[tex]\text{Given that,}\\\\A(x_1,y_1) = (-3,6)~~ \text{and}~ B(x_2,y_2) =(10,-8)\\\\AB = \sqrt{(x_2-x_1)^2 + (y_2 -y_1)^2}\\\\~~~~~=\sqrt{(10+3)^2 + (-8-6)^2}\\\\~~~~~=\sqrt{13^2 + 14^2}\\\\~~~~~=\sqrt{365}\\\\~~~~~=19.105~ units[/tex]
Nadia walks at an average speed of (x + 2) km/h for (x – 3) hours and cycles at an average speed of (3x + 5) km/h for x hours. She covers a total distance of 74 km. (i) Form an equation in x and show that it reduces to 4x2 + 4x - 80 = 0. (ii) Solve the equation 4x2 + 4x – 80 = 0. (iii) Find the time taken for her entire journey.
The time taken by Nadia for her entire journey is 5 hours
Speed and distance
Speed is the rate at which an object is moving, and it is defined as the distance traveled per unit of time. The formula for speed is:
Speed = Distance/Time
Where distance is the distance traveled by an object and time is the time taken to travel that distance.
From the fomrula, we can write as
Distance = Speed × Time
Here we have
Nadia walks at an average speed of (x + 2) km/h for (x – 3) hours and cycles at an average speed of (3x + 5) km/h for x hours.
As we know, Distance = Speed x Time
Distance walked = (x + 2)(x - 3)
Distance cycled = (3x + 5)(x)
The total distance covered is given as 74 km,
=> (x + 2)(x - 3) + (3x + 5)(x) = 74
=> x² - 3x + 2x - 6 + 3x² + 5x = 74
=> 4x² + 4x - 80 = 0
Hence, the final equation is 4x² + 4x - 80 = 0
(ii) The quadratic equation, can be solved as follows
=> x² + x - 20 = 0
=> x² + 5x - 4x - 20 = 0
=> x(x + 5) -4(x + 5) = 0
=> (x + 5) (x - 4) = 0
=> x = - 5 and x = 4
Here we cant take time as negative so take x = 4 hours
(iii) To find the time taken for her entire journey, we need to add up the time taken for walking and cycling:
Total time = (x - 3) + x
Total time = 2x - 3
Substituting the value of x
Total time = 2(4) - 3 = 8 - 3 = 5
Therefore,
The time taken by Nadia for her entire journey is 5 hours
Learn more about Speed and distance at
https://brainly.com/question/17277454
#SPJ1
If the distance between A(x,3) and B(4.3) is 16 units, find the value of x.
Answer:
[tex] - 12[/tex]
Step-by-step explanation:
[tex]x1 = x \: \: y1 = 3 \\ x2 = 4 \: \: y2 = 3 \\ distance \: betwen \: two \: points = \sqrt{(x2 - x1) {}^{2} +( y2 - y1) {}^{2} } \\ 16= \sqrt{(4 - x) {}^{2} + (3 - 3) {}^{2} } \\ 16 = \sqrt{(4 - x) {}^{2} + 0} \\ 16 = \sqrt{(4 - x) {}^{2} } \\ 16 = 4 - x \\ 16 - 4 = - x \\ 12 = - x \\ x = - 12[/tex]
The radius of a circle is 14 meters. What is the circle's area?
r=14 m
Use 3.14 for .
Answer:
The formula for the area of a circle:
[tex]A = \pi r^{2}[/tex]
You have said:
[tex]r = 14m[/tex]
So substitute the values of pi and r into the formula:
[tex]A = \pi r^{2} \\A = (3.14)(14m)^{2} \\A = (3.14)(196m^{2} )\\A = 615.44m^{2}[/tex]
HELPPPPPPPPPPPPPP ASAP
Answer:
Use the formula of Range Large-Small Data
I think it will help you.
the ratio of the 6th and 8th term of an ap is 7:9. find the ratio between the sum of its first 10 terms to sum of its first 20 terms
Step-by-step explanation:
Tn = a + (n-1)d
where a is the first term, d is the common difference and n is the nth term
For the 6th term: T6 = a + (6-1)d
= a + 5d
For the 8th term: T8 = a + (8-1)d
= a + 7d
From the question (a + 5d)/(a + 7d) = 7/9
From the Equation above, we can say that;
a + 5d = 7......1
a + 7d = 9.....2
Solving equations 1 & 2 simultaneously, we have that a = 2 and d = 1
Sn = n/2[2a + (n-1)d]
where Sn is the sum of nth terms, n is the nth term, a is the first term and d is the common difference.
