Answer:
Step-by-step explanation:
To find the distance traveled, we need to subtract the starting odometer reading from the ending odometer reading.
In this case:
Journey distance = 12714 km - 12138 km = 576 km
So the journey was 576 kilometers.
Translate the sentence into an equation. Four more than the product of a number and 8 is 6. Use the variable b for the unknown number.
Answer:
8b + 4 = 6
Step-by-step explanation:
8b + 4 = 6
It didn't say you have to solve for b, but just in case...
8b = 6 - 4 = 2
b = 2/8 = 1/4
A plane is traveling Northeast. If the eastern component of it's velocity is 300 mph, how fast is the plane traveling?
The plane is travelling at a speed of 424.26 mph.
What is Velocity?Velocity of an object is the speed of the object with a given direction. Therefore velocity is a vector quantity and speed is a scalar quantity.
Given that,
A plane is traveling Northeast.
If the plane is travelling northeast, then the angle that the plane makes with the horizontal component will be 45°.
The eastern component of it's velocity is 300 mph.
Vector v can be represented as v cos (θ) i + v sin(θ) j.
Here v cos (θ) is the eastern component and v sin(θ) is the northern component.
v cos (θ) = 300
v cos(45°) = 300
v = 300 / cos(45°)
= 300 / (1/√2)
= 424.26 mph
Hence the speed of the plane is 424.26 mph.
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a high school has 40 players on the football team. the summary of the players' weights is given in the box plot. what is the median weight of the players?
The median weight of the players on the football team is approximately 160 lbs.
The box plot provides a visual summary of the data which shows the distribution of the weights of the players on the football team. The box plot consists of a box and two "whiskers" which represent the upper and lower quartiles of the data. The box is bounded by the upper quartile and lower quartile and the two whiskers represent the highest and lowest values in the data set, excluding any outliers. The median weight of the players is represented by the line in the middle of the box, which is approximately 160 lbs. The box plot is a useful tool for summarizing the data and provides a quick and easy way to visualize the distribution of the players' weights. The median weight of 160 lbs gives us an idea of the average weight of the players, which can be used to determine the overall strength of the team.
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The complete question is
a high school has 40 players on the football team. the summary of the players' weights is given in the box plot. what is the median weight of the players and find lbs.
simplify 2m exponent of 0 n exponent of 6 over 3n exponent of 5
The simplified expression is equal to 2/3.
Simplifying Math ExpressionThe expression can be simplified as follows:2m⁰ * n⁶ / (3n⁵)
Since m⁰ is equal to 1, the expression becomes:2 * n⁶ / (3n⁵)
Dividing both numerator and denominator by n⁵ gives:2 * n / (3n) = 2/3
So the simplified expression is equal to 2/3.
The rules of arithmetic and exponentiation that I used to simplify the expression are general mathematical principles that are applicable to many mathematical problems. However, the specific techniques for simplifying an expression will depend on the particular expression and the context in which it is being used.
For example, there might be additional rules or simplification techniques that are specific to a particular field of mathematics, such as algebra, calculus, or geometry. In these cases, it's important to understand the specific rules and techniques that apply to the problem at hand in order to simplify an expression effectively.
In general, the goal of simplifying an expression is to make it easier to understand and manipulate mathematically, either for further calculations or for understanding the relationships between the variables involved.
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Manny took home a couple of his friends after soccer practice. He originally had 6 gallons of gas in his car. He used 1.04 gallons of gas to take one friend home and two fifths gallons to take the other friend home. How much gas did he have left in his car after taking both friends home?
The quantity of has he had left in his car after taking both friends home would be = 4.76gallons
How to calculate the quantity of gallons?The total amount of gas in gallons in his car = 6 gallons
The amount of gas he used to take one of his friends home = 1.04 gallons.
The second friend he used a total of = 1/5 = 0.2 gallons.
The total amount of gas he uses = 1.04+0.2 = 1.24 gallons.
Then the amount of gas remaining = 6 - 1.24 = 4.76gallons.
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Answer: For every one who is annoyed with the dude aboves answer the correct answer is: D 4.56
Step-by-step explanation:
t-9.25=5.45 what is the answer pls it due tomorrow and my mom has no clue how to do sixth grade math.....???
