Answer:
the equation will be in the form of:
y = -x + b
To find be take any point on the line. Hence we have (5,1) which is the midpoint where the line meets.
Therefore, substitute (5,1) in the above equation:
1 = -5 + b
b = 6
So the question of the line will be:
y = -x + 6
I need help answering this question please!
Answer:
p(x) = x⁴ -7x³ +59x² -343x +490
Step-by-step explanation:
Each root is the zero of a binomial factor. That is, for root x = a, the polynomial has a factor (x -a). Complex roots come in conjugate pairs, so if there is a root 7i, there is also a root -7i.
__
The given roots mean the polynomial can be written in factored form as ...
p(x) = (x -2)(x -5)(x -7i)(x -(-7i))
We can combine multiply these factors together to simplify the polynomial.
p(x) = (x² -7x +10)(x² +49)
p(x) = x⁴ -7x³ +59x² -343x +490
_____
Additional comment
Combining the conjugate complex roots uses the special form for the factoring of the difference of squares.
a² -b² = (a -b)(a +b)
(x -7i)(x +7i) = x² -(7i)² = x² -49i² = x² +49 . . . . . where i = √(-1)
Find the area of this circle. Use 3 for pi
Answer:
243 in²
Step-by-step explanation:
Diameter = 18 in
Radius ( r ) = Diameter / 2 = 18 / 2
r = 9 in
π = 3
To find : Area of circle ( A )
Formula : -
A = πr²
A = 3 x 9²
= 3 x 9 x 9
A = 243 in²
Can someone help me
5b^2+4=10b
Answer:
b = 5 ± √5 / 5
Step-by-step explanation:
Given :
5b² + 4 = 10bSubtract 10b from both sides :
5b² - 10b + 4 = 10b - 10b5b² - 10b + 4 = 0Splitting the middle term :
b = 10 ± √100 - 4(5)(4) / 10b = 10 ± √20 / 10b = 10 ± 2√5 / 10b = 5 ± √5 / 5If x and y vary inversely and x = -9 when y = -30, what is the constant of variation
Answer:
270
Step-by-step explanation:
x = k/y This is an inverse relationship with k = constant of proportion (or variation)
-9 = k/(-30)
k = -9 * -30 = 270
Answer:
Constant of variation = 270.
Step-by-step explanation:
y = k/x
-30 = k / -9
k = -30 * -9
k = 270
Solve the following system of equations algebraically.
x+y=27
y=x+3
*first person to get it right gets brainliest :)
Answer:
(x, y) = (12, 15)
Step-by-step explanation:
The given expression for y suggests that using substitution would be a good choice for the method of solution.
__
x +(x +3) = 27 . . . . substitute for y using the second equation
2x = 24 . . . . . . . subtract 3
x = 12 . . . . . . . divide by 2
y = 12 +3 = 15 . . . . use the second equation to find y
The solution is (x, y) = (12, 15).
-9<2x+1<5
A. -5
B. -4
C. 4>x>-3
D. 5>x>-2
Answer:
B
Step-by-step explanation:
1.
- 9 < 2x + 1
- 10 < 2x
X > - 5
2.
2x + 1 < 5
2x < 4
X < 2
An empty lorry weighs 3500kg. It weighs 7250 kg when loaded with 50 bags of coffee .What is the average mass of each bag ?
Answer:
The average mass of one coffee bag is 75kg.
Step-by-step explanation:
The lorry on its own weighs 3500kg.
If it weighs 7250kg alongside coffee bags, we can make the assumption that to find the total mass of the coffee bags, we must take the combined total and subtract the lorry's weight from it.
7250kg subtract 3500kg is 3750kg.
There are 50 coffee bags, so this is the mass of all 50.
If we want to find the mass of one coffee bag, we have to divide the mass of 50 coffee bags by 50.
3750kg divided by 50 is 75kg.
The average mass of one coffee bag is 75kg.
somebody please help me?
The events A and B are independent events, and the values of P(A) and P(B) are 7/12 and 1/2, respectively
The value of P(A)The event A is given as:
A : Sum greater than 6
In the sample space of a roll of two dice, there are 21 outcomes that are greater than 6, out of a total of 36 outcomes
This means that:
P(A) = 21/36
Simplify
P(A) = 7/12
The value of P(B)The event B is given as:
B : Sum is divisible by 2
In the sample space of a roll of two dice, there are 18 outcomes that are divisible by 2, out of a total of 36 outcomes
This means that:
P(B) = 18/36
Simplify
P(B) = 1/2
Hence, the probability values of P(A) and P(B) are 7/12 and 1/2, respectively
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Does anybody know this? I got told it was 828.8 by someone and it was wrong.Find the surface area of the square pyranid
Answer:
800 ft²
Step-by-step explanation:
The total surface area of a square-base pyramid is given by the formula ...
A = s(s +2h) . . . . . . where s is the side length, h is the face slant height
In this problem, we need to find the slant height of a face in order to use this formula.
