the graph shows the speed of a vehicle during the final 50 seconds of a journey at the start of the 50 seconds the speed is k metres per second
Answers
Answer:
a) 27 m/s
b) 30 m/s
c) i) 3
ii) Deceleration
Step-by-step explanation:
The question is not complete, the correct question is given as:
The graph shows information about the speed of a vehicle during the final 50 seconds of a journey. At the start of the 50 seconds the speed is k metres per second. The distance travelled during the 50 seconds is 1.35 kilometres.
(a) Work out the average speed of the vehicle during the 50 seconds
(b) Work out the value of k.
(c) (i) Calculate the gradient of the graph in the final 10 seconds of the journey
(ii) Describe what this gradient represents
Answer:
The graph is attached. The total time = 50 seconds, total distance = 1.35 km = 1350 m
a) The average speed is the ratio of the total distance traveled to the total time taken to cover this distance. The average speed is given by the formula:
[tex]Average \ speed=\frac{total\ distance}{total\ time}\\ Substituting: \\ Average \ speed=\frac{1350\ m}{50\ s} = 27\ m/s[/tex]
b) From the graph, the total distance covered is the area of the graph. The graph is made up of a rectangle and triangle, the area of the graph is equal to the sum of area of rectangle and area of triangle.
[tex]Total \ distance=Total\ area=Area\ of \ rectangle+Area\ of \ triangle\\Total \ distance=(length *breadth)+\frac{1}{2}base*height\\1350 \ m=(40*k)+0.5*10*k\\1350=40k+5k\\45k=1350\\k=1350/45\\k=30\ m/s[/tex]c) i) The gradient in the last 10 seconds is the ratio of change in speed to change in time
[tex]Gradient=\frac{change\ in\ speed }{change\ in\ time}=\frac{0-k}{50-40} \\ bt \ k=30\\Gradient=\frac{0-30}{50-40}= \frac{-30}{10} =-3[/tex]
ii) Since the gradient is negative it means it is deceleration. That is in the in the last 10 seconds the vehicle decelerates at a rate of 3 m/s²
Answer:
Step-by-step explanation:
a)34 m/s
b) 40k=34
k=34/40
k=0.85 m/s
Related Questions
Question
At a grocery store, bulk almonds sell for $3.80 per pound. The cost, y, in dollars, of x pounds of almonds is shown in the
table.
x (pounds)
y ($)
1.90
0.5
1
3.80
Hola
1.5
5.70
2
7.60
Select the correct answer from each drop-down menu.
The relation described in the table is
The domain of the relation is
The range of the relation is
Submit
INTL
Answers
Answer:
The domain is {0.5, 1, 1.5, 2}
The range is {1.9, 3.8, 5.7, 7.6}
Step-by-step explanation:
The cost, y is in dollars, and x in pounds of almonds is shown in the table.
x (pounds) y ($)
0.5 1.9
1 3.80
1.5 5.70
2 7.60
The grocery store sells almond at $3.80 per pound, the relation between y and x is given by the function:
y = 3.8x
The x values are the independent variables and they serve as the input of the function while the y values are the dependent variables (dependent on x) and the serve as the output of the function.
The domain consist of input values which is the x values. The domain is {0.5, 1, 1.5, 2}
The range consists of all output values i.e the y values. The range is {1.9, 3.8, 5.7, 7.6}
Any number of pounds of almonds can be purchased, including partial amounts, so the relation described in the table is continuous.
Because x can be any positive number of pounds, the domain of the relation is x ≥ 0, or x-values greater than or equal to 0.
Because y can be any positive dollar amount, the range of the relation is y ≥ 0, or y-values greater than or equal to 0.
In ΔIJK, the measure of ∠K=90°, KI = 5.3 feet, and JK = 2.1 feet. Find the measure of ∠I to the nearest tenth of a degree. I
Answers
Answer:
[tex]\angle I = 21.6 ^\circ[/tex] is the correct answer.
Step-by-step explanation:
Please refer to the attached figure.
[tex]\triangle IJK[/tex] is shown with the following measurements:
[tex]\angle K = 90^\circ[/tex]
Side KI = 5.3 ft
Side JK = 2.1 ft
To find : [tex]\angle I[/tex] = ?
