Answers
Answer:
13/6
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= (6 - -7)/(1 - -5)
= ( 6+7)/ (1+ 5)
= 13/6
Related Questions
Beginning 177 miles directly north of the city of Morristown, a van travels due west. If the van is travelling at a speed of 31 miles per hour, determine the rate of change of the distance between Morristown and the van when the van has been travelling for 71 miles. (Do not include units in your answer, and round to the nearest hundredth.)
Answers
Answer:
Step-by-step explanation:
From the given information;
let the hypotenuse be a , the opposite which is the north direction be b and the west direction which is the adjacent be c
SO, using the Pythagoras theorem
a² = c² + 177²
By taking the differentiation of both sides with respect to time t , we have
[tex]2a \dfrac{da}{dt} = 2c \dfrac{dc}{dt} + 0[/tex]
[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]
At c = 71 miles,[tex]a = \sqrt{ (71)^2 +(177)^2}[/tex]
[tex]a = \sqrt{ 5041+31329}[/tex]
[tex]a = \sqrt{ 36370}[/tex]
a = 190.71
SImilarly, [tex]\dfrac{dc}{dt} = \ 31 miles \ / hr[/tex]
Thus, the rate of change of the distance between Morristown and the van when the van has been travelling for 71 miles can be calculate as:
[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]
[tex]\dfrac{da}{dt} = \dfrac{71}{190.71} \times 31[/tex]
[tex]\dfrac{da}{dt} = 0.37229 \times 31[/tex]
[tex]\mathbf{\dfrac{da}{dt} = 11.54}[/tex] to the nearest hundredth.
why infinity ( ) can’t be included in an inequality?
Answers
Answer:
Step-by-step explanation:
Because then the value on the other side will be unbounded by the infinity sign while expressing the answers on a number line.
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Need help with this as soon as possible pls
Answers
Answer:
i think
x=6.77
y=11.33
What are the solutions to the system of equations? {y=2x2−8x+5y=x−2 (3.5, 0.5) and (1, −1) (7, 5) and (0.5, −1.5) (3.5, 1.5) and (1, −1) (3.5, 1.5) and (−1, −3)
Answers
Answer:
[tex](1,-1)[/tex] and [tex](3.5,1.5)[/tex]
Step-by-step explanation:
Given
[tex]y = 2x^2 - 8x+5[/tex]
[tex]y = x - 2[/tex]
Required
Determine the solution
Substitute x - 2 for y in [tex]y = 2x^2 - 8x+5[/tex]
[tex]x - 2 = 2x^2 - 8x+5[/tex]
Collect like terms
[tex]0 = 2x^2 - 8x - x + 5 + 2[/tex]
[tex]0 = 2x^2 - 9x + 7[/tex]
Expand the expression
[tex]0 = 2x^2 - 7x - 2x+ 7[/tex]
Factorize
[tex]0 = x(2x - 7) -1(2x - 7)[/tex]
[tex]0 = (x-1)(2x - 7)[/tex]
Split the expression
[tex]x - 1 = 0[/tex] or [tex]2x - 7 = 0[/tex]
Solve for x in both cases
[tex]x = 1[/tex] or [tex]2x = 7[/tex]
[tex]x = 1[/tex] or [tex]2x/2 = 7/2[/tex]
[tex]x = 1[/tex] or [tex]x = 3.5[/tex]
Recall that
[tex]y = x - 2[/tex]
When [tex]x = 1[/tex]
[tex]y = 1 -2[/tex]
[tex]y = -1[/tex]
When [tex]x = 3.5[/tex]
[tex]y = 3.5 - 2[/tex]
[tex]y = 1.5[/tex]
Hence, the solution is;
[tex](1,-1)[/tex] and [tex](3.5,1.5)[/tex]
The isotope of plutonium 238Pu is used to make thermoelectric power sources for spacecraft. Suppose that a space probe was launched in 2012 with 4.0 kg of 238Pu.
