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Determine if the triangles are similar. If similar.state how and complete the similarity statement

So the y-intercept is 4 the equation of the line in slope-intercept form is:

y = 2x + 4

When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b).

y = mx + b

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

Using the points (-4, -4) and (1, 6), we can find the slope of the line passing through them:

m = (6 - (-4)) / (1 - (-4)) = 10 / 5 = 2

So the slope of the line is 2.  Let's use the point (1, 6):

y = mx + b

6 = 2(1) + b (substitute m = 2, x = 1)

6 = 2 + b

b = 6 - 2 = 4

So the y-intercept is 4 the equation of the line in slope-intercept form is:

y = 2x + 4

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Sequence having rule  f(n) = n² - 5, the first four terms will be -4, -1, 4, and 11.

A sequence in mathematics is a group of integers that adhere to a specific pattern or rule. A sequence of numbers might be infinite or finite, and they are arranged in a certain order.

Every number in the sequence is referred to as a term, and its location within the sequence is referred to as its index. As an illustration, the first term in the series 1, 3, 5, 7, 9, is 1, the second term is 3, the third term is 5, and so on.

Now,

The explicit rule for the sequence is given by f(n) = n² - 5, which means that to find the nth term of the sequence, we need to plug in the value of n into this formula.

To find the first four terms of the sequence, we can simply substitute n = 1, 2, 3, and 4, respectively, into the formula and evaluate the expression.

The first term is f(1) = 1² - 5 = -4.

The second term is f(2) = 2² - 5 = -1.

The third term is f(3) = 3² - 5 = 4.

The fourth term is f(4) = 4² - 5 = 11.

Therefore,

                 the first four terms of the sequence defined by the explicit rule f(n) = n² - 5 are -4, -1, 4, and 11.

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Answer:

y = -3 sin(4x)

or

y = -3 cos(4(x - π/8))

Step-by-step explanation:

We can see that this is a graph of sine or cosine with the following characteristics:

amplitude: 3

period: π/2

vertical shift: 0

We can use these characteristics to form the following equations:

y = -3 sin(4x)

y = -3 cos(4(x - π/8))

Note that we solved for b using the period derivation:

period = 2π / b

[tex]\dfrac{\pi}{2} = \dfrac{2\pi}{b}[/tex]

[tex]b \cdot \dfrac{\pi}{2} = 2\pi}[/tex]

[tex]b = 2\pi \cdot \dfrac{2}{\pi}[/tex]

[tex]b = \dfrac{4\pi}{\pi}[/tex]

[tex]b = 4[/tex]

— sidenote —

These graphs can be infinitely shifted by any integer number of periods left or right, and we can show that using an auxiliary variable multiplied by the period. However, that is clearly not the intent of the problem, so I have not included that in my answer.

Dilations produce images that have a center that is the same as the pre-image.

Dilations are a type of transformation that change the size, shape, and orientation of an object. Dilation is a math operation that enlarges or reduces the size of an object or figure. It is a linear transformation that stretches or contracts shapes, which preserve the shape's angles and proportions. Dilation can be used to increase or decrease the area of a shape, or to change the distance between two points.

True statements about dilations are:
• Dilations produce images that are similar to the pre-image.
• Dilations produce images that have angles that are congruent to the pre-image.
• Dilations produce images that have sides that are proportional to the pre-image.
• Dilations produce images that have a center that is the same as the pre-image.

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Complete questions as follows-
Which statements are true about dilations? Select all that apply.
Dilations produce images that are similar to the pre-image.
Dilations produce images that are always congruent to the pre-image.
Dilations produce images that have angles that are congruent to the pre-image.
Dilations produce images that have sides that are congruent to the pre-image.
Dilations produce images that have sides that are proportional to the pre-image.

for 6 cups of water?

[tex]\begin{array}{ccll} \stackrel{cups}{water}&\stackrel{tspoons}{mix}\\ \cline{1-2} 4 & 6\\ 6& x \end{array} \implies \cfrac{4}{6}~~=~~\cfrac{6}{x} \\\\\\ \cfrac{ 2 }{ 3 } ~~=~~ \cfrac{ 6 }{ x }\implies 2x=18\implies x=\cfrac{18}{2}\implies x=9[/tex]

how about for 10?

