A line passes through the points (–1, –5) and (4, 5). The point (a, 1) is also on the line.
whats a value?

Answer:

27.6 degrees

Step-by-step explanation:

Use Cosine rule on Acute triangle

b² = a² + c² - 2ac Cos B

where b = 10, a = 14, c = 20

10² = 14² + 20² - 2(14)(20) Cos B

-496 = -560 Cos B

Cos B = (-496) / (-560)

B = [tex]Cos^{-1}[/tex] (-496) / (-560) = 0.483 radians = 27.6 degrees

Final answer:

To solve the equation (x + 6)(x - 4) = -16, expand the brackets, rearrange the equation, and factorize to find the solutions.

Explanation:

To solve the equation (x + 6)(x - 4) = -16, we can start by expanding the brackets:

x2 - 4x + 6x - 24 = -16
x2 + 2x - 24 = -16

Next, we can rearrange the equation to one side:

x2 + 2x - 24 + 16 = 0
x2 + 2x - 8 = 0

Finally, we can factorize the quadratic equation:

(x + 4)(x - 2) = 0

This gives us two possible values for x: x = -4 or x = 2.

In order to solve for x, we must do the following:

5(x - 10) = 30 - 15x

5x - 50 = 30 - 15x (Expand 5(x - 10) )

5x - 50 + 50 = 30 - 15x + 50 (Add 50 to both sides of the equation)

5x = 80 - 15x

5x + 15x = 80 - 15x + 15x (Add 15x to both sides)

20x = 80

20x/20 = 80/20 (Divide both sides by 20)

x = 4

Therefor, the correct answer is the second option (x = 4).

You can always check if this is correct by substituting your answer back into the original equation and seeing if the left side is equal to the right side (this is also a potential method for solving the question itself if it is multiple choice, but I find it is often better to actually solve the equation rather than substitute each answer to see which works):

5(x - 10) = 30 - 15x

if x = 4:

5(4 - 10) = 30 - 15(4)

5(-6) = 30 - 60

-30 = -30

The two sides are equal, therefor x = 4 is confirmed as the correct answer.

Final answer:

To solve the equation 5(x - 10) = 30 - 15x, we expand and rearrange to get 20x = 80 and divide both sides by 20 to find that x = 4.

Explanation:

The student is asking us to solve for x given the equation 5(x – 10) = 30 – 15x.

To solve for x, we first expand the left side of the equation:
5x - 50 = 30 - 15x. Next, we collect like terms by adding 15x to both sides and adding 50 to both sides to isolate x:
5x + 15x = 30 + 50.
This simplifies to:
20x = 80.

We then divide both sides by 20 to solve for x:
x = 80 / 20.
This results in:
x = 4. Therefore, x equals 4 is the solution.

As a check, substituting x = 4 back into the original equation yields the identity 5(4 - 10) = 30 - 15(4), or -30 = -30, confirming that x = 4 is indeed the correct solution.

Answer:

D

X - intercept is the point where the graph crosses the x-axis

in this case, the graph crosses at x = 2 and y = 0; or (2,0)

Answer:

(2, 0)

Step-by-step explanation:

The x- intercept is where the line crosses the x- axis at x = 2

x- intercept is (2, 0)

The y- intercept is where the line crosses the y- axis at y = - 4

y- intercept is (0, - 4)

[tex]\bf 5x-2y<-8\implies -2y<-5x-8\implies \stackrel{\textit{multiplication by a negative}}{y~~\stackrel{\downarrow }{>}~~\cfrac{-5x-8}{-2}} \\\\\\ y>\cfrac{5x+8}{2}\implies y>\cfrac{5}{2}x+4\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

x=44

Step-by-step explanation:

Making the equation in terms of x:

0.2x + 0.8 = 9.6

-0.8              -0.8

0.2x=8.8

*5      *5

x=44

Answer:

x=44

Step-by-step explanation:

Multiply by 10 from both sides of equation.

