Simplify the expression.
x^5/x^9
a. 1/x^4
b.x^14
c. 1/x^14
d.x^4
Write each equation in slope-intercept form of the equation of a line.
3x+4y–12=0
Answer:
The slope − intercept form is __
The slope is __
The y − intercept is __
The x-intercept is 4
The y-intercept is 3
The slope is -3/4
Solve for x. 6x-10≤8 or 1/3 x+6>12
The solution is
[tex]x\le 3 \:or \:x>18[/tex]
[tex]<b><u>EXPLANATION</u></b>[/tex]
[tex]6x-10\le 8\: or \frac{1}{3}x+6>12[/tex]
We group like terms, to obtain;
[tex]6x\le 8+10\: or \frac{1}{3}x>12-6[/tex]
Simplify to get,
[tex]6x\le 18\: or \frac{1}{3}x>6[/tex]
We further simplify to get;
[tex]x\le 3\: or x>18[/tex]
This can also be rewritten as;
[tex]x\le 3, x>18[/tex]
Or
[tex](-\infty 3] \cup (18,+ \infty)[/tex]
This can be represented on the number line as shown in the diagram.
Answer: (-∞,3)∪(18,∞)
Step-by-step explanation:
To solve this problem you must apply the proccedure shown below:
1. You must solve for x, as following:
[tex]6x-10\leq8\\6x\leq18\\x\leq3[/tex]
[tex]\frac{1}{3}x+6>12\\x>3(6)\\x>18[/tex]
2. Therefore, you have that the result is:
(-∞,3]∪(18,∞)
A cell phone company charges $45 a month for phone service and $0.25 for each text message. Which equation can be used to find the total number of text messages sent in a month? How many text messages were sent if the monthly bill was $75?
Only enter the capital letter of your choice into the blank (A, B, C, or D).
A) 45 + 0.25t = C; t = 480
B) 45t + 0.25 = C; t = 120
C) 45t + 0.25 = C; t = 480
D) 45 + 0.25t = C; t = 120
Hey!!
A cell phone company charges $45 a month and hence, this would be constant and would be same the same value. And the company charges $0.25 for every text message.
Let's take the number of text messages as ' t '
The question asks us to find the number of text messages needed to make it $75 for the first month.
We know, the constant is $45 and we know the number of text messages as ' t ' and we also know the cost of each text messages is $0.25. And with all this given, we can find the total cost which is denoted by ' c '.
The total cost would be the price of a month added to the cost of text messages.
The total cost = c
The price of for month = $45
The price of text messages = $0.25t
Now, let's form the equation :
... c = 45 + 0.25t ( this is the equation )
The total cost given is $75
Hence, the equation would be :
... 75 = 45 + 0.25t
Subtract 45 on both sides
... 30 = 0.25t
Divide 0.25 on both sides
... t = 120
Hence, the answer would be option ( D )
Hope my answer helps!!
what is the value 4 in 12.47
It's in the tenths place.
What is m∠M ? Enter your answer in the box. ° The figure shows what appears to be obtuse triangle M N O with obtuse angle M. The measure of angle M is left parentheses 3 times x minus 16 right parentheses degrees. The measure of angle N is x degrees. The measure of angle O is left parentheses x plus 6 right parentheses degrees.
We know:
The sum of the measures of the angles of a triangle is equal 180°.
Therefore we have the equation:
[tex](3x-16)+x+(x+6)=180\\\\3x-16+x+x+6=180\\\\(3x+x+x)+(-16+6)=180\\\\4x-10=180\ \ \ \ |+10\\\\4x=190\ \ \ \ |:4\\\\x=47.5[/tex]
m∠M = (3x-16)°
Substitute:
[tex]m\angle M=(3\cdot47.5-16)^o=(142.5-16)^o=126.5^o[/tex]
Answer: m∠M = 126.5°Answer:
98
Step-by-step explanation:
I got it wrong when I typed in 126.5, its actually 98
Go forth and Conquer
If Mckenna has 17 cups of flour how many cakes did she bake?
