A triangle has vertices on a coordinate grid at

J(-7,−7) K(−7,3) and L(−1,3)
What is the length, in units, of JK ?

10 degrees is the measure of angle x from the circle

In order to determine the value of x from the given circle, we will use the theorem ' angle at the centre of the circle is twice the angle at the circumference.

Mathematically;

360 - 140 = 2arcED

220 = 2arcED

arcED = 220/2

arcED = 110 degrees

Hence the measure of angle x from the given figure is 110 degrees

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The distance of 2√65 miles Joselyn is from where she started.

The formula of the distance between two points is P(x₁, y₁) and Q(x₂, y₂) is given by: d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ².

Her initial position is the origin (0, 0), and she ran 2 miles north to reach (0, 2). Then, she ran 10 miles east to reach (10, 2). After that, she ran 4 miles north to reach (10, 6). Then, she ran 4 miles east to reach (14, 6). Finally, she ran 2 miles north to reach (14, 8).

To find the magnitude of Joselyn's displacement, we can use the Pythagorean theorem.  

We can consider the displacement from the starting point to Joselyn's final position as the hypotenuse of a right triangle, and the north-south and east-west displacements as the two shorter sides.

Thus, the displacement (d) can be calculated as:

d = √((14 - 0)² + (8 - 0)²)

d = √(14² + 8²)

d = √(196 + 64)

d = √(260)

d = 2√65

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The slope of the segment [tex]\overline{DC}[/tex] of the line DA is equivalent to the slope of the segment [tex]\overline{BA}[/tex], which is 2/5. Therefore;

Slope of [tex]\overline{DC}[/tex] = [tex]\frac{2}{5}[/tex]

The slope, m, of a graph with points (x₁, y₁), and (x₂, y₂) can be found using the formula;

[tex]m = \frac{y_2 - y_1}{x_2-x_1}[/tex]

The colinear points are; D, C, B, and A

The slope of the each section of a straight line graph are equivalent, therefore;

The slope of the line DA using the segment [tex]\overline{BA}[/tex] is the same as the slope of the line DA found using the segment of the line [tex]\overline{DC}[/tex].

The slope of a line is the ratio of the rise to the run of the line

Slope = Rise/Run

The rise of a segment of a line is the vertical elevation of the line segment, while the run of the segment of a segment of the line is the horizontal distance between the boundaries of the segment of the line.

The rise of the line between points A and B is 2 unit while the run of the segment [tex]\overline{BA}[/tex] is 5 units.

The slope of [tex]\overline{BA}[/tex] = (2 units)/(5 units) = 2/5

The slope of [tex]\overline{DC}[/tex] = The slope of BA = 2/5

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Answer:

2. x=16

4. x=18.75, y=11.2

Step-by-step explanation:

2. x/8=30/15 ⇒x=2x8=16

4. x/15=8/6.4 ⇒x=1.25x15=18.75

  y/14=6.4/8 ⇒y=0.8x14=11.2

The missing side lengths x = 16; y = 11.2 and x = 18.75

Similar figures (2)

Given that the triangles are similar, we make use of the following equivalent ratio

8 : 15 = x : 30

Multiply the first ratio by 2

So, we have

16 : 30 = x : 30

By comparison, we have

x = 16

Similar figures (4)

Given that the triangles are similar, we make use of the following equivalent fraction equation

y/6.4 = 14/8

So, we have

y = 6.4 * 14/8

Evaluate

y = 11.2

For x, we have

x/8 = 15/6.4

This gives

x = 8 * 15/6.4

So, we have

x = 18.75

Hence, the value of x is 18.75

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Answer:

[tex]-0.281250[/tex]

Step-by-step explanation:

The given number has [tex]5[/tex] after the decimal point, so add a trailing zero.

The height of the school is approximately 5.96 meters.

Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position.

The mirror and the triangles formed by the mirror, the top of the school, and the ground are similar. This means that the corresponding sides of the triangles are proportional.

