Answer:
There is only one solution and the solution is (0,4).
Step-by-step explanation:
The given system has equations;
and
We equate the two equations to determine their point of intersection;
We put x=0 into the first equation to get;
There is only one solution and the solution is (0,4).
What is the sum of the
HCF and
LCM of the
number
2³ x 3² x 5x7 and
2² x 5² x 11
Step-by-step explanation:
. Find the factors of 330.
(a)2 x 4 x 5 x 11
(b)2 x 3 x 7 x 13
(c)2 x 3 x 5 x 13
(d)2 x 3 x 5 x 11
Show Answer
2. Find the factors of 1122.
(a)3 x 9 x 17 x 2
(b)3 x 11 x 17 x 2
(c)9 x 9 x 17 x 2
(d)3 x 11 x 17 x 3
Show Answer
3. 252 can be expressed as a product of primes as
(a)2 x 2 x 3 x 3 x 7
(b)2 x 2 x 2 x 3 x 7
(c)3 x 3 x 3 x 3 x 7
(d)2 x 3 x 3 x 3 x 7
Show Answer
4. Which of the following has most number of divisors?
(a)99
(b)101
(c)176
(d)182
Show Answer
5. A number n is said to be perfect if the sum of all its divisors (excluding n itself) is equal to n. An example of perfect number is
(a)6
(b)9
(c)15
(d)21
Show Answer
6. 1095/1168 when expressed in simplest form is
(a)13 / 16
(b)15 / 16
(c)17 / 26
(d)25 / 26
Show Answer
7. Reduce 128352 / 238368 to its lowest terms
(a)3/4
(b)5/13
(c)7/13
(d)9/13
Show Answer
8. The simplest reduction to the lowest terms of 116,690,151 / 427,863,887 is
(a)3/11
(b)7/11
(c)11/3
(d)None of these
Show Answer
9. The highest common factor of 0 and 6 is
(a)0
(b)3
(c)6
(d)Undefined
Show Answer
10. The H.C.F. of 2² x 3³ x 5⁵, 2³ x 3² x 5² x 7 and 2⁴ x 3⁴ x 5 x 7² x 11 is
(a)2² x 3² x 5
(b)2² x 3² x 5 x 7 x 11
(c)2⁴ x 3⁴ x 5⁵
(d)2⁴ x 3⁴ x 5⁵ x 7 x 11
Show Answer
11. The H.C.F. of 2⁴ x 3² x 5³ x 7, 2³ x 3³ x 5² x 7² and 3 x 5 x 7 x 11 is
(a)105
(b)1155
(c)2310
(d)27720
Show Answer
12. H.C.F. of 4 x 27 x 3125, 8 x 9 x 25 x 7 & 16 x 81 x 5 x 11 x 49 is
(a)180
(b)360
(c)540
(d)1260
Show Answer
13. Find the highest common factor of 36 and 84.
(a)4
(b)6
(c)12
(d)18
Show Answer
14. Even numbers are formed by taking at least two at a time from the numbers 0, 4, 8, 9. Their H.C.F. is
(a)2
(b)4
(c)10
(d)None of these
Show Answer
define cultural identity in your own words
Simply put, cultural identity is what identifies one with a group of shared identities such as music, traditions, among others.
What is Cultural Identity?Cultural identity can be defined as the self-perception of an individual which gives them a sense of belonging to an identical group that shares same qualities which may included music, food, traditions, social class, beliefs, ethnicity, among others.
In summary, we can say that cultural identity is what identifies one with a group of shared identities such as music, traditions, among others.
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The pH of a fruit juice is 5.6. Find the hydronium ion concentration, [H3O+], of the juice. Use the formula pH=-log[H3O+].
The hydronium ion concentrate H 30 plus as approximately? moles per liter
The hydroxonium ion concentration of the fruit juice whose pH as given in the task content is; 5.6 can be evaluated as; [H3O+] = 2.51 × 10^-6.
