Answer:
(f+g)(x) = x - 7
Step-by-step explanation:
(f+g)(x) tells you to add the functions together. It means
f(x) + g(x)
= -3x - 5 + 4x - 2
combine like terms.
= 4x-3x - 5 - 2
= x - 5 - 2
simplify.
= x - 7
(f+g)(x) means
f(x) + g(x)
= x - 7
5) Can you give some real world examples (at least two for each) of positive and negative slope?
The positive slope is tilted towards the right on a coordinate plane and the negative slope is tilted towards the left on the coordinate plane.
What is the positive and negative slope?When two variables have a positive slope, it means that they are positively correlated; that is, when x rises, y rises as well, and when x falls, y falls as well. A line on a line graph that has a positive slope rises as the line advances from left to right.
A line that slopes downward from left to right is said to have a negative slope. In other words, the rise-to-run ratio of the line is negative.
The graph of the two real-life situations is attached with the answer below. In which the equation y = 4x means that the value of y is increasing by 4. Similarly, the equation for negative slope is y = -4x means that the value of y is increasing in opposite direction by factor 4.
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a cattle rancher wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle (see the figure below). there are 510 feet of fencing available to complete the job. what is the largest possible total area of the four pens?
The largest area of the rectangle is 6502.5 square feet.
Given that,
Using fence parallel to one of the rectangle's sides, a cattle rancher wants to surround a rectangular area and divide it into four pens (see the figure below). To finish the task, 510 feet of fencing are available.
We have to find what could the four pens' combined total area be.
We know that,
The rectangular shape's length is l and its width is b.
Total fencing= 2l + 5b=510 feet
2l +5b =510 feet
We can write as,
l=1/2(510-5b)
Total area of the rectangle is length into breath
A(b) = l × b
A(b) = 1/2(510-5b)×b
A(b)= 1/2(510b -5b²)
For maximum area
A'(b)=0
1/2(510b -5(2b))=0
b=51
We get l as
l = 1/2(510-5b)
l = 1/2(510-5(51))
l = 127.5
Total area of the rectangle is 127.5 × 51
Total area of the rectangle is 6502.5 square feet.
Therefore, The largest area of the rectangle is 6502.5 square feet.
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Which statements are true about the ordered pair (5, -6) and the sys
[x+y=−1
3x - y = 21
Select each correct answer.
Select 3 correct answer(s)
The ordered pair (5, -6) is a solution to the first e
because it makes the first equation true.
The ordered pair (5, -6) is a solution to the secon
equation because it makes the second equation
The ordered pair (5, −6) is a solution to the first and second equations because it makes both equations true.
What are linear equations?In mathematics, a linear equation is one that may be written in the form where the variables are alphabets, and the coefficients are frequently real integers. An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
The given system of equations is
x + y = -1 ......(1)
3x - y = 21 ......(2)
Rewrite equation (1)
y = - x - 1 ......(3)
Put equation (4) in equation (3)
3x -(-x -1) = 21
3x + x + 1 = 21
4x = 20
x = 20/4
x = 5
Put x= 5 in equation (3)
y = - 5 - 1
y = - 6
So, both the options are correct, (5, -6) is the solution of both equations.
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A steel ball is melted down to make eight smaller identical balls. If the radius of the
original steel ball was 20 cm, calculate to the nearest millimetre the radius of each of the smaller balls.
The radius of each of the smaller balls is R = 2r.
Define volume of circle.You can use a tape measure, for instance, to directly measure the distance around the sphere's widest point. The radius of this circle, which serves as the sphere's circumference, is one. A circle's circumference is computed as 2 x x radius. Since the cross-section of the sphere is a circle, the volume in this case is dependent on the diameter of the sphere's radius. The area or region of a sphere's outer surface is known as its surface area. We can use the following formula to get the volume of a sphere whose radius is "r": A sphere's volume is equal to 4/3r³.
Given,
A steel ball is melted down to make eight smaller identical balls. If the radius of the original steel ball was 20 cm:
Let the spherical ball's radius be R.