Using trigonometric identity for tangent of an angle:
[tex]tan\theta = \dfrac{\text{Perpendicular}}{\text{Base}}[/tex]
Here [tex]\theta = \angle I[/tex]
Perpendicular is side JK.
Base is side KI.
Putting the values in above formula:
[tex]tan\theta = \dfrac{\text{JK}}{\text{KI}}\\\Rightarrow tan\theta = \dfrac{2.1}{5.3}\\\Rightarrow tan\theta = 0.3962\\\Rightarrow \theta = 21.6^\circ[/tex]
Hence, [tex]\angle I = 21.6 ^\circ[/tex] is the correct answer.
A circle , with centre O , radius 6cm has chords AB and CD which intersects at x . Find OX , if AX = 3cm and XB = 2cm
Answers
Answer:
OX = 5.4772 cm
Step-by-step explanation:
Please check image attached for the drawing of the circle with the chords and points.
From the theorem of intersecting chords, we have:
AE * EB = EF * EG
With AE = AX - EX, EB = BX + EX, EF = 6 - EO and EG = 6 + EO, we have:
(AX - EX) * (BX + EX) = (6 - EO) * (6 + EO)
(3 - EX) * (2 + EX) = 36 - EO^2
6 + EX - EX^2 = 36 - EO^2
EO^2 - EX^2 + EX = 30 (eq1)
From the triangle AEO, we have:
AE^2 + EO^2 = OA^2
(AX - EX)^2 + EO^2 = 6^2
(3 - EX)^2 + EO^2 = 36
9 - 6*EX + EX^2 + EO^2 = 36
EX^2 - 6*EX + EO^2 = 27 (eq2)
If we do (eq1) - (eq2), we have:
-2*EX^2 + 7*EX = 3
2*EX^2 - 7*EX + 3 = 0
Solving this quadratic equation, we have EX = 3 cm or EX = 0.5 cm
EX cannot be 3 cm, because AE would be 0 cm, so EX = 0.5 cm
Calculating EO, we have:
EO^2 - 0.5^2 + 0.5 = 30
EO^2 = 29.75
EO = 5.4544 cm
Now, using Pythagoras in the triangle EOX, we have:
EO^2 + EX^2 = OX^2
29.75 + 0.25 = OX^2
OX^2 = 30
OX = 5.4772 cm
Are these functions??!!
I need this for today if you do all of it i’ll fr cashapp you money for it wassupp?
Answers
Answer:
Going from left to right:
1.) Yes
2.) No
3.) Yes
4.) No
5.) No
6.) Yes
7.) No
8.) No
9.) Yes
10.) No
11.) Yes
12.) Yes
13.) No
14.) Yes
15.) Yes
16.) No
Step-by-step explanation:
Functions cannot have any repeating x-coordinates.
1.) Yes
2.) No
3.) Yes
4.) No
5.) No
6.) Yes
7.) No
8.) No
9.) Yes
10.) No
11.) Yes
12.) Yes
13.) No
14.) Yes
15.) Yes
16.) No
CD and EF are parallel lines. AB is a straight line
Answers
Answer:
x =42
q = 135°
p + q + r = 225°
Step-by-step explanation:
a)
Since, AB and BC are perpendicular lines.
[tex] m\angle ABC = 90\degree \\
\therefore 24\degree + x\degree + 24\degree = 90\degree \\
\therefore x\degree + 48\degree = 90\degree \\
\therefore x\degree = 90\degree - 48\degree \\
\huge \red {\boxed {\therefore x = 42}} \\[/tex]
b) (i)
Since, CD and EF are parallel lines and AB is a straight line.
[tex] \therefore q = 135\degree... (vertical \: \angle 's) \\\\
p + 135\degree = 180°..(straight\: line \: \angle' s) \\
p = 180\degree - 135\degree \\
\huge \purple {\boxed {p = 45\degree}} \\
\because r = p ... (vertical \: \angle 's) \\
\huge \purple {\boxed {r = 45\degree}} \\
p + q + r = 45\degree + 135\degree + 45\degree \\
\huge \purple {\boxed {p + q + r = 225\degree }}\\[/tex]
Please answer correctly !!!!!!!!!! Will
Mark brainliest !!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
The discriminant is what's under the square root sign in the quadratic equation. The equation for the discriminant is [tex]b^{2}-4ac[/tex], where b is the coefficient of x, a is the coefficient of [tex]x^{2}[/tex], and c is the number with no variable attatched to it. If we plug in the numbers ([tex]17^{2} -4*4*3[/tex]) it gives you 241, which is the discriminant. Since 241 is more than zero, it has 2 zeros. If the discriminant was 0, there'd be 1 zero, and less then zero there would be zero zeros.
