Answer:
The time it would take Kyle's mum is given as follows;
[tex]t = \dfrac{3 \cdot v^2+ 2\cdot v - 2}{v \cdot (v - 1) \cdot (v + 2)}[/tex]
Where v = Kyle's average rate
Step-by-step explanation:
The details of Kyle's mother's journey are;
The distance she drove = 12 miles
Her speed during the first third (12/3 = 4 miles), v₁ = 4 × Kyle's speed, v
Her speed in the second third(between 4 and 8 miles), v₂ = v₁ - 4
Her speed in the last third, v₃ = v₂ + 12
∴ v₁ = 4·v
v₂ = v₁ - 4 = 4·v - 4
v₃ = v₂ + 12 = 4·v - 4 + 12 = 4·v + 8
∴ t₁ = (t/3)/4 = t/12 = 4/(4·v) = 1/v
t₂ = 4/(4·v - 4) = 1/(v - 1)
t₃ = 4/(4·v + 8) = 1/(v + 2)
The total time, t = t₁ + t₂ + t₃
∴ t = 1/v + 1/(v - 1) + 1/(v + 2) = [tex]\dfrac{3 \cdot v^2+ 2\cdot v - 2}{v \cdot (v - 1) \cdot (v + 2)}[/tex]
The time it would take Kyle's mum to travel the same 12 miles by car that Kyle traveled on his bike, t = [tex]\dfrac{3 \cdot v^2+ 2\cdot v - 2}{v \cdot (v - 1) \cdot (v + 2)}[/tex]
2) Simplify: 4/3+3/5+-3/5+-11/3
Answer:
[tex]\frac{4}{3}+\frac{3}{5}+-\frac{3}{5}+-\frac{11}{3}[/tex][tex]=\frac{4}{3}-\frac{11}{3}[/tex][tex]\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex][tex]=\frac{4-11}{3}[/tex][tex]\:4-11=-7[/tex][tex]=\frac{-7}{3}[/tex][tex]\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}[/tex][tex]\frac{-a}{b}=-\frac{a}{b}[/tex][tex]\frac{-7}{3}[/tex][tex]=-\frac{7}{3}[/tex]---------------------[tex]\boxed{\boxed{\underline{\textsf{\textbf{hope it helps}}}}}[/tex][tex]\boxed{\boxed{\underline{\textsf{\textbf{have a great day!}}}}}[/tex]A train traveling at a speed of 160 km / hr will take 18 hours to cover between two cities . How long will it take a car travelling at 120 km/hr to cover the same distance
Answer:
24 hours
Step-by-step explanation:
160 x 18 = 2880
2880/120 = 24
Short Answer Note: Your teacher will grade your responses to questions 4-8 to ensure you receive proper credit for your answers. 4. Find the value of k. The diagram is not to scale. (I point) I need the answer as soon as possible
2x-5y=-3
5x+2y=6
Is this a perpendicular lines ?
Perpendiculat Line is when both slopes of equation multiplying each others and equal to -1.
[tex] \large \boxed{m_1m_2 = - 1}[/tex]
For an easier way to understand, a perpendicular line has a negative reciprocal slope. For example if we are given the equation of y = 2x then the equation that is perpendicular to y = 2x would be y = (-1/2)x.
From both equations. We can either arrange in slope-intercepy form or use the slope formula which is m = -A/B when the equation is in Ax+By+C = 0 or Ax+By = C.
[tex] \large{ \begin{cases} 2x - 5y = - 3 \\ 5x + 2y = 6 \end{cases}}[/tex]
To find if these two lines are perpendicular to each others. Use the slope formula of -A/B.
[tex] \large{ \begin{cases} m_1 = - \frac{2}{ - 5} \\ m_2 = - \frac{5}{2} \end{cases}} \\ \large{ \begin{cases} m_1 = \frac{2}{ 5} \\ m_2 = - \frac{5}{2} \end{cases}}[/tex]
Now recall that it is perpendicular when one of them is negative reciprocal of one another (-5/2 is negative reciprocal of -(-2/5) = 2/5 and 2/5 is negative reciprocal of -5/2).
