Answer:
The equation of line which is parallel to the given line is y = 3 x + k.
Step-by-step explanation:
The equation of the line is
y = 3 x - 8
Compare with the standard equation
y = mx + c
The slope of line is
m = 3
So, the line parallel to the given line is
y = 3 x + k
where, k is any real number.
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If a function is continuous at a point, then it is differentiable at that point.
Answer:
See Explanation
Step-by-step explanation:
If a Function is differentiable at a point c, it is also continuous at that point.
but be careful, to not assume that the inverse statement is true if a fuction is Continuous it doest not mean it is necessarily differentiable, it must satisfy the two conditions.
the function must have one and only one tangent at x=cthe fore mentioned tangent cannot be a vertical line.And
If function is differentiable at a point x, then function must also be continuous at x. but The converse does not hold, a continuous function need not be differentiable.
For example, a function with a bend, cusp, or vertical tangent may be continuous, but fails to be differentiable at the location of the anomaly.Variables, in statistics, refer to:
A) characteristics of experimental units
B) data that has been collected
C) unknown quantaties
Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?
acute, because 62 + 102 < 122
acute, because 6 + 10 > 12
obtuse, because 62 + 102 < 122
obtuse, because 6 + 10 > 12
Answer:
C
Step-by-step explanation:
use Pythagorean theorem
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
c is the longest side
if [tex]a^{2}[/tex] + [tex]b^{2}[/tex] > [tex]c^{2}[/tex] then it's acute (greater than)
if [tex]a^{2}[/tex] + [tex]b^{2}[/tex] < [tex]c^{2}[/tex] then it's obtuse (less than)
if they are equal, then its a right triangle
[tex]6^{2}[/tex] + [tex]10^{2}[/tex] = [tex]12^{2}[/tex]
36 + 100 = 144
136 = 144
136 < 144 obtuse
The correct classification for this triangle is:
obtuse, because 6² + 10² < 12²
Option C is the correct answer.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
To determine the classification of a triangle based on its side lengths, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, we have a triangle with side lengths of 6 cm, 10 cm, and 12 cm. Checking the sum of the lengths of each pair of sides, we have:
6 + 10 = 16 > 12
6 + 12 = 18 > 10
10 + 12 = 22 > 6
Since all three pairs satisfy the triangle inequality theorem, the given side lengths do form a valid triangle.
Next, we can use the law of cosines to determine the measure of the largest angle in the triangle, which will allow us to classify it.
The law of cosines states that, for a triangle with side lengths a, b, and c, and the angle opposite c denoted as C, we have:
[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]
In this case, the side lengths are a = 6 cm, b = 10 cm, and c = 12 cm. Substituting these values into the formula and solving for cos(C), we get:
cos(C) = (6² + 10² - 12²) / (2 x 6 x 10)
cos(C) = -1/5
Since the cosine function is negative for angles between 90 and 180 degrees, we know that angle C is obtuse.
Therefore,
The correct classification for this triangle is:
obtuse, because 6² + 10² < 12²
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Select the correct answer.
What is the value of this expression when x=-6 and y=-2?
4(x + 3) - 2y
Answer:
-8
Step-by-step explanation:
Plug in the values of each variable:
4(-6 + 3) - 2(-2)
Use PEMDAS:
4(-3) - 2(-2)
-12 + 4
-8
Answer:
-8
Step-by-step explanation:
* means multiply
just plug in the values
4 ( -6 + 3 ) - (2 * -2)
use pemdas
so parenthesis first
4 * -3 - (-4)
then multiply
-12 - (-4)
-12 + 4
-8
Kyle built a tree house 4 ft. by 6 ft. What was the area of the tree house?
2m^2-5m-3=0 by factorization
Step-by-step explanation:
It is so simple Hope u understand
Answer:
Step-by-step explanation:
Sum = -5
Product = 2*(-3) = -6
Factors = -6 , 1 {-6 + 1 = -5 & -6 *1 = -6}
2m² - 5m -3 = 0
2m² - 6m + m -3 = 0
2m(m - 3) + (m -3) = 0
(m -3)(2m + 1) = 0
m - 3 = 0 or 2m + 1 = 0
m = 3 or 2m = -1
m = -1/2
Ans: m = 3 , (-1/2)
I reallyyy need this first partt helpp!
Answer:
[tex]{ \bf{c(g) = 5g + 3}} \\ { \bf{c(6) = 5(6) + 3}} \\ { \boxed{ \tt{c(6) = 33}}}[/tex]
This year, Carlos planted 6 more than one-third of the cucumber plants he planted last year. How many cucumber
plants did he plant this year if last year he planted 12 plants?
6
9
10
12? PLEASE HELP SMB
Answer:
10 plants
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
He planted 10 this year because last year he planted 12, and 1/3 of that is 4. He planted 6 more than that this year, so 4+6=10.
