For something to be a function, the input (x value) can ONLY HAVE ONE output (y value), so if x has multiple outputs, it is not a function
B is not a function because x = 2 and x = 9 has 2 outputs
Your answer is A
Answer:
Step-by-step explanation:
A represents a function. Why? Because all the x-values are unique (no duplications).
B does not represent a function. Why? Because the input 4 is repeated and has different y-values for this one input, and similarly the input 9 is repeated.
Para medir la altura de una torre, juan se situa en un punto del suelo horizontal y observa el punto mas alto de la torre bajo un angulo de 62°. Se acerca 6 metros a la torre en linea recta y el angulo es de 79° haya la altura de la torre
Answer:
The height of the tower is 17.79 m
Step-by-step explanation:
The question in English is
To measure the height of a tower, Juan stands at a point on the horizontal ground and observes the highest point of the tower under an angle of 62°. He approaches the tower 6 meters in a straight line and the angle is 79° Find the height of the tower
see the attached figure to better understand the problem
In the right triangle ABC
tan(62°)=h/x
h=(x)tan(62°) ------> equation A
In the right triangle DBC
tan(79°)=h/(x-6)
h=(x-6)tan(79°) ------> equation B
Equate equation A and equation B and solve for x
(x)tan(62°)=(x-6)tan(79°)
(x)tan(62°)-(x)tan(79°)=-(6)tan(79°)
x=-(6)tan(79°)/[tan(62°)-tan(79°)]
x=9.46 m
Find the value of h
h=(9.46)tan(62°)=17.79 m
Answer:
son las dos en punto
Step-by-step explanation:
Suppose a box has a square base and no top. if x is the length of a side of the base, and h is the height of the box, what is the surface area of the box?
5xbxh hope it helps
(Writing Expressions) John charges $20.00 to mow each lawn and $5.00 to cut each bush. He mows x number of lawns and cuts y number of bushes. Which expression shows how much money John will earn? A) (20+5)xy B) 20y + 5x C) 20x + 5y D) (20 + 5) + (x + y)
Answer:
D
Step-by-step explanation:
Let E(x,y) represent the total earnings.
Then E(x,y) = ($20/lawn)x + ($5/bush)y (Answer D)
A six-sided number cube is rolled five times, X is the number of times an even number is rolled.
Which statement is true about this situation?
A. The variable X does not have a binomial distribution because P(success) is not constant.
B. The variable X has a binomial distribution. P(success)=0.5; number of trials = 5
C. The variable X does not have a binomial distribution because there are more than two possible outcomes.
D. The variable X has a binomial distribution. P(success)=0.2; number of trials = 5
Step-by-step explanation:
A six sided die has three even numbers, and each roll is independent, so P(success) is constant at 3/6 = 0.5. Since it's constant, the variable X does indeed have a binomial distribution.
So the answer is the second one, which you have selected.
Answer:
It is B.
Step-by-step explanation:
The probability of success of rolling an even number in 1 roll = 3/6 = 0.5. This is a constant and Probability of failure = 0.5. There are 2 possible outcomes so it is a Binomial Distribution.
While on vacation, a student visits the area around a volcano that has recently erupted. the student can expect to find samples of -?
Answer:
Volcanic Ash
Step-by-step explanation:
What transformations are needed to change the parent cosine function to y=3cos(10(x-pi))?
Answer:
The graph of [tex]y=cos(x)[/tex] is:
*Stretched vertically by a factor of 3
*Compressed horizontally by a factor [tex]\frac{1}{10}[/tex]
*Moves horizontally [tex]\pi[/tex] units to the rigth
The transformation is:
[tex]y=3f(10(x-\pi))[/tex]
Step-by-step explanation:
If the function [tex]y=cf(h(x+b))[/tex] represents the transformations made to the graph of [tex]y= f(x)[/tex] then, by definition:
If [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor c.
If [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c
If [tex]c <0[/tex] then the graph is reflected on the x axis.
If [tex]b> 0[/tex] The graph moves horizontally b units to the left
If [tex]b <0[/tex] The graph moves horizontally b units to the rigth
If [tex]0 <h <1[/tex] the graph is stretched horizontally by a factor [tex]\frac{1}{h}[/tex]
If [tex]h> 1[/tex] the graph is compressed horizontally by a factor [tex]\frac{1}{h}[/tex]
In this problem we have the function [tex]y=3cos(10(x-pi))[/tex] and our parent function is [tex]y = cos(x)[/tex]
The transformation is:
[tex]y=3f(10(x-\pi))[/tex]
Then [tex]c =3>1[/tex] and [tex]b =-\pi < 0[/tex] and [tex]h=10 > 1[/tex]
Therefore the graph of [tex]y=cos(x)[/tex] is:
Stretched vertically by a factor of 3.
