Two of the angles in a triangle measure 51° and 25°. What must be the measure of the third angle?

Answer:

i- alrighty then

Step-by-step explanation:

The slope-intercept form for the line passing through (6,5) and parallel to the line passing through (2,8) and (-8,4) is y = (2/5)x + 13/5.

To find the slope-intercept form for the line passing through (6,5) and parallel to the line passing through (2,8) and (-8,4), we need to determine the slope of the given line first.

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

Let's calculate the slope of the line passing through (2,8) and (-8,4):

slope = (4 - 8) / (-8 - 2)

     = -4 / (-10)

     = 2/5

Since the line we're looking for is parallel to this line, it will have the same slope. Now that we have the slope, we can use the point-slope form of a line to find the equation:

y - y₁ = m(x - x₁)

where (x₁, y₁) is the given point (6,5) and m is the slope (2/5). Plugging in the values, we get:

y - 5 = (2/5)(x - 6)

To convert it to the slope-intercept form (y = mx + b), we can simplify it further:

y - 5 = (2/5)x - (2/5) * 6

y - 5 = (2/5)x - 12/5

y = (2/5)x - 12/5 + 5

y = (2/5)x - 12/5 + 25/5

y = (2/5)x + 13/5

Therefore, the slope-intercept form for the line passing through (6,5) and parallel to the line passing through (2,8) and (-8,4) is y = (2/5)x + 13/5.

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The slope-intercept form for the line passing through (6,5) and parallel to the line passing through (2,8) and (-8,4) is y = (2/5)x + 13/5.

To find the slope-intercept form for the line passing through (6,5) and parallel to the line passing through (2,8) and (-8,4), we need to determine the slope of the given line first.

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

Let's calculate the slope of the line passing through (2,8) and (-8,4):

slope = (4 - 8) / (-8 - 2)

    = -4 / (-10)

    = 2/5

Since the line we're looking for is parallel to this line, it will have the same slope. Now that we have the slope, we can use the point-slope form of a line to find the equation:

y - y₁ = m(x - x₁)

where (x₁, y₁) is the given point (6,5) and m is the slope (2/5). Plugging in the values, we get:

y - 5 = (2/5)(x - 6)

To convert it to the slope-intercept form (y = mx + b), we can simplify it further:

y - 5 = (2/5)x - (2/5) * 6

y - 5 = (2/5)x - 12/5

y = (2/5)x - 12/5 + 5

y = (2/5)x - 12/5 + 25/5

y = (2/5)x + 13/5

Therefore, the slope-intercept form for the line passing through (6,5) and parallel to the line passing through (2,8) and (-8,4) is y = (2/5)x + 13/5.

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Answer:

96

Step-by-step explanation:

20 percent of 80 is 16, and added to 80 would equal 96

Answer:

C

Step-by-step explanation:

-3x+15=18

-3(-1)+15=18

3+15=18

Answer:

Correct answer is C

Step-by-step explanation:

-3 (-1) +15= 18

3+15=18

1101₂ + 1110₂ + 1001₂ = 100100₂

1101₂ = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8 + 4 + 0 + 1 = 13₁₀

1110₂ = 1×2³  + 1×2² + 1×2¹ + 0×2⁰ = 8 +  4 + 2 =  14₁₀

1001₂ = 1×2³ + 0×2² + 0×2¹ + 1×2⁰ = 8 + 1 = 9₁₀

13 + 14 + 9 = 36

36₁₀ =

36 : 2 = 18 + r 0

18 : 2 = 9 + r 0

9 : 2 = 4 + r 1

4 : 2 = 2 + r 0

2 : 2 = 1 + r 0

1 : 2 = 0 + r 1  ↑

= 100100₂

Answer:

\(\huge\boxed{1101_2+1110_2+1001_2=100100_2}\)

Step-by-step explanation:

We know:

\(0_2 + 0_2 = 0_2\\0_2 + 1_2 = 1_2\\1_2 + 1_2 = 10_2\)

\(\underline{+\begin{array}{ccc}_1\ \ \ \ \\1101\\1110\end{array}}\\.\ 11011\\\\\underline{+\begin{array}{ccc}_1\ \ _1_1 \ \\11011\\\ \ 1001\end{array}}\\.\ \ 100100\\\\\)

(2,4)

Step-by-step explanation:

I'm not sure in the slightest but with the formula I learned I think this is correct

Answer:

the fee at sunset bank will always be more than fee at Oceanview bank.

