Simplify
[tex](2x - 3) - (x - 4)[/tex]
Factorize
[tex]16 - 4 {x}^{2} [/tex]
​

Answer:

lets make this like a table

x   y

3=21

4=28

5=35

so since y is bigger lets divide that by x

21/3=7

so the rate of change is 7

Hope This Helps!!!

9x + 3 = 30
9x = 27
x = 3

Then 3x + 1 = 3 * 3 + 1 = 10

[tex]9x + 3 = 30 \\ \\ 9x = 30 - 3 \\ \\ 9x = 27 \\ \\ x = \frac{27}{9} \\ \\ x = 3.[/tex]

putting x = 3 in 3x + 1

[tex]3x + 1 \\ \\ 3 \times 3 + 1 \\ \\ 9 + 1 \\ \\ 10.[/tex]

The value of 3x + 1 is 10.

Answer:

  (a)  Horizontal line test

Step-by-step explanation:

A relation that is a function already passes the vertical line test. If it has an inverse function, that function must also pass the vertical line test.

The inverse relation will be the same graph reflected across the line y=x. That is, points that are horizontally aligned on the relation graph become vertically aligned on the inverse relation graph.

If the inverse relation is to be a function, then there must be no points on its graph that are vertically aligned. This requirement translates to the requirement that there be no horizontally-aligned points on the graph of the original relation. The "horizontal line test" checks for horizontally aligned points. If there are none, the test is said to pass.

A function will have an inverse function if it passes the Horizontal Line Test.

__

Additional comment

The attached graph shows a function (red curve) that does not pass the horizontal line test. Its inverse relation is the green curve, which you can see is not a function. It does not pass the vertical line test.

The line y=x is shown (dashed orange) so you can see the symmetry of the function and its inverse.

Answer:

  if the ratio allowance/chores is constant, it is proportional

Step-by-step explanation:

The values x and y are directly proportional if they satisfy the equation ...

  y = kx

for some constant k, the constant of proportionality.

__

If the relation that produces ordered pairs (chores, allowance) is directly proportional, all of the ratios (allowance)/(chores) will have the same value: the constant of proportionality (k).

If the ratios are not constant, Carlos's allowance is not directly proportional to the number of chores he completes.

Answer:

A , B , D

Step-by-step explanation:

Triangle ABC was rotated 90° around the point, then translated using the rule (x, y) → ( x + 5, y + 3) to form triangle A'B'C'.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and translation.

Triangle ABC was rotated 90° around the point B, then translated using the rule (x, y) → ( x + 5, y + 3) to form triangle A'B'C'.

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7[tex]\sqrt{2}[/tex]

The triangle shown is a 45-45-90 triangle. This name comes from the fact the 3 angle measurements are 45, 45, and 90 degrees.

If needed, you could find the missing angle using the equation: 180 - (45 + 90) = x.

Special Right Triangles

Special right triangles allow us to use formulas and shortcuts to find missing sides easily. Another type of special right triangle is the 30-60-90 triangle. While both of these are special right triangles, they have different formulas.

Formulas

All 45-45-90 triangles have 2 types of sides: the legs (a and b) and the hypotenuse (c).

In these triangles, both of the legs are congruent.

Solving for c

Since we are given b, we can just plug the b-value into the formula that solves for c.

The answer cannot be simplified further, so this is the final answer.

Answer:

Second option

Step-by-step explanation:

It is a right triangle isosceles

a = b = 7

c = hypotenuse

[tex]c =\sqrt{7^{2}+7^{2} } =\sqrt{49+49} =\sqrt{2(49)}=7\sqrt{2}[/tex]

Hope this helps

When we mark the coordinates (0, 2), (1, 1), (x, 0), (9, -1) on graph we obtain option C.

The given function is [tex]y=2-\sqrt{x}[/tex].

We need to find which is the graph of the given function from the options.

In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Take, x=0, 1, 4, 9, 16, 25, 36,....

Now, when x=0, y=2.

When x=1, y=1.

When x=4, y=0.

When x=9, y=-1

So, when we mark the coordinates (0, 2), (1, 1), (x, 0), (9, -1) on graph we obtain option C.

