Answer:
[tex]\boxed{\huge{\sf \dfrac{1}{4} }}[/tex]
Explanation:
Given Total Numbers: 8 numbers
Must be greater than 6, The numbers are 7 and 8 = 2 numbers
Probability:
→ favorable outcomes/total possible outcomes
→ 2/8
→ 1/4
→ 0.25
Michael drove from home to work at an average speed of 45 mph. His return trip home took 45 minutes longer because he could only drive at 35 mph. Find the distance from his home to his work.
The distance from his home to his work place is 118.125 miles
How to find the distance from his home to his work place?He drove from home to work at an average speed of 45 mph. Therefore,
speed = 45 mph
let
time = x
speed = distance / time
distance = 45x
His return trip home took 45 minutes longer because he could only drive at 35 mph. Therefore,
45 minutes = 0.75 hours
distance = 35(x + 0.75)
distance = 35x + 26.25
Therefore,
45x = 35x + 26.25
45x - 35x = 26.25
10x = 26.25
x = 26.25 / 10
x = 2.625
Therefore,
distance = 45(2.625) = 118.125 miles
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The area of a given hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. Find the length
of a side of the regular hexagon.
A triangle is a three-edged polygon with three vertices. The length of a side of the regular hexagon is √24 inches.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angle of a triangle is always equal to 180°.
Given the perimeter of the equilateral triangle is 36 inches, therefore, the length of the side of the equilateral triangle is 12 inches. Now, the area of the equilateral triangle is,
Area of the equilateral triangle = (√3)/4 a²
= (√3)/4 × (12)²
= (36√3) inches²
Since the area of the equilateral triangle is equal to the area of the hexagon , therefore we can write,
Area of equilateral triangle = Area of Hexagon
(36√3) = (3√3)/2× a²
a² = 24
a = √24 inches
Hence, the length of a side of the regular hexagon is √24 inches.
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(3x-4y)^2-(3x-4y)(3x+4y)
Answer:
[tex]-24xy + 32y^2[/tex]
Step-by-step explanation:
Hello!
We can use the special binomial product formulas:
[tex](a + b)^2 = a^2 + 2ab + b^2[/tex][tex](a + b)(a - b) = a^2 - b^2[/tex]Simplify[tex](3x - 4y)^2 - (3x - 4y)(3x + 4y)[/tex][tex](9x^2-24xy+16y^2) - (9x^2 - 16y^2)[/tex][tex]9x^2 - 9x^2 - 24xy + 16y^2 + 16y^2[/tex][tex]-24xy + 32y^2[/tex]The simplified form is [tex]-24xy + 32y^2[/tex]
Hi please help!!
Given the following function:
f(x)=2x^2
fill the table with coordinates that work for this function.
x y
(5 empty columns going down)
The table of values of the function y = 2x^2 is:
x 0 1 2 3 4
y 0 2 8 18 32
How to complete the table?The equation of the function is given as:
y = 2x^2
When x= 0, we have
y = 2 * 0^2 = 0
When x= 1, we have
y = 2 * 1^2 = 2
When x= 2, we have
y = 2 * 2^2 = 8
When x= 3, we have
y = 2 * 3^2 = 18
When x= 4, we have
y = 2 * 4^2 = 32
So, the table of values is:
x 0 1 2 3 4
y 0 2 8 18 32
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20 POINTS
Write the slope intercept form of each equation of the line. Use a fraction for slope if needed.
Parallel to y=−3/2x+1, through (0, -4)
Answer:
the answer to this question is c=-4
someone help please
Answer:
I think 40.
Step-by-step explanation:
Determine the scale of a map if the distance between 2 towns is 20km and the map distance is 5cm
The required ratio or scale will be 5cm o the map represent 20km on land
Ratio and scalingScaling is a way of enlarging or reducing the figure on an xy-plane. Given the conversion rate;
Given the following
distance between 2 towns is 20km
The distance on map is 5cm. The required ratio or scale will be 5cm o the map represent 20km on land
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The graph of f(x) = StartRoot x EndRoot is reflected across the x-axis and then across the y-axis to create the graph of function g(x). Which statements about the functions f(x) and g(x) are true? Check all that apply.
The functions have the same range.
The functions have the same domains.
The only value that is in the domains of both functions is 0.
There are no values that are in the ranges of both functions.
The domain of g(x) is all values greater than or equal to 0.
The range of g(x) is all values less than or equal to 0.
The only value that is in the domains of both functions is 0. The range of g(x) is all values less than or equal to 0. Then the correct options are C and F.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The graph of f(x) = √x is reflected across the x-axis and then across the y-axis to create the graph of function g(x).