And with r being the radius of 8 similar balls,
According to the inquiry,
Volume of 8 similar balls = the volume of a larger sphere
3/4πR³ = 8 × 3/4πr³
R³ = 8r³
R = 2r
The radius of each of the smaller balls is R = 2r.
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Using the velocity, the rocket reaches its maximum height at 3.25 seconds.
In the given question we have to find the maximum height at the rocket reaches.
From the question; a toy rocket is shot vertically into the air from a launching pad 5 feet above the ground with an initial velocity of 104 feet per second.
The height h in feet of the rocket above the ground at t seconds after launch is given by the function h(t)= -16t^2+104t+5.
As we know that at the maximum height, the velocity will be zero.
So the given function of the heigth is
h(t)= -16t^2+104t+5
Velocity(v) = dh(t)/dt = -32t+104
As the maximum height v=0
-32t+104 = 0
Subtract 104 on both side, we get
-32t= -104
Divide by -32 on both side
t= 3.25 seconds
Hence, the rocket reaches its maximum height at 3.25 seconds.
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Cual es la respuesta de:
6(-?)+1=-47
The value of missing number is 8.
What are Integers?Integers come in three types:
Zero (0)Positive Integers (Natural numbers)Negative Integers (Additive inverse of Natural Numbers)Given:
6(-?)+1=-47
let the unknown value be x.
6(-x ) + 1= -47
Now, Subtract 1 from both side
-6x + 1 - 1= -47 - 1
-6x = -48
x= -48/(-6)
x = 8
Hence, -6(8) + 1 = -47.
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3. Consider the right triangle below in which a = 5 and b = 5.
A. Use the Pythagorean Theorem to solve for c.
Show your work!
B. What is the value of c rounded to the nearest hundredth?
C. What is the value of c in simplified radical form?
Answer:
Consider the right triangle below: State the Pythagorean Theorem as it relates to the above triangle. List the trig identities as they relate to the triangle above. Now suppose hypotenuse C represents a vector R, while sides B and A represent vector components Rx and Ry respectively. Redraw the triangle with the new labels below. Using Pythagorean Theorem, derive the equation for R.
can yall please help
1. The pairs of polygons are similar.
2. The pairs of polygons are not similar.
3. The missing measure is of x = 5.2.
4. The missing measure is of x = 16.
5. The value is AB = 6.
6. The perimeter of the yellow tile is of 240 cm.
7. The value is DF = 0.75.
What are similar polygons?Similar polygons are polygons that share these two following features:
Congruent angles.Proportional side lengths.Hence, for itens 1 and 2, we have that:
1. The pairs of polygons are similar, as the side lengths are proportional.2. The pairs of polygons are not similar, as the side lengths are not proportional, as the ratio of 6 and 9 is different of the ratio of 3 and 4.For item 3, the side lengths are proportional, hence:
x/2.6 = 8/4
x/2.6 = 2
x = 2 x 2.6
x = 5.2.
Same as item 4, hence:
x/10 = 9.6/6
x/10 = 1.6
x = 16.
For item 5, considering the equivalent side lengths, we have that:
AB/8 = 12/16
AB/8 = 3/4
AB = 24/4
AB = 6.
The perimeter of the yellow tile is of 240 cm in item 6, as the ratio between the side lengths is of 3, hence the ratio of the perimeters will also be of 3, then:
3 x 80 cm = 240 cm.
For item 7, we have that:
DF/3.4 = 2.25/9
DF = 3 x 2.25/9
DF = 0.75.
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Answer:
t =2.45s
Step-by-step explanation:
H=-16t2+96t
then, -16t2= -96t
divide both sides by 16
-16t2/16 = -96t/16
-t2 = -6
t2=6
t=√6
t=2.45
a square matrix is nilpotent if for some positive integer . let be the vector space of all matrices with real entries. let be the set of all nilpotent matrices with real entries. is a subspace of the vector space ?
An matrix A is a nilpotent matrix if there exists a positive integer k such that Ak is the zero matrix.