[tex]\begin{array}{ccll} \stackrel{cups}{water}&\stackrel{tspoons}{mix}\\ \cline{1-2} 4 & 6\\ 10& y \end{array} \implies \cfrac{4}{10}~~=~~\cfrac{6}{y} \\\\\\ \cfrac{ 2 }{ 5 } ~~=~~ \cfrac{ 6 }{ y }\implies 2y=30\implies y=\cfrac{30}{2}\implies y=15[/tex]

Step-by-step explanation:

f(0):

f(0) = (0^2 - 9) / (0 + 5)

= -9/5

f(-1):

f(-1) = ((-1)^2 - 9) / (-1 + 5)

= (-8) / 4

= -2

f(1/k):

f(1/k) = ((1/k)^2 - 9) / (1/k + 5)

= (1/k^2 - 9) / (1/k) + 5

= (1 - 9k^2) / (k^2 + 5k)

Therefore, f(0) = -9/5, f(-1) = -2, and f(1/k) = (1 - 9k^2) / (k^2 + 5k).

Answer:

Step-by-step explanation:

To find the values of f(x) at the given points, we substitute the values of x into the expression for f(x) and simplify:

f(x) = (x^2 - 9)/(x + 5)

a) To find f(0), we substitute 0 for x:

f(0) = (0^2 - 9)/(0 + 5) = -9/5

Therefore, f(0) = -1.8.

b) To find f(-1), we substitute -1 for x:

f(-1) = (-1^2 - 9)/(-1 + 5) = (-10)/4

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor of 2:

f(-1) = -5/2

Therefore, f(-1) = -2.5.

c) To find f(1/k), we substitute 1/k for x:

f(1/k) = ((1/k)^2 - 9)/(1/k + 5)

We can simplify the numerator by multiplying out the square:

f(1/k) = (1/k^2 - 9)/(1/k + 5)

We can simplify the denominator by multiplying by k/k:

f(1/k) = (1 - 9k^2)/(1 + 5k)

Therefore, f(1/k) = (1 - 9k^2)/(1 + 5k).

Answer:2

Step-by-step explanation:I DONT REALLY GIVE A THING I NEED POINTS.

Answer:

0<b<=12

Step-by-step explanation:

The answer is that the Rental agency will earn a maximum income of 25200 dollars when it charges 60 dollars per day.

We can Define Income as it is the money that an individual or organization receives in return for their services or goods.

Given,

440 cars at a rate of 40 dollars per day

Each 1dollar increase in rate and 10 fewer cars rented.

Rental:

R(x) = ( 40 + x ) dollars per car per day

A number of cars rented :

N(x) = 440 - 10 x

Income:

[tex]I = (40+x)(440-10x)[/tex]

For maximum Income,

[tex]\frac{dI}{dx} = 0[/tex]

Then,

[tex]\frac{dI}{dx} = \frac{d}{dx} [(40+x)(440-10x)][/tex]

Using formula

[tex]\frac{d}{dx} (u,v)=u \frac{d}{dx}v+v \frac{d}{dx}u[/tex]

Then,

[tex]\frac{d}{dx} [(40+x)(440-10x)]=(40+x) \frac{d}{dx}(440-10x)+(440-10x)\frac{d}{dx}(40+x)[/tex]

[tex](40+x)(-10) + (440-10x)(1) = 0[/tex]

[tex]-400 -10x + 440 - 10x = 0[/tex]

[tex]40 - 20x = 0[/tex]

[tex]20x = 40[/tex]

[tex]x=\frac{40}{20}[/tex]

[tex]x = 20[/tex]

Rental :

[tex](40 +x) = (40+20) = \$\ 60[/tex]

And maximum income:

[tex]= (40+x)(440-x)[/tex]

[tex]= (40+20)(440-20)[/tex]

[tex]= 60 * 420[/tex]

[tex]= \$\ 25200[/tex]

Rental agency will earn a maximum income of 25200 dollars when it charges 60 dollars per day.

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The labels on the x-axis indicate the type of card, and the percentages are listed on the y-axis.

Algebraic expression can be defined as combination of variables and constants.

To create a percent bar graph for the cards in the deck, we first need to determine the percentage of each type of card in the deck.

There are a total of 25 cards in the deck, and the breakdown of each type of card is as follows:

4 cards labeled with a "": (4/25) x 100% = 16%

6 cards labeled with a "": (6/25) x 100% = 24%

10 cards labeled with a "": (10/25) x 100% = 40%

5 cards labeled with a "": (5/25) x 100% = 20%

Now that we have the percentage for each type of card, we can create the percent bar graph.

Cards Label    

"" 16%  

""  24%  

""   40%

""    20%

In this graph, each bar represents a type of card in the deck, and the length of each bar represents the percentage of cards that fall into that category.

