Answer:
x^2 + y^2 = 4
Step-by-step explanation:
The center-radius form (formally called the standard form) of a circle is
(x-h)^2+(y-k)^2=r^2 where (h,k) is the center and r is the radius.
So if we replace (h,k) with (0,0) since the center is the origin and r with 2 since the radius is 2 we get:
(x-0)^2+(y-0)^2=2^2
Let's simplify:
x^2 + y^2 = 4
Can someone help me with this question?
The tower is 75 feet, the wire is 20 feet below the top so the wire is 55 feet above the ground.
The length of the wire is the hypotenuse of a right triangle.
Using the law of cosine:
Cos(angle) = Adjacent leg / Hypotenuse.
Cos(46) = 55 / x
X = 55/cos(46)
x = 79.2 feet
What’s the slope of a line perpendicular to a line through points,
E(5,7), F(3,1)
Answer:
-1/3 is the slope perpendicular
Step-by-step explanation:
When we have 2 points, we can use the formula
m = (y2-y1)/(x2-x1) to find the slope
m = (1-7)/(3-5)
=-6/-2
=3
The slope is 3
We want a slope perpendicular
Remember that is the negative reciprocal
- (1/3)
-1/3
Two lines are perpendicular when,
[tex]a_1=-a_2^{-1}[/tex]
Now solve for [tex]a_2[/tex] to get [tex]a_2=-a_1^{-1}[/tex]
First we calculate the slope [tex]a_1[/tex] from the given points [tex]E(x_1,y_1),F(x_2,y_2)\longrightarrow E(5,7),F(3,1)[/tex].
[tex]a_1=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-7}{3-5}=\dfrac{-6}{-2}=3[/tex]
Now use the first formula and insert the data in it to find the value of the second slope [tex]a_2[/tex],
[tex]a_2=-3^{-1}=\boxed{-\dfrac{1}{3}}[/tex]
And that's it.
Hope this helps.
r3t40
Find the value of C in the picture please
Answer:
Option A. 93.5°
Step-by-step explanation:
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
so
∠C=(1/2)[83°+2(52°)]
∠C=(1/2)[83°+104°]
∠C=(1/2)[187°]
∠C=93.5°
I need help with number 2, you can use number 1 as an example. I’m confused on how to do this one as x and y are still in the equation, so I’m not sure how to get x or y alone. TYSM!!!! 20 POINTS!!!
Answer:
y = 1/2x+1/2Step-by-step explanation:
The ax+by+c=0 that is confusing you is just the standard form of a linear equation. It is supposed to help you formulate the linear equation. In this case, a = 1, b = -2, c = 1
Therefore,
1x -2y + 1 =0
Now, you said that you are confused on how to isolate and solve for one variable; in this case, you can't. But, you can switch around the places of the variables to solve for one variable. In this case, its best to solve for y, since linear equations are easier to understand written in Slope-intercept form:
y = mx+b
Now, you must be really confused, but look at the work I am about to do so you can learn how to make this easier for you!
1x -2y + 1 =0
-1x -1x --> Subtract 1x from both sides to isolate the y variable to the left side and to keep the equation balanced
-2y + 1=0 -1x
-1 -1 --> Subtract 1 from both sides to isolate the y variable further and to keep the equation balanced
-2y = -1x-1
(-2y/-2) = ((-1x-1)/-2) --> Divide by -2 on both sides to isolate the y variable even further and to keep the equation balanced
y = 1/2x+1/2
y = mx+b
This is written in slope-intercept form. It is called as such since it gives you the slope (written in front of the x variable,in this case 1/2; m = 1/2) and the y-intercept (the letter b; in this case b = +1/2). The y-intercept is where the x coordinate is equal to zero, but it is the place where the line crosses the y-axis. So your b = 1/2, which means that your y-intercept is (0, 1/2)
These are all things you use to graph a line and helps to make it easier to graph them!
Final Answer:
y = 1/2x+1/2
The number of users of the internet in a town increased by a factor of 1.01 every year from 2000 to 2010. The function below shows the number of internet users f(x) after x years from the year 2000:
f(x) = 3000(1.01)x
Which of the following is a reasonable domain for the function?
Answer: 3347.005 users but you cant divide people in half so its 3347 people
Answer0< x<10
Step-by-step explanation: it says reasonable so this is one of the few time it’s not all positive integers cause it’s a real world question and it’s from 2000 to 2010 so 10 years is the REASONABLE domain for this problem
how much is 2 plus 3
Answer:
5
Step-by-step explanation:
Add
2 plus 3 equals 5
Step-by-step explanation:
so put two fingers up and then put three up then you get your answer.
