Answer:
B(m)=A(m)-D(m)
B(m)=176m
Step-by-step explanation:
we are given
Walking on his own, the distance, D, in feet, that Roberto can cover in M, minutes is given by the function
D(m)=264m
When he walks on the moving sidewalk at the airport, the distance, A, in feet, that he can cover in m m minutes is given by the function
A(m)=440m
B is the distance, in feet, that Roberto would travel on the moving sidewalk in m minutes if he were standing still
moving sidewalk distance = standstill distance + walking distance
A(m)=D(m)+B(m)
so, we get
B(m)=A(m)-D(m)
now, we can plug values
B(m)=440m-264m
B(m)=176m
Final answer:
To find the distance B(m) that Roberto would travel on a moving sidewalk in m minutes if he stood still, one must subtract the function for walking alone D(m) from the function for walking on a moving sidewalk A(m). Thus, B(m) is calculated as B(m) = A(m) - D(m), resulting in B(m) = 176m.
Explanation:
The student needs to find the formula for the distance B(m) that Roberto would travel on the moving sidewalk in m minutes if he stands still, in terms of the functions D(m) and A(m). The function D(m) = 264m represents the distance Roberto covers by walking on his own in m minutes, and A(m) = 440m represents the distance covered while walking on a moving sidewalk.
Since A(m) represents the combined effect of walking and the moving sidewalk, and D(m) represents just walking, the difference A(m) - D(m) will give us the contribution of the moving sidewalk alone, while Roberto stands still. Thus, the formula for B(m) is:
B(m) = A(m) - D(m)
B(m) = 440m - 264m
B(m) = 176m
The formula B(m) indicates the distance Roberto would cover on the moving sidewalk if he did not walk and just stood still.
A brick measures 30 cm × 10 cm × 7 1/2. How many bricks will be required for a wall 30 m long. 2 m high and 3/4 m thick?
Given the dimensions of the brick, we first calculated its volume in cubic meters. Then we calculated the volume of the wall in cubic meters. Dividing the volume of the wall by the volume of a single brick, we find that we need 20,000 bricks to build the wall.
Explanation:This is a problem in Mathematics, specifically involving volume and unit conversion. The volume of the brick can be calculated using the formula for the volume of a rectangular prism, Volume = length x width x height. The dimensions given for the brick are in centimeters and the wall dimensions are given in meters. Therefore, we must convert the brick dimensions to meters: 30 cm = 0.3 m, 10 cm = 0.1 m and 7.5 cm = 0.075 m. The volume of one brick is 0.3 m * 0.1 m * 0.075 m = 0.00225 cubic meters.
The volume of the wall is also given by the formula length x width x height, so it is 30 m * 2 m * 0.75 m = 45 cubic meters. To find the number of bricks required to fill this volume, divide the volume of the wall by the volume of a single brick, 45 m³ / 0.00225 m³ = 20000 bricks. Thus, it will take 20,000 bricks to build the wall.
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What is the rate of change of the function?
Answer:
Option A
Step-by-step explanation:
The given function is a linear function therefore rate of change of this function will be the slope of the given line.
Since this line passes through two points ( 0,1 ) and ( 0.5 0 )
the slope of the line = [tex]\frac{(y-y')}{(x-x')}[/tex]
slope = [tex]\frac{(1-0)}{(0-0.5)}[/tex]
= ( -2 )
Therfore, Option A will be the answer.
The rate of change of function is,
m = - 2
We have to given that,
A function is shown in figure.
Since, The rate of change of linear function is slope of line.
Here, Two points on the line are (1, - 1) and (0, 1)
Since, The equation of line passes through the points (1, - 1) and (0, 1)
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (1 - (-1)) / (0 - 1)
m = 2 / - 1
m = - 2
So, The rate of change of function is,
m = - 2
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A hiker averages 6 3/8 kilometers per hour. If he hikes 11/15 hours, how many kilometers does he hike?
