Answer:
68.75 square yards (rounded to the nearest hundredth).
Step-by-step explanation:
To find the area of a right triangle, we can use the formula:
Area = (1/2) * base * height
Given the height of 6 and one fourth yards (6 1/4) and a base of 22 yards, we can calculate the area as follows:
Area = (1/2) * 22 * (6 1/4)
To simplify the calculation, we can convert the mixed fraction 6 1/4 to an improper fraction:
6 1/4 = (4 * 6 + 1) / 4 = 25 / 4
Now we can substitute the values into the area formula:
Area = (1/2) * 22 * (25/4)
Next, we can simplify the expression by multiplying the numbers:
Area = (11/1) * (25/4)
Multiplying the numerators and denominators:
Area = (11 * 25) / (1 * 4)
= 275 / 4
To convert the fraction to a mixed number, we can divide the numerator by the denominator:
275 ÷ 4 = 68 remainder 3
Therefore, the area of the right triangle is:
Area = 68 3/4 square yards or 68.75 square yards (rounded to the nearest hundredth).
Among the options provided, the closest match is "sixty-eight and three fourths yds2".
Answer:
68.75 square yards
Step-by-step explanation:
PART A
A manufacturer is designing a flashlight. For the flashlight to emit a focused beam, the bulb needs to be on the central axis of the parabolic reflector, 3 centimeters from the vertex. Write an equation that models the parabola formed when a cross section is taken through the reflector’s central axis. Assume that the vertex of the parabola is at the origin in the xy coordinate plane and the parabola can open in any direction.
answer: y= 1/12(x-0)^2+0
Find the equation of the directrix of the parabola found in part A.
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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Find the x- and y-intercepts of the graph.
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 )
I need some help on my exam reveiw for my math class, can someone please help me so i get a good grade and know how to do my exam?
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.
What is slope?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 all three ASAP!!!!!!!!
The answers to the questions to one significant figure are
a. 4000
b. 2000
c. 10,000
How to find the answersThe 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
How to estimate to one significant figures?[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 probability distribution below represents the probability of x number of males in a group who have a form of
color blindness.
X. P(x)
0 0.641
1 0.287
2 0.048
3 0.014
4 0.007
6 0.003
a.) Find the probability of exactly 1 male has a form of color blindness.
b.) Find the probability that 1 gr less males have a form of color blindness.
c.) Find the probability that more than 3 males have a form of color blindness.
Answer:
a
Step-by-step explanation:
i did it
for a data set of 98,67,100,88,90, the range is
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.
If a conditional statement and its converse are both true, the statement is said to be biconditional. Which of this statements is biconditional? Explain.
a) If two angles are congruent, then they have the same measure.
b) If two angles are straight angles, then they are congruent.
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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Find the area, i have a lot of problems finding the area in general. and i spent a lot of time trying to figure this out?
The total area of the composite figure is 51.5 square yards
Calculating the area of the figureFrom 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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-4x^2 + 2x - 5(1+x) which expression is equivalent to the given expression
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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Kate is firing off her homemade rockets for a project in physics class. The
maximum height of any of her rockets can be represented by the equation
h = 40t-16t², where h is the height (in feet) of the rocket after t seconds.
Find the domain and range
The domain of the height function is [0, 2.5]
The range of the height function is [0, 25]
How to find the domain and range?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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