0.2x*10+0.8*10=9.6*10

Simplify.

2x+8=96

Subtract by 8 from both sides of equation.

2x+8-8=96-8

Simplify.

96-8=88

2x=88

Divide by 2 from both sides of equation.

2x/2=88/2

Simplify, to find the answer.

88/2=44

x=44 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

1x-4

Step-by-step explanation: Less than in this occasion means -4, and the product of one and a number x means 1x, so when you put it together it's 1x-4.

Answer:

C, D and E

Step-by-step explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined.

Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.

solve 3x(x - 1)(x + 5) = 0

Equate each factor to zero and solve for x

3x = 0 ⇒ x = 0

x - 1 = 0 ⇒ x = 1

x + 5 = 0 ⇒ x = - 5

Vertical asymptotes at x = -5, x = 1 and x = 0

Answer:

0, 1, -5

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Sinusoid graphs look like regular waves.

It is obvious that only I and III look like waves.

II is known as a stepwise function.

Option: D is the correct answer.

             D.   I and III only

From the graph that is provided to us we observe that the graph I is a sinusoidal graph since it is similar to a graph of sine graph.

Also, the graph II is not a continuous graph and hence it can't be a graph of sinusoidal graph.

Also, graph III is similar to a graph of sine function and hence it represent a graph of a sinusoidal graph.

Answer:

Here is your answer in the picture..

Answer:

x = 5

Step-by-step explanation:

Given

9x + 2 = 5x + 22 ( subtract 5x from both sides )

4x + 2 = 22 ( subtract 2 from both sides )

4x = 20 ( divide both sides by 4 )

x = 5

Answer:

1 cup = 0.24 liters

Step-by-step explanation:

Answer:

x= 6.5 cm

Step-by-step explanation:

When a tangent line touches the circle, it forms a right angle triangle at that point

Apply the Pythagorean relationship in this case

Given that the height is = 20.2 cm = b

The hypotenuse is = c= x+14.7 cm

General formulae is;

a² +b² =c²

x² + 20.2² =( x+ 14.7)²

x² + 408.04= x² +14.7x+14.7x+216.09

x² + 408.04= x² + 29.4 x +216.09.........................collect like terms

x²-x² + 408.04-216.09= 29.4x

191.95= 29.4x-------------------------------divide by 29.4 t0 get x

191.95/29.4 =x

x=6.5 cm

well, the recursive rule of aₙ = aₙ₊₁ + 7, where a₁ = 15, is simply saying that

we start of at 15, and the next term is obtained by simply adding 7, and so on.

well, that's the recursive rule.

so then let's use that common difference and first term for the explicit rule.

[tex]\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=15\\ d=7 \end{cases} \\\\\\ a_n=15+(n-1)7\implies a_n=15+7n-7\implies a_n=7n+8[/tex]

Answer:

B and D

Step-by-step explanation:

The center of the first one is (-3,6)

The center of the second one is (-9,-12)

The center of the third one is (-14,14)

The center of the fourth one is (-16,-3)

The first one has center in the 2nd

The second one has center in 3rd

The third one has center in the 2nd

The fourth one has center is the 3rd

Answer:

The correct answer options are B. [tex](x + 9)^2 + (y + 12)^2 = 36[/tex] and D. [tex](x + 16)^2 + ( y + 3)^2 = 17[/tex].

Step-by-step explanation:

We know that the formula of a circle is [tex](x - h)^2 + (y - k)^2 = r^2[/tex] where [tex]k[/tex] is the value of the ordinate, [tex]h[/tex] is the value of the abscissa and [tex] r [/tex] is the radius of the circle.

