Consider the equation shown.
24
2"
What is the value of n?

Answer:

k = 53.13°

Step-by-step explanation:

[tex]{ tan (k) = \dfrac{\text{side opposite k}}{\text{side adjacent k}}}[/tex]

[tex]= \dfrac{35}{JK}\\\\\textrm{Since JK is a right triangle, by the Pythagorean theorem }\\JK = \sqrt{IK^2 - IJ^2}}\\\\= \sqrt{35^2 - 28^2}\\\\\\ =\sqrt{1225 - 784}\\\\= \sqrt{441}\\\\= 21[/tex]

[tex]\tan(k) = \dfrac{28}{21} = 1.333\\\\k = \tan^{-1}(1.333)\\\\= 53.13^\circ[/tex]

Answer:

A

Step-by-step explanation:

The area of the trapezoid is given as 100. See the explanation for the same below.

A trapezoid is a quadrilateral with at least one set of parallel sides in American and Canadian English. A trapezoid is known as a trapezium in British and other varieties of English.

To find the length of each side of the trapezoid, you need to use the distance formula.

AB = (-1,5) and (3,2)

BC = (3,2) and (0,-2)

CD =  (0,-2) and (-13, -11)

AD or DA =  (-1,5) and(-13, -11)

Now, just use the distance formula for each line.

The Distance Formula is given as: d=√((x2 – x1)² + (y2 – y1)²).

Distance AB = √((3 – (-1))² + (2 – 5)²).
= √(4)² + (-3)²
= √(16+9)
= √25
AB = 5

lets us repeat this for the other section we will get:

Doing so gives us for all the points:

AB = 5

BC = 5

CD = 15.811388300842

DA or AD = 20

Note that:

The height is AD, the first base is AB and the second base is BC. We can plug the values for these sides into the trapezoid area formula, which is:

A = (base 1 + base 2) /  2 x height.

A = (5+5)/2 x 20

A = 5 x 20

A = 100.

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Answer:  x=11

Step-by-step explanation:

Answer:

[tex] \sf \: x = 11[/tex]

Step-by-step explanation:

Given equation,

→ 0.3(4 + x) = 4.5

Now the value of x will be,

→ 0.3(4 + x) = 4.5

→ 1.2 + 0.3x = 4.5

→ 0.3x = 4.5 - 1.2

→ 0.3x = 3.3

[tex] \sf \rightarrow \: x = \frac{3.3}{0.3} [/tex]

→ [ x = 11 ]

Hence, the value of x is 11.

Step-by-step explanation:

1 inch = 25 miles

or as ratio

1 inch : 25 miles

1 : 25 or 1/25

a ratio is nothing else than a fraction (just with special meaning, but the handling, calculation, transformation and simplification is the same).

the checked distance is 20 miles.

so, we need to transform the ratio (in the same way as we transform fractions) to show 20 instead of 25 in the denominator.

25 × f = 20

f = 20/25 = 4/5

remember, we need to multiply 1/25 by f/f to keep the original value of the ratio unchanged.

1/25 × 4/5/4/5 = (4/5)/(25×4/5) = (4/5)/20

so, the distance on the map is 4/5 in.

Answer:

A. A reflection occurs when a point and its image are equidistant from a line on the opposite sides of the line and the line segment joining the two points is perpendicular to the line.

Hope this helps! :)

The value of  u + xy, if u = 18, x = 10, and y = 8​ is 98

Algebraic expressions are defined as mathematical expressions that are made up of constants, variables, coefficients, terms and factors.

These algebraic expressions are also composed of arithmetic operations, such as;

Given the expression;

u + xy

Where;

Now, substitute the values into the expression;

18 + 10(8)

expand the bracket

18 + 80

Add the values

98

Hence, the value is 98

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Point M has the same distance from point A and point B (option d).

Given,

Line segment CD is the  perpendicular bisector of line segment  AB

AB ⊥ CD

Assume the conjecture that the set of  points equidistant from A

and B is the  perpendicular bisector of AB is true

Here,  line segment CD intersect line segment AB at M

Then, M is the mid-point of line segment AB

So, the length of  line AM = the length of line MB

That is, Point M has the same distance from both point A and point B.

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The equivalent to the complex number i²⁷ is -i.

Every complex number may be represented in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element labeled I sometimes known as the imaginary unit, and satisfying the equation

i² = 1.

Given that,

i²⁷ is a complex number

i²⁷ = i²⁴⁺³

i²⁷ = i²⁴ ₓ i³

i²⁷ = i⁴⁽⁶⁾ ₓ i²⁺¹

i²⁷ = (i⁴)⁶ . i².i

Here, we know that i² = -1

so, i⁴ = (i²)²

i⁴ = 1

Hence, 1⁶(-1)(i) = -i

Therefore, the equivalent to the complex number i²⁷ is -i.

