Angles in a Triangle

So the person would save approximately 244 yards by walking diagonally across the field instead of walking the length and width of the field separately.

what is  approximately  ?

"Approximately" is a word that is used to indicate that a value, quantity, or measurement is close to the actual or precise value, but not exactly the same. It means that the stated value is an estimate or approximation, and may be slightly different from the true value.

In the given question,

Using the Pythagorean theorem, we can find the length of the diagonal of the soccer field:

diagonal² = length² + width²

diagonal² = 110² + 80²

diagonal² = 12,100 + 6,400

diagonal² = 18,500

diagonal = √18,500

diagonal ≈ 136 yards

So the person walking diagonally across the field would cover a distance of approximately 136 yards.

To compare this with the distance they would cover if they walked the length and width of the field separately, we can use the formula for the perimeter of a rectangle:

perimeter = 2(length + width)

perimeter = 2(110 + 80)

perimeter = 2(190)

perimeter = 380 yards

Therefore, if the person walked the length and width of the field separately, they would cover a total distance of 380 yards.

The difference between these two distances is:

380 - 136 = 244 yards

So the person would save approximately 244 yards by walking diagonally across the field instead of walking the length and width of the field separately.

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So the person would save approximately 244 yards by walking diagonally across the field instead of walking the length and width of the field separately.

what is  approximately  ?

"Approximately" is a word that is used to indicate that a value, quantity, or measurement is close to the actual or precise value, but not exactly the same. It means that the stated value is an estimate or approximation, and may be slightly different from the true value.

In the given question,

Using the Pythagorean theorem, we can find the length of the diagonal of the soccer field:

diagonal² = length² + width²

diagonal² = 110² + 80²

diagonal² = 12,100 + 6,400

diagonal² = 18,500

diagonal = √18,500

diagonal ≈ 136 yards

So the person walking diagonally across the field would cover a distance of approximately 136 yards.

To compare this with the distance they would cover if they walked the length and width of the field separately, we can use the formula for the perimeter of a rectangle:

perimeter = 2(length + width)

perimeter = 2(110 + 80)

perimeter = 2(190)

perimeter = 380 yards

Therefore, if the person walked the length and width of the field separately, they would cover a total distance of 380 yards.

The difference between these two distances is:

380 - 136 = 244 yards

So the person would save approximately 244 yards by walking diagonally across the field instead of walking the length and width of the field separately.

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Answer:

10.8

Step-by-step explanation:

14+10+8+10+12

_______________

5

= 54/5

= 10.8

The quadratic regression equation is y = -140.61x² + 2,954.23x - 7,512.85 and the ball's initial height is 14 feet.

Given the set of data

Using a graphing tool, we have

A quadratic regression equation is represented as

y = Ax² + Bx + C

So, we have

y = -140.61x² + 2,954.23x - 7,512.85

When the selling price is 7.75, we have

y = -140.61(7.75)² + 2,954.23(7.75) + -7,512.85

Evaluate

y = 6937

The ball's initial height is the height when t = 0, which means we need to evaluate the function h(0).

h(0) = -16(0)^2 + 14

h(0) = 0 + 14

h(0) = 14

Therefore, the ball's initial height is 14 feet.

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Answer:

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Step-by-step explanation:

We can use the trigonometric identity:

cos 2a = 1 - 2 sin^2 a

to rewrite 1 + 2cos a as:

1 + 2cos a = 1 + 2(1 - sin^2 a/2)

= 1 + 2 - 2(sin^2 a/2)

= 3 - 2(sin^2 a/2)

Now, using another trigonometric identity:

sin a = 2 sin(a/2) cos(a/2)

we can rewrite sin^2 a/2 as:

sin^2 a/2 = (1 - cos a)/2

Substituting this into the expression for 1 + 2cos a, we get:

1 + 2cos a = 3 - 2((1 - cos a)/2)

= 3 - (1 - cos a)

= 2 + cos a

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

She can make 20 6-ounce servings to make fruit punch

How to determine this

Cassie uses 1 quart cranberry juice,

1/2 gallon ginger ale,

1 1/2 pint orange juice.