B. [tex](x + 9)^2 + (y + 12)^2 = 36[/tex]

[tex][x - (-9)]^2 + [y - (-12)]^2 = 6^2[/tex]

Center (-9, -12)

D. [tex](x + 16)^2 + ( y + 3)^2 = 17[/tex]

[tex][x - (-16)]^2 + [y - (-3)]^2 =\sqrt{17}[/tex]

Center (-16, -3)

Answer:

3(x2 + 1) + 2

A. (3x + 2)(x2 + 1) WRONG bc = 3x^3

B. 3x2 + 1 + 2 Wrong bc 3x^+3

C. (3x + 2)2 + 1 wrong bc 6x+5

D. 3(x2 + 1) + 2Correct

Answer:

[tex]\sqrt{7(-14+i)}[/tex]

Step-by-step explanation:

We need to find the [tex]\sqrt{-98+7i}[/tex]

We know that 98/7 = 14.

Taking 7 common from both terms we get

[tex]\sqrt{7(-14+i)}[/tex]

Since 7 and -14 are not the perfect squares, so our answer is:

[tex]\sqrt{7(-14+i)}[/tex]

Step 1: evaluate f(x+h) and f(x)

We have

[tex]f(x+h) = -(x+h)^2+6(x+h)-5 = -(x^2+2xh+h^2)+6x+6h-5[/tex]

[tex]= -x^2-2xh-h^2+6x+6h-5[/tex]

And, of course,

[tex]f(x)=-x^2+6x-5[/tex]

Step 2: evaluate f(x+h)-f(x)

[tex]f(x+h)-f(x)=-x^2-2xh-h^2+6x+6h-5-(-x^2+6x-5)=-2xh-h^2+6h[/tex]

Step 3: evaluate (f(x+h)-f(x))/h

[tex]\dfrac{f(x+h)-f(x)}{h}=-2x-h+6[/tex]

Step 4: evaluate the limit of step 3 as h->0

[tex]f'(x) = \displaystyle \lim_{h\to 0} \dfrac{f(x+h)-f(x)}{h}=-2x+6[/tex]

So, we have

[tex]f'(1) = -2\cdot 1+6 = 4,\quad f'(2) = -2\cdot 2+6 = 2,\quad f'(3) = -2\cdot 3+6 = 0[/tex]

Answer:

The value of a - b + c + d = -4

Step-by-step explanation:

* Lets explain the linear equation

- The linear equation is the equation that represented graphically

  by a line

- The general form of its equation is ax + by = c

- The slope of the line is -a/b and the y-intercept of the line is c/a,

  where a is the coefficient of x , b is the coefficient of y and c is the

  numerical term

∵ We have two linear equation in the problem

∴ Their general form is ax + by = e , cx + dy = f

∵ The equation are 2x + 8y = 7 and 4x - 2y = 9

- By comparing the two equations with their general forms

∴ a = 2 , b = 8 , c = 4 , d = -2

- Now we can find the value of a - b + c + d

∵ a = 2 , b  = 8 , c = 4 , d = -2

∴ a - b + c + d = 2 - 8 + 4 + (-2) = 2 - 8 + 4 - 2 = -4

* The value of a - b + c + d = -4

Answer:

B. 164°

Step-by-step explanation:

arc JL = 2 (<JKL)

arc JL = 2(82)

arc JL = 164°

The measure of JL is 164°.

The correct option is (B)

An arc whose measure is less than 180 degrees is called a minor arc.

Given: angle JKL= 82°

We know by the theorem that

"When two angles are subtended by the same arc, the angle at the centre of a circle is twice the angle at the circumference."

Then,

JL= 2 (JKL)

JL= 2(82)

JL= 164°.

Hence, the measure of JL is 164°.

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The equivalent speed in meters per hour is 85000 m/hr.

Speed exists as a scalar quantity that describes how fast an object is moving, regardless of its direction.

Speed exists as the time rate at which an object exists moving along a path, while velocity exists as the rate and direction of an object's movement. Put another way, speed exists as a scalar value, while velocity is a vector.

Here given that,

A car travels 85 kilometers per hour.

Using, the general conversion method.

1 km = 1000 m

= ( 85 km/hr ) (1000 m/1km)

The unit km cancels = 85000 m/hr

Hence, 85000 m/hr is the equivalent speed in meters per hour.

