Answer:
the height of the goalpost is approximately 10.48 meters.
Step-by-step explanation:
To find the height of the goalpost, Addison needs to use the distance from the mirror to the goalpost, the distance from her eyes to the ground, and the angle formed by the goalpost, the mirror, and her eyes. She can use the law of cosines to solve for the height of the goalpost.
Let "a" be the distance from the goalpost to the mirror, "b" be the distance from the mirror to Addison's eyes, and "c" be the distance from Addison's eyes to the ground.
The law of cosines states that: c^2 = a^2 + b^2 - 2ab * cos(C), where C is the angle formed by the goalpost, the mirror, and Addison's eyes.
In this case, a = 13.25 meters, b = 1.3 meters, and c = 1.55 meters. We can substitute these values into the formula to solve for the angle C:
1.55^2 = 13.25^2 + 1.3^2 - 2 * 13.25 * 1.3 * cos(C)
Solving for cos(C) and using the inverse cosine function (arccos), we find that C = 52.22 degrees.
Now that we know the angle C, we can use the law of sines to solve for the height of the goalpost. The law of sines states that:
sin(C) / a = sin(A) / h, where A is the angle formed by the ground, the mirror, and the goalpost, and h is the height of the goalpost.
In this case, A = 180 - C - 90 = 180 - 52.22 - 90 = 37.78 degrees, and a = 13.25 meters. We can substitute these values into the formula to solve for h:
sin(52.22) / 13.25 = sin(37.78) / h
Solving for h, we find that the height of the goalpost is approximately 10.48 meters.
Therefore, the height of the goalpost is approximately 10.48 meters.
Expectation of Product of Random Variables Proof From the definition of the expected value, the expected value of the product of two random variables is E(X . Y) = EErr-r2 . P(X=Y =r2) where the sum is over all possible values of r1 and r2 that the variable X and Y can take on_ Using the definition above formally prove that if the events X = r1 and Y =r2 are independent (for any r1 and r2) , we have E(X . Y) = E(X) . E(Y). Now; if you have two random variables X and Y and Y=aI+c, show that if E[X2] # E[XJ? , then E(X . Y) # E(X) . E(Y). If you roll a die 6 times in a rOW what is the expected value of the product of the 6 outcomes?
Look to the photo and you will find the answers there ✔️
start from left to right
-6x – 9y = 0
-24x = 36y
infinite
none
or one solution?
Answer:
No solution
Step-by-step explanation:
-6x - 9y = 0
-24x -36y = 0
Multiply the top equation by -4 and add that to the second equation
24x + 36y = -4
-24x - 36y = 0
0 + 0 = -4
0 ≠ -4 Since this is a false statement, the answer is no solution.
there are 250 bricks used to build a wall that is 15 ft high. how many bricks will be used to bui;d a wall that is 75 ft high
If 250 bricks are used to build a wall of 15 ft high then, there is total 1250 bricks will be used to build a wall that is 75 ft high.
Proportion:
A proportion is an equation between two ratios or rates that is useful in solving for a single unknown.
We have given that,
It takes 250 bricks to build a 15 ft high wall. Let us consider x bricks , is needed for a 75 ft high wall, use the ratio given for a 15 ft high wall and equate it to the ratio for the unknown number of bricks for a 75-ft high wall.
In making proportions, make sure that the rate on one side has the same units as the rate on the other as shown :
x/75 = 250/15
=> 15 × x = 250 ×75
=> x = 250×75/15
=> x = 1250
Thus, it will take 1250 bricks to build a wall 75 feet high.
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Your friend thinks that the triangles shown below are congruent by SAS. Is your friend correct? Explain.
Choose the correct answer below.
A.
Yes, the figure indicates that two corresponding angles and their included side are all congruent.
B.
No, the congruent sides are not the included sides.
C.
No, the congruent angles are not the included angles.
D.
Yes, the figure indicates that three corresponding sides are congruent.
E.
No, the figure only indicates that two corresponding sides are congruent, not three as required by the SAS Postulate.
F.
Yes, the figure indicates that two corresponding sides and their included angle are all congruent.