Answer:
[tex]t=14.7[/tex]
Step-by-step explanation:
In the equation: [tex]t-9.25=5.45[/tex] we need to get [tex]t[/tex] by itself. To do that, we need to add [tex]9.25[/tex] from one side to the other. We do this because on the side where [tex]t[/tex] is, [tex]9.25[/tex] is being subtracted and we have to do the opposite of that. So:
[tex]t-9.25=5.45[/tex]
[tex]+9.25[/tex] [tex]+9.25[/tex]
In this case, we got [tex]t[/tex] by itself. The new equation is:
[tex]t=14.7[/tex]
3.1 The solutions of a quadratic equation are given by x of m will this equation have? a) Two equal solutions? -2 ±√2m+5 For which value(s)of m will the equation have? two equal solution
The value of m for which the equation will have two equal solutions is given as follows:
m = -2.5.
What is the discriminant of a quadratic equation and how does it influence the solutions?A quadratic equation is modeled by the rule presented as follows:
y = ax² + bx + c
The discriminant of the quadratic function is given as follows:
Δ = b² - 4ac.
The numeric value of the coefficient and the number of solutions of the quadratic equation is defined as follows:
Δ > 0: two real solutions.Δ = 0: one real solution = two equal real solutions.Δ < 0: two complex solutions.For this problem, the discriminant is given as follows:
Δ = 2m + 5 (it is the term that goes inside the root during the solution).
Hence, to have two equal solutions, the condition is:
Δ = 0.
Hence:
2m + 5 = 0
2m = -5
m = -5/2
m = -2.5.
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Eight years after opening her savings account, Macy had $7,880 in the account which earns annual simple interest. If Macy started with $5,000 in her account and did not make any additional deposits or withdrawals, what was the approximate annual interest rate on the savings account?
The principal amount of $5,000 deposited for 8 years with simple interest gives amount $7,880 at the annual interest of 7.2%.
Total amount 'A' in the Macy account after 8 years = $7,880
Time 't' = 8 years
Principal amount 'P' = $5,000
Let 'r' be the rate of interest given in saving account with annual simple interest.
Simple interest = Amount - Principal
= $7,880 - $5,000
= $2,880
Simple interest = ( P × r × t ) / 100
Substitute the value we get,
⇒ $2,880 = ( 5,000 × r × 8 ) / 100
⇒ r = ( 2,880 × 100 ) / ( 5,000 × 8 )
⇒ r = 7.2%
Therefore, the annual interest rate for the given amount as per simple interest is equal to 7.2%.
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The bacteria population in a small pond is decreasing because of pesticides. Each month, the
population of bacteria decreases. Initially, there were 60,000 bacteria in the pond. Fill in the
blanks for the table and the equation. Please do not use commas.
The number of bacteria after 3 months is 7500.
The equation is y = 60,000 x [tex]0.5^3[/tex].
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 8 is an equation.
We have,
Number of bacteria initially = 60,000
After one month,
The number of bacteria = 30,000
This means,
60,000 - 30,000 = 30,000
The percentage decreased.
= 30,000 / 60,000 x 100
= 1/2 x 100
= 50%
Now,
The equation for the number of bacteria after x months.
y = 60,000 x [tex]0.5^x[/tex]
For x = 3,
y = 60,000 x [tex]0.5^3[/tex]
y = 60,000 x 0.125
y = 7500
Thus,
The number of bacteria after 3 months is 7500.
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every matrix transformation is a linear transformation . t/f
"Every linear transformation is a matrix transformation." This is false. Not all linear transformations are matrix transformations, even if all matrix transformations are linear transformations.
A point, line, or geometric object can be changed in four different ways that are all referred to as transformations. The Pre-Image refers to the object's initial shape, and the Image, after transformation, refers to the object's ultimate shape and location.
Bring out the pattern blocks, tangrams, and geoboards for another low-prep, high-engagement method of teaching geometric transformations. Students can produce an original design and then hand it off to a partner so that they can add a reflection, rotation, or translation to it.
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The function f(x) = 500(1 − 0.19 )x2
models the price of a share of stock over time.
Part A
The price of the stock models exponential
Choose...
.
What is the rate of exponential growth or exponential decay?
%
Part B
Which expression is equivalent to the function f(x) = 500(1 − 0.19 )x2
?