What is nilpotent matrix?A nilpotent matrix in linear algebra is a square matrix N such thatfor some positive integer kk. The index of occasionally the degree of the smallest such k A nilpotent transformation, more generally speaking, It is a linear transformation of a vector space such that Lk=0 for some positive integer. Both of these ideas are specific examples of the more basic idea of nilpotence, which is applicable to rings' constituent parts.acc to our question-
When n=1, the only 1×1 nilpotent matrix is (0). Thus U={(0)} and it is a subspace of VIn this case, we prove that the set U of all 2×2 nilpotent matrices is not a subspace of V.The set U is not a subspace because it is not closed under addition as the following example shows.Hence,An matrix A is a nilpotent matrix if there exists a positive integer k such that Ak is the zero matrix.
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HELP MEEE PLEASEEEEE
Answer:
XY = 12.4 cm
Step-by-step explanation:
a² + b² = c²
(4 cm)² + (XY)² = (13 cm)²
16 cm² + XY² = 169 cm²
XY² = 153 cm²
XY = √(153 cm²)
XY = 12.4 cm
Find X in all three problems below
The lengths for the missing side of each case, determined by the use of trigonometric functions, are listed below:
Case D: 50.513
Case E: 46.165
Case F: 2.052
How to determine missing lengths of right triangles by trigonometric functions
In this problem we have three cases of right triangles, each of which has an unknown side length. Each length can be found by using trigonometric functions. Now we proceed to determine it for each case:
Case D
tan 29° = 28 / x
x = 28 / tan 29°
x ≈ 50.513
The missing side length is approximately 50.513 units.
Case E
tan 18° = 15 / x
x = 15 / tan 18°
x ≈ 46.165
The missing side length is approximately 46.165 units.
Case F
cos 70° = x / 46
x = 46 · cos 70°
x ≈ 2.052
The missing side length is approximately 2.052 units.
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x+3y+z=-8
4x-2y-z=-9
5x+3y+2z=-19
please help me with this
That aint no question
Which point is located on the x-axis?
Answer:7
Step-by-step explanation:
yabba dabba doo
Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks.
Skill plans
At a candy store, Dean bought 2 kilograms of jelly beans and 3 kilograms of gummy worms
for $38. Meanwhile, Sue bought 3 kilograms of jelly beans and 3 kilograms of gummy worms
for $45. How much does the candy cost?
A kilogram of jelly beans costs $
and a kilogram of gummy worms costs $
The price of one kilogram of jelly bean and gummy worms is $7 and $8 respectively.
Let the price of 1 kilogram of jelly bean cost be x
and the price of 1 kilograms of gummy worms be y
Dean bought 2 kilograms of jelly beans and 3 kilograms of gummy worms
for $38
2x + 3y = 38......equation 1
Sue bought 3 kilograms of jelly beans and 3 kilograms of gummy worms
for $45
3x + 3y = 45........equation 2
Subtracting equation 2 from equation 1
2x + 3y - (3x + 3y) = 38 - 45
2x - 3x + 3y - 3y = -7
-x = -7
x = 7
2(7) + 3y = 38
14 + 3y = 38
3y = 24
y = 8
Therefore, the price of one kilogram of jelly bean and gummy worms is $7 and $8 respectively.
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help meeeeeeeeeeeeeeeeee please
Answer:
Step-by-step explanation:
x² + (x + 2)² = (x + 3)²
x² + x² + 4x + 4 = x² + 6x + 9
x² - 2x - 5 = 0
[tex]x_{1}[/tex] = [tex]\frac{-(-2)+\sqrt{4+20} }{2}[/tex] = 1 + √6 ≈ 1 + 2.45 = 3.45 units
[tex]x_{2}[/tex] = [tex]\frac{-(-2)-\sqrt{4+20} }{2}[/tex] = 1 - √6 < 0 can not be solution of the given problem.
x ≈ 3.4 units
x + 2 ≈ 5.4 units
x + 3 ≈ 6.4 units
examples of linear equation
Calculate (8.42 x 109) − (2.35 x 108).
Answer:
Step-by-step explanation:
663.98
Answer: 663.98
Step-by-step explanation:
(8.42*109)=917.78
(2.35*108)=253.8
917.78-253.8=663.98
what is the future amount of 12,000 invested for 5 years at 14% compounded monthly?
