3 sin^{2} x +cos 2x= (5/4)
answer in radians

Answer:

C. 3x

Step-by-step explanation:

The first two choices give 1 solution each.

The last choice gives an infinite number of solutions.

Choice C. gives no solution.

3x + 9 = 3x

Subtract 3x from both sides.

9 = 0

Since 9 = 0 is false, equation 3x + 9 = 3x has no solution.

The expression can be written in the box on the other side of the equation as C. 3x.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The given expression is

3x + 9 = _

Subtract 3x from both sides;

9 = 0

Since 9 = 0 is false,

The equation 3x + 9 = 3x has no solution.

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Answer:

True options: 1, 2 and 5

Step-by-step explanation:

From the given diagram, you can see that the center of the hyperbola is placed at the origin, so first option is true (see attached diagram for definition of center, vertices, foci, i.e.)

There are two vertices of the hyperbola, they are placed at (-6,0) and (6,0), so second option is true.

The transverse axis is the segment connecting vertices, this segment is horizontal, so option 3 is false.

The foci are not placed within the rectangular reference box, so this option is false.

The directrices are vertical lines with equations [tex]x=\pm \dfrac{a}{e}[/tex], so this option is true.

Answer:1 2 5

Step-by-step explanation:

A. [tex]\sqrt{3}[/tex]

In the  Geometry, the triangle is a 3-sided polygon that consists of 3 edges and 3 vertices. The most important property of the triangle is that the sum of the internal angles of the triangle is = to 180 degrees. its property is known as angle sum property of triangle.

We have been given the image of the right triangle and we are asked to find the value of the tan(60) for our given triangle

from we know that tangent represents the relation between opposite or adjacent of the right triangle.

[tex]tan = \frac{opposite}{adjacent}[/tex]

We can see that our adjacent side is not given, but corresponding angle to adjacent side is given that is 30 degrees. So we could conclude that our given triangle is 30-60-90 triangle.

from the sides corresponding to 30-60-90 triangle equals to[tex]x,x\sqrt{3}[/tex] and [tex]2x[/tex] , so the adjacent side for our given triangle will be,

[tex]x\sqrt{3} =8 \sqrt{3\\\\\\[/tex]

[tex]\frac{x \sqrt{3} }{\sqrt{3} } =\frac{8\sqrt{3} }{\sqrt{3} }[/tex]

[tex]x=8[/tex]

Upon substituting these values on above formula we will get,

[tex]tan( 60^{0} ) = \frac{8\sqrt{3} }{8} \\tan( 60^{0})=\sqrt{3}[/tex]

hence, the value of tan(60) is  [tex]\sqrt{3}[/tex]and option B is the correct choice.

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B im pretty sure its B

Answer:

Step-by-step explanation:

Notice that the paragraph is describing some results they got of a recent survey. That is, they are giving specific statistical data about what people prefer.

So, this is an example of descriptive statistics. Remember that descriptive statistics is about using means, medians, standard deviation, percentages or any other stats that help to describe a phenomenom.

Therefore, the right answer is D.

Answer:

This is an odd question...

The couple should find out the following:

1.) is the agency legitimate?

2.) Will they be doing a hard inquiry on our credit history? if so, this could affect our current credit score

3.) Will they charge me to review my current credit reports?

Three things that should be considered about a credit agency are : Credibility and Reliability, Financial Efficiency, Accreditation and Acclamation

Given - The couple are facing debt issues. They need a credit counselling agency.

While choosing an agency, they should be careful about the following aspects of respective agency.

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[tex]4x^2 + 8x - 32 = 0\\x^2+2x-8=0\\x^2+2x+1-9=0\\(x+1)^2=9\\x+1=3 \vee x+1=-3\\x=2 \vee x=-4[/tex]

For this case we must solve the following expression by completing squares:

[tex]4x ^ 2 + 8x-32 = 0[/tex]

We divide between 4 on both sides of the equation:

[tex]x ^ 2 + 2x-8 = 0[/tex]

We add 8 to both sides of the equation:

[tex]x ^ 2 + 2x = 8[/tex]

We divide the middle term between 2 and square, this we add to both sides of the equation:

[tex]x ^ 2 + 2x + (\frac {2} {2}) ^ 2 = 8 + (\frac {2} {2}) ^ 2\\x ^ 2 + 2x + 1 ^ 2 = 8 + 1\\x ^ 2 + 2x + 1 ^ 2 = 9\\(x + 1) ^ 2 = 9[/tex]

We apply root to both sides:

[tex]x + 1 =\pm \sqrt {9}[/tex]

We have two roots:

[tex]x_ {1} = \sqrt {9} -1 = 3-1 = 2\\x_ {2} = - \sqrt {9} -1 = -3-1 = -4[/tex]

Answer:

[tex]x_ {1} = 2\\x_ {2} = - 4[/tex]

Answer:

Step-by-step explanation:

This is a way of asking you what the highest common factor is. So factor into primes and find the highest that is between them.