Yes, the figure indicates that two corresponding angles and their included side are all congruent. Option A
What is the congruency?We know that the term congruency can be used to refer to the triangles that are equivalent. For the triangles that are equivalent, we can see that there are some kind of relationship that binds the triangles together.
The kinds of congruency of the triangles that we may have are the following;
Angle Angle side
Side angle side
Side side side
Angle Side angle
If we look at the triangles that we have in the two images that have been conspicuously attached to the question that we are trying to attend to, it is clear that two triangles have similar sides and a similar included angle hence they are congruent by the theorem of SAS.
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What is 5/11 * -11/6
To solve this expression, you can first simplify the fractions:
5/11 * -11/6 = (-5/6) * (-6/5)
Then, you can multiply the fractions:
(-5/6) * (-6/5) = (-30/30) = -1
So, the result of the expression is -1.
1. What is the area of the rectangle? Must show all work.
(7 points)
a. What is the formula for the area of the rectangle?
b. Find the length of the base. Round to the nearest tenth if needed.
c. Find the length of the height. Round to the nearest tenth if needed.
d. Find the area of the rectangle.
Answer:
a. Area of rectangle: Length x Width or Base x height
b. The length of the base is 6
c. The height is 3
d. Area of the rectangle is 18
Step-by-step explanation:
a. Area of the rectangle formula is: L x W
b. We find the Length, which means we find the distance of the x; we see that to get from point A to point B the x change is 6, so the base is 6
c. We find the height, which means we find the distance of the y; we see that get from point B to point C, the y change by 3, so the height is 3
d. To find the area we take 6 times 3 = 18
Find the value of x in the triangle shown below.
8
3
Answer:
The answer should be 8.
Step-by-step explanation:
19. In Juneau, Alaska, the temperature on Tuesday at noon was -20°F. The temperature then
decreased 1.25°F each hour for the next 5 hours.
In Tacoma, WA, the temperature on Tuesday at 5:30 pm was 2/3 warmer than the temperature
recorded in Juneau, Alaska at the same moment in time.
What is the temperature in Tacoma, WA? Show your thinking.
The temperature at Tacoma WA is -26 5/12°F.
What is the temperature?The temperature at 5pm in Juneau Alaska: temperature at noon + total change in temperature
-20 + (-1.25 x 5)
-20 - 6.25 = -26.25°F = -26 1/4°F
The temperature in Tacoma WA = termpature in Juneau + difference in temperature
-26 1/4°F - 2/3 = -26 5/12°F
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This is a two part question. For the first blank, type the letter associated with with
the correct graph of this system. For the second blank, type the correct solution to
the system in point notation: (x,y).
Let
f(x) = (x + 2)² +3
g( )=2x+6
Answer: c
Step-by-step explanation:
Which of the following ratios is used to determine one's debt-to-income? A. 20/28
B. 20/36
C. 28/30
D. 28/36
Answer:
d
Step-by-step explanation:
a survey of middle school students asked: what is your favorite winter sport? the results are summarized below. using these 545 students as the sample space, a student from this study is randomly selected. if the student selected is an 8th grade student, what is the probability that the student prefers skiing or ice-skating?
The probability that the chosen student, a grade 8 student, likes skiing over ice skating is 53.89%.
Given that,
A survey of middle school students asked what is your favorite winter sport so they have given the result in the table we can see.
Below is a summary of the findings. A participant from this study is chosen at random from among these 545 students, who serve as the sample space.
We have to find what is the probability that the chosen student, a grade 8 student, likes skiing over ice skating.
The total 8th grade are 180
The skiing are 171
The ice skating are 163
Probability = 180/(171+163) = 0.5389 = 53.89%
Therefore, the probability that the chosen student, a grade 8 student, likes skiing over ice skating is 53.89%.
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Select all the statements that are true for the graph shown. Submarines descent graph of a diagonal line on a coordinate plane going down and to the right with Time in seconds on the x-axis and Height above Sea Level in feet on the y-axis. The line begins at the origin and passes through point 4 comma negative 12.
The relationship is proportional.