Or in definition of perpendicular lines, both slopes multiply and must equal to -1.
[tex] \large{( \frac{2}{5} )( - \frac{5}{2} ) = - 1} \\ \large{ - 1 = - 1}[/tex]
Thus the equation is true which makes both lines perpendicular to each others.
Answer
Both lines are perpendicular to each others.Let me know if you have any doubts!
The tennis courts are 3 blocks west and 2 blocks south of Miguel’s house. The bike path is 5 blocks east and 2 blocks south of Miguel’s house. How many blocks are the tennis courts from the bike path?
Answer:
8
Step-by-step explanation:
If Miguel's house is (0,0), then the tennis court is (-3,-2), and the bike path is (5,-2). There fore, we can just count the squares between the tennis court and the bike path, which is 8.
Hope that this helps!
From the coordinate calculation, here tennis courts are 8 blocks far from the bike path.
Given that,
The tennis courts are 3 blocks west and 2 blocks south of Miguel’s house. The bike path is 5 blocks east and 2 blocks south of Miguel’s house. How many blocks are the tennis courts from the bike path is to be detemined.
Coordinate, is represented as the values on the x-axis and the y-axis of the graph.
Here on the graph,
Assume that Miguel's house is (0,0),
then accoding to the question the tennis court is (-3,-2), and the bike path is (5,-2).
Now, difference in the position dx = 5 - (-3)
= 8
Thus, from the coordinate calculation, here tennis courts are 8 blocks far from the bike path.
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Find the median of the following data 8,6,10,12,14
Answer:
10
Step-by-step explanation:
medium is the number in the middle when all numbers are arranged in ascending order.
Answer:
10
Step-by-step explanation:
first arrange the data from ascending to descending order.
data = 6,8,10,12,14
median = N +1/2 (N means no of data)
=5 + 1/2
=6/2
=3 th term
=10
therefore median is 10
point to remember : if u are are to find the first quartile , median , or third quartile then u should arrange the data from ascending to descending order .
Question 3 of 10
In the diagram below, Ed is parallel to Xy. What is the value of x?
The value of y will be 75°. The correct option is C.
What are lines and angles?Straight lines with little depth or width are present. You will learn about a number of lines, including transversal, intersecting, and perpendicular lines.
A figure called an angle is one in which two rays originate from the same point. In this area, you could also encounter contrasting and related viewpoints.
Given that the two parallel lines are DE and XY. The angle y will be calculated as,
y = 180 - 105
y = 75°
Hence, the measure of the angle y is 75°
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Which of these quadrilateral types must have all four sides congruent?
A. Rectangle, square
B. Parallelogram, rectangle, square, rhombus
C. Square, rhombus
D. Rectangle, square, rhombus
C. Square, a rhombus is the right answer.
What does it mean that all four sides are congruent?A rhombus is a parallelogram in which all four sides are congruent. Shaped like a diamond. A square is a parallelogram with four congruent sides and four right angles. In other words, squares are rectangles and diamonds.
Exactly all the shapes on the four sides are called squares. Each type of figure here is a square type. The lengths of the congruent sides are the same. If parallel sides are drawn as lines, they never intersect.
Two triangles are congruent If the corresponding sides have the same length and the corresponding angles are the same, then the two triangles are congruent.
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If cos theta = 0.8, find 1 / sin (pi/2 - theta)
Answer:
J
Step-by-step explanation:
Using the cofunction identity
cosθ = sin([tex]\frac{\pi }{2}[/tex] - θ )
Then
[tex]\frac{1}{sin(\frac{\pi }{2}-0) }[/tex]
= [tex]\frac{1}{cos0}[/tex]
= [tex]\frac{1}{0.8}[/tex]
= 1.25 → J
The value of 1/sin([tex]\frac{\pi }{2}[/tex] - θ) is 1.25.
