Question
Simplify: (8c³ + c²d) - (9cd²-5d³) + (-3c²d-8cd²).
Answer: [tex]5d^3 -17cd^2 -2c^2 d+8c^3[/tex]
Step-by-step explanation:
Expanding the parentheses,
[tex]8c^3 +c^2 d-9cd^2 +5d^3 -3cd^2 d-8cd^2[/tex]
Combining like terms yields [tex]5d^3 -17cd^2 -2c^2 d+8c^3[/tex].
What in the world how do you solve this?
Answer:
B
Step-by-step explanation:
using the rule of radicals
• [tex]\sqrt[n]{x}[/tex] ÷ [tex]\sqrt[n]{y}[/tex] = [tex]\sqrt[n]{\frac{x}{y} }[/tex], then
32[tex]\sqrt[8]{18y}[/tex] ÷ 8[tex]\sqrt[8]{3y}[/tex]
= [tex]\frac{32}{8}[/tex] ×[tex]\sqrt[8]{\frac{18y}{3y} }[/tex] ( cancel 18y and 3y by 3y )
= 4 × [tex]\sqrt[8]{6}[/tex]
= 4[tex]\sqrt[8]{6}[/tex]
Please help with question!!
Given:
[tex]\ln x+\ln (x+14)=3[/tex]Use the formula:
[tex]\ln ab=\ln a+\ln b[/tex][tex]\begin{gathered} \ln x+\ln (x+14)=3 \\ \ln x(x+14)=3 \\ x(x+14)=e^3 \\ x^2+14x=20.085 \end{gathered}[/tex]solve the equation :
[tex]\begin{gathered} x^2+14x=20.085 \\ x^2+14x-20.085=0 \\ x=\frac{-14\pm\sqrt[]{14^2-4(1)(-20.085)}}{2} \\ x=\frac{-14\pm\sqrt[]{276.34}}{2} \\ x=\frac{-14\pm16.623}{2} \\ x=-7\pm8.312 \\ x=-7+8.312;x=-7-8.312 \\ x=1.312;x=-15.312 \end{gathered}[/tex]Answer:
[tex]\textsf{Exact form}: \quad x=-7 +\sqrt{49+e^3}[/tex]
[tex]\textsf{Decimal form}: \quad x=1.312\; \sf (3\:d.p.)[/tex]
Step-by-step explanation:
Given equation:
[tex]\ln x + \ln (x+14)=3[/tex]
[tex]\textsf{Apply the product law} \quad \ln x + \ln y=\ln xy:[/tex]
[tex]\implies \ln (x(x+14))=3[/tex]
[tex]\implies \ln (x^2+14x)=3[/tex]
[tex]\textsf{Apply the log law} \quad e^{\ln x}=x:[/tex]
[tex]\implies e^{\ln (x^2+14x)}=e^3[/tex]
[tex]\implies x^2+14x=e^3[/tex]
Subtract e³ from both sides to form a quadratic equation:
[tex]\implies x^2+14x-e^3=e^3-e^3[/tex]
[tex]\implies x^2+14x-e^3=0[/tex]
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
a = 1b = 14c = -e³Substitute these values into the quadratic formula and solve for x:
[tex]\implies x=\dfrac{-14 \pm \sqrt{14^2-4(1)(-e^3)} }{2(1)}[/tex]
[tex]\implies x=\dfrac{-14 \pm \sqrt{196+4e^3} }{2}[/tex]
[tex]\implies x=\dfrac{-14 \pm \sqrt{4(49+e^3)} }{2}[/tex]
[tex]\implies x=\dfrac{-14 \pm \sqrt{4}\sqrt{49+e^3} }{2}[/tex]
[tex]\implies x=\dfrac{-14 \pm 2\sqrt{49+e^3} }{2}[/tex]
[tex]\implies x=-7 \pm \sqrt{49+e^3}[/tex]
Solutions:
[tex]x=-7 +\sqrt{49+e^3}, \quad x=-7 -\sqrt{49+e^3}[/tex]
Decimal form:
[tex]x= 1.312, \quad x=-15.312[/tex]
As logs of negative numbers cannot be taken, the only solution is:
[tex]x=-7 +\sqrt{49+e^3}\\\\x=1.312\;\sf (3\;d.p.)[/tex]
_% of $20 = $10
PLEASE HELP ME ITS IMPORTANT
Answer:
DONT WORRY ITS FIFTY PERCENT
If √6 is the geometric mean between 4 and another number, then the number is
A. 9
B. 24
C. 1.5
Answer: THE ANSWER TO THAT IS C
Step-by-step explanation:
what is the slope of the line through (5,4),(-2,-8)
Please do it step by step and asap
Find each of the numbers below.
Simplify your answers as much as possible.