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85,000 meters per hour.

If a car travels 85 kilometers per hour, to find the equivalent speed in meters per hour, we need to convert kilometers into meters. Since 1 kilometer is equal to 1,000 meters, we multiply the speed in kilometers by 1,000 to get the speed in meters.

So, the car's speed in meters per hour would be:

85 km/h  × 1,000 m/km = 85,000 meters per hour.

This conversion is straightforward and is based on the relationship that 1 km = 1,000 m.

Answer:

C

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 180°

a point (x, y ) → (- x, - y) → C

Answer:  C) (x, y) → (−x, −y)

Step-by-step explanation:

When we rotate a figure 180°clockwise or counter-clockwise , the magnitude of x and y coordinates remains same but their signs got changed.

For example : After a rotation of 180°clockwise or counter-clockwise (3,4) becomes (-3,-4).

Algebraically , we can say

Ordered pair (x , y ) will become (-x, -y) after a rotation of 180°clockwise or counter-clockwise.

Thus , the algebraic rule describes the 180° counter-clockwise rotation about the origin will be :-

C) (x, y) → (−x, −y)

Answer:

cos 2Ф = - 161/289 , tan 2Ф = - 240/161

Step-by-step explanation:

* Lets explain how to solve the problem

∵ cos Ф = - 8/17

∵ Ф lies in the 3rd quadrant

- In the 3rd quadrant sin and cos are negative values, but tan is

 a positive value

∵ sin²Ф + cos²Ф = 1

∴ sin²Ф + (-8/17)² = 1

∴ sin²Ф + 64/289 = 1

- Subtract 64/289 from both sides

∴ sin²Ф = 225/289 ⇒ take √ for both sides

∴ sin Ф = ± 15/17

∵ Ф lies in the 3rd quadrant

∴ sin Ф = -15/17

∵ cos 2Ф = 2cos²Ф - 1 ⇒ the rule of the double angle

∵ cos Ф = - 8/17

∴ cos 2Ф = 2(-8/17)² - 1 = (128/289) - 1 = - 161/289

* cos 2Ф = - 161/289

∵ tan 2Ф = sin 2Ф/cos 2Ф

∵ sin 2Ф = 2 sin Ф × cos Ф

∵ sin Ф = - 15/17 and cos Ф = - 8/17

∴ sin 2Ф = 2 × (-15/17) × (-8/17) = 240/289

∵ cos 2Ф = - 161/289

∴ tan 2Ф = (240/289)/(-161/289) = - 240/161

* tan 2Ф = - 240/161

Answer:

so look the answer is 2090909876

Step-by-step explanation:

Answer:

1. They are met on point (-1, -3)

2. They x- values of the solution is... -1

3. There is only one solution. Proof: The slope and the y intercept is different.

4. If you plug in -1 in the x, you get the same y

Explanation:

3x = 4x +1

0 = x +1

-1 = x

plug in... y = 3(-1) = -3

Answer:

The two functions are equal at the two graphs' points of intersection. The points of intersection are (0,1) and (2,9). The x-values of the solutions are x = 0 and x = 2.

Step-by-step explanation:

The problem can be solved using trigonometric principles where the hypotenuse measures 16 inches.

The problem involving a triangular brace can be solved using trigonometry principles. As it involves a right triangle, you can use the sine function to solve the problem. In a right triangle, the sine of an angle (hypotenuse) is the length of the side opposite the angle divided by the length of the hypotenuse.

In this case, you have the opposite side (8 inches), the angle (30 degrees), and the adjacent side (base, 11 inches). Using these values and the sine rule, we can determine the length of the hypotenuse. In a 30-degree angle, the sine is 0.5, so the unknown length can be obtained by dividing the length of the opposite side by the sine of the angle. This gives: 8/0.5 = 16 inches.

Therefore, the correct statement will be that the hypotenuse of the triangular brace is 16 inches.

