What is the middle term in the simplified product for (x + 3)(x – 4)

Answer:

Option B. [tex]tan(2\theta)= -\frac{336}{527}[/tex]

Step-by-step explanation:

we know that

[tex]tan(2\theta)= \frac{sin(2\theta)}{cos(2\theta)}[/tex]

[tex]sin(2\theta)=2(sin(\theta))(cos(\theta))[/tex]

[tex]cos(2\theta)=cos^{2}(\theta)-sin^{2}(\theta)[/tex]

[tex]cos^{2}(\theta)+sin^{2}(\theta)=1[/tex]

we have

[tex]sin(\theta)=\frac{24}{25}[/tex]

step 1

Find the value of cosine of angle theta

[tex]cos^{2}(\theta)+sin^{2}(\theta)=1[/tex]

[tex]cos^{2}(\theta)+(\frac{24}{25})^=1[/tex]

[tex]cos^{2}(\theta)=1-\frac{576}{625}[/tex]

[tex]cos^{2}(\theta)=\frac{49}{625}[/tex]

[tex]cos(\theta)=\frac{7}{25}[/tex]

The value of cosine of angle theta is positive, because angle theta lie on the I Quadrant

step 2

Find [tex]sin(2\theta)[/tex]

[tex]sin(2\theta)=2(sin(\theta))(cos(\theta))[/tex]

we have

[tex]sin(\theta)=\frac{24}{25}[/tex]

[tex]cos(\theta)=\frac{7}{25}[/tex]

substitute

[tex]sin(2\theta)=2(\frac{24}{25})(\frac{7}{25})[/tex]

[tex]sin(2\theta)=\frac{336}{625}[/tex]

step 3

Find [tex]cos(2\theta)[/tex]

[tex]cos(2\theta)=cos^{2}(\theta)-sin^{2}(\theta)[/tex]

we have

[tex]sin(\theta)=\frac{24}{25}[/tex]

[tex]cos(\theta)=\frac{7}{25}[/tex]

substitute

[tex]cos(2\theta)=(\frac{7}{25})^{2}-(\frac{24}{25})^{2}[/tex]

[tex]cos(2\theta)=(\frac{49}{625})-(\frac{576}{625})[/tex]

[tex]cos(2\theta)=-\frac{527}{625}[/tex]

step 4

Find the value of [tex]tan(2\theta)[/tex]

[tex]tan(2\theta)= \frac{sin(2\theta)}{cos(2\theta)}[/tex]

we have

[tex]sin(2\theta)=\frac{336}{625}[/tex]

[tex]cos(2\theta)=-\frac{527}{625}[/tex]

substitute

[tex]tan(2\theta)= -\frac{336}{527}[/tex]

By using the Pythagorean identity and the double angle identity for tangent, it is found that the value of tan 2θ when sin θ =24/25 and 0 ≤ θ ≤ π/2 is -527/336.

In the field of Mathematics, particularly in trigonometric equations, the problem given is asking for the value of tan 2θ, given that sin θ=24/25 and 0 ≤ θ ≤ π/2.

Firstly, we can find cos θ by using the Pythagorean identity sin²θ + cos²θ = 1. This gives us cos θ = sqrt (1 - sin²θ) = sqrt (1 - (24/25)²) = 7/25.

Then, knowing that tan θ = sin θ/cos θ, we can plug in these values to get tan θ = (24/25) / (7/25) = 24/7. Finally, using the double angle identity for tan (tan 2θ = 2 tan θ / (1 - tan²θ)), we can find that tan 2θ = 2(24/7) / (1 - (24/7)²) = -527/336.

So, the exact value of tan 2θ when sin θ =24/25 and 0 ≤ θ ≤ π/2 is -527/336, which is answer option A.

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Answer:

Smallest angle = 23

Middle angle = 23 + 44 = 67

Right angle = 90

Step-by-step explanation:

Givens

Let the smallest angle = x

Let the middle angle = x + 44

Let the right angle = 90   which it always does.

