Answer:
Since the speed can't be negative it was 60 km/h for the first stage and 80 km/h on the second stage, averaging 70 km/h for the whole course.
Step-by-step explanation:
The speed of the truck for the first stage of the route is "x" km/h, while on the second one it raises to "x + 20" km/h. The time it takes to complete each stage is shown below:
[tex]t_{stage 1} = \frac{150}{x}\\t_{stage 2} = \frac{200}{x + 20}[/tex]
The sum of these times must be equal to the total time of the trip, therefore:
[tex]t_{stage1} + t_{stage2} = 5[/tex]
[tex]\frac{150}{x} + \frac{200}{x + 20} = 5\\\frac{150*(x + 20) + 200*x}{x(x + 20)} = 5\\150*x + 3000 + 200*x = 5*x*(x + 20)\\5*x^2 + 100*x - 350*x - 3000 = 0\\5*x^2 - 250*x - 3000 = 0\\x^2 - 50*x - 600 = 0\\x_{1,2} = \frac{-(-50) \pm \sqrt{(-50)^2 - 4*1*(-600)}}{2*1}\\x_{1,2} = \frac{50\pm \sqrt{2500 + 2400}}{2}\\x_{1,2} = \frac{50\pm \sqrt{4900}}{2}\\x_{1,2} = \frac{50 \pm 70}{2}\\x_{1} = 60\\x_{2} = -10[/tex]
Since the speed can't be negative it was 60 km/h for the first stage and 80 km/h on the second stage, averaging 70 km/h for the whole course.
which of the following graphs shows a negative linear relationship with a correlation coefficient, r, close to -0.5.
Answer:
In the graph attached there is a sample generated with a correlation coefficient r=-0.5.
Step-by-step explanation:
A value of r that is -0.5 shows that there is a certain correlation and that this correlation is negative.
As there are no examples in this question, I searched for a generator of random samples with a user-input correlation coefficient between the two variables.
In the graph attached there is a sample generated with a correlation coefficient r=-0.5.
Answer:
In the graph attached there is a sample generated with a correlation coefficient r=-0.5.
Step-by-step explanation:
PLEASE ANSWER WILL MARK BRAINLIEST!!!!!!In which scatterplot is the vertical line placed correctly when using the divide-center method to find the regression line? On a graph, points are grouped together and increase. A vertical dotted line goes through the points. There are 7 points to the left of the line, and 3 points to the right. On a graph, points are grouped together and increase. A vertical dotted line goes through the points. There are 4 points to the left of the line, and 6 points to the right. On a graph, points are grouped together and increase. A vertical dotted line goes through the points. There are 6 points to the left of the line, and 4 points to the right. On a graph, points are grouped together and increase. A vertical dotted line goes through the points. There are 5 points to the left of the line, and 5 points to the right.
Answer:
Answer Would Be D.
Step-by-step explanation:
There is an even amount of dots on each side of the divider.
Answer:
It is D~~
Step-by-step explanation:
If we were to imagine the trend line and draw a oval around it and then draw a line in the middle, then D would be correct.
btw sorry if this answer... is like... too late. o_o
An ellipse is graphed. Which statements about the ellipse are true? Select three options. An ellipse is graphed. Which statements about the ellipse are true? Select three options. The center is at (−4, 2). The distance between the center and each covertex is 3 units. The vertices are at (−7, 1) and (−1, 1). Each focus is approximately 2.65 units above or below the center. The directrices are horizontal lines approximately 6 units from the center on the major axis.
Answer:
b, d, e
Step-by-step explanation:
The distance between the center and each covertex is [tex]3[/tex] units.
Each focus is approximately [tex]2.65[/tex] units above or below the center.
The directrices are horizontal lines approximately [tex]6[/tex] units from the center on the major axis.
Define Ellipse.An ellipse is just a circular plane curve created by a geographical distances in such a manner that the sum of its lengths from two points is always the same.
The distance between the center and each covertex is [tex]3[/tex] units.
Each focus is approximately [tex]2.65[/tex] units above or below the center.
The directrices are horizontal lines approximately [tex]6[/tex] units from the center on the major axis.
