The two ways to find solution of the expression (17-8) are by direct arithmetic method and indirect simplification method.
In arithmetic method, the first step is to determine whether the numbers are rational or irrational, so as to simplify the solution process. If numbers are rational, then they are checked for the sign determining their position on number line and then the calculations are performed. Here, 17 is positive rational number and -8 is negative rational number. Hence, 17-8 is equalized to 9. In indirect simplification method, the numbers to be subtracted are broken down to simpler terms which can be easily subtracted and reduced to get the answer. In the subtraction of 17-8, we break 8 in the form of (7+1). Then the expression becomes 17 - (7+1). Now, this expression can easily be solved to get the answer. Therefore, 17 - (7+1) = 10 - 1 = 9.
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If 5 books of equal weight, weigh 1.755 kilograms, how many books will weigh 1.404 kilograms?
If 5 books of equal weight, weigh 1.755 kilograms, then the number of books will weight 1.404 kilogram is 4 books
The 5 books are equal weights
The weight of 5 books = 1.755 kilograms
Then the weight of one book = The weight of 5 books / 5
Substitute the values in the equation
The weight of one book = 1.755/5
= 0.351 kilograms
To find the number of books we have to use division again
The number of books will weight 1.404 kilograms = 1.404 / The weight of one book
=1.404/0.351
= 4 books
Hence, If 5 books of equal weight, weigh 1.755 kilograms, then the number of books will weight 1.404 kilogram is 4 books
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please help!!! only 20 mins left
The rule of (x, y) → (-x, y), which is reflection over y-axis.
Given that, ΔABC maps to triangle ΔA'B'C'.
What is the reflection on y-axis?When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
The coordinate points of ΔABC are A(-4, 3), B(-3, -3) and C(1, 2) and the coordinate points of ΔA'B'C' are A'(4, 3), B'(3, -3) and C'(-1, 2).
Here, A(-4, 3) → A'(4, 3), x-coordinate is negated and y-coordinate remains same.
Similarly, B(-3, -3) → B'(3, -3) and C(1, 2) → C'(-1, 2) follows the same pattern.
From this, it is clear that the coordinates of triangle ABC is reflected on y-axis.
Therefore, the rule of (x, y) → (-x, y), which is reflection over y-axis.
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If g(x) = 5x, h(x) = √x , find the composition. (g . h)(0)
The composition (g . h)(0) has a value of 0
How to evaluate the composite function?The definitions of the functions are given as
g(x) = 5x and h(x) = √x
To find the composition (g . h)(o), we make use of
(g . f)(x) = g(x) * h(x)
This can also be expressed as
(g . f)(x) = h(x) * g(x)
Substitute g(x) = 5x and h(x) = √x
So, we have
(g . f)(x) = 5x * √x
Substitute 0 for x
So, we have the following equation
(g . f)(0) = 5 x 0 * √0
Evaluate the product
So, we have the following equation
(g . f)(0) = 0
Hence, the value of the composition is 0
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The domain of a function f(x) is x< 4, and the range is y≤ 0. What are the
domain and range of its inverse function, f-¹ (x)?
A. Domain: x≤0
Range: y< 4
B. Domain: x<0
Range: y≤ 4
C. Domain: x24
Range: y> 0
D. Domain: x < 4
Range: y≤ 0
Answer:
Step-by-step explanation:
d
The probability that an adult is actively looking for a job is 0.18. The probability of an adult being unemployed and actively looking for a job is 0.04. What is the probability of an adult being unemployed given that they are actively looking for a job?
The probability of an adult being unemployed given that they are actively looking for a job is 0.22.
How to calculate the probability?It should be noted that probability gas to do with the likelihood that something will occur.
Remember the multiplication rule for conditional probability:
P(B AND A)=P(B|A)P(A)
Rearranging, we see thatP(B|A)=P(B AND A)P(A)
So if we think of A as being the event that an adult is actively looking for a job and B as the event that an adult is unemployed, then we can plug in the known information to find
P(B|A)=0.04 + 0.18
≈0.22
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An attic floor is shaped like a triangle with a height of n yd and a base of 6 yd.Which expression represents the area of the floor? 6n3nn + 63n2
In order to calculate the area, we can use the formula for the triangle area:
[tex]A=\frac{b\cdot h}{2}[/tex]Where b is the base length and h is the height relative to this base.
So, for b = 6 and h = n, we have:
[tex]\begin{gathered} A=\frac{6\cdot n}{2} \\ A=3n \end{gathered}[/tex]Therefore the correct option is the second one.
