Let's look at some logarithm properties,
[tex]\begin{gathered} p\log _b(M)=\log _b(M^p) \\ \log _b(\frac{M}{N})=\log _bM-\log _bN \\ \log _b(MN)=\log _bM+\log _bN \end{gathered}[/tex]We will use this properties to simplify and write the expression as a single logarithm.
The steps are shown below:
[tex]\begin{gathered} 2\log (x+3)+3\log (x-7)-5\log (x-2)+2\log (x) \\ =\log (x+3)^2+\log (x-7)^3-\log (x-2)^5+\log (x)^2 \\ =\log (\frac{(x+3)^2(x-7)^3(x)^2}{(x-2)^5}) \end{gathered}[/tex]The expression, as a single logarithm, is,
[tex]\log (\frac{(x+3)^2(x-7)^3(x)^2}{(x-2)^5})[/tex]From the answer choices, the correct answer is D.
Answer
D
Line CD passes through (0,1) and is parallel to x+y=3. Write the standard form of the equation of line CD
The standard form of the equation of line CD is x + y = 1
What is standard form of equation of a line?The standard form ;of equation of s line is written in the form
Ax + By = C
Line that are parallel has equal slope hence solving for the slope of line
x + y = 3 we have
y = -x + 3
The slope is -1
Equation of line CD passing through points ( 0, 1 )
( y - 1 ) = -1 * ( x - 0 )
y - 1 = -1 * x
y = -x + 1
writing to standard form
x + y = 1
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9.823 x 10^-9 = 9.823/ 10^ 9
9.823/ 1000000000 = 0.000000009823
the long form has the same number of zeros that 10^-9, then it have 9 zeros.
Charlie has 5/6 pounds of dog food. She wants to put equal portions into 3 bowls how much food will go into each bowl?
Javier exercises for 2 1/2 hours every Saturday. His exercisesincludes two parts. If he spends the same amount of timeon each part how many hours does he spend weightlifting?
According to the given data we have the following:
Javier exercises for 2 1/2 hours every Saturday, hence, he exercises for 2.5 hours.
In order to calculate the amount of time he spend weightlifting we would make the following calculation:
amount of time he spend weightlifting=total training per day/2
amount of time he spend weightlifting=2.5 hours/2
amount of time he spend weightlifting=1.25 hours
Therefore, he spends weightlifting 1 hour and 25 minutes every saturday
Choose the place where the digit 1 sits in this number 988,172,430,056
The number 1 sits in the 100 millions place.
The 100 millions place is 8 spaces to the left of the decimal. Hence, considering 1 is 8 spaces from where a decimal place could be, then 1 is in the 100 millions place.
Hope this helps!
Your lunch in the hospital cafeteria cost $6.50. Based on working 50 weeks per year, how much will you spend on lunch per year?
The total amount spent on lunch per year would be 325 dollars.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We have been given that Your lunch in the hospital cafeteria cost $6.50. Based on working 50 weeks per year, then;
The lunch in the hospital cafeteria cost = $6.50.
The total amount spend on lunch per year;
6.50 x 50
325
Hence, the total amount spent on lunch per year would be 325 dollars.
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Find the vertex of the absolute value function y = 7|x – 3| - 2.(-3, -2)(3, 2)(3, -2)(3, -1/2)
By the first term of the given function 7lx - 3l you can notice that there is a translation 3 units to the right of the pattern function lxl. This allows one to conclude that the x-coordinate of the vertex is 3.
Now, for such a value of x the function value is 7l3 - 3l - 2 = -2. Then, the y-coordinate of the vertex is -2.
Hence, the vertex of the function is (3,-2)
Why was the Battle of Fallen Timbers important for the new democracy?
Please write 3 paragraphs, stating 3 different reasons why the battle was important. (Paragraphs should be 4-6 sentences each
The Whiskey Rebellion put an end as a consequence of the Battle of Fallen Timbers; that had a significant outcome.
Why was Battle of Fallen Timbers important to the US?After the Battle of Fallen Timbers, the Indians agreed to the Treaty of Greenville, which gave the United States authority over most of the river crossings in the Old Northwest Territory as well as vital sites like Detroit.
The Battle of Fallen Timbers is considered to be the last battle of the American Revolution and which also helped the new country start expanding the territory to the west.
This will effectively ensured American dominance over the Indian tribes. The Whiskey Rebellion; which was the first significant confrontation between the nascent American government and it's inhabitants, which was put a stop to by it, and peace was restored.
