Which expressions represent the distance between -5 and 3? Choose all that apply

Answer:

[tex] \sqrt{ {( - 3 - ( - 5))}^{2} + {( - 4 - 2)}^{2} } [/tex]

[tex] \sqrt{ {2}^{2} + {( - 6)}^{2} } [/tex]

[tex] \sqrt{4 + 36} = \sqrt{40} = 2 \sqrt{10} [/tex]

The perimeter of the semicircle is approximately 66.8 cm.

The diameter of the semicircle is given as d = 26cm.

r = d/2 = 26/2 = 13cm

The circumference of a full circle with radius r is given by:

C = 2πr

Therefore, the circumference of the semicircle is:

C/2 = πr

Substituting the value of r, we get:

πr = π(13) = 13π

The perimeter of the semicircle is therefore:

P = d + C/2 = 26 + 13π

Using the value of π = 3.14, we can approximate the perimeter as:

P = 26 + 13(3.14)

= 26 + 40.82

= 66.82 cm

Rounding to 1 dp

= 66.8 cm

Therefore, the perimeter of the semicircle is approximately 66.8 cm.

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The linear equation that models the data based on the information is y = 2.2x + 0.6.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.

In conclusion, the linear equation that models the data based on the information is y = 2.2x + 0.6.

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Simplifying each of the following expressions:

a) (√5-√12)²:

First, we can simplify the square of each term using the formula (a-b)² = a² - 2ab + b²:

(√5-√12)² = (√5)² - 2(√5)(√12) + (√12)²

= 5 - 2√60 + 12

Next, we can simplify √60 by factoring out its largest perfect square factor, which is 4:

5 - 2√60 + 12 = 17 - 2√(4*15) = 17 - 4√15

Therefore, (√5-√12)² = 17 - 4√15.

b) (√12+√11)²:

We can simplify this expression using the same formula as before:

(√12+√11)² = (√12)² + 2(√12)(√11) + (√11)²

= 12 + 2√132 + 11

Next, we can simplify √132 by factoring out its largest perfect square factor, which is 4:

12 + 2√132 + 11 = 23 + 2√(4*33) = 23 + 2√132

Therefore, (√12+√11)² = 23 + 2√132.

c) (√6+√7) (√6-√7):

This expression can be simplified using the difference of squares formula, (a-b)(a+b) = a² - b²:

(√6+√7) (√6-√7) = (√6)² - (√7)²

= 6 - 7

= -1

Therefore, (√6+√7) (√6-√7) = -1.

Rationalizing each of the following expressions:

a) 1/√8:

To rationalize the denominator, we can multiply both the numerator and denominator by √8:

1/√8 = (1/√8) * (√8/√8) = √8/8

Therefore, 1/√8 = √8/8.

b) 1/√7-√1:

To rationalize the denominator, we can multiply both the numerator and denominator by the conjugate of the denominator, which is √7+√1:

1/√7-√1 = (1/√7-√1) * (√7+√1)/(√7+√1) = (√7+√1)/(7-1)

= (√7+√1)/6

Therefore, 1/√7-√1 = (√7+√1)/6.

c) 1/√8+3:

To rationalize the denominator, we can multiply both the numerator and denominator by the conjugate of the denominator, which is √8-3:

1/√8+3 = (1/√8+3) * (√8-3)/(√8-3) = (√8-3)/(8-9)

= -(√8-3)

Next, we can simplify √8 by factoring out its largest perfect square factor, which is 4:

-(√8-3) = -

Answer:

x^2 - x + 6 = 0

x = (-(-1) + √((-1)^2 - 4(1)(6)))/(2 × 1)

= (1 + √(1 - 24))/2

= (1 + √-23)/2

So there are no real solutions to this equation--we have the empty (null) set.

{ }

Answer:

(0, - 4 )

Step-by-step explanation:

the y- intercept is the point where the line crosses the y- axis

the line crosses the y- axis at (0, - 4 )

then y- intercept is (0, - 4 )

The greatest number of 40-kilogram crates that can be loaded onto the trailer = 24

Let us assume that n represents the greatest number of 40-kilogram crates that can be loaded onto the trailer.

The greatest amount of weight that can be loaded onto the trailer is 1,050 kilograms.

Here, 82-kilogram crate has already been loaded onto the trailer.