All triangles = 180 degrees.

Equation

x + x + 44 + 90 = 180

Solution

2x + 44 + 90 = 180                       Combine the left

2x + 134 = 180                               Subtract 134 from both sides

2x +134-134 = 180 - 134                Combine

2x = 46                                          Divide by 2

2x/2 = 46/2                                   Do the division

x = 23

Answer:

A: Scalene - None of the sides are congruent or have the same measurements.

E: Acute - None of the triangle's angles are 90° or greater.

~

Answer:

Applying the trigonometric functions, 8/b=Tan40

b=8/Tan40

Answer:

C) 9.53 cm

Step-by-step explanation:

We know this is a right triangle, so we can use trig relations

tan A = opposite side/ adjacent side

tan 40 = 8/b

Multiply each side by b

b tan 40 = 8

Divide each side by tan 40

b tan 40 / tan 40 = 8 / tan 40

b = 8/ tan 40

b = 9.534028741

Answer:

your answer is C.$5.55

Step-by-step explanation:

NOW TAKE THE TOTAL OF BOTH,THEN WE GET

NOW DO THE DIVIDE OF 333 BY 60, THEN WE GET

Answer:

y = -4x² + 4x -3

Step-by-step explanation:

The standard form of quadratic equation is:

y = ax² + bx + c

We need to use the points given to find the value of a, b and c

We are given point (-1,-11) where x =-1 and y=-11 putting values in the above equation

y = ax² + bx + c

-11 = a(-1)² + b(-1) +c

-11 = a -b+c      eq(1)

Now putting the point(0, -3) where x =0 and y =-3

y = ax² + bx + c

-3 = a(0)² + b(0) + c

-3 = 0 + 0 + c

=> c = -3

Now Putting the point (3, -27) where x =3 and y = -27

y = ax² + bx + c

-27 = a(3)² +b(3) + c

-27 = 9a + 3b + c  eq(2)

Putting value of c= -3 in eq(2)

-27 = 9a + 3b -3  

-27 +3 = 9a +3b

-24 = 9a + 3b

=> 3(3a+b) = -24

3a + b = -24/3

3a + b = -8     eq(3)

Putting value of c= -3 in eq(1)

-11 = a -b+c

-11 = a -b -3

-11 + 3 = a - b

-8 = a - b    

=> a - b = -8   eq(4)

Now adding eq(3) and eq(4)

3a + b = -8  

a - b = -8

__________

4a = -16

a = -16/4

a = -4

Putting value of a in equation 4

a - b = -8

-4 -b = -8

-b = -8+4

-b = -4

=> b = 4

The values of a , b and c are a= -4, b =4 and c= -3

Putting these values in standard quadratic equation

y = ax² + bx + c

y = -4x² + 4x -3

Answer:

Choice number one:

[tex]\displaystyle \frac{5}{10}\cdot \frac{4}{9}[/tex].

Step-by-step explanation:

The question is asking for the possibility that event [tex]A[/tex] and [tex]B[/tex] happen at the same time. However, whether [tex]A[/tex] occurs or not will influence the probability of [tex]B[/tex]. In other words, [tex]A[/tex] and [tex]B[/tex] are not independent. The probability that both [tex]A[/tex] and [tex]B[/tex] occur needs to be found as the product of

5 out of the ten numbers are even. The probability that event [tex]A[/tex] occurs is:

[tex]\displaystyle P(A) = \frac{5}{10}[/tex].

In case A occurs, there will only be four cards with even numbers out of the nine cards that are still in the bag. The conditional probability of getting a second card with an even number on it, given that the first card is even, will be:

[tex]\displaystyle P(B|A) = \frac{4}{9}[/tex].

The probability that both [tex]A[/tex] and [tex]B[/tex] occurs will be:

[tex]\displaystyle P(A \cap B) = P(B\cap A) =  P(A) \cdot P(B|A) = \frac{5}{10}\cdot \frac{4}{9}[/tex].

