Which conditions will construct a triangle? Mark all that apply.

Angles 30°, 30°, 30°
Angles 40°, 70°, side length 6 cm
Side lengths 11 cm, 4 cm, 8 cm
Side lengths 5 cm, 15 cm, 25 cm
Angles 20°, 150°, 10°

Answer:

7/5, 3/2, 11/4, 15/4, 13/3.

Step-by-step explanation:

Convert all to decimal then arrange from lowest to highest

Therefore, the coordinates of point P are(-3+√(2), -5-√(2)).

A coordinate is a set of values that specifies the position of a point or an object in a geometric space. In two-dimensional Euclidean space (i.e., on a plane), the most common coordinate system is the Cartesian coordinate system, which consists of two axes, the x-axis and the y-axis, that intersect at a point called the origin. Any point in the plane can then be uniquely identified by its x-coordinate (its horizontal distance from the origin) and its y-coordinate (its vertical distance from the origin).

Here,

To find the coordinates of point P, we need to use the ratio given to divide the line segment AB into two parts.

Let's first find the coordinates of point A and B:

A = (-3, -5)

B = (1, -9)

The ratio given is 1:3, which means that AP:PB is also 1:3. Let's call the coordinates of point P (x, y).

We can use the midpoint formula to find the coordinates of the midpoint M of line segment AB:

M = ((-3+1)/2, (-5-9)/2) = (-1, -7)

Now, we can use the fact that AP:PB is 1:3 to set up the following equation:

AP/PB = 1/3

We can rewrite this as:

AP = (1/4) AB

where AB is the distance between A and B:

AB = √((1-(-3))²  + (-9-(-5))²)

= √(16+16)

=4√(2)

So, we have:

AP = (1/4) AB = (1/4) * 4√(2)

= √(2)

We also know that the vector AP is in the same direction as the vector AM, which goes from A to M:

AM = (-1-(-3), -7-(-5))

= (2, -2)

To find the vector AP, we can scale AM to have length sqrt(2):

AP = (√(2)/||AM||) AM

= (√(2)/2) (2, -2)

= (√(2), -√(2))

Finally, we can find the coordinates of point P by adding AP to the coordinates of A:

P = A + AP

= (-3, -5) + (√(2), -√(2))

= (-3+√(2), -5-√(2))

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The correct statement regarding the association of the time the player spent practicing and the number of points he scored in the game is given as follows:

As the time a basketball player practices increases, the number of points scored in a game increases with a strong nonlinear association.

The more the player practices, the better he/she performs, that is, the more points are scored, hence the number of points increases as the number of hours practiced increase.

However, there reaches a certain threshold where the player is as good as possible, hence the points tend to stabilize, meaning that there is a nonlinear association between the variables.

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Answer:

Step-by-step explanation:

The digit 3 in the number 4693 has a place value of 3 tens or 30. Therefore, the value of the number 3 in the number 4693 is 30.

Equation of the line passing through (1, 5) is y = 3x + 2

A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely.

A line with no curve is called straight line.

Given,

A line is parallel to the line y = 3x - 2

To find slope of the given line, comparing with slope-intercept equation of line

y = mx + c

Slope m = 3

Line passes through point (1 , 5)

Slope of parallel lines are equal

m' = m = 3

Equation of the line

y - y' = m'(x - x')

y - 5 = 3(x - 1)

y - 5 = 3x - 3

y = 3x + 2

Hence, y = 3x + 2 is equation of the line passing through point (1,5).

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y=3x+2 is the equation of the line which is parallel to the line y=3x-2 and passes through the point 1,5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given equation is y=3x-2

3 is the slope of given line.

The line parallel to this line will have same slope, slope is 3.

Now, the equation of line passing through 1, 5

5=3(1)+b

b=2

So slope intercept form y=3x+2

Hence,  y=3x+2 is the equation of the line which is parallel to the line y=3x-2 and passes through the point 1,5

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There are no numbers between 1.8×100 and 195%.

The representation of quantities or values using numbers is a fundamental idea in mathematics. They can be applied to measure, compare, compute, and count. Depending on the situation and the chosen notational system, numbers can be represented in a variety of ways, such as digits, words, or symbols.

Based on their attributes and traits, several sorts of numbers can be distinguished in mathematics. The following list includes some of the most typical numbers:

To identify the numbers between 1.8×100 and 195%, we need to convert both numbers to the same unit of measurement.

