Work out the angle of X

The measure of the third angle in an isosceles triangle can be expressed using the expression of option c. 180° - 2(65°).

In an isosceles triangle,

Measure of the base angles is equal to 65°.

Let us consider the measure of the third angle in an isosceles triangle is equal to x degrees.

The two base angles are congruent.

Since each base angle measures 65°, the sum of the base angles is.

65° + 65° = 130°

The sum of the angles in any triangle is 180°.

This implies,

The measure of the third angle in the isosceles triangle is equal to,

x° + 130° = 180°

⇒ x° = 180° - 130°

⇒ x° = 50°

Therefore, the correct expression to calculate the measure of the third angle in an isosceles triangle is option (c) 180° - 2(65°).

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The above question is incomplete, the complete question is:

In an isosceles triangle, the base angles measure 65°. Which of the following expressions is a way to calculate the measure of the third angle?​

a. 180° - 65°

b. 180°+ 65°

c. 180° - 2(65°)

d. 180° + 2( 65°)

Answer:

C. Points have no size and no dimensions.

Answer:

I think it is choice A and choice C

Answer:

The answer is

x= -2

y= -8

Step-by-step explanation:

x=y+6

substitute into equation 1

13(y+6)-6y=22

13y+78-6y=22

13y-6y=22-78

7y=-56

divide both sides by 7

7y/7= -56/7

y= -8

x=y+6

x= -8+6

x= -2

Answer:

14

Step-by-step explanation:

l = length, w = width, h = height.

The surface area of a rectangular prism is:

2lw + 2wh + 2lh.

If the total surface area is 1648, your equation will be:

2lw + 2wh + 2lh = 1648.

lw + wh + lh = 824.

Plug in your width and height values.

16l + 16*20 + 20l = 824.

36l = 504.

Length = 14.

[tex]\boxed{\sf l=14(in)}.[/tex]

[tex]\sf SA=2(wl+hl+hw)[/tex]

Surface area (SA)= 1,648 inches;

Width (w)= 16 inches;

Height (h)= 20 inches.

[tex]\sf 1648(in)=2((16(in))l+(20(in))l+(20(in))(16(in)))[/tex]

Let's remove the units for these steps to make the algebra a little bit easier to understand.

[tex]\sf 1648=2(16l+20l+320)\\ \\1648=2(36l+320)[/tex]

Here, we apply the distributive property of multiplication. Check attached image 1.

[tex]\sf 1648=(2)(36l)+(2)(320)\\\\1648=72l+640[/tex]

[tex]\sf 1648-640=72l+640-640\\ \\1008=72l\\ \\72l= 1008[/tex]

[tex]\sf \dfrac{72l}{72} = \dfrac{1008}{72} \\ \\\\ \boxed{\sf l=14(in)}.[/tex]

If you want to verify this answer simply take the surface area formula for rectangular prisms and calculate the value for the SA using these values of lengh, width and height:

[tex]\sf SA=2((16)(14)+(20)(14)+(20)(16))=\boxed{\sf 1648}. That's\,correct![/tex]

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Answer:  if with 3.14 v= 37512.5333

if with pi v= 37531.56

Step-by-step explanation:

the formula is 1/3hπr^2

r= 2d so radius is 32

plus numbers in (square it multiple times pi or 3.14 then multiply times height and divide by 3)

To perform this and any other construction in math, you need to use the right tools which include a compass, your drawing board or paper, and a clear understanding of the instruction.

A key to getting the shape and angles of any construction includes knowing what is required of you and implementing these in your construction. In the second slide, you are told to use the segment tool to create segment AB. This tool will be a scale and the measurement will be that of a  line AB.

Next, identify the radius of the circle. This is the point from the center of the circle to any line on the circle. Understanding the instructions is key to bisecting the segment and completing the other activities.

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Callie can make 5 necklaces.

So to convert from a value in inches to one in yards, we need to divide by 36. To convert a value in yards to inches, we need to multiply by 36.