Then the function g(x) will be
g(x) = -√(-x)
The domain of the f(x) and g(x) will be [0, ∞) and (-∞, 0] respectively.
The range of g(x) will be (-∞, 0].
The only value that is in the domains of both functions is 0.
The range of g(x) is all values less than or equal to 0.
Then the correct options are C and F.
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Answer:
C AND F
Step-by-step explanation:
Edge 2023
help pls :) have a great day everyone plshelp me
The first step to solving almost any problem is to understand what the question is asking and what is given to us in order for us to solve for the question. In this problem, we are given a graph and asked two questions. One being what the coordinates of the vertex are and whether this parabola has a maximum or a minimum.
Let's define what a vertex, maximum, and minimums are.
Vertex ⇒ Vertex is the point at which it either reaches the maximum or minimum. This point can be easily defined as where the slope becomes flat.Maximum ⇒ Maximum occurs when the vertex is at the top and the lines go down in a negative-y-direction. Therefore with the vertex being at the top that would be considered a maximum as it's the largest point in the graph.Minimum ⇒ Minimum occurs when the vertex is at the bottom and the lines go up in a positive-y-direction. Therefore with the vertex being at the bottom that would be considered a minimum as it's the smallest point in the graph.Now, looking at our problem we can see that our vertex is at the bottom therefore it would classify as a minimum. Now that we know we have a minimum vertex, let us determine what the actual coordinates of the vertex are.
We can see that we travel -3 in the x direction and -5 in the y direction which means that the coordinate for our vertex is (-3, -5) where the first number represents the x-value and the second number represents the y-value.
Answer:
(-3, -5)
Step-by-step explanation:
Here the vertex is also the minimum value; its x-coordinate is -3 and its y-coordinate is -5. Thus, the vertex is at (-3, -5). As stated above, this is the minimum value of the function.
The hypotenuse of a right triangle measures 17 cm and one of its legs measures 13 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Step-by-step explanation:
13^2 + x^2 = 17^2
169 + x^2 = 289
289 - 169 = 120
x^2 = 120
[tex] \sqrt{120} = 10.9544511501[/tex]
x = 11.0
Which Graph Shows A System With One Solution?
Answer:I think it’s A
Step-by-step explanation:
because it intersects. Sorry if it’s wrong
In the figure below, which term best describes point X?
B
OA. Centroid
OB. Incenter
O C. Circumcenter
OD. Orthocenter
The term best describes point X is option A. Centroid.
What is the centroid of a triangle and its coordinates?The point of intersection of a triangle's medians is its centroid (the lines joining each vertex with the midpoint of the opposite side).
If the surface is plane triangle approximately and mass is uniformly distributed, then its center of mass will lie on the centroid of that triangle.
If the triangle has its vertices as [tex](x_1, y_1), (x_2, y_2) , \: (x_3, y_3)[/tex]then the coordinates of the centroid of that triangle is given by:
[tex](x,y) = \left( \dfrac{x_1 + x_2 + x_3}{3} + \dfrac{y_1 + y_2 + y_3}{3} \right)[/tex]
The term best describes point X is option A. Centroid.
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Question 3 of 10
If P(x,y) is the point on the unit circle determined by real number ø, then tang
The tangent on the unit circle is y/x
How to determine the tangent value?The point on the unit circle is given as:
Point = (x,y)
By default
(cos(ø), sin(ø)) = (x,y)
This means that:
cos(ø) = x
sin(ø) = y
The tangent of an angle is:
tan(ø) = sin(ø)/cos(ø)
So, we have:
tan(ø) =y/x
Hence, the tangent on the unit circle is y/x
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The function f(x) is shown on the graph.
On a coordinate plane, a curved line with 3 arcs, labeled f of x, crosses the x-axis at (negative 2, 0), (negative 1, 0), (1, 0), and (3, 0), and the y-axis at (0, negative 6).
What is f(0)?
The value of f(0) in the function f(x) is -6
How to determine the value of f(0)?The coordinates are given as:
(-2, 0), (-1, 0), (1, 0), and (3, 0), and (0, -6)
To calculate f(0), we determine the function value when x =0
From the coordinate points, we have:
Point (0, -6)
This means that:
f(0) = -6
Hence, the value of f(0) is -6
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Answer:
Step-by-step explanation:
-2,1 or 3 only
Evaluate 4x² + 3x for x=6
Answer:
162
Step-by-step explanation:
Given algebraic expression:
4x² + 3xTo:
Evaluate this expression,with : x = 6Solution:
4x²+3xSimplify by plugging x = 6
4(6)²+3(6)4(36) + 18144 + 18162We can conclude:
By evaluating this expression by x = 6 , the answer will be 162.
