What is the area of a right triangle with a height of six and one fourth yards and a base of 22 yards?

34 yds2
sixty eight and three fourths yds2
132 yds2
one hundred thirty seven and one half yds2

Answer:

see explanation

Step-by-step explanation:

the x- intercepts are the values of x where the graph crosses the x- axis

these occur at x = - 2 and x = 2

then x- intercepts are x = - 2 , x = 2

the y- intercept is the value of y where the graph crosses the y- axis

this occurs at y = 4

then y- intercept is 4

x intercept of a graph is the point(s) of the graph that intersects x-axis , y intercept of a graph is the point(s) of the graph that intersects y-axis .

x and y intersepts vary from graph to graph , a graph may have various x and y intersepts , a graph may have one x and y intersepts , or may don't have none of them , or may have only one of the intersepts

_______________________

In this graph

there are two x intersepts and one y intersept

x intersepts :

( 2 , 0 )

( -2 , 0 )

y intersept :

( 0 , 4 )

The equation of the directrix of the parabola found in part A is [tex]x^2 = -2cy + c^2.[/tex]

The equation of the parabola formed when a cross section is taken through the reflector's central axis is

[tex]y = (1/12)(x - 0)^2 + 0.[/tex]

In this equation, the vertex is at the origin (0, 0) and the coefficient 1/12 determines the shape of the parabola.

The equation implies that the parabola opens upward because the coefficient of [tex]x^2[/tex] is positive.

To find the equation of the directrix, we can use the distance formula. The directrix is a horizontal line that is equidistant from the vertex as any point on the parabola.

Since the parabola is symmetric with respect to the y-axis, the directrix will also be symmetric with respect to the y-axis.

Let's assume that the directrix is a horizontal line with the equation y = c, where c is a constant.

To find the value of c, we need to consider a point (x, y) on the parabola. The distance from the point (x, y) to the directrix y = c should be equal to the distance from the point (x, y) to the vertex (0, 0).

Using the distance formula, the distance from (x, y) to the directrix y = c is given by |y - c|, and the distance from (x, y) to the vertex (0, 0) is given by [tex]\sqrt{(x^2 + y^2)}[/tex]

Setting these distances equal, we have:

[tex]|y - c| = \sqrt{(x^2 + y^2)}[/tex]

Squaring both sides of the equation, we get:

[tex](y - c)^2 = x^2 + y^2[/tex]

Expanding and simplifying the equation, we have:

[tex]y^2 - 2cy + c^2 = x^2 + y^2[/tex]

Simplifying further, we obtain:

[tex]-2cy + c^2 = x^2[/tex]

Rearranging the terms, we get:

[tex]x^2 = -2cy + c^2[/tex]

This equation represents the equation of the directrix of the parabola formed by the reflector.

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A preimage includes a line segment with a length of x units and a slope of munits. The preimage is dilated by a scale factor of n.

The length of the corresponding line segment in the image is nx units. The slope of the corresponding line segment in the image is m.

The slope or gradient of a line is described as  a number that describes both the direction and the steepness of the line.

The is very important and tells you how steep a line is, or how much y increases as x increases.

In conclusion, the slope is constant (the same) anywhere on the line.

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Answer:

a

Step-by-step explanation:

i did it

The answers to the questions to one significant figure are

a. 4000

b. 2000

c. 10,000

The problem can be solved using calculator

a

= 24 * 65 / 0.37

= 1608 / 0.37

= 4345.946

= 4000 to one significant figure

b. 71 * 8.2 / 0.22

= 2646.364

= 2000 to one significant figure

c. 49.3 * 11.1 / 0.053

= 10325.094

= 10000  to one significant figure

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The estimation of the following numbers rounded to one significant figure are:

a. 4,000

b. 3,000

c. 10,000

[tex] \frac{24 \times 65}{0.37} [/tex]

[tex] = \frac{1560}{0.37} [/tex]

= 4216.216216216216

= 4000 to one significant figure.

[tex] \frac{71 \times8.2 }{0.22} [/tex]

[tex] = \frac{582.2}{0.22} [/tex]

[tex] = 2646.363636363636[/tex]

= 3,000 to one significant figure

[tex] \frac{49.3 \times 11.1}{0.053} [/tex]

[tex] = \frac{547.23}{0.053} [/tex]

[tex] = 10325.09433962264[/tex]

= 10,000 to one significant figure

Significant figures are digits 1 to 9

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The domain of the height function is [0, 2.5]

The range of the height function is [0, 25]

We know that the height is given by the quadratic function:

h(t) = 40t - 16t²

First, the domain. This is the set of possible values of t.

We know that we start at t = 0.

The final value of the domain is t such that the rocket returns to the ground, that is when h = 0.

We can rewrite the function as:

h(t) = 40t - 16t² = t*(40 - 16t)

It is zero when t = 0 (we already know) and when 40 - 16t = 0

Solving the second one we get:

40 - 16t = 0

40 = 16t

40/16 = t

2.5 = t

Then the domain is [0, 2.5]

For the range we need to find the maximum height, we know that the minimum height is h = 0.

The maximum one is when t = (2.5 + 0)/2 = 1.25

Evaluating there we get:

h = 40*1.25 - 16*(1.25)²

h =  25

Then the range is [0, 25]

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Answer:33

Step-by-step explanation:Range=maximum minus minimum in data set

100 - 67 = 33

Answer:

33

Step-by-step explanation:

67, 88, 90, 98, 100 is the set in order from least to greatest.

Range is the largest number (100) minus the smallest number (67).

100 - 67= 33.

Thus, your answer is 33.

The total area of the composite figure is 51.5 square yards

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

The composite figure

The total area of the composite figure is the sum of the individual shapes

So, we have

Surface area = 9 * 2 + 2 * 3 + 1/2 * (3 + 8) * 5

Evaluate

Surface area = 51.5

Hence. the total area of the figure is 51.5 square yards

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The correct option is (a) "If two angles are congruent, then they have the same measure".If a conditional statement and its converse are both true, the statement is said to be biconditional. The biconditional statement is one that can be written in the form “p if and only if q” which means that it is only true when both p and q are true.

The biconditional statement of the given options is "If two angles are congruent, then they have the same measure".

Option a) If two angles are congruent, then they have the same measure is a biconditional statement. This statement is a biconditional because it is true for both its converse and inverse.

If two angles are congruent, they have the same measure and if two angles have the same measure, they are congruent. This statement is true in both directions.

It can be written as:Two angles are congruent if and only if they have the same measure.Therefore, the correct option is (a) "If two angles are congruent, then they have the same measure".

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The given expression -4x^2 + 2x - 5(1+x) is equivalent to -4x^2 - 3x - 5, not -5 - 5x.

To simplify the expression -4x^2 + 2x - 5(1+x), we can distribute the -5 to the terms inside the parentheses:

-4x^2 + 2x - 5(1+x) = -4x^2 + 2x - 5 - 5x

Next, we can combine like terms:

-4x^2 + 2x - 5 - 5x = -4x^2 + (2x - 5x) - 5

Simplifying further, we have:

-4x^2 + (2x - 5x) - 5 = -4x^2 - 3x - 5

Therefore, the expression -4x^2 + 2x - 5(1+x) is equivalent to -4x^2 - 3x - 5.

It's important to note that when we distribute the -5 to the terms inside the parentheses, we multiply each term by -5. So, the expression becomes -5(1) - 5(x). However, -5(1) simplifies to -5, and -5(x) simplifies to -5x. Hence, the expression simplifies to -5 - 5x.

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