Answer:
i think its
-3.952
Select all of the answer choices that are solutions to the equation2x+2y=0.Ox=0y = -1O x = 1, y = -1Ox= -2O x = -2, y = -2O x = 0, y = 0
If the sum of two terms = 0, then the 2 terms must have the same value but different signs
That means x and y must have the same value but different signs
Look at the given answers
The 1st, 2nd, and 4th answers are wrong because the solution of this equation must have a value of x and a value of y together
In the 3rd answer
x = 1 and y = -1
Both have the same value and different signs
Then 3rd answer is a solution
In the 5th answer
x = -2 and y = -2
They have the same value with the same signs
The 5th answer is not a solution
In the last answer
x = 0 and y = 0
They have the same value but the zero has no sign
Then substitute them in the equation to check if it is solution or not
2(0)+2(0) = 0
0 + 0 = 0
The 2 sides of the equation are equal, then
The last answer is a solution
The answer is the 3rd and last answers
I need help its very difficult
Here is the meaning of each statement:
The percentage of households that have the internet in 2007 is 61.7%
The percentage of households that have the internet in 1984 is k%.
The percentage of households that have the internet in 2017 is greater than the percentage of households that have the internet in 2000.
The sum of the percentage of households that have the internet in 1997 and 2001 is approximately equal to the percentage of households that have the internet in 2009.
What is the meaning of each statement?Percentage is the fraction of an amount expressed as a number out of 100. In order to change a number to percentage, multiply the number by 100. The sign that represent percentage is %.
A function is an expression or rule that defines the relationship between the independent variable and the dependent variable. A function could be a linear function or an exponential function.
In this question,
x = is the number of years after 1980
and the independent variable is the percentage of households that use the internet after 1980.
H(27) = 61.7
1980 + 27 = 2007
This means that 61.7% households use the internet 27 years after 1980 or 61.7% households use the internet in 2007
H(4) = k
1980 + 4 = 1984
This means that k% households use the internet 4 years after 1980 or k% households use the internet in 194
H(37) > H(30)
This means that the percentage of households that use the internet 37 years after 1980 is greater than the percentage of households that use the internet 30 years after 1980
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Write the coordinates of the vertices after a reflection over the x-axis.-10-8-6-4-2246810-10-8-6-4-2246810xyDEFG
Solution:
Given the graphed polygon below:
To determine the coordinates of the vertices after reflection over the x-axis,
step 1: Give the coordinates of DEFG.
Thus, we have
[tex]\begin{gathered} D(0,\text{ -10\rparen} \\ E(0,\text{ 0\rparen} \\ F(10,\text{ 0\rparen} \\ G(10,\text{ -10\rparen} \end{gathered}[/tex]step 2: Give the reflection formula, over the x-axis.
For reflection over the x-axis, we have
[tex]D(x,\text{ y\rparen}\rightarrow D^{\prime}(x,\text{ -y\rparen}[/tex]step 3: Give the coordinates after reflection over the x-axis.
From the formula in step 2,
we thus have
[tex]\begin{gathered} D^{\prime}(0,\text{ 10\rparen} \\ E^{\prime}(0,0) \\ F^{\prime}(10,\text{ 0\rparen} \\ G^{\prime}(10,\text{ 10\rparen} \end{gathered}[/tex]Which expression uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3x(2x8) + 7 ?
7 + 3 × (2 × 8) is the expression that uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3 × (2 × 8) + 7.
Given, 3 × (2 × 8) + 7
Following the application of the Commutative property of addition, which stipulates that altering the order of addends does not affect the result.
The expression will be,
7 + (2 × 8) × 3
Then, using the associative principle of multiplication, which states that how elements are arranged in a multiplication issue does not affect the product.
The expression will be,
7 + 3 × (2 × 8)
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A car manufacturer announced that next year the price of a certain model car would increase by 3.5%. This year the price is 15,757. Find the increase and the new price. The increase in the price of car is?The new price of car is?
