Answer:
To complete the square for the x terms, add 4 to both sides.To convert the given equation of the circle to standard form we should do as follows.
1. Add 36 to both sides of the equation.[tex]x^{2} +y^{2}+4x-6y-36+36=36\\ x^{2} +y^{2}+4x-6y=36[/tex]
2. We order the terms according to their variables.[tex]x^{2} +4x +y^{2}-6y=36[/tex]
3. Divide the linear term by 2, then elevate it to the square power.[tex]x^{2} +4x + (\frac{4}{2} )^{2} +y^{2} -6y+(\frac{6}{2} )^{2} =36[/tex]
4. Solve operations, and add the same units to the other side of the equation.[tex]x^{2} +4x+4+y^{2} -6y+9=36+4+9\\[/tex]
5. Now, we sum costant terms, and factor both trinomials.[tex](x+2)^{2} +(y-3)^{2} =49[/tex]
As you can observe, the circle has center at (-2,3) and it has a radius of 7 units.
Notice that the second choice is correct, because we added 4 units to both sides to complete the square for the x terms.
Marcus can carry a maximum of 25kg of gravel at one time
How many joumeys will he need to make to shift one and
half tonnes of gravel?
Answer: 60 journeys
Step-by-step explanation:
1 ton = 1000 kgs
1.5 tons = 1500 kgs
1500/25 = 60 journeys
Answer:
55 journeys.
Step-by-step explanation:
907185 gm = 1 ton
453592.5 gm = 1/2 ton
1360777.5 gm = 1 1/2 ton
Convert to kg (1000g= 1kg)
Then divide by 25kg
=1360.7775/25 = 54.4311
Round up decimal to 1
= 55 journeys
Find the square number 7, 12, 20, 25, 27
Fill in the table to help you make a conjecture about the geometric sequence An=(0.5)n-1
N=1,2,3,4,5
A1=1,0.5,0.25,W,0.0625
Sn=1,1.5,x,y,1.9375
W=? X=? Y=?
Answer:
W = 0.125
X = 1.75
Y = 1.875
Step-by-step explanation:
The geometric sequence looks like of first term 1 , and of common ratio (r=0.5).
Therefore each new term is found by multiplying the previous one by 0.5:
A1 = 1
A2 = 0.5
A3 = 0.25
A4 = 0.125 = W
A5 = 0.0625
And the partial sums are the additions of the terms until the last one considered:
S1 = 1
S2 = 1.5
S3 = 1.75 = X
S4 = 1.875 = Y
S5 = 1.9375
therefore,
W = 0.125
X = 1.75
Y = 1.875
Answer:
The next answers are approaching a number and 2
Step-by-step explanation:
Math revision part 4
Answer:
First one is (d)
Second one is (c)
Third is (a)
Fourth is (21)
Can you help me please. Hint it's not 18!!!!!✌✌
Answer:
14
Step-by-step explanation:
15 × 2 = 306 × 2 = 12That gives you 5/15 remaining for the 30/35 which is 1/31/3 of six is 2that would be 12 + 214 would be the amount of red paint neededAnswer: it is b
Step-by-step explanation: because you are trying to find the total of red paint
From a point P, a boy observe that the angle of elevation of the top of a pole is 45, if the height of the
pole is 15 m, find the distance of P from the foot of the pole.
Please help
Answer:
15m
Step-by-step explanation:
The pole is perpendicular to the floor and the angle of elevation is 45. Thus, it forms a right-angled, isoceles triangle. So the distance from point P to the bottom of the pole is equal to the height of the pole, which is 15m
A: y = 13 - 2x
B: y = 8 - x
At which point do these two lines intersect?
A. (1, 7)
B. (1.5, 3.0)
C, (1.6, 3.2)
D. (2, 9)
Answer:
Step-by-step explanation:
8 -x = 13 - 2x
x + 8 = 13
x = 5
y = 8 - 5
y = 3
(5, 3)
Three shirts and two pairs of pants cost $40. Four shirts and one pair of pants cost $37.50. How much does one shirt cost?
A. $5.00
B. $9.50
C. $6.75
D. $7.00
Answer:
d, 700
Step-by-step explanation:
it's the only one that makes sense
Please help quickly I don’t understand
What is the slope of the line containing (-1,8) and (3, -12)?
Answer:
-5
Step-by-step explanation:
We can find the slope since we have two points
m = (y2-y1)/(x2-x1)
= (-12-8)/(3 - -1)
= (-12-8)/(3+1)
= -20/4
= -5
Answer:
-5
Step-by-step explanation:We can find the slope since we have two points
m = (y2-y1)/(x2-x1)
= (-12-8)/(3 - -1)
= (-12-8)/(3+1)
= -20/4
= -5
A researcher wanted to show that math test scores increased for students who attended extra study sessions for a particular school. The study sampled 5 honors students who attended the study session. Explain why this report is not reliable.
Answer:
This report is not reliable because:
A real increase could be proved with the sample of all the students who attended the study session, due to mustn't be many students (I believe the students regularly doesn't like the extra study sessions), where wouldn't just have honors students, but the regular students too, who probably would actually need increasing their math scores.
Step-by-step explanation:
To identify if a students population actually increased their math tests scores by a particular reason, the researcher should take a sample from the regular or bad students that attended to the extra session, or at least an equal sample with the same amount of good students and regular students ( or bad students), in this form he would compare the results in each individual and identify if it actually depended on the extra study sessions or from other reasons how study time in the house, learning disorders or others.
Quadrilateral ABCD is rotated 270° clockwise about the origin. What is the orientation of the rotated figure, and what quadrant does it lie in?
Answer:
The other person is right, I believe it is the fourth Quadrient
Step-by-step explanation: how ever there are two fourth Quadrient answers. I think it is the second fourth Quadrient one with C and B at the top. I rotated the shape and that's how it looked.
When a shape is rotated, it must be rotated through a point.
The orientation of the rotated figure is uprightThe quadrant of the rotated figure is quadrant IV.The current location of the quadrilateral is quadrant III.
A 270 degrees clockwise rotation would move the shape 3 quadrants backwards.
i.e. quadrant 2, quadrant I, and quadrant 4.
Hence, the quadrant of the rotated figure is quadrant IV.
Read more about rotation at:
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What is x ?
f(x)=−3
x = ?
Which property of addition is shown below?
If x = 1 + 2i and y = -1 -2i, then x + y = 0.
commutative property
identity property
associative property
inverse property
Answer:
Inverse Property
Step-by-step explanation:
This property is inverse property with respect to addition.
E.g.
If x=y and z= -y
Then,
x+z = 0
its basically d on edg :)
Which of the following is the graph of y= -x-3?
Answer:
Step-by-step explanation:
Which of the following points is the greatest distance from the origin?
(1,6)
(2,6)
(4,5)
(5,1)
The point which is farthest from the origin is required.
The point which is the greatest distance from the origin is [tex](4,5)[/tex]
Distance from originThe distance of a point from origin is given by
[tex]d=\sqrt{x^2+y^2}[/tex]
[tex](1,6)[/tex]
[tex]d=\sqrt{1^2+6^2}\\\Rightarrow d=\sqrt{37}\ \text{units}[/tex]
[tex](2,6)[/tex]
[tex]d=\sqrt{2^2+6^2}\\\Rightarrow d=\sqrt{40}\ \text{units}[/tex]
[tex](4,5)[/tex]
[tex]d=\sqrt{4^2+5^2}\\\Rightarrow d=\sqrt{41}\ \text{units}[/tex]
[tex](5,1)[/tex]
[tex]d=\sqrt{5^2+1^2}\\\Rightarrow d=\sqrt{26}\ \text{units}[/tex]
The largest number is [tex]\sqrt{41}[/tex]
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How do you solve this
Answer:
3.76 × 10^4
Step-by-step explanation:
1. Work out what they are.
1.26 × 10^4 = 12600 (check your calculator to see if I'm right)
To get this, I multiplied 1.26 by 10,000. This is because 10^4 is 10000 (it has 4 zeros). Or you could move the decimal point forward 4 spaces.
2.50 × 10^4 = 25,000
By doing the same thing above.
2. Add them together
12,600 + 25,000 = 37,600
3. Change the answer into its scientific notation
To do this we need to divide 37,600 by a number to make it less than 10, but still keeping the digits. This always ends in zeros by the way (e.g. 100, 1,000, 100,000).
37600 ÷ 10,000 = 3.76
Next:
Scientific notations always have times 10 to the power of something (× 10^x). So we put that in:
3.76 × 10^x what is x?
x is the number of of times you multiply by 10 to get back to 36700. This is 4 times.
(This is the same as multiplying by 10,000 as it has 4 zeros. This is also the same as moving the decimal point 4 spaces)
So your final answer is: 3.76 × 10^4
Which situation could the equation -3*20=-60 represent?
Answer:
total temp of 20 winter days
Step-by-step explanation:
Identifying parallel and perpendicular lines
Answer:
C (Third answer)
Step-by-step explanation:
plz help asap im timed just this and ill give u 5 stars brainliest and a thank u no cap
no its not a
Answer:
D
Step-by-step explanation:
2 x 4 = 8
8 x 2 = 16
4 x 9 = 36
36 x 2 = 72
9 x 2 = 18
18 x 2 = 36
16 + 72 + 36 = 124
124 = D
What is the product of (-3s+2t) (4s-t)?
A: -12s^2 -2t^2
B: -12s^2 + 2t^2
C: -12s^2 + 8st - 2t^2
D: -12s^2 + 11st -2t
Answer:
c
Step-by-step explanation:
(-3s+2t)(4s+t)=-12s^2-3st+8st+2t^2 = [tex]-12s^2+8st-2t^2[/tex]
Find the square root of 847
29.1032644
hope this helps
25
Write the number 0.5 in the form , using integers, to show that it is a rational number.
5/11
5/100
5/10
2/1
Answer:
5/10
Step-by-step explanation:
0.5 is 5 tenths which is 5/10
A = {1, 2, 5, 7} B = {3, 4, 6, 7} C = {0, 5, 8, 9} Find A∩B. A) {1,2,3,4,5,6,7} B) {1} C) {2,3,4,5} D) {7}
Answer:
The answer is option D.
A n B is { 7 }
Hope this helps.
What is the equation of the line that is parallel to the given
line and passes through the point (-3, 2)?
3x - 4y = -17
O 3x - 4y = -20
4x + 3y = -2
O 4x + 3y = -6
Answer:
Step-by-step explanation:
is the given line 3x - 4y = -17?
then,
- 4y = -3x -17
y=(3/4)x+17/4
it is parallel, so slope of our line is 3/4 or 0.75
y=0.75x+b
next, lets plug in the given point to get the y-int
2=0.75*(-3)+b
2=-2.25+b
b-2.25=2
b=4.25
the equation is y=0.75x+4.25
does this clear anything, or am I off topic? please tell me I will help you
The equation of line is [tex]y=\frac{3}{4}x+\frac{17}{4}[/tex]
Slope-intercept form of line :The given equation of line is,
[tex]3x-4y=-17\\\\4y=3x+17\\\\y=\frac{3}{4} x+\frac{17}{4}[/tex]
Compare above equation with [tex]y=mx+c[/tex]
Slope of given line [tex]m=\frac{3}{4}[/tex]
Since, the slope of all parallel lines are same.
So that, slope of required line is also [tex]\frac{3}{4}[/tex]
The equation of line is, [tex]y=\frac{3}{4}x+c\\[/tex]
Substitute point [tex](-3,2)[/tex] in above equation.
[tex]2=\frac{3}{4}(-3)+c\\\\\\c=2+\frac{9}{4} =\frac{17}{4}[/tex]
Substitute value of c in equation of line.
[tex]y=\frac{3}{4}x+\frac{17}{4} \\\\\\[/tex]
Thus, the equation of line is [tex]y=\frac{3}{4}x+\frac{17}{4}[/tex]
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Find the discriminant: *
7x2 – 5 = 2x + 9x2
Answer:
-36
Step-by-step explanation:
You have to rearrange the quadratic into an equation where one side is zero.
This example works by subtracting 7x^2 from both sides leaving
-5 = 9x^2 - 7x^2 + 2x
-5 = 2x^2 + 2x
Now add 5 to both sides
-5 + 5 = 2x^2 + 2x + 5
0 = 2x^2 + 2x + 5
Now the equation you gave is in the form of a quadratic. The discriminate is found from
a = 2
b = 2
c = 5
b^2 - 4ac is the discriminate
2^2 - 4(2)(5)
4 - 40
Discrimate = 4 - 40 = - 36
In a school there are 300 students 90 of them are male students. Find out the percentage of female students.
Answer:
70%
Step-by-step explanation:
Total students = 300
Male students = 90
Female students = 300 - 90 = 210
Percentage of female students
[tex] = \frac{210}{300} \times 100 \\ \\ = \frac{210}{3} \\ \\ = 70\%[/tex]
Answer:
70%
Key Points:
Total Students: 300Male Students: 90Unknowns:
Male Student PercentageFemale Student CountFemale Student PercentageWe are given the overall amount of students as well as the male students. Using these, we can determine how many females are in the school.
300 overall students - 90 male students = ____ female students
Simplify.
Given our above equation, we now know that there are 210 female students at the school.
In order to find the percentage of females at the school, we must divide the female students by the overall size of the school.
[tex]\frac{210}{300} = ?[/tex]
Our next step is to grab a calculator and input 210 ÷ 300. You can alternatively use the long division method but a calculator would work best. After calculating, your answer should come out to be 0.7
Now, you need to multiply it by 100 so that you can create a percentage.
0.7 × 100 = 70%
Therefore, 70% of the students are female.
Checking our work:
A great way to ensure that your answer is correct is by checking your work. We can do this by finding the percentage of male students and adding it to the percentage of female students.
If 70% is the correct percentage for female students, the male and female percentages should add up to 100%
Finding the male percentage:
Similar to how we found the percentage of females at the school, we must divide the male students by the overall size of the school. Reminder: there are 300 students and 90 of them are male.
[tex]\frac{90}{300} = ?[/tex]
Again, you should pull out your calculator and input 90 ÷ 300. This should give you 0.3
Next, multiply your answer by 100 to get our percentage.
0.3 × 100 = 30%
Knowns:
Female Percentage: 70%Male Percentage: 30%Add the female percentage with the male percentage: 70% + 30% = 100%
As predicted, our answer was 100%. Therefore, 70% of the students are female.
Learn more about solving for percentages by reviewing these answers!
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A deck of cards has 3 pink, 6 purple, and 4 green cards. You pick 2 cards from the deck. Cards are not returned to the deck after they are picked
P(the first card is green and the second card is -purple)
With explanation
Answer:
2/13
Step-by-step explanation:
So firstly, know that there are 13 cards in the deck (3 + 6 + 4).
Therefore, the probability of drawing a green is 4/13.
After you draw the green card, there will be 12 cards left. Therefore, the probability of drawing a purple card next is 6/12.
To find compound probability, multiply the probabilities of the two separate events happening together:
4/13 * 6/12
= 2/13
Hope this helps! Please contact me if you have any questions :)
A frozen yogurt shop offers a rewards system for frequent customers. The graph below represents how much a rewards customer pays based on the number of ounces of frozen yogurt purchased.
Answer:
A rewards customer earns 2 free ounces of yogurt because the total amount paid for 10 ounces and 12 ounces is the same.
Step-by-step explanation:
Answer:
A. A rewards customer earns 2 free ounces of yogurt because the total amount paid for 10 ounces and 12 ounces is the same. (on edg.)
Step-by-step explanation:
A school organization sells T-shirts for a fundraiser. Youth sizes sell for $10 each, and adult sizes sell for $15 each. The organization sells a total of 220 shirts for $2,375. How many adult-sized T-shirts did the organization sell?
Answer:
35 adult shirts were sold
Step-by-step explanation:
10y+15a=2375
y+a=220
y=220-a
10(220-a)+15a=2375
2200-10a+15a=2375
2200+5a=2375
5a=175
a=35
35 adult shirts were sold.