Given the points A(-8,-7) and B(8,5) find the coordinates of point P on directed line segment AB that partitions AB into the ratio 3:1
step 1
Find the distance in the x-coordinate between A and B
dABx=(8-(-8)=8+8=16 units
Find the distance in the y-coordinate between A and B
dABy=5-(-7)=5+7=12 units
step 2
we know that
point P on directed line segment AB that partitions AB into the ratio 3:1
so
AP/AB=3/(3+1)
AP/AB=3/4
Find the x coordinate of point P
APx/ABx=3/4
substitute
APx/16=3/4
APx=16*(3/4)
APx=12 units
The x-coordinate of P is
Px=Ax+APx
where
Ax is the x-coordinate of P
Px=-8+12=4
step 3
Find the y-coordinate of P
we have that
APy/ABy=3/4
substitute
APy/12=3/4
APy=12*(3/4)
APy=9
The y coordinate of P is
Py=APy+Ay
where
Ay is the y-coordinate of P
Py=9+(-7)=2
therefore
the answer is
The coordinate of P are (4,2)An ellipse has vertices (0,-5) and (0,5) and a minor axis of length 8.Part I: In what direction is this ellipse oriented? Part II: What are the coordinates of the center of this ellipse? Part III: What are the values of a and b for this ellipse? Part IV: Write the equation of this ellipse.
we know that
vertices (0,-5) and (0,5) --------> is a vertical ellipse
the minor axis of length 8 ------> 2b=8 -------> b=4
so
Part I: In what direction is this ellipse oriented?
Is a vertical ellipse
Part II: What are the coordinates of the center of this ellipse?
The center of the ellipse is the midpoint between the vertices
The midpoint between (0,-5) and (0,5) is the origin (0,0)
The center is the point (0,0)
Part III: What are the values of a and b for this ellipse?
b=4
2a=10 ---------> a=5
Part IV: Write the equation of this ellipse.
[tex]\begin{gathered} \frac{y^2}{a^2}+\frac{x^2}{b^2}=1 \\ substitute\text{ given values} \\ \frac{y^2}{5^2}+\frac{x^2}{4^2}=1 \\ therefore \\ \frac{y^2}{25}+\frac{x^2}{16}=1 \end{gathered}[/tex]if R200 is musted at 6% simple interests per year detemine the interest if earch after 4years
The interest calculated after 4 years for a principal amount of 200 at 6% rate of interest , is 48 and the total amount is 248.
Given,
P = 200
rate of interest (r) = 6%
time (t) = 4 years.
we know the simple interest formula as:
S.I = P×r×t/100
substitute the above values.
Interest = 200 × 4 × 0.06/100
= 800 × 0.06/100
= 8 × 0.06
= 0.48 × 100
= 48
Total amount = 200+48
= 248
Hence we get the total amount as 248 at the end of 4 years.
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A hemisphere bowl of radius 7ft has water in it to a depth of 2 ft. At what angle must it be tipped for the water to begin to flow out?
We have an hemisphere (a shape that is half a sphere) of radius r = 7 ft, that is a bowl filled with water up to a depth of 2 ft.
We have to find at what angle must it be tipped for the water begind to flow. We have to take into account that the level of the water will remain horizontal when we tip the bowl.
This will happen when the water level reaches the edge of the hemisphere.
This can be represented as:
The bowl have to be tipped so the edge descends 2 ft.
We can represent that in mathematical terms as:
Then, we can relate the angle with the depth using a trigonometric ratio:
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{\text{depth}}{\text{radius}}=\frac{2}{7} \\ \theta=\arcsin (\frac{2}{7}) \\ \theta\approx16.6\degree \end{gathered}[/tex]Answer: the angle is 16.6°
A giant panda gave birth to her baby at a zoo. The baby panda weighed 100 grams. At its health exam 51 days later the baby weighed 2.17 kilograms. How much weight did the panda cub gain after 51 days?