Given:
Initial amount (Base) = 15, 757
Rate of increase = 3.5% or 0.035 in decimal form
Find: new price and the price increase
Solution:
To be able to get the new price, we need to solve for the price increase first. To do that, we need to know what is 3.5% of the old price 15, 757. To calculate that, we will multiply 0.035 by 15,757.
[tex]0.035\times15,757=551.495\approx551.50[/tex]3.5% of 15, 757 is 551.50. This is the price increase of the car next year.
Hence, by next year, the new price will now be 15,757 + 551.50 = 16, 308.50.
let k(x)=3h(x)+4x^4/g(x). given the following table of values, find k'(-1)
Given the following table of values, k'(-1) is 3.
What is differentiation?The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative. finding a function's derivative, or rate of change, in mathematics. Differentiation is the process of determining a function's derivative. The derivative is the rate at which x changes in relation to y when x and y are two variables.
Given Data
k(x) = -3h(x) + [tex]\frac{4x^{4} }{g(x)}[/tex]
k(x) = -3h'(x) + 4 [tex]\frac{4x^{3}g(x)-x^{4}g'(x) }{gx^{2} }[/tex]
k'(-1) = -3h'(-1) + 4 [tex]\frac{4g(-1)-g'(-1)}{g(-1^{2}) }[/tex]
k'(-1) = -3(-1) + 4(0)
k(-1) = 3 + 0
k'(-1) = 3
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negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Simplify the expression.
the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Which expression is equivalent to 3(−4.5b − 2.1) − (6b + 0.6)?
19.5b + 1.5
−19.5b − 1.5
−19.5b − 6.9
19.5b − 6.9
The expression equivalent to 3(−4.5b − 2.1) − (6b + 0.6) is -19.5b - 6.9.
What are expressions in math?Expressions in mathematics are mathematical assertions that comprise at least two terms that contain numbers, variables, or both, and are connected by an operator in between.Addition, subtraction, multiplication, and division are examples of mathematical operators. To simplify algebraic statements, like terms might be added or removed. Similar terms have the same variable raised to the same power.Given expression:
3(−4.5b − 2.1) − (6b + 0.6)
To simplify the expression open the brackets and multiply the terms,
-13.5b − 6.3 − 6b - 0.6
Now, combine the like terms together and add them,placing a negative sign in front of the terms
-13.5b − 6b - 0.6 - 6.3
-19.5b - 6.9
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PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!ON NUMBER 4!!!!!
The absolute value function y = 3|x + 1| + 9 is y ≥ (x + 4)/3 when x ≥ 0 and
y > - (x - 2)/3 when x < 0.
What is the absolute value function?The absolute value function always outputs a positive value irrespective of the input.
Given we have to write the absolute value function as a piecewise function.
We know | x | = a implies x ≥ a and - x < a.
y = 3| x + 1 | + 9.
y - 9 = 3| x + 1|.
(y - 9)/3 = | x+ 1 |.
∴ (y - 9)/3 ≥ x + 1.
y/3 - 3 ≥ x + 1.
y/3 ≥ x + 4.
y ≥ (x + 4)/3.
OR
(y - 9)/3 = | x+ 1 |.
- (y - 9)/3 < x + 1.
-y/3 + 3 < x + 1.
-y/3 < x - 2.
-y < (x - 2)/3.
y > - (x - 2)/3.
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This is a Statistics questions please help
Considering the parameters of the normal distribution for American men's heights, it is found that:
a) The percentage greater than 74 inches is: 2.5%.
b) The proportion between 64 and 71.5 inches is: 0.815.
Normal DistributionThe z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the following equation:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure represented by X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.In the context of this problem, the mean and the standard deviation of the heights of American men are given as follows:
[tex]\mu = 69, \sigma = 2.5[/tex]
The proportion of heights that is greater than 74 inches is one subtracted by the p-value of Z when X = 74, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (74 - 69)/2.5
Z = 2.5
Z = 2.5 has a p-value of 0.9772.