A. f(x) = 202.5x
B. f(x) = 20.1246x
C. f(x) = 500(0.9)x
D. f(x) = 500(1.0909)x
The rate of exponential decay is 0.19.
f(x) = 202.5x is the equivalent function.
The correct option is A.
What is exponential decay?An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time.
The exponential decay function:
Aₙ = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.
Given:
The function f(x) = 500(1 − 0.19 )ˣ/2,
models the price of a share of stock over time.
Compared to the definition,
we get,
The rate of exponential decay is 0.19.
When x = 0,
Then f(x) = 202.5x
Therefore, f(x) = 202.5x is the equivalent function.
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the adjoining figure shows a racing track consisting of two parallel stretches which is 119 M long and 10 metre wide its other two end are semicircular the inner distance between the two parallel Streches is 70 m evaluate and also find the distance around the track along its outer edge and the area of the track
The distance around the track along its outer edge is 238 + 100 x π metres and the area of the track is 1250 x π + 2380 square metres.
The racetrack is divided by two parallel sections and two semi-circular endpoints. The two parallel segments are 119 metres long, and the track is 10 metres wide. The inner length of the two parallel sections is 70 metres.
To calculate the distance around the track's outer edge, multiply the lengths of the two parallel segments by the diameter of the two semi-circular ends. C = 2 x π x r, where r is the radius of the semi-circle, may be used to compute the circumference of each semi-circular end.
The radius of each semi-circle is calculated by subtracting the track width (10 metres) from half the inner distance between the two parallel sections (70 metres / 2 = 35 metres). So, the radius of each semi-circle is 35 metres - 10 metres = 25 metres.
As a result, the circumference of each semi-circle is 2 x π x 25 = 50 x π metres. As a result, the circumference of the track along its outside border is 119 metres + 119 metres + 50 x π metres + 50 x π metres = 238 + 100 x π metres.
To calculate the area of the track, first calculate the areas of the two semi-circular ends and the two parallel segments, then add them. A = π[tex]r^{2}[/tex], where r is the radius of the semi-circle, may be used to compute the area of each semi-circular end.
Each semi-circle has an area of π x [tex]25^2[/tex] = 625 x π square metres. The size of the two parallel lengths is 1190 square metres (119 metres x 10 metres). The track's total area(A) = 625 x π + 625 x π + 1190 + 1190
A= 1250 x π + 2380 square metres.
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Using the given diagram,
The length of the side x is 60.
What is the value of x?Pythagorean Theorem is a mathematical statement that states that in a right-angled 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. It can be written as c^2 = a^2 + b^2
Let the unknown side in the first triangle be a
We know that;
a^2 = 55^2 - 25^2
a= 49
Then again;
x^2 = 35^2 + 49^2
x = 60
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Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−15, −15), B′(15, 15), C′(0, 15). Determine the scale factor used.
5
1/5
12
1/12
Since triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−15, −15), B′(15, 15), C′(0, 15), the scale factor used is: A. 5.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)
Substituting the given parameters into the scale factor formula, we have the following;
Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)
Scale factor = -15/-3
Scale factor = 5.
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Answer: its 5
Step-by-step explanation: I did it in a test and got it right
-3x^5+x^3/2-x^2+8
3.1.1) How many terms are in this expression?
3.1.2) Determine the coefficient of x^3
3.1.3) Give the value of the constant term?
3.1.4) Find the degree of the expression.
Answer:
3.1.1) There are four terms in this expression.
3.1.2) The coefficient of x^3 is 0.5.
3.1.3) The constant term is 8.
3.1.4) The degree of the expression is 5.
What is the product of and ? Write your answer in standard form.
(a) Show your work.
(b) Is the product of and equal to the product of and ? Explain your answer.
In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Multiplication is often referred to as repeated addition because what the multiplication problem is telling you is that you have a certain number of groups of something, all containing a specific number. Confused yet? Here's an example.
You have 3 bags of candy, and each bag contains 5 pieces of candy. How many pieces of candy do you have?
There are two ways to solve this problem. The first is by adding up the pieces of candy:
5 + 5 + 5 = 15
The other way to solve this problem is to use multiplication, because you have 3 groups of candy with 5 pieces of candy in each bag.
3 * 5 = 15
The answer to this multiplication problem is the product, which in this case is 15.
Here's another example. The classroom has 8 rows of chairs and each row has 7 chairs in it. How many chairs are there?