Required:
a. If the half-life of 238Pu is 87.7 yr, write a function of the form Q(t)= Q0e- kt.to model the quantity Q(t) of 238Pu left after t-years.
b. If 1.6 kg of 238Pu is required to power the spacecraft's data transmitter, for how long will scientists be able to receive data?
Answers
Answer:
A) Q(t) = 4e^-(0.0079t)
B) t = 115.99 ≈ 116
Therefore scientist will be able to receive data after 116 years
Step-by-step explanation:
a)
to write a function of the form Q(t)= Q₀e⁻^kt to model the quantity Q(t) of ²³⁸Pu left after t-years.
so given that; half-life of ²³⁸Pu is 87.7 years,
∴ t = 87.7 years , Q(t) = 0.5Q₀
Now we substitute these value in the form Q(t)= Q₀e⁻^kt
Q(t)= Q₀e⁻^kt
0.5Q₀ = Q₀e^ -(87.7k)
0.5 = e^ -(87.7k)
now we take the natural logarithm of both sides
In(0.5) = Ine^ -(87.7k)
Now using the property logₙnᵃ = a
-87.7k = In(0.5)
k = - In(0.5) / 87.7
k = 0.0079
ALSO it was given that Q₀ = 4.0 kg
Therefore , model quality Q(t) of ²³⁸pu left after t years is:
Q(t) = 4e^-(0.0079t)
b)
to find the time left after 1.6kg of ²³⁸pu
we simple substitute Q(t) = 1.6 into Q(t) = 4e^-(0.0079t)
so we have
1.6 = 4e^-(0.0079t)
e^-(0.0079t) = 1.6/4
e^-(0.0079t) = 0.4
again we take the natural logarithm of both sides,
Ine^-(0.0079t) = In(0.4)
again using the property logₙnᵃ = a
-0.0079t = In(0.4)
t = - in(0.4) / 0.0079
t = 115.99 ≈ 116
Therefore scientist will be able to receive data after 116 years
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution? Choose the correct answer below. A. The mean and standard deviation have the values of and B. The mean and standard deviation have the values of and C. The mean and standard deviation have the values of and D. The mean and standard deviation have the values of and
Answers
Answer:
In order for a Normal Probability Distribution to be a Standard Normal Probability Distribution, the mean and standard deviation must have the values of µ = 0 and σ = 1.
Where µ refers to the Mean of the distribution and σ refers to the standard deviation.
µ is pronounced 'mu' and σ is pronounced sigma.
Cheers!
which polynomial correctly combines the like terms and expresses the given polynomial in standard form? 9xy³ -4y⁴ -10x²y² + x³y + 3x⁴ + 2x²y² - 9y⁴
Answers
Answer:
3x^4+(x^3)y-8x^2y^2+9xy^3-13y^4
Step-by-step explanation:
3x^4+(nothing)=3x^4
x^3y+(nothing)=x^3y
-10x^2y^2=2x^2y^2=-8x^2y^2
9xy^3+(nothing)=0
-4y^4-9y^4=-13y^4
Add it all up and write the terms by descending order of exponent value, and u get my answer.
Solve for x: −3|x + 7| = −12
x = 5 over 3, x = −19 over 3
x = −3, x = −11
x = −3, x = 11
No solution
Answers
Answer:
x=-3 x=-11
Step-by-step explanation:
−3|x + 7| = −12
|x + 7|=4
x+7=4 x+7=-4
x=-3 x=-11
A poker hand consisting of 7 cards is dealt from a standard deck of 52 cards. Find the probability that the hand contains exactly 3 face cards. Leave your answer as a reduced fraction.
Answers
Answer:
The probability is 2,010,580/13,378,456
Step-by-step explanation:
Here is a combination problem.
We want to 7 cards from a total of 52.
The number of ways to do this is 52C7 ways.
Also, we know there are 12 face cards in a standard deck of cards.
So we are selecting 3 face cards from this total of 12.
So also the number of cards which are not face cards are 52-12 = 40 cards
Out of all these 40, we shall be selecting exactly 4. The number of ways to do this 40C4
Thus, the required probability will be;
(40C4 * 12C3)/52C7 = (91,390 * 220)/133,784,560
= 20,105,800/133,784,560 = 2,010,580/13,378,456
An inequality is shown: −np − 4 ≤ 2(c − 3) Which of the following solves for n?