Answer:
Distance = rate x time
= 6 and 3/8 times 5 and 1/3
= 51/8 times 16/3
= 17 times 2 <---- 51 cancels 3 and 18 cancels 8
= 34 km
Answer:
34 km
Step-by-step explanation:
Distance = rate x time
= 6 and 3/8 times 5 and 1/3
= 51/8 times 16/3
= 17 times 2 <---- 51 cancels 3 and 18 cancels 8
= 34 km
Can 9 be expressed as a fraction?
Answer:
The simplest way to write 9 as a fraction is 9/1. Any number divided by 1 is still that number, dividing an integer by 1 does nothing to its value. So using 1 as a denominator in a fraction allows an integer to remain the same, but you can then work it in fraction form
Step-by-step explanation:
Answer:
[tex]\frac{9}{1}[/tex]
Step-by-step explanation:
Yes the following number 9 can be expressed as a fraction Referring to the fact it is a whole number you must put a 1 below it in the fraction form as follows [tex]\frac{9}{1}[/tex]
a 20 foot is cut into two pieces that the second piece is 5 feet longer than the length of the first piece how long is the first piece
Answer:
x + x+5 = 20
2x + 5 = 20
2x = 15
x =7.5 and
x + 5 = 12.5
The pieces are 7.5 and 12.5 feet long.
***********************************************************************
EDITED ANSWER I mistyped the equation. The 20 foot board is cut into two pieces so that the second piece is 5 feet longer than twice the length of the first piece how long is the first piece
x + (2x +5) = 20
3x +5 = 20
3x = 15
x = 5 feet
Second board is twice as long as shorter board plus 5 feet.
Second board = 2 * 5 + 5 which equals 15
The boards are 5 and 15 feet in length.
Step-by-step explanation:
Measurement of angle 1
Answer:
55 degrees
Step-by-step explanation:
Given that a circle and inside two chords with same arc length.
We are to find the angle between the two chords.
Given that two arcs subtend angle 125 degrees at the centre.
Let us join the two ends of chords to make the figure as a triangle inside a circle.
The triangle is isosceles as two arcs and hence chords are equal.
By central angle theorem we have the two equal angles as 1/2 (125) = 62.5
Hence we have a triangle with two equal angles 62.5 and another angle 1.
By triangle sum of angles theorem
angle 1+62.5+62.5 = 180
Hence angle A = 180-62.5-62.5 = 55 degrees.
Is it any of the following
Answer:
Step-by-step explanation: For me, I would say C because it says Matt had 3 times as many stamps as Bria did and the other two isnt showing multiplying. They are mostly adding.
I WILL MARK YOU BRAINILYES IF YOU HELP.
M= -⅝
(-10,-6)
And the correct equation is this
Y+6= -⅝ (x+6)
I need help understanding the math can anyone help?
Answer:
see explanation
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here m = - [tex]\frac{5}{8}[/tex] and (a, b) = (- 10, - 6), hence
y + 6 = - [tex]\frac{5}{8}[/tex](x + 10)
If you apply the changes below to the linear parent function, F(x)=x, what is the equation of the new function? vertically compress by 1/4 flip over the y-axis
Final answer:
The new function after applying the given transformations to the linear parent function f(x) = x, results in f(x) = -1/4x, representing a combined vertical compression and reflection about the y-axis.
Explanation:
Starting with the linear parent function f(x) = x, we need to apply two transformations: a vertical compression by 1/4 and then a reflection over the y-axis. Applying a vertical compression by 1/4 means we multiply the output by 1/4, resulting in f(x) = (1/4)x.
To reflect the function across the y-axis, we replace x with -x, which gives us the new function f(x) = (1/4)(-x) or, simplified, f(x) = -1/4x. Therefore, the equation of the transformed function is f(x) = -1/4x.
Find two consecutive whole numbers that \sqrt(24)
lies between.
Answer:
4 and 5
Step-by-step explanation:
Consider whole numbers 1, 2, 3, 4, 5, 6, ... and their squares
[tex]1^2=1,\\ \\2^2=4,\\ \\3^2=9,\\ \\4^2=16,\\ \\5^2=25,\\ \\6^2=36,...[/tex]
The number [tex]\sqrt{24}[/tex] has a square [tex](\sqrt{24})^2=24.[/tex]
Since [tex]16<24<25,[/tex] you can conclude that
[tex]4<\sqrt{24}<5.[/tex]
Thus, two consecutive whole numbers that [tex]\sqrt{24}[/tex] lies between are 4 and 5.
