Answer:
81 km
Step-by-step explanation:
Speed = distance / time
speed and time are measured in different units, thus, time has to be converted to seconds
60 second = 1 minute
90 x 60 = 5400 seconds
15 m /s = distance / 5400 seconds
distance = 81,000 metre
1000m = 1 km
81000 / 1000 = 81km
What is the solution for z?
24=z/0.6?
Answer:
[tex]z=14.4[/tex]
Step-by-step explanation:
One is given the following equation:
[tex]24=\frac{z}{0.6}[/tex]
Use inverse operations to solve this equation. Multiply both sides of the equation by (0.6) to undo the division of (0.6).
[tex]24=\frac{z}{0.6}[/tex]
[tex](0.6)(24)=z[/tex]
Simplify,
[tex](0.6)(24)=z[/tex]
[tex]z=14.4[/tex]
In right triangle ABC, AB = 3 and AC = 9. What is the measure of angle B to the nearest degree?
Answer:
90 degrees
Step-by-step explanation:
see image
make x A
y B
z C
AB=3 (given)
AC=9 (given)
measure of angel B or y, is 90
if
x= A
y= C
z= B
then the hypotenuse would be shorter than one of the legs
3<9
so B has to be the right angle (90 degrees)
Find the 13th term of the arithmetic sequence -3x – 1,42 + 4,112 + 9, ...
Answer:
The 13th term is 81x + 59.
Step-by-step explanation:
We are given the arithmetic sequence:
[tex]\displaystle -3x -1, \, 4x +4, \, 11x + 9 \dots[/tex]
And we want to find the 13th term.
Recall that for an arithmetic sequence, each subsequent term only differ by a common difference d. In other words:
[tex]\displaystyle \underbrace{-3x - 1}_{x_1} + d = \underbrace{4x + 4} _ {x_2}[/tex]
Find the common difference by subtracting the first term from the second:
[tex]d = (4x+4) - (-3x - 1)[/tex]
Distribute:
[tex]d = (4x + 4) + (3x + 1)[/tex]
Combine like terms. Hence:
[tex]d = 7x + 5[/tex]
The common difference is (7x + 5).
To find the 13th term, we can write a direct formula. The direct formula for an arithmetic sequence has the form:
[tex]\displaystyle x_n = a + d(n-1)[/tex]
Where a is the initial term and d is the common difference.
The initial term is (-3x - 1) and the common difference is (7x + 5). Hence:
[tex]\displaystyle x_n = (-3x - 1) + (7x+5)(n-1)[/tex]
To find the 13th term, let n = 13. Hence:
[tex]\displaystyle x_{13} = (-3x - 1) + (7x + 5)((13)-1)[/tex]
Simplify:
[tex]\displaystyle \begin{aligned}x_{13} &= (-3x-1) + (7x+5)(12) \\ &= (-3x - 1) +(84x + 60) \\ &= 81x + 59 \end{aligned}[/tex]
The 13th term is 81x + 59.
Monica took a survey of her classmates' hair and eye color. The results are in the table below.
Rewrite
4/10 : 1/25 as a unit rate.
A: 10:1
B: 25:4
C: 2:125
D: 100:1
Answer:
4/10 : 1/25
4/10 / 1/25 = 4/10 x 25/1 = 100/10 = 10.
10 can also be written as 10:1, so A is correct.
Hope this helps!
find the missing side of the triangle.
Expand the following
(x+2x)(2s-2t)
(m-n)²
(k+9)²
(4a-3b)(c+6d)
please check the attachment for solutions
What's 672 divided by 32
Answer:
the answer is 21
Step-by-step explanation:
how many square metres of floor are there in a room of 6 metres
ig something like that
Answer:
36² metres
Step-by-step explanation:
I'm assuming you mean 6 metre wide/long floor. Area is L*W so 6*6
Please help me solve this short problem guys
Answer:
Step-by-step explanation:
Given equation of the quadratic function is,
y = x² + 5x - 7
Convert this equation into vertex form,
y = x² + 2(2.5x) - 7
= x² + 2(2.5x) + (2.5)² - (2.5)² - 7
= (x + 2.5)²- 6.25 - 7
= (x + 2.5)² - 13.25
Therefore, vertex of the function is → (-2.5, -13.25)
For the solutions,
y = 0
(x + 2.5)² - 13.25 = 0
x = (±√13.25) - 2.5
x = (±3.64) - 2.5
x = 1.14, -6.14
Solutions → (-6.14, 0) and (1.14, 0)
The velocity of a particle moving along a straight line is given by v(t)=6t2+4t−5 cm/sec at time t seconds with initial position s(0)=3 cm. What is the position of the particle at t=2 seconds, in cm?