Answers
Answer:
[tex]\huge\boxed{n\leq\dfrac{2-2c}{p}\ \text{for}\ p<0}\\\boxed{n\geq\dfrac{2-2c}{p}\ \text{for}\ p>0}[/tex]
Step-by-step explanation:
[tex]-np-4\leq2(c-3)\qquad\text{use the distributive property}\\\\-np-4\leq2c-6\qquad\text{add 4 to both sides}\\\\-np\leq2c-2\qquad\text{change the signs}\\\\np\geq2-2c\qquad\text{divide both sides by}\ p\neq0\\\\\text{If}\ p<0,\ \text{then flip the sign of inequality}\\\boxed{n\leq\dfrac{2-2c}{p}}\\\text{If}\ p>0 ,\ \text{then}\\\boxed{n\geq\dfrac{2-2c}{p}}[/tex]
what is the lub and glb of the following sets, in the set of real numbe if exists E={ 0.2,0.23,0.234,0.2343,0.23434,0.23434,...}
Answers
Answer:
Hello,
Step-by-step explanation:
[tex]LUB(E)=0.2=\dfrac{1}{5} \\\\GUB(E)=0.2 34 34 34 ....=0.2+\dfrac{1}{10} *0.343434....\\\\=\dfrac{1}{5} +\dfrac{1}{10} *\dfrac{34}{99} \\\\=\dfrac{198+34}{990} \\\\=\dfrac{116}{495}[/tex]
Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 8 sin(xy), (0, 9)
Answers
Answer:
The maximum rate of change of f at (0, 9) is 72 and the direction of the vector is [tex]\mathbf{\hat i}[/tex]
Step-by-step explanation:
Given that:
F(x,y) = 8 sin (xy) at (0,9)
The maximum rate of change f(x,y) occurs in the direction of gradient of f which can be estimated as follows;
[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (x,y) \hat i \ + \ \dfrac{\partial }{\partial y } (x,y) \hat j \end {bmatrix}[/tex]
[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (8 \ sin (xy) \hat i \ + \ \dfrac{\partial }{\partial y } (8 \ sin (xy) \hat j \end {bmatrix}[/tex]
[tex]\overline V f (x,y) = \begin {bmatrix} (8y \ cos (xy) \hat i \ + \ (8x \ cos (xy) \hat j \end {bmatrix}[/tex]
[tex]| \overline V f (0,9) |= \begin {vmatrix} 72 \hat i + 0 \end {vmatrix}[/tex]
[tex]\mathbf{| \overline V f (0,9) |= 72}[/tex]
We can conclude that the maximum rate of change of f at (0, 9) is 72 and the direction of the vector is [tex]\mathbf{\hat i}[/tex]
33 points
1. A sandwich vendor offers a choice of hamburger, chicken, or fish on
either a plain or sesame seed bun. How many different types of
sandwiches are there to choose from?
*
4
6
12
3
Answers
Answer:
6 sandwiches to choose from because
3×2 = 6
Write the equation in slope-intercept form. y = 7(x + 2) + 3x
Answers
Step-by-step explanation:
y=mx+c
where m=7(x+2)and c=3xAnswer:
y= 10x +14
Step-by-step explanation:
Distribute parenthesis:
7(x+2) + 3x = 7x +14 +3x
Then combine like terms:
7x + 3x = 10x +14
Please answer my question
Answers
Step-by-step explanation:
The inequality shows by line is
i) 1<=x<=6
OR,
x is an positive integer.
explain why the APR does not compare loans for different lengths of time
Answers
Answer:
APR does not tell you how long your rate is locked for. A 15-year loan may have a lower interest rate, but could have a higher APR, since the loan fees are amortized over a shorter period of time. It is not wise to compare a 30-year loan with a 15-year loan using their respective APRs.
Step-by-step explanation:
if G is the midpoint of FH, FG = 14x + 25 and GH = 73 - 2x, find FH.
