2^{3}* 3^{3} /(1 )^{2} *3^{3} *2^{3}[/tex]

=1

Fourth,

[tex]2^{4}* 3^{5} /(2*3)^{5}\\=2^{4}* 3^{5} /2^{5}*3^{5}[/tex]

= 1/2

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Answer: 10.6

Step-by-step explanation:

[tex]\sin 62^{\circ}=\frac{x}{12}\\x=12 \sin 62^{\circ} \approx \boxed{10.6}[/tex]

Answer:

2.5 cups is equal to 1 pound.

Step-by-step explanation:

___2.5__ cups rice is equivalent to 1 pound

Hope This Helped

Answer:

2.5 cups of rice

I hope this helps

Answer:

35 is the least common denominator

Step-by-step explanation:

35 is the least (smallest) common (same) multiple of 5 and 7. We use the smallest number that both 5 and 7 go into, because its supposed to be easier to use smaller numbers.

4/5 becomes 28/35 and 5/7 becomes 25/35. And now that they have the same denominator, you could add or subtract them.

Answer: 50.5

Step-by-step explanation:

[tex]\frac{30}{22}=\frac{x}{37}\\x=(30/22)(37) \approx \boxed{50.5}[/tex]