From this information, we can formulate an equation as,

1050 = 82 + (40 × n)

We solve above equation for n.

40n = 1050 - 82

n = 968 / 40

n = 24.2

As the number of crates can not be a decimal number.

n ≈ 24

This is the greatest number of 40-kilogram crates that can be loaded onto the trailer.

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The statements 'all squares are similar' and 'all equilateral triangles are similar' is true among the given statements.

Similar shapes refer to shapes with the same angles but sides of varying magnification. We can also say the ratio in dimensions of corresponding sides is in proportion.

In the case of isosceles triangles, the angles of each triangle can be unique and to say the sizes are in proportion to each other might not be true for every case. Thus, we can't say that all isosceles triangles are similar to each other.

In the case of rectangles, though the angles of each rectangle are equal and are 90°, to say the sizes are in proportion to each other might not be true for every case as the length and breadth may vary without any proper ratio. Thus, we can't say that all rectangles are similar to each other.

In the case of squares, the angles of each side of the square are equal and are 90°, and since all sides are equal to each other, the sides are also in proportion. Thus, we can say that all squares are similar to each other.

In the case of equilateral triangles, the angles of each side of an equilateral are equal and are 60°, and since all sides are equal to each other, the sides are also in proportion. Thus, we can say that all equilateral triangles are similar to each other.

In the case of right triangles, only one of the angles of each triangle is equal and is 90°, to say the sizes are in proportion to each other might not be true for every case as each side may vary without any proper ratio. Thus, we can't say that all right triangles are similar to each other.

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Answer:

Step-by-step explanation:

im not compleatly sure but i think its C

Without additional information, it is not possible to determine the measure of 5. The angles formed by the traversal and the parallel lines can have various measures depending on the specific arrangement of the lines and the traversal.

Answer: I'm going to have to agree with the person whom of which answered before me. It would be a vain attempt to try to find the answer to this conundrum without further information.

Step-by-step explanation:

The radius of the circle as given is; 3.

The center of the circle as given is; (-4, 1).

It follows from the task content that the center and radius of the given circle image and radius are to be determined.

Recall, the center-radius equation of a circle takes the form;

(x - h)² + (y - k)² = r² where center is; (h, k) and radius is r.

By observation of the graph as well as the given equation of the circle, the pair of coordinates for the center is; (-4, 1).

Also, since the radius is the distance from the center to any point on the circumference of the circle; the radius of the circle is; 3.

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The angle between the z-axis and the given vector r with rightwards arrow on top is 33.69 degrees.

The x-component of the vector is -2, which means that the vector has a component that points in the negative x-direction. The y-component of the vector is 3, which means that the vector has a component that points in the positive y-direction. We can use these components to find the magnitude of the projection of the vector onto the xy-plane, which is given by the Pythagorean theorem:

|proj_r| = √((-2)² + 3²) = √(13)

Next, we need to find the angle between the projection of the vector onto the xy-plane and the positive x-axis. We can do this by taking the arctan of the y-component over the x-component:

theta = arctan(3/-2) = -56.31 degrees

Note that we get a negative angle because the projection of the vector lies in the third quadrant of the xy-plane, which is opposite to the positive x-axis.

Finally, we can find the angle between the z-axis and the vector by subtracting the angle between the projection of the vector onto the xy-plane and the positive x-axis from 90 degrees:

phi = 90 - 56.31 = 33.69 degrees

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The area of the given tile is 36.5 cm² which is in the form of trapezoid

A trapezoid is a four-sided geometric shape with one pair of parallel sides.

The two non-parallel sides are usually referred to as the "legs" and the other two sides are the "bases".

A trapezoid can be either isosceles or non-isosceles depending on the angles of the legs. A trapezoid can also be equilateral if all four sides have equal lengths.

The area of the tile can be calculated by using the formula for the area of a trapezoid, A = (a+b)/2× h

where a and b represent the parallel sides, and h represents the height.

In this case, a = 5 cm, b = 6 cm, and h = 3 cm

A = (5 + 6)/2 × 3

= 36.5 cm².

Hence, the area of the given tile is 36.5 cm²

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The equation of the tangent line to the graph of ƒ at the point (2,1) is y = 3.142x - 3.283.