The circumference of a circle is 9 pi m. What is the area, in square meters? Express your answer in terms of pi
Answer:
The circumference of a circle = 2πr = 9π inches
Or, 2πr = 9π
Or, r = 9/2
Or, r = 4.5 inches
The area of a circle = πr²
Or, The area of a circle = π×4.5×4.5
Or, The area of a circle = 20.25π square inches
Step-by-step explanation:
Can someone pls help?
Answer:
D
Step-by-step explanation:
If you think of the x-axis as your horizontal line, you can see that there is more than one value for x for y=0.
For instance, (-2,0), (0,0), (0,2).
3x + 12+ 9x - 72
Solve?
Answer:
12x - 60
Step-by-step explanation:
[tex]3x+12+9x-72\\=3x+9x+12-72\\=12x+12-72\\=12x-60[/tex]
Please help me thanks!
Problem 1
Any pair of equilateral triangles are always similar triangles. We can use the SSS (side side side) similarity theorem to prove this. One triangle is an enlarged copy of the other, or a shrunken reduced copy.
The rectangle is NOT similar to the square. They are different shapes. Similar figures are figures that are the same shape, but different sizes.
==========================================================
Problem 2
horizontal/vertical = horizontal/vertical
24/x = 6/5
24*5 = 6x
120 = 6x
x = 120/6
x = 20
Answer: The flagpole is 20 ft high (about 2 stories tall)
==========================================================
Problem 3
The formula to use is [tex]z = \sqrt{x*y}[/tex]
z = geometric mean of x and y
We multiply the numbers and take the square root. This only works for two values at a time. The geometric mean of three numbers will involve the cube root. Four numbers involves the 4th root, and so on.
Geometric mean of 6 and 10 is sqrt(60) = 7.74597 approximatelyGeometric mean of 2 and 32 is 8 exactlyGeometric mean of 2 and 8 is 4 exactlyGeometric mean of 7 and 9 is sqrt(63) = 7.93725 approximately==========================================================
Problem 4
For each figure, the y is the altitude and can be determined using the geometric mean formula.
Figure on the left: y = sqrt(2*6) = sqrt(12) = 3.4641Figure on the right: y = sqrt(6*14) = sqrt(84) = 9.1652The decimal values are approximate.
==========================================================
Problem 5
For 45-45-90 triangles, we divide the hypotenuse over sqrt(2) to find the leg length.
For the first triangle in the first row, we have y = 18/sqrt(2) = 9*sqrt(2) after rationalizing the denominator. Multiply top and bottom by sqrt(2).
Take this process in reverse to determine the hypotenuse if you know the leg length. This explains why the hypotenuse is 3.2*sqrt(2) for the second triangle in the first row.
-------------------
For 30-60-90 triangles, we go from the short leg x to the hypotenuse 2x.
Double the short leg to get the hypotenuse.
2x = 36
x = 36/2
x = 18
This is for the first triangle in the bottom row.
For the other triangle in this bottom row, we have a long leg of 4*sqrt(3). This must mean the short leg is exactly 4 units long. Therefore, the hypotenuse is 2*4 = 8 units long.
-------------------
Summary:Top row, first column: y = 9*sqrt(2)Top row, second column: y = 3.2*sqrt(2)Bottom row, first column: x = 18Bottom row, second column: y = 8The bouncy kat toys are manufactured using a layering process. the plastic is
added to the ball one layer at a time, with the radius of each ball increasing at a
rate of 0. 1 inch per second. we have been unable to correctly manage the volume
of plastic flowing into the machine. assuming the machine produces 100 toys at a
time, what is the appropriate flow rate of the plastic (in cubic inches per second)
when the radius of each toy is 0. 5 inch? what should the average flow rate of the
plastic be over each 10-second production cycle?
The flow rate to produce the balls is 12.5in/s and 1.25in/s
a. The rate flow to produce the ballsThe number of toys = 100
The increase in radius = 1inch/sec
5 toys are going to increase by 0.5 radius
The rate flow to produce the balls
5x100 = 500
Rate flow = 500 x 0.5³ / 5
= 12.5inch/s
b. New productionTime = 10 seconds x 5 = 50 seconds
radius = 0.5 inches
Flow rate = 50 * 0.5³/5*10
= 1.25 inches/s
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help i need answers fast now
Which equation is in point slope form and is depicted by the line in the graph?
A.(y-3) = 3/5 (x-2)
B. (y-3) = -(3)/(5) (x+2)
C. (y-3)= 5/3 (x-2)
D. (y+3) = 5/3 (x+2)
The equation of line passing through (-2,3) and (3,0) will be (y - 3) = - 5/3 (x + 2). Then the correct option is B.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The graph is given below.