What is the hydroxonium ion concentration of the fruit juice whose pH is 5.6?Since the given pH of the fruit juice is 5.6, the hydroxonium ion concentration of the fruit juice can be evaluated by means of the formula as follows;
pH=-log[H3O+].
5.6 = -log[H3O+].
-5.6 = log[H3O+].
[H3O+] = antilogarithm (-5.6)
[H3O+] = 2.51 × 10^-6.
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select the correct answer which graph is defined by f(x)= |x^2 -x-2|
The graph of the absolute value function can be seen below.
How to get the graph of f(x)?Here we have the absolute value function:
[tex]f(x) = |x^2 - x -2|[/tex]
Notice that the argument of the absolute value function is a quadratic equation, then the graph of the function f(x) will be the graph of the quadratic equation, but such that the part below the horizontal axis is reflected.
Then the graph of the function is the one you can see below:
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The equation y=123.1(1.065)* models the number of college students (in thousands) who studied abroad each year from 1998 through 2013. In this equation, y is the
number of students from a certain country studying abroad (in thousands) and x represents the number of years after 1998.
a. Estimate the number of students studying abroad in 2003.
b. Assuming this equation continues to be valid in the future, use this equation to predict the number of students studying abroad in 2018.
The estimate of the number of students studying abroad in 2003 is 169 and the estimate of the number of students studying abroad in 2018 is 433
a. Estimate the number of students studying abroad in 2003.The function is given as:
y = 123(1.065)^x
Where x represents years from 1998 to 2013
2003 is 5 years from 1998.
This means that
x = 5
Substitute the known values in the above equation
y = 123(1.065)^5
Evaluate the exponent
y = 123 * 1.37008666342
Evaluate the product
y = 168.520659601
Approximate
y = 169
Hence, the estimate of the number of students studying abroad in 2003 is 169
b. Assuming this equation continues to be valid in the future, use this equation to predict the number of students studying abroad in 2018.2018 is 20 years from 1998.
This means that
x = 20
Substitute the known values in the above equation
y = 123(1.065)^20
Evaluate the exponent
y = 123 * 3.52364506352
Evaluate the product
y = 433.408342813
Approximate
y = 433
Hence, the estimate of the number of students studying abroad in 2018 is 433
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Two friends, Jamie and Devin, are working together at the Sparrowtown Cafe today. Jamie works every 2 days, and Devin works every 7 days. How many days do they have to wait until they next get to work together?
Answer:
14 days
Step-by-step explanation:
let assume they both work on Monday (today)
devin works every 7 days,that is devin works every Monday.
jamie has to work for 14 days inorder to work with devin again
Select the correct answer from each drop-down menu.
What structural element of the paragraph is the underlined sentence, and how does it connect ideas in the text?
The underlined sentence
1.the thesis statement for the text
2.the conclusion of the text
3.a piece of evidence for the texts argument
4.a piece of reasoning in the text
It connects ideas in the text by
1.making the main claim of the text
describing why the information provided matters to readers
3. relating a fact or story that demonstrates the texts argument
4. suggesting how a specific example relates to the broader argument
The underlined sentence in the text simply functions as; the conclusion of the text and connects ideas in the text, by making the main claim of the text describing why the information provided matters to readers.
What is the function of the underlined text in the passage?The underlined text in the passage functions as the conclusion to the passage in which case, the information intended to be conveyed is that on the occasion that, regular feeding, good housing, occasional gentle corrections and kindness are in place, there'd be no need for such a cat to steal.
Therefore, the structural element of the paragraph in the underlined sentence, and how it connect ideas in the text is; by making the main claim of the text
describing why the information provided matters to readers.
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correct the error 4⁴- 4³=4¹
The error is that
[tex] {x}^{y} - {x}^{z} \neq {x}^{y - z} [/tex]
Instead, it should be 4⁴ - 4³ = 256 - 64 = 192.
Graph the line Y=2/5X+5
Geometry Question!! PLEASE HELp
The difference between the distance travelled by any point on the record and it's label is; 27.57cm.