1 - 0.9772 = 0.0228, hence the percentage is of 2.28%. Using the Empirical Rule, this percentage is rounded to 2.5%.
The proportion of heights between 64 inches and 71.5 inches is the p-value of Z when X = 71.5, subtracted by the p-value of Z when X = 64, hence:
X = 71.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (71.5 - 69)/2.5
Z = 1
Z = 1 has a p-value of 0.84. (rounded with the Empirical Rule).
X = 71.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (64 - 69)/2.5
Z = -2
Z = -2 has a p-value of 0.025. (rounded with the Empirical Rule).
Hence the proportion is:
0.84 - 0.025 = 0.815.
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16. In Barry's state, the weekly unemployment compensation is 58% of the 26-week average forthe two highest-salaried quarters. A quarter is three consecutive months. For July, August, andSeptember, Ben earned a total of $17,500. In October, November, and December, he earned atotal of $18,300. Determine Barry's weekly unemployment compensation.
~ 399.3 $ / w
. The average for the 2 highest-salaried quarters:
(17 500 $ + 18 300 $ ) / 2 = 35 800 $ / 2 = 17 900$
. The 58% compensation representing the total amount Barry will be compensated:
17 900 * 58 / 100 = 10 382 $
. The weekly compensation:
10 382 $ / 26 week ~= 399.307692 $ / w
21. A truck is driving N35oE at a speed of 110 km/h. Determine the components of the vector representing this force.
Solution:
The question will be represented below as
To figure out the horizontal component (x), we will use the trigonometric ratio below
[tex]\begin{gathered} sin\theta=\frac{opp}{hyp} \\ \theta=35^0,opp=x,hyp=110 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} s\imaginaryI n\theta=\frac{opp}{hyp} \\ sin35=\frac{x}{110} \\ x=110\sin35^0 \\ x=63.1\text{ km/h} \end{gathered}[/tex]Step 2:
To figure out the vertical component (y), we will use the trigonometric ratio below
[tex]\begin{gathered} \cos\theta=\frac{adj}{hyp} \\ \theta=35^0,adj=y,hyp=110 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \cos(\theta)=\frac{adj}{hyp} \\ \cos35=\frac{y}{110} \\ y=110cos35^0 \\ y=90.1 \end{gathered}[/tex]Hence,
The horizontal component is = 63.1 km/h
The vertical component is = 90.1 km/h
The table shows a proportional relationship. x 14 6 26 y 7 3 13 Describe what the graph of the proportional relationship would look like. A line passes through the point (0, 0) and continues through the point (7, 14). A line passes through the point (0, 0) and continues through the point (14, 7). A line passes through the point (0, 0) and continues through the point (3, 6). A line passes through the point (0, 0) and continues through the point (13, 26).
The proportional relationship graph that represents the table of values given would look like the graph shown below.
What is a Proportional Relationship?A proportional relationship graph always passes through the point of origin, (0, 0). The slope of the graph of a proportional relationship is also called the constant of proportionality, k, which can be calculated by using the coordinates of any point on the line, (x, y).
Constant of proportionality, k = y/x.
The equation for a proportional relationship is given as y = kx.
Given the table of values above which represents a proportional relationship, the graph of the table of values will go through the points below:
(0, 0)
(14, 7)
(6, 3)
(26, 13)
Therefore, the graph of the proportional relationship would look like the graph attached below which passes through:
B. (0, 0) and continues through the point (14, 7).
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f(x)= {4-3x if x [tex]\leq[/tex] 1
{2x if 1
{5x+5 if x[tex]\geq[/tex]9
f(-4)=?
f(1)=?
f(5)=?
f(7)=?
f(9)=?
All the values are;
1) f (-4) = 16
2) f (1) = 1
3) f (5) = 10
4) f (7) = 14
5) f (9) = 50
What is substitution method?