Let x be the distance from the mirror to the top of the school. Then:

[tex]\dfrac{x} {7.95} = \dfrac{(x + h) }{ 2.3}[/tex]

We can simplify this equation by cross-multiplying and solving for x:

2.3x = 7.95(x + h)

2.3x = 7.95x + 7.95h

5.65x = 7.95h

[tex]x = \dfrac{7.95h} { 5.65}[/tex]

Now we can use the measurement of the distance from Ai Mi's eyes to the ground to find h. Let d be the distance from the mirror to Ai Mi's eyes. Then:

d = 1.15 meters

The triangles formed by Ai Mi's eye, the mirror, and the ground are similar, so:

[tex]\dfrac{h} { d} =\dfrac{ x} { (d + 2.3)}[/tex]

We can substitute the value of x from earlier:

[tex]\dfrac{h} { 1.15} = \dfrac{(\dfrac{7.95h} { 5.65)}} { 3.45}[/tex]

Simplifying:

[tex]h = \dfrac{(1.15 \times 7.95\times 3.45)}{ 5.65}[/tex]

h = 5.96 meters

Therefore, the height of the school is approximately 5.96 meters. Rounded to the nearest hundredth of a meter, the answer is 5.96 meters.

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Answer:

A : 0.9 B: 45.2 C:0.006 D:3/500 E:25% F: 1/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

a)C

b)D

c)B

d)A

ok so 5/10=0.5

and 5/50=0.1

and 5/100=0.05

and 5/20=0.25

The nth term of the sequence is a{n} = 35 + (-5)(n - 1) and the 100th term would be a{100} = - 460.

A sequence in which the difference of the consecutive terms remain constant is called a arithmetic sequence.

Given is the sequence as -

35, 30, 25, 20

We can write the nth term of the sequence as -

a{n} = a + (n - 1)d                                            ... { 1 }

a{n} = 35 + (-5)(n - 1)

For {n} = 100, we can write -

a{100} = 35 + (-5)(99)

a{100} = 35 - 495

a{100} = - 460

Therefore, the nth term of the sequence is a{n} = 35 + (-5)(n - 1) and the 100th term would be a{100} = - 460.

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9 is the value of C.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The three given angles are (3c)° 42° 111°

We need to find the value of C.

The figure might be a triangle because there are three angles.

From angle sum property , the sum of three angles of triangle is 180 degrees.

3c+42+111=180

3c+153=180

Substitute 153 from both sides

3c=27

Divide both sides by 3

c=9

Hence, the value of c is 9.

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The following table contains the appropriate values for A, B, and C:

White 13 52 91 130 Black 9 36 63 90

The definition of a proportionate relationship is as follows:

y = kx.

where k is the proportionality constant.

The following are the input and output variables for this issue:

Number of black keys to enter.

Number of white keys is the output.

The constant k is then obtained using the formula:

91 = 63k

k = 91/63

k = 13/9.

Hence the equation is:

y = 13x/9.

Hence the values are given as follows:

A: when x = 9, y = 13.

B: when x = 36, y = 13 x 36/9 = 52.

C: when x = 90, y = 13 x 90/9 = 130.

Hence the first table is correct.

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Answer:

The one you provided in your text: Yes, each input has exactly one output.

The second one: No. 3 has two outputs.

The third one: No, two outputs for each x>-4.

The fourth one: Yes, unique y for each x.

The range of the given piecewise function is -

-4 ≤ x ≤ 3.

A piecewise function is a function that is defined on a sequence of intervals. A common example is the absolute value function.

Given is the piecewise function as shown in the image.

Range is the set of values that exist for a specific value in the domain of the function. So, we can write the range as the set of {y} values for the function. From the graph, we can write the range as -

-4 ≤ x ≤ 3

Therefore, the range of the given piecewise function is -

-4 ≤ x ≤ 3.

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Answer: The correct pair of functions that could have been used to create the graphs of q and w is:

q(x) = x² - 18 and w(x) = x²

The vertex of the graph of q is (0, -18) and the vertex of the graph of w is (0, 0). Since the vertex of the graph of q is 18 units below the vertex of the graph of w, this is the pair of functions that would produce the given information.