What is the difference between the distance travelled in each case?According to the task content, it follows from observation that the quantity required is the difference between the circumference in each case and can be evaluated as follows;
Difference = π(17.78 - 9)
Difference = (22/7) × 8.78
Difference = 27.57cm.
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Your local pizza store sells medium pizzas for $6.79 each, and breadsticks for $2.49 per order.
For a party, you decide to order 4 pizzas and 2 orders of breadsticks. There is a $3 delivery fee, and a 9.4% sales tax will be added to the total. What will be the total bill after tax?
The total bill after tax is $38.44.
What is the total bill?The first step is to determine the total cost of 4 pizzas and 2 orders of breadsticks: (4 x $6.79) + (2 x 2.49) = $32.14
Now, determine the total cost after delivery fee has been added : $3 + $32.14 = $35.14
Now determine the total cost after tax : (1.094) x $35.14 = $38.44
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The total bill after tax of 9.4% is $38.44.
It worthy of note that the sales tax of 9.4% is a percentage of the total purchase bills prior to tax computation, it is the tax due on purchases which is an added percentage of the sales price
total cost of 4 pizzas= $6.79 *4
total cost of 4 pizzas=$27.16
total cost of 2 orders of breadsticks=$2.49*2
total cost of 2 orders of breadsticks=$4.98
total cost of purchase prior to adding delivery cost=$27.16+$4.98
total cost of purchase prior to adding delivery cost=$32.14
total cost of purchase after delivery cost=$32.14+$3
total cost of purchase after delivery cost=$35.14
total cost inclusive of 9.4% sales tax=$35.14*(1+9.4%)
total cost inclusive of 9.4% sales tax=$35.14*1.094
total cost inclusive of 9.4% sales tax=$38.44
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Find the length of a segment in the coordinate plane with endpoints (-4,-5) and (8, 1).
Answer:
Step-by-step explanation:
d = 13.416408
For:
(X1, Y1) = (-4, -5)
(X2, Y2) = (8, 1)
Answer:
L = 9.49 units
Step-by-step explanation:
From the 1st point to the 2nd, x changes by 12; from the 1st to the 2nd, y changes (increases) by 6. These results (12 and 6) represent the leg length of a right triangle whose diagonal length we wish to calculate using the Pythagorean Theorem:
12^2 = 144 and 6^2 = 36.
Combining these results in the length of the diagonal:
L = √(144 + 36) = √180 = 13.42 units using the Pythagorean Theorem
Rounding off, we get L = 9.49 units
NO LINKS!! Please help me with this problem.
What is the standard form of the equation of the ellipse?
Answer:
[tex]\dfrac{x^2}{49}+\dfrac{y^2}{36}=1[/tex]
Step-by-step explanation:
From inspection of the given graph, we can see that the center of the ellipse is the origin (0, 0) and the longest diameter of the ellipse is across the x-axis.
Therefore, we can use the general equation of a horizontal ellipse with its center at (0, 0):
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]
where:
center = (0, 0)Vertices = (±a, 0)Co-vertices = (0, ±b)Foci = (±c, 0) where c²=a²−b²Major Axis: longest diameter (2a)Minor Axis: shortest diameter (2b)Major radius: one half of the major axis (a)Minor radius: one half of the minor axis (b)From inspection of the ellipse:
Vertices = (-7, 0) and (7, 0)Co-vertices = (0, 6) and (0, -6)Therefore, a = 7 and b = 6
Substitute the found values of a and b into the formula:
[tex]\implies \dfrac{x^2}{7^2}+\dfrac{y^2}{6^2}=1[/tex]
[tex]\implies \dfrac{x^2}{49}+\dfrac{y^2}{36}=1[/tex]
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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The given figure shows a Horizontal Ellipse with its centre at origin, and as we observe the figure, we can conclude that :
Length of major axis is :
[tex]\qquad \sf \dashrightarrow \: 2a = 14[/tex]
[tex]\qquad \sf \dashrightarrow \: a = 7[/tex]
and that of minor axis :
[tex]\qquad \sf \dashrightarrow \: 2b = 12[/tex]
[tex]\qquad \sf \dashrightarrow \: b = 6[/tex]
Equation of Ellipse will be ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{ {x}^{2} }{ {a}^{2} } + \dfrac{ {y}^{2} }{ {b}^{2} } = 1[/tex]
[ plug in the values ]
[tex]\qquad \sf \dashrightarrow \: \dfrac{ {x}^{2} }{ {7}^{2} } + \dfrac{ {y}^{2} }{ {6}^{2} } = 1[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{ {x}^{2} }{ {49}^{} } + \dfrac{ {y}^{2} }{ {36}^{} } = 1[/tex]
I need help with the slope
Answer:
1/5 :D
Step-by-step explanation:
Lets pick 2 point on the graph :)
We need this to find the slope!
