[tex]\dfrac{a^b}{a^c}=a^{(b-c)}[/tex]
Step-by-step explanation:An exponent represents repeated multiplication. For example, ...
... x^3 = x·x·x
... x^2 = x·x
If we divide these, the x's in the denominator cancel an equal number in the numerator:
... (x·x·x)/(x·x) = x
If we represent the repeated multiplication using exponents, we can represent the cancellation by subtraction:
... (x^3)/(x^2) = x^(3-2) = x^1 = x
Once we have this idea in mind that division can be done by subtracting denominator exponents, we can use it regardless of the magnitude or sign of the exponents involved.
There are 100 sophomores at the school. 85% of them are good students. What would be the percent of good students at school if (rounding the answer to the nearest whole number): b ten "A" students were to join this school
Answer:
86%
Step-by-step explanation:
77% students are good students after 10 students join the school.
What is percentage?Percentage is a part of the whole number. It is denoted by % sign.
1 %= 1/100.
Given that,
The number of sophomores in the school = 100
Also, the percentage of good students = 85%
So, number of good students = 100x85/100 = 85
If 10 students join the group,
Then total number of students = 100+10 =110
Percentage of good students = 85 x 100/110
= 77.181
= 77%(round to whole number)
The percentage of good students is 77% in school.
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At 55 mph it will take you approximately _____ feet to stop the car. A. 5 feet B. 100 feet C. 228 feet
Answer:
The correct answer is option C, 228 feet
Step-by-step explanation:
As per Newton’s third law of motion:
V2 – U2 = 2 x a x S
Where V = final velocity
U = Initial Vlocity
a = acceleration (-ve)
S= distance travelled
V= 0 mph
U= 55 mph = 80.6667 ft /sec
0 – (80.6667 ft /sec)2 = 2 x (-g/2) x S
S = (80.6667 ft /sec)2 /(32.2 feet per second per second x0.5)
S = 202.1 feet
So the most nearest option is option C
What's the product of 42⁄3 and 111⁄4 ?
A. 83⁄7
B. 56⁄135
C. 442⁄12
D. 521⁄2
Change the mixed numbers to the impropert fractions:
[tex]4\dfrac{2}{3}=\dfrac{4\cdot3+2}{3}=\dfrac{14}{3}\\\\11\dfrac{1}{4}=\dfrac{11\cdot4+1}{4}=\dfrac{45}{4}[/tex]
[tex]4\dfrac{2}{3}\cdot11\dfrac{1}{4}=\dfrac{14}{3}\cdot\dfrac{45}{4}=\dfrac{7}{1}\cdot\dfrac{15}{2}=\dfrac{105}{2}=52\dfrac{1}{2}\to\boxed{D.}[/tex]
What is the smallest possible integer value of x in order for the product of 720 and x to result in a perfect square?
Answer:
x = 5
Step-by-step explanation:
720 = 2^4 × 3^2 × 5
√720 = 2^2 × 3 × √5
√(720×5) = 2^2 × 3 × 5
Factor x^3-4x^2-3x+18=0 given that 3 is a zero.
A) (x+2)(x-3)^2=0
B) (x-2)(x-3)^2=0
C) (x-2)(x-3)(x+3)=0
D) (x+2)(x-\sqrt{3})(x+\sqrt{3})=0
Answer:
B: (x + 2)(x - 3)^2
Step-by-step explanation:
This is only going to have 3 roots. One of them is (x - 3)
D does not look right. So let's solve it using synthetic division.
3 || 1 - 4 -3 18
3 -3 -18
========================
1 -1 -6 0
So what you have is a quadratic
x^2 - x - 6 = 0 which will factor(x - 3)(x + 2) = 0x - 3 = 0x = 3x + 2 =0x = - 2(x - 3)(x - 3)(x + 2 ) = 0The answer is B
The table shows the value of an account x years after the account was opened. Based on the exponential regression model, which is the best estimate of the value of the account 12 years after it was opened? $8,910 $8,980 $13,660 $16,040
Answer:
Correct choice is B
Step-by-step explanation:
The exponential regression model can be written as exponential function
[tex]y=a\cdot b^x.[/tex]
Then
[tex]5,000=a\cdot b^0=a,\\ \\5,510=a\cdot b^2\Rightarrow 5,510=5,000\cdot b^2,\\ \\b^2=\dfrac{5,510}{5,000}=\dfrac{551}{500}\Rightarrow b\approx 1.05.[/tex]
Thus,
[tex]y=5,000\cdot (1.05)^x.[/tex]
When [tex]x=12,[/tex] you get
[tex]y(12)=5,000\cdot (1.05)^{12}\approx \$8,980.[/tex]
A store had 88 diet sodas.The ratio of diet sodas to regular sodas was 8:4.How many regular sodas were there?