The opposite of 0:
The opposite of 7:0
The opposite of the opposite of 6:
The opposite of 0 is 0, the opposite of 7 is -7 and the opposite of 6 is -6.
If we consider a number x, then the opposite of the number x will be equal to -x. In a number line the opposite of a number lying on the positive side always lies on the negative side of number line. Also, the opposite of a number -x is the x that is the number itself. It is given in the question that we need to find opposite of 0, 7 and 6.
Let x = 0, opposite of x is -x.
=> -x = -0
=> -x = 0
Now, let x = 7, opposite of x is -x
=> -x = -7
Now, let x = 6, opposite of x is -x
=>-x = -6
Thus, the opposite of the numbers 0, 7 and 6 are 0, -7 and -6 respectively.
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your class mate was asked to square (2x - 3) , he answered 4x² - 9 . is his answer correct?
His answer is incorrect
The correct answer is:
[tex]4x^2-12x+9[/tex]This is the square of (2x - 3)
Explanation:Given (2x - 3)
The square of this is:
[tex]\begin{gathered} (2x-3)^2 \\ =4x^2-12x+9 \end{gathered}[/tex]His answer of 4x² - 9 is incorrect.
Which side of EFGH corresponds with CD
nswer
The side of EFGH that corresponds with CD is GH.
xplanation
One of the key points for two figures to be similar is that the angles are the same.
Since parallelograms have opposite angles equal, and adjacent angles sum up to give 180 degrees. We know that ABC
Angle = 180 - 523 = 127
And this makes the similarity makes the order of similarity here to be
BCD = EFGH
o,
dD = GH
Hope this Helps!!!
The speed limit on a road is 30 miles per hour. Drivers on this road typically vary their speed around the
limit by as much as 3 miles per hour. What is the range of typical speeds on this road?
The range of typical speeds (in miles per hour) is
Answer:
Between 30 and 33 mph or, simply
Range: [30,33]
Step-by-step explanation:
A Range is all possible values of a certain variable or piece of information commonly notated by a minimum and maximum. In this example, our variable is the speed traveled by drivers in a road. We are provided a minimum of 30 mph as this is the speed limit, and told that drivers may speed up to a maximum of 3 mph faster ( or 33 mph).
Therefore, our minimum would be 30, maximum would be 33, and Range would be [30, 33].
Brackets are used here because both our minimum and maximum values are included in the range.
HOPE THIS HELPS!!
Select the relation that is a function
the digits 3,4,5,6,7 and 8 are randomly arranged to form a three-digit number. (Digits are not repeated.) Find the probability that the number is even and greater than 800.
The probability of getting an even number greater than 800 is 0.08
Total outcomes possible when a three-digit number is formed without repetition:
Using the digits 3,4,5,6,7 and 8:
The first digit can be filled in using any of the 6 options
The second digit can be filled using the remaining 5 options
The third digit can be filled in using the remaining 4 options
So, total outcomes possible = 6*5*4 = 120 possibilities
Now, finding even number greater than 800:
The first digit can only be filled by 8 for a number to be greater than 800 which means there is only one option for the first digit
The second digit can be filled using any of the remaining options except 8 which means there are 5 options
The last digit can be filled using 4 and 6 because these are the only even numbers which mean 2 options
Total possible outcomes = 1*5*2 = 10 possibilities
The probability that the number is even and greater than 800:
= 10/120 = 0.08
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Given the function f(x) in red, write the equation for the transformed function g(x)in green
Two numbers have a difference of 1,200 and a total of 6,484
What are the two numbers
3842 and 2642 are the two numbers.
What is linear equations?
Linear equations are a subset of first order equations. One homogeneous variable of degree one constitutes a linear equation in one variable (i.e., only one variable). A linear equation could contain multiple variables. When a linear equation comprises two variables, for instance, linear equations in two variables are utilized. A mathematical statement known as an equation contains an algebraic expression and the equal symbol (=). It is the equation for a straight line. The equation is shown to be valid when values are substituted for the unknown values in the solutions of linear equations. When there is just one variable, there is just one answer.
How to Solve?
Solving a linear equation involves determining the answer to a linear equation with one, two, three, or more variables. The answer to a linear equation is the value or values of the variable(s) that are part of the equation. There are six main ways to resolve linear equations. For the purpose of solving linear equations, these methods include the Graphical Method, Elimination Method, Substitution Method, Cross Multiplication Method, Matrix Method, and Determinants Method.
Let the greater of the two numbers be "x" and the smaller one be "y".
Given, x - y = 1200 --(i) & x + y = 6484 --(ii)
Adding (i) and (ii), we get, 2x = 7684 ⇒ x = 3842
Subtracting (i) from (ii), we get, 2y = 5284 ⇒ y = 2642
Thus, the greater number of the two numbers is 3842 and the smaller number is 2641.