What are four quadrants of trigonometry?The coordinate axes divide the plane into four quadrants, labelled first, second, third and fourth as shown. Angles in the third quadrant, for example, lie between 180 degrees and 270 degrees.
Given
1/cosθ = 0.8
1/sin([tex]\frac{\pi }{2}[/tex] - θ) =?
By using quadrants in trigonometry
we know that sin([tex]\frac{\pi }{2}[/tex] - θ) = cosθ
= 1/sin([tex]\frac{\pi }{2}[/tex] - θ)
= 1/cosθ
= 1/0.8
= 1.25
1/sin([tex]\frac{\pi }{2}[/tex] - θ) = 1.25
Hence, the value of 1/sin([tex]\frac{\pi }{2}[/tex] - θ) is 1.25.
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What is the coefficient in the expression 10x^3-7?
Answer:
10 :)
Step-by-step explanation:
I hope this helped :)
3/4x + 12 =48 what is the value of ' x '
Answer:
3/4x + 12 =48
3/4x=36
x=48
Jaclyn used the slope formula to find the slope of the line through the points given in the table.
A 2-column table with 2 rows. Column 1 is labeled x with entries 0, negative 3. Column 2 is labeled y with entries 4, 0.
1. Point 1: (0, 4); Point 2: (negative 3, 0). 2. Slope = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction = StartFraction 0 minus 4 Over negative 3 minus 0 EndFraction = StartFraction negative 4 Over negative 3 EndFraction. 3. Slope = four-thirds.
In which step did Jaclyn make an error?
Answer: She didn't make an error.
Step-by-step explanation:
She just didn't I got it right.
Answer:
answer is D
Step-by-step explanation:
factorise the following (a+b)⁴-(a-b)⁴
Answer:
hope it is helpful to you
this is another answer
sorry for bad handwriting
actually its my sista handwriting
Evaluate the following expression. 4x2+6
hurrrrrryyyy aaahhhh
Someone pls help me ill give out brainliest pls don’t answer if you don’t know
Answer:
B
Step-by-step explanation:
√256=16
√289=17
Answer:
b.√256 and √289 . play basketball
Answer two questions about Equations A and B:
A. 3x – 1= 7
B. Зx=8
1) How can we get Equation B from Equation A?
Answer:
1. c) Add/ Subtract the same quantity to/from both sides
2) Yes
Step-by-step explanation:
Answer two questions about Equations A and B:
A. 3x – 1= 7
B. Зx = 8
1) To get Equation B from Equation A we need to take the following steps
A. 3x – 1 = 7
We add one to both sides
3x - 1 + 1 = 7 + 1
3x - 0 = 8
3x = 8
Option c is the correct option.
2) We are given Equations:
A. 3x – 1= 7
B. Зx = 8
3x - 1 = 7 = 3x = 8
3x = 7 + 1 = 3x = 8
3x = 8 = 3x = 8
Therefore, we can say, Yes, Equation A is equivalent to Equation B, hence they have the same solution.
Determine the domain of the following graph:
answer:
(-1,8]
explanation I just did something close to this
44
Match each ratio with its simplest form.
12:15
20:36
18:24
Pls answer ASAP I need to finish this today and I’m stuck
What is the best name for the figure with vertices at the following coordinates?
(0,0), (-1, 1), (6, 1), and (2, 0)
A.
rectangle
B.
square
C.
trapezoid
D.
rhombus
Answer: C) Trapezoid
Refer to the figure below. Note how sides BC and AD are parallel. We have exactly one pair of parallel sides, so that's why we have a trapezoid.
The figure with the vertices (0,0), (-1, 1), (6, 1), and (2, 0) is a trapezoid
What is a trapezoid?The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.