Answer:
s(2) = 17 cm
Step-by-step explanation:
We are told that the velocity function is;
v(t) = 6t² + 4t − 5 cm/sec
Integral of velocity gives distance.
Thus;
s(t) = ∫v(t) = ∫6t² + 4t − 5
s(t) = 2t³ + 2t² - 5t + c
We are told that s(0)=3 cm
Thus;
s(0) = 2(0)³ + 2(0)² - 5(0) + c = 3
Thus; c = 3
Thus;
s(t) = 2t³ + 2t² - 5t + 3
At t = 2 secs
s(2) = 2(2)³ + 2(2)² - 5(2) + 3
s(2) = 17 cm
x3 + (y +z) factorize
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
Answer: Choice B
Open circle at 3. Shading to the right
========================================================
Work Shown:
3(8 - 4x) < 6(x - 5)
24 - 12x < 6x - 30
24 + 30 < 6x + 12x
54 < 18x
18x > 54
x > 54/18
x > 3
We use an open circle at 3 to indicate we don't include this endpoint as part of the solution. The solution set is everything larger than 3, so we shade to the right of this open circle.
TRIGONOMETRY
Could someone please help me with 5.2 please...it would really help alot:)
sin(x+y) - sin(x-y) - 1 = cos(2x)
sin(90) - sin(x-y) - 1 = cos(2x)
1 - sin(x-(90-x)) - 1 = cos(2x)
-sin(2x-90) = cos(2x)
-1*(sin(2x)cos(90) - cos(2x)sin(90)) = cos(2x)
-1*(sin(2x)*0 - cos(2x)*1) = cos(2x)
-1*(0 - cos(2x)) = cos(2x)
-1*(-cos(2x)) = cos(2x)
cos(2x) = cos(2x)
This confirms the identity is true.
Notice that throughout this proof, I only changed the left hand side.
On the 5th line, I used the identity sin(A-B) = sin(A)cos(B)-cos(A)sin(B).
The function (1) describes the height, in feet, of an object at time, in seconds, when it is launched upward from the ground at an initial speed of 112 feet per second.
a. Find the domain.
b. What does the domain mean in this context?
Answer:
see below
Step-by-step explanation:
The domain is the values that the input takes
The values go from 0 to 7
0≤x≤7
This is the time from the initial launch until the object hits the ground
Nghiệm của bất phương trình | 2x - 3| - 1 <0
Answer:
x = 1 và 2 x= 1 and 2
Step-by-step explanation:
Đầu tiên trừ đi 1 để được 2x-3 nhỏ hơn -1 sau đó bạn lập phương trình bằng 2x-3 = -1 và 2x-3 = 1 để nhận được kết quả cuối cùng là 1 và 2 do đó x = 1 và 2
First subtract 1 to get 2x-3 is less then -1 then you let the equation equal 2x-3=-1 and 2x-3=1 to get a final answer of 1 and 2 therefore x=1 and 2
Find the equation of a line perpendicular to 8x - 2y = 4 and passes through the point (4, 3).
y = -2x-3
Lines that are perpendicular have slopes that are negative reciprocals of each other. Meaning, if a line has slope , then a line perpendicular to this has slope . That means the slope of our perpendicular line is
The equation of the line that is perpendicular to 8x - 2y = 4 and passes through the point (4, 3) is y = (-1/4)x + 4.
To find the equation of a line that is perpendicular to the line 8x - 2y = 4 and passes through the point (4, 3), we can use the fact that the slopes of perpendicular lines are negative reciprocals of each other.