Also as [tex]h=10[/tex] the graph is compressed horizontally by a factor [tex]\frac{1}{10}[/tex] .
Also, as [tex]b =-\pi < 0[/tex] The graph moves horizontally [tex]\pi[/tex] units to the rigth
The sum of the polynomials 6x3 + 8x2 – 2x + 4 and 10x3 + x2 + 11x + 9 is . Adding 3x – 2 to this sum gives a sum of .
Answer:
The sum of polynomials [tex](6x^{3} +8x^{2} +2x+4)[/tex] and [tex](10x^{3} +x^{2} +11x+9)[/tex] is [tex]16x^{3} +9x^{2} +13x+13[/tex].
Adding [tex](3x-2)[/tex] to the sum above gives a sum of [tex]6x^{3} +9x^{2} +16x+11[/tex]
Step-by-step explanation:
To add two polynomials, the coefficients of the terms of the same degree must be added together. The result of adding two terms of the same degree is another term of the same degree. If any term is missing from any of the grades, it can be completed with 0.
[tex](6x^{3} +8x^{2} +2x+4)+(10x^{3} +x^{2} +11x+9)= 16x^{3} +9x^{2} +13x+13[/tex]
If we adding [tex](3x-2)[/tex] to the sum above, we get:
[tex](16x^{3} +9x^{2} +13x+13)+(0x^{3} +0x^{2} +3x-2)= 16x^{3} +9x^{2} +16x+11[/tex]
11.
♡
What is the standard form of the equation of a circle with center (3,-2) and radius 4?
AO (X - 3)2 + (y + 2)2 = 16
BO (x – 3)2 + (y + 2)2 = 4
C. (x + 3)2 + (y – 2)2 = 16
D. (x – 3)2 + ( – 2)2 = 16
Answer:
(x-3)^2+(y+2)^2=16
Step-by-step explanation:
The standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where h and k are the coordinates of the center and r is the radius, which is squared. From our information, h is 3--> (x-3) and k is -2--> (y-(-2))--> (y+2) and 4 squared is 16. Your choice is A.
Answer:
(x-3)^2+(y+2)^2=16
Step-by-step explanation:
The standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where h and k are the coordinates of the center and r is the radius, which is squared. From our information, h is 3--> (x-3) and k is -2--> (y-(-2))--> (y+2) and 4 squared is 16. Your choice is A.
Need help with geometry
Answer:
V = 60
Step-by-step explanation:
The formula for the volume of a square based pyramid is: V = a² × h/3 where a = the edge and h = the height
to solve we just plug it in:
V = 6² × 5/3
V = 36 × 5/3
V = 36/1 ×5/3 (another way of writing the above)
V = 180/3 <-- simplify
V = 60
Answer:
48
Step-by-step explanation:
Formula: a^2*(h/3)
We know a is 6ft, but to find h, the height, we'll need to use Pythagoreon Theorem. The hypothenuse of the triangle is 5 and one of the legs is 3, because you need to divide 6 by 2.
3^2+b^2=5^2
9+b^2=25
b^2=16
b=4
Now plug in a and h into the formula to get 48.
for the following right triangle, find the side length of x. round your answer to the nearest hundredth.
top side: x
left side: 15
right side: 8
Answer:
17 units
Step-by-step explanation:
The sides of all right triangles share the same relationship known as the Pythagorean Theorem a² + b² = c². Substitute the lengths of the triangle into the theorem and solve for the unknown side. Since the problem does have an attached a picture, assume that a = 8, b = 15, and c = x.
8² + 15² = x²
64 + 225 = x²
289 = x²
√289 = √x²
17 = x
Final answer:
To find the length of side x in the right triangle, we use the Pythagorean theorem, which yields a hypotenuse value of 17 units. The exact value does not require rounding to the nearest hundredth.
Explanation:
To find the side length of x in a right triangle with a perpendicular side of 15 and a base of 8, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here's how you do it:
Let's call the perpendicular side a, the base b, and the hypotenuse c.
According to the theorem, we have the equation a2 + b2 = c2.
Insert the known values into the equation: 152 + 82 = c2.
Solve for c: 225 + 64 = c2, which simplifies to 289 = c2.
Take the square root of both sides to solve for c: c = √289.
Calculate the square root, which gives us c = 17.