Answer:

D

Step-by-step explanation:

i got it correct and go to k-12

Zeroes of a function are the values of x when f(x) = 0

So to find the zeroes of the function from the graph search for the points whose y-coordinates = 0

The y-coordinates of the point = 0, if the points lie on the x-axis

That means the zeroes of the function are the points of intersection between the graph and the x-axis

let us see that in the graph

I will draw it and post it here

From the graph

The graph intersects x-axis at points (-7, 0) and (-2, 0)

Then the zeroes of the function are (-7, 0) and (-2, 0)

Let us make the table

x f(x)

-2 0

-1 6

0 14

1 24

2 36

Answer:

$4 per pound

Step-by-step explanation:

34/8.5(or 8 1/2) is equal to 4.

Answer:

1/6

Step-by-step explanation:

because there is six sides

option 2, \(\frac{2}{6}\)

Answer:

-4 =x

Step-by-step explanation:

2x - 5= 5x + 7

Subtract 2x from each side

2x-2x - 5= 5x-2x + 7

-5 = 3x+7

Subtract 7 from each side

-5-7 = 3x+7-7

-12 = 3x

Divide by 3

-12/3 = 3x/3

-4 =x

The chord length (C) between PC and P is 5.831 cm.

A chord is a straight-line segment that connects two points on a circle. P is a point on the circumference of the circle, while PC is a chord of the circle that passes through P.

Therefore, the chord length (C) between PC and P is equal to half of the length of the chord PC. In other words, we need to find the length of PC and divide it by 2. We can do this using the Pythagorean Theorem since we have a right triangle formed by PC and the diameter of the circle.

Diameter of the circle (AB) = 20 cm

Radius of the circle (OA) = AB/2 = 10 cm

Height of the triangle (OP) = 6 cm

Using the Pythagorean Theorem, we can find the length of PC as follows:

PC² = PO² + OC²PC² = 10² + 6²PC² = 136PC = √136PC ≈ 11.661

Therefore,  is equal to C = PC/2C = 11.661/2C ≈ 5.831 cm.

So, the answer to the question "What is the chord length (C) between PC and P? when the diameter of the circle = 20 cm and the Height of the triangle = 6cm" is 5.831 cm.

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The correct statements regarding activity diagrams are:

a. There can be multiple end points, but only one starting point.

c. A branch can have multiple incoming arrows.

d. A decision point may have more than 2 outgoing arrows.

e. An indeterminacy is created when the successors of an activity have non-mutually exclusive conditions.

f. An activity can be nested within another activity.

Activity diagrams are graphical representations used in software engineering to depict the flow of activities or actions within a system. The correct statements regarding activity diagrams are as follows:

a. There can be multiple end points, but only one starting point:

Activity diagrams typically illustrate the flow of activities from a single starting point to multiple end points. This allows for depicting different termination points in the system's behavior.

c. A branch can have multiple incoming arrows:

A branch in an activity diagram represents a decision point where the flow of activities can diverge. It is possible for multiple incoming arrows to converge at a branch, indicating different paths leading to the decision point.

d. A decision point may have more than 2 outgoing arrows:

A decision point in an activity diagram represents a condition or a decision that determines the subsequent flow of activities. It is possible for a decision point to have more than two outgoing arrows, indicating different paths based on the decision outcome.

e. An indeterminacy is created when the successors of an activity have non-mutually exclusive conditions:

In an activity diagram, if the subsequent activities following a certain action have conditions that are not mutually exclusive, it creates an indeterminacy. This means that multiple paths may be followed simultaneously based on the different conditions.

f. An activity can be nested within another activity:

Activity diagrams support the nesting of activities within each other. This allows for representing complex activities or sub-processes within a larger activity, providing a hierarchical structure to the diagram.

In conclusion, the correct statements regarding activity diagrams include multiple end points and a single starting point, the possibility of multiple incoming arrows at a branch, the presence of more than two outgoing arrows at a decision point, the creation of indeterminacy with non-mutually exclusive conditions, and the ability to nest activities within one another.

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We are interested in the activity diagram. Check all the correct answers.

Please select at least one answer.

O a. There can be multiple end points, but only one starting point.

O b. Any joint must have been preceded by a branch.

O c. A branch can have multiple incoming arrows.

O d. A decision point may have more than 2 outgoing arrows.

Oe. An indeterminacy is created when the successors of an activity have non-mutually exclusive conditions.

Of. An activity can be nested within another activity.