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Bài 1.5 Tính hạng của các ma trận:
1.
1 2 1 −1 0
2 −1 1 3 4
2 −1 2 1 −2
2 −3 1 2 −2
−4 1 −3 1 8
,
2.
25 31 17 43
75 94 53 132
75 94 54 134
25 32 20 48
Answer:
1 is the awnsewer
Step-by-step explanation:
1
Let sets A and B be defined as follows. A is the set of integers greater than -8 and less than -4.B={b,h,i,l,r,s}
A
Concept
The cardinality of a set is a measure of the "number of elements" of the set. For example, the set contains 3 elements, and therefore. has a cardinality of 3.
Set A is the set of integers greater than -8 and less than -4.
Therefore set A = {-7, -6, -5,}
-7 is greater than -8 and -5 is less than -4 from the number line.
Therefore, set A = { -7, -6, -5 }
B = {b, h, i, l. r, s }
Cardinalities of
n(A) = 3 n(B) = 6
B
[tex]\begin{gathered} -5\text{ }E\text{ A = true} \\ -12\text{ E A = false} \\ b\text{ E B = true} \\ t\text{ }\notin\text{ B = true} \end{gathered}[/tex]
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
600
Step-by-step explanation:
[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]
The angle measures in a triangle are 25 degrees, 135 degrees, and 20 degrees. what type of triangle is it. isosceles triangleobtuse triangle right triangle acute triangle
25 degrees, 135 degrees, and 20 degrees
no 90 degree angle, so not a right triangle
all three angles are different, so not an isosceles triangle
135 > 90, so not an acute triangle
must be an obtuse triangle
Subtract these equations.
INFORMATION:
We have the next subtraction
And we must solve it
STEP BY STEP EXPLANATION:
To solve a subtraction of two expressions, we must multiply the second expression by -1 and then add up the first expression and the result of the multiplication.
1. Multiply the second expression by -1
[tex]\begin{gathered} -1(3x+2y=3) \\ -3x-2y=-3 \end{gathered}[/tex]2. Add up the first expression and the result of the multiplication. We must add similar terms
[tex]\begin{gathered} 3x+4y=17 \\ -3x-2y=-3 \\ -------- \\ 0x+2y=14 \\ →2y=14 \end{gathered}[/tex]Finally, the result of the subtraction is 2y = 14
ANSWER:
aA. 2y = 14
Write the equation of the line that passes through the points (0,3) and (2,-1). Put your answer in point-slope form, using fractional form for m and b.
The equation of the line will be y = -2x + 3.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
Given that the equation of the line that passes through the points (0,3) and (2,-1).
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
First calculate the slope of the line:-
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -1 - 3 ) / ( 2 - 0 )
Slope = -2
The y-intercept will be:-
y = mx + c
3 = 0 + c
c = 3
Equation of the line:-
y = mx + c
y = -2x + 3
Therefore, the equation of the line will be y = -2x + 3.
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Jacob ran 10 miles in 80 minutes at that rate how far would he run in 21/2 hours? (*hint - 1 hour = 60 minutes)
If Jacob ran 10 miles in 80 minutes at that he will run the distance of 18.75 miles in [tex]2\frac{1}{2}[/tex] hours
Number of miles that Jacob will run in 80 minutes = 10 miles
Number of miles that Jacob will run in 1 minutes = Number of miles that Jacob will run in 80 minutes/ 80
= 10/80
= 0.125 miles
We know,
1 hour = 60 minutes
[tex]2\frac{1}{2}[/tex] hours = 2.5×60
= 150 minutes
Number of of miles that Jacob will run in 150 minutes = Number of miles that Jacob will run in 1 minutes × 150
= 0.125×150
= 18.75 miles
Hence, if Jacob ran 10 miles in 80 minutes at that he will run the distance of 18.75 miles in [tex]2\frac{1}{2}[/tex] hours .
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a figure is made of 2 rectangular prisms...
what is the volume?
The volume of the figure that is composed of two rectangular prisms is: 146 cubic in.
What is the Volume of a Rectangular Prism?The volume of a rectangular prism = (length)(width)(height).
The figure can be decomposed into two rectangular prisms. Find the volume of each of the prisms.
Volume of rectangular prism 1:
Length of the prism = 8 in.
Width of the prism = 7 in.
Height of the prism = 1 in.
Volume of rectangular prism 1 = (8)(7)(1) = 56 in.³
Volume of rectangular prism 2:
Length of the prism = 10 in.
Width of the prism = 9 in.
Height of the prism = 1 in.
Volume of rectangular prism 1 = (10)(9)(1) = 90 in.³
Volume of the figure = 90 + 56 = 146 cubic in.
