The function g(x) = -2x + 3. Compare the slopes and y-intercepts. A. Both the slopes and the y-intercepts are different. B. Both the slopes and the y-intercepts are the same. C. The slopes are the same but the y-intercepts are different. D. The slopes are different but the y-intercepts are the same. ​

[tex]\text{L.H.S}\\\\=\dfrac{1+\tan x}{ 1+ \cot x}\\\\\\=\dfrac{1+ \tan x}{ 1+ \tfrac 1{\tan x}}\\\\\\=\dfrac{1+\tan x}{\tfrac{\tan x+1}{\tan x}}\\\\\\=(1+\tan x) \times \dfrac{\tan x}{1+ \tan x}\\\\=\tan x\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]

Answer: -5=2x+11

Step-by-step explanation:

3x-5=5x+11

subtract 3x to both sides

3x-5 - 3x =5x+11 - 3x

simplify

-5 = 2x +11

answer is -5=2x+11

Answer:

a = 6

Step-by-step explanation:

g(x) = 5x - 2

h(x) = √(x + 3)

g(h(x)) = 5[tex]\sqrt{x+3}[/tex] - 2

g(h(a)) = 5[tex]\sqrt{a+3}[/tex] - 2

5[tex]\sqrt{a+3}[/tex] - 2 = 13

5[tex]\sqrt{a+3}[/tex] = 15

[tex]\sqrt{a+3}[/tex] = 3

( [tex]\sqrt{a+3}[/tex] )² = 3²

a + 3 = 9

a = 6

Answer:

u=30

x=150

z=150

y=30

Step-by-step explanation:

u=y [ being vertically opposite angle]

x+u=180[ being linear pair]

x+30=180

x=180-30

x=150

z=x[being vertically opposite angle]

z=150

y=u[ being voa]

Answer:

=40°

Step-by-step explanation:

Sorry that's all I know

^keep safe^

Answer:

the first option

Step-by-step explanation:

hope the answer helps...

Answer:

(5.5, 5 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = A (8, 2 ) and (x₂, y₂ ) = B (3, 8 ) , then

midpoint = ( [tex]\frac{8+3}{2}[/tex] , [tex]\frac{2+8}{2}[/tex] ) = ( [tex]\frac{11}{2}[/tex] , [tex]\frac{10}{2}[/tex] ) = (5.5, 5 )

The probability of picking two snacks of the same type is 0.308.

The probability of picking 2 potato will be:

= 6/14 × 5/13

= 0.429 × 0.385

= 0.165

The probability of picking 2 doritos will be:

= 5/14 × 4/13

= 0.357 × 0.308

= 0.110

The probability of picking 2 corn curls will be:

= 3/14 × 2/13

= 0.214 × 0.154

= 0.033

Therefore, the probability of picking two snacks of the same type will be:

= 0.165 + 0.110 + 0.033

= 0.308

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The equivalent expression of 3/2(6x^2 - 2/3x) is 9x^2 - x

The expression is given as:

3/2(6x^2 - 2/3x)

Open the bracket

3/2*6x^2 - 3/2*2/3x

Evaluate the product

9x^2 - x

Hence, the equivalent expression of 3/2(6x^2 - 2/3x) is 9x^2 - x

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For this problem, let's think of this shape as a rectangle and a triangle put together. We'll calculate the area of each shape and add them together to get the total area.

For the rectangle, the equation is b*h. Here the base = 7 cm and the h = 4cm

For the triangle, the equation is 1/2 * (b*h). Here the base is a little tricky to find. We know the total length is 12cm and the rectangle length was 7cm. So 12-7= 5cm, which is the base of the triangle. The height would be the same (4cm).

Once you calculate those two areas and add them up, you'll have the total area of this shape.

Answer:

Yes

Step-by-step explanation:

Answer: 247 the Answer

  c

Step-by-step explanation:

The trigonometric ratios show that the angle FHE is 48.59°.

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: [tex](hypothenuse)^2=(leg_1)^2+(leg_2)^2[/tex]. And the main trigonometric ratios are:

[tex]sin(\alpha) =\frac{opposite \;leg }{hypotenuse} \\ \\ cos(\alpha) =\frac{adjacent\;leg }{hypotenuse} \\ \\ tan(\alpha) =\frac{sin(\alpha )}{cos(\alpha )}= \frac{opposite \;leg }{adjacent\;leg } \\ \\[/tex]

It is important to remember that the sum of internal angles for any triangle is 180°.