The scale factor used in the dilation is -2

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

Figure with vertices at L(1, 1)

Image with vertices at L'(-2, -2)

The scale factor is calculated as

Scale factor  = L'/L

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

Scale factor  = (-2, -2)'/(1, 1)

Evaluate

Scale factor  = -2

Hence, the scale factor is -2

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Answer:

very confusing but i'm guessing the glide reflection on triangle DEF

Step-by-step explanation:

1/2 = 4+D/ xy 7*

Answer:

A number that describes both the direction and the steepness of the line is known as slope of the line .

h'(1) is equal to (g'(1) - 2g(1)). To find the specific value of h'(1), you would need to know the explicit form or additional information about the function g(x) and evaluate it at x = 1.

To find h'(1), we will differentiate h(x) using the quotient rule and then substitute x = 1 into the derivative expression.

Using the quotient rule, the derivative of h(x) = g(x)/\(x^{2}\) is given by:

h'(x) = (g'(x) × \(x^{2}\) - g(x) × 2x) / \((x^{2})^{2}\)

= (g'(x) × x^2 - 2g(x) × x) / \(x^{4}\)

= (\(x^{2}\) × g'(x) - 2x × g(x)) / \(x^{4}\)

= (x × (x × g'(x) - 2g(x))) / x^4

= (x × (x × g'(x) - 2g(x))) / (\(x^{2}\) × \(x^{2}\))

= (x × (x × g'(x) - 2g(x))) / (\(x^{2}\))

Now, substitute x = 1 into the derivative expression:

h'(1) = (1 × (1 × g'(1) - 2g(1))) / (1)

= (g'(1) - 2g(1))

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The volume of the Solid -

V = ∫[-2,2] 4x^2(2x^2 - 1)(12x^2 - 1) dx

What is volume?

Volume is a measure of the amount of three-dimensional space occupied by an object or a region. It quantifies the extent or size of a solid object or a container. In simpler terms, volume is a measure of how much space an object takes up.

What is integral?

In mathematics, an integral is a fundamental concept in calculus that allows us to compute the total accumulation of a quantity over a given interval. It is used to find the area under a curve, the length of a curve, the volume of a solid, and many other applications.

To find the volume of the solid enclosed by the paraboloid z = 3x^2(y - 2)^2 and the planes z = 1, x = -2, x = 2, y = 0, and y = 2, we need to set up a triple integral over the given region.

The limits of integration for x, y, and z are as follows:

x: -2 to 2

y: 0 to 2

z: 1 to 3x^2(y - 2)^2

The volume V can be calculated as follows:

V = ∫∫∫R dz dy dx

where R represents the region defined by the given planes.

V = ∫∫∫R 3x^2(y - 2)^2 dz dy dx

To evaluate this triple integral, we integrate with respect to z first, then y, and finally x, using the given limits of integration:

V = ∫[-2,2] ∫[0,2] ∫[1,3x^2(y-2)^2] 3x^2(y - 2)^2 dz dy dx

Performing the integration:

V = ∫[-2,2] ∫[0,2] [3x^2(y - 2)^2z]∣[1,3x^2(y-2)^2] dy dx

V = ∫[-2,2] ∫[0,2] 3x^2(y - 2)^2[3x^2(y-2)^2 - 1] dy dx

V = ∫[-2,2] [x^2(y - 2)^2(3x^2(y-2)^2 - 1)]∣[0,2] dx

V = ∫[-2,2] 4x^2(2x^2 - 1)(12x^2 - 1) dx

Evaluate this integral using appropriate techniques or numerical methods, such as numerical integration or computer software, to find the volume of the solid enclosed by the paraboloid and the given planes.

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Answer: A.

Step-by-step explanation:

This is the only option in which the terms are ordered from least to greatest.

Therefore, A is the correct answer.

The value of x that makes 25x^2 + 70x + c a perfect square trinomial is c = 1225.

To make the quadratic expression 25x^2 + 70x + c a perfect square trinomial, we need to determine the value of c.

A perfect square trinomial can be written in the form (ax + b)^2, where a is the coefficient of the x^2 term and b is half the coefficient of the x term.

In this case, a = 25, so b = (1/2)(70) = 35.

Expanding (ax + b)^2, we have:

(25x + 35)^2 = 25x^2 + 2(25)(35)x + 35^2

= 25x^2 + 70x + 1225.

Comparing this with the given quadratic expression 25x^2 + 70x + c, we can see that c = 1225.

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Answer:

They are similar by SAS similarity.

Step-by-step explanation:

The angles SRQ and UTV are congruent, as given. The sides of both angles are proportionate, as 64/32=16/8. This means that the triangles have similar sides SR, UT and QR, VT. Since the angle is in the middle, we can conclude it's SAS or side angle side similarity.