Final answer:
√24 lies between the consecutive whole numbers 4 and 5 because 4² is 16 and 5² is 25, and 24 is between these two perfect squares.
Explanation:
To find two consecutive whole numbers that √24 lies between, we should first identify the perfect squares that are closest to 24 but less than and greater than 24.
The perfect square less than 24 is 4², which is 16, and the perfect square greater than 24 is 5², which is 25. Since √24 is greater than √16 (which is 4) and less than √25 (which is 5), √24 lies between the whole numbers 4 and 5.
Shelly bought a 2-ounce tube of blue paint. She used 2/3 Ounce to paint the water,3/5 once to paint the sky and some to paint a flag. After that she has 2/15 ounce left.How much paint did Shelby used to paint her flag?(PlS ANSWER)
Answer:
I think what you should do is 2/3 + 3/5 and then sutract it from the 2-ounce tube or you can do 2/15 - 2-ounces.
Step-by-step explanation:
Shelby used [tex]\frac{9}{15}[/tex] or [tex]\frac{3}{5}[/tex] ounce to paint the flag.
She bought 2-ounce tube of blue paintShe used [tex]\frac{2}{3}[/tex] ounce to paint the waterShe used [tex]\frac{3}{5}[/tex] ounce to paint the skyShe had [tex]\frac{2}{15}[/tex] ounce leftThe ounce used to paint a flag is unknownFurther ExplanationTo determine how much paint Shelby used to paint her flag then, we have:
= [tex]\frac{2}{3}[/tex] + [tex]\frac{3}{5}[/tex] + [tex]\frac{2}{15}[/tex] (let solve the first 2 fractions)
= [tex]\frac{2}{3}[/tex] + [tex]\frac{3}{5}[/tex] (the lowest common denominator of 3 and 5 is 15)
= (5 x 2) + (3 x 3) / 15
= (10) + (9) / 15
= 10 + 9 / 15
= [tex]\frac{19}{15}[/tex] .
Now we should add [tex]\frac{9}{15}[/tex] with the fraction of ounce she had left: [tex]\frac{2}{15}[/tex]
Therefore, we have
= [tex]\frac{19}{15}[/tex] + [tex]\frac{2}{15}[/tex] (the lowest denominator of 15 and 15 is 15)
= (19 x 1) + (1 x 2) / 15
= (19) + (2) / 15
= [tex]\frac{21}{15}[/tex] .
Recall that the total paint is 2-ounce. Therefore, to get the fraction of ounce used to paint a flag, we have to subtract the ounce of the total paint from the [tex]\frac{21}{15}[/tex] .
Therefore we have:
2-[tex]\frac{21}{15}[/tex] (can also be expressed as [tex]\frac{2}{1}[/tex] – [tex]\frac{21}{15}[/tex] )
= (15 x 2) – (1 x 21) / 15 (the lowest denominator is 15)
= (30) – (21) / 15
= 30 – 21 / 15
= [tex]\frac{9}{15}[/tex] or [tex]\frac{3}{15}[/tex] .
Therefore Shelby used [tex]\frac{9}{15}[/tex] or [tex]\frac{3}{5}[/tex] ounce to paint the flag.
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fraction brainly.com/question/6201432lowest common denominator brainly.com/question/10962736KEYWORDS:
fractionsbodmasshellyounceflaglowest common denominatorWhich type of transformation maps ABC to A'B'C?
Answer:
Translation.
Step-by-step explanation:
Answer:
Transformation Shifted by 4 units right and 2 units down .
Step-by-step explanation:
Given : Graph .
To find : Which type of transformation maps ABC to A'B'C.
Solution : We have given graph with transformation maps ABC to A'B'C.
Coordinates of A ( -3 , 2) , B( -2 ,4) , C( -1 ,3) .
Coordinates of A' (1 , 0) , B'( 2 ,2) , C'( 3 ,1) .
We can see from given graph triangle ABC is shifted right ( x axis) by 4 units and move down by 2 units (y axis ).