The projected worth (in millions of dollars) of a large company is modeled by the equation w = 221(1.06) t. The variable t represents the number of years since 2000. What is the projected annual percent of growth, and what should the company be worth in 2009?
Answer:
Step-by-step explanation:
Well the percent of growth is 6%
The reason is because when we look at a exponential function, if the number in the percent is more than 1 subtract the number from 1 and multiply it by 100 thats your percent
Now to find the company's value in 2009 or 9 years after 2000
we just replace the variable representing time "t" for 9
221(1.06^9)= 373.37484994
the value of the company in 9 years is 373.37484994 (in million dollars)
the percentage of annual growth is 6%
pls give brainliest
question 3 help pls in algebra
Answer:
50
Step-by-step explanation:
simplify the radical by breaking the redicand up into a product of known factors, assuming positive real numbers.
Find the value of x.
A. About 57.6
B. About 42.6
C. About 12.6
D. About 27.6
Answer:
about 27.6
Step-by-step explanation:
The sum of interior angles for this rectangle is 1080
119+140+124+6x+132+132+102 = 1080 add like terms
749 + 12x = 1080 subtract 749 from both sides
12x = 331 divide both sides by 12
x = 27.6 approximately
Question
The quotient of a number and 5 has a result of 2. What is the number?
Answer:
10.
Step-by-step explanation:
Answer:
The number is 10.
Step-by-step explanation:
x/5 = 2
Multiply both sides by 5.
5 * x/5 = 5 * 2
x = 10
Answer: The number is 10.
What is the mean change in the forecasted low temperatures over the next 7 days? Remember, this can be found by averaging the values in the Difference column for the low temperatures. If your answer is not an integer, explain what two integers your answer is between.
LOW TEMPTURES:
WEDNESDAY-79
THURSDAY- 79
FRIDAY- 73
SATURDAY- 73
SUNDAY - 73
MONDAY- 73
TUESDAY- 75
Answer:
75
Step-by-step explanation:
WILL GIVE BRAINLIEST!!!
CR and DS are perpendiculars dropped from AB to PQ, and AB is perpendicular to CR and DS. If CR = DS, which statement must be true?
A. m
B. m
C. m
D. m
E. m
Answer:
The answer is C.) m∠RCD = m∠ACD ÷ 2
RCD = ACD divided by two.
RCD = 90 degrees
ACD ÷2 = 180÷2 = 90 degrees.
So, your answer is C.
Hope this helped. Have a grey day!
Answer:
C. m∠RCD = m∠ACD ÷ 2
Hope this helps!
Step-by-step explanation:
I got it right.
how do you get sin theta
PLS HELP ASAP
what is the equation for the line of symmetry for the function below?
y-1=-2(x+3)^2
A. x=3
B. x=-2
C.x=-3
D.y=7
I THINK ITS C BUT IM NOT SURE
Five students are lined up in a row. How
many arrangements could be made if
the position of the last boy remains
unchanged?
(WAEC)
Step-by-step explanation:
16 arrangement can be done
The 24 arrangements could be made if the position of the last boy remains unchanged.
Arrangement
Arrangement is a plans or preparations for a future event.
How to solve this problem?The steps are as follow:
Given, Five students are lined up in a rowWe have make the arrangment such that last boy should remain unchangedTo find how many arrangements are possible in a set of objects, use the formula below, where x is the number of objects.x! , where,! is factorial
x! is equal to x*(x-1)*(x-2)*(x-3)*…(x-(x-1))
In this case we have to take x equal to 4 because last boy to remain unchanged∴ 4*3*2*1 = 24 arrangments
Therefore total 24 arrangements could be made if the position of the last boy remains unchanged.
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If EF = 117 , FG = 100, EG = 94, IJ = 40 , and HJ = 37.6 , find the perimeter of HIJ. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.
Answer:
124.4
Step-by-step explanation:
Perimeter of ∆HIJ = IJ + HJ + HI
IJ = 40
HJ = 37.6
HI = ?
Let's find HI
∆HIJ and ∆EFG are similar. Since they have equal corresponding angles. Therefore, the ratio of their corresponding sides would be equal.
Thus:
EF/HI = FG/IJ
EF = 117 (given)
HI = ?