Therefore, The labels on the x-axis indicate the type of card, and the percentages are listed on the y-axis.

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The cost for 17 computers, 18 printers, 5 DVDs, and 30 CDs would be around $12,125.

Cost is the amount of money or resources that must be exchanged for goods, services, or activities. It is typically associated with the purchase of goods and services and related to production, labor, and other expenses. Cost is a crucial factor in business operations, as it affects both the budget and the profitability of any venture. In addition to monetary costs, businesses may also incur opportunity costs, which are the costs associated with foregoing alternative investments or activities.

The cost of 17 computers, 18 printers, 5 DVDs, and 30 CDs would depend heavily on the type, brand, and quality of the items being purchased. However, an estimate of the cost of these items can be made.

Computers can range from $200 to $2,000, depending on the type and specs. An average cost for 17 computers would be around $10,000. Printers can range from $50 to $500, depending on the type and specs. An average cost for 18 printers would be around $2,000. DVDs can range from $2 to $25, depending on the type and specs. An average cost for 5 DVDs would be around $50. CDs can range from $1 to $10, depending on the type and specs. An average cost for 30 CDs would be around $75.

In total, the cost for 17 computers, 18 printers, 5 DVDs, and 30 CDs would be around $12,125.

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The statement that cannot be true is "length RW is a midsegment of the triangle".

option D.

The midsegment of a triangle is a line segment that connects the midpoints of two sides of a triangle. More specifically, if a triangle has sides of lengths a, b, and c, then the midsegment connects the midpoints of the two sides of length a and is parallel to the side of length c.

The length of the midsegment is half the length of the third side (c/2).

In other words, if a triangle has sides AB, BC, and AC, then the midsegment connects the midpoint of AB (denoted as M) to the midpoint of BC (denoted as N) and is parallel to AC. The length of the midsegment MN is equal to half the length of AC (MN = 1/2 * AC).

For the given diagram, the midpoint is S, so the length RW cannot be the length of the midsegment.

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Answer: |a|=−4

Step-by-step explanation:Divide each term in −|a|=4by −1 and simplify.

Based on the table, to the nearest whole number, 7000 people in the total population of 60,000 have green eyes.

We know that;

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Here, We have;

The total number of respondents in the survey is:

= 32 + 14 + 25 + 49

= 120

And, The proportion of respondents with green eyes is:

= 14/120

= 0.1167

Hence, To estimate the number of people in the total population of 60,000 who have green eyes, we can multiply the proportion by the total population:

0.1167 x 60,000 = 7,002

After Rounding this to the nearest whole number gives us:

7,002 ≈ 7,000

Therefore, The answer is, 7,000 people.

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A survey is conducted to investigate the self-identified eye colors of a representative portion of a population. The table shows the results.

Self-Identified Eye Color

Number of Respondents

blue

32

green

14

hazel

brown

25

49

Based on the table, to the nearest whole number, how many people in the total population of 60,000 have green eyes?

O 140 people

O 700 people

O 1,400 people

O 7,000 people

The value of x for the given tangent angle is 1.5.

The value of x can be determined by applying the following circle theorem about tangle angles as shown below.

2 x ∠LMN = 16x - 12 ( angle at tangent is half of the angle subtended at the arc)

2 ( 4x ) = 16x - 12

8x = 16x - 12

16x - 8x = 12

8x = 12

x = 12/8

x = 1.5

Thus, if ML is tangent to the circle at L, then the value of x is 1.5 (Written as a decimal)

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Answer:

Coordinates of center: (0, 5)

Radius of circle: 3

The actual perimeter of triangle will be 1.3m

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle. The perimeter is the whole side covered by the all sides.

The sum of all angle of triangle = 180

The blueprint for a new house includes a triangular-shaped room in the attic.

If the blueprint was made using a scale factor of 12

centimeter = 1 meter

The perimeter will be 9cm

12/9 = 1.3m

So the actual perimeter will be 1.3m.

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The total distance driven during the 4-hour trip is approximately 294.05 miles

An element of a number or any number of equal pieces is represented by a fraction. There is a fraction with an upper value (numerator) and a lower value (denominator) (lower value).

We must sum up the distances for each hour of the 4-hour journey to get the overall mileage.

1 hour's worth of driving covered 55.25 miles.

64 3/4 miles were covered in Hour 2 of driving.

52 3/10 miles were covered in Hour 3 of driving.

67.89 miles were covered in Hour 4 of driving.