1 quart of cranberry juice when converted to ounce

1 quart = 32 ounces

1/2 gallon of ginger ale when converted to ounce

1 gallon = 128 ounces

1/2 gallon = 128/2

1/2 gallon = 64 ounces

1 1/2 pint orange juice to make fruit punch

1 pint = 16 ounces

1 1/2 pint = 16 + 16/2 ounces

= 16 + 8

= 24 ounces

How many 6-ounces servings can she make

32 + 64 + 24

= 120 ounces

6-ounces that can be made

= 120 ounces/6 ounces

= 20 servings

Therefore, 20 6-ounce servings can be make for fruit punch

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If the "Lawyer's-Joke" is rates as the funniest, then the rating which is the top 10% of participant rating for this joke is 20 marks.

A "Normal-Distribution" is defined as a probability distribution that is symmetric, bell-shaped, and characterized by its mean and standard deviation.

First, we standardize the rating of 14.48 using the formula:

⇒ z = (x - μ) / σ;

where x is = rating of 14.48, μ is = mean rating, and σ is = standard deviation,

⇒ z = (14.48 - 14.48) / 4.38,

⇒ z = 0,

Next, we take the "z-score" that corresponds to the top 10% of the standard normal distribution.  We know that the "z-score" is approximately 1.28,

Substituting the value in formula,

We get,

⇒ z = (x - μ) / σ   ⇒ 1.28 = (x - 14.48)/4.38,

⇒ x - 14.48 = 1.28 × 4.38,

⇒ x = 20.97 ≈ 20 marks.

Therefore, the rating that marks the cutoff for the top 10% of participant ratings for this joke is approximately 20 on the scale of 1 to 21.

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Answer:

Step-by-step explanation:

(a) Lena got 33 more

(b) Last one

Answer:

Any number multiplied by 10 equals to the number and a 0 at the end

Therefore 3×10=3

The area and circumference of a circle with diameter of 3 m is 7.0165 m² and 9.42 m² respectively

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The diameter (d) of the circle is 3 meter. Hence:

Area = π * diameter²/4 = π * 3²/4 = 7.0165 m²

Circumference = π * diameter = π * 4 = 9.42 m²

The area and circumference are 7.0165 m² and 9.42 m²

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The length of a scaled drawing with a width of 9cm and the scale factor 3/4 s 6.75 cm

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

Width =  9cm

Scale factor = 3/4

Using the above as a guide, we have the following:

Length of a scaled drawing = Width * Scale factor

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

Length of a scaled drawing = 9 * 3/4

Evaluate

Length of a scaled drawing = 6.75

Hence, the length of a scaled drawing is 6.75 cm

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The creation of an isosceles triangle quilt can only be achieved through a number of discreet steps:

Initially, select the bespoke size of both individual triangles and the full-scale length and breadth of the snug.

Subsequently, draft a lattice on either a sheet of paper or digital drafting software, with each square serving as a single triangular unit.

Commencing your task from the bottom row, resonate along the equidistant bases while drawing with precision to ensure an immaculate line-up.

Then, for the succeeding section, diverge by slightly altering the position of the point of each triangle in accordance with the intermediary gap that exists between two triangles below it.

Continue repeating this pattern while constructing rows, enveloping further ground until fully complete coverage has been ensured.

Last but not least, rigorously maintain accuracy by exploiting straight edges strategically laid beside precise measuring instruments.

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The limits on the vertical asymptotes of the function are given as follows:

lim x→6- f(x) = ∞

lim x→6+ f(x) = - ∞

lim x→2- f(x) = ∞

lim x→2+ f(x) = - ∞

lim x→6- f(x) = - ∞

lim x→6+ f(x) = ∞

The values of x that are outside of the domain—in a fraction, the zeroes in the denominator—are the vertical asymptotes.

When a graph reaches its vertical asymptotes, it just approaches the point rather than crossing it.