First, let's rewrite the given equation in slope-intercept form (y = mx + b), where m represents the slope:
8x - 2y = 4
-2y = -8x + 4
Divide both sides by -2:
y = 4x - 2
The slope of the given line is 4.
The slope of a line perpendicular to this line would be the negative reciprocal of 4, which is -1/4.
Now, we have the slope (-1/4) and a point (4, 3). We can use the point-slope form of a linear equation:
y - y₁ = m(x - x₁)
Substituting the values, we have:
y - 3 = (-1/4)(x - 4)
Expanding and simplifying, we get:
y - 3 = (-1/4)x + 1
Adding 3 to both sides, we have:
y = (-1/4)x + 4
To learn more about equation click on,
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Rewrite the expression in the form z^n.
z^3/4 x z^2
Step-by-step explanation:
here's the answer to your question
What is the median for the set of data? 6, 7, 10, 12, 12, 13
Answer choices:
6
7
10
12
12
13
Answer:
11
Step-by-step explanation:
If the set of numbers are not in least to greatest first set them up into their positions. But since this set is already in least to greatest we can go to the next step.
6, 7, 10, 12, 12, 13
Cross off all numbers until you get to the middle:
6, 7, 10, 12, 12, 13
Find the mean of the numbers in the middle:
10 + 12 = 22
22 / 2 = 11
The answer is 11
Hope this helped.
Answer:
11
Step-by-step explanation:
10+12=22
22÷2=11
median is equal to the middle number after being arranged in ascending order.
In an experiment, a student is to flip a quarter 10 times and record the number of times heads appears. A group of students performs the experiment 21 times, with these results.
6 4 5 6 5 6 4 6 2 4 3 4 5 7 5 8 7 5 3 5 5
Construct a dotplot with these data and then identify the dotplot you created.
Answer:
The average, mode, and median of the results are 5, meaning that half of the time the quarter will land on heads.
Step-by-step explanation:
The required dot plot shows the result of the experiment performed by flipping a quarter 21 times.
In an experiment, a student is to flip a quarter 10 times and record the number of times heads appears. A group of students performs the experiment 21 times, with these results. 6 4 5 6 5 6 4 6 2 4 3 4 5 7 5 8 7 5 3 5 5.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
What is Statistic?Statistics is the study of mathematics that deals with relations between comprehensive data.
Here,
The dot plot has been made, for the number of outcomes and their frequencies. The dot plot gives the info about the mean mode and median.
Thus, the required a dot plot showing the result of the experiment performed by flipping a quarter 21 times.
Learn more about arithmetic here:
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Find the center and foci of the ellipse: 9x2 + 16y² + 126x + 96y + 441 = 0
Center : ( –7 , –3 )Focus 1: (–7 + √7 , –3 )Focus 2: ( –7 –√7 , –3 )
[tex] \frac{(x + 7)^{2} }{16} + \frac{(y + 3) ^{2} }{9} = 1 \\ \frac{(x - h)^{2} }{ {a}^{2} } + \frac{(y - k)^{2} }{ {b}^{2} } = 1[/tex]
a= 4 , b= 3 , k = – 3 , h = –7 The center: ( h , k ) —> ( –7 , –3 )[tex]c = \sqrt{ {a}^{2} - {b}^{2} } = \sqrt{ {4}^{2} - {3}^{2} } \\ = \sqrt{16 - 9} = \sqrt{7} [/tex]C = √7Focus 1: ( h + c , k ) —> ( –7 + √ 7 , –3 )Focus 2: ( h – c , k ) —> ( –7 –√7 , –3 )
I hope I helped you^_^
x = 3
x = 5
x = 0
x = 2
Answer:
x=2 is incorrect
Step-by-step explanation:
Y(2)=(3/4)*x^2=(3/4)*4=3
Find the y-intercept of the following equation. Simplify your answer.
y = -10x -3/7
Answer: (0, -3/7)
Step-by-step explanation:
The Y-intercept would be the value of y when x is at 0, which is when the Y axis is intercepted. -3/7 is the starting position of the function when the the X = 0.