Answer:
44
Step-by-step explanation:
diet : regular = 8:4
=> 88:44
PLEASE HELP!!
Given: e || f and g is a transversal
Prove: 1 8
Given that e || f and g is a transversal, we know that 4 5 by the alternate interior angles theorem. We also know that 1 4 and 8 5 by the . Therefore, 1 8 by the transitive property.
Answer:
Vertical angle property
Step-by-step explanation:
We are given that e is parallel to f and g is a transversal. Using the alternate interior angles property, ∠4=∠5 which is given.
Since, g is a transversal of the two parallel lines e and f, then ∠1=∠4 and ∠8=∠5 by the vertical opposite angle property.
Hence, ∠1≅∠8 by the transitive angle property.
Answer:
verticle angles theorem
Step-by-step explanation:
hope this helps :)
Who does this describe? The country was in chaos, but this scholar helped bring order to society through his teachings about family and government relationships, and the Golden Rule.
A. Siddhartha Gautama
B. Ramayana
C. Asoka
D. Confucius
Answer:
The correct answer is D. This statement describes Confucius.
Step-by-step explanation:
Confucius was a Chinese philosopher, whose teachings had a great influence in China, Korea, Japan and Vietnam. According to tradition, he was born in the city of Qufu, in the Kingdom of Lu, now part of Shandong Province. He is said to have become Minister of Justice in Lu's kingdom. After being forced to resign, he toured the small kingdoms of northeast and central China, explaining his ideas about governance.
He emphasizes his philosophy of morality, right social relationships, justice and honesty, both in personal life and in government. During the Han Dynasty period in China, his teachings became the official philosophy of the state. His teachings were introduced to Europe by the Jesuit Matteo Ricci, the first to Latinize his name as "Confucius."
A gardener is planting two types of trees: Type A is 8 feet tall and grows at a rate of 3 inches per year. Type B is 7 feet tall and grows at a rate of 4 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.
Answer:
Exactly 12 years it will take for these trees to be the same height
Step-by-step explanation:
Slope intercept form: An equation of line is in the form of [tex]y = mx+b[/tex] where m is the slope or unit rate and b is the y-intercepts.
Let x represents the time in years and y represents the height of the tree.
Use conversion:
1 ft = 12 inches
As per the given statement:
Type A is 8 feet tall and grows at a rate of 3 inches per year.
⇒unit rate per year = 3 inches = [tex]\frac{1}{4}[/tex] ft
Then, we have;
[tex]y =\frac{1}{4}x + 8[/tex] ......[1]
Similarly for;
Type B is 7 feet tall and grows at a rate of 4 inches per year.
⇒unit rate per year = 4 inches = [tex]\frac{1}{3}[/tex] ft
then;
[tex]y =\frac{1}{3}x + 7[/tex] .....[2]
To find after how many years it will take for these trees to be the same height.
Since, trees to be the same height;
⇒equate [1] and [2], to solve for x;
[tex]\frac{1}{4}x + 8 = \frac{1}{3}x +7[/tex]
Subtract 7 from both sides we get;
[tex]\frac{1}{4}x + 8-7= \frac{1}{3}x +7-7[/tex]
Simplify:
[tex]\frac{1}{4}x + 1= \frac{1}{3}x[/tex]
Subtract [tex]\frac{1}{4}x[/tex] from both sides we get;
[tex]1= \frac{1}{3}x-\frac{1}{4}x[/tex]
Simplify:
[tex]1 = \frac{x}{12}[/tex]
Multiply both sides by 12 we get;
x = 12
Therefore, exactly it will take for these trees to be the same height is, 12 years
An elephant can run 1/4 of a mile in 36 seconds. At this rate, which expression can be used to determine how fast an elephant runs in miles per hour?
A) 36seconds/1/4 mile = 25 miles per hour
B) 1/4 mile/36 seconds=144 miles per hour
C) 1/4 mile/36 seconds= 25miles per hour
D) 36 seconds/1/4 mile= 144 miles per hour
Answer:
an elephant can run 25 miles per hour
Step-by-step explanation:
60 minutes x 60 seconds = 3,600 seconds in an hour
3600 / 36 = 100
100 x .25 = 25 miles an hour
How to get 5% of 220 files
To find 5% of 220 files, convert the percentage to a decimal (5/100 = 0.05) and multiply it by 220. The result is 11, meaning 5% of 220 files is 11 files.