A fish tank in the shape of a rectangular prism has a volume of 24 cubic feet. The length of the fish tank is 2 feet less than twice the width w, and the height is 1 foot less than the width. Find the equation, in terms of w, that could be used to find the dimensions of the fish tank in feet. Your answer should be in the form of a polynomial equals a constant.
Answer in the form of a polynomial equals a constant:
2w^3-4w^
1. The number of fans produced by a manufacturer in a week can be no more than five times the number of lamps produced by the same manufacturer during the same week. If the number of fans produced this week by the manufacturer was 20, what is the minimum number of lamps produced by the manufacturer this week?
A) 4
B) 5
C) 15
D) 20
Could you please help me with this exercise? Thanks for your help!
ANSWER
• Distance:, 7.81
,• Midpoint: ,(-4.5, -6)
EXPLANATION
The distance between two points (x₁, y₁) and (x₂, y₂) is given by the Pythagorean Theorem,
[tex]d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2_{}}[/tex]In this problem, the points are (-7, -9) and (-2, -3),
[tex]\begin{gathered} d=\sqrt[]{(-7-(-2))^2+(-9-(-3))^2} \\ d=\sqrt[]{(-7+2)^2+(-9+3)^2}\text{ } \\ d=\sqrt[]{(-5)^2+(-6)^2}=\sqrt[]{25+36} \\ d=\sqrt[]{61}\approx7.81 \end{gathered}[/tex]Hence, the distance between P1 and P2 is 7.81 units.
To find the midpoint, we have to find the average between the coordinates of the points,
[tex](x_m,y_m)=\mleft(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\mright)[/tex]The midpoint in this problem is,
[tex](x,y)=\mleft(\frac{-7-2}{2},\frac{-9-3}{2}\mright)=\mleft(\frac{-9}{2},\frac{-12}{2}\mright)=(-4.5,-6)[/tex]Hence, the midpoint between P1 and P2 is (-4.5, -6).
get me some help with it she of them
We are given the following expression:
[tex](6+4i)(9-11i)[/tex]Using the distributive property:
[tex](6)(9)+(6)(-11i)+(4i)(9)+(4i)(-11i)[/tex]Solving the products:
[tex]54-66i+36i-44i^2[/tex]Now we use the following property:
[tex]i^2=-1[/tex]Substituting:
[tex]54-66i+36i+44[/tex]Adding like terms:
[tex]98-22i[/tex]Since we can't simplify any further this is the answer.
What is the measure of ZABD? What is the reason?60° , isosceles triangle theorem48°, equilateral triangle theoremCO 48°, isosceles triangle theorem60° , equilateral triangle theoremB66°DA
Consider the traingle ABD,
The side AB and A are equal means that angle A is equal to angle D.
Determine the angle B of traingle ABD by using angle sum property of triangle.
[tex]\begin{gathered} \angle A+\angle B+\angle D=180^{\circ} \\ 66^{\circ}+66^{\circ}+\angle B=180^{\circ} \\ \angle D=48^{\circ} \end{gathered}[/tex]So angle D is of 48 degree and two sides are equal so isoceles traingle theorem is used for angle measurement. Option C is correct.
In desperate need of help with my college algebra problem
To find the nth degree of polynomial function f(x) = x^4 - 4x^3 + 27x^2 -46x +60
What is Function?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
For polynomial with real coefficients, the complex zeros come with conjugates so 2+4i must come with 2-4i , then for 4th degree polynomial
f(x) =a (x+1)(x-3)(x-2-4i)(x-2+4i). With given f(1)=-68
a(1+1)(1-3)(1-2-4i)(1-2+4i)= -68.
By this we can find a
a (2)(-2)(-1-4i)(-1+4i) = -68
a(-4)(1+4i-4i-16i^2) = -68
a(-4)(1+16) = -68
a(-4)(17) = -68
a(-68) = -68
a = 1
Now, solving
f(x) =(x+1)(x-3)(x-2-4i)(x-2+4i)
f(x) = (x+1)(x-3)(x^2 - 2x + 20)
f(x) = (x^2 - 2x - 3)(x^2 - 2x + 20)
f(x) = x^4 - 2x^3 + 20x^2 - 2x^3 + 4x^2 - 40x + 3x - 6x + 60
f(x) = x^4 - 4x^3 + 27x^2 -46x +60
Hence, the for 4th degree polynomial is f(x) = x^4 - 4x^3 + 27x^2 -46x +60
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Choose the figure that accurately represents the following relation on the Cartesian coordinate plane? {(-2,-2),(2,-3),(4,-1),(5,-6),(6,-8),(6,9)}
Recall that, in a point (a,b), the first entry represents the x-entry, and the second entry represents the y-entry, and its graph is as follows:
Therefore, the graph of the given relation is:
Answer:
PLEASEE I NEED HELP!!