Find out more information about ellipse here:
https://brainly.com/question/19507943?referrer=searchResults
PLEASE HELP use trigonometry to solve for a missing angle x of the right triangle
Answer:
x = 80°
Step-by-step explanation:
from SOH CAH TOA
we are going for TOA
where TOA => Tan x = Opposite side of the Angle
Adjacent Side of The Angle
Tan x = 27500
5000
Tan x = 5.5
x = Tan⁻¹ 5.5
or
= arctan 5.5
= 79.70°
≈ 80°
Answer:
x = 80°
Step-by-step explanation:
The arithmetic sequences 1, 5, 9, 13,... and 1, 8, 15, 22,... have infinitely many terms in common. Calculate the sum of the first three common terms.
Answer:
87
Step-by-step explanation:
Sequence 1 has common difference of 4 and sequence 2 has 7
The first terms are common
We need a new sequence with common difference of:
LCM(4,7)= 4*7=28So the next common term is 1+28= 29 and the following one is 29+28= 57
Sum of 3 terms:
1+29+57= 87Answer:
87
Step-by-step explanation:
The first sequence:
1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61...
The second sequence:
1, 8, 15, 22, 29, 36, 43, 50, 57, 63...
The first three common terms are 1, 29, 57.
The sum of the first three common terms:
1 + 29 + 57
= 87
The number r is irrational. Which statement about r+7 is true? r+7 is rational r+7 is irrational r+7 can be rational or irrational depending on the value of r
Answer: r+7 is irrational
Step-by-step explanation:
1) If r is irrational, that means that it goes on and on forever.
2) 7 is a rational number because it can be expressed as a quotient of 2 integers (7÷1=7)
3) If you add a rational number to an irrational number it is still irrational. The numbers after the decimal point keep going and going. You are just changing the whole number, which if to the left of the decimal point.
You are walking near a river. While standing at A, you measure an angle of 90° between B and C, as shown. You then walk to B and measure an angle of 77° between A and C. The distance between A and B is about 1.5 miles. How wide (in miles) is the river between A and C? Round your answer to the nearest tenth.
Answer:
Length of AC = 6.67 miles
Step-by-step explanation:
Given:
Angel between B and C = 90°
Angel between A and C = 77°
AB = 1.5 miles
Find:
Length of AC
Computation:
Using trigonometric laws
Cos 77° = Base / hypotenuses
0.225 = 1.5 / hypotenuses
hypotenuses = 6.67 miles
Length of AC = 6.67 miles
If you use exactly eight cups of cauliflower to make 6 veggie burritos and if you continue to make burritos using the same recipe how many burritos can he make with 12 cups of cauliflower
Answer:
9 burritos
Step-by-step explanation:
We can use ratios to solve
8 cups 12 cups
---------- = -----------------
6 burritos x burritos
Using cross products
8x = 6*12
8x = 72
Divide by 8
8x/8 =72/8
x = 9
9 burritos
a traffic light can either be green, yellow or red. for every minute, the light stays green for 35 seconds, yellow for 5 seconds, and red for 20 seconds. At any given moment of the day, what is the probability that the light will be yellow? a. 1/12 b. 1/9 c. 1/8 d. 1/6 e. 1/3
Answer:
a. 1/12 (hope it help)
Step-by-step explanation:
5sec/60sec=1/12
can you pls help thank you
Answer:
not a function
Step-by-step explanation:
This is not a function. For the value x =2 there are two different y values
To be a function each value of x has only one value for y
This would also fail the vertical line test
18 dogs are in a dog show the number of dogs in the show. The number of dogs in the show was 6 times the number of handlers how many handlers are in the show
Answer:
H = 3 handlers
There are 3 handlers in the show.
Step-by-step explanation:
Given;
Number of dogs in the show N = 18 dogs
Number of handler in the show H;
The number of dogs in the show was 6 times the number of handlers
N = 6H
H = N/6
Substituting the value of N;
H = 18/6
H = 3
There are 3 handlers in the show.
Answer:
H = 3 handlers
Step-by-step explanation:
Please help. I don't understand how to solve this problem.
Answer:
BF=16
Step-by-step explanation:
To find BF, (I will be calling it x) you need to use the equation
CF/FB=CE/EA Substitute
FB=x
24/x=18/12 cross multiply
18x=288 divide both sides by 18
x=16
FB=16
Hope this helps, if it does, please consider giving me brainliest, it will help me a lot.