Answers
Answer:
FH = 134
Step-by-step explanation:
From the question given:
G is the midpoint of FH
FG = 14x + 25
GH = 73 - 2x
FH =?
Next, we shall determine the value of x. The value of x can be obtained as follow:
Since G is the midpoint of FH, this implies that FG and GH are equal i.e
FG = GH
With the above formula, we can obtain the value of x as follow:
FG = 14x + 25
GH = 73 - 2x
x =?
FG = GH
14x + 25 = 73 - 2x
Collect like terms
14x + 2x = 73 - 25
16x = 48
Divide both side by 16
x = 48/16
x = 3
Next, we shall determine the value of FG and GH. These can be obtained as shown below:
FG = 14x + 25
x = 3
FG = 14x + 25
FG = 14(3) + 25
FG = 42 + 25
FG = 67
GH = 73 - 2x
x = 3
GH = 73 - 2x
GH = 73 - 2(3)
GH = 73 - 6
GH = 67
Finally, we shall determine FH as follow:
FH = FG + GH
FG = 67
GH = 67
FH = FG + GH
FH = 67 + 67
FH = 134
Therefore, FH is 134
pls help! I need the answer quickly! thank you!
Answers
Answer:
C) 82/2
Step-by-step explanation:
The area of a square is calculated by multiplying a side by itself
so one side of the square is 9 in
the area of a triangle is calculated by multiplying height and base and that divided by 2
since E is the midpoint, if we draw a line show the height from there
the height would be 9
9*9/2 = 82/2
Using the identity (a + b) (a - b) = a - b², evaluate 49 × 51.
Answers
[tex]\\ \sf\longmapsto 49\times 51[/tex]
[tex]\\ \sf\longmapsto (50-1)(50+1)[/tex]
[tex]\\ \sf\longmapsto (50)^2-(1)^2[/tex]
[tex]\\ \sf\longmapsto 2500-1[/tex]
[tex]\\ \sf\longmapsto 2499[/tex]
49 × 51
Using Identity(a + b) (a - b) = a - b²Solution⇛(50 + 1) (50 - 1)
⇛(50)² - (1)²
⇛2500 - 1
⇛2499
Each student in a school was asked, "What is your favorite color?" The circle graph below shows how they answered
Which color was chosen by approximately one fourth of the students?
Approximately what percentage of the students chose purple or green?
Answers
Answer:
a). BLUE color
b). 20%
Step-by-step explanation:
a). "Which color was chosen by approximately one fourth of the students?"
Since one fourth of the students will be represented by one fourth area of the circle given.
That means color of choice represented by the quarter of the circle will be the color liked by one fourth students.
In the figure attached, BLUE color is the choice of one fourth students in the class.
b). Area represented by purple, green and other colors is a quarter of the circle.
If we divide this quarter into five equal sections, then the total of purple and green will be [tex]4\times \frac{1}{5}[/tex] of the the quarter of the circle.
Measure of the angle defined by purple or green sections = [tex]\frac{4}{5}\times 90[/tex]
= 72°
Percentage of the students who preferred purple or green = [tex]\frac{72}{360}\times 100[/tex]
= 20%
Answer:
blue
20%
Step-by-step explanation:
Chen is bringing fruit and veggies to serve at an afternoon meeting. He spends a total of $28.70 on 5 pints of cut veggies and 7 pints of cut fruit. The food cost is modeled by the equation 5 v plus 7 f equals 28.70, where v represents the cost of one pint of cut veggies and f represents the cost of one pint of cut fruit. If the cost of each pint of fruit is $2.85, what is the approximate price of a pint of veggies?
Answers
Answer:
(7 x 2.85) + 5v = 28.70. 19.95 + 5v = 28.70. 5v = 28.70 - 19.95. 5v = 8.75. v = 8.75/5. v = 1.75. A pint of veggies costs $1.75.
A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles. HINT [See Example 7.] How many sets of seven marbles include at least one yellow one but no green ones
Answers
Answer: 8
Step-by-step explanation:
Given: A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles.