Hope this helps :)

In order to consider an outlier, two things are taken into consideration, which are:First, The value is away from the mean of the data set.Secondly, The standard deviation of the data set.Using the standard deviation is considered one of the best ways to determine if a data point is an outlier or not.

Generally, any data point that falls more than three standard deviations from the mean of the data set is considered as an outlier.This is also known as the "68-95-99.7 rule".This rule states that approximately 68% of the data in a normal distribution fall within one standard deviation from the mean, 95% of the data falls within two standard deviations, and 99.7% of the data falls within three standard deviations.Therefore, if a data point falls beyond three standard deviations from the mean, it is considered as an outlier.Example:Let's say you have a data set of exam scores that have a mean of 75 and a standard deviation of 5. If you have a score of 60 in this data set, it would be considered an outlier since it falls more than three standard deviations away from the mean (60-75)/5 = -3.

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Answer:

$120.00

Step-by-step explanation:

2000/100 = $20 = 1%

20x12 = $240 = annual intrest = 12m

June 15 - December 15 = 6m

240/2 = $120 for half a year intrest!

Answer:

$120.00

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

Given the points, we can see that as x increases by 4, y decreases by 4, which means the slope is -1. Working backwards from (5, -8), we can decrease x by 5 (and thus increase y by 5, since we're subtracting a negative) and add that to -8 to find the y-intercept = -3

50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that a punch recipe calls for 1(¹/₂) quart of sparkling water and 3/4 of a quart of grape juice.

The ratio of sparkling water to grape juice is,

1(¹/₂) : (3/4 quarts) = (3/2) : (3/4) =  2 : 1

The amount sparkling water in the total volume is 2 : (2+1) = 2/3 of the total volume. For a volume of 100 quarts, the sparkling water content is

2/3 · 75quarts = 50 quarts

Then the grape juice content is,

1/3 · 75 quarts = 25 quarts

Therefore, 50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

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a) There are 8 different three-child families possible with respect to gender.

b) The probability of a three-child family with zero girls is 1/8.

a) To determine the number of different three-child families with respect to gender, we need to consider the possible combinations of boys (B) and girls (G) in each family. Birth order is taken into account, so the order of the children matters.

Let's analyze the possible combinations:

1. Three boys: BBB

2. Two boys and one girl: BBG, BGB, GBB

3. One boy and two girls: BGG, GBG, GGB

4. Three girls: GGG

Therefore, there are 8 different three-child families possible with respect to gender.

b) To calculate the probability of a three-child family with zero girls, we need to determine the favorable outcome (zero girls) divided by the total number of possible outcomes (8).

There is only one combination with zero girls: BBB. So, the probability of a three-child family with zero girls is 1/8.

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Step-by-step explanation:

6 men → 4 days → 3 metres

1 man → 24 days → 3 metres

1 man → 8 days → 1 metres

1 man → 56 days → 7 metres

10 men → 5.6 days → 7 metres

therefore, 5.6 days

Topic: direct n inverse proportions

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Answer:

It will take 5.6 days for the 10 men to dig the same hole 7 m deep.

Step-by-step explanation:

Laying the data in column

----------------------------------------------------

6 men            3 m hole              4 days

10 men           7 m hole             x days

-----------------------------------------------------

As \(6\) men dig a hole in \(4\) days, so their rate will be:

\(rate\:=\:\frac{4}{3}\)

Then  \(6\) men would take \(7\times \frac{4}{3}=\frac{28}{3}\) days to dig a hole of depth 7 m.

As we are letting 10 men do work, so they would

take \(\frac{6}{10}\times \frac{28}{3}=\frac{28}{5}\) days.

so

\(\frac{6}{10}\times \frac{28}{3}=\frac{28}{5}\)

             \(=5.6\)   days

Therefore, it will take 5.6 days for the 10 men to dig the same hole 7 m deep.

Answer:

6.4331 × 10 5N

Step-by-step explanation:

Given the following :

Mass (m) of car = 1200kg

Initial Velocity (u) of car = 60 mph

Final velocity = 0 ( comes to rest)

Velocity in m/s = 60 / 2.24 = 26.785 m/s

Time (t) = 0.0500

Using the relation :

Ft = m(v - u)

Where,

v = final velocity ; u = initial velocity ; t = time ; F = force

F*0.05 = 1200(26.785 - 0)

0.05F = 32142.86 - 0

F = 32142.86 / 0.05

F = 642857.14 N

F = 6.43 × 10^5 N