Step-by-step explanation:

Answer:

a = 9.114

Step-by-step explanation:

[tex]\frac{a}{2.1}[/tex] = 4.34 ( multiply both sides by 2.1 to clear the fraction

a = 2.1 × 4.34 = 9.114

The correct answer is option D. We can be 95% confident that the sample proportion is captured by the confidence interval.

The margin of error of plus or minus three percentage points at a 95% confidence level means that the true proportion of people who jog regularly in the population is estimated to be between 15% and 21%. We can be 95% confident that the true proportion of people who jog regularly falls within this interval.

Therefore, option B is correct. Option A is incorrect because it implies that the margin of error always holds true for any sample size, which is not the case. Option C is incorrect because it presents a range of values for the population, not for the estimate. Option E is incorrect because it refers to the proportion of samples that would find the same sample proportion, not the range of values within which the true proportion lies.

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To reflect a point across the y-axis, you multiply the x-coordinate of the original point by -1 while keeping the y-coordinate the same. So, reflecting the point (-9, -5) across the y-axis results in the point (9, -5).

Answe

To reflect a point across the y-axis, you multiply the x-coordinate of the original point by -1 while keeping the y-coordinate the same. So, reflecting the point (-9, -5) across the y-axis results in the point (9, -5).

Step-by-step explanation:

The gallon is a unit of volume that represents the capacity of a liquid in both conventional and US imperial systems of measurement. 1 gallon is defined as 4.54609 liters.

Gallon:

The gallon is a common unit of volume in both English and US customary units. There are three types of gallons in use today: Imperial Gallon, US Gallon, and US Dry Gallon. There are 4 quarts in a gallon, for a total of 8 pints, and each system has a different volume.

Current use of the imperial gallon as of 2021 is still used as the standard unit of petrol in four British overseas territories. It is also the standard unit of measure for six countries: Antigua and Barbuda, Grenada and Saint Lucia.

Liter:

A liter is a metric unit of volume. A liter costs 1/1000 of a cubic meter. The liter was used as the base unit of the basic French metric system. 1 liter is the volume of a cube, i.e. 10 cm x 10 cm x 10 cm, so 1 liter = 1000 cm3 and 1 liter = 0. 2641720524 gallons.

This unit of volume can be used in the International System of Units even though it is not an SI unit. Current use of liters . The liters are primarily used for pourable items (these items can be solid or liquid). These items are measured by the size or capacity of the container. It is also used to measure non-liquid volumes such as backpacks, car trunks, etc.

Formula for Converting Gallons to liters

The formula for converting 1 gallon of water in liters is :

Liter = Gallon x 3.785411784

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Answer:

2,412

Step-by-step explanation:

[tex]\displaystyle E(X)=np=(36180)\biggr(\frac{14}{210}\biggr)=2412[/tex]

Therefore, we can expect 2,412 students at the university to speak 3 or more languages.

The amount of square feet that will be needed is given as follows:

122 ft².

The amount of square feet needed is given by the total area of the figure, which is composed as follows:

The area of the rectangle is given by the multiplication of the dimensions, hence:

Ar = 6 x 15 = 90 ft².

The area of the trapezoid is given by half the multiplication of the sum of the bases and the height, hence:

At = 0.5 x 4 x (6 + 10) = 32 ft².

Hence the total area is given as follows:

A = Ar + At

A = 122 ft².

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the mile-a-minute weed can grow up to 0.25 inches per hour.

A fraction is a mathematical expression that represents a part of a whole. It is written as a ratio of two numbers, the numerator and the denominator, separated by a horizontal line. The numerator represents the part of the whole that is being considered, while the denominator represents the whole.

Given by the question.