The rate of change is −32
The rate of change is −83
The relationship is linear.
The correct option for the graph shown are-
The relationship is proportional.The relationship is linear.Explain the term proportional relation?Relationships across two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, each variable is consistently equal to the other's constant value.The question's line traverses the origin and (4,-12).
The line's rate of change is;
m = -12 - 0 / 4 - 0
m = -3
The slope of the line or its rate of change is -3.
The line's equation is provided by;
y - 0 = -3(x - 0)
y = -3x
This relationship is linear as a result.
The relationship is proportionate if we take any value of x because there will only ever be one value of y.
Therefore, the following claims are accurate:
The relationship is proportional.The relationship is linear.To know more about the proportional relation, here
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Solve for y
6/8 = 15/y
Answer:
The answer is 20
Step-by-step explanation:
6/8 = 15/y
(6) × y = (8) × (15)
6y = 120
6y/6 = 120/6
y = 20
Thus, The value of y is 20
Answer:
[tex] \sf \: y = 20[/tex]
Step-by-step explanation:
Given equation,
[tex] \sf \rightarrow \: \frac{6}{8} = \frac{15}{y} [/tex]
Now the value of y will be,
[tex] \sf \rightarrow \: \frac{6}{8} = \frac{15}{y} [/tex]
[tex] \sf \rightarrow \: 6y = 15 \times 8[/tex]
[tex] \sf \rightarrow \: 6y = 120[/tex]
[tex] \sf \rightarrow \: y = \frac{120}{6} [/tex]
[tex] \sf \rightarrow \boxed{ \sf y = 20}[/tex]
Hence, the value of y is 20.
which graph shows a polynomial function with a positive leading coefficient?
The graph shows a polynomial function with a positive leading coefficient B.
What is meant by polynomial function with a positive leading coefficient?The function will reach its maximum value of + in the case of a positive leading coefficient and its minimum value of - in the case of a negative leading coefficient. This indicates that even degree polynomials with positive leading coefficients have a range of [ymin, ∞), where ymin stands for the global minimum that the function reaches.
When a variable in an equation like the quadratic equation, cubic equation, etc. has only non-negative integer powers or only positive integer exponents, the function is said to be polynomial.
Leading coefficients are the values listed before the variable with the biggest exponent. They can be positive, negative, real, imaginary, whole, fractional, or decimal, much like conventional coefficients, and they can also be positive, negative, real, or imaginary.
Therefore, the correct answer is option B.
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If point R is the greatest integer smaller than √51 on a number line, what is the value of point R?
The value of R is 7 , we can find answer using concept of greatest integer and square root .
What is square root of a number ?
Square root , in mathematics , a factor of a number that , when multiplied by itself , returns the original number.
e.g. Square root of 9 are both 3 and -3.
Symbol = " √ "
In given que, we need to find greatest integer smaller than √51.
Root of 51 will not give exact integer value.
As we know root of 49 is 7 and root of 64 is 8.
And 51 lie between 49 and 64,
So, Square root of 51 will also lie between 7 and 8.
So, the greatest integer smaller than √51 will be 7.
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What are the zeros of the quadratic function whose graph is shown?
A. -3,2
B. 6
C. This cannot be determined from the information given
D. -2,3
On solving the provided question, the equation will be [tex]y^2 = - 4ax[/tex] and the factors - This cannot be determined from the information given
what is parabola?When points on a curve are equally spaced from a fixed point and line, the curve is said to have a parabola as its equation. The parabola's fixed point is referred to as the focus, and its fixed line is referred to as the directrix. Remember that the fixed point is not on the fixed line as well. A parabola is the locus of any point that is equidistant from both a focus and a straight line. A conical curve of interest in coordinate geometry is a parabola.
The equation will be
=> [tex]y^2 = - 4ax[/tex]
=> [tex]y^2 = -24x[/tex]
Factors - This cannot be determined from the information given
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if a carpenter wants to make sure that the corner of a room is square and measures 12 ft and 35 ft along the walls, how long should he make the diagonal?