Figure 3 can also be created by transforming figure 1 with a sequence of two transformations. Which statement describes a possible sequence of transformations that transforms figure 1 into figure 3?
A. a rotation 180 degrees clockwise about the origin, followed by translation 2 units to the left.
B. a rotation 90 degrees clockwise about the origin, followed by a reflection across the x-axis.
C. a rotation 180 degrees clockwise about the origin, followed by a reflection across the y-axis.
D. a rotation 90 degrees clockwise about the origin, followed by a translation 3 units to the right.
the correct answer is A. Option A describes a rotation of 180 degrees clockwise, which would result in figure 1 being upside down, and then a translation of 2 units to the left.
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
To transform figure 1 into figure 3, we need to apply two transformations. We can eliminate option B because a rotation of 90 degrees followed by a reflection across the x-axis would transform figure 1 into a mirror image of figure 2, not figure 3.
Option A describes a rotation of 180 degrees clockwise, which would result in figure 1 being upside down, and then a translation of 2 units to the left. This would transform figure 1 into figure 3, so option A is a possible sequence of transformations.
Option C describes a rotation of 180 degrees clockwise followed by a reflection across the y-axis. This would transform figure 1 into a mirror image of figure 2, not figure 3.
Option D describes a rotation of 90 degrees clockwise followed by a translation of 3 units to the right. This would transform figure 1 into a position that is similar to figure 3, but the orientation of the triangle would be different.
Therefore, the correct answer is A.
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In a triangle one angle is three times the smallest angle and the third angle is 45 more than twice the smallest angle. find the measure of all 3 angles. Hint: the angles of a triangle add up to 180.
The three angles of the triangle are 22.5, 67.5 and 90 degrees.
How to find the angles of a triangle?A triangle is a polygon with three sides.
The sum of angles in a triangle is 180 degrees.
Therefore, the angles of the triangle can be found as follows;
In the triangle one angle is three times the smallest angle and the third angle is 45 more than twice the smallest angle.
Therefore,
let the smallest angle = x
Therefore, the three angles are as follows;
x3x45 + 2xTherefore,
x + 3x + 45 + 2x = 180
6x + 45 = 180
6x = 180 - 45
6x = 135
divide both sides by 6
x = 135 / 6
x = 22.5
Therefore, the three angles are as follows;
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What’s the correct answer answer asap i need help can somebody answer this question?
il give you brainlist
Answer: A
Step-by-step explanation:
Selwyn wanted to place point V on the same number line to represent the opposite number of point W . Which instruction should he follow to place point V
Move ten units to the left of point W.
1) Counting the marks on the number line, we can tell that Selwyn placed point V 5 units to the right of zero.
2) Since we need to find the opposite number, we need to find the negative 5 ( -5). Hence, we need to:
Move ten units to the left of point W.
Because we need to remember that the reference is not zero but W.
HELP!
Do units affect significant figures? For example, I know that the number 5600 has two significant figures. But if I wrote it as 5600 L, would the unit "L" count as a sig fig? Please help me!!
need help for mathhh
Using implicit differentiation, the rates are given as follows:
2. dV/dt = 144π cm³/sec.
3. dh/dt = 2/5π cm/s.
4. dr/dt = -0.2/π cm/day.
What is the rate of change of the volume of an sphere?The volume of an sphere of radius r is given by the following equation:
[tex]V = \frac{4}{3}\pi r^3[/tex]
Applying implicit differentiation, differentiating both variables relative to t, the rate of change is given as follows:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
For item 2, the parameters are given as follows:
[tex]\frac{dr}{dt} = 2, r = 4[/tex]
Hence the rate is given as follows:
dV/dt = 4π x 4² x 2 = 144π cm³/sec.
For item 4, the parameters are:
[tex]\frac{dV}{dt} = -0.2, r = 5[/tex]
Negative because the orange is shrinking.
Hence the rate of the radius can be found as follows:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
[tex]-0.2 = 4\pi (5)^2\frac{dr}{dt}[/tex]
dr/dt = -0.2/100π
dr/dt = -0.2/π cm/day.