Find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The function is;
f (x) = { 4 - 3x ; if x ≤ 1
= { 2x ; if x > 1
= { 5x + 5 ; if x ≥ 9
Now, Find all the values as;
Since - 4 is belong in x ≤ 1, so we get;
f (x) = 4 - 3x
f (-4) = 4 - 3 × -4
f (-4) = 4 + 12
f (-4) = 16
And, Number 1 is belong in x ≤ 1, so we get;
f (x) = 4 - 3x
f (1) = 4 - 3 × 1
f (1) = 4 - 3
f (1) = 1
And, Number 5 is belong in x > 1, so we get;
f (x) = 2x
f (5) = 2 × 5
f (5) = 10
And, Number 7 is belong in x > 1, so we get;
f (x) = 2x
f (7) = 2 × 7
f (7) = 14
And, Number 9 is belong in x ≥ 9, so we get;
f (x) = 5x + 5
f (9) = 5 × 9 + 5
f (9) = 50
Thus, All the values are;
1) f (-4) = 16
2) f (1) = 1
3) f (5) = 10
4) f (7) = 14
5) f (9) = 50
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Q:Find the distance from the red point to the origin. Sketch on the graph to convince us.
Distance Between Two Points
We are given two points on the graph attached to the question.
The red point has coordinates (7,3) and the origin is at (0,0)
I'll work out the graph to show the required distance.
The required distance (in the red drawing) is the hypotenuse of a right triangle of lengths 7 and 3, thus the distance is calculated as:
[tex]d=\sqrt[]{7^2+3^2}=\sqrt[]{49+9}=\sqrt[]{58}[/tex]Calculating, we get d is approximately 7.62
What is the x-intercept of the following equation?15x + 5y =30
the Given
[tex]15x+5y=30[/tex]We are asked to find the x-intercept of the linear equation. This can be seen below.
Explanation
To find the x-intercept, we must recall that x-intercept is the point at which the graph of the equation crosses the x-axis. We can find this point by plotting the given equation.
From the graph, we can determine the x-intercept as
Answer: (2,0)
You're flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 165 km south and 152 km east. Mt. Rainier is located approximately 56 km east and 40 km south of JBLM. If you are flying at a constant speed of 800 km/hr, how long after you depart JBLM will you be the closest to Mt. Rainier?
For the constant speed, it take 5 minutes 3 seconds after you depart JBLM will you be the closest to Mt. Rainier.
Speed:
Speed means a rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.
Given,
You're flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 165 km south and 152 km east. Mt. Rainier is located approximately 56 km east and 40 km south of JBLM.
Here we need to find the time taken after you depart JBLM will you be the closest to Mt. Rainier for the constant speed of 800 km/hr.
Let us consider +x direction is east, and the -y direction is south.
We know that, JBLM is at the origin (0, 0). All distance units are presented in kilometers.
While we consider that, you are flying on line
165x + 152y = 0
We know that the slope of the line
ax + by = c
is given by -a/b, which suggests we can form the equation of a perpendicular line by swapping x and y coefficients and negating one of them.
Then, we get the equation as,
152x - 165y = c
That is perpendicular to the flight path.
Now we need to find c so that this is true at the coordinates of Mt. Rainier.
The perpendicular line through (56, -40) is
152x - 165y - (152(56) - 165(-40)) = 0
When we expand it then we get,
152x - 165y - (8512 + 6600 ) = 0
152x - 165y - 15112 = 0
We know that the distance in km from JBLM (0, 0) to this line is given by
So, when we apply the value of (x,y) as (0,0) then we get,
=> | 152(0) - 165(0) - 15112 |/√(152²+165²)
=> 15112/√50329
=> 15112/224.34
≈ 67.362
Therefore at the constant speed of 800 km/hr, you will have flown that 67. 362 km.
Then for one km you would take,
=> 62.076/800 hr ≈ 0.0842 hr
When we convert this then we get,
=> 0.0842 = 5 minutes 3 seconds.
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An initial population of 350 flying squirrels triples every year. Write an exponential equation to represent the population growth of the flying squirrels after any given number of years, x.