The limits on the vertical asymptotes of the function are given as follows:

lim x→6- f(x) = ∞

lim x→6+ f(x) = - ∞

lim x→2- f(x) = ∞

lim x→2+ f(x) = - ∞

lim x→6- f(x) = - ∞

lim x→6+ f(x) = ∞

The vertical asymptotes are then provided as x = -6, x = -2, and x = 2.

Each asymptote has limits to the left (shown by the minus sign) and the right (shown by the plus sign).

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Check the picture below.

The congruency rules which satisfy the given triangles are (B) AAS and (D) HA.

What is triangle congruency?

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Slide, twist, flip, and turn these triangles to create an identical appearance.

If two triangles meet all 5 requirements for congruence, then they are congruent.

They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS). (RHS).

So, according to the given, we can observe that:

2 pairs of angles are congruent one pair of which is 90°.

And 1 pair of sides are congruent.

Then, the rules that satisfy here will be:

AAS and HA

Therefore, the congruency rules which satisfy the given triangles are (B) AAS and (D) HA.

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Complete question:

Based only on the information given in the diagram, which congruence theorems or postulates could begin as reasons why HIJ = KLM?

Answer:

y = 4

Step-by-step explanation:

[tex]y = -3*-2 - 2\\y = 4[/tex]

Answer:

1. f(x)= -2x^2-12x-19

2. f(x)= 2x^2+12x+17

3. f(x)= -2x^2+12x-17

4. f(x)= 2x^2-12x+17

Step-by-step explanation:

Hope this helps!

Answer: f(x)=-2x^2+12x-17 is the 3rd picture (vertex at (3,1))

f(x)=2x^2-12x+17 is the 4th picture (vertex at (3,-1))

f(x)=2x^2+12x+17 is the 2nd picture (vertex at (-3,-1))

f(x)=2x^2+12x-17 does not correlate to a picture.

f(x)=-2x^2-12x-19 is the 1st picture (vertex at (-3,-1))

Answer:

Step-by-step explanation:

After 5 years at a simple interest rate of 10%, Patrick would have earned $500 in interest ($1000 x 10% x 5 years). So at the end of the 5 years, he would have $1500 in the account.

If this entire amount is deposited into a new account that earns 10% compounded quarterly, we need to determine the quarterly interest rate first.

The quarterly interest rate is (1 + 0.10/4)^4 - 1 = 0.025 (rounded to three decimal places).

After 10 years (or 40 quarters) at a quarterly interest rate of 0.025, the compounded amount is:

$1500 x (1 + 0.025)^40 = $4045.56

Therefore, Patrick would have $4045.56 in the account after 10 years when rounding to the nearest cent.

Hope that Helps :)

Answer:

He took 3 3/4 hours to clean both rooms.

Step-by-step explanation:

1/2 = 2/4

3 1/4 + 2/4 = 3 3/4

Therefore, he took 3 3/4 hours.

The quadrant or axis for each of the given ordered pairs is:

a. (-x, y) - second quadrant

b. (-x, 0) - X-axis

c. (x, -y) - fourth quadrant

d. (0, y) - Y-axis

a. (-x, y):

As the x-coordinate is negative (-x), and the y-coordinate is positive (y), the ordered pair (-x, y) will lie in the second quadrant.

b. (-x, 0):

The x-coordinate being negative (-x), and the y-coordinate 0 renders that the ordered pair (-x, 0) lies on the x-axis. This horizontal axis records an unchanging value for y: zero.

c. (x, -y):

The x-coordinate here is a positive value (x), and the y coordinate a negative one (-y); it implies that the ordered pair (x, -y) lies within the fourth quadrant.  

d. (0, y):

In this case, the x-coordinate is 0 and the y-coordinate is positive (y); therefore, the ordered pair (0, y) has its place on the y-axis. The y-axis is the vertical line on which x retains a permanent numerical value of zero.

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Answer:

Yes, triangles ABC and DEC are similar by AA. Angles ABC and DEC are congruent, and angles ACB and DCE are congruent.