To find the equation of the tangent line to the graph of the function ƒ at the point (2,1), we can use the formula for the equation of a line:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line. The slope of the tangent line to the graph of ƒ at x = 2 is given by the derivative of ƒ at x = 2:

m = ƒ'(2)

Using a graphing calculator, we can find the derivative of ƒ at x = 2 by entering the function into the calculator and then finding the derivative at x = 2. Let's say we find that ƒ'(2) = 3.14159.

Now we have all the information we need to write the equation of the tangent line to the graph of ƒ at the point (2,1):

y - 1 = 3.14159(x - 2)

Simplifying, we get:

y = 3.14159x - 3.28318

Rounding to three decimal places, we have:

y = 3.142x - 3.283

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Answer:

For question 1 the answer is C, and for question 2 the answer is A

Step-by-step explanation:

For Question 1

A histogram can be used to compare the height of different students

For Question 2:

Boxplots are a great way to visualize interquartile ranges and their relation to the median and the overall distribution. These graphs display ranges of values based on quartiles and show asterisks for outliers that fall outside the whiskers.

- Hope this helps

The annual interest rate of the account is 3.5%

From the question, we have the following parameters that can be used in our computation:

Principal = 12000

Time = 14 years

Amount = 17880

The amount of simple interest is calculated using

A = P(1 + RT)

Substitute the known values in the above equation, so, we have the following representation

12000 * (1 + R * 14) = 17880

So, we have

(1 + R * 14) = 1.49

This gives

14R = 0.49

Divide

R = 3.5%

Hence, the interst is 3.5%

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Antonia's probability of making a free throw is 0.75, and the probability of her missing a free throw is 0.25. Based on the results of a simulation of 10 trials, the experimental probability that Antonia makes both of her next two free throw attempts is 0.6 or 60%.

Using the given information, we know that Antonia's probability of making a free throw is 75%, which is equivalent to 0.75. Therefore, the probability of her missing a free throw is 25%, which is equivalent to 0.25.

Looking at the table of results from the simulation, we can see that there are 6 instances where Antonia made both of her next two free throw attempts (YY), out of a total of 10 trials. Therefore, the experimental probability of Antonia making both of her next two free throw attempts is

Experimental probability = Number of trials where Antonia made both of her next two free throws / Total number of trials

Experimental probability = 6/10

Experimental probability = 0.6

Therefore, based on the results of the simulation, the experimental probability of Antonia making both of her next two free throw attempts is 0.6 or 60%.

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The area of the side walk is is 138.16m²

A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.

The area of a circle is expressed as;

A = πr²

The area of the pathway = area of big circle - area of small circle

The diameter of the big circle = 20+4 = 24m

Area of big circle = 3.14 × 12²

= 452.16m²

Area of the small circle =

3.14 × 10²

= 314m²

therefore the of the path way = 452.16 - 314m²

= 138.16m²

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Answer:

Since ∠CAB = 90°, we know that AC is the hypotenuse of the right triangle ABC. Let's use the sine function to find the length of BC:

sin(∠ABC) = BC/AC

sin(64°) = BC/9.1

BC = 9.1 * sin(64°)

Now, using the Pythagorean theorem, we can find the length of AB:

AB = sqrt(AC^2 - BC^2)

AB = sqrt(9.1^2 - (9.1*sin(64°))^2)

AB ≈ 5.222

Rounding this to 3 significant figures, we get:

AB ≈ 5.22

Therefore, the length of AB rounded to 3 significant figures is approximately 5.22 units.

The total amount that the invisible man will pay for the chair is $9, 240.

Seeing as this is simple interest, the total amount paid for the chair would be the total amount the man pays the bank after 5 years:

= Principal borrowed x Interest rate x Time

= 6, 600 x 8 % x 5

= 6, 600 x 40 %

= $ 2, 640

The total amount the invisible man would pay is:

= Cost of chair + Interest over 5 years

= 6, 600 + 2, 640

= $ 9, 240

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230.26

"How so?"

First of all, formulate: 70.2% x 328

Then convert the percentage to decimals: 0.702 x 328

Now calculate the quotient: 230.256 and round it: 230.26

I apologize if anything is incorrect! Have a good day and good luck! <3

Answer: 230.58

Step-by-step explanation:

To find 70.2% of 328, we multiply 70.2% (or 0.702 as a decimal) by 328:

0.702 x 328 = 230.5776

Rounding this to the nearest hundredth gives:

230.58

Therefore, 70.2% of 328 rounded to the nearest hundredth is 230.58.