Factor the expression over the complex numbers.
x^2+52
Here we are given the expression:
[tex]x^{2}+52[/tex]
Now let us equate it to zero to find x first,
[tex]x^{2}+52=0[/tex]
Now subtracting 52 from the other side,
[tex]x^{2}=-52[/tex]
taking square root on both sides,
So we will get two values of x as ,
[tex]x=+2\sqrt{-13}[/tex]
[tex]x=-2\sqrt{-13}[/tex]
Now we can write square root -1 as i,
So our factors become,
[tex]x=+2i\sqrt{13}[/tex]
[tex]x=-2i\sqrt{13}[/tex]
Answer:
The final factored form becomes,
[tex](x+2i\sqrt{13})(x-2i\sqrt{13})[/tex]
Convert to decimal expression 0.2777... To a fraction
Jose can read 7 pages of his book in 5 minutes at this rate how long will it take for him to read the full 175 page book
Answer:
125 minutes
Step-by-step explanation:
At 2pm the level of water in the pool was 10 feet.At 6pm the level of water was 2 feet .Find the constant rate of the water.
Answer:boi
Step-by-step explanation:
q + 12 - 2 (q-22)>0
step by step please hurry ); <3
q + 12 - 2(q - 22) > 0 |use distributive property
q + 12 +(-2)(q) + (-2)(-22) > 0
q + 12 - 2q + 44 > 0 |combine like terms
(q - 2q) + (12 + 44) > 0
-q + 56 > 0 |subtract 56 from both sdies
-q > -56 |change the signs
q < 56Six students want to participate in the spelling bee, but there are only three spots. In how many ways can a group of three students be chosen?
The number of ways can a group of three students be chosen is 20 ways
What are Combinations?The number of ways of selecting r objects from n unlike objects is given by combinations
ⁿCₓ = n! / ( ( n - x )! x! )
where
n = total number of objects
x = number of choosing objects from the set
Given data ,
Let the number of ways of selecting students be A
Now , the total number of students = 6
And , to choose 3 students out of 6 without regard to order. The formula for combinations is
n C r = n! / r!(n-r)!
where n is the total number of items, and r is the number of items to choose
6 C 3 = 6! / 3!(6-3)! = 20
Hence , there are 20 ways to choose a group of three students out of six
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The correct number of ways to choose a group of three students from six is [tex]\boxed{20}.[/tex]
To solve this problem, we can use the concept of combinations from combinatorics. A combination is a way of selecting items from a collection, such that the order of selection does not matter. In our case, we have six students and we want to choose three of them to participate in the spelling bee. The order in which we choose the students does not matter since all three will participate equally.
The formula for calculating combinations is given by:
[tex]\[ C(n, k) = \frac{n!}{k!(n-k)!} \][/tex]
where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial, which is the product of all positive integers up to that number.
For our problem:
[tex]- $n = 6$[/tex] (total number of students)
[tex]- $k = 3$[/tex] (number of students to choose)
Plugging these values into the formula, we get:
[tex]\[ C(6, 3) = \frac{6!}{3!(6-3)!} \][/tex]
Calculating the factorials, we have:
[tex]\[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \][/tex]
[tex]\[ 3! = 3 \times 2 \times 1 = 6 \][/tex]
[tex]\[ (6-3)! = 3! = 6 \][/tex]
Now, we substitute these values into the combination formula:
[tex]\[ C(6, 3) = \frac{720}{6 \times 6} \][/tex]
[tex]\[ C(6, 3) = \frac{720}{36} \][/tex]
[tex]\[ C(6, 3) = 20 \][/tex]
Therefore, there are 20 different ways to choose a group of three students from six for the spelling bee.
please help asap 25 pts
Remark
This is much the same as the last inequality that you posted. When it tells you that you have 1 condition that is more than and one condition that is less than, then you need a compound statement. One of A and B is correct. C or D never will be.
At Least 4
This is the more than condition. You need 4 or more pennies to add to the collection. The rule is the same. The pointy end always points towards the smallest amount
4 ≤ x
No more than 2
That means that you can have 2 or under. The pointy end points to the x
2 ≥ x The biggest number (open end of the arrow) points at the 2.
Answer
2 ≥ x or 4 ≤ x That means the answer is A
A cereal box that is shaped like a rectangular prism has a length of 5 centimeters, a width of 4 centimeters, and a height of 10 centimeters. What is the volume?
200 is the volume of the cereal box
Can someone help me do this?
A. -13ab
B. 5a^2b
C. 3
Alleen can read 1.5 pages for every page her friend can read.Alleen's mom was very extcited and she said to alleen: "so,if your friend reads 20 pages, you can read 25 in tge same time period!" is alleen mom correct ?
Answer:
no. she can read 30
Ingrid types 3 pages in the same amount of time that tanya types 4.5 pages. If the grid and tanya start typing at the same time how many pages will tanya have typed when ingrid has typed 11 pages ?