I will mark it as brainliest whoever has the clearest explanation
Answers
Answer:
44 cm
Please see the attached picture for full solution
Hope it helps....
Good luck on your assignment
Which of the following is a quadratic function?
1. f(x) = 0x^2 + 3x - 6
2. f(x) = 3 - 4x^2
3. f(x) = 2^x
4. f(x) = 2x + 5
Answers
the function of quadratic is number4
At the beginning of football season, Coach Carnes takes inventory of the team equipment to see what he needs. He counts 24 footballs, but he needs to start off the season with at least 75. The footballs that he uses are sold in packages of 4. How many packages could the coach buy?
Answers
Answer:
13
Step-by-step explanation:
To solve this, lets first find the number of footballs he still needs:
75-24 = 51
Now to find the number of packages, divide by 4, since there are 4 balls per package:
51/4 = 12 Remainder 3
Since there is a remainder, and the Coach MUST have at least 75, then we need to add a package to include the remainder:
12 + 1 = 13 Packages
someone please help me, I’m struggling :(
Answers
Answer:
constant because it isn't going up or down, just moving straight
Step-by-step explanation:
Answer:
constant
Step-by-step explanation:
Since this is a horizontal line the slope is zero
This means the graph is constant
Please help someone……………………
Answers
Answer:
I think it's number one
Step-by-step explanation:
Can someone answer this question please please help me I really need it if it’s correct I will mark you brainliest .
Answers
Answer:
JKM AND GHK
Step-by-step explanation:
THE SUM OF THE TWO ANGLES IS 180°
_______________________________
Hey!!
The supplementary angles are <IHK and < IHF
Supplementary angles are those angles which is exactly 180 degree.
Hope it helps..
Larry rolls 2 fair dice and adds the results from each. Work out the probability of getting a total that is a multiple of 3.
Answers
Answer:
12/36 = 1/3
Step-by-step explanation:
draw a possibility diagram or table where you get the possible outcomes. 1 to 6 along the bottom and 1 to 6 across.
you will results such as 11 12 13 14 15 16
21 22 23 24 25 26
and so on.
Then, you total up each of them and will get
2 3 4 5 6 7 from the first row
3 4 5 6 7 8 from 2nd row
and so on.
from the final results, count how many are multiples of 3.
we should get 12 and over total possible outcomes which is 36, since it's a 6 by 6 table.
What is the length of EF?
Answers
Answer:
5
Step-by-step explanation:
the measure DF is 7
DE = 2
to get EF, you have to subtract 2 from 7
7 - 2 = 5
XYZ is an isosceles triangle inscribed I a circle, center O. XY=XZ= 20 and YZ=18. Calculate to 3.s.f.
a) the altitude of ∆XYZ
b) the diameter of the circle
Answers
Answer: 17.9
Step-by-step explanation:
Using Heron's formula:
Area of a triangle is given by:
√s(s-a)(s-b)(s-c)
Where a, b and c ara sides of the triangle and
S = (a+b+c) / 2
In the question above sides are :
XY=XZ= 20 and YZ=18
S = (20 + 20 + 18) / 2 = 58/2 = 29
Area = √29(29-20)(29-20)(29-18)
Area = √29(9)(9)(11)
Area = √25839
Area = 160.74513
Altitude = height(h)
Area = 0.5 × base × height
Base = yz = 18
160.74513 = 0.5 × 18 × h
160.74513 = 9 × h
h = 160.74513 / 9
h = 17.9 (3 s.f)
Trenton works for a company that is promoting its line of LED lightbulbs. He is selling boxes of the lightbulbs at a local store. A box of 60-watt bulbs costs $7.00, and a box of 100-watt bulbs costs $12.00. During the promotion, Trenton wants to sell more than 100 boxes total and make at least $1,000. The graph and the system of inequalities represent this situation, where x represents the number of boxes of 60-watt bulbs sold and y represents the number of boxes of 100-watt bulbs sold. 7x + 12y ≥ 1,000 x + y > 100 Which solution is valid within the context of the situation?