1.8×100 = 180

195% = 1.95 (since 195% is equal to 1.95 times the original quantity)

Now, we need to identify all numbers between 180 and 1.95. To do this, we can simply list all the numbers that are greater than 180 and less than 1.95, excluding 180 and 1.95 themselves. However, we notice that there are no such numbers, because:

Any number greater than 180 is also greater than 1.95 since 1.95 is less than 2 and 180 is greater than 2.

Any number less than 1.95 is also less than 180 since 180 is greater than 100 (which is 1% of 10,000) and 1.95 is less than 2.

Therefore, there are no numbers between 1.8×100 and 195%.

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Answer:

1 7/8

Step-by-step explanation:

i took the test

Answer:

First choice

Step-by-step explanation:

Answer:

Th answer is the FIRST CHOICE(A).

Have a GOOD DAY!

Maura will have 5, 206 points at either hotel by booking 301 nights.

To find the number of points, we shall assume that nights are denoted as n. The number of points for Hotel Elegance will be shown as :

= Signing up points + ( Number of points per night x Number of nights)

= 89 + 17 n

The number of points for Hotel Paradiso is:

= 691 + 15 n

The number of nights that Maura needs to stay for the points to be the same is :
89 + 17 n = 691 + 15 n

17 n - 15 n = 691 - 89

2 n = 602

n = 602 / 2

n = 301 nights

The number of points would be :

= 691 + 15 n

= 691 + 15 x 301

= 5, 206 points

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that in the second year, we use the beginning book value of $639,900

a. Sum-of-the-years’-digits method:

To compute the depreciation using the sum-of-the-years’-digits method, we first need to determine the total number of years of the asset's useful life. We do this by subtracting the salvage value from the cost and dividing by the estimated yearly depreciation.

Cost of asset = $711,000

Salvage value = $60,000

Useful life = 20 years

Yearly depreciation = (Cost - Salvage value) / Useful life

Yearly depreciation = ($711,000 - $60,000) / 20 = $32,550

To calculate the sum-of-the-years’-digits (SYD) for this asset, we add up the digits of the useful life in descending order. For a 20-year useful life, the SYD would be:

SYD = 20 + 19 + 18 + ... + 1 = 210

Using the SYD and the number of remaining years, we can calculate the depreciation expense for each year as follows:

Year 2020:

Depreciation expense = (20/210) x ($711,000 - $60,000) = $64,286

Year 2021:

Depreciation expense = (19/210) x ($711,000 - $60,000) = $60,952

b. Double-declining-balance method:

To compute the depreciation using the double-declining-balance (DDB) method, we first need to determine the asset's straight-line depreciation rate, which is calculated as follows:

Straight-line depreciation rate = 1 / Useful life

Straight-line depreciation rate = 1 / 20 = 0.05

The DDB depreciation rate is twice the straight-line rate, or 0.10. We can then calculate the depreciation expense for each year as follows:

Year 2020:

Depreciation expense = Beginning book value x DDB rate

Beginning book value = Cost of asset

Depreciation expense = $711,000 x 0.10 = $71,100

Year 2021:

Depreciation expense = Beginning book value x DDB rate

Beginning book value = Cost of asset - Accumulated depreciation from previous years

Accumulated depreciation (2020) = $71,100

Beginning book value (2021) = $711,000 - $71,100 = $639,900

Depreciation expense = $639,900 x 0.10 = $63,990

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Answer:

- 4

Step-by-step explanation:

(f + g)(3) = f(3) + g(3)

f(3) = - 5

g(3) = 1

f(3) + g(3) = - 5 + 1 = -4

Answer:

Step-by-step explanation:

sh45haaa           aaaa

Answer:

Step-by-step explanation:

half the base times the height

Answer:

y- intercept = 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (4, - 1 ) into the partial equation

- 1 = - 2(4) + c = - 8 + c ( add 8 to both sides )

7 = c

that is the y- intercept = 7

The volume of the sand pit is V = 694.6 feet²

The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle

Volume of Rectangle = Length x Width x Height

Volume of Rectangle = Area of Rectangle x Height

Given data ,

Let the volume of the rectangle be represented as V

Now , the length of the sand pit = 30.2 feet

The width of the sand pit = 9.2 feet

The depth of the sand pit = 30 inches = 2.5 feet

Now , the volume of the rectangular pit = L x W x H

On simplifying the equation , we get

The volume of the rectangular pit V = 30.2 x 9.2 x 2.5

The volume of the rectangular pit V = 694.6 feet²

Hence , the volume of the rectangular sand pit is 694.6 feet²

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Based on the distance formula, when the total distance is 7 miles and the average speed is 7 miles per hour, the time taken is 1 hour.