The exponential equation that represents the growth of the flying squirrels is F = 350 X 3^t.
What is the exponential function?An exponential equation can be described as an equation with exponents. The exponent is usually a variable. An exponential equation exhibits a compound growth rate.
The general form of exponential function is f(x) = [tex]e^{x}[/tex]
Where:
x = the variable e = constantThe population of the bird = present population x (1 + growth rate)^number of years
350 x (1 + 2)^t
F = 350 X 3^t
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A spinner has 3 equal sections that are white, yellow, and green. Another spinner has 3 equal sections that are blue, purple, and red. How many different combinations of colors are possible if you spin each spinner once?A. 6B. 9C. 12D. 16
ANSWER
[tex]B)9[/tex]EXPLANATION
We want to find the number of different combinations of colors possible if both spinners are spun at once.
To do this, we have to find the product of the number of colors on each spinner.
That is:
[tex]\begin{gathered} 3\cdot3 \\ \Rightarrow9 \end{gathered}[/tex]The answer is option B.
nitrogen has half-life of 15 hours. how much nitrogen will remain in an 18.0 g sample after 60 hours?
If the half-life is 15 hours and there are 18 g, it means that after 15 hours,
18/2 grams would decay, leaving behind 18/2 grams
This means that 9 grams would be left.
After another 15 hours (making a total of 30 hours), 9/2 grams would decay leaving behind 9/2 grams (i.e 4.5 grams.
After another 15 hours (making a total of 45 hours), 4.5/2 grams would decay leaving behind 4.5/2 grams. Hence 2.25 grams are left
After another 15 hours (making a total of 60 hours), 2.25/2 grams would decay leaving behind 2.25/2 grams.
Hence after 60 hours, only 1.125 grams would be left
3. The number of zeroes in the end of perfect square is never_______
(vi) The cube of a two digit number may have seven or more digits. (vii) The cube of a single digit number may be a single digit number. Q. The number of zeroes at the end of a perfect square is always odd.
I hope it will be helpful for you.
the graph of a quadratic function is given. determine the function's equation.
Here, we are given a quadratic equation graph and we are tasked with getting the equation of the quadratic equation from the graph
The first thing we need to note here is the shape of the parabola.
This in the sense that if the parabola opens up or faces down
On the graph we can see that the parabola faces the positive x-direction
Generally, the equation of a quadratic graph is usually in the form below;
[tex]y=ax^2\text{ + bx + c}[/tex]So by identifying the values of a,b and c, we can get the complete equation of the graph
The above form is called the standard form while the form we have in the options is referred to as the vertex form
The vertex form can be written as;
[tex]y=a(x-h)^2\text{ + k}[/tex]Now, looking at the graph, we can see that the graph crosses the y-axis at the point y = 6
At this point, the value of x is 0
The vertex (h,k) represents the center point of the parabola
In the case of this question, the point is (-2,2)
so h =-2 and k is 2
What is left is to get a
we can obtain this from the value of y = 6 and x = 0
Thus;
6 = a(0-(-2))^2 + 2
6 = a(2)^2 + 2
6 = 4a + 2
4a = 6-2
4a = 4
a = 4/4 =1
So the equation in the vertex form is f(x) = (x + 2)^2 + 2
The grounds crew at a college is installing a path around a pond on campus as shown.9x + 10x2 - x4x2 - 7x + 8- x?+ 9x + 12What is the perimeter of the path?A. – 3 + 15x2 + 25% + 20B. 12x2 + 2x + 20C. -13 + 13x2 + 11x + 20D. 1232 + 25x + 20
The perimeter of a figure or shape is the distance around it.