Therefore, the length of side x (which is the hypotenuse in our case) is 17 units. We don't need to round our answer because 17 is already to the nearest hundredth.
Find the value for 4x if x = 5
Answer:
20
Step-by-step explanation:
4 multiplied by 5 is equal to 20. You substitute 5 for x.
Answer:
20
Step-by-step explanation:
You are to multiply 5 by 4: the outcome is 20. That's all.
Using the Distributive Property to factorize the equation 3x2 + 24x = 0, you get . The solution of the equation is .
Answer:
0, -8
Step-by-step explanation:
3x² + 24x = 0
Taking out common factor 3x.
3x(x + 8) = 0
Apply zero product property.
3x = 0 or x + 8 = 0
Evaluate.
x = 0 or x = -8
Answer:
First is 3x (x + 8) =0. The second is x = 0, x = -8.
Step-by-step explanation:
These are the correct answers on Plato, I got it correct.
Help PLZZZ!!!
Select the correct answer from the drop-down menu.
The roots of the quadratic equation_________ are x = 2 ± i.
options
a. x^2-4x-5=0
b. x^2+4x+5=0
c. x^2-4x+5=0
d. x^2+4x-5=0
Answer:
Option C
Step-by-step explanation: I think this is right because when you substitute the 2 for x you get the answer. Hope this helps darling!!
A quadratic equation is in the form of ax²+bx+c. The roots of the quadratic equation x² - 4x + 5 = 0 are x = 2 ± i. Thus, the correct option is C.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
Given the roots of the quadratic equation are x = 2 ± i. Therefore, we can write the roots as,
α = 2+i
β = 2-i
Now, we know that a quadratic equation can also be written in the form,
x² - (α+β)x + αβ = 0
Therefore, we need to find the value of (α+β) and αβ,
α+β = 2 + i + 2 - i
α+β = 4
αβ = (2+i)(2-i)
αβ = 2²-i²
αβ = 4 + 1
αβ = 5
Thus, the quadratic equation is x² - 4x + 5 = 0.
Hence, The roots of the quadratic equation x² - 4x + 5 = 0 are x = 2 ± i. Thus, the correct option is C.
Learn more about Quadratic Equations:
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A quadrilateral has two right angles. The measure of the third angle is 99°. What is the measure of the fourth angle?
Answer:
The measure of the fourth angle is 81°
Step-by-step explanation:
we know that
The sum of the internal angles of a quadrilateral must be equal to 360 degrees
Let
x----> the measure of the fourth angle
we have
90°+90°+99°+x=360°
Solve for x
279°+x=360°
x=360°-279°=81°
please help it would be much appreciated!
Answer:
Part a) Option d
Part b) Option a
Step-by-step explanation:
Part a
if we look at the options given and the data available
Option a) x^4+9
Putting x= 2 we get (2^4) + 9 =25
Putting x= 3 we get (3^4) + 9 =90 but f(x) =125 so not correct option
Option b) (4^x)+9
Putting x= 2 we get (4^2) + 9 =25
Putting x= 3 we get (4^3) + 9 =73 but f(x) =125 so not correct option
Option c) x^5
Putting x= 2 we get (2^5) =32 but f(x) =25 so not correct option
Option d) 5^x
Putting x= 2 we get (5^2) =25
Putting x= 3 we get (5^3) =125
Putting x= 4 we get (5^4) =625
So Option d is correct.
Part (b)
3(2)^3x
can be solved as:
=3(2^3)^x
=3(8)^x
So, correct option is a
Velma must make five bottles of lemonade for the kids playing outside. Each bottle requires 3?4 cup of sugar. How much sugar does she need?
5×3/4=3.75
she needs 3.75 cups of sugar
A store pays $29.99 for a pair of jeans. The percent of markup is 20%. What is the selling price, including markup, for 5 pairs of jeans?
Answer:
$179.94 for 5 pairs of jeans
Step-by-step explanation:
Please help me out!!!!
Answer:
3√10
Step-by-step explanation:
27² + y² = x²
⇒⇒⇒ y² = x² - 27² ----------------- [ 1 ]
3² + y² = z²
⇒⇒⇒ y² = z² - 3² ----------------- [ 2 ]
Equate [ 1 ] and [ 2 ] :
x² - 27² = z² - 3²
x² - z² = 27² - 3²
x² - z² = 720 ----------------- [ 3 ]
x² + z² = 30²
x² + z² = 900 ----------------- [ 4 ]
[ 3 ] - [ 4 ] :
-2z² = -180
z² = 90
z = √90
z = 3√10
Please help me ..........