__
slant heightThe distance from the middle of one edge of the base to the peak of the pyramid is the slant height of a face of the pyramid. It is the hypotenuse of a right triangle whose legs are the pyramid height, and half the width of the base. For this pyramid, that is a right triangle with legs 15 and 8.
The Pythagorean theorem is used to find the hypotenuse of that triangle:
c² = a² +b² . . . . square of hypotenuse = sum of squares of legs
c² = 15² +8² = 225 +64 = 289
c = √289 = 17
The slant height of a face of the pyramid is 17 ft.
total areaThe area formula tells us the total surface area is ...
A = s(s +2h)
A = (16 ft)(16 ft + 2×17 ft) = (16 ft)(50 ft)
A = 800 ft²
The total surface area is 800 square feet.
A class contains 5 girls and 5 boys. Two are selected for a class committee. What is the probability that a girl and boy are selected?
Answer:
20/39.
Step-by-step explanation:
There are a total of 13 students.
Prob(Boy is selected) = 8/13
Prob(Girl is then selected) = 5/12
So probability ( Boy selected then a girl) = 8/13 * 5/12 = 10/39
- and the probability of Girl then a boy selected is also 10/39
So the required probability = 2 * 10/39
= 20/39.
PLEASE HELP ILL MARK BRAINEST!!!
Answer:
0,5
Step-by-step explanation:
label the quadrants IV
Answer:
Quadrant IV is always in the bottom right corner.
P+d= 19 9p+ 5.50d= 150 solve the system of equations , step by step
Answer:
d=6 & p=13
Step-by-step explanation:
1. P+d=19
×9
2. 9p +5.50d=150
×1
9p+9d=171
-
9p +5.50d=150
3.5d=21
d=6
Substituting d=6 in 1.
P+6=19
P=13
73-74 express the limit as a definite integral.
73. [tex]\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{i^{4}}{n^{5}}[/tex] [hint: consider [tex]$f\mleft(x\mright)=x^4$.\rbrack[/tex]
Pull out a factor of 1/n from the summand and the result follows.
[tex]\displaystyle \lim_{n\to\infty} \sum_{i=1}^n \frac{i^4}{n^5} = \lim_{n\to\infty} \frac1n \sum_{i=1}^n \left(\frac in\right)^4 = \boxed{\int_0^1 x^4 \, dx}[/tex]
bonjour je n'y arrive pas, quelqu'un pourrait m'aider s'il vous plaît ?
Answers:
BD = 6
AC = 7.5
=================================================
Work Shown:
BD/BA = BE/BC
x/9 = 4/6
6x = 9*4
6x = 36
x = 36/6
x = 6
BD = 6
---------
DE/AC = BE/BC
5/y = 4/6
5*6 = y*4
30 = 4y
4y = 30
y = 30/4
y = 7.25
AC = 7.5
Which expression could represent the phrase shown? (1 point)
"Add 4 and 5, divide the sum by 3, and then add the product of 6 and 5"
Group of answer choices
4 + 5 ÷ 3 + (6 x 5)
(4 + 5) ÷ 3 + 6 x 5
4 + (5 ÷ 3) + 6 x 5
4 + 5 ÷ (3 + 6 x 5)
Answer:
(4+5) ÷ 3 + 6 x 5
Step-by-step explanation:
pemdas
Simplify each expression, and classify the result as rational or irrational.
The number 2√5×3√6 is irrational, number √42/√168 is rational as we know π is an irrational number but 22/7 is rational.
What is an irrational number?It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words the irrational number cannot be expressed in the form of p/q form.
A rational number is a sort of real number that has the form p/q and does not equal zero.
= 2√5×3√6
= 6√30
= √1080 = 32.863353450309965
The number is irrational.
= √42/√168
= 1/2
The number is rational.
= 5(4√5 - 3√5)
= 5√5
= √125 = 11.180339887498949
The above number is irrational.
= √64/32
= 1/4
The above number is rational.
= (5√3—√3)/2√3
= 2
The above number is rational.
Similarly, we can find whether a number is irrational or rational
Thus, the number 2√5×3√6 is irrational, number √42/√168 is rational as we know π is an irrational number but 22/7 is rational.
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1. what are the amounts of interest and maturity value of a loan for 250,000.00 at 5.5% simple interest for 4 months?
the amount of maturity is 254583
How many yards is 6 inches
Answer: 6 inches equals 0.16666667 yards, or about 0.2 yards.
Step-by-step explanation: 1 yard equals 36 inches. By that reasoning, we can divide 6 by 36, since we are trying to find out how many yards are in 6 inches.
6/36 = 0.16666667
The answer is 0.16666667 yards, or about 0.2 yards.
The numbers in this sequence increase by 12 each time
24
36
48
60
The sequence is continued with the same rule.
Which number in the sequence will be closest to 100?
Consider the line shown on the graph. Enter the
equation of the line in the form y = mx + b where m is
the slope and b is the y-intercept.
y=
From the graph, we concluded that line passes through the points (0, 3) and (1, 4) respectively.
