What additional piece of information is needed to show that DEF andPQR are congruent by ASA?

By quadratic formula, the roots of the quadratic function 2 · x² - 2 · x + 5 = 0 are two conjugated complex numbers: x₁ = 0.5 + i 1.5 and x₂ = 0.5 - i 1.5, respectively.

Let be a quadratic function of the form a · x² + b · x + c = 0, whose roots can be found by means of the following formula:

[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]     (1)

Where a, b, c are the coefficients of the quadratic function.

In we know that 2 · x² - 2 · x + 5 = 0, then the roots of the polynomial are, respectively:

[tex]x_{1} = \frac{2 + \sqrt{(-2)^{2}-4\cdot (2)\cdot (5)}}{2\cdot (2)}[/tex]

[tex]x_{1} = \frac{2 + \sqrt{4-40}}{4}[/tex]

x₁ = 0.5 + i 1.5

[tex]x_{2} = \frac{2 - \sqrt{(-2)^{2}-4\cdot (2)\cdot (5)}}{2\cdot (2)}[/tex]

[tex]x_{2} = \frac{2 - \sqrt{4-40}}{4}[/tex]

x₂ = 0.5 - i 1.5

By quadratic formula, the roots of the quadratic function 2 · x² - 2 · x + 5 = 0 are two conjugated complex numbers: x₁ = 0.5 + i 1.5 and x₂ = 0.5 - i 1.5, respectively.

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Answer:

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

Step-by-step explanation:

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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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:

My guess would be b or d

Step-by-step explanation:

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: 50.5

Step-by-step explanation:

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

Answer:

y = 7x +2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (- 1, - 5 )

m = [tex]\frac{-5-2}{-1-0}[/tex] = [tex]\frac{-7}{-1}[/tex] = 7

the line crosses the y- axis at (0, 2 ) ⇒ c = 2

y = 7x + 2 ← equation of line

"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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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:

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

Based on the calculations, the first three (3) iterations of the given function are 120, 96 and 76.8.

In this exercise, you're required to find the first three (3) iterations of the given function. Thus, we would substitute the value of x₀ into the function and then evaluate as follows:

First iteration:

f(x) = 0.80x

f(x₀) = 0.80x₀

f(150) = 0.80 × 150

f(150) = 120.

Second iteration:

f(x) = 0.80x

f(x₁) = 0.80x₁

f(120) = 0.80 × 120

f(120) = 96.

Third iteration:

f(x) = 0.80x

f(x₂) = 0.80x₂

f(96) = 0.80 × 96

f(120) = 76.8.

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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 :)

Answer: 10.6

Step-by-step explanation:

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

The probability that sample the proportion of adults with hypertension is greater than 0.5 is 0.090

The given parameters are:

p = 47%

Sample size, n =500

The standard deviation is calculated as:

[tex]\sigma = \sqrt{np(1 - p)[/tex]

So, we have:

[tex]\sigma = \sqrt{500 * 47\%(1 - 47\%)[/tex]

Evaluate

σ = 11.16

The number of adults with hypertension is calculated as:

x = 500 * 0.5 = 250

And the mean is:

μ = 500 * 0.47 = 235

Start by calculating the z-score

[tex]z = \frac{x - \mu}{\sigma}[/tex]

This gives

[tex]z = \frac{250 - 235}{11.16}[/tex]

Evaluate

z = 1.34

The probability is then calculated as:

P(z >1.34) = ??

From z table of probabilities, we have:

P(z >1.34) =  0.090

Hence, the probability that sample the proportion of adults with hypertension is greater than 0.5 is 0.090

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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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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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The exponential function of the table is y = 0.75(2)^x

From the table, we have the following points

(x,y) = (0,0.75) and (1,1.5)

An exponential function is represented as:

y = ab^x

At (0,0.75), we have:

0.75 = ab^0

a = 0.75

Substitute a = 0.75 in y = ab^x

y = 0.75b^x

At (1,1.5), we have:

1.5 = 0.75b^1

Evaluate

1.5 = 0.75b

Divide both sides by 0.75

b =2

Substitute b =2 in y = 0.75b^x

y = 0.75(2)^x

Hence, the exponential function is y = 0.75(2)^x

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Answer:

A. median

explain i just aced the test rn

Answer:

Angle bisector

Step-by-step explanation:

The line AD bisects both sides of the triangle. Both angles are congruent to each other since both sides are congruent to each other.

Answer: The correct answers are the first and the fourth one.

Step-by-step explanation:

For the given function, the domain is D : { x ≥ 7} and the range is R: { y ≥ 9}

Here we have a square root, remember that the argument of the square root must be equal or larger than zero, so the domain is such that:

x - 7 ≥ 0.

Solving for x we get:

x ≥ 0 + 7

Then the domain is:

x ≥ 7

To get the range, we evaluate in the minimum of the domain:

f(7) = √(7 - 7) + 9 = 9

Then the range is the set of all values larger than 9, because the function is increasing.

So the range is R: y ≥ 9.

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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:

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:

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!

Answer:

45m

Step-by-step explanation:

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

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.

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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