To convert 0.5 ft per day to inches per hour, we can use the following conversion factors:

1 ft = 12 inches (since there are 12 inches in a foot)

1 day = 24 hours (since there are 24 hours in a day)

So, to convert 0.5 ft per day to inches per hour, we can use the following steps: Convert feet to inches:

0.5 ft x 12 inches/ft = 6 inches

Convert days to hours:

1 day = 24 hours, so:

6 inches/24 hours = 0.25 inches per hour

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Answer:

x = 9 , y = 5

Step-by-step explanation:

Consider the figure to be a parallelogram.

• the diagonals bisect each other

then

2x - 4 = x + 5 ( subtract x from both sides )

x - 4 = 5 ( add 4 to both sides )

x = 9

and

9y - 13 = 5y + 7 ( subtract 5y from both sides )

4y - 13 = 7 ( add 13 to both sides )

4y = 20 ( divide both sides by 4 )

y = 5

The common factors of 20 and 45 are 1 and 5, since these are the only factors that both numbers share.

To find the common factors of two numbers, we need to find the factors of each number and then identify the ones that they have in common. For example, if we want to find the common factors of 20 and 45, we first find the factors of 20 and 45:

The factors of 20 are: 1, 2, 4, 5, 10, 20

The factors of 45 are: 1, 3, 5, 9, 15, 45

The factor 1 is always a common factor of any two numbers, since every number is divisible by 1. The factor 5 is a common factor of 20 and 45 because both 20 and 45 are divisible by 5. It is important to note that the other factors of 20 and 45 are not common factors, since they are not shared by both numbers.

Therefore, the common factors of 20 and 45 are 1 and 5, since these are the only factors that both numbers share.

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Answer:

the value of x is 12 as per my calculation it goes in equation

The value of x in the given figure is 6.

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size.

Given that, two lines are parallel, line U ║ line V, we need to find the value of x,

Using the concept of alternate interior angles between parallel lines,

Alternate angles between the parallel, line are equal,

Therefore,

16x-6 = 90

16x = 96

x = 6

Hence, the value of x in the given figure is 6.

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The elevation of the diver after the dive can be found to be 42 feet below sea level or - 42 feet.

If the diver's elevation is -30 feet relative to sea level, and she dives down 12 feet, we can find her new elevation by adding the change in depth to her initial elevation:

New elevation = Initial elevation + Change in depth

New elevation = - 30 feet + ( - 12 feet )

New elevation = - 42 feet

Therefore, the diver's new elevation after the dive is -42 feet relative to sea level.

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The full question is :

A divers elevation is -30 feet below sea level. She dives down 12 feet. What is her elevation after the dive?

Answer:

(4,0)

Step-by-step explanation:

I will assume the fiorst equation is missing an "x," so I'll assume it was meant to be:  y = -x + 4

See the attached graph.  The lines cross at (4,0).

The standard form, of the expression 3x³+7x-1+4x³-9x²-11x+1 is 7x³-9x²-4x

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, 3x³+7x-1+4x³-9x²-11x+1 we need to make it in a standard form,

To arrange this expression in a standard form, we will just have to perform operations in like terms and then arrange them in decreasing order of the power of the variables,

Therefore,

3x³+7x-1+4x³-9x²-11x+1

Adding the like terms

= 4x³+3x³+7x-11x-9x²+1-1

= 7x³-9x²-4x

Hence, the standard form, of the expression 3x³+7x-1+4x³-9x²-11x+1 is 7x³-9x²-4x

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Triangle JKL is congruent to triangle MLK based on angle - angle - side congruency theorem

A triangle is a polygon that has three sides and three angles. Types of triangles are equilateral, isosceles, scalene, right angled triangle. In an equilateral triangle, two sides are equal.

Two triangles are said to be congruent, if all angles and all sides are congruent to each other.

From the diagram:

∠KJL = ∠LMK (Given)

∠JKL = ∠MLK (Given)

KL ≡ KL

PS = QS (Definition of equilateral triangle)

ΔJKL ≅ ΔMLK (angle - angle - side congruency theorem)

Triangle JKL is congruent to triangle MLK

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Answer: 70.08

Step-by-step explanation:

0.96*73=