By substituting the values gotten into this equation. You would be able to find the ration between the sum of the first 10 terms to the sum of the first 20 terms
Answer:
see analysis for detailed explanation
Selim walked 1/12 of a mile to the coffee shop in 712 of a mile to the dry cleaners how far apart is the coffee shop from the dry cleaners grid your answer NOTE: grid your answer as a fraction not a mixed number
Answer:
6/12 of a mile
Step-by-step explanation:
7/12-1/12=16/12
state the restrictions on the domain of the equation.
Answer: Choice E
[tex]x \ne -4, -1[/tex]
This is the same as saying [tex]x \ne -4 \text{ and } x \ne -1[/tex]
======================================================
Reason:
If we plugged x = -4 into the function, then the x+4 in the denominator turns to 0.
x+4 = -4+4 = 0
Dividing by zero is not allowed. It leads to a division by zero error. Therefore, we need to exclude -4 from the domain. Similar reasoning will exclude -1 as well because it makes the x+1 in the denominator to be zero.
Any other x value is valid.
Side note: The (x+1) terms cancel, which may appear that x = -1 is valid. However, your calculator will likely not perform such a simplification. It will simply try to directly compute the result using PEMDAS. That means x = -1 is likely to produce a division by zero error.
For 100 points!!!
Three times a number, plus nine, equals negative two times the same number, plus forty-four. The number is?
Answer:
4A - 8 = 3A + 4
Step-by-step explanation:
Answer:
31/5
Step-by-step explanation:
3x+9=-2x+40
when you solve the equation, you get 31/5!
Please mark as brainliest if you can. Hope this helps!
which function does the graph represent
a: f(x)=-0.5(x+4)^2-5
b: f(x)=0.5(x+4)^2-5
c: f(x)=0.5(x-4)^2-5
d:f(x)=-0.5(x-4)^2-5
Answer:
C: f(x) = 0.5(x-4)^2-5
Step-by-step explanation:
I graphed each function on Desmos, and matched it up with option C:
Answer:
the answer is C
Step-by-step explanation:
c: f(x)=0.5(x-4)^2-5
7. What is the area of the white border?
8 cm
2 cm
9 cm
15 cm
What is the area of the white border
Answer:
119 cm^2
Step-by-step explanation:
To find the area of the white border, simply find the area of the outside rectangle and subtract the middle(dark) rectangle's area from that value.
White rectangle: 15x9 = 135
Dark rectangle: 8x2 = 16
135 - 16 = 119 cm^2
The unit is squared when finding the area of a two dimensional figure.
The vertices of a rectangle are E(−1, 1), F(−1, 3), G(−5, 3), and H(−5, 1). Find the coordinates of the figure after reflecting in the x-axis, and then translating 3 units right.
The resulting points of the rectangle after applying rigid transformations are E'(x, y) = (2, -1), F(x, y) = (2, -3), G(x, y) = (-2, -3), H(x, y) = (-2, -1).
How to apply rigid transformations on geometrical loci
Rigid transformations are transformations in which Euclidean distances are conserved in every point of the geometrical locus. Reflections and translations are sound examples of rigid transformations.
Based on all the information given in the statement, we must apply the following vectorial formula to each vertex of the rectangle EFGH:
(x', y') = (x + 3, -y) (1)
If we know that E(x, y) = (-1, 1), F(x, y) = (-1, 3), G(x, y) = (-5, 3) and H(x, y) = (-5, 1), then the new coordinates are calculated below:
E'(x, y) = (2, -1), F(x, y) = (2, -3), G(x, y) = (-2, -3), H(x, y) = (-2, -1)
To learn more on rigid transformations, we kindly invite to check this verified question: https://brainly.com/question/1761538
B
An athlete ran uphill at 3 metres per second for x seconds , downhill
at 6 metres per second for y seconds and covered a total distance
of 375 metres . If the athlete took 5 seconds longer to run uphill than
downhill, calculate the values of xandy.
(5)
Step-by-step explanation:
- The distance traveled to get to the top of the hill will be equal to the distance traveled to get to the bottom of the hill. Distance down the hill = Distance up the hill = 187.5 meters.
- Only the speed of going up the hill and down the hill will be different.