Day 1 Weight of Baby Panda = 100 grams
Day 52 (after 51 days) Weight of Baby Panda = 2.17 kg
To determine the weight increase of our baby panda, we have to convert first the units from kg to grams.
[tex]1kg=1000grams[/tex]Please know that 1kg = 1000 grams. Therefore, 2.17 kg is equal to:
[tex]2.17kg\times1000grams=2170grams[/tex]So now, the weight of our baby panda after 51 days is 2170 grams. To determine weight increase, we will subtract 100 grams from 2170 grams.
[tex]2,170grams-100grams=2,070grams[/tex]Therefore, the panda cub gained 2,070 grams after 51 days or 2.07kg.
Hi can you help me with this question it is timed i just need an quick answer please and thank you .
ANSWER
EXPLANATION
When triangle DEF is reflected over the y-axis, its vertices are mapped to,
Then, after the translation down 4 units and right 3 units, D' is mapped to S, E' is mapped to R, and F' is mapped to U.
Hence, the congruency statement that describes the two triangles is ΔDEF
Interpret the remainder Solve each problem. Write A, B, C, D, or E to Indicate how you interpreted the remainder. A Use only the whole number. B Round up to the next whole number. C Use a mixed number. D Use a decimal. E Use only the remainder. 1. A group of 347 people have signed up for a bus trip to a baseball game. Each bus holds a maximum of 42 passengers. How many buses will be needed to take all the people to the game? 2. Andre and his sisters picked 105 pounds of grapes for their family's farm stand. They put the same amount of grapes into each of 30 bags. How many pounds of grapes were in each bag? 3. Paula charges an hourly rate for babysitting. Last month she worked 12 hours babysitting and earned $81. What does Paula earn per hour? 4. Mr. Parker owns The Glass Store. He received a shipment of 144 glass animals. He put an equal number of glass animals on each of 11 display shelves. How many glass animals were on each shelf? 5. Create Your Own Which letter did you not use in your answer? Make up a word problem of your own that uses this interpretation of the remainder.
question number 1
number of people = 347
number of buses = 42
number of buses that'll be required to take all passenger =
[tex]\frac{347}{42}=8.26[/tex]the reminder is a decimal hence the answer is option D.
7a) The roots of the equation 4x^2 - 7x - 1 = 0 are G and H. Evaluate G^2+ H^2B) Write the equation of a quadratic with integer coefficients whose solutions are G^2 and H^2.Pls see the pic for more detail.
Given:
[tex]4x^2-7x-1=0[/tex]Solve:
Quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where,
[tex]ax^2+bx+c=0[/tex]Compaire the equation then:
[tex]\begin{gathered} ax^2+bx+c=0 \\ 4x^2-7x-1=0 \\ a=4,b=-7,c=-1 \end{gathered}[/tex]So roots of equation is:
[tex]\begin{gathered} x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4(4)(-1)}}{2(4)} \\ x=\frac{7\pm\sqrt[]{49+16}}{8} \\ x=\frac{7\pm\sqrt[]{65}}{8} \end{gathered}[/tex]So value of G and H is:
[tex]\begin{gathered} G=\frac{7+\sqrt[]{65}}{8};H=\frac{7-\sqrt[]{65}}{8} \\ G=\frac{7}{8}+\frac{\sqrt[]{65}}{8};H=\frac{7}{8}-\frac{\sqrt[]{65}}{8} \end{gathered}[/tex]So:
[tex]\begin{gathered} =G^2+H^2 \\ =(\frac{7}{8}+\frac{\sqrt[]{65}}{8})^2+(\frac{7}{8}-\frac{\sqrt[]{65}}{8})^2 \\ =(\frac{7}{8})^2+(\frac{\sqrt[]{65}}{8})^2+2(\frac{7}{8})(\frac{\sqrt[]{65}}{8})+(\frac{7}{8})^2+(\frac{\sqrt[]{65}}{8})^2-2(\frac{7}{8})(\frac{\sqrt[]{65}}{8}) \\ =2(\frac{49}{64}+\frac{65}{64}) \\ =2(\frac{114}{64}) \\ =\frac{114}{32} \\ =3.5625 \end{gathered}[/tex](B)
If roots is a and b the equation is:
[tex]x^2-(a+b)x+ab=0[/tex]Then equation is:
[tex]G^2+H^2=3.5625[/tex][tex]\begin{gathered} G^2H^2=(\frac{7}{8}+\frac{\sqrt[]{65}}{8})^2(\frac{7}{8}-\frac{\sqrt[]{65}}{8})^2 \\ =(0.875+1.00778)^2(0.875-1.00778)^2 \\ =(3.54486)(0.01763) \\ =0.0624 \end{gathered}[/tex]So equation is:
[tex]x^2-3.5625x+0.0624[/tex]DIoll Solve the equation x³ + 2x² - 5x-6=0 given that 2 is a zero of f(x)= x³ + 2x² - 5x-6.The solution set is(Use a comma to separate answers as needed.)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
f(x) = x³ + 2x² - 5x - 6
zero:
x = 2
Step 02:
roots:
solution set:
2 | 1 2 -5 -6
| 2 8 6
________________
1 4 3 0
x² + 4x + 3 = 0
(x + 3)(x + 1) = 0
x = - 3
x = - 1
The answer is:
solution set:
{-3 , -1 , 2}
Find the values of x and y in the parallelogram.A46x+2211 BO x= 11, y = 24O x = 24, y = 11Ox=-11, y = 46O x=46, Y =-11
Since the opposite sides of a parallelogram are congruents, we can write the following equations:
[tex]\begin{cases}DA=BC \\ AB=CD\end{cases}[/tex]From the first one, we have:
[tex]y=11[/tex]From the second one, we have:
[tex]\begin{gathered} x+22=46 \\ x=46-22 \\ x=24 \end{gathered}[/tex]So we have x = 24 and y = 11, therefore the correct option is the second one.
Write the probability of getting 2 heads when flipping a coin 2 times. (Write as a reduced fraction)
we have that
The probability of getting 1 head when flipping a coin one time is
P=1/2
so
the probability of getting 2 heads when flipping a coin 2 times is
P=(1/2)*(1/2)=1/4
therefore
the answer is
P=1/4Which coordinate plane contains the points (4 1/2,1) and (–2 1/2, –2)?
option C
Explanation:
To determine the graph with the coordinates given, let's check and state some of the coordinates of each graph in the option:
[tex]\begin{gathered} \text{Given coordinates:} \\ (4\frac{1}{2},1)\text{ : x = 4}\frac{1}{2},\text{ y = 1} \\ (-2\text{ }\frac{1}{2},\text{ -2) : x = }-2\text{ }\frac{1}{2},\text{ y = -2} \end{gathered}[/tex]a) Coordinates: (-2, -3), (4, 4)
There is no point at -4 1/2 or -2 1/2 on this graph
b) coordinates: (-2, -3), (3, 1/2)
Tere is no x value at -4 1/2 or -2 1/2 on this graph
c) when x = -2 1/2, y = -2
when x = 4 1/2, y = 1
d) There is no x value at 4 1/2 on this graph. There is also no x value at -2 1/2 on this graph
Hence, the coordinate plane that contains points (4 1/2, 1) and (-2 1/2, -2) is option C
solve the quadratic equation by the square root method. show all steps.