Answer:

Step-by-step explanation:

0 = x2 + 3x - 10

10 = 2x+3x

10 = 5x

x = 2

0x = 5.2

0x = 10

x = 10.2 = 20

x = 20

0x = -5.-2

0x = -10

x = -10.2 = -20

x = -20

x = -5.2

x = -10

x = 5-2​

x = 3

GOOD LUCK ! ;)

Answer:

-44

Step-by-step explanation:

We have the expression

[tex]-2|6x - y|[/tex]

We need to find the value of the expression when x = -3 and y = 4

Then we must replace the variable with the number -3 and the variable y with the number 4

This is:

[tex]-2|6(-3) - (4)|[/tex]

[tex]-2|-18 - 4|[/tex]

[tex]-2|-22|[/tex]

Remember that the absolute value always results in a positive number.

So

[tex]-2|-22| = -2(22)=-44[/tex]

the answer is -44

Answer:

The correct answer is -44

Step-by-step explanation:

Points to remember

|x| = x

|-x| = x

To find the value of  –2|6x – y|

We have  –2|6x – y|  When x = -3 and y = 4

Substitute the value of x and y

–2|6x – y| =  –2|(6 * -3)  – 4|

 = -2|-18 - 4|

 = -2|-22|

 = -2 * 22

 = -44

Therefore the value of –2|6x – y|  when x = -3 and y = 4

–2|6x – y|

Answer:

the awncer would be x=0

Step-by-step explanation:

.

Answer:

Two solutions were found :

t =(16-√288)/-2=8+6√ 2 = 0.485

t =(16+√288)/-2=8-6√ 2 = -16.48

Step-by-step explanation:

Answer:

-IF THE EQUATION IS [tex]\frac{1}{t-2}=\frac{t}{8}[/tex], THEN:

[tex]t_1=4\\t_2=-2[/tex]

-IF THE EQUATION IS [tex]\frac{1}{t}-2=\frac{t}{8}[/tex], THEN:

[tex]t_1=-16.485\\t_2=0.485[/tex]

Step-by-step explanation:

-IF THE EQUATION IS [tex]\frac{1}{t-2}=\frac{t}{8}[/tex] THE PROCEDURE IS:

Multiply both sides of the equation by [tex]t-2[/tex] and by 8:

[tex](8)(t-2)(\frac{1}{t-2})=(\frac{t}{8})(8)(t-2)\\\\(8)(1)=(t)(t-2)\\\\8=t^2-2t[/tex]

Subtract 8 from both sides of the equation:

[tex]8-8=t^2-2t-8\\\\0=t^2-2t-8[/tex]

Factor the equation. Find two numbers whose sum be -2 and whose product be -8. These are -4 and 2:

[tex]0=(t-4)(t+2)[/tex]

Then:

[tex]t_1=4\\t_2=-2[/tex]

-IF THE EQUATION IS [tex]\frac{1}{t}-2=\frac{t}{8}[/tex] THE PROCEDURE IS:

Subtract [tex]\frac{1}{t}[/tex] and [tex]2[/tex]:

[tex]\frac{1}{t}-2=\frac{t}{8}\\\\\frac{1-2t}{t}=\frac{t}{8}[/tex]

Multiply both sides of the equation by [tex]t[/tex]:

[tex](t)(\frac{1-2t}{t})=(\frac{t}{8})(t)\\\\1-2t=\frac{t^2}{8}[/tex]

Multiply both sides of the equation by 8:

[tex](8)(1-2t)=(\frac{t^2}{8})(8)\\\\8-16t=t^2[/tex]

Move the [tex]16t[/tex] and 8 to the other side of the equation and apply the Quadratic formula. Then:

[tex]t^2+16t-8=0[/tex]