The perimeter of the given path would be
9x + 10x^2 - x^3 + 4x^2 - 7x + 8 - x^2 + 9x + 12
We would collect like terms. It becomes
- x^3 + 10x^2 + 4x^2 - x^2 + 9x + 9x - 7x + 8 + 12
= - x^3 + 13x^2 + 11x + 20
The correct option is C
Bobby read a total of 20 books over 2 months. If Bobby has read 90 books so far, how many months has he been with his book club? Solve using unit rates
Step 1
From the question;
[tex]\begin{gathered} Bobby\text{ reads 20 books in 2 months} \\ \end{gathered}[/tex]We are required to find how many months it will take him to read 90 books
Step 2
We will use the ratio below to solve the problem.
[tex]\begin{gathered} \frac{20\text{ books}}{90\text{ books}}=\frac{2months}{x} \\ x=months\text{ to read 90books} \\ x=\frac{90\times2}{20} \\ x=9\text{ months} \end{gathered}[/tex]Answer; It will take Bobby 9months to read 90 booj
[tex]9\text{ months}[/tex]PLEASE HELP!! I DON'T KNOW THE ANSWER BUT OF I CLOSE IT I CAN'T GET BACK IN I CAN ONLY ACCESS THIS ONE PLEASE HELP!!!!! ⚠⚠⚠⚠⚠⚠
Answer:
The answer is the third one.
Step-by-step explanation:
They show the points plotted correctly.
A 14-foot ladder is leaning against a house with the base of the ladder 6 feet from the house. How high up the house does the ladder reach? If necessary, round to the nearest tenth foot.
The ladder leaning on the house formed a right angled triangle
Using an illustration from the diagram given:
To get the height the house makes with the ladder, we will apply pythagoras' theorem:
Hypotenuse² = opposite² + adjacent²
[tex]\begin{gathered} \text{hypotenuse = 14, adjacent = 6, opposite = }? \\ 14^2=opposite^2+6^2 \\ 196\text{ = }opposite^2\text{ + 36} \\ \\ \text{subtract 36 from both sides:} \\ 196\text{ - 36 = }opposite^2 \\ 160\text{ = }opposite^2 \end{gathered}[/tex][tex]\begin{gathered} \text{square root both sides:} \\ \sqrt[]{160}\text{ = }\sqrt[]{opposite^2} \\ \text{opposite = }12.649 \\ \\ \text{To the nearest tenth, the height of the house betw}een\text{ the ladder and base of the house is 12.6 ft (option B)} \end{gathered}[/tex]Given g(-2) = -4 and g'(-2) = 5, find the value of h'(-2) based on the function below.
h(x) = (-2x + 6) • g(x)
Step-by-step explanation:
so,
h(x) = f(x) × g(x)
h'(x) = f'(x) × g(x) + f(x)×g'(x)
with f(x) = -2x + 6
f'(x) = -2
so,
h'(-2) = -2 × g(-2) + (-2×-2 + 6) × g'(x) =
= -2 × -4 + 2 × 5 = 8 + 10 = 18
Lauren used the Quantitative Reasoning Process to budget and to start a savings account. Each month she makes about $185 from a part-time job. Lauren's parents also send her $120 per month. The sum of Lauren's paycheck and the money she gets from her parents is 11% more than her total expenses. How much money does Lauren have available to add to her savings account each month?
Lauren can add $30 each month to her savings account
Income made by Lauren from part-time job = $185
Money sent to Lauren by her parents = $120
Total income of Lauren = Money from job+ money received from parents = 120+185 = $305
Let her total expenses be x
Substituting the values in the formula we get:
Sum of Lauren's paycheck + Money she gets from her parents = Total expenses+ 11% more than her total expenses
185 + 120 = x+11% of x
305=x+11/100*x
305 = 1.11x
x=274.77 or 275
Money she can add in her savings account each month = Total money received - Expenses = 305 - 275 = $30
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A fan in a baseball stadium is sitting in a seat withtheir eye level is a vertical distance of 350 ftabove level.A) When the fan is looking at home plate, theangle of depression is 30°. What is the horizontaldistance from the fan to home plate? Round to thenearest 10th. Explain two different ways todetermine this distanceB) The same fan makes eye contact with a secondfan in the stands that is seated at a lower row inthe stadium. The straight-line distance betweenthe eyes of the two fans is 300 ft and the angle ofdepression is 48°. What is the vertical distancebetween field level and the eyes of the secondfan? Round to the nearest tenth.