Now, She has a pieces of leather cord that has a length of 4 yards.

Each necklace will have a length of 28 inches.

We have to determine the how many necklaces can Callie make?

We know that :

1 yard= 36 inches

So, Multiply by 36 into 4 yards

4 yards= 36x4= 144

Length of leather cord is 4 yards

144/4 = 5.14

Callie can make 5 necklaces.

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Sides AB = 3√2 and BC = 6.

The given triangle ABC is a right-angled triangle, as ∠BAC = 90°.

In the given right triangle ABC,

Hypotenuse of the triangle = BC

Base and height = AC and AB.

Also, we see from the diagram that ∠ACB and ∠ABC are equal.

∴ Triangle ABC is isosceles, with sides AC = AB = 3√2.

Now, by Pythagoras' theorem,

Hypotenuse² = Base² + Height²

Or, BC² = AC² + AB²

Or, BC² = (3√2)² + (3√2)²

⇒ BC² = 36

Or, BC = 6

Hence, sides AB = 3√2 and BC = 6.

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Answer:A,D

Step-by-step explanation:

y = [5.3, 27]

x= [-1,3]

Evaluating the exponential decay we can see that 200 years, there will be 47.43 pounds left of the material.

A general exponential decay is:

f(x) = A*(b)^x

Where A is the initial value, b is the rate of decay, x is the variable.

We know that we start with 68 pounds, and after 40 years there are 63.3 pounds left, so we have an exponential decay:

63.3 = 68*(b)^40

Where b defines how it decays, we can solve that equation for b to get:

(63.3/68)^(1/40) = b

0.9982 = b

Then the decay is:

f(x) = 68*(0.9982)^x

The amount left after 200 years will be:

f(200) = 68*(0.9982)^200 = 47.43

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Answer:

Do whatever you want, but paying attention would really help you.

Step-by-step explanation:

If you find yourself bored in class, consider the following options to make the most of your time and stay engaged:

1. Actively participate: Ask questions, contribute to discussions, and try to engage with the material. Active participation can make the class more interesting and help you retain the information better.

2. Take notes: Focus on taking detailed notes, even if you think you understand the material. This will help you stay engaged and make it easier to review the content later.

3. Find connections: Try to relate the class material to your interests or real-world applications. This can make the content more engaging and relevant.

4. Set learning goals: Set specific learning objectives for each class, and try to achieve them during the session. This can help you stay focused and motivated.

5. Practice active listening: Pay attention to the teacher and try to understand the main points they are making. This can help you stay focused and better comprehend the material.

6. Break down the material: Divide the content into smaller chunks and focus on understanding each part. This can make the material more manageable and engaging.

7. Speak with your teacher: If you're consistently bored in class, consider discussing your concerns with your teacher. They may be able to offer suggestions or modify their teaching approach to better suit your learning style.

Remember, it's essential to stay engaged in class to maximize your learning experience and make the most of your education.

Answer:

watch RUN BTS EPISODE simple

Answer: The correct answer is (5, 11π/6). or C

Step-by-step explanation:

The polar coordinates of the point (x, y) = (5√3/2, -5/2) are (r, θ) = (5, 11π/6).

Explanation:

Using the formulas for converting Cartesian coordinates to polar coordinates:

r = √(x^2 + y^2)

θ = atan2(y, x)

Plugging in the given values:

r = √((5√3/2)^2 + (-5/2)^2)

= √(75/4 + 25/4)

= √(100/4)

= 5

θ = atan2(-5/2, 5√3/2)

≈ 11π/6 radians

So, the correct polar coordinates of the point (5√3/2, -5/2) are (r, θ) = (5, 11π/6).

Answer:

the corresponding sides are proportional

The correct inequality to represent the normal temperature range of a dog is |t − 101.8| ≤ 0.7. So, correct option is B.