[tex]t=\frac{-b\±\sqrt{b^2-4ac}}{2a}\\\\t=\frac{-16\±\sqrt{16^2-4(1)(-8)}}{2(1)}\\\\t_1=-16.485\\t_2=0.485[/tex]

Answer: 8 remainder 2

Step-by-step explanation:

3 • 8 = 24

26 - 24 = 2

Your answer is 8 with a remainder of 2

Answer:

8 r2

Step-by-step explanation:

Answer:

4x+6

Step-by-step explanation:

f(x)=8x-3

g(x)=4x-9

f(x)-g(x) = 8x-3-(4x-9)=8x-3-4x+9=4x+6

The value of f(x) - g(x) is 4x+6 and The domain is all real value of x.

A function can be defined as a mathematical expression which establishes relation between a dependent variable and an independent variable.

It always comes with a defined range and domain.

It is given in the question

functions f and g

f(x) = 8x - 3; g(x) = 4x - 9

f- g = ?

The value of f(x) - g(x) = 8x -3 - (4x -9)

f(x) - g(x) = 8x -3 - 4x +9

f(x) - g(x) = 4x +6

h(x) = 4x+6

The domain is all real value of x.

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With 5 pounds of lasagna, where each serving is 1 pound, the lunch lady can make 5 servings of lasagna.

The subject of this question is simple division in Mathematics. The problem states that the lunch lady has 5 pounds of lasagna left over and each serving is 1 pound. So, to find out how many servings of lasagna can be made, we divide the total amount of lasagna (5 pounds) by the size of each serving (1 pound).

5 pounds / 1 pound per serving = 5 servings

Therefore, the lunch lady can serve 5 servings of lasagna with the amount left over.

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Answer:

All seed plants share two characteristics. They have vascular tissue and use seeds to reproduce. In addition, they all have body plans that include leaves, stems, and roots. Most seed plants live on land.

Step-by-step explanation:

All seed plants have the ability to produce seeds. Seeds contain an embryo and stored food and can withstand harsher conditions, staying dormant until conditions for growth are ideal. This trait is seen across all seed plants, which includes both gymnosperms and angiosperms.

All seed plants, also known as spermatophytes, share a key characteristic that they have the ability to produce seeds. This is a common trait and allows seed plants to reproduce. Seeds contain an embryo and stored food wrapped in a protective coat. They can withstand harsher conditions and can stay dormant until the conditions for growth are favorable. Seed plants include gymnosperms, such as conifers, and angiosperms, which are flowering plants.

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Answer: Last option.

Step-by-step explanation:

You can observe in the table provided that the values of "x" represent the time in minutes and the values of "y" represent the distance in meters.

Then, in order to find the ratio of the change in y-values to the change in x-values, you can divide any value of "y" (distance) by its corresponding value of "x" (time).

So, this is:

[tex]\frac{2,400}{2}=\frac{1,200}{1}[/tex]

Since the ratio can also be written in the form [tex]a:b[/tex], you get:

[tex]1,200:1[/tex]

Answer:

D) 1,200 meters per minute

Step-by-step explanation:

Answer:

Find the place value you want (the "rounding digit") and look at the digit just to the right of it.

If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it.

If that digit is greater than or equal to five, add one to the rounding digit and drop all digits to the right of it.

Step-by-step explanation:

Step-by-step explanation: To round a decimal, you first need to know the indicated place value position you want to round to. This means that you want to first find the digit in the rounding place which will usually be underlined.

Once you locate the digit in the rounding place, look to the left of that digit. Now, the rules of rounding tell us that if a number is less than 4, we round down but if a number is greater than or equal to 5, we round up.

I'll show an example.

Round the following decimal to the indicated place value.

0.8005

To round 0.8005 to the indicated place value position, first find the digit in the rounding place which in this case is the 0 in the thousandths place.

Next, find the digit to the right of the rounding place which in this case is 5. Since 5 is greater than or equal to 5, we round up.