The slope of the line is -4, which means that the swimmer will complete 4 laps every minute.  For 5 weeks they have the same amount of money. The direction is 270° clockwise rotation. The pattern of scatter plot is that there is a weak, negative linear association. The measurement of FD = 1.52. The slope of the line is negative three halves. The probability of No Heads is 25%. The scale factor is one half. The correct answers are C), B), A), B), A), D), D) and B).

The slope of the line is the change in y divided by the change in x, which represents the rate of change of the line. In this case, the slope is negative 4, which means that for every minute that passes, the number of laps remaining decreases by 4. So, the swimmer completes 4 laps every minute.

To find the point at which the two savings accounts have the same amount of money, we need to set the two equations equal to each other and solve for x

10x + 25 = 5x + 50

5x = 25

x = 5

So, after 5 weeks, the two siblings will have the same amount of money saved.

The direction of rotation can be determined by looking at the relative positions of the vertices of the original polygon and its image. In this case, the vertices of the image are in quadrant 1, while the vertices of the original polygon are in quadrant 2. This means that the image has been rotated counterclockwise. Additionally, we can see that the image has been rotated by 90 degrees, so the angle of rotation is 90 degrees counterclockwise.

The scatter plot shows a general trend of decreasing cost per cupcake as the number of cupcakes in an order increases. However, there is a fair amount of variability in the data, so the association between the two variables is weak. Additionally, the association is negative, as the cost per cupcake decreases as the number of cupcakes in an order increases.

Similar triangles have proportional side lengths, so we can set up a proportion using corresponding side lengths of the two triangles

AB/DE = BC/EF = CA/FD

Plugging in the known values, we get

11/2.2 = 7.9/EF = 7.6/FD

Solving for FD, we get

FD = (7.6 * 2.2)/11 = 1.52

So, FD has a length of 1.52 units.

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula

slope = (y2 - y1)/(x2 - x1)

Plugging in the given values, we get

slope = (-10 - (-1))/(3 - (-3)) = -9/6 = -3/2

So, the slope of the line is negative three halves.

The probability of getting no heads in two flips can be found by adding the frequencies of the outcomes where no heads occur (Tails, Tails) and (Tails, Heads) and dividing by the total number of trials

P(No Heads) = (50 + 35)/200 = 85/200 = 0.425 = 42.5%

So, the probability of getting no heads is 42.5%, which is equivalent to 0.425.

Dilations involve multiplying the coordinates of each vertex by a scale factor. To find the scale factor used in this dilation, we can compare the corresponding side lengths of the original triangle and its image. In this case, we can see that the sides of the image are half as long as the corresponding sides of the original triangle. So, the scale factor used to create the image is one half.

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We can deduce that option A is likely to be true based on the given graph of rolling dice median data.

The median is the value in the middle of a data set, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median.

The graph illustrates that the median value of the rolls is closer to the center of the possible outcomes (numbers 3, 4, and 5) than the extremes (numbers 1 and 6).

This implies that when rolling a dice several times, the median is less likely to fall between the numbers 1 and 6.

However, because rolling the dice is a random process, there is always a degree of uncertainty in predicting the outcomes.

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Answer:

if you park for 12 hours in both parking lots A and B, it will cost the same amount, which is $64.50.

Step-by-step explanation:

Let's assume that the cost of parking for x hours in both lots is the same, then we can set up the following equations:

For 5 hours of parking:

36.50 = 38.00

This is not true, so we know that the cost for parking in both lots will not be the same for 5 hours.

For 7 hours of parking:

49.50 = 50.00

This is also not true, so we know that the cost for parking in both lots will not be the same for 7 hours either.

Let's try setting up the equation for x hours of parking:

Fee for parking in Lot A = Fee for parking in Lot B

36.50 + (x-5)*7 = 38.00 + (x-5)*7

Simplifying the equation, we get:

36.50 + 7x - 35 = 38.00 + 7x - 35

Solving for x, we get:

x = 12

Therefore, if you park for 12 hours in both parking lots A and B, it will cost the same amount, which is $64.50.