The total amount accrued, principal plus interest, with compound interest on a principal of $12,000.00 at a rate of 14% per year compounded 12 times per year over 5 years is $24,067.32.The amount of the initial loan, or principal, is multiplied by one plus the annual interest rate raised to the number of compound periods minus one to determine compound interest.
what is compound interest?To begin, change R from a percentage to a decimal, using the formula:
r = R/100 r = 14/100
r = 0.14 rate per year;
Next, find A by solving
A = P(1 + r/n)nt A = 12,000.00(1 + 0.14/12)(12). (5)
A = 12,000.00(1 + 0.011666666666667)(60) (60)
A = $24,067.32
Summary: The total amount accrued, principal plus interest, with compound interest on a principal of $12,000.00 at a rate of 14% per year compounded 12 times per year over 5 years is $24,067.32.
The amount of the initial loan, or principal, is multiplied by one plus the annual interest rate raised to the number of compound periods minus one to determine compound interest. You will then be left with the loan balance plus compound interest.
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(x+5)-(x - 5)² for x = 3
six thousand seven hundred and fifty (6750) people who were free of disease x were enrolled in a cohort study in 1985 and followed with annual exams and interviews through 1995. exposure to factor a was determined at study enrollment and the participants were followed until 1995 to observe new cases of disease x. data from the study at the end of follow-up are shown in the table (below). what is the incidence rate of disease x among persons exposed to factor a?
Option A is the correct choice (0.04)
The incidence rate of disease x among persons exposed to factor a is 0.04
The frequency of a particular incident over a predetermined time period is measured by the incidence rate or incidence. In the corporate world, sampling, surveys, and product testing can all be used to calculate an incidence rate.
Because 120 divided by the total number of exposed people yields the occurrence rate for disease X among those who have been exposed.
The incidence rate would be 4 per 100 people if multiplied by 100, however, this statistic is not specifically specified.
Therefore, those who were exposed to factor a had an incidence risk of disease x of 0.04
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COMPLETE QUESTION:
6,750 people who were free of disease X were enrolled in a cohort study in 1985 and followed by annual exams and interviews through 1995. Exposure to factor A was determined at study enrollment and the participants were followed until 1995 to observe new cases of disease X. Data from the study at the end of the follow-up are shown in the following table. What is the incidence rate of disease X among persons exposed to factor A? Exposure to Factor A People with Disease X People without Disease X Not Exposed 30 3,720 Exposed 120 2,880
Select one:
a. 0.04
b. 0.19
c. 0.25
d. 4.00
e. 5.17
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The function has a maximum value of 30 at x = 3.
Given Function:
f(x) = -3+18x+3
here a = -3 , b = 18 , c = 3
a is negative so it has maximum value
x = -b/2a
= -18/2*(-3)
= -18/-6
= 18/6
= 3
f(x) = -3* + 18*3 + 3
= -3*9+54+3
= -27+54+3
= 27+3
= 30
Therefore the function has a maximum value of 30 at x = 3.
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The equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.
In the given question we have to find the equation of parabola in the form of f(x)=a(x-h)^2+k
The given function is f(x)=7x^2.
The given vertex = (3,5)
The equation of the parabola with the vertex of (h,k) is
y=a(x-h)^2+k
On comparing we get; a=7, h=3, k=5
Now putting the value
f(x)=7(x-3)^2+5
Hence, the equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.
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consider the polynomial function p given by p(x)=5x^3+6x^2+4x
evaluate the function at x=-5 and x=15
Answer:
p(-5) = -495p(15) = 18285Step-by-step explanation:
You want the value of p(x)=5x^3+6x^2+4x for x=-5 and x=15.
Horner formWriting a polynomial in Horner form can simplify evaluation.
p(x) = ((5x +6)x +4)x
p(-5)p(-5) = ((5(-5) +6)(-5) +4)(-5) = (-19(-5) +4)(-5) = 99(-5) = -495
p(15)p(15) = ((5(15) +6)(15) +4)(15) = (81(15) +4)(15) = 1219(15) = 18285
One leg of a right triangle is 8 units long, and its hypotenuse is 14 units long. What is the length of the other leg? Round to the nearest whole number.
