Answer:
C(-3,3)
Step-by-step explanation:
Given
A = (7,-1)
B = (2,1)
AB:AC = 1:2
Required
Determine the coordinates of C
Since, B is between A and C; we need to determine ratio BC as follows;
[tex]AB:AC = 1:2[/tex]
Convert to division
[tex]\frac{AB}{AC} = \frac{1}{2}[/tex]
AC = AB + BC;
[tex]\frac{AB}{AB + BC} = \frac{1}{2}[/tex]
Cross Multiply
[tex]2 * AB = 1 * (AB + BC)[/tex]
[tex]2 AB = AB + BC[/tex]
[tex]2AB - AB = BC[/tex]
[tex]AB = BC[/tex]
Divide both sides by BC
[tex]\frac{AB}{BC} = 1[/tex]
Rewrite as
[tex]\frac{AB}{BC} = \frac{1}{1}[/tex]
Write as ratio
[tex]AB:BC = 1:1[/tex]
Next is to determine the coordinates of C as follows;
Because B is between both points. we have:
[tex]B(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
Where
[tex]m:n = AB:BC = 1:1[/tex]
[tex]B(x,y) = B(2,1)[/tex]
[tex]A(x_1,y_1) = A(7,-1)[/tex]
So; we're solving for x2 and y2
[tex]B(2,1) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
Where
Solving for x2;
[tex]x = \frac{mx_2 + nx_1}{m+n}[/tex]
[tex]2 = \frac{1 * x_2 + 1 * 7}{1+1}[/tex]
[tex]2 = \frac{x_2 + 7}{2}[/tex]
Cross Multiply
[tex]2 * 2 = x_2 + 7[/tex]
[tex]4 = x_2 + 7[/tex]
[tex]x_2 = 4 - 7[/tex]
[tex]x_2 = -3[/tex]
Solving for y2;
[tex]y = \frac{my_2 + ny_1}{m+n}[/tex]
[tex]1 = \frac{1 * y_2 + 1 * -1}{1+1}[/tex]
[tex]1 = \frac{y_2- 1}{2}[/tex]
Cross Multiply
[tex]2 * 1 = y_2 - 1[/tex]
[tex]2 = y_2 - 1[/tex]
[tex]y_2 = 2 + 1[/tex]
[tex]y_2 = 3[/tex]
Hence, the coordinates of C are: C(-3,3)
please prove this...
Answer: see proof below
Step-by-step explanation:
Use the following Sum to Product Identities:
sin (A) - sin (B) = 2 cos (A+B)/2 · sin (A-B)/2
sin (A) + sin (B) = 2 sin (A+B)/2 · cos (A-B)/2
Given: sin Ф = k sin β --> (sin Ф)/(sin β) = k
Proof RHS → LHS
[tex]\text{RHS:}\qquad \qquad \qquad \dfrac{k-1}{k+1}\tan\dfrac{\theta+\beta}{2}[/tex]
[tex]\text{Given:}\qquad \qquad \dfrac{\frac{\sin \theta}{\sin \beta}-1}{\frac{\sin \theta}{\sin \beta}+1}}\cdot \tan\dfrac{\theta +\beta}{2}[/tex]
[tex]\text{Simplify:}\qquad \qquad \dfrac{\frac{\sin \theta}{\sin \beta}-\frac{\sin \beta}{\sin \beta}}{\frac{\sin \theta}{\sin \beta}+\frac{\sin \beta}{\sin \beta}}}\cdot \tan\dfrac{\theta +\beta}{2}\\\\\\.\qquad \qquad \qquad = \dfrac{\sin \theta -\sin \beta}{\sin \theta +\sin \beta}\cdot \tan\dfrac{\theta +\beta}{2}[/tex]
[tex]\text{Product to Sum:}\qquad \quad \dfrac{2\cos \frac{\theta+\beta}{2}\cdot \sin \frac{\theta-\beta}{2}}{2\sin \frac{\theta+\beta}{2}\cdot \cos \frac{\theta-\beta}{2}}\cdot \tan\dfrac{\theta +\beta}{2}[/tex]
[tex]\text{Expand:}\qquad \qquad \dfrac{2\cos \frac{\theta+\beta}{2}\cdot \sin \frac{\theta-\beta}{2}}{2\sin \frac{\theta+\beta}{2}\cdot \cos \frac{\theta-\beta}{2}}\cdot \dfrac{\sin\frac{\theta +\beta}{2}}{\cos \frac{\theta +\beta}{2}}[/tex]
[tex]\text{Simplify:}\qquad \qquad \quad \quad \dfrac{\sin \frac{\theta +\beta}{2}}{\cos \frac{\theta+ \beta}{2}}\\\\\\.\qquad \qquad \qquad \quad =\tan\dfrac{\theta +\beta}{2}[/tex]
[tex]\text{LHS = RHS:}\quad \tan\dfrac{\theta +\beta}{2}=\tan\dfrac{\theta +\beta}{2}\quad \checkmark[/tex]
A graph where the horizontal axis shows time (t), numbered 1 to 4, and the vertical axis shows height (h) numbered 10 to 60. Solid circles appear at point (0, 48), point (1, 64), point (3, 0). A solid curved line connects all 3 points. Leon throws a ball off a cliff. The graph represents a relation that models the ball’s height, h, in feet over time, t, in seconds. What is the domain? {t| 0 ≤ t ≤ 3} {t| 0 ≤ t ≤ 48} {t| 0 ≤ t ≤ 64} {t| all real numbers}