48: 2 * 2 * 2 * 2 * 3

60: 2 * 2 * 3 * 5

The answer is Bolded and underlined.

HCF: 2 * 2 * 3

HCF: 12

The greatest number that could be in a pack is 12

Answer:

- 1

Step-by-step explanation:

The average rate of change of f(x) in the close interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [ - 4, 1 ]

From the graph

f(b) = f(1) = - 1

f(a) = f(- 4) = 4

average rate of change = [tex]\frac{-1-4}{1-(-4)}[/tex] = [tex]\frac{-5}{5}[/tex] = - 1

Answer:

The correct answer option is B. (x - 1).

Step-by-step explanation:

We are to determine the factor of the polynomial function [tex]f(x)[/tex] which is graphed on the given coordinate plane.

We know that if the zeros (or intercepts) of an equation are [tex] r _ 1 [/tex] and [tex] r _ 2 [/tex] then the factors for this equation will be [tex] ( x - r _ 1 ) [/tex] and [tex]( x - r _ 2 ) [/tex].

From the graph, we can see that it intercepts the x axis at [tex]1[/tex] and [tex]6[/tex]. So the roots will be [tex](x-1)[/tex] and [tex](x-6)[/tex].

Therefore, the correct answer option is B. (x - 1).

Answer: SECOND OPTION.

Step-by-step explanation:

We can verify each option by making eac equal to zero and solving for "x":

First option

[tex]x-3=0\\x=0+3\\x=3[/tex]

The first option is not a factor of the polynomial function, because the parabola does not intersect the x-axis at [tex]x=3[/tex].

Second option

[tex]x-1=0\\x=0+1\\x=1[/tex]

The second option is a factor of the polynomial function, because the parabola intersects the x-axis at [tex]x=1[/tex].

Third option

[tex]x+1=0\\x=0-1\\x=-1[/tex]

The third option is not a factor of the polynomial function, because the parabola does not intersect the x-axis at [tex]x=-1[/tex].

Fourth option

[tex]x+3=0\\x=0-3\\x=-3[/tex]

The fourth option is not a factor of the polynomial function, because the parabola does not intersect the x-axis at [tex]x=-3[/tex].

slope of DE would be [tex]\( m_{DE} = \frac{(2c - b)}{(0 - (-a))} = \frac{(2c - b)}{a} \).[/tex]

slope of FG would be[tex]\( m_{FG} = \frac{(0 - c)}{(0 - (a+b))} = \frac{-c}{-(a+b)} = \frac{c}{a+b} \).[/tex]

To find the slope of line segments DE and FG from a trapezoid on a coordinate plane, we can follow these steps:

1. Identify the Coordinates of Endpoints:

  - For DE, identify coordinates D and E.

  - For FG, identify coordinates F and G.

2. Use the Slope Formula:

  - The slope  m  of a line passing through two points [tex]\( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m = \frac{(y_2 - y_1)}{(x_2 - x_1)} \).[/tex]

3. Calculate the Slope for DE:

  - Plug the coordinates of D and E into the slope formula.

4. Calculate the Slope for FG:

  - Plug the coordinates of F and G into the slope formula.

Given the coordinates in the image, let's calculate the slopes for DE and FG:

For DE:

- Let's say D has coordinates  (-a, b)  and E has coordinates (0, 2c)

- The slope of DE would be [tex]\( m_{DE} = \frac{(2c - b)}{(0 - (-a))} = \frac{(2c - b)}{a} \).[/tex]

For FG:

- Let's say F has coordinates[tex]\( (a+b, c) \)[/tex] and G has coordinates  (0, 0) .