The other leg has its length to be 11.49 units
How to determine the length of the other leg distance?To calculate the length of the other leg distance, we make use of the Pythagoras theorem
Mathematically, this theorem is represented by:
w² = y² + z²
Such that x = hypotenuse, y = leg and z = other leg
From the question, we have the following parameters
w = 14, y = 8 and z = the other leg
Substituting these values in w² = y² + z²
14² = 8² + y²
Evaluate the exponents
196 = 64 + y²
Evaluate the like terms
y² = 132
Take the square roots of both sides
y = 11.49
Hence, the length of the other leg is 11.49 units
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Answer: 11 units
Step-by-step explanation: i took the test and got it right
What is the interquartile range of the data set???
Answer:
14.
Step-by-step explanation:
The interquartile range (IQR) contains the second and third quartiles or the middle half of your data set.
Please give brainliest, will be appreciated.
Answer:
The interquartile range (IQR) measures the spread of the middle half of your data.
Complete the proof that
With the help of angles we can say that ∠HJI=∠FJG.
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created.The vertex of an angle is the location where two points come together.The Latin word "angulus," which means "corner," is where the term "angle" originates.Vertex: The intersection of two lines or sides at an angle is called a vertex. In the diagram, O is the vertex.Arms: The angle's two sides linked at a single end. The arms of an angle are OA and OB.Initial Side: A straight line from which an angle is drawn, sometimes referred to as the reference line. The reference line is OB.The side that the angle measurement is done up to is known as the terminal side. OA is the terminal side in the diagram that is shown below.Acc to our question-
∠HJI=∠FJG=180 , they are forming linear pairs.due to transitive property of inequality we can say that-they both are equal and congruent.Hence, ∠HJI≅∠FJG are equal and congruent.
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Miguel took his son to college in boulder, colorado, 300mi from their hometown. on his way home, he was slowed by a snowstorm so that his speed was 10mph less than when he was driving to boulder. his total driving time was 11hr. how fast did miguel drive on each leg of the trip?
Miguel drove at a speed of 60 mph in the first part of the trip and at a speed of 50 mph in the second part of the trip.
Let the speed while dropping his son to college be x mph
Therefore speed while returning is (x - 10) mph
The distance is 300 mi
Speed = Distance/Tie
or, Time = Distance/Speed
Hence the time taken during the first part of the journey = 300/x hrs
and,
Time taken for the next part of the journey
= 300/(x - 10) hrs
It is given that the total time taken was 11 hrs
Hence we get
300/x + 300/(x - 10) = 11
or, (300x - 3000 + 300x) / x(x - 10) = 11
or, (600x - 3000) / (x² - 10x) = 11
or, 600x - 3000 = 11x² - 110x
or, 11x² -710x + 3000 = 0
Applying the shreedharacharya rule gives us
x = (710 ± √(710² -132000)/22)
x = 50/11 or x = 60
If x = 50/11 then x - 10 will be negative.
hence x = 60
Therefore Miguel drove at a speed of 60 mph in first half and 50 mph in second half.
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Compare and Explain: Are they equivalent?
$3 for 6 bagels; $9 for 24 bagels
Answer: No
Step-by-step explanation: You want to find the unit rate for each bagel. 6/3 is 2 dollars, so each bagel is going to cost 2 dollars. If your getting 24 bagels for 9 dollars, 24/9 is 2 2/3 dollars for each bagel. 2 ≠ 2 2/3 so therefore, they're not the same.
Is 4x + 7y divisible by 2?
⇒ Is 4x + 7y divisible by 2?⇔ This question simply is asking you if there is a possibility that you can take out the highest common factor of 2 in the expression 4x+7y.
⇒ We cannot take out the highest common factor of 2 in this expression since there is the term 7y that has the coefficient 7 which is NOT divisible by 2. the expression 4x+7y
cannot be written in the form a(b+c)
⇒∴ 4x + 7y is not divisible by 2
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