Lets use (-5,1) and (0,2) :)
First we subtract the y coordinates! :)
2 - 1 = 1
Then we subtract the x coordinates!
0 - (-5) = 5
Now we divide!
1/5
Our answer is 1/5!
Have an amazing day!!
Please rate and mark brainliest!!
Answer:
first choice : 1/5
Step-by-step explanation:
need 2 points
one point is (0,2)
another is (5,3)
slope formula is
y2 - y1 / x2 - x1
3 - 2 / 5 - 0
1/5
You have a $10,000, you must choose between Gamble A and Gamble B. Gamble A will cost $5,000. If you win, you will get $15,000, but if you lose, you will get nothing. On the other hand, Gamble B will cost $10,000 that will give $30,000 if you win, otherwise get nothing if lost. You are risk averse, and your preference for wealth (W) is specified by the relationship U(W)= √W. Probability of wining is 0.4 and losing is 0.7. Which gamble will you choose and why?
Part of your job as manager is to count the cash for the daily bank deposit. When you count the cash, you have 47 ones, 22 fives, 9 tens and 17 twenties. You also have 67 pennies, 12 nickels, 9 dimes and 15 quarters. What is the total amount of the deposit?
The total amount of the deposit is $592.92.
What is the total amount of the deposit?The total amount of the deposit can be determined by adding all the money deposited together.
(47 x 1) + (22 x 5) + (9 x 10) + (17 x 20) + (67 x 0.01) + (0.05 x 12) + (9 x 0.1) + (15 x 0.25)
47 + 110 + 90 + 340 + 0.67 + 0.60 + 0.9 + 3.75 = $592.92
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Petsmart's marketing team finds in their most recent report that they sell 45 guinea pigs a
year. Their sales team wanted to increase their sales and grabbed a sample of 8 types of
rodents to put on a flash sale. They sold an average of 34 rodents with a standard
deviation of 21 rodents.
Answer:
p(x)=x3-3x2+4x+50 and g(x)=x-3
For csc 330:
a) state value of the ratio exactly
b) find one equivalent expression
c) draw a diagram to illustarte.
The value of the ratio based on the angle illustrated is 1:12.
How to illustrate the information?From the information given, it should be noted that the angle in a circle is 360°. Therefore, the value of theta will be:
= 360° - 330°
= 30°
The equivalent expression based on the angle will be:
= 30/360
= 1/12
= 1:12
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which of the following statements is true about the solution of the system? 2x-y=8 and y=2x-3
Answer:
no roots.
Step-by-step explanation:
[tex]\left \{ {{2x-y=8} \atop {y=2x-3}} \right. \ = > \ \left \{ {{2x-y=8} \atop {2x-y=3}} \right. \ = > \ no \ solution.[/tex]
Given that L1 || L2, find the measures of angles a and b when 0 = 43°
Answer:
a = 43 degrees
b = 137 degrees
Step-by-step explanation:
according to the alternate interior angle theorem, angle a equals angle theta, so angle a = 43 degrees
angle b is the supplement of angle a, so angle b = 180-angle a, or 137
A tree is 14 meters tall. What is its height in feet? Use the following conversion: 1 meter is 3.3 feet
Billy eats 28 apples and he had 40 apples at the start a kid asks for an apple how many apples are there left?