This means we add 1 to the digit in the rounding place so 0 becomes 1. So we have 0.801. Now, we change all digits to the right of the rounding place to 0 so 5 changes to 0.

Finally, we can drop of any zeroes to the right of our decimal as long as they're also to the right of the rounding position.

So we can write 0.8010 as 0.801.

Image provided.

Answer:

A, D

Step-by-step explanation:

for this table:

x    0  5 10 15 20 25 30 35 40

f(x) 5  6  7  8  9    10   11  12  13

A, assuming it's supposed to say f(5)=6, is true since 5 in x corresponds to 6 in f(x)

B is false, since the domain would be the set of all numbers in x, since domain corresponds to input (x) and range corresponds to output (f(x))

C is false, the range is not all real numbers since it is a defined set of numbers

D is true, since 15 in x corresponds to 8 in f(x)

Therefore, A and D are true

To find the area you multiply the length by the width.

W = the width, and you are told the length is 5 meters longer, so the length would be (W +5)

Now multiply those together to equal 20,000 square meters:

w(w+5) = 20,000

Answer:

15625

Step-by-step explanation:

Let us consider each dial individually.

We have 25 choices for the first dial.

We then have 25 choices for the second dial.

We then have 25 choices for the third dial.

Let us consider any particular combination, the probability that combination is right is (probability the first number is right) * (probability the second number is right) * (probability the third number is right) = 1/25 * 1/25 * 1/25 = 1/15625

Therefore there are 15625 combinations

This is your answer:

if then number is $499.49 that would mean it rounds down to $499.00

but in your case $499.76 rounds to $500.00

(Remember .50 and up goes up!)

Therefor your answer is $500.00

Answer:

$499.76 rounded to the nearest dollar is $500 !!

Step-by-step explanation:

Why?

  A dollar ($1) would be in the ones column and it's asking for the nearest dollar! So you would round it by the number on the right of the dollar, the tenths.

Answer:

Initial speed:

Step-by-step explanation:

Both equations are concerned about the time differences between A and B. To avoid unknowns in the denominators,

First equation:

"A takes 3 hours more than B to walk 30 km."

[tex]x = y + 3[/tex].

[tex]x - y = 3[/tex].

When A doubles his pace, he takes only 1/2 the initial time to cover the same distance. In other words, now it takes only [tex]x/2[/tex] hours for A to walk 30 km.

Second equation:

"[A] is ahead of B by 3/2 hours [on their 30-km walk.]"

[tex]\displaystyle \frac{x}{2} + \frac{3}{2} = y[/tex].

[tex]\displaystyle \frac{1}{2}x - y = -\frac{3}{2}[/tex].

Hence the two-by-two linear system:

[tex]\left\{\begin{aligned}&x - y = 3\\&\frac{1}{2}x - y = -\frac{3}{2}\end{aligned}\right.[/tex].

Solve this system for [tex]x[/tex] and [tex]y[/tex]:

Subtract the second equation from the first:

[tex]\displaystyle \frac{1}{2}x = \frac{9}{2}[/tex].

[tex]x = 9[/tex].

[tex]y = 6[/tex].

It initially takes 9 hours for A to walk 30 kilometers. The initial speed of A will thus be:

[tex]\displaystyle v = \frac{s}{t} = \rm \frac{30\; km}{9\; h} = \frac{10}{3}\; km/h[/tex].

It takes 6 hours for B to walk 30 kilometers. The speed of B will thus be:

[tex]\displaystyle v = \frac{s}{t} = \rm \frac{30\; km}{6\; h} = 5\; km/h[/tex].

Answer:

A

Step-by-step explanation:

Linear functions go into a straight line in order

Y in set b goes from 2 to 1250 so it is traveling much faster than set A

ANSWER

{[tex]x | x \in \: R[/tex]}

EXPLANATION

From the graph, the given quadratic inequality is

[tex] {(x + 3)}^{2} \geqslant 0[/tex]

We can see that the corresponding quadratic function is a perfect square.

