Answer:
(1 , -2) and r = 4
Step-by-step explanation:
x² + y² - 2x + 4y - 11 = 0
x² - 2x + 1 - 1 + y² + 4y + 4 - 4 - 11 = 0
(x - 1)² - 1 + (y + 2)² - 4 - 11 = 0
(x - 1)² + (y + 2)² = 16
We know equation of circle is of the form
(x - h)² + (y - k)² = r²
So, center is (1 , -2) and radius is 4
How many 6-digit whole numbers have the digits 2, 0, 2, and 2 as a 4-digit consecutively ordered block with no other digits between them?
There are 1680 digits 2, 0, 2, and 2 as a 4-digit consecutively ordered block with no other digits between them
How to determine the selectionTo determine the number of whole numbers, the following must be true
Case 1: If the sequence starts from the first digit
The first digit can be any of the three 2's (i.e. 3 digits)The second digit can only be 0The third digit can be any of the remaining 2's (i.e. 2 digits)The fourth digit can only be the last 2 (i.e. 1 digit)The fifth digit can be any of 0 - 9 (i.e. 10 digits)The sixth digit can be any of 0 - 9 (i.e. 10 digits)So, we have:
[tex]Case\ 1 = 3 * 1 * 2 * 1 * 10 * 10[/tex]
[tex]Case\ 1 = 600[/tex]
Case 2: If the sequence starts from the second digit
The first digit can be any of 1 - 9 (i.e. 9 digits)The second digit can be any of the three 2's (i.e. 3 digits)The third digit can only be 0The fourth digit can be any of the remaining 2's (i.e. 2 digits)The fifth digit can only be the last 2 (i.e. 1 digit)The last digit can be any of 0 - 9 (i.e. 10 digits)So, we have:
[tex]Case\ 2 = 9 * 3 * 1 * 2 * 1 * 10[/tex]
[tex]Case\ 2 = 540[/tex]
Case 2: If the sequence starts from the third digit
The first digit can be any of 1 - 9 (i.e. 9 digits)The second digit can be any of 0 - 9 (i.e. 10 digits)The third digit can be any of the three 2's (i.e. 3 digits)The fourth digit can only be 0The fifth digit can be any of the remaining 2's (i.e. 2 digits)The last digit can only be the last 2 (i.e. 1 digit)So, we have:
[tex]Case\ 3 = 9 * 10 * 3 * 1 * 2 * 1[/tex]
[tex]Case\ 3 = 540[/tex]
The total number of whole numbers is:
[tex]Total = 600 + 540 + 540[/tex]
[tex]Total = 1680[/tex]
Hence, there are 1680 6-digit whole numbers that the digits
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Solve the equation.
-5 - 2 3/7 =
Answer:
-52/7 or 7 3/7
Step-by-step explanation:
-5 is also -35/7
2 3/7 is also 17/7
-35/7-17/7 = -52/7
-52/7 = 7 3/7
Answer:
-7 3/7
Step-by-step explanation:
-5 -2 3/7
Factor out the negative sign
-(5 + 2 3/7)
Write as a sum
-(5 + 2 + 3/7)
Calculate
-(7 + 3/7)
Write as a mixed number
-7 3/7
Hope this helps :)
find the value of x
picture attached
Answer:
x must be 4
Step-by-step explanation:
Write and solve an equation of ratios. Start with the ratio of the hypotenuses:
x + 2 x
----------- = --------
x + 5 x + 2
Cross multiplying results in (x + 2)^2 = x^2 + 5x
performing the indicated squaring, (x + 2)^2 = x^2 + 4x + 4. And therefore:
x^2 + 4x + 4 = x^2 + 5x
Simplifying, we get 4x + 4 = 5x, so x must be 4
Marcia bought a 500 g packet of flour. She used some flour to bake a cake, and she used two thirds of the remaining flour to make some scones. She used 60 g more flour for the cake than for the scones. How much flour did Marcia use for the cake?
Answer:
The answer should be 236g.
Step-by-step explanation:
If we take the amount of flour used for the cake as 'x,' the flour used to make the scones would be (500-x)×2/3 as 2/3 of the remaining is used for the scones.
We know that 60g more flour is used for the cake.
So,
x-60=(500-x)×2/3
Cross multiply, and brng the 3 to the other side.
3(x-60)=(500-x)2
3x-180=1000-2x
Bring the x-terms to one side and the numbers to one side.
3x+2x=1000+180
5x=1180
Divide both sides by 5 to find x(the amount of flour used to make the cake)
Therefore,
x=236g
A line going through the points (-3, -10) with a slope m = 1/4.