Answer:
242.4 ft
Step-by-step explanation:
The angle immediately adjacent to the 29° angle is (90° - 29°) , or 61°.
The cosine function relates this 61° angle to the 500 ft hypotenuse and the unknown adjacent side y:
y
cos 61° = -----------
500 ft
so that y = (500 ft)(cos 61°) = (500 ft)(cos 61°) = (500 ft)(0.485) = 242.4 ft
An apple farmer is deciding how to use each day's harvest. She can use the harvest to produce apple cider or apple juice for the apple festival in two weeks. The information she uses to make the decision is listed below.
- 1 bushel of apples will make 20 quarts of apple cider
- 1 bushel of apples will make 15 quarts of apple juice
- The apple farmer collected 18 bushels of apples
- Today the apple farmer needs to produce a total of 330 quarts
The information given can be modeled with a system of equations. Define your x and y variables
x- variable ________
y- variable ________
Write two different equations that can be used to model the situation. (explain what each equation represents)
Equation 1: ___________
Explanation:
Equation 2_____________
Explanation:
Answer:For this item, we let x and y be the number of bushels of apple that will be used to produce apple cider and apple juice, respectively. The situation above is best represented by the following equations,
x + y = 18
20x + 15y = 330
The values of x and y from the equations above are 12 and 6, respectively. Therefore, 12 bushels will be used to make apple cider and 6 bushels will be used to make apple juice.
Step-by-step explanation:
Answer:
For this item, we let x and y be the number of bushels of apple that will be used to produce apple cider and apple juice, respectively. The situation above is best represented by the following equations, x + y = 18 20x + 15y = 330The values of x and y from the equations above are 12 and 6, respectively. Therefore, 12 bushels will be used to make apple cider and 6 bushels will be used to make apple juice.
Step-by-step explanation:
Please help me ...............
Answer:
b= 7 times the square root of 2
Step-by-step explanation: In a 45-45-90 degree triangle the base and the height both equal x and the hypotenuse is equal to x times the square root of 2.
Hope this helps
Answer:
a = 7
b = 7√2
Step-by-step explanation:
45 45 90 right triangle and it's also isosceles right triangle
a = 7
Ratio of leg : hypotenuse = x : x√2
leg a = 7
hypotenuse b = 7√2
A county in Alabama has a population of 90,000 people. It has an area of 800 mi2. How many people are there per square mile? A) about 72 B) about 88 C) about 113 D) about 720
Answer:
C) about 113
Step-by-step explanation:
"How many people are there per square mile?" means that we want a ratio with miles as denominator. In other words, to find the population density, we just need to divide the population by the land area (miles squared):
[tex]population-density=\frac{people}{land-area}[/tex]
We know that the population of Alabama is 90,000 people and its land area is 800 miles squared, so [tex]people=90000[/tex] and [tex]land-area=800mi^{2}[/tex].
Replacing values:
[tex]population-density=\frac{people}{land-area}[/tex]
[tex]population-density=\frac{90000}{800mi^{2}}[/tex]
[tex]population-density=112.5[/tex]
Which rounds to:
[tex]population-density=113[/tex]
We can conclude that there are approximately 113 people per square mile in Alabama.
Answer:
About 113
Step-by-step explanation:
Hope this help
Bodhi has a collection of 175 dimes and nickels. The collection is worth $13.30. Which equation can be used to find n, the number of nickels in the collection? 0.1n + 0.05(n – 175) = 13.30 0.1n + 0.05(175 – n) = 13.30 0.1(n – 175) + 0.05 = 13.30 0.1(175 – n) + 0.05n = 13.30
Answer: Option D
Step-by-step explanation:
What is the correlation coefficient r for the data set?
Enter your answer to the nearest hundredth in the box.
X Y
0 8
1 7.5
2 6
2 5.5
3 5.5
3 4
4 3
5 3
6 2.5
Answer:
-0.95
Step-by-step explanation:
The value of R is -0.9538.
What is correlation coefficient?A correlation coefficient is a metric that expresses a correlation, or a statistical link between two variables, in numerical terms. Two columns of a specific data set of observations, sometimes referred to as a sample, or two parts of a multivariate random variable with a known distribution may serve as the variables.
Given
X Values
∑ = 26
Mean = 2.889
∑(X - Mx)² = S[tex]S_{x}[/tex] = 28.889
Y Values
∑ = 45
Mean = 5
∑(Y - My)²= S[tex]S_{y}[/tex] = 32
X and Y Combined
N = 9
∑(X - Mx)(Y - My) = -29
R Calculation
r = ∑((X - My)(Y - Mx)) / √((S[tex]S_{x}[/tex])(S[tex]S_{y}[/tex]))
r = -29 / √((28.889)(32)) = -0.9538
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What is the most appropriate unit you would use to measure the weight of a house?