Solve and graph the absolute value inequality: |2x + 4| > 8. number line with open circles on negative 6 and 2, shading in between. number line with closed circles on negative 6 and 2, shading going in the opposite directions. number line with open circles on negative 6 and 2, shading going in the opposite directions. number line with open circles on negative 2 and 2, shading going in the opposite directions.
Answer:
Part 1) The solution of the absolute value is (-∞,-6)∪ (2,∞)
Number line with open circles on negative 6 and 2, shading going in the opposite directions
Part 2) The graph in the attached figure
Step-by-step explanation:
we have
[tex]\left|2x+4\right|>8[/tex]
we know that
The absolute value has two solutions
step 1
Find the positive case
[tex]+(2x+4)>8[/tex]
[tex]2x>8-4[/tex]
[tex]2x>4[/tex]
[tex]x>2[/tex]
The solution is the interval ----> (2,∞)
All real numbers greater than 2
step 2
Find the negative case
[tex]-(2x+4)>8[/tex]
Multiply by -1 both sides
[tex](2x+4)<-8[/tex]
[tex]2x<-8-4[/tex]
[tex]2x<-12[/tex]
[tex]x< -6[/tex]
The solution is the interval ----> (-∞,-6)
All real numbers less than -6
therefore
The solution of the absolute value is
(-∞,-6)∪ (2,∞)
Number line with open circles on negative 6 and 2, shading going in the opposite directions
step 3
using a graphing tool
see the attached figure
A coffee franchise is opening a new store. The company estimates that there is a 70% chance the store will have a profit of $50,000, a 5% chance the store will break even, and a 25% chance the store will lose $3,500. Determine the expected gain or lose for this store.
Step-by-step explanation:
The expected value is the sum of each outcome times its probability.
E = (0.70)(50000) + (0.05)(0) + (0.25)(-3500)
E = 34125
The store is expected to gain $34,125.
To calculate the expected gain or loss for the new store, we multiply each possible outcome by its probability, then sum these values. This results in an expected gain of $34,125 for the store.
The problem requires calculating the expected value of the coffee franchise's new store opening. We use probability and finance to estimate the expected gains or losses.
The expected value (EV) is calculated as follows:
Multiply each outcome by its respective probability.
Sum these products to get the EV.
So, the expected value is:
EV = (0.70 imes $50,000) + (0.05 imes $0) + (0.25 imes -$3,500)
EV = $35,000 + $0 - $875
EV = $34,125
This implies an expected gain of $34,125 for the new store.
What is the surface area of the solid that can be formed by this net?
plz help fast!!!
Answer:
58 in^2.
Step-by-step explanation:
This is the sum of the area of 4 small rectangles + the area of the 2 larger rectangles
= 2*4*1 + 2*5*1 + 2*4*5
= 8 + 10 + 40
= 58 in^2
Answer:
58in^2
Step-by-step explanation:
If .... a-b=5 Then what is 2(a-b) ??
Answer: 10
Step-by-step explanation:
if we know a-b=5, to get the answer of 2(a-b) multiply 5 by 2.
Answer:
10
Step-by-step explanation:
a-b=5
Multiply each side by 2
2(a-b) = 2*5
2 (a-b) = 10
G-1/6=1/6. Solve for G
G -1/6= 1/6
Move -1/6 to the other side
sign changes from -1/6 to 1/6
G-1/6+1/6=1/6+1/6
G = 2/6
Reducing: divide by 2 for 2/6
2/2= 1
2/6= 3
Answer : G= 2/6= 1/3
If (x - 5) is a factor of f(x), which of the following must be true?
O A root of f(x) is x = -5.
O A root of f(x) is x = 5.
O Both x = -5 and x = 5 are rots of f(x).
O Neither x = -5 nor x = 5 is a root of f(x).
Answer:
A root of f(x) is x=5
Step-by-step explanation:
If (x-5) is a factor of f(x), then 5 is a root.
If (x+5) is a factor of f(x), then -5 is a root.
So we are only given that (x-5) is a factor of f(x), so we only know that x=5 is a root.
This is by factor theorem. It says if (x-c) is a factor then f(c)=0 which means c is a root of f(x) because it makes the expressions equal to 0.
Find the length of the hypotenuse.
Answer:
6
Step-by-step explanation:
Using the sine ratio in the right triangle
let x = hypotenuse and sin45° = [tex]\frac{\sqrt{2} }{2}[/tex], then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3\sqrt{2} }{x}[/tex]
and
[tex]\frac{3\sqrt{2} }{x}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )
[tex]\sqrt{2}[/tex] × x = 6[tex]\sqrt{2}[/tex]
Divide both sides by [tex]\sqrt{2}[/tex]
x = 6
3x-2y=-1 Y=-x+3 is (1,2) a solution of the system
Answer:
Yes
Step-by-step explanation:
To be a solution of the system, it has to satisfy both the equations.