Step-by-step explanation:
(-3,5) and (x,y)
Slope = (y - 5)/[x - (-3)] = (y - 5)/(x + 3)
(y - 5)/(x + 3) = -1/4
y - 5 = -1/4(x + 3)
y - 5 = (-1/4)x - 3/4
y = (-1/4)x - 3/4 + 5
y = (-1/4)x + 17/4.
Solve, solve , solve
Answer:
1.) 5 1/4
2.)1 1/2
Step-by-step explanation:
umm.....
Answer:
1) 5 2/8
2) 1 2/6
Step-by-step explanation:
1) 2 7/8 + 2 3/8
Write these fractions as improper fractions.
23/8 + 19/8
Add the fractions
42/8
Write the answer as a mixed number.
5 2/8
2) 3 1/4 -1 3/4
Write these fractions as improper fractions.
13/4 - 7/4
Subtract the fractions
6/4
Write these fractions as improper fractions.
1 2/6
The continental U.S. is about 200 miles wider than Australia.
What number should replace the question mark on the U.S. map?
Answer:
i think it is 300 miles,,,,.......
What are the first five terms of the recursive sequence?
9, 30, 93, 282, 849
====================================================
Explanation:
The first term is 9 because of the notation [tex]a_1 = 9[/tex]
To get the second term, we use the recursive rule given to us which is
[tex]a_n = 3a_{n-1} + 3[/tex]
I recommend using parenthesis to separate things like this
[tex]a_n = 3(a_{n-1}) + 3[/tex]
If n = 2, then,
[tex]a_n = 3(a_{n-1}) + 3\\\\a_2 = 3(a_{2-1}) + 3\\\\a_2 = 3(a_{1}) + 3\\\\a_2 = 3(9) + 3\\\\a_2 = 27 + 3\\\\a_2 = 30[/tex]
The second term is 30.
You can use the same idea as above to find the third term, or you can use this slightly different approach
[tex]\text{third term} = 3*(\text{second term}) + 3\\\\\text{third term} = 3*(30) + 3\\\\\text{third term} = 90 + 3\\\\\text{third term} = 93[/tex]
To generate any new term, we first triple the previous term and then add on 3.
One of the angles in an isosceles triangle is 74°.
What could the other two angles be?
HELP QUICK!!!
complete the equation represents the relationship between C and A.
Answer:
a = 11c - 4
Step-by-step explanation:
7,18,29,40
constant difference = 11
now,
an = a+(n-1)d
or, an = 7+(n-1)11
or, an = 7 + 11n - 11
or, an = 11n - 4
Would this ratio be
maintained if she used
1 cup of vinegar and 4
cups of water? Explain.
Hi!
The ratio in the picture is 3:12. There are 3 tbsp of vinegar for every 12 tbsp of water.
[tex]\frac{3}{12}[/tex] can be simplified to [tex]\frac{1}{4}[/tex] by dividing the numerator and denominator by 3.
1 cup of vinegar to 4 cups of water is also [tex]\frac{1}{4}[/tex].
Therefore, they are equal and the ratio is maintained.
(NOTE: the unit of measurement DOES not matter - they're still equivalent)
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A television is on sale for $75 off,
The price of the television with the sale is $300,
If you use the equation n - 75 = 300 to solve this problem, what does n represent?
The term n is the initial amount that the television is to be sold.
What is the meaning of n?We are told that the television in this case is to be sold at a discount piece. The implication of this is that there is something that has to be removed from the price of the television as it is sold.
We are told that what they are to remove from the price of the television is about $75 and that when this is done, the price of the television would be about $300. Thus n is the original price of the television.
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The variable n represents the initial value of the television
How to interpret the variable nFrom the question, we have the following parameters that can be used in our computation:
Amount off = $75
New price = $300
When represented as the equation, we have
n - 75 = 300
Add 75 to both sides of the equation
So, we have the following representation
n = 375
This means that the initial price of the television is $375
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a decreased by 50% and then increased by 50% of your result
20 points for answer!
Answer:
VVV
Step-by-step explanation:
A number that is increased by 50% and then decreased by 50% is called sequential percentage calculation or successive percentage calculation.
50 percent minus 50 percent is 0 percent, but you cannot simply take 0 percent of a number to get the correct answer when you want to increase a number by 50 percent and then decrease the result by 50 percent.
Put the following equation of a line into slope-intercept form, simplifying all fractions. 2x-10y=-20.