On solving the provided question, we got to know that - carpenter should make the diagonals 37 ft
What are the diagonals?A diagonal is a line connecting two vertices of a solid or polygon whose vertices do not share an edge in mathematics. The vertices of a shape are connected by oblique or sloping lines, which are known as diagonals. A horizontal shape with sides/edges, corners, and is called a diagonal.
We can answer this problem using Pythagoras' Theorem since the diagonal would turn the angle into a right angle.
[tex]12^2+35^2= d^2[/tex]
[tex]d^2 = 144 + 1225\\d^2 = 1369\\d = 37\\[/tex]
So, carpenter should make the diagonals 37 ft
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find the quotient and remainder when 6x^4+ 11x^3+13x^2 -3x+27 is divided by 3x+4. also check the remainder obtained by using the remainder theorem.
The division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 will have a quotient of 2x³ + x² +3x -5 and a remainder of 47 using the remainder theorem.
What is the remainder theoremThe remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a).
We shall divide the 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 as follows;
x⁴ divided by 3x equals 2x³
3x + 4 multiplied by 2x³ equals 6x⁴ + 8x³
subtract 6x⁴ + 8x³ from 6x⁴ + 11x³ + 13x² - 3x + 27 will give us 3x³ + 13x² - 3x + 27
3x³ divided by 3x equals x²
3x + 4 multiplied by x² equals 3x³ + 4x²
subtract 3x³ + 4x² from 3x³ + 13x² - 3x + 27 will give us 9x² - 3x + 27
9x² divided by 3x equals 3x
3x + 4 multiplied by 3x equals 9x² + 12x
subtract 9x² + 12x from 9x² - 3x + 27 will give us -15x + 27
-15x divided by 3x equals -5
3x + 4 multiplied by -5 equals -15x - 20
subtract -15x - 20 from -15x + 27 will result to a remainder of 47
using the remainder theorem, x = -4/3 from the the divisor 3x + 4
thus:
f(-4/3) = 6(-4/3)⁴ + 11(-4/3)³ + 13(-4/3)² - 3(-4/3) + 27 {putting the value -4/3 for x}
f(-4/3) = (1536/81) - (704/27) + (208/9) + (12/3) + 27
f(-4/3) = (1536 - 2112 + 1872 + 324 + 2157)/81 {simplification by taking the LCM of the denominators}
f(-4/3) = (5919 - 2112)/81
f(-4/3) = 3807/81
f(-4/3) = 47
Therefore, the quotient of after the division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 is 2x³ + x² +3x -5 and there is the remainder of 47 using the remainder theorem.
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please help asap! theres a picture below to help
The coefficient and constant in the system of linear equations are identified below
System of Linear EquationThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.
In this question, we are given two equations to define the variables.
3x + 7y = 18 ...eq(i)
2x - 4y = 9 ..eq(ii)
In the equations above;
3 = The coefficient of x in the first equation7 = The coefficient of y in the first equation2 = The coefficient of x in the second equation-4 = The coefficient of y in the second equation18 = The constant in the first equation9 = The constant in the second equationLearn more on system of linear equation here;
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Find the probability of getting a tail on a coin and 4 on the dice, when a coin is tossed and a dice is thrown simultaneously
P(tail) = Probability of getting a tail on the coin
P(tail)=1/2
P(4)=Probability of getting the number '4' on the dice.
P(4)=1/6
P(tail and 4)=Probability of getting tail on the coin and number '4' on the dice.
P(tail and 4)=p(tail multiply with 4)
P(tail and 4)= 1/2×1/6
P(trail and 4)=1/12
Hope this helps!
the formula would be used to find a) the first quartile of a data set using the inclusive method. b) the third quartile of a data set using the exclusive method. c) the first quartile of a data set using the exclusive method. d) the median of a data set using the inclusive method.
The given formula would be used to find the first quartile of a data set using the exclusive method.
What is quartile?
A quartile is a type of quantile used in statistics that divides the total number of data points into four roughly equal parts, or quarters. To compute quartiles, the data must be arranged from smallest to largest; therefore, quartiles are a type of order statistic.