Total marbles other than green = 8
Total marbles other than green and yellow = 6
Then the number of sets of seven marbles include at least one yellow one but no green ones:-
[tex]^{2}C_1\times^{6}C_6+ ^2C_2\times^6C_5\\\\= 2\times 1+1\times6\\\\=2+6=8[/tex]
Number of sets of seven marbles include at least one yellow one but no green ones = 8
The length of a rectangle is three times its width. If the perimeter of the rectangle is 160 cm, what are the dimensions of this rectangle?
Answers
Answer:
The dimensions or Area of the rectangle is 1200cm².
Use the following conversions to answer the question.
60 seconds = 1 minute
60 minutes = 1 hour
24 hours = 1 day
How many minutes are there in a week?
A. 420
B. 1,400
C. 10,080
D. 604,800
Answers
Answer:
C. 10,080
Step-by-step explanation:
We can multiply to find how many minutes there are in 1 day.
24 * 60 = 1,440
Now, we can multiply that value by 7 to find out how many minutes there are in 1 week.
1,440 * 7 = 10,080
Best of Luck!
32. Identify all real and non-real zeros of the function f(x) = x^3 + 5x^2 + 3x + 15.
options:
A. x = 0, −5, 1.7i, −1.7i
B. x = 0,−5, 1.7i
C. x = −5, 1.7i, −1.7i
D. x = 0,−3, −5
Answers
Answer:
x = -5 or x = i sqrt(3) or x = -i sqrt(3)
Step-by-step explanation:
Solve for x:
x^3 + 5 x^2 + 3 x + 15 = 0
The left hand side factors into a product with two terms:
(x + 5) (x^2 + 3) = 0
Split into two equations:
x + 5 = 0 or x^2 + 3 = 0
Subtract 5 from both sides:
x = -5 or x^2 + 3 = 0
x = (0 ± sqrt(0^2 - 4×3))/2 = ( ± sqrt(-12))/2:
x = -5 or x = sqrt(-12)/2 or x = (-sqrt(-12))/2
sqrt(-12) = sqrt(-1) sqrt(12) = i sqrt(12):
x = -5 or x = (i sqrt(12))/2 or x = (-i sqrt(12))/2
sqrt(12) = sqrt(4×3) = sqrt(2^2×3) = 2sqrt(3):
x = -5 or x = (i×2 sqrt(3))/2 or x = (-i×2 sqrt(3))/2
(2 i sqrt(3))/2 = i sqrt(3):
x = -5 or x = i sqrt(3) or x = (-2 i sqrt(3))/2
(2 (-i sqrt(3)))/2 = -i sqrt(3):
Answer: x = -5 or x = i sqrt(3) or x = -i sqrt(3)
Answer:
C. x = −5, 1.7i, −1.7i
Step-by-step explanation:
Quick answer:
C. x = −5, 1.7i, −1.7i
explanation:
C. is the only answer option that does NOT have 0 as a root, which is impossible, because there is a constant term, which means that all roots are non-zero. In other words, we cannot extract x as a factor.
Complete answer:
All odd degree polynomials have at least one real root.
By the real roots theorem, we know that
if there is a real root, it must be of the form [tex]\pm[/tex]p/q where q is any of the factors of the leading coefficient (1 in this case) and p is any factor of the constant term d (15 in this case).
Values of [tex]\pm[/tex]p/q are
On trial and error, using the factor theorem, we see that
f(-5) = 0, therefore -5 is a real root. By long division, we have a quotient of x^2+3 = 0, which gives readily the remaining (complex) roots of +/- sqrt(5) i
The answer is {-5, +/- sqrt(5) i}, or again,
C. x = −5, 1.7i, −1.7i
In a random sample of 205 people, 149 said that they watched educational television. Find the 95% confidence interval of the true proportion of people who watched educational television. Round intermediate answers to at least five decimal places.
Answers
Answer: Given a sample of 200, we are 90% confident that the true proportion of people who watched educational TV is between 72.1% and 81.9%.