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The combination of both integer and rational numbers gives
Answer:
Step-by-step explanation: Answer is real number
I need an answer for 1,2,3,4,5, and 6
Using alternate exterior angles,
[tex]3x-31=x+59\\\\2x=90\\\\x=45\\\\\implies 3x-31=x+59=104[/tex]
So,
[tex]\angle 1[/tex]: 76 degrees using linear pairs
[tex]\angle 2[/tex]: 104 degrees using corresponding angles
[tex]\angle 3[/tex]: 76 degrees using vertical angles
[tex]\angle 4[/tex]: 104 degrees using same-side interior angles
[tex]\angle 5[/tex]: 76 degrees using linear pairs
[tex]\angle 6[/tex]: 76 degrees using vertical angles
Please help I couldn’t go to school today and I don’t understand
Answer:
the value of x is 2
Step-by-step explanation:
3x + 6
x = 6 ÷ 3
x = 2
3x + 6
3× 2 + 6
6+6
12
-4 + 8x
-4 + 8×2
-4+16
12
Evaluate the expression for j = 8.
-7 + 2j =
Answer:
The answer tp this question is: 9.
Solve the quadratic equation x2=2536.What are the solutions of the equation x2=2536?
Given
[tex]x^2=2536[/tex]Answer
[tex]\begin{gathered} x^2=2536 \\ x=5036 \end{gathered}[/tex]if the company decides to produce 2,000 containers of regular crunchy peanut butter, how many containers of new extra crunchy peanut butter would it produce?
The number of extra crunchy peanut butter that the company would produce (current production units) is 1,700 containers.
How is the number determined?Using the mathematical operation of subtraction, the number of units to be produced can be determined.
First, we have that the ending inventory for the last period was 300 containers.
This ending inventory is subtracted from the required production level, to determine the number of containers to produce for this period.
Thus, to meet the production requirements, the company would produce additional 1,700 containers of crunchy peanut butter.
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Question Completion:Ending inventory of regular crunchy peanut butter from last period = 300 containers.
Cynthia Besch wants to buy a rug for a room that is 25 ft wide and 31 ft long. She wants to leave a uniform strip
of floor around the rug. She can afford to buy 567 square feet of carpeting. What dimensions should the rug
have?
Answer:
21 ft by 27 ft
Step-by-step explanation:
You want the dimensions of a rug with an area of 567 square feet such that it fits in a 25 ft by 31 ft room with a uniform space all around.
SetupWe note the room is 31-25=6 ft longer than it is wide. Since the rug has a uniform border around it, the rug dimensions will be 6 ft longer than wide. We want the rug area to be 567 square feet, so for width w we have ...
w(w+6) = 567
Solutionw² +6w +9 = 576 . . . . . . add 9 to complete the square
(w +3)² = 24² . . . . . . . . express as squares
w +3 = 24 . . . . . . . . . positive square root
w = 21 . . . . . . . . . . subtract 3 to find the width
w+6 = 27 . . . . . . add 6 to find the length
The rug should have dimensions 21 ft wide by 27 ft long.
__
Additional comment
The uniform strip of floor around the rug will be 2 feet wide.
Can the triangles be proven congruent with the information given in the diagram? If so, state the theorem you would use.noyes; ASA Congruence Theoremyes; AAS Congruence Theorem
The diagramof the triangles is shown below
Looking at the two traingles, they meet at a vertex. Vertically opposite angles are equal.
(50 x 2) plus (15 x 2)
Answer:
130
Step-by-step explanation:
100+30
Answer:
130
Step-by-step explanation:
100+30=130
The length of sides of a triangle are xem, (x + 1)cm and (x + 2)cm. Determine x so that this triangle is a right- angled triangle.
The value of x = 3
3cm, 4cm, and 5cm are the sides of a right-angled triangle.
What is Pythagoras theorem?
In a right-angled triangle, the hypotenuse is the largest of the three sides, so hypotenuse is (x +2).
As a result of Pythagoras' theorem,
hyp² = base² + alt²
here ,
x² + (x+1)² = (x+2)²
by simplifying the equation,
x² + x² + 2x +1 = x² + 4 + 4x
=> 2x² + 2x + 1 = x² + 4x + 4
=> x² - 2x -3 = 0
=> x² - 3x + x - 3 = 0
=> x(x-3) + 1(x-3) = 0
=> (x+1) (x-3) = 0
so, x+1 = 0 or x-3 = 0
x = -1 or x = 3
since length cannot be negative,
x = -1 is not considered .
so x= 3.
value of x is 3.