Have a good day! :)
Solve for the value of x 3x + 8 = 2
Answer:
-2
Step-by-step explanation:
Answer: x = -2
Step-by-step explanation:
3x + 8 = 2
3x = -6
x = -2
define the type of sequence 7, 14, 28, 56, 112
Answer:
This is a geometric sequence.
Raven earns extra money when her neighbors are on vacation. Raven is paid $12 per day when she cares for the Martin family's cat. She paid $5.50 per day when she waters the Clark Family's pants.Write and simplify an expression to represent how much Raven earns if she performs both jobs for n days. Explain what the simplified expression means.
Answer:
12n + 5.50
Step-by-step explanation:
Since 12 represents how much money she gets paid from the Martin's family: the 'n' is the variable which stands for each day because we don't kknow how many days she watches the cat but when we multiply the 12 by the 'n', we get the days. We add an additional 5.50 because she has a side job as well with the Clark's family. which is how you get 12n+5.50
Each side of a regular pentagon is m + 10 inches. The formula for finding the perimeter of the pentagon is shown below. P = 5 (m +10) Which equation shows this formula solved for m? A. M = P − 5 / 10 B. M = 5P − 50 C. M = P − 50 / 5 D. M = P/5 − 50
Answer:
m = p/5 -10
m= (p-50)/5
Step-by-step explanation:
What we practically want to here is to make m the subject of the formula.
Start by opening the brackets
P = 5m + 50
P-50 = 5m
Divide through by 5
(P-50)/5 = m
P/5 -50/5 = m
P/5 -10 = m
The option that looks probable is C ; M = (P-50)/5
Answer:
D.) m=P−505
Step-by-step explanation:
The given line segment has a midpoint at (3, 1).
On a coordinate plane, a line goes through (2, 4), (3, 1), and (4, negative 2).
What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?
y = One-thirdx
y = One-thirdx – 2
y = 3x
y = 3x − 8
Answer:
[tex]y=\frac{1}{3}x[/tex]
Step-by-step explanation:
The given line segment has a midpoint at (3, 1) and goes through (2, 4), (3, 1), and (4, -2). We can use any two of the three points to calculate the equation of the line. Let us use the points (2, 4) and (4, -2)
Therefore the line goes through (2, 4) and (4, -2). The equation of a line passing through [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex] is:
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex].
Therefore the line passing through (2, 4) and (4, -2) has an equation:
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}\\\frac{y-4}{x-2}=\frac{-2-4}{4-2}\\\frac{y-4}{x-2}=\frac{-6}{2}\\y-4=x-2(-3)\\y-4=-3x+6\\y=-3x+10[/tex]
Comparing with the general equation of line: y = mx + c, the slope (m) = -3 and the intercept on the y axis (c) = 10
Two lines are said to be perpendicular if the product of their slope is -1. If the slope of line one is m1 and the slope of line 2 = m2, then the two lines are perpendicular if:
[tex]m_1m_2=-1[/tex].
Therefore The slope (m2) of the perpendicular bisector of y = -3x + 10 is:
[tex]m_1m_2=-1\\-3m_2=-1\\m_2=\frac{1}{3}[/tex]
Since it is the perpendicular bisector of the given line segment, it passes through the midpoint (3, 1). The equation of the perpendicular bisector is:
[tex]\frac{y-y_1}{x-x_1}=m\\\frac{y-1}{x-3}=\frac{1}{3}\\ y-1= \frac{1}{3}(x-3)\\ y-1=\frac{1}{3}x-1\\y=\frac{1}{3}x[/tex]
the equation, in slope-intercept form, of the perpendicular bisector of the given line segment is [tex]y=\frac{1}{3}x[/tex]
Answer:
I believe the answer is A. y = 1/3x
Step-by-step explanation:
Apply the square root principle to solve (x - 2)2 + 20 = 0.
OA) x = 2 + 2115 , X = 2 - 2015
OB) x = 2 + 215 , X = 2 - 215
OC) x = -2 + 2i15, x = -2 - 2115
OD) x = -2 + 215,= -2 - 2 15
help me plsss guys x
Answer:
B. 2/6
Step-by-step explanation:
A fair ordinary dice has 6 sides.