Let's check first one:
3x - 2y = -1
3 (1) - 2(2) = 3 - 4 = -1
So correct (satisfies).
Now, 2nd one:
y = -x + 3
y = -(1) + 3
y = -1 +3
y = 2
Yes, this is satisfied.
Hence, (1,2) IS A SOLUTION OF THE SYSTEM
What is the maximum number of turns for the graph of f(x)=x^4+3x^2?
Answer:
The turns of a graph is represented by the number of maximum or minimum that the function has.
If we differenciate f(x) we get:
f'(x)=4x^3+6x
f'(x)=2x(2x^2 + 3)
Therefore f'(x) =0, when x=0. Given that negative roots are not defined.
Therefore, the number of turns will be given by the number of solutions of f'(x) which is 1.
Attached you find the graph of the function which confirms the number of turns.
If the function had other solutions, the maximum number of turns it could have is 3! because f'(x) is a third degree polynomial, therefore it can't have more than 3 solutions!
Please help
10 minutes!!
Find the value of x and the value of y.
A. x = 15, y = 10
B. x = 20, y = 50
C. x = 50, y = 10
D. x = 50, y = 20
For this case we have from the first quadrant that:
[tex]70 + A1 = 90[/tex]
Clearing angle 1:
[tex]A1 = 90-70[/tex]
[tex]A1 = 20\ degrees[/tex]
Ahors, the angle A3 of the third quadrant measures 70 degrees, it is observed that it is opposed by the vertex at the angle of 70 degrees of the first quadrant. So:
[tex]A3-A1 = 70-20 = 50[/tex]
Answer:
Option B
Un triángulo tiene un área de 48 cm2 y una base de 6cm . Encuentra la longitud de la altura.
c) Over a period of 3 years, the company's sales of biscuits increased from 15.6 million packets to
20.8 million packets.
The sales increased exponentially by the same percentage each year.
Calculate the percentage increase each year.
In order to calculate the percentage you must:
1. Divide 15.6/20.8
2. Your answer will be 0.75
3. Turn this into a fraction 75/100
4. Now turn it into a percent 75%
75% is your answer.
I need help with this
A certain triangle has two 45° angles. What type of triangle is it?
A. Acute Triangle
B. Right triangle.
C. Right isosceles
D. Acute isosceles
Answer:
C. Right isosceles
Step-by-step explanation:
We have 2 angles that are the same, that means two sides have to be the same. That makes the triangle isosceles
There are 3 angles in a triangle. They add to 180
45+45+x = 180
90+x=180
90-90+x=180-90
x=90
The other angle is a 90 degree angle. A ninety degree angle is a right angle.
That makes the triangle a right isosceles triangle
NEED HELP ASAP! The graph gx is a translation of the function fx=x2. The vertex of gx is located 5 units above and 7 units to the right of the vertex of Fx. Which equation represents gx
Answer:
g(x) is option 1 or g(x) = (x + 7)^2 + 5
A quadratic equation has the general form of:
y=ax² +bx + c
It can be
converted to the vertex form in order to determine the vertex of the parabola.
It has the standard form of:y =a(x+h)² + k
where hand k represents the vertex, h represent the point in the x axis and k is thepoint in the y axis. Therefore, from the details given in the problem, the equation that represents
g(x) is option 1 or g(x) = (x + 7)^2 + 5
3x-2>5x+10 solve for x
Answer:
-6 > x
Step-by-step explanation:
First, no matter which variable and coefficient you move, you will be dividing by a negative in the end, so reverse the inequality symbol when your answer is found. Next, you move whichever term [NOT associated with a variable (negative or positive)] is near the variable and coefficient over to the left or right side of the inequality symbol depending on where they are in the inequality. Finally, you divide by the negative coefficient it gives you, and you will arrive at your answer with your inequality symbol reversed. The answer just happens to be written in reverse. Although it is written in reverse, it is still the same answer.
I hope this helps you understand the concept, and as always, I am joyous to assist anyone at any time.
If the domain of the square root function f(x) is x<7, which statement must be true?
7 is subtracted from the x-term inside the radical.
The radical is multiplied by a negative number.
7 is added tihe radical term.
The x-term inside the radical has a negative coefficient.
Answer:
The x-term inside the radical has a negative coefficient
Step-by-step explanation:
The argument of a square root should be ALWAYS greater or equal to zero. If the domain of the function is x<7, rearranging, we have: 0<x-7
Therefore the argument is: x-7, and the function is: y = √(x-7)
The statement "The x-term inside the radical has a negative coefficient" is the right answer.