- The slope of FG would be[tex]\( m_{FG} = \frac{(0 - c)}{(0 - (a+b))} = \frac{-c}{-(a+b)} = \frac{c}{a+b} \).[/tex]

Answer:

The probability that the student scored an A is : 0.778

Step-by-step explanation:

There are 55% boys and 45% girls

So, No of boys is: 55/100

No of girls is: 45/100

So, total no of girls are: 45

Since 35% of the girls scored A on test

No of girls who scored A on test = 35

The probability that the student scored an A is: 35/45

The probability that the student scored an A is : 0.778

Answer:

[tex]P(A | B)=\frac{7}{9}=0.778[/tex]

Step-by-step explanation:

Let's call B the event that consists of the selected student being a girl

Call A to the event in which the selected student obtained an A.

Then we look for the probability that A will occur given that B. That is, we look for P(A | B)

This is a conditional probability and is calculated using the following formula

[tex]P(A | B)=\frac{P(A\ and\ B)}{P(B)}[/tex]

In this case

[tex]P(B)=0.45\\P(A\ and\ B)=0.35[/tex]

So

[tex]P(A | B)=\frac{0.35}{0.45}[/tex]

[tex]P(A | B)=\frac{7}{9}=0.778[/tex]

let's firstly convert the mixed fractions to improper fractions and then divide.

[tex]\bf \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{3\frac{4}{5}}\implies \cfrac{3\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{19}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{4}\div\cfrac{19}{5}\implies \cfrac{5}{4}\cdot \cfrac{5}{19}\implies \cfrac{25}{76}[/tex]

Answer:

1/3

Step-by-step explanation:

covert the mixed number to an improper fraction

1x4+1 / 4

any expression multiplied by 1 remains the same

4+1 / 4

Add the numbers

5 / 4

Dividing is equivalent to multiplying with the reciprocal value

5 / 4 x 1 / 3 x 4 / 5

reduce the numbers with greatest common divisor 5

1 / 4 x 1 / 3 x 4

reduce the numbers with greatest common divisor 4

1 /3

Answer:

4/20

Step-by-step explanation:

20 %

Percent means out of 100

20/100

Divide top and bottom by 10

2/10

We want the denominator to be 20 so multiply the top and bottom by 2

4/20

For this case we must find a fraction equivalent to 20%

We have to:

[tex]\frac {1} {20} =[/tex] 0.05 * 100% = 5%

[tex]\frac {2} {20} =[/tex] 0.1 * 100% = 10%

[tex]\frac {4} {20} =[/tex] 0.2 * 100% = 20%

[tex]\frac {5} {20} =[/tex] 0.25 * 100% = 25%

Answer:

[tex]\frac {4} {20}[/tex]

Option C

Answer:

Step-by-step explanation:

Acceleration due to gravity is the rate at which an object changes its velocity due to the force of gravity.On Earth, the average acceleration due to gravity is -9.81 m/s².The acceleration due to gravity is ALWAYS negative.  Any object affected only by gravity (a projectile or an object in free fall) has an acceleration of -9.81 m/s², regardless of the direction.

The acceleration is negative when going up because the speed is decreasing.  The acceleration is negative when going down because it is moving in the negative direction, down.  Even at the top of the path where the instantaneous speed is 0 m/s, the acceleration is still -9.81 m/s². ...

Angle 6, an acute angle, measures below 90 degrees, reflecting a sharp inclination. Angle 4, a right angle at precisely 90 degrees.

In the geometric configuration, Angle 6 is characterized as an acute angle, signifying that its measure falls between 0 and 90 degrees. Acute angles are typically associated with sharp inclinations, emphasizing a compact angular span. On the other hand, Angle 4 is identified as a right angle, precisely measuring 90 degrees.

Right angles are distinctive for their perpendicular alignment, forming the cornerstone of rectangular shapes and providing structural stability. The significance of Angle 4 lies in its pivotal role in defining perpendicularity within geometric constructs.

This geometric interplay showcases the diversity of angles, with acute angles like Angle 6 emphasizing sharpness and right angles like Angle 4 embodying orthogonality, contributing to the intricacies and precision inherent in geometric relationships.

Answer:

y = -x - 3

Step-by-step explanation:

Plug in -1 for x and your result will come out to 1 because of that double negative [-(-1) = 1]. Next, deduct 3 from 1 to get -2.

I am joyous to assist you anytime.

Answer:

n=4

Step-by-step explanation:

To solve combine your like terms.

