What is the measure of X?

The value of variable x is,

⇒ x = 42

We have to given that;

In a right triangle,

⇒ sin (x + 10)° = cos (4x - 4)°

Now, We can simplify as;

⇒ sin (x + 10)° = cos (4x - 4)°

⇒ cos (90 - (x + 10))° = cos (x - 4)°

⇒ 90 - (x + 10) = x - 4

⇒ 90 - x - 10 = x - 4

⇒ 80 + 4 = 2x

⇒ 2x = 84

⇒ x = 42

Thus, The value of variable x is,

⇒ x = 42

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Answer:

800700

Step-by-step explanation:

800000 + 00000 + 0000 + 000 + 00 + 0

000000 + 00000 + 0000 + 700 + 00 + 0

------------------------------------------------------------

= 800700

Answer:

Hey there!

800000+700=800700

Hope this helps :)

Answer:

d

Step-by-step explanation:

The integers in the set S: {−2, −3, −4, −5} which would make the inequality 4p − 7 ≥ 9p + 8 true are: S:{−3, −4, −5}

In order to determine which integers are true with respect to a solution of the given inequality, we would have to test the given integers by substituting their values into the inequality as follows;

For integers (-2, -3), we have:

4p − 7 ≥ 9p + 8

4(-2) − 7 ≥ 9(-2) + 8

-8 - 7 ≥ -18 + 8

-15 ≥ -10 (False).

For integers (-2, -3), we have:

4p − 7 ≥ 9p + 8

4(-3) − 7 ≥ 9(-3) + 8

-12 - 7 ≥ -27 + 8

-19 ≥ -21 (True).

For integers (-3, -4), we have:

4p − 7 ≥ 9p + 8

4(-3) − 7 ≥ 9(-3) + 8

-12 - 7 ≥ -27 + 8

-19 ≥ -21 (True).

For integers (-3, -4), we have:

4p − 7 ≥ 9p + 8

4(-4) − 7 ≥ 9(-4) + 8

-16 - 7 ≥ -36 + 8

-23 ≥ -28 (True).

For integers (-4, -5), we have:

4p − 7 ≥ 9p + 8

4(-4) − 7 ≥ 9(-4) + 8

-16 - 7 ≥ -36 + 8

-23 ≥ -28 (True).

For integers (-4, -5), we have:

4p − 7 ≥ 9p + 8

4(-5) − 7 ≥ 9(-5) + 8

-20 - 7 ≥ -45 + 8

-23 ≥ -37 (True).

Therefore, -3, -4, and -5 are integers that would make the inequality true.

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Therefore, the solutions to the equation 0 = |3x + 3| + 3 are x = -2 and x = 0.

To solve the equation 0 = |3x + 3| + 3, we need to eliminate the absolute value. Remember that the absolute value of a number is always non-negative.

First, let's isolate the absolute value term on one side of the equation:

|3x + 3| = -3

Since the absolute value cannot be negative, there are no solutions to the equation as it stands. However, if we modify the equation to make the right side positive, we can find a solution.

To eliminate the absolute value, we can rewrite the equation as two separate equations, considering both the positive and negative cases:

   3x + 3 = -3

   -(3x + 3) = -3

Solving equation 1:

3x + 3 = -3

3x = -6

x = -2

Solving equation 2:

-(3x + 3) = -3

-3x - 3 = -3

-3x = 0

x = 0

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Answer:

15

Step-by-step explanation:

multiply the 6 by 3 and get 18, so do the same for the top, so 5 x3 = 15

Recall De Morgan's Law:

In this case,

Therefore,

Hence, the required negation follows from De Morgan's Law as:

The required negation is:

(A) "We are not having pie or it is not Jessica's birthday"

(B) The given statement is:

It is not the case that "walnuts grow on lily pads or caterpillars turn into butterflies"

By using De Morgan's Law, the equivalent statement is as follows:

Walnuts don't grow on lily pads and caterpillars don't turn into butterflies

Answer:

no solution

Step-by-step explanation:

If you end up with a false equality, then the initial statement is false, meaning that there are no solutions.

Given data:

The given expression is 4s-12=5s+51.

The given expression can be written as,

4s-12=5s+51

4s-5s=51+12

-s=63

s=-63

Thus, the value of s is -63.

Answer:

Step-by-step explanation:

a) The other leg of the right triangle is ...

  b = √(10² -6²) = √64 = 8

The area of the triangle is ...

  A = 1/2bh = 1/2(6)(8) = 24

Then the height to the long side is ...

  h = 2A/c = 48/10 = 4.8

The three heights are 4.8, 6, 8.

__

b) The medians to the hypotenuse is half its length, because that is also the radius of the circumcircle: 10/2 = 5.

The medians to the legs are computed from the Pythagorean theorem:

  median to "b" = √(4² +6²) = √52 = 2√13

  median to "a" = √(3² +8²) = √73

The three medians are 5, 2√13, √73.