The equation of line passing through (-2,3) and (3,0) will be
The equation of line will be
(y - 3) = [(3 + 2) / (0 - 3)] (x + 2)
(y - 3) = - 5/3 (x + 2)
Then the correct option is B.
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Mr. Mason paints his fence on Monday, Tuesday, Wednesday, and Thursday. It takes him a total of 6 2/4 hours to paint his fence. Write a digit in each box to show how many hours he could have painted each day.
A fraction is a way to describe a part of a whole. The number of hours that Mr Mason painted each day is 1.625 hours.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The total number of hours that Mr Mason took to paint the fence is 6 2/4 hours, while the number of days taken by him is 4 hours. Therefore, the number of hours for which Mr Mason painted each day can be written as,
= (6 ²/₄)/4
= (26/4)/4
= 26/16
= 1.625 hours a day
Hence, the number of hours that Mr Mason painted each day is 1.625 hours.
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A submarine travels 19 degrees west of north. What is its compass heading? PLS HELP WILL GIVE BRAINLIEST
Answer:
NNW(North-northwest)
The required compass heading of the submarine is 341 degrees.
To find the compass heading of the submarine, we need to determine the angle it makes in the north direction, clockwise.
Since the submarine is traveling 19 degrees west of north, the compass heading can be calculated as follows:
Compass Heading = 360 degrees - (Angle west of North)
Compass Heading = 360 degrees - 19 degrees
Compass Heading = 341 degrees
So, the compass heading of the submarine is 341 degrees.
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Do you know the answer to this
Answer:
[tex] 4x^2y\sqrt[4]{3y} [/tex]
Step-by-step explanation:
[tex] \sqrt[4]{768x^8y^5} = [/tex]
[tex] = \sqrt[4]{256 \times 3(x^2)^4y^4y} [/tex]
[tex] = \sqrt[4]{4^4 \times 3(x^2)^4y^4y} [/tex]
[tex] = 4x^2y\sqrt[4]{3y} [/tex]
Do the ordered pairs in the table represent a linear function?
Answer:
No.
Step-by-step explanation:
If you look at the y values, they do not have a constant rate of change. The numbers in the row for y: 3+1 is 4. 4+1 is 5. 5+7 is 12 .12+19 is 31. 31+ 37 is 68. So, as you can see, the rates at which each number changes are not constant. Therefore, the table does not represent a linear function.
Mike knows that (3,6.5) and (4,17.55) are points on the graph of an exponential function, g(x), and
he wants to find another point on the graph of this function.
First, he subtracts 6.5 from 17.55 to get 11.05.
Next, he adds 11.05 and 17.55 to get 28.6.
He states that (5,28.6) is a point on g(x).
Is he correct? Explain your reasoning.
Mike's claim that (5,28.6) is a point on the exponential function g(x) is incorrect
How to determine if he is correct?The points are given as:
(3,6.5) and (4,17.55)
Calculate the rate of change using:
r = y4/y3
This means that:
r = 17.55/6.5
r = 2.7
So, the next point on the graph is:
Next point = 2.7 * y4
Substitute 17.55 for y4
Next point = 2.7 * 17.55
Evaluate
Next point = 47.39
This means that the next point on the graph is (5,47.99)
Hence, Mike's claim that (5,28.6) is a point on the exponential function g(x) is incorrect
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1 stick butter is equivalent to _____ ounces.
Answer:
4 ounces
Step-by-step explanation:
Answer:
1 stick butter is equivalent to __4___ ounces.
Step-by-step explanation:
1 stick of butter is equal to 4 ounces
The function f(x) is shown in this graph.
--5-
The function g(x) = -6x + 3.
Compare the slopes and y-intercepts.
OA. Both the slopes and the y-intercepts are the same.
OB. The slopes are the same but the y-intercepts are different.
C. Both the slopes and the y-intercepts are different.
OD. The slopes are different but the y-intercepts are the same.
f(x)
(0,3)
Both the slopes and the y-intercepts are different. Option C is the correct answer.
What is Straight Line?A straight line is an infinite length line that does not have any curves on it. A straight line can be formed between two points also but both the ends extend to infinity.
Here, slope intercept form of given equation:
y = mx + c ............(i)
where, m is slope of line and c is y-intercept.
Given equation of line;
g(x) = y = -6x + 3
On comparing this with equation (i), we get
m = -6 and c = 3
Thus, Both the slopes and the y-intercepts are different. Option C is the correct answer.
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Using the expansion of (1-(x/2))^8 and a suitable value of x, evaluate 0.996^8 to 5 d p
Answer:
4j8rd⁸8xud4 ex fiiu8rftsuf