Then
A ( -3 + 4 , 2 -2) →→A' (1 , 0)
B( -2+4 ,4 -2) →→ B'( 2 ,2)
C( -1+ 4 ,3 -2) →→ C'( 3 ,1) .
Therefore, Transformation Shifted by 4 units right and 2 units down .
The ropes on either side of a swing are 1.9 m long. If a child swings through a arc length of 0.9 Determine the angle (in radians) through which the child swings
Answer:
theta = 9/19 radians or approximately .4737 radians
Step-by-step explanation:
The formula for arc length is
S = r theta
where theta is in radians. Lets put in what we know. The radius would be 1.9 since the ropes would be the radius.
.9 = 1.9 theta
Divide by 1.9 on each side.
.9/1.9 = theta
theta = 9/19 radians
or in decimal form it is approximately .4737 radians
Evaluate 6g +1 for g =7
Answer:
43
Step-by-step explanation:You first have to write the equation down. Then replace any variables with numbers. Do 6 times 7 which equals 42. Then add 1 to the answer which equals 43. Hope this is helps!! ☺☻
Answer:
Your answer is 43
Step-by-step explanation: You have to substitue 7 for g since it says g=7
6g +1 --- GIVEN
6(7) + 1 --- SUBSTITUTION
42 + 1 --- MULTIPLICATION
43 --- ADDITION
I need to know these asap
Answer: (-3, -5)
Step-by-step explanation:
-6x + y = 13
6x + 3y = -33
4y = -20
÷4 ÷4
y = -5
6x + 3y = -33
6x + 3(-5) = -33
6x - 15 = -33
6x = -18
x = -3
*********************************************************************************
Answer: ([tex]\frac{1}{3}[/tex], 2)
Step-by-step explanation:
9x + y = 5 → 1(9x + y = 5) → 9x + y = 5
3x - 3y = -5 → -3(3x - 3y = -5) → -9x + 9y = 15
10y = 20
÷10 ÷10
y = 2
9x + y = 5
9x + (2) = 5
9x = 3
x = [tex]\frac{1}{3}[/tex]
solve for x= 4x+18°+5x°=90°
Answer: x = 8
Step-by-step explanation:
4x + 18 + 5x = 90
9x + 18 = 90 Added like terms
9x = 72 Subtracted 18 from both sides
x = 8 Divided both sides by 9
BONUS: The sum of these two angles is 90°, which means these angle are complementary.
Twelve subtracted from a number equals 25. Find the number
Answer:
37 is your answer
Step-by-step explanation:
let "a number" = x
"twelve subtracted from [x]" = x - 12
"equals 25" = = 25
Set the equation
x - 12 = 25
Isolate the variable. Note the equal sign, what you do to one side, you do to the other. Add 12 to both sides
x - 12 (+12) = 25 (+12)
x = 25 + 12
x = 37
37 is your answer
~
The question is asking for a number that results in 25 when 12 is subtracted from it. This is an algebraic expression represented as x - 12 = 25. The solution is x = 37.
Explanation:The question is asking to find a number when 12 is subtracted from it; the result is equals to 25. This is a basic algebraic expression where we let the unknown number be represented by the letter 'x'.
So, we can rewrite the question as an equation: x - 12 = 25.
To find 'x', we need to isolate it on one side of the equation, and to do so, we add 12 to both sides of the equation. This gives us: x = 25 + 12.
Adding 25 and 12, we get 37. So, the number you're looking for is 37.
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solve for x
(x+7)^2-49=0
find the smaller and larger x
smaller x=
larger x=
[tex](x+7)^2-49=0\qquad\text{add 49 to both sides}\\\\(x+7)^2=49\iff x+7=\pm\sqrt{49}\\\\x+7=-7\ or\ x+7=7\qquad\text{subtract 7 from both sides}\\\\\boxed{x=-14\ or\ x=0}\\\\Answer:\\\\smaller\ x=-14\\larger\ x=0[/tex]
Answer:
x = -14 and x=0
Step-by-step explanation:
(x+7)^2-49=0
Add 49 to both sides
(x+7)^2-49+49=0+49
(x+7)^2 = 49
Take the square root of each side
sqrt((x+7)^2) = ±sqrt(49)
(x+7) = ±sqrt(49)
x+7 = ±7
Subtract 7 from each side to isolate x
x+7-7 = -7±7
x = -7±7
x = -7+7 and x = -7-7
x = 0 and x=-14
you are taking a test worth 130 points. There are a total of 50 five-point and two-point questions. How many five-point questions are there on the test?