To calculate 5% of 220 files, you need to use the concept of percentage from basic mathematics. Here's a step-by-step explanation:
Understand that 'percent' means 'per hundred'. So, 5% can be expressed as 5/100.
Multiply the percentage (in this case, 5/100) by the total number of files (which is 220).
Perform the calculation: (5/100) times 220 = 0.05 times 220 = 11.
Therefore, 5% of 220 files is 11 files.
Carolina is mowing lawns for a summer job. For every mowing job, she charges an initial fee plus \$6$6 for each hour of work. Her total fee for a 44-hour job, for instance, is \$32$32. Let F(t)F(t) denote Carolina's fee for a single job FF (measured in dollars) as a function of the number of hours tt it took her to complete it.
Answer:
y=8+6t
Step-by-step explanation:
Answer:
[tex]F(t)=6t+8[/tex].
Step-by-step explanation:
Let t represent number of hours.
We have been given that Carolina charges $6 for each hour of work. So amount charged for t hours of work would be [tex]6t[/tex].
Let us find initial cost by subtracting charges for 4 hours from 32 as:
[tex]\text{Initial cost}=32-4\times 6[/tex]
[tex]\text{Initial cost}=32-24[/tex]
[tex]\text{Initial cost}=8[/tex]
The total cost for t hours of work would be initial cost plus cost per hour: [tex]6t+8[/tex].
Our required function would be [tex]F(t)=6t+8[/tex].
The taxpayer had a qualifying child who is not disabled and who turned 13 on may 31, 2017. They paid a child care provider to care for the child for the entire year while they worked. How many months of child care expenses can they deduct on their tax return?
Answer:
5 months
Step-by-step explanation:
The taxpayer can only deduct the first five months of the qualifying child. May is the fifth month. On June 1st, the qualifying child is going to be 14 years old. Therefore he cannot be included in work-related expenses as specified in the Publication 503 - Main Content from the IRS. Please see the Working-Related Expenses, Indent (b) which is as follows:
(b) The parent of your qualifying person if your qualifying person is your child and under age 13.
A circle has an arc of length 48(3.14) that is intercepted by a central angle of 120°
Jewish people light a menorah on each of the 8 nights. On the first night, 1 candle plus the shamash candle is lit. On the second night, 2 candle plus the shamash candle is lit, and so forth. Over the course of Chanukah, how many candles are lit in all??
Answer:
Step-by-step explanation:
General Remark
Let's start with the long way.
Each day 1 traditional candle (shamash) is lit along with a number of candles representing that day of Chanukah. I'm taking it that a new Shamash candle must be used each day.
Total Candles = 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 44
Givens
a = 2L = 9n = 8Formula
Sum = (a + L)*n/2
Solution
Sum = (2 + 9)*8/2Sum = (11)*4Sum = 44If this is wrong can you tell me what assumption I'm making that is incorrect.
Answer: Your answer is Hanukkah
is 2i a real or complex root?
By definition, i = sqrt(-1) because it is used to solve the equation x^2+1 = 0 or x^2 = -1, which has no real number solutions.
Since i is imaginary or complex, then so is 2i
You can express it as 2i = 0+2i to be in the form a+bi with a = 0 as the real part and b = 2 as the imaginary component.
A 54-kg jogger is running at a rate of 3 m/s. What is the kinetic energy of the jogger? A. 18 J B. 81 J C. 162 J D. 243 J
[tex]\displaystyle\bf\\\text{\bf kinetic energy}=\frac{mv^2}{2}=\frac{54\times3^2}{2}=27\times9=\boxed{\bf243~J} \\\\\text{\bf Correct answer: D.}[/tex]
Answer:
The answer would be be D.243 j
Step-by-step explanation:
Which isn't a function?