Step-by-step explanation:
[tex]\frac{154}{200} =0.77[/tex]
[tex]1-0.77=0.23[/tex]
[tex]\sqrt{\frac{(0.77)(0.23)}{200} }[/tex]=0.049
0.77±0.049< 0.819, 0.721
It takes a graphic designer 1.5h to make one page of a website. Using a new software, the designer could complete each page in 1.25h, but it takes 8h to learn the software. How many web pages would the designer have to make in order to save time using the new software?
Answers
Answer:
33 web pages (at least)
Step-by-step explanation:
We can set up an inequality to represent this, where x represents the number of web pages made.
1.5x > 1.25x + 8
1.5x represents the number of hours it will take normally, and 1.25x + 8 represents the time with the new software. 1.5x (amount of hours using old software) needs to be larger than the time it takes with the new software.
Solve for x:
1.5x > 1.25x + 8
0.25x > 8
x > 32
So, the designer would have to make at least 33 pages.
The number of web pages would the designer have to make in order to save time using the new software will be 33 web pages (at least).
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
We can set up an inequality to represent this, where x represents the number of web pages made.
1.5x > 1.25x + 8
The time with the new software is represented by 1.25x + 8 and the normal time is represented by 1.5x. The number of hours spent using the old software must be 1.5 times greater than the time spent using the new product.
Solve for x:
1.5x > 1.25x + 8
0.25x > 8
x > 32
Therefore, the number of web pages would the designer have to make in order to save time using the new software will be 33 web pages (at least).
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Triangle DEF has sides of length x, x+3, and x−1. What are all the possible types of DEF?
Answers
Triangle DEF is scalene
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The triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.
What is a scalene triangle?A scalene triangle is a type of triangle which have all the sides to be unequal and similarly, all the angles will also be unequal to each other.
Given that:-
Triangle DEF has sides of length x, x+3, and x−1it is given that all the sides of the triangle are x, x+3, and x−1 we can clearly see that for any value of x all the three sides will have different values. we can conclude from this that the triangle DEF is a scalene triangle.
Therefore triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.
To know more about the scalene triangle follow
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- Which of the following is the correct distance between the points (-5, 3) and (7,8)?
Answers
Answer:
13 units
Step-by-step explanation:
(x₁,y₁) = (-5 , 3) & (x₂ , y₂) = (7 ,8)
[tex]Distance = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}} \\[/tex]
[tex]= \sqrt{(7-[-5])^{2}+(8-3)^{2}} \\\\= \sqrt{(7+5)^{2}+(8-3)^{2}} \\\\= \sqrt{(12)^{2}+(5)^{2}}\\\\=\sqrt{144+25}\\\\=\sqrt{169}\\\\= 13[/tex]
A prism and two nets are shown below: Prism 1 E 3 Net A Net Part A: Which is the correct net for the prism? Explain your answer. (2 points) Part B: Write the measurements of Sides AB. BC, and CD of the correct net. (4 points) Part C: What is the surface area of the prism? Show your work. (4 points)
Answers
Answer:
A) Net A (see explanation)
B) AB = 3 in. | BC = 5 in. | CD = 7.2 in.
C) SA = 98.4 in²
Step-by-step explanation:
Part A
Net A is the correct net for the prism. If you look at the way the folds are, the flaps on the top and bottom would fold up to make the side of the prism. On net B, the flaps wouldn’t fit the shape correctly.
Part B
AB = This is the height of the prism.
= 3 in.
BC = This is the slant on the front of the prism.
= 5 in.
CD = This is the length of the prism.
= 7.2 in.
Part C
* First we’ll solve for the two triangles. They are the same shape and size, so we just need to solve one then duplicate it.
One triangle:
A = 1/2bh
= 1/2 (4) (3)
= 6 in²
Back rectangle:
A = bh
= 7.2 (3)
= 21.6 in²
Front rectangle:
A = bh
= 7.2 (5)
= 36 in²
Bottom rectangle:
A = bh
= 7.2 (4)
= 28.8 in²
Total:
A = 6 + 6 + 21.6 + 36 + 28.8
= 98.4 in²