A. (90,25)
B. (40,64.50)
C. (30,80)
D. (200,-10)
Answers
Answer:
C) 30,80 PLATO
Step-by-step explanation:
This is the only answer that goes into the solution set on the graph, and the rest can be ruled out because they have either a half (you can't have half a bulb lol) or negative (how you gone have negative bulbs smh) and if you didn't rule out all others with these two they also have to LOOk like they are in the solution set. Thats how i solve ALL of them and get them correct.
Hopefully i helped and corrected the wrong answer up there!
This question is based on system of linear equation.Therefore, the correct option is ( C ), (30,80) solution is valid within the context of the situation.
Given:
7x + 12y ≥ 1,000
x + y > 100
We need to determined the solution which is valid within the context of the situation.
According to question,
A. (90,25)
Put this value in given both equation.
We get,
7(90) + 12(25) ≥ 1,000630 + 300 [tex]\ngeqslant[/tex] 1000
⇒ 930 [tex]\ngeqslant[/tex] 1,000
x + y > 10090 + 25 > 100
⇒ 115 > 100
B. (40,64.50)
7(40) + 12(64.50) ≥ 1,000280 + 774 [tex]\geq[/tex] 1000
⇒ 1054 [tex]\geq[/tex] 1000
x + y > 10040 + 64.50 >100
⇒ 104.50 > 100
C. (30,80)
7(30) + 12(80) ≥ 1,000210 + 960 [tex]\geq[/tex] 1000
⇒ 1170 [tex]\geq[/tex] 1000
x + y > 10030 + 80 = 110 >100
D. (200,-10)
7(200) + 12(-10) ≥ 1,0001400 -120 [tex]\geq[/tex] 1000
⇒ 1280 [tex]\geq[/tex]1000
x + y > 100200 - 10 >100
⇒ 190>100
Therefore, the correct option is (C), (30,80) solution is valid within the context of the situation.because this is the only answer that goes into the solution set on the graph, and the rest can be ruled out because they have either a half (you can't have half a bulb lol) or negative (how you gone have negative bulbs smh).
For more details, prefer this link:
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The Griffins bought a new car for $23,865. The total price was $26,959 which included $1,589 for tax and license, $742 for shipping, and payment for accessories. How much were the accessories?
Answers
PLEASE HELP! Suppose the hypotenuse of a right triangle is 24 cm and one of the legs is 11 cm. Use the Pythagorean Theorem to find the measure of the triangle’s other leg. Round the measure to the nearest tenth if needed.
Answers
Answer:
The other leg is about 21.3 cm
Step-by-step explanation:
Pythagorean Theorem: a²+b²=c²
11²+b²=24²
121+b²=576
Subtract 121 from both sides
b²=455
b=[tex]\sqrt{455}[/tex]
b≈21.3
Answer:
21.3 cm
Step-by-step explanation:
We need to apply the Pythagorean Theorem.
The Pythagorean Theorem is an equation that can only be applied to right triangles. It states that for a right triangle with legs (two shorter sides) a and b and hypotenuse (longest side) c:
a² + b² = c²
Here, we know the hypotenuse is 24 cm and that one of the legs is 11 cm. We can hence say that c = 24 and a = 11 (or b = 11, but it doesn't really matter). Plug these values into the equation to find the other leg length:
a² + b² = c²
11² + b² = 24²
121 + b² = 576
b² = 576 - 121 = 455
b = √(455) ≈ 21.3 cm
Thus, the answer is 21.3 cm.
~ an aesthetics lover
Which of the following are linear measurements?
A) Length and width
B) Depth and height
C) Diameters, clearance, end play, and thickness
D) All of the above
Answers
Answer:
a. length and width
Step-by-step explanation:
option a is correct answer
What is the quotient?
StartFraction (negative 3) Superscript 0 Over (negative 3) squared EndFraction
Answers
Answer:
1/9
Step-by-step explanation:
Where my coins at bruh and yo number jhit
The value of the expression {(-3)⁰}/{(-3)²} is 1/9.