12. PLEASE HELP ME
Which of the following are the coordinates of the vertex of y= x2 - 10x + 2?
A. (–10, 2)
B. (2, –10)
C. (–5, 23)
D. (5, –23)
Answer:
I think b no. is the correct answer
Answer:
D. (5, –23)
Step-by-step explanation:
The vertex is in essence the turning point of the parabola y = x² − 10x + 2
the x coordinate of the turning point =
=
= 5
when x = 5, y = (5)² - 10(5) + 2
= -23
Thus coordinate or vertex is ( 5, -23)
5 right 23 down
What is the range of the given data set? OA) 30 OB) 32 OC) 37 OD) 40
Answer:
Range = maximum number - minimum number
maximum number = 99minimum number = 62Range = 99 - 62 = 37
Answer:
37
Step-by-step explanation:
The range is the difference between the highest number and the smallest number.
Looking at the stem and leaf plot we can identify the largest and smallest number
Largest number: 99
Smallest number: 62
If range = largest number - smallest number then range = 99 - 62 = 37
Please answer this, I don't have much time left!
Answer
1 + 5 ÷ 5
This would equal 2, using BIDMAS.
Need help on this activity!!
In this activity, you will rearrange and solve a rational equation and find and use the inverse of a rational equation.
As we’ve seen, for a circuit with two resistors arranged in parallel, we can calculate the total resistance in the circuit, , in ohms, with this equation.
Question 1
Part A
Question
Rewrite the equation to represent the resistance of resistor 2, , in terms of and .
Answer:
My best guess rn is the first option
Step-by-step explanation:
the last dude had it close but it was basically flipped as you can tell.
The answer is (C) [tex]R_2=\frac{R_TR_1}{(R_1-R_T)}[/tex]
We need to make [tex]R_2[/tex] the subject of the formula [tex]R_T=\frac{R_1R_2}{R_1+R_2}[/tex]
First remove the denominator by multiplying both sides by the binomial [tex](R_1+R_2)[/tex]
[tex]R_T\times (R_1+R_2)=\frac{R_1R_2}{R_1+R_2}\times(R_1+R_2)\\\\R_TR_1+R_TR_2=R_1R_2[/tex]
Arrange all terms containing [tex]R_2[/tex] on one side
[tex]R_1R_2-R_TR_2=R_TR_1[/tex]
Factor out [tex]R_2[/tex] from the LHS
[tex]R_2(R_1-R_T)=R_TR_1[/tex]
Finally, divide both sides by the binomial [tex](R_1-R_T)[/tex] to leave [tex]R_2[/tex]
[tex]R_2(R_1-R_T)\times\frac{1}{(R_1-R_T)}=R_TR_1\times\frac{1}{(R_1-R_T)}\\\\R_2=\frac{R_TR_1}{(R_1-R_T)}[/tex]
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Can I please get help with these 2 questions about polygons
Answer:
a)139°
Step-by-step explanation:
two co interior angles make one opposite exterior angle
49+90=139°
Calcula el valor de “x” en:
5(3x – 4) – 17 = 5(x + 8) – 17
Answer: x = 6
Step-by-step explanation:
Sume 17 a ambos lados
5(3x-4)-17 + 17=5(x+8)-17 +17
Simplifica
5(3x-4)=5(x+8)
Expandir 5(3x -4) : 15x - 20
Expandir 5(x+8) : 5x +40
15x - 20 = 5x +40
Sume 20 a ambos lados
15x - 20 + 20 = 5x +40 +20
Simplifica
15x = 5x +60
Restar 5 de ambos lados
15x - 5x = 5x + 60 - 5x
Simplifica
10x = 60
Divide ambos lados entre 10
10x/10 = 60/10
Simplifica
x = 6
Find the nth term of each of the sequences.
(a) 16, 19, 22, 25, 28, ...
(b) 1,3,9,27,81,...
Answer:
a) 16, 19, 22, 25, 28, 31, 34, 37, 40
b) 1, 3, 9, 27, 81, 243, 729, 2187
Explanation:a) Add 3 on every number.
b) Multiply every number by 3.