Answer:
Step-by-step explanation:
It is the first one because a parabola cannot go sideways from a funtion because there are more than one y values for each x value
what is -2 sqrt20 - sqrt125
Answer:
-9sqrt(5)
Step-by-step explanation:
-2 sqrt20 - sqrt125
Lets simplify the square roots
sqrt(ab) = sqrt(a)sqrt(b)
-2 sqrt(4) sqrt(5) - sqrt(25) sqrt(5)
-2 *2sqrt(5) - 5sqrt(5)
-4sqrt(5) -5sqrt(5)
-9sqrt(5)
In ?ABC, the measure of ?C=90°, the measure of ?A=30°, and CA = 68 feet. Find the length of BC to the nearest foot
Answer:
39 feet
Step-by-step explanation:
Since the triangle is right we can use the tan ratio to find BC
tan 30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{68}[/tex]
multiply both sides by 68
68 tan 30° = BC ⇒ BC ≈ 39 feet ( to nearest foot )
sin(x)/1-cos(x) - 1-cos(x)/sin(x) = 2cot(x)
let's recall the pythagorean identity that sin²(θ) + cos²(θ) = 1.
[tex]\bf \cfrac{sin(x)}{1-cos(x)}-\cfrac{1-cos(x)}{sin(x)}=2cot(x) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{sin(x)}{1-cos(x)}-\cfrac{1-cos(x)}{sin(x)}\implies \cfrac{[sin(x)]^2-[1-cos(x)]^2}{sin[1-cos(x)]} \\\\\\ \cfrac{[sin^2(x)]-[1^2-2cos(x)+cos^2(x)]}{sin[1-cos(x)]}\implies \cfrac{sin^2(x)-1+2cos(x)-cos^2(x)}{sin[1-cos(x)]} \\\\\\ \cfrac{sin^2(x)-[\underline{sin^2(x)+cos^2(x)}]+2cos(x)-cos^2(x)}{sin[1-cos(x)]} \\\\\\ \cfrac{sin^2(x)-sin^2(x)-cos^2(x)+2cos(x)-cos^2(x)}{sin[1-cos(x)]}[/tex]
[tex]\bf \cfrac{-2cos^2(x)+2cos(x)}{sin[1-cos(x)]}\implies \cfrac{2cos(x)[-cos(x)+1]}{sin[1-cos(x)]}\implies \cfrac{2cos(x)[\underline{1-cos(x)}]}{sin[\underline{1-cos(x)}]} \\\\\\ \cfrac{2cos(x)}{sin(x)}\implies 2\cdot \cfrac{cos(x)}{sin(x)}\implies 2cot(x)[/tex]
Convert Fahrenheit to Celsius is C=5/9(F-32) convert 18c to Fahrenheit
Answer:
-7.77778
If you use google it will help u
Which system of equations correspond to this matrix equation?
Question 9 options:
5x + 2x = -7
3y - 4y = -6
5x + 2y = -7
3x + 4y = -6
5x + 2y = -7
3x - 4y = -6
5x - 2y = -7
3x - 4y = -6
Answer:
5x + 2x = -7
3y - 4y = -6
Step-by-step explanation:
Given the matrix, we can multiply across the constant matrix and down the variable matrix
5x +2y = -7
3x -4y = -6
Answer: (C)
Step-by-step explanation:
When multiplying matrices:
Row 1 x Column 1 = the value in Row 1 Column 1
[tex]\left[\begin{array}{cc}5&2\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]= -7[/tex]⇒ 5(x) + 2(y) = -7⇒ 5x + 2y = -7Row 2 x Column 1 = the value in Row 2 Column 1
[tex]\left[\begin{array}{cc}3&-4\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]= -6[/tex]⇒ 3(x) + -4(y) = -6⇒ 3x - 4y = -6Combine the two equations to get:
[tex]\left \{ {{5x + 2y = -7} \atop {3x - 4y = -6}} \right[/tex]
The manufacturer ID number for Proctor and Gamble is (037000) and the item number for a box of Bounce Fabric Softener is (80049). What is the valid UPC?
A) 0-37000-80049-9
B) 0-37000-80049-1
Eliminate
C) 1-37000-80049-1
D) 1-80049-37000-0
Answer:
A) 0-37000-80049-9
Step-by-step explanation:
For a standard bar code, it consists of a five digit manufacturer number and a five digit product number. Check digits are a single digit computed from the other characters in the string of numbers. Check digits are on the far right.
Add the odd number digits: 0+7+0+8+0+9 = 24.
Multiply the result by 3: 24 × 3 = 72.
Add the even number digits: 3+0+0+0+4 =7.
Add the two results together: 72 + 07 = 79.
The last digit is 9
Answer:b
Step-by-step explanation: USA test prep
Please help! Urgent! Will mark brainliest!