Step-by-step explanation:

The given equation is:

4x - 3y = 21

To solve for y, we can rearrange the equation as follows:

4x - 21 = 3y

Dividing both sides by 3, we get:

y = (4x - 21) / 3

Therefore, the solution to the equation is:

y = (4x - 21) / 3

Answer :

Answer : 1.796

The explanation is in the pictures.

The missing values are b = 4.37, C = 11° and A = 134°

Given is a triangle, we need to find the missing lengths and angles,

So,

Using the cosine rule,

b² = a²+c² - 2ac Cosb

b = √4²+7²-2(4)(7)cos35°

b = √16+49-45.87

b = √19.13

b = 4.37

Now, using the sine rule,

Sin C / 7 = Sin 35° / 4.37

C = 11°

Applying the angle sum property of triangles,

A = 180°-(11°+35°)

A = 134°

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The statement  that is true about standard deviation is

Option D is the correct answer.

We have,

Standard deviation is a measure of how spread out the data is in a set.

A smaller standard deviation indicates that the data points are closer to the mean, while a larger standard deviation indicates that the data points are more spread out from the mean.

Since the standard deviation of set A is 6 and the standard deviation of set B is 9, we can conclude that the data in set A varies less than the data in set B.

So,

The data in set A varies less than the data in set B.

Thus,

The statement  that is true about standard deviation is

The data in set A varies less than the data in set B.

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The statement  that is true about standard deviation is

Option D is the correct answer.

We have,

Standard deviation is a measure of how spread out the data is in a set.

A smaller standard deviation indicates that the data points are closer to the mean, while a larger standard deviation indicates that the data points are more spread out from the mean.

Since the standard deviation of set A is 6 and the standard deviation of set B is 9, we can conclude that the data in set A varies less than the data in set B.

So,

The data in set A varies less than the data in set B.

Thus,

The statement  that is true about standard deviation is

The data in set A varies less than the data in set B.

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The range of function for the given domain are {25, 8, -7, 11}

Given that, a function f(x) = 2x²-7, we need to find the range of the function, for the given domain, x = {-4, -2, 0, 3},

So,

Domain = All the input values.

Range = All the output values.

So, to find the range we will put the value of x which is the domain and the value obtained of f(x) will be the range,

f(x) = 2x²-7

For, x = -4,

f(-4) = 16×2 - 7 = 25

f(-4) = 25

f(-2) = 4 × 2 - 7 = 8

f(-2) = 8

f(0) = -7

f(3) = 9 × 2 - 7

f(3) = 11

Hence the range of function for the given domain are {25, 8, -7, 11}

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Answer:

554.76 miles per hour

Step-by-step explanation:

[tex]\frac{248 meters}{1 second}[/tex] x [tex]\frac{3600 seconds}{1 hour}[/tex] x [tex]\frac{1 mile}{1609.34 meters}[/tex]

= 554.76 miles per hour

[tex]\sf 554.76(mi/h).[/tex]

[tex]\sf \dfrac{248(m)}{s}[/tex]

a) First, convert the meters to kilometers.

[tex]\sf 248(m)*\dfrac{1(km)}{1000(m)} =0.248(km)[/tex]

Here, the meters cancel, since one is on the numerator and the other one is expressed as a denominator, and we simpyl multiply the value by the fraction, resulting in a number that would be a value for kilometers.

b) Convert from kilometers to miles.

[tex]\sf 0.248(km)*\dfrac{1(mi)}{1.60934(km)} =0.1541(mi)[/tex]

[tex]\sf 1(seconds)*\dfrac{1(hour)}{3600(seconds)} =\frac{1}{3600}(h)[/tex]

[tex]\sf \dfrac{0.1541(mi)}{\dfrac{1}{3600} (h)} =554.76(mi/h)[/tex]

Answer:

Step-by-step explanation:

Use a simple Equation

Price = Number x Price

So Price = 536.

Since it was 67% off we multiple the price of the original by .67.

So

536 = .67x

Solve for x = 536/.67 = 800

The original Price is $800.

check by multiplying by the sale %.