Here, |t - 101.8| represents the absolute value of the difference between the body temperature of the dog (t) and the average temperature of dogs (101.8° F). The inequality states that this absolute value must be less than or equal to 0.7° F, which is the maximum amount that the temperature of a dog can vary from the average.

If the temperature of a dog is within this range, it is considered to have a normal body temperature. If the temperature is outside this range, it may indicate an underlying health issue or illness.

The other answer choices are incorrect because they do not accurately represent the relationship between the body temperature of a dog and the normal temperature range. For example, |t - 0.7| ≥ 101.8 makes no sense in the context of the problem, as there is no logical reason to subtract 0.7 from the body temperature.

So, correct option is B.

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Answer: The correct answer is B

Step-by-step explanation:

Remember that the coordinates (4,π3) tell us the radius r=4 and the angle θ=π3. So the point should be on the circle labeled 4 and form an angle of π3 with the positive x-axis. Point B is the correct point

The approximate solution to the trigonometric inequality tan(x/4) < 1/5 over the interval 0 <= x <= 2π radians is 0 <= x <= 0.75. Option 1 is correct.

To solve the trigonometric inequality tan(x/4) < 1/5 over the interval 0 <= x <= 2π radians, we can use a graphing calculator and follow these steps:

Using this method, we can see that the two graphs intersect at approximately x = 0.75, x = 4.6, and x = 8.4 (or their equivalents within the interval 0 <= x <= 2π). We can also see that the tan(x/4) function is less than 1/5 between the first two intersection points (0 <= x <= 0.75 and 4.6 <= x <= 2π), but not between the second and third intersection points. Hence Option 1 is correct.

Note: Since we are rounding to the nearest degree, the approximate values may not be exact and may need to be adjusted slightly to ensure accuracy.

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The chances of rolling between 20 and 40 aces (inclusive) in 180 rolls is approximately 0.9544 or 95.44%.

We can first standardize the values of 20 and 40 using the formula:

z = (x - μ) / σ

where x is the value we want to standardize (20 or 40), μ is the expected value (30), and σ is the standard deviation (5).

For x = 20, we get:

z = (20 - 30) / 5 = -2

For x = 40, we get:

z = (40 - 30) / 5 = 2

probability of getting a z-score between -2 and 2.

Using a standard normal distribution table or calculator, we find that the probability of getting a z-score between -2 and 2 is approximately 0.9544.

Therefore, the chances of rolling between 20 and 40 aces (inclusive) in 180 rolls is approximately 0.9544 or 95.44%.

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Answer:

Step-by-step explanation:

2344

If Cole brought 21 cans and his sister brought 7 cans less, then the total number of cans brought by them is 35 cans.

The number of cans which Cole brought = 21 cans of food.

His sister brought in 7 fewer cans than he did, which means she brought in:

⇒ 21 - 7 = 14 cans of food,

Let the total number of food-cans be = "f",

So, the equation to find the number of cans is written as :

⇒ x = 21 + 14,

On adding the number of cans,

We get,

⇒x =  21 + 14 = 35,

Therefore, together they brought in 35 cans of food.

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Answer: 358 miles

Step-by-step explanation:

Answer: 385

Step-by-step explanation: 77x5

An example of simple random sampling is given as follows:

C. In a bag of more than 500 marbles, reaching the hand into a bag and drawing 25 of them.

Samples may be classified as:

Hence the samples for this problem are classified as follows:

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$9,664.47

After 15 years the account will have $9,664.47

What does not make the context given as such is since PPI measures the change of the price the producer receives for their product and the CPI measure the change of the price the consumer pays for the product, one should rise while the other will fall. The Option D is correct.

This is because two indexes measure different things. The PPI measures change in prices of goods and services at the producer level while CPI measures the change in prices of goods and services at the consumer level.

That tells us PPI assess prices producers receive for their goods while CPI assess prices consumers pay for those same goods. So, while we have overlap between them, they are measuring different aspects of the economy and their trends may not always move in lockstep with each other.

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The required two column proof is explained below.