Answer:
{t| 0 ≤ t ≤ 3}
Step-by-step explanation:
Answer:
Option A
Step-by-step explanation:
It right on edge 2020
-5(k + 6) + 7(k – 4)
-1/2m=-9 what does m=
Answer:
m = 18
Step-by-step explanation:
Step 1: Write out equation
-1/2m = -9
Step 2: Multiply both sides by -2
m = 18
The length of an alligator in a zoo is 14 5/6 feet.The everglades national parks list the longest alligator ever reocord in florida at 17 5/12 feet. Which is the differnce in their lenghth
Answer:
The difference in the lengths of the two alligators = 3
Step-by-step explanation:
First, let us make the lengths improper fractions, then we will find the difference from there.
Alligator 1:
Length = [tex]14\frac{5}{12} = \frac{173}{12}[/tex]
To convert to improper fraction, multiply the denominator by the whole number, and then add the denominator [(12 × 14) + 5]
Alligator 2:
Length = [tex]17\frac{5}{12} = \frac{209}{12}[/tex]
Now Let us find the difference between the lengths:
[tex]\frac{209}{12} - \frac{173}{12} = \frac{36}{12} =3[/tex]
Therefore the difference in the lengths of the two alligators = 3
There are 7 more sweaters than shirts in the drawer. There are 15 sweaters and shirts in the drawer in all. How many shirts are there in the drawer? Let S represent the number of shirts. Which equation represents the situation
Answer:
7 + 2s = 15
4 shirts
Step-by-step explanation:
Let's say w denotes sweaters and s denotes shirts.
Since there are 7 more sweaters than shirts:
w = 7 + s
There are a total of 15 sweaters and shirts in all, so:
w + s = 15
Substitute 7 + s in for w in the second equation:
w + s = 15
7 + s + s = 15
7 + 2s = 15
Solving for s:
7 + 2s = 15
2s = 15 - 7 = 8
s = 8/2 = 4 shirts
Thus, the equation is 7 + 2s = 15, and there are 4 shirts.
~ an aesthetics lover
PLEASE HELP, DUE AT MIDNIGHT >>>>>
Answer:
BELOWStep-by-step explanation:
7.
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-8,\:-11\right),\:\left(x_2,\:y_2\right)=\left(17,\:4\right)\\\\m=\frac{4-\left(-11\right)}{17-\left(-8\right)}\\\\m = \frac{4+11}{17+8}= \frac{15}{25} \\\mathrm{Refine}\\\\m=\frac{3}{5}[/tex]
8.
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(10,\:-15\right),\:\left(x_2,\:y_2\right)=\left(13,\:-17\right)\\\\m=\frac{-17-\left(-15\right)}{13-10}\\\\m = \frac{-17+15}{13-10}\\ \\m = \frac{-2}{3}\\ \\Simplify\\m=-\frac{2}{3}[/tex]
9.
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-6,\:-7\right),\:\left(x_2,\:y_2\right)=\left(5,\:-7\right)\\\\m=\frac{-7-\left(-7\right)}{5-\left(-6\right)}\\\\m = \frac{-7+7}{5+6}\\ \\m = \frac{0}{11}\\ \\Simplify\\m=0[/tex]
10.
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-4,\:-3\right),\:\left(x_2,\:y_2\right)=\left(2,\:-9\right)\\\\m=\frac{-9-\left(-3\right)}{2-\left(-4\right)}\\\\m = \frac{-9+3}{2+4}\\ \\m = \frac{-6}{6} \\\\Simplify\\m =-1[/tex]
11.
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\mathrm{When\:}y_1\ne \:y_2\mathrm{\:and\:}\:x_1=x_2\mathrm{\:the\:slope\:is\:}\infty \\\\m = \infty[/tex]
12.
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-5,\:3\right),\:\left(x_2,\:y_2\right)=\left(19,\:-6\right)\\\\m=\frac{-6-3}{19-\left(-5\right)}\\\\m = \frac{-6-3}{19+5}\\ \\m = \frac{-9}{24}\\ \\Simplify\\m=-\frac{3}{8}[/tex]
13.