__

c) The angle bisectors to the legs can be found in a fashion similar to the medians, using the angle bisector theorem to locate the point of intersection on the leg.

The angle bisector to "b" divides it into segments in the ratio 6:10, so the point  of intersection is 6/(6+10)×8 = 3 units from the right angle. Then its length is ...

  bisector to "b" = √(6² +3²) = √45 = 3√5

The angle bisector to "a" divides it into segments in the ratio 8:10, so the point of intersection is 8/(8+10)×6 = 8/3 units from the right angle. Then its length is ...

  bisector to "a" = √(8² +(8/3)²) = (8/3)√10

I find it easier to compute the bisector to the hypotenuse by considering the hypotenuse to be a line with x- and y-intercepts at 8 and 6. Then its equation can be 3x+4y=24, and its intersection with the line y=x will be x = y = 24/7. The  length of the segment to that point is ...

  bisector to "c" = (24/7)√2

The three angle bisectors are (24/7)√2, 3√5, (8/3)√10.

__

d) The radius of the inscribed circle can be found from the formula ...

  r = √((s-a)(s-b)(s-c)/s) . . . .  where s is the semiperimeter = 24/2 = 12

  r = √(2×4×6/12) = 2

The hypotenuse is the diameter of the circumscribed circle, so the radius of that circle is c/2 = 5.

The radii of the incircle and circumcircle are 2 and 5, respectively.

The limit of the given function as x approaches 1 is 0.

To find the limit of the given function as x approaches 1, we need to evaluate the expression by substituting x = 1. Let's break it down step by step:

1. Begin by substituting x = 1 into the numerator:

\(\[12\sin\left(\frac{\pi}{2}\cdot 1\right)\ln(1) = 12\sin\left(\frac{\pi}{2}\right)\ln(1) = 12(1)\cdot 0 = 0\]\)

2. Now, substitute x = 1 into the denominator:

(1³ + 5)(1 - 1) = 6(0) = 0

3. Finally, divide the numerator by the denominator:

0/0

The result is an indeterminate form of 0/0, which means further analysis is required to determine the limit. To evaluate this limit, we can apply L'Hôpital's rule, which states that if we have an indeterminate form 0/0, we can take the derivative of the numerator and denominator and then evaluate the limit again. Applying L'Hôpital's rule:

4. Take the derivative of the numerator:

\(\[\frac{d}{dx}\left(12\sin\left(\frac{\pi}{2}x\right)\ln(x)\right) = 12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{x} + \frac{\sin\left(\frac{\pi}{2}x\right)\ln(x)}{x}\right)\]\)

5. Take the derivative of the denominator:

\(\[\frac{d}{dx}\left((x^3 + 5)(x - 1)\right) = \frac{d}{dx}\left(x^4 - x^3 + 5x - 5\right) = 4x^3 - 3x^2 + 5\]\)

6. Substitute x = 1 into the derivatives:

Numerator: \(\[12\left(\cos\left(\frac{\pi}{2}\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{1} + \sin\left(\frac{\pi}{2}\right) \cdot \frac{\ln(1)}{1}\right) = 0\]\)

Denominator: 4(1)³ - 3(1)² + 5 = 4 - 3 + 5 = 6

7. Now, reevaluate the limit using the derivatives:

lim as x approaches 1 of \(\[\frac{{12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{{-1}}{{x}} + \sin\left(\frac{\pi}{2}x\right) \cdot \frac{{\ln(x)}}{{x}}\right)}}{{4x^3 - 3x^2 + 5}}\]\)

= 0 / 6

= 0

Therefore, the limit of the given function as x approaches 1 is 0.

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Answer:

t = 2 and t = 3.

Step-by-step explanation:

To solve the equation 2^(2t) - 12(2^t) + 32 = 0, we can use a substitution to simplify the equation. Let's set u = 2^t:Substituting u = 2^t, the equation becomes:u^2 - 12u + 32 = 0Now we have a quadratic equation in terms of u. We can solve it by factoring or using the quadratic formula. Let's try factoring:(u - 4)(u - 8) = 0Setting each factor equal to zero, we have:u - 4 = 0 or u - 8 = 0Solving for u:u = 4 or u = 8Now, substitute back u = 2^t:For u = 4:

2^t = 4Taking the logarithm base 2 of both sides:

t = log2(4)

t = 2For u = 8:

2^t = 8Taking the logarithm base 2 of both sides:

t = log2(8)

t = 3

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:

B. The SAS Postulate

Step-by-step explanation:

In the given figure, we are shown two triangles, \(\triangle ADE\) and \(\triangle ABC\).

Since triangle ADE is inscribed in triangle ABC, both triangles must share angle \(A\). Furthermore, let's take a look at the two legs of each triangle, if we say that their respective bases are DE and BC.