I need help please help me
Find the area of the figure. Use 3.14 as π.
area triangle:
b×h/2
= 11 in×10 in/2
=55 in²
area half-circle:
pi×r² /2
= 3.14×5in² /2
=78.5in² /2
=39.25 in²
Total area: area triangle+ area half-circle
= 55 in²+39.25 in²
=94.25 in²
Jack has $15,000 to invest. If he invests two-thirds of it into a high-yield savings account with an annual interest rate of 8%, compound continuously, and the other third in a regular savings account at 6% simple interest, how much does Jack earn after one year?
Based on the amounts that Jack invested into the different investment vehicles, the amount Jack earns a year would be $1,132.87.
How much does Jack earn from the high-yield savings account?The amount invested is:
= 2 / 3 x 15,000
= $10,000
Amount after a year:
= Amount x e ^ (rate x time)
= 10,000 x e ⁰.⁰⁸ ˣ ¹
= $10,832.87
How much does Jack make from the regular savings account?Amount invested:
= 1/3 x 15,000
= $5,000
Amount after a year:
= 5,000 x (1 + 6%)
= $5,300
How much did Jack earn in a year:= (10,832.87 + 5,300) - 15,000
= $1,132.87
#SPJ1
Find out more on continious compounding at https://brainly.com/question/3932907.
A safe's lock has a three number combination. The
numbers on the safe lock are 0 - 9. How many
combinations are possible if no number may be used
more than once?
Answer:
720 combinationsStep-by-step explanation:
Each number has initially 10 options.
If one option used for the first number then the second number has one less, 9 options. Similarly, the third number has one less number of options than the second number, 8 options.
Total number of combinations is
10*9*8 = 720What's the answer for this!
The options for each paragraph are listed below:
First paragraph50100001000Second paragraph0maximum18.498.6017.2How to fill the blanks in paragraphs on applications of second order polynomialsIn this question we are supposed to understand and apply concepts related to second order polynomials to fill the blanks when required in the following two paragraphs.
First paragraph talks about second order polynomials applied to economics and the second paragraph talks about second order polynomials applied to kinematics.
First paragraphThe roots of the quadratic function describing the relationship between number of products produced and overall profit margin are x = 0 and x = 100. The vertex is (50, 1000).
The maximum profit of $ 50 is reached when 1000 items are produced.
The first root tells us that the profit will be 0 when 0 products are produced. The second root says once 1000 items are made, the company is no longer making any profit. (They do not have production capacity and have to outsource for anything over 50)
Second paragraphThe trajectory of a golf ball in a chip from the rough has a parabolic pattern. The height, in feet, of the ball is given by the equation h(x) = -0.25 · x² + 4.3 · x, where x is the number of feet away from the golf club (along the ground) the ball is.
The ball starts 0 feet above the ground.
The ball reaches a maximum height of 18.49 feet at a horizontal distance of 8.60 feet away from the golf club its was hit with.
The ball returns to the ground at about 17.2 feet away.
To learn more on polynomials, we kindly invite to check this verified question: https://brainly.com/question/11536910
17. Instructions: Use the ratio of a 45-45-90 triangle to solve for the variables. Leave your answers as radicals in simplest form.
Answer:
u = v = 14
Step-by-step explanation:
The ratios of side lengths in a 45-45-90 triangle are ...
1 : 1 : √2
Here, the long side is 14√2, so is 14 times this basic ratio.
1 : 1 : √2 = u : v : 14√2 = 14 : 14 : 14√2
This means ...
u = v = 14
Answer:
Below in bold.
Step-by-step explanation:
The ratio of the sides in a 45-45-90 are 1:1:√2.
so V / 14√2 = 1 / √2
V = 14√2 / √2 = 14.
and U = V = 14 also.
I’m just trying to check my math, I got 159
Wellington city engineers are designing two parallel roads by the International Polo Club to help with traffic flow during tournaments.
Answer:
159°
Step-by-step explanation:
Angle 21° and <4 are supplementary angles!
21 + x = 180
x = 159°
Hope this helps!
The measure of angle ∠4 is 159.
What are corresponding angles?The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.
Corresponding angles are always equal.
We can also have alternate angles which are always equal.
We can also have alternate interior and exterior angles which are equal.
The angles on the same side make upto 180 degrees
We have,
From the figure,
The angle opposite to 21° and ∠4 sum is 180.
This means,
Angles on the same side.
Now,
Opposite angles are equal.
So,
21 + ∠4 = 180
∠4 = 180 - 21
∠4 = 159
Thus,
The measure of angle ∠4 is 159.