What is an exponent?Exponentiation is one of the mathematics operations.
Let mᵃ, where m and a are the real numbers.
And m is multiplied by a times to itself.
So, a is the exponent of m.
Given:
Start Fraction (negative 3) Superscript 0 Over (negative 3) squared End Fraction
In numerator form:
{(-3)⁰}/{(-3)²}
= 1/9
Therefore, 1/9 is the value.
To learn more about the exponents;
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.............................
Answers
Answer:
[tex]\frac{18p-5}{30}[/tex]
Step-by-step explanation:
Answer:
18p-5 over 30.
Found in the LCM method
In your own words what is a polygon
Answers
Answer:
A polygon is a plane figure with at least three straight sides and angles, and typically five or more.
Step-by-step explanation:
Please answer correctly !!!!!! Will mark brainliest answer !!!!!!!!!!
Answers
What is the solution to log (10x-1)= logs(9x+ 7)?
6
O X=
6
19
O X=
19
X= 7
X= 8
Answers
Answer:
[tex]x=8[/tex]
Step-by-step explanation:
[tex]\log _{10}\left(10x-1\right)=\log _{10}\left(9x+7\right)\\\mathrm{Apply\:log\:rule:\:\:If}\:\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\:\mathrm{then}\:f\left(x\right)=g\left(x\right)\\10x-1=9x+7\\\mathrm{Add\:}1\mathrm{\:to\:both\:sides}\\10x-1+1=9x+7+1\\\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}\\10x-9x=9x+8-9x\\\mathrm{Simplify}\\x=8\\[/tex]
The solution of the equation ㏒₅(10x - 1) = ㏒₅(9x + 7) is x = 8.
What are Logarithms?A logarithm is simply the opposite function of the exponentiation.
It is the exponent to which a number or value is raised to get some other number.
That is, if c = aˣ, then we can write it as x =logₐ c.
Given that,
㏒₅(10x - 1) = ㏒₅(9x + 7)
Let the value of both be n.
So, ㏒₅(10x - 1) = n and ㏒₅(9x + 7) = n
By the definition of logarithms,
10x - 1 = 5ⁿ and 9x + 7 = 5ⁿ
So,
10x - 1 = 9x + 7
10x - 9x = 7 + 1
x = 8
Hence the value of x is 8.
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What are the ordered pairs of the
solutions for this system of equations?
f(x) = x2 – 2x + 3; f(x) = -2x + 7
Answers
Hey there! :)
Answer:
(2, 3) and (-2, 11).
Step-by-step explanation:
To solve this system of equations, we can set both equations equal to each other:
x² -2x + 3 = -2x + 7
Combine like terms:
x² -4 = 0
Factor using difference of squares:
(x - 2)(x + 2) = 0
Therefore, x = 2 and -2. Plug both of these into an equation to solve for the 'y' value:
f(x) = -2(2) + 7
f(x) = -4 + 7
f(x) = 3
------------------
f(x) = -2(-2) + 7
f(x) = 4 + 7
f(x) = 11
Therefore, the two ordered pairs are (2, 3) and (-2, 11).
what’s the perimeter
Answers
Answer:
the answer is 10
Step-by-step explanation:
the other shape is half of all the degreed of the first one
Answer: 10
Step-by-step explanation:
AB: 3.0/2 = 1.5 = EF
BC: 5.0/2 = 2.5 = FG
CD: 4.0/2 = 2.0 = GH
DA: 8.0/2 = 4.0 = EH
1.5+2.5+2.0+4.0 = 10
If you solve this, you are a critical thinker:
Mr. Smith had 4 daughters. Each daughter had 4 brothers. How many kids does Mr. Smith have?
Answers
Let's organize what the problem gives us:
Mr. Smith had 4 daughters.Each daughter had 4 brothers.We want to find how many kids Mr. Smith has.Step 2: WorkWe can already tell that the initial amount of kids Mr. Smith has before we factor in the brother count is equal to 4, for the 4 daughters that were stated as a given in the problem.
Now, the tricky part comes in the form of "each daughter had 4 brothers." Remember that within a family, everyone has the same siblings. It doesn't matter which family member's perspective you are looking from, but your siblings will always stay the same. We can show this with an example:
Suppose I had a family of 4 kids total. I had 2 daughters and 2 sons. Their names were Rose, Sakura, David, and Andrew. Rose would then have 3 siblings: Sakura, David, and Andrew. Sakura would also have 3 siblings: Rose, David, and Andrew, so on and so forth.