Distance refers to the length from one point to another.

To compute the distance, we need to know the speed and the time taken.

Distance formula is:

Distance = Time x Speed

When the distance is given, the time or average speed can be obtained as the quotient of distance and average speed or time, as the case may be.

Thus, using the distance, time, and speed formulas, the time taken to cover a distance of 7 miles at an average speed of 7 miles per hour is 1 hour.

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esta es la respuesta 8 B)

porque si lo restas y sumas da a 8

Answer:

Step-by-step explanation:

In a circle with a radius of 0.1, an arc length of 0.4 is intercepted by an angle. To find the angle in radians, we use the formula:

angle in radians = arc length / radius

Substituting the given values, we have:

angle in radians = 0.4 / 0.1 = 4

So the angle in radians is 4 radians, to the nearest tenth.

Answer:

The solution is 11

Step-by-step explanation:

To solve this question is quite easy, here are the step-by-step:

[tex] \sf \lim_{ t \to - 3} \sf ( - {t}^{2} - 6t + 2) \\ \\ \sf = - ( - 3)^{2} - 6( - 3) + 2 \\ \\ = \sf { - ( 9)} + 18 + 2 \\ \\ = \sf 9+ 2 \\ \\ = \sf 11[/tex]

The equation of rational function is f(x) = 3 - (5/2)(x - 5)(x + 1) / ((x + 2)(x + 6))

One possible equation for a rational function with the given properties is:

f(x) = 3 + (k(x + 5)(x - 5)) / ((x + 2)(x + 6))

Here, k is a constant that determines the vertical scale of the function. We choose the factor (x + 5)(x - 5) in the numerator to make the x-intercepts at x = 5 and x = -5. We choose the factors (x + 2) and (x + 6) in the denominator to make the vertical asymptotes at x = -2 and x = -6. We choose the constant term 3 in the equation to make the horizontal asymptote at y = 3.

To determine the value of k, we can use one of the x-intercepts, say x = 5. Substituting x = 5 into the equation and setting the result to 0 (since the function has an x-intercept at x = 5) gives:

0 = 3 + (k(5 + 5)(5 - 5)) / ((5 + 2)(5 + 6))

Simplifying the right-hand side, we get:

0 = 3 + 0 / (7 * 11)

0 = 3

This equation is not true, which means that we have made a mistake somewhere. The mistake is in assuming that the x-intercepts occur at x = 5 and x = -5. Instead, we should have x-intercepts at x = 5 and x = -1, which are the roots of the numerator (x - 5)(x + 1). So we need to adjust the numerator in the equation to (x - 5)(x + 1) in order to get the correct x-intercepts.

The correct equation for the rational function is:

f(x) = 3 + (k(x - 5)(x + 1)) / ((x + 2)(x + 6))

To determine the value of k, we can use the other x-intercept, x = -1. Substituting x = -1 into the equation and setting the result to 0 gives:

0 = 3 + (k(-1 - 5)(-1 + 1)) / ((-1 + 2)(-1 + 6))

Simplifying the right-hand side, we get:

0 = 3 + 6k / 5

Multiplying both sides by 5, we get:

0 = 15 + 6k

Solving for k, we get:

k = -15 / 6 = -5/2

So the final equation for the rational function is:

f(x) = 3 - (5/2)(x - 5)(x + 1) / ((x + 2)(x + 6))

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The measures of the angles are given as A' = 103, B' =100, c' = 80, D' = 77

∠x

125 + ∠x = 180 (angle on a straight line)

∠x = 55 degrees

∠y

∠x + ∠y + 48 = 180 angles in a triangle

55 + ∠y + 48 = 180

∠y = 77 degrees

∠D

∠d = ∠Y vertically opposite

∠a + ∠D = 180

∠A = 180 - 77

= 103 degrees

∠B  + 80 = 180

∠b = 100 degrees

∠c + ∠ b = 180

∠c = 180 - 100

= 80 degrees

hence A' = 103, B' =100, c' = 80, D' = 77

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Answer: -1/2

Step-by-step explanation: The formula is y=mx+b where m is your slope and b is your y-intercept. Therefore, your b or y-intercept is -1/2

Answer:

[tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

In the equation [tex]y=mx+b[/tex], m is the slope and b is the y intercept. In this equation, we are given the slope is 4 and the y intercept as [tex]-\frac{1}{2}[/tex] because the equation can be simplified to [tex]y=4x+-\frac{1}{2}[/tex]

volume of a cube = x³

where x the length of the side of the cube

so, the volume = (4.2)³

= 74.088 in³

Answer:

Step-by-step explanation:

Let's begin by calculating Jim's total cost for creating one painting:

Cost of paint and canvas + Cost of brushes = $44 + $1 = $45

This means that Jim makes a profit of $45 - $45 = $0 per painting sold until he breaks even.