From the question, it is possible to see 2 right triangles (HGF and FHE).

You can find the hypotenuse of the triangle HGF from the  trigonometric ratio: sen Θ

[tex]sin45=\frac{opposite\; leg }{hypotenuse} =\frac{\sqrt8}{hypotenuse}\\ \\ \frac{\sqrt{2} }{2} =\frac{\sqrt{8} }{hypotenuse} \\ \\ \sqrt{2}*hypotenuse=2\sqrt{8} \\ \\ hypotenuse=\frac{2\sqrt{8} }{\sqrt{2}} =2\sqrt{4} =2*2=4[/tex]

The hypotenuse of triangle HGF is one of legs for the triangle FHE. The, you can find the angle FHE from the  trigonometric ratio: tan β. Thus,

[tex]sin \beta =\frac{opposite\; leg }{adjacent\; leg} =\frac{3}{4}\\ \\ sin \beta=\frac{3}{4}=0.84806\\ \\ arcsin\beta =48.59^{\circ \:}[/tex]

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The line a is an illustration of a proportional linear equation, and the equation of line a is y = 1.4x

The line a passes through the following points:

(x,y) = (0,0) and (1.3, 1.82(

The above means that line a is a proportional linear equation

The constant of proportionality (k) is calculated using:

k = y/x

Using the values on the table, we have:

k = 1.82/1.3

Divide

k = 1.4

Substitute k = 1.4 in k = y/x

y/x = 1.4

Multiply both sides by 1.4

y = 1.4x

Hence, the equation of the line a is y = 1.4x

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Answer:

B.

Step-by-step explanation:

We can start by dividing 3.5 and 0.75.

3.5/0.75 is 4.67.

Now, we multiply 4.67 by 1 since we are finding how much she walks in 1 hour.

1*4.67 is 4.67.

Answer:

2nd option

Step-by-step explanation:

the recursive rule is

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d ( d is the common difference )

use the explicit rule to find a₁ and d

a₁ = 48 - 11(1) = 48 - 11 = 37

a₂ = 48 - 11(2) = 48 - 22 = 26

then

d = a₂ - a₁ = 26 - 37 = - 11

recursive rule is then

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 11

a₁ = 37

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ U(\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad V(\stackrel{x_2}{10}~,~\stackrel{y_2}{4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 10 +4}{2}~~~ ,~~~ \cfrac{ 4 +6}{2} \right)\implies \left( \cfrac{14}{2}~~,~~\cfrac{10}{2} \right)\implies (7~~,~~5)[/tex]

Problem 4

Draw any right triangle you want. Afterward, draw a perpendicular segment that goes from the 90 degree angle to the hypotenuse. Call this new segment the altitude. It might help to have the hypotenuse laying flat or horizontal.

The length of this altitude can be found using the geometric mean formula. Search out "geometric mean for triangles" (or similar) and you should get a diagram that visually summarizes what is going on. I've provided a screenshot of an example using GeoGebra. See below.

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Problem 5

The two special types of right triangles are: the 45-45-90 triangle and the 30-60-90 triangle.

If x is the leg length of the first triangle type mentioned, then [tex]x\sqrt{2}[/tex] is the hypotenuse. We can confirm this using the pythagorean theorem. Recall that the legs of any 45-45-90 triangle are the same, meaning we have an isosceles triangle.

For the second type of triangle, the short leg x leads to the hypotenuse 2x and long leg [tex]x\sqrt{3}[/tex]

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Problem 6

If you know say the opposite and adjacent sides of a right triangle, then you can use the tangent ratio because tan = opposite/adjacent.

Sine is used for opposite/hypotenuse, while cosine is used for adjacent/hypotenuse. Those are the main 3 trig functions. Technically there are 3 more, but they are just reciprocals of the previous three.

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

Problem 7

Use inverse trig functions to find the missing angles if you know the sides. The inverse trig functions have an exponent of -1.

For instance, let's say the triangle has an opposite side of 10 and hypotenuse of 15

The reference angle would be...

