D = {f, g, k}
L = {a,f,j}

Find the intersection of D and L.
Find the union of D and I.

The equation that has the same solution as x² + 8x + 15 = -4x is x = -6± √21.

Step 1 - Move terms to the left

x² + 8x + 15 = -4x

x² + 8x + 15-(-4x) = 0

Step 2  - Combine the terms

x² + 8x + 15 + 4x = 0

x² + 12x + 15 = 0

Step 3 - Apply the quadratic formula

x = (-b ± √(b² - 4ac) )/ 2a

Recall that form our equation:

a = 1

b = 12

c = 15

Thus,  x = (-12 √(12² - 4 * 1 *15) )/2 *1

⇒x = -6 ± √21


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Answer: -2

Step-by-step explanation: The answer is -2 because -1 x 8 = -8, and -8 x 4 = -32. Because multiplying two negatives cancels out and becomes positive, we can apply this same principle and figure out that -32 x -2 would give us positive 64. Hope this helps!

Answer: C.5.18 because you cant have a decimal as an integer

Step-by-step explanation: brainliest???

Answer:

√33

Step-by-step explanation:

it is a right triangle and we use Pythagoras

x² = 7² - 4²

x² = 49 - 16

x² = 33

x = √33

Answer:

No Hablo Espaniol

Step-by-step explanation:

The total sales of the year after is Rs. 1857143

He gets 1.5% commission on the total annual sales and a bonus of 2% on the sales above Rs. 20,00,000.

Therefore, since he received a bonus, the sale is over Rs. 20,000.

Hence,

let

x = total sales

Therefore,

1.5% of x + 2% of x   = 65000

1.5 / 100 × x + 2 / 100 × x = 65000

0.015x +0.02x = 65000

0.035x = 65000

x = 65000 / 0.035

x = 1857142.85714

Therefore,

total sales = Rs. 1857143

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Answer:

Ally

Step-by-step explanation:

The fastest time of the race will be the one lesser in value.

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

Comparing the tenths place :

⇒ Jill = 8 in the tenths place

⇒ Ally = 8 in the tenths place

⇒ Maria = 9 in the tenths place

Since Maria's time's tenth place value is greater than that of the other two, she had the slowest time.

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

Comparing the hundredths place (for Jill and Ally) :

⇒ Jill = 7 in the hundredths place

⇒ Ally = 2 in the hundredths place

Since Ally has the lower hundredths' place value, she has the fastest time.

The new sample size based on the information will be B-M, B-C, B-R, 8.

Sample size is the number of participants or observations that are included in a study. This is usually represented by n.

When the boys and girls are to be chosen, the new sample size based on the information will be B-M, B-C, B-R, 8.

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Answer:

Step-by-step explanation:

B-M, B-C, B-R, 8.

Answer:

x=1

y=−2

z=5

(heres how i got the answer)

Step-by-step explanation:

x+2y+3z=12

x−3y+4z=27

−x+y+2z=7

Solve x+2y+3z=12 for x.

x=−2y−3z+12

Substitute −2y−3z+12 for x in the second and third equation.

−2y−3z+12−3y+4z=27

−(−2y−3z+12)+y+2z=7

Solve equations for y and z respectively.

y=−3+

5

1

​

z

z=

5

19

​

−

5

3

​

y

Substitute −3+

5

1

​

z for y in the equation z=

5

19

​

−

5

3

​

y.

z=

5

19

​

−

5

3

​

(−3+

5

1

​

z)

Solve z=

5

19

​

−

5

3

​

(−3+

5

1

​

z) for z.

z=5

Substitute 5 for z in the equation y=−3+

5

1

​

z.

y=−3+

5

1

​

×5

Calculate y from y=−3+

5

1

​

×5.

y=−2

Substitute −2 for y and 5 for z in the equation x=−2y−3z+12.

x=−2(−2)−3×5+12

Calculate x from x=−2(−2)−3×5+12.

x=1

The system is now solved.

x=1

y=−2

z=5

The x-intercepts are (-2, 0) and (2, 0), the minimum is at (0, -3), and the line of symmetry is x = 0 if the equation of the parabola is y = x²—4

It is defined as the graph of a quadratic function that has something bowl-shaped.