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Answer: 6.782

Step-by-step explanation:

An individual has a body fat percentage of 14.4% and weighs 148 pounds,

total pounds of her weight is made up of fat is 21.3pounds (nearest tenth).

As given in the question,

Total weight of an individual =148pounds

Percentage of her weight made up of fat = 14.4%

Pounds  of her weight is made up of fat = 14.4% of 148

                                                                  = ( 14.4 / 100 ) × 148

                                                                  = 21.3 pounds (nearest tenth)

Therefore, an individual has a body fat percentage of 14.4% and weighs 148 pounds, total pounds of her weight is made up of fat is 21.3pounds(nearest tenth).

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Answer: DF

Step-by-step explanation:

Answer:

C. x ≥ 11 or x ≤ 1

Step-by-step explanation:

x - 6 + 6 ≥ 5 + 6

x ≥ 11

x - 6 ≤ -5

x - 6 + 6 ≤ -5 + 6

x ≤ 1

Hope this helps! :)

The distance between the 2 given points is √45.

So, the distance between (3, 2) and (0, -4) is:

Now, substitute the values in the formula and solve as follows:

Therefore, the distance between the 2 given points is √45.

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Answer:

question tho??

Answer: x=21

Step-by-step explanation:

2x-8=34 (change the -8 into a positive since it doesn't have a variable)

34+8=42 (divide 34 by 2)

42/2=21

Check your answer

2 x 21 = 42

42-8=34

x=21

When Ramona reflect the original figure over the x-axis, the coordinate of point T' will be (-2, -4). When Elias reflect the original figure over the y-axis, the coordinate of point T' will be (2, 4).

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In Mathematics, a reflection over the x-axis is given by this transformation rule:

(x, y)                   →               (x, -y)

Point T = (-2, 4) → Point T' = (-2, -4)

In Geometry, a reflection over the y-axis of a graph is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, the coordinates of point T' after a reflection over the y-axis is as follows:

Point T = (-2, 4) → Point T' = (-(-2), 4) = (2, 4)

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In a case whereby  two members of the math competition team solve at the rate  13 problems in 1 hour, the members that are needed to solve 39 problems in 1 hour is 6 member of the team.

Since two members solve 13 problems in 1 hour, which implies that

2 members= 13 problem/ hr

Then if we want to calculate the number of the team that will be able to solve the problem at the rate of 39 problems in 1 hour, we can represent the number required as X.

Then X = 39 problems/hr.

2 members= 13 problem/ hr

Then in this case we can cross multiply as follows:

13 problem/ hr * X =  39 problems/hr * 2

Then we can make X the subject of the formular as X =( 78 /13)

= 6 member of the team.

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Answer:710.48 miles

Step-by-step explanation:

look it up

Answer:

f = 90 + 32

= 122° (exterior angle)

Answer:

69

Step-by-step explanation:

15*3=45

12*2=24

45+24= 69

Answer: 114

Step-by-step explanation:

15×3+12×2

15×3=45

45+12=57

57×2=114

Answer:

y - intercept = 14

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 )

y = - 10x + 14 ← is in slope- intercept form

with y- intercept c = 14

Answer:

see explanation

Step-by-step explanation:

1

1 + [tex]\frac{x-5}{2}[/tex] - [tex]\frac{x+3}{5}[/tex] ≤ 0

multiply through by 10 ( the LCM of 2 and 5 ) to clear the fractions

10 + 5(x - 5) - 2(x + 3) ≤ 0 ← distribute parenthesis on left side and simplify

10 + 5x - 25 - 2x - 6 ≤ 0

3x - 21 ≤ 0 ( add 21 to both sides )

3x ≤ 21 ( divide both sides by 3 )

x ≤ 7

2

[tex]\frac{6x}{5}[/tex] - [tex]\frac{2}{3}[/tex] ≥ 4

multiply through by 15 ( the LCM of 5 and 3 ) to clear the fractions

18x - 10 ≥ 60 ( add 10 to both sides )

18x ≥ 70 ( divide both sides by 18 )

x ≥ [tex]\frac{70}{18}[/tex] , that is

x ≥ [tex]\frac{35}{9}[/tex]

3

[tex]\frac{x}{10}[/tex] - [tex]\frac{2}{8}[/tex] ≥ 1

multiply through by 40 ( the LCM of 10 and 8 ) to clear the fractions

4x - 10 ≥ 40 ( add 10 to both sides )

4x ≥ 50 ( divide both sides by 4 )

x ≥ [tex]\frac{50}{4}[/tex] , that is

x ≥ [tex]\frac{25}{2}[/tex]

Answer:

[tex]\textsf{1.} \quad x \leq 7[/tex]

[tex]\textsf{2.} \quad x \geq \dfrac{35}{9}[/tex]

[tex]\textsf{3.} \quad x \geq \dfrac{25}{2}[/tex]