We have to solve the equation with the square root method:
[tex]\begin{gathered} 2(x-4)^2-6=18 \\ 2(x-4)^2=18+6 \\ 2(x-4)^2=24 \\ (x-4)^2=\frac{24}{2} \\ (x-4)^2=12 \\ \sqrt[]{(x-4)^2}=\sqrt[]{12} \\ x-4=\pm\sqrt[]{12} \\ x=4\pm\sqrt[]{12} \\ x=4\pm2\sqrt[]{3} \end{gathered}[/tex]Answer: The solutions are:
[tex]\begin{gathered} x_1=4-2\sqrt[]{3} \\ x_2=4+2\sqrt[]{3} \end{gathered}[/tex]11.Graph the function.For the function whose graph is shown below, which is the correct formula for the function?4ns2-4-224Functionss and Functions
To find the formula for the function, we would find the equation of the line in the slope intercept form which is expressed as
y = mx + c
where
m represents slope
c represents y intercept. This is also the point where the line cuts the y axis. Looking at the graph,
c = - 2
We would find the slope by applying the formula,
m = (y2 - y1)/(x2 -x1)
where
y2 and y1 are initial and final values of the y coordinate of two suitable points chosen on the graph
x2 and x1 are initial and final values of the x coordinate of two suitable points chosen on the graph
From the graph,
x1 = - 1, y1 = - 4
x2 = 3, y2 = 4
m = (4 - - 4)/(3 - - 1) = (4 + 4)/(3 + 1) = 8/4
m = 2
Thus, the equation of the graph is
y = 2x - 2
Thus, the correct formula for the function is
y = 2x - 2
Solve the equation for c: 52 = 4(c + 5)
Given:
[tex]52\text{ = 4(c + 5)}[/tex]Solution
We are required to solve the equation for c.
First, we open the bracket:
[tex]52\text{ = 4c + 20}[/tex]Next, we make c the subject of formular:
[tex]\begin{gathered} 4c\text{ = 52 - 20} \\ 4c\text{ = 32} \\ \text{Divide both sides of the equation by 4} \\ c\text{ = 8} \end{gathered}[/tex]Answer: c = 8
use a model to solve2/3×6
Here, we want to use a model to solve the multiplication
We have this as follows;
Mathematically;
[tex]\frac{2}{3}\times6\text{ = 4}[/tex]How wide is the space betweeneach number on this clock?
Solution:
Given:
We have the angle between each hands of the clock to be
[tex][/tex]2. Select ALL coordinate pairs that are solutions to the inequality 5x + 9y<45. *
From the problem we have the inequality 5x + 9y < 45
Substitute the options and check if it satisfies the inequality.
(0, 0)
5(0) + 9(0) < 45
0 + 0 < 45
0 < 45
TRUE!
(5, 0)
5(5) + 9(0) < 45
25 < 45
TRUE!
(9, 0)
5(9) + 9(0) < 45
45 < 45
FALSE!
(0, 5)
5(0) + 9(5) < 45
45 < 45
FALSE!
(0, 9)
5(0) + 9(9) < 45
81 < 45
FALSE!
(-5, -9)
5(-5) + 9(-9) < 45
-25 - 81 < 45
-106 < 45
TRUE!
ANSWERS :
(0, 0), (5, 0) and (-5, -9)
14. Imagine a particle starting at (1,0) and making one counterclockwise revolution on the unitcircle. Let t be the angle in standard position that corresponds to the particle's position. At howmany points along the path of the particle are the x and y coordinates equal?
Let's make a graph to better understand the question:
a.) A particle starting at (1,0) and making one counterclockwise revolution on the unit
circle.
In the given description, we can assume that the center of the circle when the particle makes a revolution is at the origin (0,0). Thus, the equation of the circle that the particle will make is:
[tex](x-h)^2+(y-k)^2\text{ = }r^2[/tex]At (h,k) = (0,0) and r = distance between (0,0) to (1,0).
We get,
[tex](x-0)^2+(y-k)^2=(\sqrt[]{(1-0)^2+(0-0)^2})^2[/tex][tex]x^2+y^2\text{ = }1[/tex]Plotting the graph,
In conclusion, there will be two points along the path of the particle that the x and y coordinate equal.
At, x = y, let's substitute this to the formula of the graph of the circle to get the coordinates.