Again, you could add:
7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 56
Or, you can find the product by multiplying:
7 * 8 = 56
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CORRECT QUESTION FORMAT IS GIVEN BELOW -----
Q. What is the Product in Math?
Triangle JKL is similar to triangle MNO. Find MN. Round your answer to the
nearest tenth if necessary. Figures are not drawn to scale.
N
L
19
J
26
K
58
X
M
The length of MN is roughly 13.89 units.
Describe a triangleThe polygonal shape of a triangle has three sides and three corners. It is one of the fundamental geometric shapes. Triangle ABC is a symbol for a triangle with vertices A, B, and C. When three points are not collinear, unique triangles and planes are found using Euclidean geometry.
Triangle JKL and triangle MNO are comparable, thus we can use the aspect ratio to determine the appropriate side lengths.
MN is 'x' in length. Then, it appears as follows:
JK/MN = 26/x, and KL/NO = 19/x
We can use their ratio to get x because we are aware of the lengths of JK and KL. We obtain: using the first ratio.
26/x = 58/26
x=26*26/58
x = 26^2/58
x = 13.89 (rounded to nearest integer)
Therefore, MN is approximately 13.89 units long.
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Solve this equation 20 POINTS
A local bike race is broken into 12 parts. Each stage is 14 1/2 miles. What is the total distance of the bike race?
Answer: 174 miles
Step-by-step explanation: 14.5 (14 1/2) times 12 is 174
The ratio of boys to girls Ms. Garcia’s class is 4:5.
b. If she randomly selects a student from the class to present their solution to a math problem, what is the probability the student will be a girl?
The probability of randomly selecting a girl from Ms. Garcia's class is 5/9.
The ratio of boys to girls in Ms. Garcia's class is 4:5Which means that for every 5 students in the class, 4 of them are boys and 5 of them are girls.
To calculate the probability of selecting a girl from the class, we need to divide the number of girls by the total number of students:
Number of girls: 5 students
Total number of students: 4 students + 5 students = 9 students
Probability of selecting a girl: 5 students / 9 students = 5/9
So the probability of randomly selecting a girl from Ms. Garcia's class is 5/9.
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8t+1+(−4t)+(−6) ?????????????
I need help so please help guys!
Step-by-step explanation:
So to start
Perpendicular lines are lines that form 90 degree angles when they meet.
Parallel lines will never touch, no matter how far they go.
So
Top left
A vertical line and a horizontal line
This would be perpendicular
Lines that intersect to form right angles
As mentioned above this would be perpendicular
Two nonvertical lines that have a product of -1 for their slopes.
Parallel lines always have the same slope, so this goes for parallel.
Equations that can be written in slope intercept form
This would be both as all lines can be written in this form
Non vertical lines that have the same slope and different y-intercepts
As they have the same slope this would make it parallel
You can determine the relationship between two lines by comparing their slopes and y-intercepts.
This is both as this is a way to compare all lines
Lines in the same plane never intersect
This would be parallel
Slopes are opposite reciprocals
This is perpendicular as the slopes of perpendicular lines are reciprocals
Vertical lines that have different x-intercepts
This would be parallel
Sorry this is a lot
Hope this helped though :)
help meeeeee please lol
Answer:A
Step-by-step explanation:
pls help me if ur able to thanks
Write the quadratic function f(x)=-3x^2-3x-46
in the form f(x)=a•(x-h)^2+k
Answer:
-3(x+0.5)^2-181/4 (if I calculated correctly)
Step-by-step explanation:
f(x)=-3x^2-3x-46
=-3(x^2+x+46/3)
=-3(x+0.5)^2-(0.5)^2+46/3
=-3(x+0.5)^2+181/12
=-3(x+0.5)^2-181/4
Use substitution to solve the system of equations.
y=3x−34
y=2x−5
The solution for this equation system is x= 29, y=53, (29, 53).