A star track runner ran 315 feet in nine seconds. What was his average speed in feet per second?
If it is multiplied by the identity matrix, what is the resulting matrix?
Answer:
D. [tex]\left[\begin{array}{cc}4&5\\-3&2\\\end{array}\right][/tex]
Step-by-step explanation:
The reason it is called an "identity matrix" is that it doesn't change anything. The result is what you started with.
When the matrix A = [ [2, 3], [4, 5] ] is multiplied by the 2x2 identity matrix, the resulting matrix is still A itself: [ [2, 3], [4, 5] ].
When you multiply a matrix by the identity matrix, the result is the original matrix itself. In this case, matrix A is given as A = [ [2, 3], [4, 5] ], and you want to find A * I, where I represents the identity matrix.
The identity matrix is a square matrix with ones on the main diagonal and zeros everywhere else. In this case, since A is a 2x2 matrix, you would use a 2x2 identity matrix, which looks like:
I = [ [1, 0], [0, 1] ]
Now, when you multiply A by I:
A * I = [ [2, 3], [4, 5] ] * [ [1, 0], [0, 1] ]
You can perform matrix multiplication as follows:
[ (2*1 + 3*0), (2*0 + 3*1) ]
[ (4*1 + 5*0), (4*0 + 5*1) ]
Simplifying the calculations:
[ 2, 3 ]
[ 4, 5 ]
The resulting matrix is exactly the same as matrix A. So, A * I equals the original matrix A: [ [2, 3], [4, 5] ].
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The probable question maybe:
Given the matrix A = [ [2, 3], [4, 5] ], what is the resulting matrix when it is multiplied by the identity matrix of the appropriate size?
What is the distance between these two points on a number line?
178 and 313
A.
–491
B.
–135
C.
135
D.
491
Below is the graph of y = g(x)
Translate it to make it the graph of y = g(x)^2
PLEASE SOMEONE HELP ME??
Instead of y = g(x)^2, it should be y = g(x)+2
What this means that every point on g(x) will be shifted up 2 units. A point like (2,-1) which is the saddle point shown on the graph, will move up to (2,1) after you shift up 2 units. Every other point will follow the same path. Another example: The point (0,-5) -- which is the y intercept -- will move up to (0,-3).
Check out the attached image below for a visual of what's going on.
The graph of the translation to make it y = g(x) + 2 is added as an attachment
Translating the graph to make it y = g(x) + 2From the question, we have the following parameters that can be used in our computation:
The graph of y = g(x)
Translating the graph to make it y = g(x) + 2, we simply move the given up by 2 units
This means that the curves are moved up by 2 units
The graph to make it y = g(x) + 2 is added as an attachment
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HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
1 and 4 are correct. 2 and 3 are not.
Step-by-step explanation:
1.
When x = 0 where does the horse start?
y = 1.5*sin(0 + 0.5)*2*pi + 1.5
y = 1.5*sin(0.5*2pi) + 1.5
y = 1.5*sin(pi) + 1.5 But sin pi = 0
y = 0 + 1.5 So the horse is starting at the midpoint of it's travel.
2.
This one is a trick question. You can reason it without exact answers. At some point the sin(x + 0.5)*2pi will equal 1. When it does 1.5 * 1 + 1.5 = 3.0 At some other point sin(x + 0.5)*2pi = -1. When that happens the whole thing goes to 0. So the total of the distance traveled is 6 not three.
3.
You can figure this one out by letting x = 0.01 When it does then the value of the function is
y = 1.5*sin [(0.01 + 0.5)*2pi] + 1.5
y = 1.5*sin(0.51*2*pi) + 1.5
y = 1.5*sin(3.204424) + 1.5
y = 1.5*(- .0623) + 1.5
y = -0.9418 + 1.5
y = 1.4058 so it is going downward The value is getting smaller.
4.
The horse starts out in the middle of the pole. What does x need to equal so that x + 0.5 = 1 ? And why 1. The answer to why 1 is that then the sine function will equal sin(2*pi)
That happens when x = 0.5 which is 1/2 a minute. If it takes 1/2 a minute to execute 1 complete cycle, then in 5 minutes the cycle will be executed 10 times. This one is correct.
To convert 4,450 m to cm, you would move the decimal point _____ places to the _____.
move the decimal point 2 places to the right
note 1m = 100 cm
4450m = 4450 × 100 cm
multiplying by 100 is equivalent to moving the decimal point 2 places to the right
Name three ways you can solve a system of nonlinear equations.