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Answer:

i think the answer is C. 1/2

Answer:

Just simply input in your calculator arcsin of -5/6. Arcsin is the sign that looks like sin to the power of -1, even though it doesn't mean sin to the power of -1. This comes out to 303.6 degrees. So, it actually isn't in quadrant 3, it's in quadrant 4.

Step-by-step explanation:

The answers are given below:

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.

1. (cos x. cos y)(tan x + tan y) = sin (x+ y)

  (cos x. cos y)(tan x + tan y)

= cos x. cos y (sinx/ cos x + sin y/ cos y)

= sin x cos y + sin y cos x

= sin (x+ y)    [ sin ( x +y)]= sin x cos y + sin y cos x

= RHS

3. [tex]-\sin ^2\left(x\right)-\cos \left(2x\right)=0[/tex]

Using identity

[tex]-\cos ^2\left(x\right)=0[/tex]

cos ² x=0

Applying [tex]x^{n} =0[/tex] then x=0

So, cos x =0

General solution will be [tex]x=\frac{\pi }{2}+2\pi n,\:x=\frac{3\pi }{2}+2\pi n[/tex].

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The possible values of x are 5 and -1/12

Given that 2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1 find the possible values of x

The ratio is given as:

2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1

Express as fraction

[tex]\frac{2x - 1}{x-4} = \frac{16x + 1}{2x -1}[/tex]

Cross multiply

4x^2 -4x + 1 = 16x^2 + x  -64x - 4

Collect like terms

-16x^2 + 4x^2 + 64x - x - 4x + 1 + 4 = 0

Evaluate the like terms

-12x^2 + 59x + 5 = 0

Divide through by -1

12x^2 - 59x - 5 = 0

Expand

12x^2  + x - 60x - 5 = 0

Factorize

x(12x + 1) - 5(12x + 1) = 0

Factor out 12x + 1

(x - 5)(12x + 1) = 0

Expand

x  - 5 = 0 or 12x + 1 = 0

Solve for x

x = 5 or x = -1/12

Hence, the possible values of x are 5 and -1/12

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Answer:

5, 8, 11, ...

Step-by-step explanation:

f(n)=3n+2

the first three terms will be f(1), f(2), and f(3).

f(1)=3(1)+2=5

f(2)=3(2)+2=8

f(3)=3(3)+2=11

Hope this helps!

If not, I am sorry.

Answer:

75

Step-by-step explanation:

We use Tan in this case:

Tan=(opposite/adjacent)

Tan(36)=23/x

x=23/Tan(36)

x=31.64 length

Hope it helps!

Answer:

x ≈ 31.64

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

The given trigonometric ratios all use the angle of 36°.

From inspection of the given diagram:

Therefore, we should use the tan trig ratio.

[tex]\implies \sf \tan(36^{\circ})=\dfrac{23}{x}[/tex]

[tex]\implies \sf x=\dfrac{23}{\tan(36^{\circ})}[/tex]

Substituting the given value for tan 36°:

[tex]\implies \sf x \approx \dfrac{23}{0.727}[/tex]

[tex]\implies \sf x\approx31.64[/tex]

From unit conversion, it is found the following results:

6km ≈ 3.73 mi

2.5 L≈ 0.66 gal

90 lb ≈ 40.82 kg

Units of measurement are part of our daily lives. There are different units for area, length, volume, mass, and others.  Because of this, it is important to know converting them.

For solving this question you need some information as:

1 km = 0.621371 mi ( unit for length and distance)

1 L = 0.2641722 gallons (unit for volume)

1 lb = 0.453592 kg (unit for mass)

Therefore,

           1 km --------  0.621371 mi

           6 km --------  x mi

           x= 6* 0.621371

           x=3.73 mi

Thus, 6km ≈ 3.73 mi.

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Answer:

Step-by-step explanation:

basically all you do is

Note that

[tex]x^2 - y^2 = (x - y) (x + y)[/tex]

and

[tex]x^2 + 2xy + y^2 = (x + y)^2[/tex]

Then their LCM is [tex]\boxed{x + y}[/tex].

Answer:

B

Step-by-step explanation:

We see the graph of y=x², so eliminate A.

Since the second graph opens downwards, the coefficient of x² must be negative, so eliminate C.

Also, the axis of symmetry is x = 0, so eliminate D.

This leaves us with B

The value of the expression, g/2 + 3 when x = 8 is: 7.