Answer:
tons
Step-by-step explanation:
Michele correctly solved a quadratic equation using the quadratic formula as shown below.
Which could be the equation Michele solved?
Answer:
The original equation must have been:
[tex]7x^{2} -5x-2=0[/tex]
Step-by-step explanation:
A quadratic equation is in the form of :
[tex]ax^{2} +bx+c=0[/tex]
And it is solved in the form of :
[tex]x=\frac{-b+\sqrt{b^{-4ac} } }{2a}[/tex] and [tex]x=\frac{-b-\sqrt{b^{-4ac} } }{2a}[/tex]
Now the given equation is :
[tex]x=\frac{-(-5)+-\sqrt{(-5)^{2} -4(7)(-2)} }{2(7)}[/tex]
We can see that here;
a = 7
b = -5
c = -2
So, the original equation must have been:
[tex]7x^{2} -5x-2=0[/tex]
Answer:
Look at the picture
The equation of a parabola is (y−1)2=16(x+3) .
What is the equation of the directrix of the parabola?
Enter your answer in the box.
Answer:
x = -7
Step-by-step explanation:
Since the equation for a directrix of a parabola that opens horizontally is x = h-p, we can plug it in. So h = -3 and p = 4. So x = -3-4 or x = -7.
Answer:
x=-7
Step-by-step explanation:
Given that U is the centroid of triangle OPQ find PS.
Answer:
PS=5.4
Step-by-step explanation:
The centroid divides each median in the ratio 2:1
If U is the centroid, then
[tex]3.6:x+0.8=2:1[/tex]
We use ratio to obtain;
[tex]\frac{3.6}{x+0.8}=\frac{2}{1}[/tex]
Cross multiply;
[tex]3.6=2(x+0.8)[/tex]
Expand;
[tex]3.6=2x+1.6[/tex]
Group similar terms;
[tex]3.6-1.6=2x[/tex]
[tex]2=2x[/tex]
x=1
PS=PU+US
PS=3.6+1+0.8
PS=3.6+1+0.8
PS=5.4
Lorenz needs to run 13 1/2 miles this week to meet his goal for his training plan. So far this week he has run 3 1/2 miles on Monday and 4 1/4 Tuesday. How many moremiles does he needs to run this week in order to meet his goal
Answer:
The Answer is 5 (3/4) more miles.
Step-by-step explanation:
For this we just need to add and subtract fractions.
We we want to get to 13 (1/2) miles...however we have already ran
3 (1/2) + 4 (1/4) ... this is the same as 3.5 plus 4.25. When we add those up we get...
3.5+4.25 = 7.75 then we subtract ... 13.5 - 7.75 = 5.75 = 5 (3/4) our answer.
Final answer:
Lorenz needs to run 5 3/4 more miles to meet his goal for his training plan this week.
Explanation:
To find out how many more miles Lorenz needs to run this week to meet his goal, we need to add up the miles he has already run and subtract that from his goal. Lorenz has already run 3 1/2 miles on Monday and 4 1/4 miles on Tuesday, so we can add these two amounts to get 3 1/2 + 4 1/4 = 7 3/4 miles. Next, we subtract this amount from his goal of 13 1/2 miles: 13 1/2 - 7 3/4 = 5 3/4 miles. Therefore, Lorenz needs to run 5 3/4 more miles to meet his goal for his training plan this week.
Use the given graph to determine the limit, if it exists. Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x..
By the confront theorem we know that the limit only exists if both lateral limits are equal
In this case they aren't so we don't have limit for x approaching 2, but we can find their laterals.
Approaching 2 by the left we have it on the 5 line so this limit is 5
Approaching 2 by the right we have it on the -3 line so this limit is -3
Think: it's approaching x = 2 BUT IT'S NOT 2, and we only have a different value for x = 2 which is 1, but when it's approach by the left we have the values in the 5 line and by the right in the -3 line.
ANSWER
The limit does not exist.
EXPLANATION
From the graph the left hand limit is the value the graph is approaching as x-values approaches 2.
[tex] \lim_{x \to {2}^{ - } }(f(x)) = 5[/tex]
Also the right hand limit is the value that the graph approaches, as x-values approach 2 from the right.
[tex]\lim_{x \to {2}^{ + } }(f(x)) = - 3[/tex]
Since the left hand limit is not equal to the right hand limit, the limit as x approaches 2 does not exist