We must transform the mixed number from Hour 2 into an improper fraction in order to sum these distances:

Driving distance in hour two: 64 3/4 = (4 x 64 + 3) / 4 = 259 / 4

We can now calculate the distances:

55.25 + 259/4 + 52.3 + 67.89

We need to find a common denominator so that we can add these numbers:

55.25 = 221/4

259/4 = 259/4

52.3 = 523/10

67.89 = 6789/100

We may now multiply the fractions:

221/4 + 259/4 + 523/10 + 6789/100 = 5881/20

5881/20 = 294 1/20 is the result of converting this improper fraction to a mixed number.

As a result, the 4-hour trip's total mileage came to about 294.05 miles.

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Therefore , the solution of the given problem of volume comes out to be  chocolate bar therefore has a 2940 cubic centimetre (cm3) capacity.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Two instances of cubic units are the numbers cm3 as well as in3. But mass can be used to measure an object's dimensions. Typically, an object's weight is transformed into mass units like kilos or kilogrammes.

Here,

The length, breadth, and height of the rectangular, prism-shaped chocolate bar can be multiplied to determine its volume.

Size = 15 centimetres

Width = undefined

Size equals 2 centimetres (thickness)

To solve for the width, we can rearrange this algorithm as follows:

=> Area/Length =  Width

We are aware that the necessary length is 15 centimetres and the necessary area is 1470 cm2, so:

=> width =  1470/15

=>  98 centimetres.

Now that we are aware of every aspect of the chocolate bar, we can calculate its volume:

=> Volume = Length * Width * Height

=>  15 cm x 98 cm x 2 cm = 2940 cm³

The chocolate bar therefore has a 2940 cubic centimetre (cm3) capacity.

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The probability is approximately 0.129 or 12.9%.

Probability can also be used to describe more complex events, such as the likelihood of a stock price increasing by a certain amount in a given period of time, or the probability of a medical treatment being effective for a certain disease.

To calculate the probability that Cindy will get at least 48 orange Stattles in her next 14 ounce bag, we need to use the binomial probability formula:

P(X >= 48) = 1 - P(X < 48)

Where

X is the number of orange Stattles in a 14 ounce bag

P(X < 48) is the probability of getting less than 48 orange Stattles in a 14 ounce bag

To calculate P(X < 48), we need to use the binomial probability formula:

[tex]P(X = x) = (nCx) * p^x * q^{(n-x)[/tex]

Where

n is the number of Stattles in a 14 ounce bag (we don't know this value)

x is the number of orange Stattles in a 14 ounce bag (we want to find the probability of getting less than 48)

p is the probability of getting an orange Stattle (0.4)

q is the probability of getting a non-orange Stattle (0.6)

nCx is the binomial coefficient

nCx is the binomial coefficient, which can be calculated using the formula:

nCx = n! / (x! * (n-x)!)

where ! denotes the factorial function.

We can use a cumulative binomial distribution table or a binomial calculator to find the probability of getting less than 48 orange Stattles in a 14 ounce bag. For example, using an online calculator, we find that:

P(X < 48) = 0.871

Therefore, the probability that Cindy will get at least 48 orange Stattles in her next 14 ounce bag is:

P(X >= 48) = 1 - P(X < 48) = 1 - 0.871 = 0.129

So, the probability is approximately 0.129 or 12.9%.

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A statement with more than two variables or numbers can be written as an expression using addition, subtraction, multiplication, and division operations. Tickets for the film are $16 each.

A combination of symbols and/or numbers that infers a quantity or a mathematical relationship between two quantities is known as an expression in mathematics. Variables, constants, and operators like addition, subtraction, multiplication, and division can all be found in expressions.

Given that,

Total amount spent = $24.

Cost of the movie ticket = m

Cost of popcorn and soft drinks = 1/2 x m = $(m/2)

The cost of the movie will be calculated as,

Cost of popcorn + Cost of soft drinks + Cost of the movie = $24

[tex]\dfrac{m}{2} + m = 24[/tex]

[tex]\dfrac{(m + 2m)} { 2} = 24[/tex]

[tex]\dfrac{3m}{2} = 24[/tex]

3m = 24 x 2

m = 8 x 2

m = $16

The cost of the movie ticket is $16.

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The complete question is given below.

Rafael spent 24 dollars on a movie ticket, popcorn, and a soft drink. if the combined cost of the popcorn and soft drink was 1/2 the boost of the movie ticket, what was the cost of the movie ticket?