The numbers 4 or 5 on the dice are 2 numbers out of 6 total numbers.
2/6
Answer:
B. 2/6
Step-by-step explanation:
A ordinary dice has 6 sides.
4 and 5 make 2 sides.
So the answer will be 2/6
Find the maximum/minimum value of the function y = x2 - (5/3)x + 31/36.
A. 1/6
B. 5/6
C. 25/36
D. 10
Answer:
A
Step-by-step explanation:
Given a parabola in standard form, y = ax² + bx + c ( a ≠ 0 ), then
minimum/ maximum value is the y- coordinate of the vertex.
The x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = x² - [tex]\frac{5}{3}[/tex] x + [tex]\frac{31}{36}[/tex] ← is in standard form
with a = 1 and b = - [tex]\frac{5}{3}[/tex] , thus
[tex]\frac{x}{vertex}[/tex] = - [tex]\frac{-\frac{5}{3} }{2}[/tex] = [tex]\frac{5}{6}[/tex]
Substitute this value into y
y = ([tex]\frac{5}{6}[/tex] )² - [tex]\frac{5}{3}[/tex] ([tex]\frac{5}{6}[/tex] ) + [tex]\frac{31}{36}[/tex]
= [tex]\frac{25}{36}[/tex] - [tex]\frac{25}{18}[/tex] + [tex]\frac{31}{36}[/tex] = [tex]\frac{1}{6}[/tex]
Since a > 1 then the vertex is a minimum, thus
minimum value = [tex]\frac{1}{6}[/tex] → A
Divide up the number 60 in 2:3:5 ratio.
Answer:
Step-by-step explanation:
Jaya agreed to give matt a loan for $80 but she’ll also be charging him 8% interest.How much will he have to pay her back
Answer:
Step-by-step explanation:
Let organise our information :
Jaya will charge Matt an 8 percent interest for 80 dollars loanwe can say that :
80 dollars⇒ 100 percentx ⇒ 8 percent
so :
x =( 8*80 )/ 100= 6.4
so the interest is 6.4 dollars
so the total cost is 86.4
5. The monthly rent of a flat in New Delhi is 32 860 rupees.
How much is this in euros?
1
Answer:
386.11
Step-by-step explanation:
32,860=€386.11
Calculate: 1/1×3 + 1/3×5 + ... + 1/47×49 .
Answer: 1/1x3+1/3x5 = 14/3 or 4 2/3
Step-by-step explanation:
And please, next time give the problem fully.
Solve for rrr: \dfrac{7}{10}=r-\left(-\dfrac{8}{5}\right) 10 7 =r−(− 5 8 )start fraction, 7, divided by, 10, end fraction, equals, r, minus, left parenthesis, minus, start fraction, 8, divided by, 5, end fraction, right parenthesis r =r=r, equals
Answer:
r = -9/10
Step-by-step explanation:
Given
7/10 = r - (-8/5)
Required
Solve for x
7/10 = r - (-8/5)
We start by opening the bracket
7/10 = r + (- -8/5)
7/10 = r + (8/5)
7/10 = r + 8/5
Subtract 8/5 from both sides
7/10 - 8/5 = r + 8/5 - 8/5
7/10 - 8/5 = r
Solve the fraction by taking their LCM
(7 - 16)/10 = r
-9/10 = r
Reorder the above
r = -9/10
Hence, the value of r is -9/10
Answer:
4(− 5/7 )
Step-by-step explanation:
Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 temporary employees consist of 3 women and 1 man
Answer:
70 possible groupsStep-by-step explanation:
Given the total number of employee to be equal to 12 temporary employee.
Number of women employee = 5 women
Number of men employee = 12 - 5 = 7 men
If 4 will be hired as permanent employees, the possible ways they can be grouped so that the 4 temporary employees consists of 3 women and 1 man can be done by applying the combination formula.
Combination has to do with selection. For example, if r objects are to be selected from n pool of similar objects, this can be done in nCr different ways.
[tex]nCr = \frac{n!}{(n-r)!r!}[/tex]
According to question, we are to select 3 women from 5 women and 1 man from 7 men. Based on similarity in sex, this can be done in (5C3* 7C1) different ways .