Learn more about corresponding angles here:
https://brainly.com/question/1597341
#SPJ7
solve for y: -32y^2 -24y = 0
Answer:
y = 0 , y = - [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
- 32y² - 24y = 0 ← factor out - 8y from each term
- 8y(4y + 3) = 0 equate each factor to zero and solve for y
- 8y = 0 ⇒ y = 0
4y + 3 = 0 ⇒ 4y = - 3 ⇒ y = - [tex]\frac{3}{4}[/tex]
What information must you know about a triangle in order to use the Pythagorean Theorem to find the length of a missing side?
In order to use the Pythagorean Theorem, you must know the length or lengths of
Choose...
of the triangle and know that the measure of one of the angles is
Choose...
.
Answer: your obviously going to need to use the method a2+b2=c2
Try to calculate the radius if not given to you.
Step-by-step explanation:
In order to use the Pythagorean Theorem, you must know the lengths of at least 2 sides (any 2 sides, but it has to be 2.) of the triangle and know that the measure of one of the angles is 90 degrees.
(3.6×10−5)÷(9×10−7) in Standard Form
Answer: 31/83 (decimal form 0.373494)
Step-by-step explanation:
What pair of factors of -28 has a sum of -3
Answer:
4 and -7
Step-by-step explanation:
Factors of -28: - 1, 1, - 2, 2, -4,4 ,-7,7,-14,14,-28,28
Factors with a sum of -3 = 4 and -7.
i need help 9th grade math
Answer:
g(x) = 4x + 5
Step-by-step explanation:
f(x) + g(x) = 10x + 7 , then
6x + 2 + g(x) = 10x + 7 ← subtract 6x + 2 from both sides
g(x) = 10x + 7 - 6x - 2 ← collect like terms
g(x) = 4x + 5
Let's find
(f+g)(x)=f(x)+g(x)10x+7=6x+2+g(x)g(x)=10x-6x+7-2g(x)=4x+5Option D
Hello, I need help with my work, someone ANYONE please help me, you will make my day if you help me.
Answer:
2.5, 3, 6, 9, 2.8, 6, 1.5
Is this what you're asking for?
Step-by-step explanation:
The line graphed below has a slope of ____.
To find the slope, we must have two points
--> Two points: (-3,1) and (-1, -5)
The slope's formula is --> [tex]\frac{y2-y1}{x2-x1}[/tex]
(x1, y1) --> (-3,1)(x2, y2) --> (-1, -5)So the slope = [tex]\frac{-5-1}{-1--3} =\frac{-6}{2} =-3[/tex]
The line graphed below has a slope of -3
Hope that helped!
Find f(-2) for (x) = 3 . 2^x
O A. -36
O B. -12
O c.1/36
O D. 3/4
[tex]\sf f(x) = 3 \ * \ 2^x[/tex]
insert x = -2
[tex]\sf f(-2) = 3 \ * \ 2^{-2}[/tex]
[tex]\sf f(-2) = 3 \ * \ \dfrac{1}{4}[/tex]
[tex]\sf f(-2) = \dfrac{3}{4}[/tex]
option D. 3/4 will be the correct answer.
[tex]\\ \rm\Rrightarrow f(x)=3.2^x[/tex]
Put -2[tex]\\ \rm\Rrightarrow f(-2)[/tex]
[tex]\\ \rm\Rrightarrow 3.2^{-2}[/tex]
[tex]\\ \rm\Rrightarrow 3(1/4)[/tex]
[tex]\\ \rm\Rrightarrow 3/4[/tex]
A summer camp had
440
campers register this year. This is a
10
%
increase over the number registered last year.
Part A
The equation below relates
440
and
c
,
the number of campers registered last year. Complete the equation by entering a number in the
□
.
Enter only a whole number or decimal.
c
=
440
Part B
Enter a number in the
□
to show how many campers,
c
,
were registered last year.
campers
The equation that relates the number of campers this year to the number of campers last year is c = 440 / 1.10
The number of campers last year is 400.
What are percentages?
Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentages are used to measure frequency.
How many campers attended last year?The number of campers last year = number of campers this year / (1 + percentage increase)
440 / 1.1 = 400
To learn more about percentages, please check: https://brainly.com/question/25764815
Yo I need to bring up my grade bad so
-3x-9=-3y
(please show it graphed already :D)
Answer:
Step-by-step explanation:
The average rate of change for a function is greater from x = 110 x=2 than from x=2 to x=3. What type of function could it be? Select all that apply
Аlinear
Bquadratic
Cexponential
Answer:
The type of function is cexponential and Alinear