Substitution.
Elimination.
Using a Combination of methods.
Using absolute value
I hope this helps!
The coordinates of the vertices of △PQR are P(1, 4) , Q(2, 2) , and R(−2, 1) . The coordinates of the vertices of △P′Q′R′ are P′(−1, 4) , Q′(−2, 2) , and R′(2, 1) .
Which statement correctly describes the relationship between △PQR and △P′Q′R′ ?
△PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a translation 2 units to the left, which is a rigid motion.
△PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a reflection across the y-axis, which is a rigid motion.
△PQR is not congruent to △P′Q′R′ because there is no sequence of rigid motions that maps △PQR to △P′Q′R′ .
△PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a reflection across the x-axis, which is a rigid motion.
ANSWER
The correct answer is B
EXPLANATION
If we analyse the coordinates carefully, you realize there is a mapping of
[tex](x,y)\rightarrow(-x,y)[/tex]
This is a reflection in the y-axis.
Since the transformation is a reflection, the shape is preserved. Therefore, the image triangle P'Q'R' of triangle
PQR are congruent.
Answer:
B
Step-by-step explanation:
Need help asap please! A toy company has determined that the revenue generated by a particular toy is modeled by the following equation: 13x - 0.025x² The variable x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars. What is the maximum revenue the company can earn with this toy?
The equation is r(x) = 10x - 0.025x² where x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars.
For maximum r, r'(x) = 0
It becomes: r'(x) = [tex]10-0.025\times2x=0[/tex]
= [tex]10-0.5x=0[/tex]
[tex]x=\frac{10}{0.05}[/tex]
x= 200
Hence, r(200) = [tex]10\times200-0.025\times200^{2}[/tex]
Solving it we get,
r(200) = 1000
Hence, maximum revenue the company can earn with this toy is $1000.
The zoo feeds the tortoise, rhinoceros, and zebra a total of 23 pounds of vegetables a day. How many pounds does the zoo feed the animals a month based on an average 30 day month? Write an equation to show how the supply changes each month.
PLEASE HELP ME
If I understand your question correctly, you want to know how many pounds of vegetables the zoo feeds the animals a month if its a 30 day month?
In that case it would be 23 pounds times 30 days which is 690 pounds of vegetables. SO the zoo feeds the animals 690 pounds of vegetables to the animals each month.
Is that what your asking for?
To calculate the total monthly vegetable supply for the zoo animals, you multiply the daily feed amount by the average number of days in a month (23 pounds/day * 30 days/month = 690 pounds/month).
Explanation:The student's question involves calculating the total amount of vegetables fed to the animals at the zoo over a month. To find this, we can set up a simple multiplication equation, where we multiply the daily food requirement by the number of days in a month. According to the question, the zoo feeds the tortoise, rhinoceros, and zebra a total of 23 pounds of vegetables a day. We are given that an average month is considered to have 30 days. So, the equation to find the total monthly vegetable supply for the animals would be:
23 pounds/day × 30 days/month = Total pounds/month
By multiplying these two numbers together, we get:
23 pounds/day × 30 days/month = 690 pounds/month
So, the zoo feeds the animals a total of 690 pounds of vegetables in an average 30 day month. If we want to express how the supply changes each month, we can write the equation as S = 23 × D, where S represents the total monthly supply and D represents the number of days in the month.
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Mitchel are 45 hotdogs in 3 minutes at the annual hot for eating contes. What is mitchel’s unit rate
Mitchel Unit rate is 15 hotdogs per minute we know this because it show 45 hotdogs in 3 minutes and 45 divided by 3 is 15 so the unit rate is 15.
How many solutions are there to the equation below? 14x + 2 = 12x
this is an equation in one variable and has only one solution
14x + 2 = 12x ( subtract 12x from both sides )
2x + 2 = 0 ( subtract 2 from both sides )
2x = - 2 ( divide both sides by 2 )
x = [tex]\frac{-2}{2}[/tex] = - 1 ← one solution
The equation 14x + 2 = 12x has only one solution.
14x + 2 = 12x
subtract 12x from both sides
14x - 12x + 2 = 12x - 12x
2x + 2 = 0
subtract 2 from both sides
2x + 2 - 2 = 0 - 2
2x = - 2
divide both sides by 2
2x / 2 = -2 / 2
x = -1
Therefore, the equation have only one solution.
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