Given the expression, g/2+3, to find it's value when g = 8, plug in the value of g into the expression and solve.

g/2 + 3

8/2 + 3

Divide

4 + 3

= 7

The value of the expression is: 7.

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Answer:An algorithm is a set of instructions for solving a problem or accomplishing a task.

Step-by-step explanation:

Any series of well defined steps that shows a procedure for solving a given type of problem is called an algorithm.

Step-by-step explanation:

Answer:

The equation of the graph is   y = -lx - 4l - 1.

Step-by-step explanation:

As the values of y are same before and after (4, -1)

the slope of the graph is change on point (4, -1)

the equation of first line is

y - (-1) = 1 (x -4)

the equation of the second line is:

y - (-1) = -1 (x - 4)

As value of y should remain same in both equations

therefore: y - (-1) = - lx - 4l

y = - lx - 4l -1

The equation of the graph is   y = -lx - 4l - 1.

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Answer:

Step-by-step explanation:

Let k: y = a₁x + b₁ and l: y = a₂x + b₂. Then

We have the euation of a line in point slope form:

Convert to the slope intercept form:

y - 4 = 2(x - 6)

y - 4 = 2x - 12

y - 4 + 4 = 2x - 12 + 4

y = 2x - 8

The slope is m₁ = 2.

Let y = m₂x + b.

The lines is perpendicular. Therefore:

2m₂ = -1     |divide both sides by 2

The line passes through the point (-3, -5).

Substitute to the point slope equation:

y - (-5) = -1/2(x - (-3))

y + 5 = -1/2(x + 3)

Answer:

C

Step-by-step explanation:

if you rotate either of the triangles by 180 degrees, compare the angles and you will see that the answer is C

Answer:

Using the concept of linear equations, we find that we need 40 gallons of the 65% antifreeze and 10 gallons of the 90% antifreeze.

Step-by-step explanation:

Let x = amount of 20% antifreeze

Let y = amount of 70% antifreeze

Given that the total amount of antifreeze is 80 gallons

So, x + y = 80

Also given that the purity of the total antifreeze is 60%.

0.65x + 0.90y = 0.70(x + y)

65x + 90y = 70(x + y)

Simplify and solve the system of equations

65x + 90y = 70x + 70y      

65x -70x+ 90y-70y = 0    

-5x + 20y = 0      

Now we have the following system of equations:

x + y = 50

-5x + 20y = 0

Multiply the first equation by 5 to get opposite coefficients for x;  

add the equations to eliminate x

5x + 5y - 5x + 20y = 250

25y = 250

y = 10              

Since the total mixed gallons is 50,

x = 50 - 10 = 40

So we need 40 gallons of the 65% antifreeze and 10 gallons of the 90% antifreeze

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The statements and reasons that complete the proof are:

4. ∠SPQ ≅ ∠TQR [alternate interior angles theorem]

5. ΔPQS ≅ ΔQRT [ASA congruence theorem]

When two pairs of corresponding angles and one pair of included sides of two triangles are congruent, they are congruent triangles based on the ASA congruence theorem.

We are given the following:

QT ≅ PS [a pair of congruent sides]

∠T ≅ ∠S [a pair of congruent angles]

Thus, since QT is parallel to PS, therefore:

∠SPQ ≅ ∠TQR [alternate interior angles theorem]

Therefore, we can now state that  ΔPQS ≅ ΔQRT based on the ASA congruence theorem.

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Answer:

HOW IS THAT EASY??!?!?!?!?!?

Step-by-step explanation:

The statements and reasons that complete the proof are:

4. ∠SPQ ≅ ∠TQR [alternate interior angles theorem]

5. ΔPQS ≅ ΔQRT [ASA congruence theorem]

What is the ASA Congruence Theorem?

When two pairs of corresponding angles and one pair of included sides of two triangles are congruent, they are congruent triangles based on the ASA congruence theorem.

We are given the following:

QT ≅ PS [a pair of congruent sides]

∠T ≅ ∠S [a pair of congruent angles]

Thus, since QT is parallel to PS, therefore:

∠SPQ ≅ ∠TQR [alternate interior angles theorem]

Therefore, we can now state that  ΔPQS ≅ ΔQRT based on the ASA congruence theorem.