Ali read 5 pages of her book in 7 minutes. At this rate, how long will it take Ali to read 15 pages of her book? A. 21 minutes. B. 17 minutes. C. 14 minutes. D. 12 minutes.
The shortest side of an isosceles triangle is 26 cm less than twice as long as the other sides. The perimeter of the triangle is 70 cm. Find the lengths of the three sides and list them in ascending order.
Answer:
22 cm, 24 cm, and 24 cm.
Step-by-step explanation:
Isosceles Triangle is a type of triangle in which two of the three sides are equal in length. The perimeter is 70 cm. Therefore, in this question, since the sides are unknown, we can assume that:
Length of the shorter side = x cm.
Length of the other sides = y cm.
The relationship between x and y is given by:
x = (2y - 26) cm (because it is mentioned that the shortest side is 26 cm less than twice as long as the other sides).
Perimeter of a triangle = sum of all sides.
Since its an isosceles triangle, therefore:
Perimeter of the triangle = x + 2y.
Substituting the values in the perimeter formula gives:
Perimeter of the triangle = 2y - 26 + 2y.
70 = 4y - 26.
4y = 96.
y = 24 cm.
Substituting y = 24 in the equation x = 2y - 26 gives x = 2(24) - 26 = 22 cm.
So in the ascending order, the lengths are 22 cm, 24 cm, and 24 cm!!!
Which of the following shows the length of the third side, in inches, of the triangle below?
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{61}\\ a=adjacent\\ b=\stackrel{opposite}{11}\\ \end{cases} \\\\\\ \sqrt{61^1-11^2}=a\implies \implies \sqrt{3600}=a\implies 60=a[/tex]
on a piece of paper,graph c(x)=3X+2.00.Then determine which answer matches the graph you drew,including the correct axis labels.
Answer:
Attached
Step-by-step explanation:
The equation for the graph is
c(x)=3x+2
rewrite as
y=3x+2.............................................(1)
Then graph equation to visualize as attached.
Let the x-axis to represent minutes and the y-axis to represent cost
Answer:
The graph of required function is shown below.
Step-by-step explanation:
The given function is
[tex]c(x)=3x+2.00[/tex]
In this function c(x) is the cost for a taxi ride and x is the number of minutes.
It means, in the graph of cost function x-axis represents the time in minutes and y-axis represents the cost.
Time can not be negative. So, the function is defined for all non-negative values of x.
Table of values:
x c(x)
0 2.00
1 5.00
2 8.00
3 11.00
Plot any two points from these points on a coordinate plane and connect them by straight line.
Therefore, the graph of required function is shown below.
What is the area of the triangle formed from (0,-1), (0.4), and (4,-1)?
Answer:
10 squared units
Step-by-step explanation:
This triangle is pretty easy since it creates a right triangle. So the base length and height length are pretty easy to identify.
The area of a triangle is .5*base*height.
The base length after drawing the points is a horizontal so just count it or do 4-0=4.
The height length after drawing the points is a vertical so just count it or do 4-(-1)=4+1=5.
So the area of the triangle is .5*4*5=.5(20)=10 units squared.
Now if you didn't fill like drawing it and you knew how to find the determinant.
You just compute
.5 times det| 0 -1 1 |
| 0 4 1 |
| 4 -1 1 |
.5[ 0 det| 4 1 | - -1 det| 0 1 | + 1 det | 0 4 | ]
| -1 1 | | 4 1 | | 4 -1 |
.5[ 0 - -1(0-4) + 1(0-16)]
.5[ 0 -4 -16]
.5[-20]
-10
And if you get a negative just take the absolute value of it giving you 10.
please help with this question
We know that [tex]\sin(45)=\cos(45)[/tex] and this is the only point when sin and cos are equal lengths. Because both [tex]\sin(45),\cos(45)=\dfrac{\sqrt{2}}{2}[/tex]
Now if the sin of 30° is a half that would mean that cos of 60° is also a half.
Hope this helps.
r3t40
How many solutions does the following system of equations have
Answer:
D. ZeroStep-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=\dfrac{5}{2}x+2&(1)\\2y=5x+8&(2)\end{array}\right\\\\\text{substitute (1) to (2)}:\\\\2\left(\dfrac{5}{2}x+2\right)=5x+8\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(2)\left(\dfrac{5}{2}x\right)+(2)(2)=5x+8\\\\5x+4=5x+8\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\4=8\qquad\bold{FALSE}\\\\\text{The system of equations has no solution.}[/tex]