Here the graph or equation is not given:

So we are assuming the equation for the parabola is:

y = x²—4

If we plot the graph of the parabola, we can say:

Thus, the x-intercepts are (-2, 0) and (2, 0), the minimum is at (0, -3), and the line of symmetry is x = 0 if the equation of the parabola is y = x²—4

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Answer: [tex]17 \div 2[/tex]

Step-by-step explanation:

[tex]a/b[/tex] is the same thing as [tex]a \div b[/tex]

Answer:

[tex]13 \times 1 \div 67 [/tex]

Answer:

18 cm

Step-by-step explanation:

To find the distance, take the larger number and subtract the smaller number

26 cm - 8 cm

18 cm

Answer: [tex]x^{2}+14x-6y[/tex]

Step-by-step explanation:

[tex]4(3x+y)+2(x-5y)+x^{2} \\ \\ 12x+4y+2x-10y+x^{2} \\ \\ \boxed{x^{2}+14x-6y}[/tex]

Answer:

See below

Step-by-step explanation:

There could be INFINITE possibilities....(you didn't list any choices to choose from)

 here is one to change to base 10

     log5 ( 13)   =   log10 ( 13) / log10 ( 5)  

When we solve the equation, we will get the real answer x=40 as a variable.

First degree equation is a mathematical sentence, which has values represented by letters.

These letters can indicate a variable or an unknown - which at the end of the equation will be the final value.

— To solve this equation, just: apply the distributive property (multiply the terms that are outside the parentheses, for the terms that are inside the symbol).

— Next, let's add the real numbers together. Next, we'll subtract the like terms before the equality, thus moving the common term after the equality by adding.

— Finally, let's divide the equation, thus obtaining the final result.

4 + 3(x + 22) = 5x - 10

4 + 3x + 66 = 5x - 10

70 + 3x = 5x - 10

3x - 5x = -10 - 70

-2x = -80

x = 80 ÷ 2

x = 40

Therefore, the correct value of X in this equation, will be x = 40.

The answer that I got is 7 500

Answer:

Y = - 24

Step-by-step explanation:

Y/-6 +5=9 /*6 (Multiply the whole equation by the number 6 to eliminate the fraction. That is, you multiply each member of the equation by 6 because 6 is in the denominator of the fraction.
[tex]\frac{Y}{-6} *6=-Y[/tex],     [tex]5*6=30[/tex],    [tex]9*6=54[/tex]

-Y + 30 = 54
-Y = 54-30
-Y=24 /*(-1)
Y= -24

Answer:

A. $3,535.20.

To find the total amount paid, you can simply multiply the monthly payment by the number of payments:

$98.20 x 36 = $3,535.20

By solving a quadratic equation, we will see that the length is 10m and the width is 6.5m

For a rectangle of width W and length L, the area is:

A = W*L

In this case, we know that the area is 65m² and that the length is 3 meters less than 2 times the width, so:

L = 2*W - 3m

Then we can write:

65m² = (2*W - 3m)*W = 2*W² - 3m*W

This is a quadratic equation:

2*W² - 3m*W - 65m² = 0.

The solutions are given by the Bhaskara's formula:

[tex]W = \frac{3 \pm \sqrt{(-3)^2 - 4*2*(-65)} }{2*2} \\\\W = \frac{3 \pm 23 }{4}[/tex]

We only care for the positive solution, which is:

W = (3m + 23m)/4 = 26m/4 = 6.5m

Then the length is:

L = 2*6.5m - 3m = 10m

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Answer:

there is no line

Answer:

[tex]\dfrac{\text{d}}{\text{d}x} \tan^{-1}x=\dfrac{1}{1+x^2}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Trigonometric Identity}\\\\$\tan^{-1}(A)-\tan^{-1}(B) \equiv \tan^{-1}\left(\dfrac{A-B}{1+AB}\right)$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{3 cm}$\displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1} \theta}{\theta} \right]=1$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Differentiating from First Principles}\\\\$\text{f}\:'(x)=\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]$\\\end{minipage}}[/tex]

Given function:

[tex]\text{f}(x)=\tan^{-1}x[/tex]

[tex]\implies \text{f}(x+h)=\tan^{-1}(x+h)[/tex]

Differentiating from first principles:

[tex]\begin{aligned}\text{f}\:'(x) & =\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]\\\\& =\lim_{h \to 0} \left[\dfrac{\tan^{-1}(x+h)-\tan^{-1}x}{(x+h)-x}\right]\end{aligned}[/tex]

Using the trigonometric identity to rewrite the numerator:

       [tex]\begin{aligned}& =\lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{x+h-x}{1+x(x+h)}\right)}{(x+h)-x}\right]\\\\& =\lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{h}{1+x^2+xh)}\right)}{h}\right]\end{aligned}[/tex]

[tex]\textsf{Multiply the denominator by }\dfrac{1+x^2+xh}{1+x^2+xh}:[/tex]

       [tex]= \displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{h}{1+x^2+xh)}\right)}{\dfrac{h(1+x^2+xh)}{(1+x^2+xh)}}\right][/tex]

Separate:

       [tex]= \displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{h}{1+x^2+xh)}\right)}{\dfrac{h}{(1+x^2+xh)}} \right] \cdot \displaystyle \lim_{h \to 0} \left[\dfrac{1}{1+x^2+xh}\right][/tex]

[tex]\textsf{Use }\displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1} \theta}{\theta} \right]=1:[/tex]

       [tex]= 1 \cdot \displaystyle \lim_{h \to 0} \left[\dfrac{1}{1+x^2+xh}\right][/tex]

As h gets close to zero:

       [tex]= 1 \cdot \left[\dfrac{1}{1+x^2}\right][/tex]

Simplify:

       [tex]=\dfrac{1}{1+x^2}[/tex]

Answer:

To find the derivative of [tex]\tan^{-1} x[/tex] using the first principle of derivative, we need to use the definition of the derivative:

f'(x) = lim(h->0) [(f(x + h) - f(x)) / h]

where f(x) = [tex]\tan^{-1} x[/tex].

Substituting f(x) into the definition of the derivative, we get:

f'(x) = lim(h->0) [([tex]\tan^{-1}[/tex](x + h) - [tex]\tan^{-1}/tex) / h]

To simplify this expression, we can use the formula for the inverse tangent of a sum:

[tex]\tan^{-1}[/tex](a + b) = [tex]\tan^{-1}[/tex]a + [tex]\tan^{-1}[/tex]b - [tex]\pi[/tex]/2

Using this formula, we can rewrite the numerator of the expression above as:

([tex]\tan^{-1}[/tex](x + h) - [tex]\tan^{-1}/tex) = [tex]\tan^{-1}[/tex]((x + h) / (1 + (x + h)^2)) - [tex]\tan^{-1}[/tex](x / (1 + x^2))

Now, substituting this expression back into the definition of the derivative, we get:

f'(x) = lim(h->0) [[tex]\tan^{-1}[/tex]((x + h) / (1 + (x + h)^2)) - [tex]\tan^{-1}[/tex](x / (1 + x^2))] / h

We can simplify this expression using algebra and trigonometry, and we get:

f'(x) = lim(h->0) [h / (1 + x^2 + hx + h^2 + x^2h + xh^2)] / h

f'(x) = lim(h->0) 1 / (1 + x^2 + hx + h^2 + x^2h + xh^2)

Now we can simplify this expression by dropping the terms that contain h^2 or higher powers of h, since they will approach zero faster than h as h approaches zero. We also drop the term containing x^2h, since it is a second-order term and will also approach zero faster than h. This leaves us with:

f'(x) = lim(h->0) 1 / (1 + x^2 + hx)

Now we can evaluate the limit as h approaches zero:

f'(x) = 1 / (1 + x^2)

Therefore, the derivative of [tex]\tan^{-1} x[/tex] by first principle of derivative is:

[tex]\frac{d}{dx}[/tex][tex]\tan^{-1} x[/tex] = 1 / (1 + x^2)

500 represents the initial amount of medication, since when t=0, a=500.

Step-by-step explanation:

[tex]5 = {a}^{x} [/tex]

[tex] \frac{5}{a} = \frac{a {}^{x} }{a} [/tex]

[tex] \frac{5}{a} = {a}^{x - 1} [/tex]

Answer:

Area of a rectangle = l × b

11. 35 = 5 × b

b = 35/5

b = 7 m

12. 48 = 6 × h

h = 48/6

h = 8 ft

13. 24 = b × 3

b = 24/3

b = 8 in

Hope it helps!

Answer: 1.5

Step-by-step explanation:

If we translate the triangle right one unit, we get it has vertices (3,4), (0[tex]\frac{1}{2}|(9)(3)-(4)(6)|=\boxed{1.5}[/tex],0), and (6,9).

So, the area is

Answer:

There are eight sides so it's an octagon

Step-by-step explanation:

Answer:

29

the triangle on the right has 2 sides the same so the lower two corners have the same angle which would be (180-64)/2 = 58 degrees

the lower right angle of the triangle on the left Sadie would be 180-58 = 122.

Since 2 sides of the triangle on the left are the same the other two angles would be equal to each other.

x = (180-122)/2 = 29 degrees

Answer:

x = 29°

Explanation:

The triangle on right side is an isosceles triangle with two similar angles.

Let that angle be z:

⇒ z + z + 64° = 180°

⇒ 2z = 180° - 64°

⇒ 2z = 116°

⇒ z = 58°

After finding z, find the opposite angle:

⇒ 180° - 58° = 122°

Find the value of x:

⇒ x + x + 122° = 180°

⇒ 2x = 180° - 122°

⇒ 2x = 58°

⇒ x = 29°