Write an algebraic expression for the verbal description. the distance a car travels in t hours at a rate of 50 miles per hour
The algebraic expression is D = 50t where D is the distance covered in miles and t is the time taken in hours.
What is the distance?Distance is defined as the product of speed and time.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
The operator that performs the arithmetic operations is called arithmetic operator.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
Given that the distance a car travels in t hours at a rate of 50 miles per hour
Let the distance covered in miles = D
And t is the time taken in hours
Since distance is defined as the multiplication of speed and time.
So an algebraic expression for the verbal description as
⇒ D = 50t
Hence, the algebraic expression is D = 50t where D is the distance covered in miles and t is the time taken in hours.
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Factor this trinomial completely.
–6x2 + 26x + 20
A. –6x2 + 26x + 20
–2(3x2 – 13x – 10)
–2(3x + 2)(x – 5)
B. –6x2 + 26x + 20
–2(3x2 + 11x + 10)
–2(3x + 5)(x + 2)
C. –6x2 + 26x + 20
–2(3x2 – 13x – 10)
–2(3x – 10)(x + 1)
D. –6x2 + 26x + 20
–2(3x2 – 13x + 10)
–2(3x – 5)(x – 2)
First, factor out -2 from the trinomial, and then factor the resulting quadratic expression by grouping. The correct factored form is -2(3x + 2)(x - 5).
To factor the trinomial “6x² + 26x + 20 completely, follow these steps:
First, factor out the greatest common factor, which is -2:Therefore, the correct factored form is (Option A) “2(3x + 2)(x – 5).
SOLVE FOR X one question 20 points
Answer:
ANSWER IS
Step-by-step explanation:
On a map, 1 inch equals 9.2 miles. two houses are 3.5 inches apart on the map. what is the actual distance between the houses? use pencil and paper. show how you can represent the scale with two different ratios. what ratio is more helpful for solving the problem? explain.
The actual distance between the houses is 18.9 miles.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
Given that On a map, 1 inch equals 9.2 miles. Two houses are 3.5 inches apart on the map.
To find the actual distance between the houses.
Given that,
1 inch = 9.2 miles
Therefore,
∴ we get
3.5 inches = 3.5 × 9.2 miles
= 13.8 miles
The actual distance is 13.8 miles.
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Final answer:
To find the actual distance between the houses, we can set up a proportion using the given map scale. The actual distance between the houses is 32.2 miles. Using the ratio 1 inch/9.2 miles = 3.5 inches/x is more helpful in solving the problem.
Explanation:
To find the actual distance between the houses, we need to use the scale of 1 inch equals 9.2 miles. We are given that the two houses are 3.5 inches apart on the map.
First, we can set up a proportion to find the actual distance:
1 inch / 9.2 miles = 3.5 inches / x
Cross-multiplying, we have:
1x = 3.5 * 9.2 miles
Simplifying, we get:
x = 32.2 miles
The actual distance between the houses is 32.2 miles.
To represent the scale with two different ratios, we can use the proportion:
1 inch / 9.2 miles = 3.5 inches / x
This ratio is more helpful for solving the problem as it allows us to directly calculate the actual distance using the given map distance and the scale ratio.
describe the steps you would use to solve the following inequality
Answer:
Rewrite the inequality so there is a single rational expression on one side, and 0 on the other.
Combine under a common denominator.
Test points in the critical regions.
Construct the solution.
Step-by-step explanation:
Answer Above
Solve system by elimination
y=x^2
y=x+2
SHOW YOUR WORK
Group terms that contain the same variable, and move the constant to the opposite side of the equation
(x²-x)=2Rewrite as perfect squares
(x-0.5)²=2+0.5²How many degrees is w?
The shorter leg of a right triangle is 7 inches shorter than the longer leg. The hypotenuse is 17 inches longer than the longer leg. Find the side lengths of the triangle.
a² + b² = c²
c² - a² = b²
17² - 7² = x² ↓
289 - 49 = √240
√240 = 15.49193338482967 (rounded 15.49 or 15.5)
Hope this helps,
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Write the inverse function for the function, ƒ(x) = x + 4. Then, find the value of ƒ -1(4). Type your answers in the box.
ƒ -1(x) = _________ x ___________ ______
ƒ -1(4) = _____________
Answer: The required values are
[tex]f^{-1}(x)=x-4~~~~~~~~\textup{and}~~~~~~~~~f^{-1}(4)=0.[/tex]
Step-by-step explanation: We are given the following function f(x) :
[tex]f(x)=x+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We are to find the values of [tex]f^{-1}(x)[/tex] and [tex]f^{-1}(4).[/tex]
Let us consider that
[tex]y=f(x)~~~~~~~~\Rightarrow x=f^{-1}(y).[/tex]
So, from equation (i), we get
[tex]f(x)=x+4\\\\\Rightarrow y=f^{-1}(y)+4\\\\\Rightarrow f^{-1}(y)=y-4\\\\\Rightarrow f^{-1}(x)=x-4.[/tex]
Substituting x = 4 in the above equation, we get
[tex]f^{-1}(4)=4-4=0\\\\\Rightarrow f^{-1}(4)=0.[/tex]
Thus, the required values are
[tex]f^{-1}(x)=x-4~~~~~~~~\textup{and}~~~~~~~~~f^{-1}(4)=0.[/tex]
A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds:f(t) = −16t2 + 48t + 100The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____feet per second.