A pie chart is effective for demonstrating percentages that make up a whole. It shows the proportions of a whole by dividing it into slices, where the size of each slice represents the percentage of the whole that it represents.

Pie charts are commonly used to represent data such as market share, budget allocations, or demographic breakdowns.

They are useful for quickly conveying the relative sizes of different categories within a dataset.

However, pie charts may not be as effective for showing trends over time, where things are located on a map, or relationships between variables, as other types of graphs such as line charts, maps, or scatter plots may be more appropriate for these purposes.

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Karim and Ali have different conclusions about the closure property for whole numbers and integers because when two whole numbers are subtracted, the result may not be a whole number, but when two integers are subtracted, the result is always an integer. Therefore, integers are closed under subtraction, but whole numbers are not.

Karim and Ali, both  have different conclusions about the closure property for whole numbers and integers because of their definitions.

Whole numbers are defined as all positive integers, including zero. When two whole numbers are subtracted, the result may not be a whole number because the result may be a negative number.

For example, when 3 is subtracted from 2, the result is -1, which is not a whole number.

Integers, on the other hand, are defined as all positive and negative whole numbers, including zero. When two integers are subtracted, the result is always an integer because the result may be a negative or positive number, but it will always be a whole number.

For example, when 3 is subtracted from 2, the result is -1, which is still an integer.

Therefore, Karim and Ali have different conclusions because whole numbers are not closed under subtraction, but integers are closed under subtraction.

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Answer:

Vertical translation

Step-by-step explanation:

Answer:

Step-by-step explanation:

In a right-angled triangle, one of the angles is always 90° (the right angle). The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

However, in the case of a right-angled triangle, there is no side opposite to the 90° angle. The opposite side is the side that is opposite to one of the acute angles, and the adjacent side is the side that is adjacent to that acute angle. Since there is no acute angle opposite to the 90° angle, there is no opposite side to the 90° angle.

Therefore, the tangent of 90° is undefined because there is no opposite side to the 90° angle in a right-angled triangle. Mathematically, we can say that:

tan(90°) = opposite/adjacent = undefined/adjacent

Since the opposite side is undefined, the value of the tangent is undefined.

The required value of the x is 13 in the measures of the angle.

Given that,

Line A and B are parallel lines and intersect by a transversal line.

Here,

If a pair of parallel lines intersect by the transversal line then their corresponding angles are equal in measure,

Thus, we get;

8x + 2 = 14x - 76

6x = 78

x = 78 / 6

x = 13

Thus, the required value of the x is 13 in the measures of the angle.

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Answer: 5

Step-by-step explanation:

You will use Pythagorean theorem for this problem (a²+b²=c²)

This will be 13² - 12² = a

13² - 12² = 25

you must square root your answer

√25 = 5

x=5

Result:

A (is an angle)  = 70°.

Based on the provided information:

AB = BC

BCD = 110

We can use the information to find the value of A.

Since AB = BC, we can assume that triangle ABC is an isosceles triangle, where AB and BC are the two equal sides. For an isosceles triangle, the angles opposite to the equal sides are also equal.

So, ∠ABC = ∠BCA (opposite angles of an isosceles triangle are equal).

Since BCD = 110, we can deduce that  ∠BCA + ∠ BCD = 180 (sum of angles in a triangle equals 180 degrees).

Substituting the values, we get:

∠BCA + 110 = 180

Subtracting 110 from both sides, we get:

∠BCA = 180 - 110

∠BCA = 70

Now, since ∠ABC = ∠BCA, we have:

∠ABC = 70°

Therefore, A = 70 degrees.

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The total volume of the composite figure is 123cm³

First let's do the prism, the volume is the product of the 3 dimensions, so we will get:

v = 12cm*1cm*5cm = 60cm³

Now let's do the cone, the formula for the volume is given, so we can just replace the numbers that we know, notice that the diameter is given and we need the radius which is half of that, so:

r = 6cm/2 = 3cm

Then the volume is:

V = 3*(3cm)²*7cm/3 = 63cm²

So the total volume is 63cm² + 60cm³ = 123cm³

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Answer:

25

Step-by-step explanation:

25 sqrt= 5

2+5=7; 7 is a prime number