Since the graph opens upwards and it is always above the x-axis, any real number you plug into the inequality, the result is greater than or equal to zero.

Hence the solution set is

{[tex]x | x \in \: R[/tex]}

The correct answer is A

Answer:

Answer 64*sqrt(2)

Step-by-step explanation:

Givens

c = 128 cm

a = b = ??

formula

a^2 + b^2 = c^2                            combine the two equal legs.

2a^2 = c^2                                    Substitute 128 for c

2a^2 = 128^2                                Square

2a^2 = 16384                               Divide by 2

a^2 = 16384/2                  

a^2 = 8192                                   Factor (8192)

8192 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2    count the 2s

8192 = 2^13                                 Break 13 into 2 equal values with 1 left over

sqrt(8192) = sqrt(2^6   *   2^6    *    2^1)

sqrt(8192) = 2^6 * sqrt(2)

The length of one leg is 64*sqrt(2)

Answer:

Length of one leg of the given triangle will be 64√2 cm.

Step-by-step explanation:

Length of the hypotenuse of a 45°- 45°- 90° triangle has been given as 128 cm.

Since two angles other than 90° are of same measure so other two sides of the triangle will be same in measure.

Therefore, by Pythagoras theorem,

Hypotenuse² = Leg(1)² + Leg(2)²

Let the measure of both the legs is x cm

(128)² = 2x²

16384 = 2x²

x² = [tex]\frac{16384}{2}[/tex]

x² = 8192

x = √8192

  = 64√2 cm

Therefore, length of one leg of the given triangle will be 64√2 cm.

we know the center of the circle, and we also know a point on the circle, well, the distance from the center to a point is just the radius.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[4-(-6)]^2+[-2-7]^2}\implies r=\sqrt{(4+6)^2+(-2-7)^2} \\\\\\ r=\sqrt{10^2+(-9)^2}\implies r=\sqrt{100+81}\implies r=\sqrt{181} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-6}{ h},\stackrel{7}{ k})\qquad \qquad radius=\stackrel{\sqrt{181}}{ r}\\[2em] [x-(-6)]^2+[y-7]^2=(\sqrt{181})^2\implies (x+6)^2+(y-7)^2=181[/tex]

Answer:

Pick an answer from below.

Step-by-step explanation:

Rounded to which place?

2/7 = 0.285714285714...

Nearest tenth: 0.3

Nearest hundredth: 0.29

Nearest thousandth: 0.286

Nearest ten-thousandth: 0.2857

etc.

Answer:

0.29

Step-by-step explanation:

To convert fractions to decimals, divide the numerator by the denominator.

2/7= 0.285

Round 0.285 to 0.29

Answer:

the second one

The average speed is the ratio of the total distance traveled to the time taken

The correct option for the interval with the greatest average speed is option  (1) the first hour to the second hour

The procedure by which the above option was arrived at is as follows:

The given table of values for the graph is presented as follows;

[tex]\begin{array}{|c|cc|} \mathbf{Time}&&\mathbf{Distance}\\1&&40\\2&&110\\4&&180\\6&&230\\8&&350\\10&&390\end{array}\right][/tex]

[tex]Average \ speed = \dfrac{Distance}{Time}[/tex]

The average speed of each interval in distance per hour are given as follows;

[tex]First \ and \ second \ hour, \ average \ speed = \dfrac{110 - 40}{2 - 1} = 70[/tex]

[tex]Second \ and \ fourth \ hour, \ average \ speed = \dfrac{180 - 110}{4 - 2} = 35[/tex]

[tex]Sixth \ and \ eight \ hour, \ average \ speed = \dfrac{350 - 230}{8 - 6} = 60[/tex]

[tex]Eight \ and \ tenth \ hour, \ average \ speed = \dfrac{390 - 350}{10 - 8} = 20[/tex]

Therefore the interval in which their average speed was the greatest is the first hour to the second hour

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