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-7,\:-12\right),\:\left(x_2,\:y_2\right)=\left(1,\:-16\right)\\\\m=\frac{-16-\left(-12\right)}{1-\left(-7\right)}\\\\m = \frac{-16+12}{1+7} \\\\m = \frac{-4}{8} \\\\Simplify\\m=-\frac{1}{2}[/tex]
14.
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-18,\:0\right),\:\left(x_2,\:y_2\right)=\left(-13,\:1\right)\\\\m=\frac{1-0}{-13-\left(-18\right)}\\\\m = \frac{1-0}{-13+18}\\ \\m = \frac{1}{5} \\[/tex]
15.
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(1,\:-11\right),\:\left(x_2,\:y_2\right)=\left(-2,\:-4\right)\\\\m=\frac{-4-\left(-11\right)}{-2-1}\\\\m = \frac{-4+11}{-2-1}\\ \\m = \frac{7}{-3} \\\\Simplify\\m=-\frac{7}{3}[/tex]
-5(4x-2)=-2(3+6x) multi step equation
Answer:
X=2, please mark me brainliest
Step-by-step explanation:
−5(4x−2)=−2(3+6x)
(−5)(4x)+(−5)(−2)=(−2)(3)+(−2)(6x)(Distribute)
−20x+10=−6+−12x
−20x+10=−12x−6
Step 2: Add 12x to both sides.
−20x+10+12x=−12x−6+12x
−8x+10=−6
Step 3: Subtract 10 from both sides.
−8x+10−10=−6−10
−8x=−16
Step 4: Divide both sides by -8.
−8x
−8
=
−16
−8
x=2
check the image needed more words :p
What is the explicit formula used for?
Answer:Explicit formulas define each term in a sequence directly, allowing one to calculate any term in the sequence without knowing the value of the previous terms. Explicit formulas define each term in a sequence directly, allowing one to calculate any term in the sequence without knowing the value of the previous terms
Step-by-step explanation:
What is
the circumference of a circle with radius 3.5cm. Take [Pi=22/7]
Answer:
22cm
Step-by-step explanation:
Circumference of a circle = 2πr
π = 22/7
r = 3.5
Circumference of a circle = 2 × (22/7) × 3.5
Circumference of a circle = 22cm.
What is -4(x+6) can someone pls help
Answer:
-4x - 24
Step-by-step explanation:
distribute the -4 by multiplying it by what is in the parenthisis. Since it is negative that makes a -4x and a -24
Hey there!
ANSWER: [tex]-4x-24[/tex]EXPLANATION:[tex]-4(x+6)[/tex]
Let's separate -4 and x+6 with parenthesis.
[tex](-4)(x+6)[/tex]
Now let's separate all with parenthesis.
[tex](-4)(x)+(-4)(6)=-4x-24\\-4x-24(ANSWER)[/tex]
Hope this helps!
[tex]\text {-TestedHyperr}[/tex]
The product of twice the length and the width
Answer:
The answer to the question is 2(l+w).
A cylindrical cup has a circular base of radius 7cm and height 10cm, calculate its curved surface area. take pie as 3.1
Answer:
264.89cm^2
Step-by-step explanation:
CSA of cylinder=πrl
= 3.1 × 7 ×√149
= 264.89cm^2
PLEASEEEE HELP ASAPPP ILL MARK BRAINLIEST IMPORTANT TO SHOW YOUR WORK
Answer:
AC = 7.5 cm
Step-by-step explanation:
Given that the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{AC}{DE}[/tex] = [tex]\frac{BC}{DE}[/tex] , substitute values
[tex]\frac{AC}{3.5}[/tex] = [tex]\frac{7+8}{7}[/tex] , that is
[tex]\frac{AC}{3.5}[/tex] = [tex]\frac{15}{7}[/tex] ( cross- multiply )
7AC = 52.5 ( divide both sides by 7 )
AC = 7.5 cm
√45 rounded to the nearest 0.05 ????
Answer:
6.7082039325......tbc
Solve the following equation, answer as a reduced, mixed number. Then place the correct number in the box provided. 4(3 - 2x) = 15
Answer:
x = -3/8
Step-by-step explanation:
4(3 - 2x) = 15
Distribute
12 -8x = 15
Subtract 12 from each side
12-8x-12 =15-12
-8x =3
Divide by -8
-8x/-8 = 3/-8
x = -3/8
The correct answer is: -3/8
HELLPPPP PLEASE QUICKK ASAP
Answer:
9
Step-by-step explanation:
The reason why it is 9 is because if you look to the bigger triangle, you can see that 15 is 3/4 the size of 20, so once you find what number is 3/4 of 12, you have the answer, 9! Hope this helps!