What is the rate of change of the volume of an cylinder?The volume of a cylinder of radius r and height h is given as follows:
[tex]V = \pi r^2h[/tex]
The rate of change of the volume as a function of time is given by:
[tex]\frac{dV}{dt} = 2\pi rh\frac{dr}{dt} + \pi r^2\frac{dh}{dt}[/tex]
For item 3, the parameters are given as follows:
[tex]r = 5, \frac{dV}{dt} = 10, \frac{dr}{dt} = 0[/tex]
The radius is of 5 as r² = 25, due to the area of the base.
Hence the rate of change of the height is found as follows:
[tex]\frac{dV}{dt} = \pi r^2\frac{dh}{dt}[/tex]
10 = 25π dh/dt
dh/dt = 10/25π
dh/dt = 2/5π cm/s.
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Shiori is working on a stem project and her model is represented by the quadratic function below. She eventually wants to build a 3D model si she needs to understand each part of the function . She is trying to find the coordinate of the vertex of the following function and determine whether the graph opens up or down. F(x)=3x^2-2x-71. What are the coordinates of the vertex of the parabola of the function. There are several wars to determine this answer but state clearly all the steps you look to find the solution.2.Just by looking at the equation (without graphing it) does the graph open up or down(How do you know).3.what does the -7 tell you about the parabola specifically.
1) To get the vertex of the function, the formulae is given as:
[tex]x=-\frac{b}{2a}[/tex]This gives the x coordinate of the vertex. Where a and b are the coefficients of the 1st and 2nd terms respectiely.
[tex]x=\frac{-(-2)}{2(3)}=\frac{1}{3}=0.333333[/tex]To get the y coordinate, we substitute this x value into the original equation.
[tex]f(x)\text{ = 3(}\frac{1}{3})^2-2(\frac{1}{3})-7=\frac{-22}{3}=-7.333333[/tex]The coordinates of the the vertex (0.33, -7.33)
2) The graph opens upwards. Because the coefficient of the 2nd power of x is a negative number.
3) The -7 tells us that the graph cuts the vertical axis at -7.
Identify a solution to the system of equation
-4x+ 3y=23
x - y =7
x = - 44 and y = - 51
How are the linear equations solved?
-4x+ 3y=23 ---(1)
x - y =7 ----(2)
4*(2) => 4x- 4y =28 ---- (3)
(3) + (1)
4x- 4y =28 (+)-4x+ 3y=23
- y = 51
y = -51
Substituting y in (2)
x - y =7
x + 51 = 7
x = -44
What are linear equations ?
A linear equation is one in which the variable's maximum power is consistently 1.A one-degree equation is another name for it. A linear polynomial over a field, from which the coefficients are taken, can be reduced to a linear equation by equating it to zero. Due in part to the fact that linear equations are typically good approximations for non-linear systems, linear equations are ubiquitous in all mathematics and their applications in physics and engineering.To learn more about linear equations, refer:
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Answer: x = -2
y = 5
Step-by-step explanation:
-4x+3y=23
x-y= -7
First take x-y= -7 and make it x=-7+y place it into the first equation
-4 (-7+y)+3y = 23
28-4y+3y = 23
28-y = 23
+y +y
28=23+y
-23 -23
5=y
Not that you have y you can replace it into the original
-4x+3(5)=23
-4x+15=23
-15=-15
-4x = 8
x= -2
The answer would be (-2,5)
Scientific notation of 100+6*10^2
Answer: The answer is 700
Step-by-step explanation:
is that the answer you're looking for?
Answer:
7e2
Step-by-step explanation:
10^2=100
100*6=600
600+100=700
there are 2 zeros in 700 so
7e2
Round 18,792 to the nearest thousand is the answer 18,790 or 00019 or 00018 or 18800 please due today please give brainiest.
Answer:
The answer is 19,000
Step-by-step explanation:
18,792 you round to the thousand which is 8 and the number after is 7 which is above 5 so the 8 turns into a 9
Answer:
19000
Step-by-step explanation:
18,792
Rounding to the nearest thousand
The 8 is in the thousands place
We look at the number in the hundreds place, 7
It is 5 or higher so we will round the 8 up to 9 and everything else to the right will become zeros
18,792 becomes 19000
Identify the pre-image and the image. Then determine if the transformation is a rigid motion or not
The pre-image is the figured formed by the points VWUST and the image is V'W'U'S'T'.
To produce the image from the pre-image a rotation is performed around the point (2, -2). A rotation doesn't change the dimensions of the figure, therefore it is not a rigid motion.