[tex]\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(x) = \frac{10}{15}\\\\x = \sin^{-1}\left(\frac{10}{15}\right)\\\\x \approx 41.81^{\circ}\\\\[/tex]

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Problem 8

Imagine looking completely horizontal at the horizon. The angle in which you are currently looking is 0 degrees. If you look upward, say 10 degrees, then the angle of elevation is 10 degrees. Looking down means we have an angle of depression. These two types of angles help us determine various distances and lengths.

Use the alternate interior angle theorem to help show that angles of depression are congruent to angles of elevation. It will depend on context which type of angle is more useful.

Answer:

D

Step-by-step explanation:

Since we don't know how many people we don't know how many servings would be consumed. therefore this is an indirect variation

The value of x so that lines s and t are parallel is 12

The angle are alternate exterior angles.

Therefore, alternate exterior angle theorem states that when two parallel lines are intersected by a transversal, then the exterior angles formed on either side of the transversal are equal.

Hence,

7x - 20 = 4x + 16

7x - 4x= 16 + 20

3x = 36

x = 36 / 3

x = 12

Therefore, the value of x is 12.  

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The error interval for the length of the piece of wood is 293.5 ≤ length < 294.5

Error Interval can be defined as the limit of Accuracy when a number has been truncated.

It is given that the length of the piece of wood is 294 cm truncated to the nearest centimeter.

To determine the error interval for the length of the piece of wood

length ≥ 293.5

length < 294.5

293.5 ≤ length < 294.5

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Answer:

a = z/mb

Step-by-step explanation:

Given:

[tex]\displaystyle \large{z=mab}[/tex]

To solve for a, divide both sides by the variables mb to isolate a-term.

[tex]\displaystyle \large{\dfrac{z}{mb}=\dfrac{mab}{mb}}[/tex]

Simplify the expression and we finally have solved for a-term.

[tex]\displaystyle \large{\dfrac{z}{mb}=a}\\\\\displaystyle \large{a=\dfrac{z}{mb}}[/tex]

Therefore, the answer to this question is a = z/mb.

Please let me know if you have any questions regarding my answer or explanation!

Answer:

Happy birthday <3

Step-by-step explanation:

:)

The area of the entire rectangle is 4x² + 12x + 8

The given parameters are:

height = 4

Width = x² + 3x + 2

The area of the rectangle is:

Area = Width * Height

So, we have:

Area = (x² + 3x + 2) * 4

Expand

Area = 4x² + 12x + 8

Hence, the area of the entire rectangle is 4x² + 12x + 8

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Answer: 80

Step-by-step explanation:

We can use the formula [tex]A=\frac{d_{1}d_{2}}{2}[/tex], where [tex]d_{1}, d_{2}[/tex] are the lengths of the diagonals.

By the distance formula,

[tex]AC=\sqrt{(-2-2)^{2}+(-1-7)^{2}}=\sqrt{16+64}=4\sqrt{5}\\BD=\sqrt{(-8-8)^{2}+(-1-7)^{2}}=\sqrt{256+64}=8\sqrt{5}[/tex]

So, the area is [tex]\frac{(4\sqrt{5})(8\sqrt{5})}{2}=\boxed{80}[/tex]

The average rate of change is 12 the interval from x=3 to x=5.

Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:

[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

where when

[tex]x = x_1, y = y_1\\and \\x = x_2, y = y_2[/tex]

Given:

Interval; x = 3 to x = 5

We can represent these by

[tex]x_1 = 3\\x_2 = 5[/tex]

The corresponding y values are as follows

When x = 3, y = 8

When x = 5, y = 32

This will also be represented

[tex]y_1 = 8\\y_2 = 32[/tex]

The average rate of change is then calculated as follows

[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}\\\\\\m = \dfrac{32 -8}{5-3}\\\\m = \dfrac{24}{2}\\\\m = 12[/tex]

Hence, the average rate of change is 12.

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Answer:

IT'S A !

Step-by-step explanation:

Took the quiz on edge 2022 .

the correct statement is:

"The lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope of 0, and the graph of x = dx is a vertical line with an undefined slope."

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Find correct statement is true about the graphs of the two lines y=-6 and x = dx

Since, horizontal line with a slope of 0, and the graph of x = dx is a vertical line with an undefined slope.

Therefore, the correct statement is:

"The lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope of 0, and the graph of x = dx is a vertical line with an undefined slope."

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