4 x ((-4)= (-2) - (-3) + (-6))
Answer:
x=5/16
Step-by-step explanation:
Let's solve your equation step-by-step.
4x(−4)=−2−(−3)−6
Step 1: Simplify both sides of the equation.
4x(−4)=−2−(−3)−6
−16x=−2+3+−6
−16x=(−2+3+−6)(Combine Like Terms)
−16x=−5
−16x=−5
Step 2: Divide both sides by -16.
−16x
−16
=−5/−16
x=5/16
can I be the brainiest please!!
Write the algebra expression: six times the sum of four and a number
Answer:
6(4+x)
Step-by-step explanation:
Answer:
6(x+4)
Step-by-step explanation:
We want to write an algebraic expression for "six times the sum of four and a number"
Let's break this down.
The sum of four and a number:
The words "sum" indicates addition. We can call " a number" x, since it is unknown.
So, the sum of four and a number is: (x+4).
Six times:
The word "times indicates multiplication. We are multiplying six and the sum of four and a number.
So, we have: 6(x+4)
The algebra expression for "six times the sum of four and a number" is 6(x+4)
Can somebody help me and answer this question for me f(g(6))=
Steven reads 6 books each month as part of his book club. If Steven has read 18 books so far, how many months has he been with his book club?
Answer:
3
Step-by-step explanation:
18/6 is 3
I need help it says what could I change in this polynomial to make them like terms.
[tex] {2x}^{2} + 5x - 6y + 2y - 7[/tex]
Answer:
2x² + 5x - 4y - 7
Step-by-step explanation:
combine the like terms -6y and 2y
2x² + 5x - 6y + 2y - 7
2x² + 5x - 4y - 7
i need answers because it's very hard i need to pass.
Answer:
whats the question
Step-by-step explanation:
9. Krista and Emily wrote an equation of a line that is parallel to the line y = 3x - 1 and passing
through the point (5,9). Is either of them correct? Explain your reasoning?
Krista:
9 = 3(5) + b
9 = 15 + b
-6 = b
y = 3x - 6
Emily:
y- 9 = 3(x - 5)
y- 9 = 3x - 15
y = 3x - 24
Answer:
Explanation:
Step-by-step explanation:
Hey there!
The equation, of a st. line that passes through point (5,9) is,
[tex](y - y1) = m1(y - y1)[/tex]
Put the values,
[tex](y - 9) = m1(x - 5)[/tex]
It is 1st equation.
Now, another equation is,
y = 3x-1.........(ii)
Comparing the equation with y = mx+c.
Slope (m2)= 3
As per the parallel lines,
m1=m2=3
Putting,
the value of m1 in equation(i)
(y-9)= 3(x-5)
y-9= 3x - 15
y = 3x - 6.
So, Krista equation is correct.
Hope it helps...
6 to the 2nd power x 3 to the 3rd power
Answer:
972
Step-by-step explanation:
[tex] {6}^{2} \times {3}^{3} \\ = 36 \times 27 \\ = 972[/tex]
Juan, an avid golfer, used two strokes on a miniature golf hole, which was one stroke below par. What was par for this hole?
1 because two strokes minus 1 for being one stroke above par is 1.
Hugh bought some magizines that cost 3.95 each and some books that cost 8.95 each. He spent a total of 47.65.If Hugh bought 3 magazines,how many books did he buy
Answer:
4 books
Step-by-step explanation:
We are told that: Hugh bought some magazines that cost 3.95 each
Hugh bought 3 magazines.
Hence, total cost of magazines = 3 magazines × 3.95
= 11.85.
Total cost of magazines = 11.85
From the question, we know that, the total amount Hugh spent = 47.65
Hence, The total cost for books =
Total amount spent - Total cost of magazines
= 47.65 - 11.85
= 35.80
Therefore, the total cost of books = 35.80
We are told in the question that the cost of books is 8.95 each or 8.95 per book.
Hence, the number of books that Hugh bought is calculated as :
35.80/8.95
= 4 books
Therefore, Hugh bought 4 books
what is the answer to g+3=17
Answer:
g=14
Step-by-step explanation:
do 17-3, the answer is 14, meaning 14=g
Answer:
g = 14
Step-by-step explanation:
g+3 = 17
Subtract 3 from each side
g+3-3 = 17-3
g = 14
Mrs. Bowman spent $110 to rent a popcom machine for the school
carnival and $75 to buy popcorn, oil, and other supplies. If she sold
263 bags of popcorn for $1.50 each, how much money did she make after paying for the machine and the supplies?
Answer:
200 minutes I am getting poi tea yayyyy
Answer:
$209.50
Step-by-step explanation:
First, find how much she made selling the popcorn:
263(1.5)
= 394.50
Then, find how much she spent on supplies and the machine:
110 + 75
= 185
Subtract the expenses from the profit:
394.50 - 185
= $209.50