FG = 100 (given)
IJ = 40 (given)
Plug in the values
117/HI = 100/40
117/HI = 2.5
117 = HI*2.5
117/2.5 = HI
HI = 46.8
✔️Perimeter of ∆HIJ = IJ + HJ + HI
= 40 + 37.6 + 46.8
= 124.4
what is the length of KM ? no links . HELP
Answer:
40 units
Step-by-step explanation:
9x-5=7x+7
9x-7x=7+5
2x=12
x=6
6x+4
6(6)+4
36+4
40
Help plsssssss ,it would mean a lot thankyou
Answer:
Part 1;
(0, 0)
Part 2;
(0, 2.5)
Step-by-step explanation:
Part 1
The given system of inequalities is presented as follows;
f(x) < x + 4; f(x) > -x - 3; and f(x) < 5
We check each of the points as follows;
The point (0, 0) in the inequality f(x) < x + 4, gives;
f(0) < 0 + 4
f(0) = 0 < (is less than) 0 + 4 = 4
Therefore, (0, 0) is a solution of the inequality f(x) < x + 4
The point (0, 0) in the inequality f(x) > -x - 3, gives;
f(0) < -0 - 3
f(0) = 0 > (is larger than) -0 - 3 = -3
Therefore, (0, 0) is a solution of the inequality f(x) > -x - 3
The point (0, 0) in the inequality f(x) < 5, gives;
f(0) < 5
f(0) = 0 < (is less than) 5
Therefore, (0, 0) is a solution of the inequality f(x) < 5
The point (-6, 0) in the inequality f(x) > -x - 3, gives;
f(-6) = -6 - 3 = 3
The point (-6, 0) with y = 0 < (is less than) f(-6) = 3, therefore (-6, 0) is not a solution to (not included in the graph of) the inequality f(x) > -x - 3 and therefore to the system of inequalities because at x = -6, the values of f(x) > -x - 3 are larger than 3
The point (-3, 4) in the inequality f(x) < x + 4, gives;
f(-3) = -3 + 4 = 1
The point (-3, 4) with y = 4 < (is larger than) f(-2) = 1, therefore (-3, 4) is not a solution to (not included in the graph of) the inequality f(x) < x + 4 and therefore to the system of inequalities because at x = -3, the values of f(x) < x + 4 are less than 1
The point (4, 6) is not a solution to (not included in the graph of) the inequality f(x) < 5 and therefore to the system of inequalities because f(x) is larger than 5 for all x
Therefore, the point which is part of the solution set of the system of inequalities is (0, 0)
Part 2
The given system of inequalities are, f(x) ≥ 2·x + 2; f(x) ≤ -4·x + 3; and f(x) ≤ 6·x + 5
Plotting the given system of inequalities on MS Excel the point which is part of the solution is given by points which are within the triangular intersection area of the three inequalities, with coordinates, (1/6, 7/3), (-3/4, 1/2), and (-1/5, 19/5)
Therefore, the points, (0, 0), (-2.5, 0) are not solutions because, the y-value of the solution area are all higher than the line y = 0
The point (0. 6.5) is not a solution because the points in the triangular solution area all have x-values lesser than x = 6.5
The point which is part of the solution by examination is the point (0, 2.5) which is a point between the lines y = 19/5 = 3.8, y = 1/2, x = -3/4, and x = 1/6.
Solve: 7x-12< 7( x-1)
X> 7
X < 5
all real numbers
no solution
Answer:
no solution
Step-by-step explanation:
7x-12<7x-7
-13<-7
no solution
65. A city has a population of 25,000. The population is expected to increase by 5.5% annually for the
next decade. (See Example 5)
a. Write a function that represents the
City Population
population y after t years.
УГ
40,000
35,000
30,000
25,000
b. Graph the function from part (a). Use the 20,000
graph to estimate the population after 4
15,000
years.
10,000
5000
0
0 1 2 3 4 5 6 7 8 t
Year
Population
Answer:
The answer will be 0.45%
Step-by-step explanation:
im right
Mrs.Carlyle bought a bag of peanuts for her children. When Phillip, Joy, Brent, abd Preston came home from school, they each took some peanuts from the bag.
QUICKLY!! We know that a triangle with side lengths x^2-1,2x and x^2+1 is a right triangle. Using those side lengths, find the missing triples and x-values.
Write the triples in parentheses, without spaces between the numbers, and with a comma between numbers. Write the triples in order from least to greatest.
Type the correct answer in each box.