Compare the corresponding legs of each triangle with proportions:

\(\frac{AC}{AE}=\frac{10}{5}=2,\\\\\frac{AB}{AD}=\frac{8}{4}=2,\\\\\overline{AC}:\overline{AE}=\overline{AB}:\overline{AD}\)

Since two corresponding legs/sides of triangle are in a constant proportion, the triangles must be similar from the SAS (Side-Angle-Side) Postulate.

Answer:

As a claustrophobia, I can ????

O 35°, 35°, 20°

Answer:

8.7 ≈ 9

Step-by-step explanation:

2πr = 55, so r = 55/(2*3.14) ≈ 8.7579...

Answer: B. 35

Step-by-step explanation: The ratio of apples to oranges is 2:5. That means for every 2 apples there will be 5 oranges.

We want to know how many total pieces of fruit will be in the basket where there are 10 apples.

Lets use the ratio to get the total number of fruits when we have 10 apples.

2:5 there is 2 apples when there is 5 oranges;

4:10 there is 4 apples when there is 10 oranges;

6:15 there is 6 apples when there is 15 oranges;

8:20 there is 8 apples when there is 20 oranges;

10:25 there is 10 apples when there is 25 oranges;

Now simply add the total amount of apples and oranges. 10 + 25 = 35 total fruit.

A function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6 then g(-13) = 20

A relation is a function if it has only One y-value for each x-value.

Given a a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45

and that g(0) = -2 and g(-9) = 6,

x=-20 then g(-20)=-5

x=-19 then g(-19)=-4

x=-18 then g(-18)=-3

x=-17 then g(-17)=-2

x=-16 then g(-16)=-1

x=-15 then g(-15)=0

x=0 then g(0)=-2

x=-9 then g(-9)=6

By observing this we can say that as x values are decreasing the function values are increasing and vice versa

So option D is correct

Hence, a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6 then g(-13) = 20

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Answer:

The series is convergent

Sum = 30

Step-by-step explanation:

Given the geometric series 3 + 2.7 + 2.43 + 2.187 + ..., to determine whether the geometric series is convergent or divergent, we need to check the value of its common ratio. A geometric series is tested for convergence or divergence based on the value of its common ratio.

If |r|< 1, the series is convergent

if |r|≥ 1, the series is divergent.

r is the common ratio

From the series given, the common ratio r = 2.7/3 = 2.43/2.7 = 2.187/2.43 = 0.9

since r = 0.9 which is less than 1, then the series is convergent.

Since the geometric series is tending to infinity, we will use the formula for calculating the sum to infinity of a geometric series to find its sum.

S∞ = a/1-r

a is the first term = 3

r is the common ratio = 0.9

S∞ = 3/1-0.9

S∞ = 3/0.1

S∞ = 30

The sum of the geometric series is 30

Answer:

Positive: 7-(-4) and -10+12

Negative -3+(-2) and 5-8

Step-by-step explanation:

Addition and subtraction rules:

2 negatives make a positive

A bigger positive number added to a smaller negative number is positive

A negative plus a negative is a negative.

Answer:

I'm terrible at explaining so here is a screenshot

                                                                                 -ripper

Step-by-step explanation:

well, let's notice that A F, B G and C E all converge at point D, without much fuss, that simply means they're all medians, because all medians in a triangle meet at the centroid.

The length of segment AC is 2.96 units

From the question, the given parameters are

Line segment AB = 7 units

Angle A = 65 degrees

The line segment AC can be calculated using the following cosine ratio

cos(Angle) = Adjacent/Hypotenuse

Where

Adjacent = Side length AC

Hypotenuse = Side length AB

So, we have

cos(65) = AC/AB

This gives

cos(65) = AC/7

Make AC the subject

AC =7 * cos(65)

Evaluate

AC = 2.96

Hence, the side length AC has a value of 2.96 units

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Answer:

breathe in

Step-by-step explanation:

Answer:

Addition = 3656999

Step-by-step explanation:

Predecessor of number = (Number - 1)

Predecessor of 365000 = 365000 - 1

                                         = 364999

Successor of a number = (Number + 1)

Successor of 3291999 = 3291999 + 1

                                      = 3292000

Now we have have to add the predecessor of 365000 and successor of 3291999,

364999 + 3292000 = 3656999

In other words addition of predecessor of any number and successor of other number will be same as the sum of both the numbers.

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 41 and 15 is 1

Divide both the numerator and denominator by the GCD

41 ÷ 1

15 ÷ 1

Reduced fraction:

41

15

Therefore, 41/15 simplified to lowest terms is 41/15.

Answer:

42

Step-by-step explanation:

Shanice =88

If greg won x pieces of gum, and 88 was 4 more than twice as many as Greg

2x+4=88

2x=84

x=42

Answer: 70  

Step-by-step explanation:

First you multiply 17x8 then you subtract it by 64 then you divide it by 2 please double check  with a parent to make su