You can start by adding 0.8 to both sides and subtracting 0.7n from both sides.

[tex]-0.8+1.4n=2+0.7n\\1.4n=2.8+0.7n\\0.7n=2.8[/tex]

Next, divide both sides by 0.7 to isolate for n.

[tex]0.7n=2.8\\n=4[/tex]

Answer:

52

Step-by-step explanation:

2 kg is the same as 2000 g.

2000 g / 38 g = 52.6

There will be 52 bags (with some cinnamon left over).

ok i think your answer will be from least to greatest it would be this 3 1/5, 3.1, 3.5, 4.2

Hope i helped let me know if i got it right if not i am very sorry.

The order of four line segments from least to greatest is 3.1, 3.2, 3.5, 4.2  or 3.1. 3 1/5, 3.5, 4.2.

A number is a mathematical entity that can be used to count, measure, or name things. For an example, 1, 2, 56, 2.6, 34 etc. are the numbers.

We have:

The lengths in centimetres of four line segments are:

3.1, 3.5, 3 1/5, 4.2

We can write 3 whole 1/5 as 16/5 or 3.2

3 1/5  = 3.2

3.1, 3.5, 3.2, 4.2

Order from least to greatest:

3.1, 3.2, 3.5, 4.2   or

3.1. 3 1/5, 3.5, 4.2

Thus, the order of four line segments from least to greatest is 3.1, 3.2, 3.5, 4.2  or 3.1. 3 1/5, 3.5, 4.2.

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Answer:

3/4

Step-by-step explanation:

3/14 ÷ 2⁄7

Copy dot flip

3/14 * 7/2

We rewrite

3/2 * 7/14

Canceling a 7 from 7 and 14

3/2 * 1/2

Multiplying straight across

3*1 =3

2*2=4

3/4

For this case we must solve the following expression:

[tex]\frac {\frac {3} {14}} {\frac {2} {7}} =[/tex]

Applying double C we have:

[tex]\frac {3 * 7} {14 * 2} =\\\frac {21} {28} =[/tex]

for simplify we divide the numerator and denominator by 7, then we have:

[tex]\frac {\frac {21} {7}} {\frac {28} {7}} =\\\frac {3} {4}[/tex]

In decimal form we have to:

[tex]\frac {3} {4} = 0.75[/tex]

Answer:

[tex]\frac {3} {4} = 0.75[/tex]

Answer:

Step-by-step explanation:

Answer:

Answer is 1.98

You're welcome.

Answer:

The exact distance is √(29) or 29^(1/2)

Step-by-step explanation:

Find the answer using the distance formula (aka the Pythagorean theorem)

d=√(x1+x2)^2+(y1+y2)^2)

d=√(-1+6)^2+(4+-2)^2), Solve for d:

d= √((25)+(4))

d=√(29)

Answer:

[tex]\sqrt{35}[/tex]

Step-by-step explanation:

To calculate the distance (d) use the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (6, - 2)

d = [tex]\sqrt{(6+1)^2+(-2-4)^2}[/tex]

  = [tex]\sqrt{7^2+(-6)^2}[/tex]

  = [tex]\sqrt{49+36}[/tex] = [tex]\sqrt{85}[/tex] ← exact value

Answer: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.

Step-by-step explanation:

1 x 1 = 1

2 x 2 = 4

3 x 3 = 9

4 x 4 = 16

5 x 5 = 25

6 x 6 = 36

7 x 7 =49

8 x 8 = 64

9 x 9 = 81

10 x 10 = 100

11 x 11 = 121

12 x 12 = 144

13 x 13 = 169

14 x 14 = 196

15 x 15 = 225

Answer:

B

Step-by-step explanation:

let's recall that

1² = 1

1⁴ = 1

1¹⁰⁰⁰⁰⁰⁰⁰⁰⁰ = 1

[tex]\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) \\\\ a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^{12}y^{18}+1\implies x^{4\cdot 3}y^{6\cdot 3}+1^3\implies (x^4)^3(y^6)^3+1^3\implies (x^4y^6)^3+1^3 \\[2em] [x^4y^6+1][(x^4y^6)^2-(x^4y^6)(1)+1^2]\implies (x^4y^6+1)(x^8y^{12}-x^4y^6+1)[/tex]

Answer:

[tex]x=4.459[/tex]

Step-by-step explanation:

We have the following equation

[tex]2^{(x-1)} =11[/tex]

To solve the function, apply the equation [tex]log_2[/tex] on both sides of the equation

[tex]log_2(2^{(x-1)}) =log_2(11)[/tex]

Remember that

[tex]log_b(b)^x =x[/tex]

So

[tex](x-1) =log_2(11)[/tex]

[tex]x =log_2(11) + 1[/tex]

Finally

[tex]x=4.459[/tex]

Answer:

x = 4.46

Step-by-step explanation:

We are to solve the following expression:

[tex]2^{(x-1)}=11[/tex]

Taking the natural logarithm of both sides of the equation to remove the variable from the exponent. to get:

[tex] ln ( 2 ^ { x - 1 } ) = l n ( 1 1 ) [/tex]

[tex] ( x - 1 ) l n ( 2 ) = l n ( 1 1 ) [/tex]

Applying the distributive property:

[tex]xln(2)-1ln(2)=ln(11)[/tex]

Solving for x to get:

[tex]x=\frac{ln(11)}{ln(2)} +1[/tex]

x = 4.46

Answer:

The equation is y= 2x+5

Step-by-step explanation:

Lets find the slope of the line through the points (-2,1) and (-4,-3).

where x1 = -2,  y1= 1,  x2= -4,  y2 = -3.

Now apply slope formula:

m= y2-y1/ x2-x1

m= -3-1/-4-(-2)

m = -4/-4+2

m= -4/-2

Divide the term by 2:

m = 2

Now we will apply point slope formula:

y-y1 = m (x-x1)

Now substitute the values in the formula:

y-1=2(x-(-2))

y-1 =2(x+2)

y-1=2x+4

Now combine the constants:

y= 2x+4+1

y=2x+5

So the equation is y= 2x+5 ....

Answer:

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

Step-by-step explanation:

There are 4 steps to complete to go from 0 to 1. Hence each step is:

1 out of 4, or simply  [tex]\frac{1}{4}[/tex]

F is located at the 3rd mark, which will be  [tex]\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{3}{4}[/tex]

Hence, F is located at  [tex]\frac{3}{4}[/tex]

Answer:

F is on [tex]\frac{3}{4}[/tex] on the number line

Step-by-step explanation:

Notice in the image that between 0 and 1 there are 4 subdivisions.

Then divide.

[tex]\frac{1}{4} = 0.25[/tex].

Each subdivision is equal to 0.25 units.

Point F is in the third subdivision.

This means that the distance between 0 and F is:

[tex]\frac{1}{4}*3 = \frac{3}{4} = 0.75[/tex].

Finally F is on [tex]\frac{3}{4}[/tex] on the number line

Answer:

168°

Step-by-step explanation:

∠QRS is an angle formed by 2 chords of the circle and is half the measure of its intercepted arc QS, that is

m QS = 2 × 84° = 168°

Applying the inscribed angle theorem, the measure of arc QS is: 168°.

According to the inscribed angle theorem, the measure of an inscribed angle in a circle equals half of the measure of the intercepted arc.

Based on the inscribed angle theorem,

arc QS = 2(m∠QRS)

arc QS = 2(84)

arc QS = 168°

Therefore, applying the inscribed angle theorem, the measure of arc QS is: 168°.

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Answer:

hello : answer: A

Step-by-step explanation:

a(1) = –10 and a(n) = 4a(n– 1) + 7, if n ≥ 2.

n=2 : a(2)=4a(1)+7        a(2) =4(-10)+7 = -33

n=3 : a(2)=4a(2)+7        a(3) =4(-33)+7 = -125

n=4 : a(2)=4a(3)+7        a(4) =4(-125)+7 = -493

n=5 : a(2)=4a(4)+7        a(5) =4(-493)+7 = -1965

n=6 : a(2)=4a(5)+7        a(6) =4(-1965)+7 = -7853

Answer:

[tex]\$19,710[/tex]

Step-by-step explanation:

step 1

Find the volume of the composite figure

The volume of the composite figure is equal to the volume of the cube plus the volume of the square prism

so

[tex]V=15^{3}+15^{2}(45)[/tex]

[tex]V=13,500\ cm ^{3}[/tex]

step 2

Find the value of the figure

Multiply the volume by $1.46 per cubic centimeter

[tex]13,500(1.46)=\$19,710[/tex]