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c(n) = -6 (-1/3) *n-1What is the 2nd term in the sequence ?
We are given the following sequence
[tex]c(n)=-6(-\frac{1}{3})^{n-1}[/tex]We are asked to find the 2nd term of the above sequence
Let us substitute n = 2 into the given sequence
[tex]\begin{gathered} c(2)=-6(-\frac{1}{3})^{2-1} \\ c(2)=-6(-\frac{1}{3})^1 \\ c(2)=6\cdot\frac{1}{3} \\ c(2)=2 \end{gathered}[/tex]Therefore, the 2nd term of the given sequence is 2
The product of the digits of a five-digit number is 6! (factorial). How many such numbers are there
There are 720 of such numbers that consists of five-digits which their product is 6! by permutation.
What is permutation?The mathematical term permutation can simply be defined as a process of arrangement or selection of objects. It involves each of several possible ways in which a set or number of things can be ordered or arranged.
We can apply the formula for permutation;
[tex]p(n,r) = \frac{n!}{(n - r)!} [/tex]
where n = total number of object and r = number of objects selected.
We can calculate the arrangement by applying the permutation formula as follows
[tex]p(6,5) = \frac{6!}{(6- 5)!}[/tex]
[tex]p(6,5) = \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{1!}[/tex]
[tex]p(6,5) = \frac{720}{1}[/tex]
[tex]p(6,5) = 720[/tex]
Hence, with good application of the formula for permutation, we can say that there are 720 arrangement of such numbers which their product is 6!.
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Find the equation of a line perpendicular to y +1 = -x that passesthrough the point (-8, 7).
Two lines are perpendicular if the product of their slopes is equal to -1.
Find the slope of the given line. Then, use that result to find the slope of a line perpendicular to it. Use the slope of the line perpendicular to the given line to find the equation of the one that passes through the point (-8,7).
To find the slope of the given line, write it in slope-intercept form by isolating y:
[tex]\begin{gathered} y+1=-x \\ \Rightarrow y=-x-1 \end{gathered}[/tex]The coefficient of x is -1. Then, the slope of the given line is -1.
Let m be the line perpendicular to y+1=-x.
Since the product of the slopes of perpendicular lines is equal to -1, then:
[tex]\begin{gathered} -1\times m=-1 \\ \Rightarrow m=\frac{-1}{-1} \\ \therefore m=1 \end{gathered}[/tex]The equation of a line with slope m that passes through the point (a,b) in slope-point form is:
[tex]y=m(x-a)+b[/tex]Replace m=1, a=-8 and b=7 to find the equation of the line perpendicular to y+1=-x that passes through the point (-8,7):
[tex]\begin{gathered} y=1(x-(-8))+7 \\ \Rightarrow y=(x+8)+7 \\ \therefore y=x+15 \end{gathered}[/tex]Therefore, the equation of the line perpendicular to y+1=-x that passes through (-8,7) is:
[tex]y=x+15[/tex]The office floor is 250 ft. X 80 ft. The conference room floor is 50 ft. X 20 ft. , which covers __?__ of the office
The percentage of area covered by the conference room is 5%.
What is area?
A region's size on a flat or curved surface is expressed in terms of area, a unit of measurement. A surface region or plane area is the area of an open surface or the boundary of a three-dimensional object, whereas a plane region or area refers to the area of a form or planar lamina.
The quantity of unit squares necessary to completely encompass a form is its area. In order to express and measure it, square units are used.
Given, the dimension of office as
Length= 250 ft and breadth is 80 ft
Area of office = length ×breadth = 250 ×80 = 20,000
Length of conference room = 50 ft
Breadth of conference room = 20 ft
Area = 50 (20) = 1000
Percentage of office covered by conference room is given as:
1000/20000×100=5
Hence, 5% is occupied
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the side opposite the right angle measures 8 in. what is the measurement of the side opposite of the 60 degree angle (draw and label the triangle before solving)
1) The best way to tackle this question is by sketching out the triangle:
2) Considering that 60º angle we can write out the following trig ratio:
[tex]\begin{gathered} \sin (60^{\circ})=\frac{x}{8} \\ \frac{\sqrt[]{3}}{2}=\frac{x}{8} \\ 2x=8\sqrt[]{3} \\ x=\frac{8\sqrt[]{3}}{2} \\ x=4\sqrt[]{3} \end{gathered}[/tex]Note that if we had drawn the 60º angle to the lowe right in that triangle we would find the same measure, by using the cosine of (30º) instead.
And that's the answer