[tex]x^2+y^2\text{ = }1[/tex][tex]x^2+x^2\text{ = }1[/tex][tex]2x^2\text{ = 1 }\rightarrow\text{ }\frac{2x^2}{2}=\text{ }\frac{1}{2}[/tex][tex]x\text{ = }\sqrt[]{\frac{1}{2}}[/tex][tex]x\text{ = y = }\pm\frac{1}{\sqrt[]{2}}[/tex]Therefore, the two points where the x and y will be equal is at:
[tex]\text{ x = y = +}\frac{1}{\sqrt{2}}\text{ and }-\frac{1}{\sqrt[]{2}}[/tex]< Previous1Next >Factoring Polynomials: Mastery Test1Select the correct answer.What is the completely factored form of this polynomial?x3 + 3x2 - 6x-18A. (x-2)(x - 3)(x + 3)OB. (x2 - 6/x+3)C. (x2 + 3)(x-6)OD. (x+6)(x - 1)(x + 3)ResetNext
Solution
[tex]x^3+3x^2-6x-18[/tex]We can do the following:
[tex]x^2(x+3)-6(x+3)=(x+3)(x^2-6)[/tex]Then the correct answer would be:
[tex]B\mathrm{}(x^2-6)(x+3)[/tex]For the second case we have the following:
[tex]9x^2-64y^2[/tex]We can do this:
[tex](3x-8y)(3x+8y)[/tex]determine the domain of each function y=2x^4-3x^4+7x^2-1
Given:
[tex]y=2x^4-3x^4+7x^2-1[/tex]Simplify the function,
[tex]\begin{gathered} y=2x^4-3x^4+7x^2-1 \\ y=-x^4+7x^2-1 \end{gathered}[/tex]Domain: The domain of the function is the set of all possible input values for which the function is real or defined.
So, the domain of the given function is,
[tex]-\inftyPlease help will mark Brainly
Answer:
Below
Step-by-step explanation:
A yes all values of y
B yes slope is undefined for a vertical line
C no there is no y axis intercept for this line
D yes the line intercepts the x-axis at x = -2
E no the domain is only x = -2
Use the figure below to match each item on the left with the correct side ratio
The right triangle is given with sides a , b and c.
ExplanationTo determine the side ratio of the trigonometric function.
[tex]\begin{gathered} sinA=\frac{a}{c} \\ cosA=\frac{b}{c} \\ tanA=\frac{a}{b} \\ \end{gathered}[/tex][tex]\begin{gathered} sinB=\frac{b}{c} \\ cosB=\frac{a}{c} \\ tanB=\frac{b}{a} \end{gathered}[/tex]AnswerFor sin A , b is correct.
For cos A, d is correct.
For tan A, a is correct.
For sin B, d is correct.
For cos B, b is correct.
For tan B ,c is correct.
Find the area of the triangle with the given measurements. Round the solution to thenearest hundredth if necessary.B = 74º, a = 14 cm, c = 20 cm (5 points)
Let's begin by listing out the given information:
[tex]\begin{gathered} \angle B=74^{\circ} \\ a=14\operatorname{cm} \\ c=20\operatorname{cm} \end{gathered}[/tex]We will calculate the area as shown below:
[tex]\begin{gathered} \text{We will obtain the third side using the Cosine Rule:} \\ b^2=a^2+c^2-2ac\cdot cosB \\ b=\sqrt[]{a^2+c^2-2ac\cdot cosB} \\ b=\sqrt[]{14^2+20^2-2(14)(20)\cdot cos74^{\circ}} \\ b=21.02cm \end{gathered}[/tex]The formula for area is given by Heron's formula:
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ s=\frac{a+b+c}{2}=\frac{14+21.02+20}{2}=\frac{55.02}{2}=27.51 \\ s=27.51 \\ \Rightarrow A=\sqrt[]{27.51(27.51-14)(27.51-21.02)(27.51-20)} \\ A=134.58cm^2 \end{gathered}[/tex]Therefore, the area f
rs + 2r210rs5s2Find the binomial factors
Rs+2r^2-10rs-5s^2
Combine like terms
2r^2-9rs-5s^2
solve: 10+7-4y=-5+6y+22 and decide whether it has infinite solutions or no solutions or one solution
answer is one solution
Find the missing length,a, in the right triangle below using the pythagorean theorem.Round to the nearest tenth if necessary.The answer choices are A:28.9 ftB:73.5 ftC:27.1 ftD:4.6 ft
We get that
[tex]a=\sqrt[]{28^2-7^2}=\sqrt[]{784-49}=\sqrt[]{735}\approx27.1[/tex]hello this is a plane trigonometry question hopefully you can help I did every thing else it's just the last one I can't get the reference angle for five in this question
22. Find the 20th term: -30, -22, -14, -6, ....(Hint: Finding the nth term if an Arithmetic Sequence formula: a, = a, + (n − 1)d. )
Arithmetic Sequences
It consists in a series of terms with the condition that each term is calculated as the previous term plus a fixed number called the common difference (d).