Answer:
10 five-point questions and 40 two-point questions
Step-by-step explanation:
Let x represent the total number of five-point questions and y represent the total number of two-point questions.
Equation 1: 5x+2y=130
Equation 2: x+y=50
Multiplying Equation 2 by 2: 2x+2y=100 (Equation 3)
(Equation 1) - (Equation 3): 3x=30
x=10
Substituting x=10 into x+y=50: 10+y=50
y=40
Therefore, there are 10 five-point questions and 40 two-point questions.
Substituting x=10 and y=40 into Equation 1:
LHS=5x+2y=5(10)+2(40)=50+80=130
RHS=130
LHS=RHS
Substituting x=10 and y=40 into Equation 2:
LHS=x+y=10+40=50
RHS=50
LHS=RHS
Since in both cases the left-hand side is equal to the right-hand side, the answer is correct.
(LHS: left-hand side, RHS: right-hand side)
Final answer:
To find the number of five-point questions on the test, set up an equation using the given information and solve for x.
Explanation:
To find the number of five-point questions on the test, we need to first determine the total number of points available. The test is worth 130 points, and there are a total of 50 five-point and two-point questions. Let's denote the number of five-point questions as x.
The total points from the five-point questions would be 5x, and the total points from the two-point questions would be 2(50 - x) = 100 - 2x. Since the test is worth 130 points, we can set up the equation 5x + 100 - 2x = 130.
Simplifying the equation, we get 3x + 100 = 130. Solving for x, we subtract 100 from both sides, resulting in 3x = 30, and then divide both sides by 3, giving us x = 10. Therefore, there are 10 five-point questions on the test.
2 to the 6 th power divided by 4 to the 2 nd power
Hi there!
Lets first put the question into equation format. It will look like this,
2^6 ÷ 4^2
"^" means "raised to a power of"
Now, solve the powers and divide.
2^6 = 64
4^2 = 16
Divide,
64 ÷ 16 = 4
Your answer is 4
Hope this helped!~
Cube A has a volume of 125 cubic inches. The edge lengths of cube B measure 4.8 inches. Which cube is larger and why?
Answer: Cube A is larger. This is because volume is found by multiplying length × width × height. The length, width, and height of a cube are ALWAYS equal. Therefore if cube B has a length of 4.8 inches it also has a height of 4.8 inches and a width of 4.8 inches. To find its volume multiply 4.8×4.8×4.8 this will give you 110.592 cubic inches. This means cube A is larger.
Cube A is bigger because of bigger volume.
Given that;Volume of cube A = 125 cubic inches
Side of cube B = 4.8 inches
Find:Which cube is big
Computation:Volume of cube = Side³
Volume of cube B = 4.8³
Volume of cube B = 110.592 cubic inches
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Is it possible to draw an isosceles right triangle with side lengths of 15,20,25? Explain.
Answer:
NO
Step-by-step explanation:
The rule for Isosceles Triangle is that two of the sides (leg) must be congruent (have the same meaurement), while the base can be larger or smaller.
~
The sum of two numbers is 13 two times the first number minus three times the second number is 1. If you let x stand for the first number and y for the second number what are the two numbers
Graph y+6=45(x+3) using the point and slope given in the equation
Step-by-step explanation:
We have been given an equation y+6=45(x+3) in point slope form.
It says to use the point and slope from given equation to create the graph.
So compare equation y+6=45(x+3) with point slope formula
y-y1=m(x-x1)
we see that m=45, x1=-3 and y1=-6
Hence first point is at (-3,-6)
slope m=45 is positive so to find another point, previous point will move 45 units up then 1 unit right and reach at the location (-2,39).
Now we just graph both points (-3,-6) and (-2,39) and join them by a straight line. Final graph will look like the attached graph.
.