So the triangle's three sides are 3cm, 4cm, and 5cm.
to double-check the answer
Pythagoras' theorem substitute values
hyp² = b²+a²
hyp = [tex]\sqrt{3^{2}+4^{2} }[/tex]
= [tex]\sqrt{9+16}[/tex]
= [tex]\sqrt{25}[/tex]
= 5
As a result, the three sides of a right-angled triangle are 3cm, 4cm, and 5cm.
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7 times blank equals 1
Answer: 0.1429.
Step-by-step explanation: To double-check our work, multiply 0.1429 by 7 to see that it equals 1.
f(x)=3x+2 and g(x)=2x2−5
Given also that fg(x)=ax2+bx+c work out the value of a+b−c
Answer:
a= -4
b -15
c -10
Step-by-step explanation:
by avoiding x^3 you can find your problem
Write the equations for the lines parallel and
perpendicular to the given line j that passes
through Q. SEE EXAMPLE 4
26. y = -4x + 1; Q(6, -1)
27. y = ¾x + 4; Q(−1, 1)
LESSON 2-4 Slopes of Parallel and Perpendicular Lines 97
y = -4x + 1 and y = ¾x + 4, Clearly by values we can see that they are neither parallel nor perpendicular.
What is a slope?The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which produces the same number for every two distinct points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.
The slope's absolute value serves as a gauge for a line's steepness, incline, or grade. A steeper line is indicated by a slope with a higher absolute value. A line can be drawn with one of four directions: upward, downward, horizontal, or vertical.
If a line rises from left to right, it is said to be growing. The slope is upward, or m>0.If a line slopes downward from left to right, it is diminishing. The slope, m0, is negative.The slope of a line is 0 if it is horizontal. This function is constant.A line's slope is ambiguous if it is vertical.Clearly by values we can see that they are neither parallel nor perpendicular.
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how many weeks would be spent per year if you spend 2 hours tutoring per week, for the last 3 years?
Answer: .619 weeks per year
Step-by-step explanation:
52 weeks * 2 hours * 3 years = 312 hours tutored over 3 years
24 hours in a day * 7 days in a week = 168 hours in a week
312 / 168 = 1.857 weeks tutored over 3 years
1.857 / 3 = .619 weeks tutored per year
[tex] \frac{x}{3} + 1 = \frac{2}{3} [/tex]find the value of x
Given:
[tex]\frac{x}{3}+1=\frac{2}{3}[/tex]Find: x
Explanation:
[tex]\begin{gathered} \frac{x}{3}+1=\frac{2}{3} \\ \frac{x}{3}=\frac{2}{3}-1 \\ \frac{x}{3}=\frac{-1}{3} \\ x=-1 \end{gathered}[/tex]Final answer: the required value of x is -1
I'll give brainliest!
Answer: D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
...................
0,2% of what number is 8?
LE THE UNKNOWN NUMBER BE x WHEN I SOLVE
[tex] \frac{0.2}{100} \times x = 8 \\ \frac{0.2x}{100} = 8 \\ [/tex]
I WILL USE CROSS MULTIPLICATION
[tex]0.2x = 8(100) \\ 0.2x = 800 \\ \frac{0.2x}{0.2} = \frac{800}{0.2} \\ x = 4000[/tex]
OF ( 4000) IS 0.2% OF 8.
HOPE THIS HELPS.
Which is a counterexample for the conditional statement shown?
If the numerator of a fraction is larger than the denominator of the fraction, then the fraction is greater than 1.
any fraction with a denominator of 0
any fraction with a numerator of 0
any fraction with a positive numerator and a negative denominator
any fraction with a negative numerator and a positive denominator
Answer: Choice C
any fraction with a positive numerator and a negative denominator
======================================================
Explanation:
Consider the fraction 10/(-5) where we divide 10 over -5
The numerator 10 is larger than the denominator -5, as any positive number is larger than a negative number. But 10/(-5) simplifies to -2 which is not greater than 1.
This is one counterexample to show that the original conditional statement is false.
Determine whether the sequence 15,13,11,9 is an arithmetic sequence if yes, identify the common difference.