[tex]5C3 * 7C1\\= \frac{5!}{(5-3)!3!} * \frac{7!}{(7-1)!1!}\\\\= \frac{5!}{2!3!} * \frac{7!}{6!1!}\\\\= \frac{5*4*3!}{3!*2} * \frac{7*6!}{6!*1}\\\\= \frac{20}{2} * \frac{7}{1}\\ \\= 10*7\\\\= 70\ possible\ groups[/tex]
for how many values of k will x² + kx + 12 factor?
Answer:
6
Step-by-step explanation:
We want to factor the trinomial into a product of binomials. In general, we have ...
(x +a)(x +b) = x² +(a+b)x +ab
So, the values of "a" and "b" need to have a product of 12. There are 6 ways to do that:
12 = 1·12 = 2·6 = 3·4 = (-1)(-12) = (-2)(-6) = (-3)(-4)
The values of k are the sums of these factors of 12, so are
1+12 = 13
2+6 = 8
3+4 = 7
-1-12 = -13
-2-6 = -8
-3-4 = -7
There are 6 possible integer values of k that will make the trinomial factorable in integers:
k ∈ {-13, -8, -7, 7, 8, 13}
Keenan buys an embroidery machine for $1,400. He uses it to embroider
T-shirts. His total profit in dollars from selling the T-shirts is represented with
the function f(x) = 12x - 1,400. When the machine breaks, he pays $135 to
have it fixed. How does that cost affect a graph of Keenan's profit function?
Answer:
the graph shift down 135 units
Step-by-step explanation:
when there is no fixing cost:
f(x)=12x-1400
when there is fixing cost (0ne time): 12x-(1400+135)
the graph shift down 135 units
Those $ 135 will be added to the fixed cost, by increasing the expense with respect to the embroidery, with which the function will become the following: f (x) = 12x - (1,400 + 135).
Since Keenan buys an embroidery machine for $ 1,400, and he uses it to embroider T-shirts, and his total profit in dollars from selling the T-shirts is represented with the function f (x) = 12x - 1,400, and when the machine breaks, he pays $ 135 to have it fixed, to determine how does that cost affect a graph of Keenan's profit function, the following mathematical analysis must be performed:
Keenan's fixed expense is 1,400, which is the value of the embroider, and which must be considered when evaluating profit or loss from business operations.Thus, 1400 must be divided by the total number of T-shirts sold, to determine the cost per product sold.Therefore, those $ 135 will be added to the fixed cost, by increasing the expense with respect to the embroidery, with which the function will become the following: f (x) = 12x - (1,400 + 135).
Learn more in https://brainly.com/question/15853856
In terms of x? pls solve and show your work! Will give u brainliest!
Answer:
[tex] \sqrt{ {x}^{2} - 1 } [/tex]
Solution,
base=1
perpendicular=?
hypotenuse=X
now,
using Pythagoras theorem,
x^2=p^2+b^2
or, x^2=p^2+1^2
or,p^2=x^2-1
or, p=√x^2-1
tan theta=perpendicular/ base
tan theta =√x^2-1/1
tan theta=√x^2-1
z=tan theta
z=√x^2-1
Hope this helps...
Good luck on your assignment..
Answer:
[tex]\sqrt{x^{2}-1}}[/tex].
Step-by-step explanation:
The tangent of theta means that you are trying to find opposite over adjacent.
You already have the value of the adjacent (1), so all you need to do is find the opposite. That would be the square root of the hypotenuse squared minus the adjacent squared.
The opposite would be sqrt(x^2 - 1^2) = [tex]\sqrt{x^{2}-1}}[/tex].
When you put it together, tan(theta) = [tex]\frac {\sqrt{x^{2}-1} }{1}[/tex]
That is [tex]\sqrt{x^{2}-1}}[/tex].
So, z, in terms of x, is [tex]\sqrt{x^{2}-1}}[/tex].
Hope this helps!
solve inequality for x
x/-4<16
The answer to this problem is x> -64
Step-by-step explanation:
[tex]x - 4 < 16 \\ x < 16 + 4 \\ x < 20[/tex]
x={...17,18,19}