The sequence is given as:
-30, -22, -14, -6,...
First, we need to find the common difference by subtracting two consecutive terms:
d = -22 - (-30) = -22 + 30 = 8
We can try another couple of terms:
d = -14 - (-22) = -14 + 22 = 8
If we test all the consecutive terms, we'll find the same value of d.
Now to use the formula:
an = a1 + (n - 1) * d
We need to find a1, the first term of the sequence. The value of a1 is -30.
Now we are ready to find the 20th term of the sequence (n=20) by substituting the values in the formula:
a20 = -30 + (20 - 1) * 8
Calculating:
a20 = -30 + 19 * 8 = -30 + 152 = 122
Thus the 20th term is 122
Daig 20. Sample Problem using Daum Equation Editor 4 - [3 :) and B - [: 6 51 Determine -3A + 2B Show all work using the Daum Equation Editor. Insert your image here:
The question is given as : -3A +2 B
[2 5] + { 6 5 }
[7 0 } { 1 1 }
For the first matrix , multiply by -3 and the second matrix multiply by 2
To multiply a matrix, every value in the bracket is multiplied by the scalar.
For -3A multiply the values in the bracket with -3 as;
[tex]\begin{bmatrix}{2} & {5} & \\ {7} & {0} & {} \\ {} & {} & \end{bmatrix}\times-3\text{ = }\begin{bmatrix}{-6} & {-15} & \\ {-21} & {0} & {} \\ {} & {} & {}\end{bmatrix}=-3A[/tex]For 2B
[tex]\begin{bmatrix}{6} & {5} & {} \\ {1} & {1} & {} \\ {} & {} & {}\end{bmatrix}\times2=\begin{bmatrix}{12} & {10} & \\ {2} & {2} & {} \\ {} & {} & {}\end{bmatrix}=2B[/tex]Now perform the addition as; -3A + 2B
[tex]\begin{bmatrix}{-6} & {-15} & \\ {-21} & {0} & {} \\ {} & {} & {}\end{bmatrix}+\begin{bmatrix}{12} & {10} & \\ {2} & {2} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{-6+12} & {-15+10} & \\ {-21+2} & {0+2} & {} \\ {} & {} & {}\end{bmatrix}[/tex]This will give the following;
[tex]\begin{bmatrix}{6} & {-5} & {} \\ {-19} & {2} & {} \\ {} & {} & {}\end{bmatrix}[/tex]Which pair of expressions are equivalent?
The pair of equivalent expression are 6(8f) and 48f
What is equivalent expression?Equivalent expressions are expressions that have similar value or worth but do not look the same.
Two expressions are said to be equivalent if they have the same value
irrespective of the value of the variable(s) in them.
Therefore, let's check the pair of expression and find which are equivalent.
6(8f) and 48f are equivalent expression.
If we simplify 6(8f), it will be as follows:
6(8f) = 6 × 8f = 48f
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