Step-by-step explanation:

Given inequality:

[tex]1+\dfrac{x-5}{2}-\dfrac{x+3}{5} \leq 0[/tex]

[tex]\textsf{Add \; $\dfrac{x+3}{5}$ \; to both sides}:[/tex]

[tex]\implies 1+\dfrac{x-5}{2}-\dfrac{x+3}{5} +\dfrac{x+3}{5}\leq 0+\dfrac{x+3}{5}[/tex]

[tex]\implies 1+\dfrac{x-5}{2}\leq \dfrac{x+3}{5}[/tex]

[tex]\textsf{Rewrite $1$ as $\dfrac{2}{2}$}:[/tex]

[tex]\implies \dfrac{2}{2}+\dfrac{x-5}{2}\leq \dfrac{x+3}{5}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]

[tex]\implies \dfrac{2+x-5}{2}\leq \dfrac{x+3}{5}[/tex]

[tex]\implies \dfrac{x-3}{2}\leq \dfrac{x+3}{5}[/tex]

Cross multiply:

[tex]\implies 5(x-3)\leq 2(x+3)[/tex]

[tex]\implies 5x-15\leq 2x+6[/tex]

Subtract 2x from both sides:

[tex]\implies 5x-15-2x\leq 2x+6-2x[/tex]

[tex]\implies 3x-15\leq 6[/tex]

Add 15 to both sides:

[tex]\implies 3x-15+15\leq 6+15[/tex]

[tex]\implies 3x\leq 21[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3x}{3}\leq \dfrac{21}{3}[/tex]

[tex]\implies x \leq 7[/tex]

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

Given inequality:

[tex]\dfrac{6x}{5}-\dfrac{2}{3} \geq 4[/tex]

[tex]\textsf{Add \; $\dfrac{2}{3}$ \; to both sides}:[/tex]

[tex]\implies \dfrac{6x}{5}-\dfrac{2}{3} +\dfrac{2}{3}\geq 4+\dfrac{2}{3}[/tex]

[tex]\implies \dfrac{6x}{5}\geq \dfrac{12}{3}+\dfrac{2}{3}[/tex]

[tex]\implies \dfrac{6x}{5}\geq \dfrac{12+2}{3}[/tex]

[tex]\implies \dfrac{6x}{5}\geq \dfrac{14}{3}[/tex]

Cross multiply:

[tex]\implies 3(6x) \geq 14(5)[/tex]

[tex]\implies 18x \geq 70[/tex]

Divide both sides by 18:

[tex]\implies \dfrac{18x}{18} \geq \dfrac{70}{18}[/tex]

[tex]\implies x \geq \dfrac{70}{18}[/tex]

Reduce the fraction by dividing the numerator and the denominator by 2:

[tex]\implies x \geq \dfrac{70 \div 2}{18 \div 2}[/tex]

[tex]\implies x \geq \dfrac{35}{9}[/tex]

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

Given inequality:

[tex]\dfrac{x}{10}-\dfrac{2}{8} \geq 1[/tex]

[tex]\textsf{Add \; $\dfrac{2}{8}$ \; to both sides}:[/tex]

[tex]\implies \dfrac{x}{10}-\dfrac{2}{8} +\dfrac{2}{8}\geq 1+\dfrac{2}{8}[/tex]

[tex]\implies \dfrac{x}{10}\geq \dfrac{8}{8}+\dfrac{2}{8}[/tex]

[tex]\implies \dfrac{x}{10}\geq \dfrac{8+2}{8}[/tex]

[tex]\implies \dfrac{x}{10}\geq \dfrac{10}{8}[/tex]

Cross multiply:

[tex]\implies 8(x) \geq 10(10)[/tex]

[tex]\implies 8x \geq 100[/tex]

Divide both sides by 8:

[tex]\implies \dfrac{8x}{8} \geq \dfrac{100}{8}[/tex]

[tex]\implies x \geq \dfrac{100}{8}[/tex]

Reduce the fraction by dividing the numerator and the denominator by 4:

[tex]\implies x \geq \dfrac{100 \div 4}{8 \div 4}[/tex]

[tex]\implies x \geq \dfrac{25}{2}[/tex]

The ordered pair at which the function f(x) = √(x - 4) + 7 would begin on the coordinate plane is (4, 7).

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

An ordered pair can be defined as a pair of two elements that are typically written in a fixed order within parentheses as (x, y), which represents the x-axis (abscissa) and the y-axis (ordinate) on a coordinate plane.

By critically observing the graph of this function (see attachment), the ordered pair would begin at (4, 7) on the cartesian coordinate.

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Complete Question:

At which ordered pair will the function f(x) = √(x - 4) + 7 begin on the

coordinate plane?

Answer: d

Step-by-step explanation:

im new at this but i am pretty sure it would be d

Answer: Where P is.

Step-by-step explanation