Step-by-step explanation:1. Write the equations.[tex](1)y=3x-34\\ \\(2)y=2x-5[/tex]
2. Substitute "y" in equation "1" by the expression on equation "2".[tex](2x-5)=3x-34\\\\2x-5=3x-34[/tex]
3. Add "5" on both sides of the equation.[tex]2x-5+5=3x-34+5\\ \\2x=3x-29[/tex]
4. Subtract "3x" from both sides of the equation.[tex]2x-3x=3x-29-3x\\ \\-1x=-29\\ \\-x=-29[/tex]
5. Multiply both sides by "-1".[tex]-x(-1)=-29(-1)\\ \\x=29[/tex]
6. Find a value of "y".To find a value of "y", use the calculated value of "x" (29), and substitute in any of the two equations to find the value of "y". For this solution, we're going to use equation 2.
[tex]y=2(29)-5\\ \\y=58-5\\ \\y=53[/tex]
7. Verify the answer.On step 6 we proved that the value of "x=29" returns a value of "53" when evaluating with equation 2. Now, if equation 1 returns the same "y" value when evaluating "x=29", then the calculated values of both "x" and "y" are correct. Let's verify!
[tex]y=3(29)-34\\ \\y=87-34\\ \\y=53[/tex]
8. Conclude.Both of the equations return the same value of "y" (53) when evaluated with "x=29". Therefore, the solution for this equation system is x= 29, y=53, (29, 53).
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Ed runs 1/6 mile in 7/9 minutes, what is his speed in miles per minute?
Answer:
Let's first convert 1/6 mile into minutes by multiplying the distance by the number of minutes per mile:
1/6 mile * (1 minute/1/6 mile) = 6 minutes/mile
Next, let's convert the 7/9 minutes into miles:
7/9 minutes * (1/6 mile/minute) = 7/9 * 1/6 mile = 7/54 miles
Now that we have the distance and time in the same units, we can calculate Ed's speed as:
Speed = Distance / Time = 7/54 miles / 7/9 minutes = 7/54 miles / (7/9 * 1 minute) = 7/54 miles / (7/9) minutes = 7/54 miles / (7/9) = 54/7 miles/minute
So, Ed's speed is 54/7 miles per minute.
Step-by-step explanation:
Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal places.
r = 10.26 inches, θ = 240°
A) 42.98 inches B) 43.08 inches C) 43.28 inches D) 43.18 inches
The length of the arc is 42.98 inches, so the correct option is A.
How to find the length of the arc?For an arc defined by an angle θ on a circle of radius r the length of the arc is given by:
L = (θ/360°)*2*pi*r
Where pi = 3.1416
Here we know that:
r = 10.26 inches
θ = 240°
Then we can replace that in the formula above, we will get:
L = (240°/360°)*2*3.1416*10.26 in
L = 42.98 inches
The correct option is A.
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The length of a rectangle is 5 cm longer than its width.
If the perimeter of the rectangle is 74 cm, find its length and width.
The length and the width are 21cm and 16cm respectively.
How to determine the length and widthThe formula for calculating the perimeter of a rectangle is expressed as;
P = 2(l +w)
Given that;
P is the perimeterl is the length of the rectanglew is the width of the rectangleBut we have that;
Length = 5 + w
Substitute the value
74 = 2(5 + w + w)
collect like terms
74=2 (5 + 2w)
expand the bracket
64 = 4w
Make 'w' the subject of formula
w = 16cm
Then, length = 5 + 16 = 21cm
Hence, the values are 16cm and 21cm
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place the numbers 2 , 6 , 7 , 8 , and 9 in the circles so that the sums across (horizontally) and down (vertically) are equal. which number will you place in the middle?
The number 7 will be placed in the middle circle.
To place the numbers 2, 6, 7, 8, and 9 in the circles so that the sums across and down are equal, you can use the following method:
1. Place the median number (7) in the middle circle.
2. Place the two smallest numbers (2 and 6) on either side of the median number.
3. Place the two largest numbers (8 and 9) in the top and bottom circles.
Here is a list of them. Each group of three numbers makes up a side of the triangle. Of course, within a side you can replace round numbers that are not on a corner, but that does not really give any new solutions.
So, the final arrangement would be:
6 2 7
9 8 7
6 2 7
Therefore, the number 7 will be placed in the middle circle.
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Damari wants to sell laptops and smartphones. Each laptop is sold for the same amount of money, and each smartphone is sold for the same amount of money. She wants to sell at least 12 total devices and make at least $4500 to cover expenses and turn a profit. Laptops sell for $425 and smartphones sell for $125.
Answer:
12000
Step-by-step explanation:
4500:12=470
425:125=100
1000×12=12000