Answer: 11
Step-by-step explanation: 40-28= 12-1=11
Answer:
11 apples are left.
Step-by-step explanation:
Since Billy ate 28 apples from the 40 apples he had at the start, you have to subtract 40-28, which equals 12. Lastly, you subtract 12-1, since a kid asks Billy for an apple.
What is the solution to the equation below? (Round your answer to two
decimal places.)
5 Inx= 3.5
A. x = 4.17
B. x = 3.98
C. x = 42.40
D. x=201
Answer: 2.01
Step-by-step explanation:
[tex]5\ln x=3.5\\\\x=\frac{3.5}{5}\\\\x=e^{3.5/5}\\\\x \approx 2.01[/tex]
If someone could help me with this problem
The equation of the given Absolute Value Function is; y = |-2x + 4|
How to interpret Linear Graphs?We can see that the given graph is a Linear graph but since it is V-shaped, we can say that it is a graph of an absolute value function.
Now, from the graph we see that;
At x = 0, y = 4
At x = 1, y = 2
At x = 2, y = 0
At x = 3, y = -2
At x = 4, y = 0
At x = 5, y = 2
We can see that the y-intercept is at y = 4.
Slope between two consecutive points is;
(2 - 4)/(1 - 0) = -2
Equation is; y = -2x + 4
Now, this is an absolute value function and as such we will write it as;
y = |-2x + 4|
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josh is looking to get a new car because he decided he was spending too much on gas. over the past year he found that he drove 7,700 miles. at current gas prices [ youll need to actually consider your current cost for gasoline ]. he was getting about 27 miles per gallon. if he bought a vehicle that realizes 33 miles per gallon. what might be a reasonable estimate of monthly gas costs?
Josh's monthly fuel expenses are $1,050.
PricesGiven that Josh is looking to get a new car because he decided he was spending too much on gas, and over the past year he found that he drove 7,700 miles, and at current gas prices of $4.5 he was getting about 27 miles per gallon, To determine, if he bought a vehicle that realizes 33 miles per gallon, what might be a reasonable estimate of monthly gas costs, the following calculation must be made:
27 = 10033 = X3300 / 27 = X122.22 = X122.22 = 100100 = X10000 / 122.22 = X81.81 = X(7700 / 33) x 4.5 = X233.33 x 4.5 = X1050 = XTherefore, Josh's monthly fuel expenses are $1,050.
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Answer:Josh's monthly fuel expenses are $1,050.
Step-by-step explanation:
Find the surface area of this cone.
60π m2
20π m2
36π m2
54π m2
The surface area of a cone with radius of 4 m and slant height of 5 m is 36π m²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The surface area of a cone with radius (r) and slant height (l) is:
S.A = πr(r + l)
Given that r = 4, l = 5, hence:
S.A = π(4)(4 + 5) = 36π m²
The surface area of a cone with radius of 4 m and slant height of 5 m is 36π m²
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Answer:
36π m2
Step-by-step explanation:
The Florida VPK assessment is considered a progress monitoring tool when administered at two assessments periods across the school year.
a. True
b. False
The given statement about the Florida VPK assessment administered at two assessments periods across the school year is; B: False
What is the Progress Monitoring Tool?Progress monitoring or CBM is a term used in the education field to describe the process whereby the progress of students in areas like mathematics, reading, and writing are monitored on a daily and weekly basis.
Now, in Florida in the United States, This progress monitoring is called Florida Voluntary Prekindergarten (VPK) Assessment. There is usually a different version of each assessment measure that will be administered at three different times during the school-year VPK Program.
Thus, the given statement is false.