There are three types of trapezoids , and those are given below:
a) Isosceles Trapezoid
b) Scalene Trapezoid
c) Right Trapezoid
The area of the Trapezoid is given by
Area of Trapezoid = ( ( a + b ) h ) / 2
where , a = shorter base of trapezium
b = longer base of trapezium
h = height of trapezium
Given data ,
Let the coordinates of the figure be represented as ABCD
Now , the vertices of the figure is
A ( 0 , 0 ) , B ( -1 , 1 ) , C ( 6 , 1 ) and D ( 2 , 0 )
On plotting the coordinates in the graph , we get a trapezoid with
The longer base = BC
The shorter base = AD
So , the figure is a trapezoid
Hence , the vertices represents a trapezoid
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What is the measure of x?
Answer:
x = 10
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
4*x = 5*8
4x = 40
Divide by 4
4x/4 = 40/4
x = 10
What is the difference between the ordinates of the points ( -2 , 3 ) and ( 5, 8 ) ?
Answer:
the difference in the coordinate points is (7, 5)
Step-by-step explanation:
Given;
first coordinate point, (x₁, y₁) = (-2, 3)
second coordinate point, (x₂, y₂) = (5, 8)
The difference in the coordinate points is calculated as follows;
Δ(x, y) = (x₂ - x₁, y₂ - y₁)
= (5 - -2, 8 - 3)
= (7, 5)
Therefore, the difference in the coordinate points is (7, 5)
Point G is located at (6, 2) on the coordinate plane. Point G is reflected over the y -axis to create point G^ prime . What ordered pair describes the location of G?
Answer:
The ordered pair that best describes the location of G' is (-6,2).
Step-by-step explanation:
Reflecting a point over the y-axis:
When a point (x,y) is reflected over the y-axis, it's x coordinate is multiplied by -1, while the y-coordinate stays the same. Thus:
(x,y) -> (-x,y).
Point G is located at (6, 2)
When reflected over the y-axis:
G'(-6,2).
The ordered pair that best describes the location of G' is (-6,2).
please help me :((!!!!
3 / 1/3 dividend by 1 / 1/5
im confused pls help......
Answer:
the answer is B
Step-by-step explanation:
I think it's B because it was just because the reporter got then skiers from florida
Someone help please struggling on this answer thank you so much!
Answer:
-x+8=6
Step-by-step explanation:
x+5-1(2x)+(-1)(-3)=6
x+5-1-2x+3=6
ans (-x+8=6)
x+8
Which is equivalent to
1/4x
Answer:
1/4x is basically x divided by 4/multiplied by 1/4
this can be applied in examples such as:
1/4(2) = 0.5
etc.
Step-by-step explanation:
i hope this helped, if not, please leave a comment specifically requiring what exactly you are stuck with.
Answer:
1/8x+1/8x
Step-by-step explanation:
which of the two rational numbers 3/5 and -2/3 is greater
7th grade math help me pleaseeee
Answer:
option A
Step-by-step explanation:
Distance from earth to moon = 2.4 × 10⁵ miles
Distance from earth to sun = 9.3 × 10⁷
x × 2.4 × 10⁵ = 9.3 × 10⁷
[tex]x = \frac{9.3 \times 10^7}{2.4 \times 10^5}[/tex]
[tex]=\frac{9.3}{2.4} \times 10^2\\\\=3.875 \times 10^2\\\\=3.9 \times 10^2[/tex]
The distance from the earth to the sun is 3.9 × 10² times distance from the earth the moon
Hi, does anyone know the answer to this question? I’m bad at geometry and I’m struggling to answer it.
Answer:
QT = 16
Step-by-step explanation:
ΔQRS ~ ΔQRT
In similar triangles, corresponding angles are in same ratio.
[tex]\frac{QS}{QR}=\frac{QR}{QT}\\\\\frac{25}{20}=\frac{20}{QT}[/tex]
Cross multiply,
QT * 25 = 20 * 20
[tex]QT =\frac{20*20}{25}\\\\QT = 4*4\\\\QT = 16[/tex]