As a result, the slope is 1/5 and the y-intercept is 2, and the equation is written in slope-intercept form as y = (1/5)x + 2.
what is slope intercept ?On a two-dimensional coordinate plane, the equation of a line is shown using the slope-intercept form. Y = mx + b, where m is the line's slope and b is the y-intercept, is how the equation is expressed. The pace at which the line is rising or dropping is indicated by the slope (m). It is the ratio of any two places on the line's vertical change (rise) to horizontal change (run). In other words, it informs you of the line's steepness. The line is rising from left to right if the slope is positive, and descending from left to right if the slope is negative.
given
We must find y in order to convert the equation 2x - 10y = -20 into slope-intercept form, which is represented by the formula y = mx + b, where m is the slope and b is the y-intercept.
2x - 10y = -20
Initially, we must separate the y term from the other terms by deducting 2x from both sides:
-10y = -2x - 20
The next step is to separate y by multiplying both sides by -10:
y = (2/10)x + 2
When we simplify the fraction, we obtain:
y = (1/5)x + 2
As a result, the slope is 1/5 and the y-intercept is 2, and the equation is written in slope-intercept form as y = (1/5)x + 2.
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Don't you dare keep scrolling. Help me out m8.
Answer:
option C gives, x = 8
Step-by-step explanation:
A.
[tex]\frac{5}{2}x+\frac{7}{2}=\frac{3}{4}x+14[/tex]
[tex]\frac{5}{2} x-\frac{3}{4} x = 14-3.5[/tex]
[tex]\frac{10}{4} x-\frac{3}{4} x = 10.5[/tex]
[tex]\frac{7}{4} x = 10.5[/tex]
[tex]x=\frac{10.5*4}{7}[/tex]
[tex]x = 6[/tex]
B.
[tex]\frac{5}{4}x-9=\frac{3}{2}x-12[/tex]
[tex]\frac{5}{4}x-\frac{3}{2}x=-12+9[/tex]
[tex]\frac{5-6}{4} x = -3[/tex]
[tex]-x = 4(-3)[/tex]
[tex]x =12[/tex]
C.
[tex]\frac{5}{4}x-2=\frac{3}{2}x-4[/tex]
[tex]\frac{5}{4}x-\frac{3}{2}x=-4+2[/tex]
[tex]\frac{5}{4}x-\frac{6}{4}x=-2[/tex]
[tex]-x = (-2)*4[/tex]
[tex]x=8[/tex]
D.
[tex]\frac{5}{2} x-7 = \frac{3}{4}x+14[/tex]
[tex]\frac{5}{2} x-\frac{3}{4}x = +14+7[/tex]
[tex]\frac{10}{4} x-\frac{3}{4}x = +21[/tex]
[tex]\frac{7}{4} x=21[/tex]
[tex]x= \frac{21*4}{7}[/tex]
[tex]x = 12[/tex]
solve cos(2x)=1-sin(x)
Given:
[tex]cos(2x)=1-sin(x)[/tex]
Expanding using double angle formula,
[tex]1 - 2 \sin^{2} (x) = 1 - \sin(x) [/tex]
Rearranging into a single equation,
[tex]1 - 2 \sin^{2}(x) - 1 + \sin(x) = 0[/tex]
Combining like terms,
[tex] - 2 \sin^{2} (x) + \sin(x) = 0[/tex]
Now multiplying each term by -1,
[tex]2 \sin^{2} (x) - \sin(x) = 0[/tex]
Factor greatest common factors out,
[tex] \sin(x)(2 \sin(x) - 1) = 0[/tex]
Applying Zero property rule,
[tex] \sin(x) = 0 \: or \: 2 \sin(x) - 1 = 0[/tex]
{ For sin(x) = 0• Solve the trignometric equation to find a particular solution,
[tex]x = 0 \: or \: x = π[/tex]
[tex] = > x = 2nπ \: or \: x = π + 2nπ[/tex]
• Find the union of the solution sets,
[tex]x = nπ[/tex]}
{ For 2 sin(x) - 1 = 0 ,• Rearrange unknown terms to the left side,
[tex]2 \sin(x) = 1[/tex]
• Divide both sides of the equation by the coefficient of variable,
[tex] \sin(x) = \frac{1}{2} [/tex]
• Solve the trignometric equation to find a particular solution,
[tex]x = \frac{π}{6} \: or \: x = \frac{5π}{6} [/tex]
[tex] = > x = \frac{π}{6} + 2nπ \: or \: x = \frac{5π}{6} + 2nπ,n∈Z[/tex]
}
☆ Now finding the union of both sets
[tex]x = nπ \: or \: x = \frac{π}{6} + 2nπ \: or \: x = \frac{5π}{6} + 2nπ,n∈Z[/tex]
Hence, the answer is [tex]x = nπ \: or \: x = \frac{π}{6} + 2nπ \: or \: x = \frac{5π}{6} + 2nπ,n∈Z[/tex]
There are about 208,000,000,000 different 8-letter passwords that can be formed using a 26-letter alphabet.