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Using the principles of trigonometry, specifically the sin and cos functions, applied to a triangle with a 30 degrees angle and known lengths of the sides opposite and adjacent to this angle, we can calculate the length of the hypotenuse.

The question asked pertains to the principles of trigonometry. In particular, we have a triangle with one angle of 30 degrees, and we know the lengths of the side opposite this angle (8 inches) and the base of the triangle, which is adjacent to this angle (11 inches).

With a 30 degree angle, we can use sin, cos, and tan functions to form relationships with the opposite, adjacent, and hypotenuse sides of the triangle. In this scenario, the sin(30 degrees) = opposite length/hypotenuse = 8 inches/hypotenuse. Alternatively, the cos(30 degrees) = adjacent length/hypotenuse = 11 inches/hypotenuse.

To solve for the hypotenuse using the sin, you'd do 8/sin(30 degrees). From the cos, you'd do 11/cos(30 degrees).

Note that while you have two ways to solve for the hypotenuse, these should give you the same answer if your angle and side lengths are correct.

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Answer:

C. p(x) = 5x - 12.

Step-by-step explanation:

p(x) = 8x - (3x + 12)     (Note you have to put the 3x+12 in parentheses).

p(x) = 8x - 3x - 12

p(x) = 5x - 12

Answer:

(3x-15)(x+1)

Step-by-step explanation:

Given an expression in the form ax²+bx+c, where a,b and c are constants,  we can factor it by first finding the two numbers that when multiplied equal to ac and when added equal to b

The expression 3x²-12x-15 can be factored as follows:

The two numbers that can be added to give 3×(-15) and when added result to -12 are -15 and 3.

Thus, 3x²+3x-15x-15

3x(x+1)-15(x+1)

The simplified form becomes: (3x-15)(x+1)

Answer:

A

Step-by-step explanation:

3(x + 1)(x – 5)

Answer:

Hi there!

The answer is A, and C

Step-by-step explanation:

cos(-x)=cos(x)

sec(-x)=sec(x)

Answer:

A and C.

Step-by-step explanation:

Graphs that have symmetry with respect to the y-axis are called even functions. So, let's check each of the graphs:

1. As we can see in the graph attached, y=cos(x) is symmetrical with respecto to the y-axis.

2. As we can see in the graph attached, y=sin(x) is not symmetrical with respecto to the y-axis.

3. As we can see in the graph attached, y=sec(x) is symmetrical with respecto to the y-axis.

4. As we can see in the graph attached, y=csc(x) is not symmetrical with respecto to the y-axis.

Answer:

[tex]P =\frac{1}{12}[/tex]

Step-by-step explanation:

The probability is defined as the number of ways to obtain the desired result among the number of possible outcomes.

The number of possible ways to select 3 hatfields from a group of 5 hatfields is:

[tex]3C5 =\frac{5!}{3!(5-3)!} =10[/tex]

The number of ways to select 3 people from a group of 10 is:

[tex]10C3 =\frac{10!}{3!(10-3)!} =120[/tex]

Then the probability is:

[tex]P =\frac{10}{120}[/tex]

[tex]P =\frac{1}{12}[/tex]

Answer: Options 'A', 'C' and 'F' are correct.

Step-by-step explanation:

Since we have given that

Corresponding angles are those angles which takes the same corresponding position at intersection when a transversal cut the two parallel lines.

so, According to this , we get that

∠1 and ∠5

∠2 and ∠6

∠3 and ∠7

∠4 and ∠8

so, Options 'A', 'C' and 'F' are correct.

Answer:

3x - 2y = 10

Step-by-step explanation:

We are given that the sum of two numbers is 0 and twice the smaller number subtracted from 3 times the larger number is 10.

Assuming x to be the large number and y to be the smaller number we can write an equation to represent this.

Sum of two numbers is 0:

[tex]x+y=0[/tex]

Twice the smaller number subtracted from 3 times the larger number is 10:

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