The given formula is [tex]L_P = (n + 1)\frac{25}{100} \\[/tex]
This formula can also be written as,
[tex]R = (n + 1)\frac{25}{100}[/tex]
where 25 is the percentile of the data set.
So, the option (c) is correct.
The first quartile of a data set using the exclusive method.
Hence, the given formula would be used to find the first quartile of a data set using the exclusive method.
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according to the video, what percentage of your brain is dedicated to decoding images? group of answer choices 23% 18% 40% 30%
The movie claims that 40% of your brain is used for visual decoding.
Williams, the William G. Allyn Professor of Medical Optics, notes that processing visual information takes up more than 40% of the cortex, the surface of the brain.
Light and dark pixels in the eye are where our visual experience begins. These signals are sent to the V1 region in the rear of the brain, where they are changed to match to the borders of visual scenes.
The visual cortex processes information from the sensory periphery in accordance with a highly regulated hierarchy, according to experiments utilizing static stimuli, such as images. The information about visual sceneries is subsequently translated by deeper brain areas into more intricate forms, objects, and ideas.
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A sports drinks recipe calls for 2 tablespoons of powder mix for every 12 ounces of water. how many can you make with 6 tablespoon and 36 ounces of water explain.
Answer: 3 sports drinks
Step-by-step explanation:
6 divde by 2= 3
36 divided by 12 =3
in other words
3x2=6
12x3=36
hope this helps
How to factor x^2-2x
Answer:
x(x-2)
Step-by-step explanation:
Find the area enclosed by the circle (x-2)^2 + y^2 = 4 and the line x = 3.
Step-by-step explanation:
(3-2)^2+y^2=4
(9-4)+y^2=2^2
the power of y and 2 should be cut now
5+y=2
5-2=y
3=y
y=3
:. the area of enclosed by a circle is 3 cm
Geometry-need help i dont get it
Answer:
z = 11
Step-by-step explanation:
To find the answer we need to set up an expression with the two values they gave us:
8z = z + 77
This works because side IJ is the same length as side JK. So, all we have to do is solve for z:
8z = z + 77
-z - z
7z = 77
/7 /7
z = 11
determine which integers will make the inequailty 5x 6 < 2x 15 flase
The value of x (B) 5 makes the inequality 5x + 6 ≤ 2x + 15 FALSE.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
The equal sign (=) indicates that two expressions in an equation are believed to be equivalent.
The symbols >, <, ≤ or ≥ indicate that the two expressions in inequality are not always equal.
So, we have the inequality:
5x + 6 ≤ 2x + 15
Now put the given values and check as follows:
(A) -2
5x + 6 ≤ 2x + 15
-10 + 6 ≤ -4 + 15
-4 ≤ 11
TRUE
(B) 5
5x + 6 ≤ 2x + 15
25 + 6 ≤ 10 + 15
31 ≤ 25
Correct: 31 > 25
FALSE
Therefore, the value of x (B) 5 makes the inequality FALSE.
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Complete question:
Determine which integer will make the inequality 5x + 6 ≤ 2x + 15 false.
a:{−2}
b:{5}
c:{2}
d:{−5}
What is the measure of ABC
Answer:
Step-by-step explanation:
find x
7x+10=2x+40+3x
2x=30
x=15
ABD = 7(15)+10 = 115
ABD + ABC =180
115+ABC=180
ABC=65
The function h is defined by h (x) = 5x + 2 .
What is the value of h(8) ?
Responses
A) 30
B) 42
C) 38
D) 45
Answer:
Option B is the correct answer
Step-by-step explanation:
h(x) = 5x + 2, h(8)
h(8) = 5(8) + 2
h(8) = 40 + 2
h(8) = 42
Thus, The answer is 42
5x+2y-2z=-57
3x-10y-z=-11
Y=-2
First up is 5x+2y-2z=-57
5x+2y-2z=-57 /You gotta subtract 27 and 2z from both sides
5x+2y-2z- (2y-2z)=-57- (2y-2z) Then simplify-5x =-57-2y+2z
Then divide by both sides:
Answer is: x=-57-2y+2z / over 5