The sequence is not an arithmetic sequence because. The n-term for an arithmetic sequence is:
[tex]a_n\text{ = }a_1\text{ + }(n-1)d[/tex]where d is the difference between two consecutive numbers. In this case d = 2. Because
15-13 = 2
13-11 = 2
11- 9 = 2
now, the first term for 15,13,11,9 is 15 = a_1, the second term would be:
[tex]a_2\text{ = }a_1\text{ + }(2-1)d\text{ }[/tex]that is equivalent to say:
[tex]a_2\text{ = 15 + }(2)2=19\ne13\text{ }[/tex]So we can conclude that 15,13,11,9 is not an arithmetic sequence.
Isaac creates a scatter plot showing the association between the height and weight of his maleclassmates. He models the association with the equation w = 6.5h - 275, where h is theclassmate's height in inches and w is the classmate's weight in pounds. What is the meaning of theslope in this equation?
solution
for this case we have the following equation:
w = 6.5h -275
For this case the slope is the number next to the h so then m = 6.5
And the best answer would be:
D) For every 6.5 inch in height , 275 pounds is subtracted to get the weight
Tools Question 2 Nicolas makes toys at a toy shop. The graph represents the relationship between the number of toys (1) that Nicolas makes and the number of hours Toy Making 50 45 40 35 30 Number of Toys 25 20 15 10 2 6 10 Number of Hours Which of the following equations represents a toy-making rate, in toys per hour, that is HALF that of Nicolas's toy-making rate?
The equation of a proportional relationship between two variables x and y with a constant of proportionality k, is:
[tex]y=kx[/tex]If y represents the number of toys and x represents the number of hours, substitute the corresponding values of x and y to find the constant of proportionality k. Use, for instance, the fact that Nicholas made 40 toys in 10 hours:
[tex]40=k\cdot10[/tex]Divide both sides of the equation by 10:
[tex]k=4[/tex]Since Nicholas's toy-making rate is 4 toys per hour, half that rate would be 2 toys per hour. Then, out equation would become:
[tex]y=2x[/tex]Using the letter "t" for toys instead of y and "h" for hours instead of x, then:
[tex]t=2h[/tex]Solve each system using substitution show your answer as an ordered pair no solution or infinite solution
1) Given y = x+2 and y = -4x-8.
Since the left hand sides of both equations are same, equate the right hand side of both the equations.
[tex]x+2=-4x-8[/tex]Add 4x on both sides.
[tex]\begin{gathered} x+2+4x=-4x-8+4x \\ 5x+2=-8 \end{gathered}[/tex]Add -2 on both sides.
[tex]\begin{gathered} 5x+2-2=-8-2 \\ 5x=-10 \end{gathered}[/tex]Divide by 5 on both sides.
[tex]\begin{gathered} x=-\frac{10}{5} \\ =-2 \end{gathered}[/tex]Substitute the value of x into y = x+2.
[tex]\begin{gathered} y=-2+2 \\ =0 \end{gathered}[/tex]Solution is (-2,0).
2) Given y = 3x+1 and y = -2x+6.
Since the left hand sides of both equations are same, equate the right hand side of both the equations.
[tex]3x+1=-2x+6[/tex]Add 2x on both sides.
[tex]\begin{gathered} 3x+1+2x=-2x+6+2x \\ 5x+1=6 \end{gathered}[/tex]Add -1 on both sides.
[tex]\begin{gathered} 5x+1-1=6-1 \\ 5x=5 \end{gathered}[/tex]Divide by 5 on both sides.
[tex]\begin{gathered} x=\frac{5}{5} \\ =1 \end{gathered}[/tex]Substitute the value of x into y = 3x+1.
[tex]\begin{gathered} y=3\cdot1+1 \\ =4 \end{gathered}[/tex]Solution is (1, 4).
3) Given y = -3x-6 and 6x+2y = -2.
Substitute -3x-6 for y into 6x+2y = -2.
[tex]\begin{gathered} 6x+2(-3x-6)=-2 \\ 6x-6x-12=-2 \\ -12=-2 \end{gathered}[/tex]which is not possible. Hence the given system of equations has no solution.
4) Given y = -5 and -8x+4=-20.
From the second equation, -8x+4 = -20, solve for x.
Add -4 on both sides.
[tex]\begin{gathered} -8x+4-4=-20-4 \\ -8x=-24 \end{gathered}[/tex]Divide by -8 on both sides.
[tex]\begin{gathered} x=\frac{-24}{-8} \\ =3 \end{gathered}[/tex]Solution is (-5, 3).