On a scatter plot what does it mean when both variables are increasing
find the greatest common factor 9x^2a + 9xa^2
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.
Rewrite with only sin x and cos x. Sin2x-cos2x
Troy has a box of 600 tiny blocks. Each block is a cube with dimensions of 1 cm x 1cm x 1cm. The blocks are arranged in the box in rows and layers so that there are no gaps. Which could be the dimensions of the box?
a. 5 cm x 10 cm x 12 cm
b. 5 cm x 10 cm x 10 cm
c. 10 cm x 10 cm x 12 cm
d. 200 cm x 200 cm x 200 cm
divide r+5/ r^2+5r-14 by r^2+4-21/r-2
Blue marbles, green marbles and red marbles are in a ratio of 5 to 7 to 8 in a box. if the total number of marbles is 240, how many green marbles are in the box?
If the ratio of the radii of two spheres is 8:9, what is the ratio of the volumes of the two speheres
What is the value of x?
a. 6
b. 6√3
c. 12
d. 12√3
i really need help. please help
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4^−x and y = 8^(−x−1) intersect are the solutions of the equation 4^−x = 8^(−x−1). (4 points)
Part B: Make tables to find the solution to 4^−x = 8^(−x−1). Take the integer values of x between −3 and 3. (4 points)
Part C: How can you solve the equation 4^−x = 8^(−x−1) graphically? (2 points)
Given y = 4x + 3, what effect does changing the equation to y = 2x + 3 have on the slope?
Changing the slope of the equation from 4 to 2 reduces the steepness of the line in the graph, with the y-intercept remaining constant at 3.
Explanation:The student asked about the effect on the slope of the linear equation when changing from y = 4x + 3 to y = 2x + 3. The slope of the first equation is 4, which can be seen from the coefficient of x, indicating a rise of 4 on the vertical axis for every increase of 1 on the horizontal axis. When the equation changes to y = 2x + 3, the slope is reduced to 2, which means there is a rise of 2 on the vertical axis for every increase of 1 on the horizontal axis. This change in the slope would cause the line to rotate clockwise when graphed on a coordinate plane. The y-intercept remains the same at 3 since it is unchanged in both equations. Therefore, changing the equation has the effect of decreasing the steepness of the line, but the location where the line crosses the y-axis does not change.
Which of these is an example of continuous random variable
A. Number of flights leaving an airport
B. Distance of a javelin throw
C. Pieces of mail in your mailbox
D. Attendance at a sporting event
The B. distance of a javelin throw is an example of a continuous random variable.
Explanation:A continuous random variable is a variable that can take any value within a specified range, often associated with measurements and quantities. Unlike discrete variables, it can assume an infinite number of values, typically represented by intervals on the real number line.
Out of the given options, the distance of a javelin throw is an example of a continuous random variable. A continuous random variable is one that can take on any value within a given range. In the case of a javelin throw, the distance can be any real number value within a certain range, such as 0 to infinity. This is in contrast to the other options, which are discrete random variables that can only take on specific whole number values.
does anyone know the surface area for this problem. if so i will mark brainliest.
What is the best estimate of the mean price of all the sunglasses on the rack?
Help with algebra 2 please!!!!!!!
if (x+1) is a factor of x^3+2x^2-x-2, find the remaining factors.
Answer:
The other factors are (x-1) and (x+2).
The product of a number (n) and 12 is 64. Which equation shows this relationship
12+n=64
64n=12
12n=64
64-n=12
The equation that shows the relationship between the number (n) and 12 being multiplied to equal 64 is 12n = 64, the correct option is C.
In this equation, the variable n represents the number we are trying to find. The equation states that when we multiply 12 and n together, the result is 64.
To solve this equation and find the value of n, we divide both sides of the equation by 12:
(12n)/12 = 64/12
n = 64/12
Which can be further simplified to:
n = 16/3
Therefore, the equation that represents the relationship between the number (n) and 12 being multiplied to equal 64 is 12n = 64.
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A field goal post in football is 3.33 yards above the ground. If a football player kicks the ball at a 10 degree square angle in a straight line toward the goal post what is the distance away in yards where the ball barely goes over the goal post
Given that the two triangles shown are congruent, explain one way to verify that the corresponding angles of the two triangles are congruent.
A) reflect triangle 1 across the y-axis
B) reflect triangle 2 across the y-axis
C) rotate triangle 2 counter-clockwise 90° about the origin
D) reflect triangle 2 across the y axis and rotate 90° about the origin at
Answer:
The correct option is C.
Step-by-step explanation:
From the given graph it is noticed that the vertices of triangle 1 are P'(-2,2), Q'(-4,4) and R'(-2,4). The vertices of triangle 2 are P(2,2), Q(4,4) and R(4,2).
If a figure rotated counter-clockwise 90° about the origin, then
[tex](x,y)\rightarrow (-y,x)[/tex]
If we rotate triangle 2 counter-clockwise 90° about the origin, then[
[tex]P(2,2)\rightarrow P'(-2,2)[/tex]
[tex]Q(4,4)\rightarrow Q'(-4,4)[/tex]
[tex]R(4,2)\rightarrow R'(-2,4)[/tex]
If we rotate triangle 2 counterclockwise, then we get the triangle 1.
Therefore the correct option is C.
Find the area of the shaded region.