Most TCS foods cool from 135°F to 70°F within two hours and from 70°F to 41°F within four hours when they're stored.

TCS foods are those foods that require time and temperature control to prevent the growth of harmful bacteria and other microorganisms that can cause foodborne illness.

The general rule is that TCS foods should be cooled from 135°F to 70°F within two hours and from 70°F to 41°F within an additional four hours. This means that the total time for cooling TCS foods should not exceed six hours.

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The full question is:

Fill in the blanks:

Most TCS foods cool from _________ within two hours and from _______ within four hours when they're stored. This means that they are considered safe since bacterial growth has not reached dangerous levels yet.

Answer:

Step-by-step explanation:

Let's simplify - 4 - (-5):-

[tex]\tt -4 - (-5)[/tex]

[tex]\tt -4+5[/tex]

[tex]\tt 1[/tex]

Now, let's see which expression has the same value:-

F. -4 + (-5)

[tex]\tt -4 + (-5)[/tex]

[tex]\tt -4-5[/tex]

[tex]\boxed{\tt -9}[/tex]

________________

G. -4 +5

[tex]\tt -4 +5[/tex]

[tex]\boxed{\tt 1}[/tex]

_________________

H. -5 + (-4)

[tex]\tt -5 + (-4)[/tex]

[tex]\tt -5-4[/tex]

[tex]\boxed{\tt -9}[/tex]

_________________

J. -5-(-4)

[tex]\tt -5-(-4)[/tex]

[tex]\tt -5+4[/tex]

[tex]\boxed{-1}[/tex]

Therefore, we can say that G. -4 +5 has a similar value as

-4 - (-5).

________________________

Hope this helps! :)

Answer: 9g+10

Step-by-step explanation:

Simple addition 6+3=9

Since 10 doesnt have a variable you just add it to the end of the equation, make sure to keep the sign = 9g-10

The diagonal of rectangular prism with dimensions 7 in x 5 in x 12 in is 14.76 in

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases.

A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.

Given is a rectangular prism with dimensions 7 in x 5 in x 12 in, we need to find the diagonal of the rectangular prism,

Diagonal of a rectangular prism = √l²+w²+h²

L = length

W = width

H = height

Diagonal of a rectangular prism = √7²+5²+12²

= 14.76 in

Hence, the diagonal of rectangular prism with dimensions 7 in x 5 in x 12 in is 14.76 in

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The correct equation represents the relationship in the table is,

⇒ w =  d - 1.25

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The table shows the relationship between d, the amount of money Alice has at the beginning of each day, and w, the amount of money she has after riding the bus to work.

Hence, By all the options;

The correct equation satisfy the given values in table.

For first option;

w = d + 1.25

Put  d = 15.75;

w = 15.75 + 1.25

w = 17

Hence, It is wrong.

For fourth equation;

w =  d - 1.25

Put  d = 15.75;

w = 15.75 - 1.25

w = 14.50

Hence, It is correct equation.

Thus, The correct equation represents the relationship in the table is,

⇒ w =  d - 1.25

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The statement missing in the proof is option D. m ∠ ⁢ 3 + m ∠ ⁢ 5 = 180 ∘.

A triangle is classified as a geometric shape with three sides and three angles. It is one of the basic shapes in geometry, and is typically characterized by its three interior angles, which must add up to 180 degrees. The most common types are the equilateral triangle (all sides equal), the isosceles triangle (two sides equal), and the scalene triangle (no equal sides).

A proof involves logical deduction of the statements in order to arrive at a conclusion. In this case, the conclusion is that the angles 3, 5, and 7 are all congruent. To do this, the proof must show that the angles add up to 180 degrees, which is the sum of the angles in a triangle. Option D, m ∠ ⁢ 3 + m ∠ ⁢ 5 = 180 ∘, is the statement that must be included in the proof to show that the angles are congruent. Without this statement, it is impossible to prove that the three angles are congruent. Therefore, Option D is the missing statement in the proof.

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Given- Square root of 14 multiplied by square root of 10

To find - which is equivalent to the product below

Explanation - We can write the square root of 14 as

[tex]\sqrt{14} =\sqrt{2} \sqrt{7}[/tex]

and square root of 10 as

[tex]\sqrt{10} =\sqrt{2} \sqrt{5}[/tex]

Now

[tex]\sqrt{14} \sqrt{10} =\sqrt{2} \sqrt{5} \sqrt{2} \sqrt{7} =2\sqrt{35}[/tex]

Hence the choice is equivalent is D

Final answer - The final answer is D