Applying this example and knowledge to our current problem, if Mr. Smith's daughters each had 4 brothers, then the total number of kids Mr. Smith has is 8 total kids (4 daughters + 4 sons) since each daughter's brother would be the same sibling.
This would be called double-counting if you counted that each daughter would have 4 different siblings, resulting in a false answer of 16 kids (4 daughters multiplied by 4 brothers for each daughter).
Answer∴ Mr. Smith has 8 kids.
___
Topic: Math
Unit: ?
Evaluate:
12.16 x .13 =
Answers
Answer:
1.5808
Step-by-step explanation:
rounded
hundreds
1.58
tens
1.6
first
2
Now look at this information
[tex]2y + 3 \leqslant 11[/tex]
What is the largest value that y could be?
Answers
Answer:
4
Step-by-step explanation:
Given
2y + 3 ≤ 11 ( subtract 3 from both sides )
2y ≤ 8 ( divide both sides by 2 )
y ≤ 4
Since y has to be less than or equal to 4
Then the largest value y could be is 4
Find the volume of the sphere. Use 3.14 for Pi. Round your answer to the nearest thousandth. A sphere with diameter 10 inches. a. 4186.667 cu. in. b. 523.333 cu. in. c. 104.667 cu. in. d. 294.375 cu. in. Please select the best answer from the choices
Answers
Volume of a Sphere Formula:
[tex]\displaystyle V = \frac{4}{3} \pi r^3[/tex]
Diameter/Radius Relationship:
[tex]\displaystyle r = \frac{d}{2}[/tex]
ApplicationStep 1: Define
Let us clearly sort out what information this specific problem gives us:
We are given that the shape is a sphere.We are also given that the diameter of the sphere is equal to 10 inches.Finally, we are asked to find the volume of the sphere.We can consolidate this into mathematical symbols:
[tex]\displaystyle d = 10 \ \text{in}[/tex][tex]\displaystyle V_{\text{Sphere}} = \ ?[/tex]Step 2: WorkGiven what we know, we now need to find the volume of the sphere. With knowledge implied, found under the General Formulas and Concepts section above, we can first solve for the radius [tex]\displaystyle r[/tex]:
[tex]\displaystyle\begin{aligned}r & = \frac{d}{2} \\& = \frac{10 \ \text{in}}{2} \\& = \boxed{5 \ \text{in}} \\\end{aligned}[/tex]
∴ the radius of the sphere is equal to 5 inches.
Now that we have our radius, we can substitute this value into our volume of a sphere formula and evaluate:
[tex]\displaystyle\begin{aligned}V & = \frac{4}{3} \pi r^3 \\& = \frac{4}{3} \pi (5 \ \text{in})^3 \\& = \frac{4}{3} \pi (125 \ \text{in}^3) \\& = \boxed{ \frac{500}{3} \pi \ \text{in}^3 } \\\end{aligned}[/tex]
∴ the volume of the sphere is equal to [tex]\boxed{ \frac{500}{3} \pi \ \text{in}^3 }[/tex].
To estimate our answer, we can simply substitute the value of [tex]\displaystyle \pi[/tex] for 3.14, as defined by the problem, and evaluate once more:
[tex]\displaystyle\begin{aligned}V & = \frac{4}{3} \pi r^3 \\& = \frac{4}{3} \pi (5 \ \text{in})^3 \\& = \frac{4}{3} \pi (125 \ \text{in}^3) \\& = \frac{500}{3} \pi \ \text{in}^3 \\& = \frac{500}{3} (3.14) \ \text{in}^3 \\& \approx \boxed{ 523.333 \ \text{in}^3 }\end{aligned}[/tex]
∴ the volume of the sphere is approximately equal to [tex]\displaystyle \boxed{ 523.333 \ \text{in}^3 }[/tex].
Answer∴ the best answer choice that corresponds to our gathered result is answer choice b. 523.333 cu. in.
___
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Learn more about geometry: https://brainly.com/question/16893579
___
Topic: Geometry
Unit: Volume