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Tell whether the ordered pair is a solution to the system of equations. You must show work to support your answer.a) (5,2)2x-3y=42x+8y=11
Replace x by 5 and y by 2 on both equations, and check if the equalities remain:
2x-3y=4
2(5)-3(2) =4
10-6= 4
4=4 EQUAL
2x+8y= 11
2(5) + 8(2)=11
10 + 16 = 11
26=11
26 is not equal to 11
The ordered pair is NOT a solution to the system of equations.
Match each slope and y-intercept with the appropriate linear equation.
m = 3, b=4
m = 5, b = -2
m = 4, b=3
m = -2, b=5
Intro
↑
↑
y = 4x +3
y = 3x + 4
y = 5x-2
y = -2x + 5
Done
Answer:
Slope-intercept form: y = mx + b
(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)
y = 1.5x - 7 m = 1.5 b = -7
(y = (1.5)x + (-7) ----> y = 1.5x - 7)
y = -1.5x - 4 m = -1.5 b = -4
y = -3x + 4 m = -3 b = 4
y = 3x m = 3 b = 0
y = 7 m = 0 b = 7
(y = (0)x + 7 ---> y = 7)
Step-by-step explanation:
Your uncle wants to buy a monthly garage parking pass that costs $49.75.
He has five $10 bills, one $5 bill, five $1 bills, and 3 quarters. Use the table
to show three different ways your uncle could pay for the pass and the
change that he receives.
Answer:
See below
Step-by-step explanation:
Answer
Denomination
10 5 1 0.75 Change
5 0 0 0 0.25
4 1 4 0.75
These are the only 2 ways I see of paying the parking pass. The tens can't drop down to 3 because the rest will never add up to 19.95
Dixon and his little sister Ariadne stand next to each other on the playground on a sunny afternoon. Their mother measures their shadows. Ariadne's shadow is feet long and Dixon's shadow is feet long. If Ariadne is feet tall, how tall is Dixon?
Using the similar triangle principle, the height of Dixon in feet is 6 feet.
How to find the side of similar triangle?Ariadne's shadow is 15 feet long and Dixon's shadow is 18 feet long.
Ariadne is 5 feet tall.
The height of Dixon can be found using similar triangle principle.
Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Therefore, using the similar triangle theory,
Let
x = height of Dixon
Hence,
shadow length of Ariadne / Ariadne height = Dixon shadow length / Dixon height
shadow length of Ariadne = 15 ft
Ariadne height = 5 feet
Dixon shadow length = 18 feet
15 / 5 = 18 / x
cross multiply
15 × x = 18 × 5
15x = 90
divide both sides by 15
15x / 15 = 90 / 15
x = 6 ft
Therefore, Dixon height is 6 feet.
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Directions: Watch the directions video for how to complete sample work. You must
answer all questions completely, and show all of your work in order to receive credit.
1. ERROR ANALYSIS
Your friend is trying to find the maximum value of P = -x + 6y subject to the
following four constraints.
(y ≤-2x + 4
y≤ x+1
x≥0
y20
The maximum value of P = 11.
Given: P = -x + 6y
In this question we have to first solve the given system of equations.
Ignore the greater or lesser than sign that is:
y = -2x+ 4 -------- 1
And y = x + 1 --------- 2
On solving these two equations we get;
0= -3x + 3
⇒ -3x = -3
⇒ x= 1
Substituting the value of x in equation 2 we get
y = x+ 1
= 1 + 1 = 2
Thus y = 2 and x = 1
So on putting these values in P = -x + 6y we get
P = - 1 + 6× 2
P = - 1 + 12 = 11
Therefore P= 11.
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2 digit by 2 digit multiplacation 97x57
Answer:
11,280
Step-by-step explanation:
so first you write the equation 97*57. then you multiply them, ( 7*7=49; 5*7= 35, now 9*7= 63; 5*9= 45) and the answer is 11,280
I might be wrong in my calculations because the calculator says the answer is 5,529 so yeah the answer is either 11,280 or 5,529.
Hope this helps
Please help solve equation
EXPLANATION
The first equation is a line with the following slope-intercept form:
[tex]4x+4y=-8[/tex]Subtracting -4x to both sides:
[tex]4y=-4x-8[/tex]Dividing both sides by 4:
[tex]y=-\frac{4}{4}x-\frac{8}{4}[/tex]Simplifying:
[tex]y=-x-2[/tex]The slope is -1 and the y-intercept is -2
Applying the same reasoning to the second equation we get:
[tex]y=-x+3[/tex]3
Now, we can write and graph both linear equation
Please answer Part A and B
Answer:
a 47 b 34
Step-by-step explanation:
so basically its very easy im just trying to do a task so this is most probabilly noot correct
Answer: Part A: Figure D I Part B 3 Units to the left...
Step-by-step explanation: Because they are the same, but in different locations... : )