GIVEN:
We are told that a baseball fan is sitting at a point where his eyes are 350 feet vertical distance from the ground. When the fan is looking at the home plate the angle of depression is 30 degrees.
Required;
Find the horizontal distance from the fan to the home plate.
Step-by-step solution;
We begin by making a sketch of the scene to determine the shape and angles formed. This is shown below;
From the sketch above we can see the that the baseball fan has effectively formed a right triangle with the home plate from his position and the dimensions, that is, angles and sides, have been labeled.
We have the reference angle given as 60 degrees and the opposite is x (horizontal distance from the fan to home plate). That means the adjacent side is 350.
We can now use the following trig ratio;
[tex]tan\theta=\frac{opposite}{adjacent}[/tex][tex]tan60\degree=\frac{x}{350}[/tex]We now cross multiply;
[tex]\begin{gathered} tan60\degree\times350=x \\ \\ 1.73205080757\times350=x \\ \\ 606.217782649=x \\ \\ x=606.2ft\text{ }(rounded\text{ }to\text{ }the\text{ }nearest\text{ }tenth) \end{gathered}[/tex]A second way to determine this distance is by using the triangle formed by the angle 30 degrees, in which case the horizontal distance will be the green line as shown in the sketch above. In that case, the vertical distance of 350 feet will be the opposite while the horizontal distance will be the adjacent while the reference angle will be 30 degrees.
For the second scenario, the straight line distance between both sets of eyes is 300 feet, and the angle of depression is 48 degrees. Note that the second fan is being watched at an angle of depression of 48 degrees which means he is at a lower level.
Now we are required to determine the vertical distance between the field level and the eyes of the second fan.
Let us begin by calculating the value of x as indicated in the triangle.
We shall use the trig ratio of;
[tex]cos\theta=\frac{adjacent}{hypotenuse}[/tex][tex]cos42\degree=\frac{x}{300}[/tex]Now we cross multiply;
[tex]\begin{gathered} cos42\degree\times300=x \\ \\ 0.743144825477\times300=x \\ \\ 222.943447643=x \\ \\ x=222.9ft\text{ }(rounded\text{ }to\text{ }the\text{ }nearest\text{ }tenth) \end{gathered}[/tex]Observe carefully that the distance calculated as x (222.9 ft) is the vertical distance between both fans. If we subtract this value from 350 feet we will now derive the vertical distance from the second fan to the field level.
[tex]\begin{gathered} Vertical\text{ }distance=350-222.9 \\ Vertical\text{ }distance=127.1ft \end{gathered}[/tex]Therefore,
ANSWER:
[tex]\begin{gathered} (A)\text{ }606.2ft \\ \\ (B)\text{ }127.1ft \end{gathered}[/tex]Graph the solution set of the following linear equation
2x+2y<-6
Graph the inequality by finding the boundary line, then shading the appropriate area.
y < −x −3
can you please help me with this algebra 2 question please
If we consider a, b and c all positive constants and b > 1, a exponential growth in general is represented by a function like:
[tex]f(t)=a\cdot b^{ct}[/tex]In otherwise, a exponential decay can be represent by:
[tex]g(t)=a\cdot b^{-ct}=a\cdot(\frac{1}{b})^{ct}[/tex]Now we can check whose functions are similar to one of these:
h(x) = 3x + 1.3 is a linear function, therefore, this is neither exponential growth or decay;
f = 3*(4.2^x) is an exponential growth;
y = (5/6)*(7^x) is an exponential growth;
T = 0.6*(1.3^x) is an exponential growth;
W(x) = (1/8)*[(3/5)^x] is an exponential decay, since in this case we have 3/5 < 1.
K = 4.2*(0.28^x) is an exponential deacay by the same argument.