x value--------------------pythagorean triple
3 ____________
________ (8,15,17)
5 ______________
__________ (12,35,37)
Answer:
[tex]\begin{array}{ccl}x \ value&&Pythagorean \ triple\\3&&(6, 8, 10)\\4&&(8, 15, 17)\\5&&(10, 24, 26)\\6&&(12, 35, 37)\end{array}[/tex]
Step-by-step explanation:
The given side lengths of the right triangle are;
x² - 1, 2·x and x² + 1
A Pythagorean triple are three numbers, a, b, and c, such that, we have;
a² + b² = c²
From the given side lengths, we have;
We note that (x² + 1) > (x² - 1)
(x² + 1) > 2·x for x > 1
Therefore, with (x² + 1) as the hypotenuse side, we have;
(x² - 1)² + (2·x)² = (x² + 1)²
Therefore, when the x-value is 3, we have;
(3² - 1)² + (2 × 3)² = (3² + 1)²
8² + 6² = 10²
The least is 6² = (2 × 3)², from (2·x)²
Therefore;
The Pythagorean triple is 6, 8, 10
The order of the triple is (2·x), (x² - 1), (x² + 1)
2) The x-value for the triple, (8, 15, 17), is obtained as follows;
The least, 8 = 2·x
∴ x = 8/2 = 4
The x-value = 4
3) The Pythagorean triple where the x-value = 5 is therefore;
(2·x), (x² - 1), (x² + 1), where x = 5 gives; (2×5 = 10), (5² - 1 = 24), (5² + 1 = 26)
Therefore, the Pythagorean triple where x = 5 is 10, 24, and 26
4) The x-value for the Pythagorean triple (12, 35, 37) is given by 12 = 2·x
Therefore, x = 12/2 = 6
Therefore, we get;
[tex]\begin{array}{ccl}x \ value&&Pythagorean \ triple\\3&&(6, 8, 10)\\4&&(8, 15, 17)\\5&&(10, 24, 26)\\6&&(12, 35, 37)\end{array}[/tex]
Write the equation for a parabola with a focus at (6,-4) and a directrix at y= -7
Given:
The focus of the parabola is at (6,-4).
Directrix at y=-7.
To find:
The equation of the parabola.
Solution:
The general equation of a parabola is:
[tex]y=\dfrac{1}{4p}(x-h)^2+k[/tex] ...(i)
Where, (h,k) is vertex, (h,k+p) is the focus and y=k-p is the directrix.
The focus of the parabola is at (6,-4).
[tex](h,k+p)=(6,-4)[/tex]
On comparing both sides, we get
[tex]h=6[/tex]
[tex]k+p=-4[/tex] ...(ii)
Directrix at y=-7. So,
[tex]k-p=-7[/tex] ...(iii)
Adding (ii) and (iii), we get
[tex]2k=-11[/tex]
[tex]k=\dfrac{-11}{2}[/tex]
[tex]k=-5.5[/tex]
Putting [tex]k=-5.5[/tex] in (ii), we get
[tex]-5.5+p=-4[/tex]
[tex]p=-4+5.5[/tex]
[tex]p=1.5[/tex]
Putting [tex]h=6, k=-5.5,p=1.5[/tex] in (i), we get
[tex]y=\dfrac{1}{4(1.5)}(x-6)^2+(-5.5)[/tex]
[tex]y=\dfrac{1}{6}(x-6)^2-5.5[/tex]
Therefore, the equation of the parabola is [tex]y=\dfrac{1}{6}(x-6)^2-5.5[/tex].
If A and B are independent events, P(A and B) =
Answer:
If A and B are independent events, then the events A and B' are also independent. Proof: The events A and B are independent, so, P(A ∩ B) = P(A) P(B). From the Venn diagram, we see that the events A ∩ B and A ∩ B' are mutually exclusive and together they form the event A.
Answer:
Step-by-step explanation:
Given A and B are independent events, P(A and B) = P(A)*P(B)
What is the equation of the line graphed below?
5
-5
5
(1, -3)
-5
O A. y = 3x
B. y=-3x
c. y=-5
D. y =
-X
Answer:
C: y=-3x
Step-by-step explanation:
Rise over run: in this case you go down so -3/1=-3
brainlest if correct !!!!!
Answer: C. x > 0
Step-by-step explanation:
It is an empty circle, meaning the value of 0 is not included in the inequality, so it's not ≤ or ≥.The arrow goes to the right, towards values greater than 0, therefore it is > and not <.The answer would be x > 0.
Answer:
C
Step-by-step explanation:
How do I write 4(3x+2)-9 in written form?
Answer:
12x-1
Step-by-step explanation:
First, you would have to distribute. Would mean to multiply the 4 with every number in the parenthesis.
4(3x+2)-9
12x+8-9
Now combine like terms
8-9 = -1
The answer is 12x-1
Step-by-step explanation:
4 times 3x+2 subtracted by9
hope it helps
stay safe healthy and happy.Are the lines parallel, perpendicular, or neither?
y = 7x +3
y = 1/7x - 5
Answer:
Neither (Answer)
Step-by-step explanation:
Comparing both the equations with slope-intercept form (y = mx + c), where 'm' is the (slope/gradient) and and 'c' is the (y-intercept).
If slopes are equal then the lines are parallelIf the product of slopes is equal to '-1' then lines are perpendicularOtherwise, lines are intersecting (Neither)Note: If the slopes are equal as well as the y-intercepts then they are same lines (overlapping) i.e lines are scaler multiple of each other.
Slope of line 1 = m1 = 7
slope of line 2 = m2 = 1/7
neither the slopes are equal nor the their product is equal to '-1'