To determine how many paintings Jim needs to sell to break even, we can set up an equation:

Total Cost = Total Revenue

Let's say Jim sells x paintings. Then his total revenue would be:

Total Revenue = $45x

His total cost would be the cost of materials plus the cost of brushes multiplied by the number of paintings:

Total Cost = $45 + $1)x = $46x

Setting these equal, we get:

$46x = $45x

Solving for x, we get:

x = 45

So Jim needs to sell 45 paintings to break even.

Once he has sold 45 paintings, he will have earned:

Total Revenue = $45 x 45 = $2025

So Jim will have earned $2025 after selling 45 paintings.

Answer:

Step-by-step explanation:

To break even, Jim's total revenue from selling his paintings should be equal to his total cost of producing them, including the cost of materials and the cost of the brushes. Let's call the number of paintings he needs to sell to break even as "x".

The cost of producing each painting is $44 + $1 = $45.

The revenue from selling each painting is $45.

So, Jim's total revenue from selling x paintings would be:

Total revenue = Price per painting x Number of paintings sold

Total revenue = $45 x x

Total revenue = $45x

Jim's total cost of producing x paintings would be:

Total cost = Cost per painting x Number of paintings produced + Cost of brushes

Total cost = $45 x x + $1

Total cost = $45x + $1

For Jim to break even, his total revenue must equal his total cost:

Total revenue = Total cost

$45x = $45x + $1

Solving for x:

$45x - $45x = $1

0 = $1

This is a contradiction, meaning that the situation is impossible. It is impossible for Jim to break even by selling his paintings at the given prices. If he sells each painting at $45, which is the same price he paid to produce it, he will not make any profit. In fact, he will lose $1 for every painting he sells due to the cost of the brushes.

If Jim wants to break even or make a profit, he will need to increase the selling price of his paintings or find ways to reduce the cost of producing them.

The coordinates of the point R: (0, 3.4)

What is the slope?

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line

Slope PQ 5–0/ 2–6 = 5 /-4

equation of PQ y =-5/4 x +c ;

this passing through 2,5

5 =-5/4*2 +c ; C = 5 -5/2 =5/2

y =-5x/4+5/2 =-5x+10/4 ; 4y =-5x +10 ;

equation of PQ =5x +4y-10 =0 ;

slope of PR : m1 *m2 =-1 ;m2 = -1/ [-5/4 ] = 4/5

equation of PR y = mx +c this passes through [2,5]

5 = 4/5*2 +C so C = 5- 8/5 =17/5

y =4 x /5 +17/5 so coordinates of R = [0, 3.4]

Hence, the coordinates of the point R: (0, 3.4)

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Applying the law of sines, the value of c is calculated as: c ≈ 11.8.

The Law of Sines, also known as the Sine Rule, is a theorem in trigonometry that relates the side lengths of a triangle to the sine of its angles.

Specifically, it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all three sides of the triangle. Mathematically, this can be expressed as:

a / sin A = b / sin B = c / sin C

Where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides.

Applying the law of sines, we have:

c/sin 105 = 7/sin 35

Cross multiply:

c * sin 35 = 7 * sin 105

c = 7*sin 105/sin 35

c ≈ 11.8

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The ratio of people waiting in line for the slingshot is 2:21

A ratio is a relationship between two quantities that expresses how many times one quantity is contained in the other. It can be expressed in different ways, such as with the use of a colon (:), a fraction (/), or the word "to.

From the question, the total number of people is 15 + 4 + 12 + 11 = 42

The number of people waiting for slingshot is = 4

The ratio of slingshot waiting in line = 4/42

The ratio = 2:21

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Answer:

Step-by-step explanation:

a. The average rate of change in the cost of the hamburger during the period from 2012 to 2022 can be calculated as the difference in the cost of the hamburger divided by the number of years between the two prices.