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Answer:
Step-by-step explanation:
false
In math class, James, Hadley, and Gwen were challenged to go stand on the field in a random location and find the distance between themselves using only one length. They were also each given a protractor to find the angle between each other. Using this diagram, solve for the missing side lengths of the triangle. Round to the nearest hundredth. A triangle where James, Hadley, and Gwen are labelled on the vertices. The angle of James is 61 degrees, Hadley is 73 degrees, and Gwen is 46 degrees. The one length that is labelled is between James and Hadley and measures at 15 meters. Gwen to Hadley is what? Gwen to James is what?
The interior angles of the triangle of 61°, 73°, and 46°, and the distance from James to Hadley of 15 meters gives;
Gwen to Hadley ≈ 18.24 metersGwen to James ≈ 19.94 metersHow can the distances between the students be found?The given angles are;
At James's location; 61°
At Hadley's location; 73°
At Gwen's location; 46°
The distance between James and Hadley = 15 meters
The angle facing the distance between James and Hadley is the angle at Gwen, 46°
The angle facing the distance between Gwen and James is the angle at Hadley, 73°
The angle facing the distance between Gwen and Hadley is the angle at James, 61°
The angle that faces the 15 meter length is the angle at Gwen, which is 46°
By the rule of sines, the distance from Gwen to Hadley is therefore;
[tex] \frac{15}{sin( 46 ^ \circ)} = \frac{Gwen \: to \: Hadley}{sin( 61 ^ \circ)} [/tex]
Which gives;
[tex] Gwen \: to \: Hadley= \frac{15 \times sin( 61 ^ \circ) }{sin( 46 ^ \circ)} \approx 18.24[/tex]
Gwen to Hadley ≈ 18.24 metersSimilarly, we have;
[tex] \frac{15}{sin( 46 ^ \circ} = \frac{Gwen \: to \: James}{sin( 73 ^ \circ)} [/tex]
Therefore;
[tex] Gwen \: to \: James = \frac{15 \times sin( 73 ^ \circ) }{sin(46 ^ \circ)} \approx 19.94 [/tex]
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Miguelle is deciding which type of heating system to put in his house. An oil system costs $2700 to install and
$900 per year to operate. A solar system costs $9000 to install and $200 per year to operate.
Determine your variables
Let=
Let=
2. Create your equations and number them.
3.Solve the linear system using ELIMINATION OR SUBSTITUTION.
Answer: (9, 10800)
Step-by-step explanation:
We will first let x be the number of years and y be the total cost.
In that case, let's plug in the values for each into the equation y=mx+b, where m is the slope and b is the y-intercept.
The y-intercept will be the value we start with before any years pass, so it will be the installation cost. The slope is how fast the total cost will increase. Since the operation costs have to be added on every year, it will be our slope.
With that in mind, let's create both of our equations:
y = 900x + 2700 (Oil system)y = 200x + 9000 (Solar system)Since y is solved for in the first equation, we can substitute it into the second equation:
[tex]900x + 2700 = 200x + 9000[/tex]
[tex]700x + 2700 = 9000[/tex] [Subtracting 200x from both sides]
[tex]700x = 6300[/tex] [Subtracting 2700 from both sides]
[tex]x = 9[/tex] [Dividing both sides by 700]
We can now substitute 9 for x in any equation and solve for y. Here I substituted it into the first one:
[tex]y = 900(9) + 2700[/tex]
[tex]y = 8100 + 2700[/tex] [Multiplying]
[tex]y = 10800[/tex] [Adding]
Hence, the solution to this linear system is (9, 10800).
3 to 2 if there are 120 children who like pizza, how many total
Answer:
320
Step-by-step explanation:
Is the 3 to 2 part to part? Out of every 5 people, 3 prefer pizza and 2 do not. We can us this to set up a proportion.
3/5 = 120/x The 3 represent the part that like pizza over the whole of 5. The second ratio is showing the actual number of people that liked pizza over the total number of people.
What would be multiply 3 by to get 120? 40. So, we will multiply 5 times 40 to get the total number of people. 5 x 40 = 200