Express this number using scientific notation.
Answer:
2.08 × 10^11
Step-by-step explanation:
Estimate a 25% tip on a bill of $61.77 by first rounding the bill amount to the nearest ten dollars
Answer:
total bill amount + tip = $77.21
Step-by-step explanation:
6) Write the equation, g(x), that is 9 units below f(x) = 3^X+ 2.
Answer:
g(x) = 3^x -7
Step-by-step explanation:
In an exponential function like this, the constant at the end of the function represents the vertical shift. This means that the original function is shifted 2 units up. So, 9 units lower than +2 is -7. Thus, the new function, g(x), is g(x)=3^x - 7.
We can prove that g(x) is 9 units lower through y-intercepts. The function f(x) has a y-intercept of 3 and g(x) is -6. Since -6 is 9 lower than 3, we know that there is a 9 unit difference between the functions.
Sofia is going to drive from her house to City A without stopping. Let DD represent Sofia's distance from City A t hours after leaving her house. The table below has select values showing the linear relationship between t and D. Determine how long Sofia has been driving the moment she was 157.5 miles away from City A.
Answer:
3.5 Hours
Step-by-step explanation:
I do not know what measurement or timelapse you're looking for. But this should be the answer to it, no I don't have an explanation though.
The distance between the city and the house is 260 miles.
What is an equation?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 = 15, for instance. There are different types of equations like linear, quadratic, cubic, etc.
t d
1 195
2 130
2.5 97.5
The distance will be calculated by the equation of the line,
y = mx + c
m = ( 130 - 195 ) / ( 2 - 1 )
m = -65
y = -65x + c
195 = -65 + c
c = 260miles
Hence, the distance will be 260 miles.
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Write a congruence statement for the given polygons
Answer:
b
Step-by-step explanation:
A boy band is performing a concert on the 10th of December and the stadium has 5000 square metres of space for the audience. The stadium is split such that 40% of the space is the mosh pit and 60% of the space is seated and each seat is 2 square metres in size. If 80% of the people assigned to a seat stand up during the performance, now many people are sitting down during the performance?
A 4,000
B 1,200
C. 1000
D. 300
E. 600
Answer:
C
Step-by-step explanation:
Because 80% of 5,000=4,000 and if there is 5,000 then what is left?
1,000 because 4,000 to 5,000 is 1 more thousand
Also I need my tickets to the concert!
A seesaw is 3 metres long. It is balanced when child A sits 0.8 m from the pivot and child B sits 0.6 m from the pivot. Child A has a weight of 300 N. i. Draw a force diagram to represent this system. (Ensure that you label the force and distances given.) ii. Use the principle of moments to determine the weight of child B.
Answer:
i) see attached diagram
ii) 400 N
Step-by-step explanation:
Since we don’t know the mass of the seesaw, take moments about M (so we don’t have to consider R or mg).
Moment = Force x Perpendicular Distance to the Pivot
As the system is in equilibrium, total anti-clockwise moment = total clockwise moment:
⇒ 300 × 0.8 = b × 0.6
⇒ 0.6 b = 240
⇒ b = 400 N
What does is 9 times 9
Answer:
81
Step-by-step explanation:
The number of students taking classes at RSM Branch A is 1 4 more than the number of students taking classes at RSM Branch B. If Branch A has 1,650 students, how many students does Branch B have? Write an equation that shows the relationship between the number of students at the two branches, A and B.
The equation illustrates that the number of students that Branch B have will be 2100.
How to solve the equationFrom the question, the number of students taking classes at RSM Branch A is 1.4 more than the number of students taking classes at RSM Branch B. If
Since Branch A has 1,650 students, the number of students that Branch B have will be:
= 1500(1.4)
= 2100
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Nicholas rode his bike three times as far as
Kenny. Nicholas rode 16 miles farther than
Kenny. How many miles did Nicholas ride?
Consider the equation y = 3x - 1
Identify the slope and y-intercept and
sketch the graph.
Answer:
The slope is 3/1
Y-intercept is at 0,1
Step-by-step explanation:
Please please please help
Answer: 2nd option
Step-by-step explanation:
Identify the sum of the angle measures in a decagon (a 10-sided polygon)
O 1800°
0 1440°
0 1620°
O 1260°
Answer:
1440°
Step-by-step explanation:
(n - 2)180° - (10 - 2)180° = 8(180°) = 1440°
Answer:
1440 degrees
Step-by-step explanation:
formula for calculating sum of angles in a polygon is (n-2) 180 where n is 10 that's 10-2 which is 8 and 8 * 180 which is 1440
QUESTION 4
Screenshots
Answer:
2
Step-by-step explanation:
hope it helps.........