So, the average rate of change in the cost of the hamburger is:

(6.12 - 4.32) / (2022 - 2012) = 0.18

Therefore, the average rate of change in the cost of the hamburger during this period is $0.18 per year.

b. We can use the point-slope form of a linear equation to model the cost of the hamburger as it changes over time. Let y be the cost of the hamburger in dollars, and t be the number of years since 2012. We know that the cost of the hamburger in 2012 was $4.32, so we have a starting point of (0, 4.32).

Using the average rate of change calculated in part a, we can find the slope of the line:

slope = (6.12 - 4.32) / (2022 - 2012) = 0.18

Now we can write the equation of the line as:

y - 4.32 = 0.18t

y = 0.18t + 4.32

So, the linear equation that models the cost of the hamburger in terms of years since 2012 is y = 0.18t + 4.32.

c. To find when the cost of the hamburger will reach $7.02, we can substitute y = 7.02 into the equation we found in part b and solve for t:

7.02 = 0.18t + 4.32

2.7 = 0.18t

t = 15

So, the cost of the hamburger will reach $7.02 in the year 2012 + 15 = 2027.

The solution to the matrix is x1 = (-555 - 356x3)/90, x2 = (138 + 89x3)/10 and x3 = free variable

To find the solution to this matrix, we need to perform row operations to put it into row echelon form or reduced row echelon form. We can do this by adding multiples of one row to another row, multiplying a row by a nonzero scalar, and swapping two rows.

Here are the row operations we can use to put this matrix into row echelon form:

1. Add 5 times the first row to the third row to eliminate the 5 in the (3,1) entry:

0 0 -9 6

0 -1 -4 4

25 35 11 38

2. Multiply the second row by -1 to make the pivot in the second row, second column equal to 1:

0 0 -9 6

0 1 4 -4

25 35 11 38

3. Add 9 times the second row to the first row to eliminate the -9 in the (1,3) entry:

0 9 0 -30

0 1 4 -4

25 35 11 38

4. Add -25 times the second row to the third row to eliminate the 25 in the (3,1) entry:

0 9 0 -30

0 1 4 -4

0 10 -89 138

5. This matrix is now in row echelon form. We can solve for the variables by back-substitution. Starting with the last row:

0 10 -89 138 | x3

We have:

10x2 - 89x3 = 138

Solving for x2, we get:

x2 = (138 + 89x3)/10

Substituting this expression for x2 in the second row, we have:

Copy code

0 1 4 -4 | (138 + 89x3)/10

Solving for x1, we get:

9x1 + 4(138 + 89x3)/10 = -30

Simplifying and solving for x1, we get:

x1 = (-555 - 356x3)/90

So the solution to the matrix is:

x1 = (-555 - 356x3)/90

x2 = (138 + 89x3)/10

x3 = free variable

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After Justin leaves his house he reaches a maximum distance of 20 blocks away from his house after 7 minutes of being out of his home.

To graph Justin's displacement we must use a Catersian plane. In this case we put the time on the X axis (time) and the distance on the Y axis (blocks). Once we set these parameters, we must put the information on the graph.

In the places where a time takes only the progressing of time without any displacement. Additionally, when you travel it is important to take into account the speed (blocks/minute) that Justin has to obtain a correct graph.

According to the above, after 7 minutes Justin is 20 blocks away from his house and this distance travels in 4 minutes to return home.

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The dimensions of the rectangle after dilation by a sclae factor of 3 is,

Length = 15 inches

Breadth = 27 inches.

A dilation is a transformation that produces an image of a different size but with a similar overall shape to the original.

A dilation that enlarges an image is called an enlargement, and a dilation that shrinks an image is called a reduction.

The scale factor, which is employed to enlarge a mathematical entity, will determine the size of the image (compared to the original object). When the absolute value of the scaling factor is greater than 1, an expansion occurs.

The given rectangle dimension is :

width= 5 inches and

length= 9 inches.

When the sides of a rectangle are multiplied by a scale factor of 3, the rectangle is said to be dilated by that factor.

So, the width of rectangle is after dilation is 5×3 = 15  inches

So, the length of rectangle is after dilation is 9×3 = 27 inches

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The composite function has its value to be 54168

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

f(x)=10x^2-8x

g(x)=7x-3.

Given the composite function [f o g] (11)., we have

[f o g] (11) = f(g(11))

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

g(11) =7 * 11 - 3

Evaluate

g(11) =74

So, we have

[f o g] (11) = f(74)

[f o g] (11) = 10(74)^2 - 8(74)

[f o g] (11) = 54168

Hence, the solution is 54168

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