A midpoint is a point which divides a line segment into two equal parts. Thus it can be referred to as the middle point of the line segment.

The two column proof for the information is given as:

M is the midpoint of CD    (Given)

CD = CM + MD   (addition property of a line segment)

CM = MD  (definition of a midpoint)

So that;

5x – 2 = 3x + 2    (Definition of midpoint)#

Then,

5x - 3x = 2 + 2 (collecting like terms)

2x = 4

x = 2

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It looks like there are five data points in the box plot, representing Juan's total sales during each shift. The third data point is $200, which is the median value. Since there are an odd number of data points, we know that the median is exactly in the middle of the data set. This means that two of the data points are less than $200, and two of the data points are greater than $200.

The last data point is $300, which is the maximum value. So we know that only one of the data points is between $200 and $300. Therefore, the fraction of Juan's shifts that had total sales of $225 or more is 1/5, or 20%.

Answer:

Step-by-step explanation:

Integration of   [tex]\int\limits^6_0 {\frac{8}{1+74e^{-0.3t} } } \, dt[/tex]   is 2.199.

We can solve this integral using the substitution method, where u = 1 + 74[tex]e^{-0.3t}[/tex] . Taking the derivative of both sides, we have du/dt = -222[tex]e^{-0.3t}[/tex] .

We can rewrite the integral in terms of u:

∫[8/(1+74[tex]e^{-0.3t}[/tex] )]dt = ∫[8/u * (-1/222) * (-222[tex]e^{-0.3t}[/tex] )]du

Simplifying this expression, we have:

= (-8/222) ∫[1/u] du

= (-4/111) ln|u| + C

where C is the constant of integration.

Substituting back for u, we have:

= (-4/111) ln|1 + 74[tex]e^{-0.3t}[/tex] | + C

To evaluate the definite integral from 0 to 6, we plug in the limits of integration:

= (-4/111) [ln | 1 + 74[tex]e^{-0.3(6)}[/tex] | - ln | 1 + 74[tex]e^{-0.3(0)}[/tex] |]

= (-4/111) [ln|1 + 74[tex]e^{-1.8}[/tex]| - ln75]

≈ 2.199

Therefore, the value of the definite integral is approximately 2.199.

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To find the equation of the circle with center (0, −1) that contains the point (−8, 10), we can use the standard form of the equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle and r is the radius.

Since the center of the circle is given as (0, −1), we have:

(x - 0)^2 + (y + 1)^2 = r^2

We still need to find the radius, r. We know that the circle passes through the point (−8, 10), so we can substitute these values for x and y and solve for r:

(-8 - 0)^2 + (10 + 1)^2 = r^2

64 + 121 = r^2

r^2 = 185

So the equation of the circle is:

x^2 + (y + 1)^2 = 185

Alternatively, we can expand the equation to get it in standard form:

x^2 + y^2 + 2y + 1 = 185

x^2 + y^2 + 2y - 184 = 0

So another form of the equation is:

x^2 + (y + 1)^2 = 185

Step-by-step explanation:

5^(x+2)  <= 3^x    

5^x  *  5^2  <= 3^x

25 <=  3^x / 5^x

25<= (3/5)^x                  LOG both sides

log 25 <= x log (3/5)

log 25 / log (3/5) <= x

- 6.3 <= x

The properties of the exponents are solved and the expression is given by the relation ( 2s )⁻¹ = 1 / 2s

Given data ,

Let the expression be represented as A

Now , the value of A is

( 2s )⁻¹ = 1 / 2s

From the laws of exponents , we get

m⁻ᵃ = ( 1 / mᵃ )

So , on simplifying , we get

( 2s )⁻¹ = 1/ ( 2s )

On further simplification , we get

1/ ( 2s ) = ( 2s )⁻¹

Hence , the expression is ( 2s )⁻¹ = 1/ ( 2s )

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The complete question is attached below :

Use properties of exponents to verify that ( 2s )⁻¹ = 1/ ( 2s ) are equivalent.