Lamar wanted to explain why the measure of angle 5 is equal to the sum of the measures of angles 1 and 3.
Which geometry concepts should be used in Lamar’s work?
A) supplementary angles and the sum of the measures of interior angles of a triangle
B) complementary angles and the sum of the measures of interior angles of a triangle
C) supplementary angles and vertical angles
D) the sum of the measures of interior angles of a triangle and vertical angles
Answer:
B
Step-by-step explanation:
Because the angles make up the interior parts of the triangle without the extra endings
Answer: The answer would be B
Drag one model next to each situation. The correct model for each group represents that situation
The question involves creating and analyzing scientific models, collaborating in groups to build and refine these models based on experimental evidence, and engaging in critical thinking about their accuracy and limitations.
Explanation:The question involves students creating and analyzing models that represent certain scientific situations. Creating a model is a fundamental part of scientific inquiry as it helps in visualizing and understanding complex concepts. Students are tasked with exchanging and labeling pictures or drawings of their models, which aids in the development of the communication of scientific ideas. They then apply their models to specific situations, test these models, and note the outcomes to assess the accuracy and limitations of the models they have built. This process involves critical thinking, collaboration, and application of scientific knowledge.
Moreover, students are required to modify their models based on experimental evidence and discussions about the limitations of their models. When building models of atoms, for example, students must consider basic ratios, an understanding of atomic structure, and the unique characteristics of the element they are representing.
The complete question is:Drag one model next to each situation. The correct model for each group represents that situation
Becki put some stamps into her stamp collection book she put 14 stamps on each page if she completely filled 16 pages how many stamps did she put in the book?
Answer:
224 stamps.
Step-by-step explanation:
We have been given that Becki put 14 stamps on each page.
To find the total number of stamps that Becki put in the book we will multiply the number of stamps put on each page by the number of completely filled pages.
[tex]\text{The total number of stamps in the book}=14\times 16[/tex]
[tex]\text{The total number of stamps in the book}=224[/tex]
Therefore, Becki put 224 stamps in the book.
To find out how many stamps Becki added to her collection, we multiply the number of stamps per page, which is 14, by the number of filled pages, which is 16, resulting in a total of 224 stamps.
To determine how many stamps Becki put into her stamp collection book, we need to calculate the total number of stamps populated over the completely filled pages. She placed 14 stamps on each page and filled 16 pages. The total number of stamps is the product of the number of stamps on each page and the number of pages filled.
The formula we will use is:
Total stamps = Number of stamps per page x Number of filled pages
Substituting the given values:
Total stamps = 14 stamps/page x 16 pages = 224 stamps
Therefore, Becki put 224 stamps in her stamp collection book.
ughhhh please help me i don’t wanna fail again
Answer:
Step-by-step explanation:
Start with (1,2) . One of the pairs has to begin with a 1. Look around to see which set of points has a 1 for the x value.
B and C do. So all you have gotten rid of is A and D. D looks like it might work, but it really does not. It has - 1 as it's starting point. The point must start with 1.
The next step is to find the distance between the 2 given points. The y value for the two points already on the graph is the same so they do not contribute anything to the distance. -3 and 1 are 4 units apart.
1 and ? must also be 4 units apart. Only D does. 1 and -3 are the x values 2 and 6 are the y values. The answer is B
Verify the identity.
cotangent of x divided by quantity one plus cosecant of x equals quantity cosecant of x minus one divided by cotangent of x
Identity to verify:
[tex]\dfrac{\cot x}{1+\csc x}=\dfrac{\csc x-1}{\cot x}[/tex]
Recall that
[tex]\cos^2x+\sin^2x=1[/tex]
Divide both sides by [tex]\sin^2x[/tex] and we get
[tex]\cot^2x+1=\csc^2x[/tex]
or
[tex]\cot^2x=\csc^2x-1=(\csc x-1)(\csc x+1)[/tex]
So if we multiply the numerator and denominator of
[tex]\dfrac{\cot x}{1+\csc x}[/tex]
by [tex]\csc x-1[/tex], we get
[tex]\dfrac{\cot x(\csc x-1)}{(1+\csc x)(\csc x-1)}=\dfrac{\cot x(\csc x-1)}{\csc^2x-1}=\dfrac{\cot x(\csc x-1)}{\cot^2x}[/tex]
Then as long as [tex]\cot x\neq0[/tex], we can cancel terms to end up with
[tex]\dfrac{\csc x-1}{\cot x}[/tex]
and establish the identity.