A ___ is a number written with a variable to indicate the product of the number and the variable in a term.
relation
function
rate
coefficient
Answer:
coefficient
Step-by-step explanation:
A coefficient is a number written with a variable to indicate the product of the number and the variable in a term.
What is a variable term?In any of the algebraic expressions or an equation or a polynomial, a term contains at least one variable and a coefficient (numerical value). Thus, the coefficient of the term is one of the factors. So, the coefficient is indicated by the product of the number and the variable in a term.
Given statement:The number written with a variable indicates the product of the number and the variable in a term is its coefficient. This is because it is a numerical value and it is the factor for the term.
E.g., 4xy - here 4 is the coefficient, and x y are the variables.
This can be written as 4 × x × y (product form).
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Mako runs m miles each day. Anthony runs twice as many miles as Mako, Altogether, they run 18 miles each day. How many miles does Mako run each day?
Answer:
6
Step-by-step explanation:
I do not answer how I should but, how I found the answer:
18 divided by 3 (two for Anthony and one for Mako)
18/3= 6
ahh yeah, hope the answer helps the rest is unneeded haha!
What is the ratio of the width to the length?
Answer:
the ratio is 41:21
Step-by-step explanation:
Which expression is equivalent to the following complex fraction? X+5/x+2-x+1/x^2+2x
Answer:
Final answer will be the choice which matches best with expression
[tex]\frac{x^2+4x-1}{x\left(x+2\right)}[/tex] or
[tex]\frac{x^2+4x-1}{x^2+2x}[/tex]
Step-by-step explanation:
Given expression is:
[tex]\frac{\left(x+5\right)}{\left(x+2\right)}-\frac{\left(x+1\right)}{\left(x^2+2x\right)}[/tex]
We begin by factoring denominators:
[tex]=\frac{\left(x+5\right)}{\left(x+2\right)}-\frac{\left(x+1\right)}{x\left(x+2\right)}[/tex]
Multiply and divide first term by (x) to make denominators equal.
[tex]=\frac{x\left(x+5\right)}{x\left(x+2\right)}-\frac{\left(x+1\right)}{x\left(x+2\right)}[/tex]
Since denominators are equal so we can combine numerators.
[tex]=\frac{x\left(x+5\right)-\left(x+1\right)}{x\left(x+2\right)}[/tex]
Now simplify
[tex]=\frac{x^2+5x-x-1}{x\left(x+2\right)}[/tex]
[tex]=\frac{x^2+4x-1}{x\left(x+2\right)}[/tex]
[tex]=\frac{x^2+4x-1}{x^2+2x}[/tex]
Hence final answer will be the choice which matches best with expression
[tex]\frac{x^2+4x-1}{x\left(x+2\right)}[/tex] or
[tex]\frac{x^2+4x-1}{x^2+2x}[/tex]
If x=-2 is a solution to the equation f(x) = g(x) which of these statements must be true?
A f and g intersect at -2
B f and g intersect a x=2
C f and g intersect the x-axis at -2
D f and g intersect the y-axis at -2
If choice A says the two functions intersect at x = -2, then it would be the correct answer. Though it seems the "x=" part is left off. I'm not sure if this is intentional, or a typo.
The correct option is A) f and g intersect at x = -2
Step-by-step explanation:
Given :
x = -2 is a solution to the equation f(x) = g(x).
Solution :
x = -2 must be an intersection point of the equations f(x) and g(x) because
f(x) = g(x). And the point x = -2 satisfy both the equations.
Therefore, the correct option is A) f and g intersect at x = -2.
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Find u -2v given u = (-2, 5) and v = 6i -4j
A. U - 2v = -14i +13j
B. U - 2v = -10i + 13j
C. U - 2v = 4i + j
D. U - 2v = 10i - 3j
Answer:
A. U - 2v = -14i +13j
Step-by-step explanation:
If u = (-2, 5) and v = 6i -4j
Then 2v = 2*(6i-4j) = 12i-8j
u-2v = -2i +5j - (6i -4j)
Distribute the minus sign
-2i +5j -6i+4j
-2i +5j
-12i + 8j
---------------
-14i +13j
Answer:
1.) d
2.) c
3.) a
Step-by-step explanation: