Indicate in standard form the equation of the line through the given points P(0,-4), Q(5,1)

Answer: A) y = -5 cos(2x - π)

Step-by-step explanation:

[tex]\text{The standard form of a cosine equation is: y=A sin(Bx - C) + D}\\\\\bullet\text{A = amplitude}\\\\\bullet\text{Period = }\dfrac{2\pi}{B}\\\\\bullet\text{Phase Shift = }\dfrac{C}{B}\\\\\bullet\text{D = vertical shift (up if positive, down if negative)}[/tex]

In the given graph,

[tex]\implies \large\boxed{y = -5cos(2x-\pi)}[/tex]

see graph below for verification

Answer:the x intercept is (0,-7) that is number 9 and number 10 is (0,2)

Step-by-step explanation:

Answer:

x ≈ 6.7

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan40° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{8}[/tex]

Multiply both sides by 8

8 × tan40° = x, hence

x = 6.7 ( to 1 dec. place )

Answer:

theres the answer I got it right

Step-by-step explanation:

There are 12 inches in every feet and the area will be increased by 144 factors.

Feet and inches are the units of length. One inch is equal to 1/12 times the feet.

The length and the breadth are given as 11 feet and 13 feet.

The area of the bedroom is 143 square feet.

We know that 1ft = 12 in

So, The length would become 11 feet to 132 inches.

The breadth would become 13 feet to 156 inches.

The area would become

The area of the rectangle = length × Width

                                         = 132 ×  156

                                         = 20592 in .sq

The area of the bedroom increased by 144 factors.

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To find all zeros of f(x) = x^3 - 2x^2 - 4x + 8, we can use the Rational Root Theorem to test possible rational roots. The only rational root is x = 2. The complex roots can be found by dividing the equation by (x - 2) and solving the resulting quadratic equation.

To find all zeros of the equation f(x) = x^3 - 2x^2 - 4x + 8, we can use the Rational Root Theorem to test possible rational roots. By factorizing the constant term, 8, and the leading coefficient, 1, we find that the possible rational roots are ±1, ±2, ±4, ±8. By testing these values in the equation, we can find that the only rational root is x = 2. To find the complex roots, we can use polynomial long division or synthetic division to divide the original equation by (x - 2) and solve the resulting quadratic equation.

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Answer:

Part 1) The value of x is 69°

Part 2) Angle 1=64.5°

Part 3) Angle 2=84.5°

Part 4) Angle 3=31°

Part 5) Angle 4=84.5°

Part 6) Angle 5=95.5°

Part 7) Angle 6=95.5°

Part 8) Angle 7=54.5°

Part 9) Angle 8=30°

Step-by-step explanation:

Part 1) Find the value of x

we know that

arc SN+arc QS+arc QP+arc PN=360° -----> by complete circle

substitute the values

60°+x°+(x+40)°+(2x-16)°=360°

solve for x

84°+4x°=360°

4x=276°

x=69°

Part 2) Find the measure of angle 1

we know that

The inscribed angle is half that of the arc it comprises

so

m∠1=(1/2)[arc QSN]

arc QSN=arc QS+SN

arc QSN=x+60°=69°+60°=129°

substitute

m∠1=(1/2)[129°]=64.5°

Part 3) Find the measure of angle 2

we know that

The measure of the inner angle is the semi-sum of the arcs that comprise it and its opposite

m∠2=(1/2)[arc SN+arc QP]

substitute the values

m∠2=(1/2)[60°+(x+40)°]

m∠2=(1/2)[60°+(69+40)°]

m∠2=(1/2)[169°]=84.5°

Part 4) Find the measure of angle 3

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

m∠3=(1/2)[arc PN-arc SN]

substitute the values

m∠3=(1/2)[(2x-16)°-60°]

m∠3=(1/2)[(2(69)-16)°-60°]

m∠3=(1/2)[62°]=31°

Part 5) Find the measure of angle 4

we know that

m∠4=m∠2 -----> by vertical angles

so

m∠4=84.5°

Part 6) Find the measure of angle 5

we know that

m∠5+m∠2=180° -----> by supplementary angles

so

m∠5+84.5°=180°

m∠5=180°-84.5°=95.5°

Part 7) Find the measure of angle 6

we know that

m∠6=m∠5 -----> by vertical angles

so

m∠6=95.5°

Part 8) Find the measure of angle 7

we know that

The inscribed angle is half that of the arc it comprises

so

m∠7=(1/2)[arc QP]

arc QP=(x+40)°=(69+40)°=109°

substitute

m∠7=(1/2)[109°]=54.5°

Part 9) Find the measure of angle 8

we know that

The inscribed angle is half that of the arc it comprises

so

m∠8=(1/2)[arc SN]

arc SN=60°

substitute

m∠8=(1/2)[60°]=30°

The addition problem can be solved in two ways: treating each column separately without carrying and writing down the sum of each column even if it is 10 or more. Examples demonstrate each method using single-digit addition without carrying and adjusting sums that exceed single digits.

The question at hand involves solving a unique addition problem where each letter corresponds to a digit between 0 and 9. To find 2 different ways to make the addition problem work, we need to apply traditional addition rules along with the clues provided.

First, let's analyze the given examples:

To construct two solutions, let's use the same principle:

It's important to follow the instructions closely and understand that digits in these sum calculations are handled independently based on the context provided.

Answer:

[tex]1.5m+1\leq 25[/tex]

Step-by-step explanation:

Given that Miguel can use all or part of his $25 gift card to make a music purchase. Each song costs $1.50, and there is a $1.00 per account activation fee.

This activation fee is once for all and hence fixed independent of the number of songs.

Thus total amount available = 25 dollars

This should be spent for both activation fee and songs

Let number of songs = m

Total cost [tex]= 1.5m+1[/tex]

This cannot exceed 25 dollars

So the ineqality would be

[tex]1.5m+1\leq 25[/tex]

Answer:

C

Step-by-step explanation:

The right triangle on the right side of the figure has a height of 6 (two same sides lengths) and a base of 3.

x is the hypotenuse (side opposite of 90 degree angle).

We can use the pythagorean theorem to find x. The pythagorean theorem tells us to square each leg (height and base) of the triangle and add it. It should be equal to the hypotenuse square.

For this triangle it means, we square 6 and 3 and add it. It should be equal to x squared. Then we can solve. Shown below:

[tex]6^2 + 3^2 = x^2\\36 + 9 = x^2\\45 = x^2\\x=\sqrt{45}[/tex]

Now we can use property of radical  [tex]\sqrt{x}\sqrt{y}  =\sqrt{x*y}[/tex]  to simplify:

[tex]x=\sqrt{45} \\x=\sqrt{5*9} \\x=\sqrt{5} \sqrt{9} \\x=3\sqrt{5}[/tex]

Correct answer is C

Answer:

The correct answer is option C.  3√5

Step-by-step explanation:

Points to remember

For a right angled triangle

Hypotenuse ² = Base² + Height²

From the attached figure we can see a square and a right angled triangle associated with the square.

Sides of square = 6

To find the value of x

Base = 3 and height = 6

Hypotenuse  = x

x² = 3² + 6²

 = 9 + 36 = 45

x = √45 = 3√5

Therefore the  correct answer is option C.  3√5

Answer:

100 minutes?

lol

Answer:

5 minutes

Step-by-step explanation:

duh...

Answer:

Slope = 1/2

y-intercept = 30

Equation : y = 1/2x + 30

D. 150 miles

Step-by-step explanation:

We can use the two visible points you marked on the graph.

They are (0,30) which is also the y-intercept and (20,40).

Calculate change of y over change of x.

10/20 or 1/2

So the slope is 1/2 and the y-intercept is 30.

Therefore, using y = mx + b form, the equation is y = 1/2x + 30

Then, to find how many miles you drove if the cost was $105, we can plug in 105 for y in the equation.

105 = 1/2x + 30

75 = 1/2x

x = 150

To solve the given system of linear equations -3x = 42-16y and 14x = 76-16y, use the method of elimination to find the solution (20-6y, y).

To solve the system of linear equations -3x = 42-16y and 14x = 76-16y, we can use the method of substitution or elimination. Let's use the method of elimination:

Multiply the first equation by 2 to make the coefficients of y in both equations equal. The equations become:

-6x = 84-32y and 14x = 76-16y

Add the two equations together:

-6x + 14x = 84-32y + 76-16y

Simplify:

8x = 160-48y

Rearrange the equation to solve for x:

x = (160-48y)/8

Simplify further:

x = 20-6y

The solution to the system of equations is x = 20-6y. To separate the x- and y-values, we write it as (20-6y, y).

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Answer:

f(x) translated 3 units to the left and 8 units down, there is no reflection occurred

Step-by-step explanation:

* Lets revise some transformation for the functions

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new

function g(x) = f(-x)

- If the function f(x) translated horizontally to the right  

by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

by k units, then the new function g(x) = f(x) – k

* Now lets study the problem

∵ g(x) = 2(x + 3)² - 8

# x + 3 ⇒ means f(x) translated 3 units to the left

# -8 ⇒ means f(x) translated 8 units down

# There is no reflection occurred

The factored form of the given expression is 14(10c + 2 - a).

Given is an expression 140c + 28 - 14a, we need to factor it to simplify in equivalent expression.

We search for common term that can be eliminated in order to factor the expression 140c + 28 - 14a.

In this instance, we may factor the terms that share a common factor of 14 out.

The expression changes to:

140c + 28 - 14a

Let's now subtract 14:

14(10c + 2 - a)

Therefore, the expression's factored form is 14(10c + 2 - a).

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I believe the answer is 14.42

The length of AC is 14.42 in the triangle ΔABC where AB=17cm, BC=9cm and angle ∠ACB=90°. This can be obtained by using Pythagoras' theorem.

Given that, AB=17cm, BC=9cm and angle ∠ACB=90°.

By using Pythagoras' theorem,

AB² = AC²+BC²

17² = AC²+9²

AC² = 17²-9² =289-81 = 208

AC = √208 =14.42

⇒AC = 14.42cm

Hence the length of AC is 14.42 in the triangle ΔABC where AB=17cm, BC=9cm and angle ∠ACB=90°.

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Answer:

the answer is 1,194

Step-by-step explanation:

what you want to do is find the area of 2 triangles and 3 rectangles

area of 1st rectangle

1 = ae

=(22 ft) (19 ft)

=418 sq. ft.

area of 2nd rectangle

2 = ab

=(22 ft.) (14 ft.)

=308 sq. ft.

area of 3rd rectangle

3=ad

=(22 ft.) (13 ft.)

=286 sq. ft.

area of 1st triangle

Area of triangle =  1/2 cb

=1/2 (13ft) (14ft)

= 1/2 (182 sq. ft)

=91 sq. ft.

***this would be the same for 2nd triangle*** 91 sq ft.

Next add all areas together to get the total surface area

Total surface area = ae + ab + ad + 2 (1/2 cb)

= 418 sq. ft + 308 sq. ft. + 286 sq. ft. + 2(91 sq. ft)

=418 + 308 + 286 + 182

= 1,194 sq. ft.

Answer:

the sine of angle R is 5/7.

Step-by-step explanation:

Recall that the sine function is defined as sin Ф = (opposite side) / hypotenuse.

The side opposite Angle R is √65 and the hypotenuse is √91.

Thus, the sine of angle R is sin R = √65 / √91, or 5/7.

5 weeks .... 35 days

Lizzy and Don will both receive their paychecks on the same day after 70 days, as 70 is the Least Common Multiple (LCM) of their paycheck intervals of 10 and 14 days.

Lizzy and Don are trying to find out when they will both receive their paychecks on the same day again. To solve this, we need to find the Least Common Multiple (LCM) of their paycheck intervals which are 10 days for Lizzy and 14 days for Don. The LCM of 10 and 14 is the smallest number that both 10 and 14 can divide into without leaving a remainder.

Let's list the multiples of each:

Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...

Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, ...

The smallest common multiple they share is 70. This means that after 70 days, both Lizzy and Don will receive their paychecks on the same day again.

The estimate and the answer of the given real numbers are:

Estimate    Answer

[tex]\dfrac{21}{4}[/tex]                5.25

[tex]\dfrac{4}{3}[/tex]                   1.33

[tex]\dfrac{4}{1}[/tex]                     4

Multiplication of real numbers.

The multiplication of real numbers (rational or irrational) can take different forms or processes. Here, we are to multiply the following numbers.

[tex]1\frac{3}{4} \times 3[/tex]

Let us convert the mixed fraction to an improper fraction to find the estimate.

[tex]\dfrac{7}{4} \times 3[/tex]

The estimate [tex]=\dfrac{21}{4}[/tex]

The answer  [tex]\dfrac{21}{4} = 5.25[/tex]

The second question:

[tex]\dfrac{8}{9}\times 1\dfrac{1}{2}[/tex]

[tex]=\dfrac{8}{9}\times \dfrac{3}{2}[/tex]

[tex]=\dfrac{4}{3}\times \dfrac{1}{1}[/tex]

Estimate = [tex]\dfrac{4}{3}[/tex]

Answer = 1.33

The third question

[tex]3\dfrac{1}{2}\times 1\dfrac{1}{7}[/tex]

[tex]=\dfrac{7}{2}\times \dfrac{8}{7}[/tex]

[tex]=\dfrac{1}{1}\times \dfrac{4}{1}[/tex]

Estimate = [tex]\dfrac{4}{1}[/tex]

Answer = 4

x=0.12634012+

[tex]\\\pi144445618[/tex]

Answer:

A. 30

Step-by-step explanation:

The correct form is:

4sin^2 x − 1 = 0

First step is add 1 to both sides:

4sin^2 x-1+1=0+1

4sin^2 x=1

Now to eliminate 4 divide both sides by 4

4sin^2 x/4=1/4

sin^2 x=1/4

Take square root at both sides

√sin^2 x = √1/4

sinx = 1/2

Thus the correct option is 30° ....

Answer:

ok so it can either be 0.07x or 1/15x (they are equal)

(both being 1/15th of a cookie per minute)

Opel's rate of making cookie dough is determined by recognizing that she makes one batch every 15 minutes. Therefore, per minute, she can make about 0.067 batches.

In the context of this problem, we're examining Opel's productivity in creating batches of cookie dough. Specifically, Opel can make a batch of cookie dough in 15 minutes. Therefore, to find her rate per minute, we simply recognize that one task (making a batch of cookie dough) corresponds to 15 minutes. Thus, her rate is 1 batch per 15 minutes. But we want to express this in terms of batches per minute. To do this, we simply take the reciprocal of 15, which is approximately 0.067. So, Opel's rate of making cookie dough is roughly 0.067 batches per minute.

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Answer:

[tex]D=14.56[/tex]

Step-by-step explanation:

We know that the diameter of a circle is twice the radius.

Calculate the radius of the circle with the formula for calculate the distance between two points:

[tex]d=r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Where "r" is the radius.

Knowing that the center of the circle is at point (3, 1) and the circle passes through the point (1, -6), we can substitute values into the formula to find the radius:

[tex]r=\sqrt{(3-1)^2+(1-(-6))^2}=\sqrt{53}[/tex]

Then the diameter of the circle  is:

[tex]D=2r\\D=2\sqrt{53}[/tex]

[tex]D=14.56[/tex]

Answer:

[tex]y=Sin(x-\frac{\pi}{4})[/tex]

Step-by-step explanation:

The basic graph of y = Sin(x), starts at x = 0.

Looking at the graph, the basic sin curve starts at x = π/4

So this function is the parent sin function shifted π/4 units to the right.

Note:

y = Sin(x-a)  is the parent function ( y= Sinx) shifted a units right

y = Sin(x+a)  is the parent function shifted a units left

Since this function is shifted π/4 units right, the equation would be:

y = Sin (x-π/4)

The third answer choice is right.

For this case we evaluate the following inequality in the given point and verify if it is met:

[tex]2x-3y\geq  5[/tex]

[tex](x, y) = (\frac {1} {2}, \frac {1} {3})[/tex]

Substituting:

[tex]2 \frac {1} {2} -3 \frac {1} {3}\geq5[/tex]

[tex]1-1\geq 5\\0\geq 5[/tex]

It is not fulfilled!

The point does not satisfy the inequality

ANswer:

False

Answer:

False

Step-by-step explanation:

(1/2, 1/3) ⇒ x = 1/2 and y = 1/3

Substitute these values in the given equation;

   2x - 3y ≥ 5

  2(1/2) - 3(1/3) ≥ 5

   [tex]\frac{2}{2}[/tex]  -   [tex]\frac{3}{3}[/tex]

= 1 - 1 = 0

Thus the inequality is not satisfied by the given points, since 0 < 5 and ≠ 5.

It's the second option.

y = -2 sin x + 2

Tell me if I'm wrong :)

It looks spiker because my graph is more spread out with the intervals.

Answer: b) y = -2 sin x + 2

Step-by-step explanation:

The standard equation for a sine graph is: y = A sin (Bx - C) + D

[tex]\text{Amplitude (A) = }\dfrac{max-min}{2}=\dfrac{4-0}{2}=\dfrac{4}{2}=2\\\\\\\text{Vertical Shift (D) = max - amplitude = }4 - 2 = 2[/tex]

A sine graph starts at the origin and tends upward.  The given graph stars at the origin and tends downward so it is a reflection → - sin x

⇒ y = -2 sin x + 2

Answer:

4x^2−12x+9

If you have another question ask

The solution of expression is,

⇒ 4x² + 9 - 12x

We have to given that,

An expression to solve,

⇒ (2x - 3)²

Now, We can used the formula,

⇒ (a - b)² = a² + b² - 2ab

Hence, We get;

⇒ (2x - 3)² = (2x)² + 3² - 2×2x×3

                = 4x² + 9 - 12x

Therefore, The solution of expression is,

⇒ 4x² + 9 - 12x

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Answer:

[tex]x=111[/tex]

Step-by-step explanation:

Since these angles are supplementary, they add up to 180°.

Let's make an equation.

[tex]360=(x+23)+(2x+4) \\ \\ 360=x+23+2x+4 \\ \\ 360=3x+27 \\ \\ 3x=333 \\ \\ x = 111[/tex]

Answer:

[tex]x=51[/tex]

Step-by-step explanation:

We have been given an image of two intersecting lines. We are asked to find the value of x.

We can see that both angles are supplementary, so we can set an equation as:

[tex]x+23+2x+4=180[/tex]

[tex]x+2x+4+23=180[/tex]

[tex]3x+27=180[/tex]

[tex]3x+27-27=180-27[/tex]

[tex]3x=153[/tex]

[tex]\frac{3x}{3}=\frac{153}{3}[/tex]

[tex]x=51[/tex]

Therefore, the value of x is 51.

The answer is 26 miles.

Explanation:

10:30-8:00= 2:30.

10.4÷2=5.2

10.4 ×2÷ 20.8 +5.2= 26

Answer:

101

Step-by-step explanation:

3 to the fourth power is 3*3*3*3 which is 81. 4*5=20. 81+20=101

Answer: 3^4 + 4 * 5 = 101

Step-by-step explanation:

You have to use the order of operations (PEMDAS)

3^4 is an exponent, so you simplify this first

3^4 = 81

4*5 is multiplication, so you do this next

4*5 = 20

81+20 = 101