So, slope of the line (m) passing through the points (a, b) and (c, d) is
m = d - b/ c - a
So, on substituting the values, we getm = 4 - 3 / 1 - 0 = 1/1 = 1
Also, line makes an intercept of 3 units in positive direction of y - axis.
So, c = 3
So, Equation of line is given byy = mx + c
y = 1 × x + 3
y = x + 3Alternative Method :-We know, Equation of line passing through the points (a,b) and (c, d) is given by
y - b = d - b / c - a (x - a)
Here,a = 0
b = 3
c = 1
d = 4
So, on substituting these values in above result, we get :-y - 3 = 4 - 3 /1 - 0 ( x - 0 )
y - 3 = 1/1 ( x - 0 )
y - 3 = x
y = x + 3Different forms of equations of a straight line :-1. Equations of horizontal and vertical lines
Equation of line parallel to x - axis passes through the point (a, b) is y = b.
Equation of line parallel to y - axis passes through the point (a, b) is x = a.
2. Point-slope form equation of lineEquation of line passing through the point (a, b) having slope m isy - b = m(x - a)
3. Slope-intercept form equation of lineEquation of line which makes an intercept of c units on y axis and having slope m is y = mx + c.
4. Intercept Form of LineEquation of line which makes an intercept of a and b units on x - axis and y axis respectively is x/a + y/b = 1.
5. Normal form of LineEquation of line which is at a distance of p units from the origin and perpendicular makes an angle B with the positive X-axis is x cosB + y sinB = p.
The radius of the surface of the water in the tank is increasing at a rate of 0.25m/min. at what rate is the area of the surface changing when the radius is 1.2m?
Answer:
1.88 m^2/min to the nearest hundredth.
Step-by-step explanation:
Area = π r^2
Using Calculus notation:
dA/dr = 2π r
dr/dt = 0.25 (given)
So the rate of change of area
dA/dt = dA/dr * dr/dt
So when r = 1.2
dA/dt = 2 π * 1.2 * 0.25
= 0.6π m^2/min.
= 1.88 m^2/min to the nearest hundredth.
QUESTION 10 SOMEONE HELP ME
which of the following is a true statement
Answer:
b
Step-by-step explanation:
[tex] = \frac{68}{5} - \frac{18}{5} \\ [/tex]
[tex] = \frac{50}{5} \\ [/tex]
Change into lowest term
[tex]10...[/tex]
A party favor is made up of four equal solids and is constructed from paper. each of the four solids is open at the end. the net represents one of the solids. a net of a solid has a square base with side lengths of 2 inches, and 4 triangular sides with a height of 3 inches. b is the base, and c, d, and a are the triangular sides. how much paper is needed to make a party favor? to calculate the surface area, you would exclude the area of face . one of the four pyramids has a surface area of in.2. one party favor, which consists of four of the equal solids, has a surface area of in.2.
The surface area of the solid is 4 + 6b
How to determine the area of the solid?The solid consist of the following shapes:
1 square of length 2 inches4 triangles of height 3 inches and base bThe area of the solid is:
Area = Area of square + 4 * area of triangle
This gives
Area = 2 * 2 + 4 * 0.5 * 3 * b
Evaluate
Area = 4 + 6b
Hence, the surface area of the solid is 4 + 6b
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A right rectangular prism has a base area of 20 cm? and a height of 9. 2 cm.
Answer:
the answer to this question is 184cm^2 because the formula to find the area for a rectangular prism is A= BH so we need to multiply 20 which is the base times 9.2 which is the height and when we do those steps of multiplying we get an answer of 184cm^2 so 184 cm^2 is hopefully the correct answer for this problem.
Step-by-step explanation: hopefully that is the correct and have a great day.
The scatterplot that represents the monthly values of stock QRS has an r-
value of -0.993. Which best describes the correlation of the graph?
OA. Weak correlation
B. Strong positive correlation
C. Strong negative correlation
OD. No correlation
Answer:
C
Step-by-step explanation:
Because it's a negative, then we could assume that it is a negative correlation. And because it's closer to -1, it is a strong negative correlation.
The value -0.993 is Strong Negative correlation.
What is Coefficient Correlation?The strength and direction of two variables in a scatterplot are quantified by the correlation coefficient, or r value. It goes from one to one.
A perfect positive correlation is denoted by +1.A perfect negative correlation is denoted by -1.0 indicates a lack of associationSo, the value close to 1 is Strong positive correlation and close to -1 is Strong Negative correlation.
Thus, -0.993 close to -1 is Strong Negative correlation.
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It is recommended that one fire extinguisher be available for every 6,000 square feet inside a building. a school superintendent is working to determine the number of fire extinguishers needed for a school building that has a floor plan with 132,000 square feet. let the variable x represent the number of fire extinguishers.
What is the area of this figure? PLS ANSWER
Answer:
42 units ^2
Step-by-step explanation:
Break in to a top triangle a middle rectangle and a bottom triangle
area = 1/2 7 *2 + 4 * 7 1/2 * 2 * 7 = 42 units ^2
7 mi.
7 mi.
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
4)
C =
miles
