The given points are (1,6) and (-5,-3).
First, we have to find the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing given points, we have
[tex]m=\frac{-3-6}{-5-1}=\frac{-9}{-6}=\frac{3}{2}[/tex]Now, we use the point-slope formula
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-6=\frac{3}{2}(x-1) \\ y=\frac{3}{2}x-\frac{3}{2}+6 \\ y=\frac{3}{2}x+\frac{-3+12}{2} \\ y=\frac{3}{2}x+\frac{9}{2} \end{gathered}[/tex]Therefore, the equation would be y = 3/2x + 9/2A 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°
I need to graph thid inequality, while showing work. I get some right and others wrong.
Y < 2x^2 - 1
Then first graph equation parabolic
2x^2 -1,
Then draw green lines , below 2x^2 -1
watch your P's and Q's texas instruments incorporated
Start by graphing your function in the calculator or systme you are using to graph.
we can get closer to the zeros of the functions.
The zeros of a function are the points the function cross over the x-axis, menaing that y is always 0.
According to the graph the functions has 2 zeros.
The approximate zeros will be (-9,0) and (0,0) since they are the closer to the actual point crossing th x.-axis.
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]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.
Debra started washing at 8:33 AM and finished at 9:22 AM.How long did it take her? Give your answer in minutes.
According to the given data we have the following:
Debra started washing at 8:33 AM
finished at 9:22 AM
One easy way to find out the amount of time it took to her washing her clothes would be the following:
Debra started washing at 8:33 AM, so from 8:33 am to 9 o clock 27 minutes passed.
So, if she finished at 9:22 AM, that means that we would have to add to the 27 minutes another 22 minutes, so 27+22=49 minutes.
Therefore, it took to her 49 minutes to wash her clothes.
I need to know what 152x4241 is
Multiplying:
[tex]152\cdot4241=644632[/tex]Answer: 644632
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]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]Bх1-7-6-5.-303141516-4Find the distance between A and B.OA. V6 unitsB. 2/3 unitsC. 2V5 unitsD.4 units
With the information in the graph we have to:
[tex]\begin{gathered} AB=\sqrt{4^2+2^2} \\ AB=\sqrt{16+4} \\ AB=\sqrt{20}=\sqrt{2^2\cdot5} \\ AB=2\sqrt{5} \end{gathered}[/tex]therefore the answer is C.
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
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
< 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]The junior class is selling fruit bars to raise money. They purchased 1250 fruit bars and paid a delivery fee of $25. The total cost, including the delivery fee, was $800. What was the cost of each bar?
Number of fruit bars purchased = 1250.
Delivery fee = $25
Total cost including the delivery fee = $800.
Therefore, the cost without delivery fee = 800-25 = $775.
Therefore, the cost of fruit bars purchased = $ 775.
So, the cost of 1 fruit bar, is,
[tex]\frac{775}{1250}=0.62[/tex]Therefore, the cost of 1 fruit bar is $ 0.62.
how manh 1- miligram doses are there in one 2- decagram container?
1 decagram = 10 grams
Also 1000 milligrams = 1 gram
From the information provided, 2 decagrams = 20 grams
If 1000 milligrams = 1 gram, then
1000 x 20 = 20 x 20 grams
20,000 milligrams = 400 grams
Similarly, If 1 decagram = 10 grams, then
0.1 decagram = 1 gram
(that is, divide 1 decagram by 10 and also divide 10 grams by 10)
However, a 2-decagram container can hold 20 grams.
(Remember that 1000 milligrams = 1 gram).
If a 2-decagram container can hold 20 grams, which is equal to 20,000 milligrams, then;
2 decagrams = 20,000 milligrams
Therefore, a 2-decagram container can hold 20,000 1-milligram doses.
Below, the two-way table is given for a classof students.FreshmenSophomore Juniors Seniors TotalMale4622Female 3463TotalIf a student is selected at random, find theprobability the student is a male given that it's asophomore.
The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes.
We want to calculate the probability the student is a male given that it's a sophomore. Since we already know the student is a sophomore, the possible outcomes are only male sophomores(6) and female sophomores(4) and the favourable outcomes are the male sophomores(6), therefore, this probability is:
[tex]P(Male|Sophomore)=\frac{6}{6+4}=\frac{6}{10}=\frac{60}{100}=60\%[/tex]The probability the student is a male given that it's a sophomore is 60%.
can you please help me
we have the equation
y=-4x+4
this is the equation of the line in slope intercept form
where
the slope is m=-4 ----> is a negative slope
the y-intercept is b=4
that means
the y-intercept is the point (0,4)
Find out the x-intercept
For y=0
0=-4x+4
4x=4
x=1
x intercept is (1,0)
therefore
the answer is
a line that slopes down
An applicant receives a job offer from two different companies. Offer A is a starting salary of $58,000 and a 3% increase for 5 years. Offer B is a starting salary of $56,000 and an increase of $3,000 per year. Determine whether offer B can be represented by an arithmetic or geometric series and write the equation for Bn that represents the total salary received after n years. Justify your reasoning mathematically.
Offer B canbe represented by an arithmetic sequence because there is a constant difference between the salary of two consecutive years.
The sequence can be written as follow:
Bn = 56,000 + 3,000n
where n is the number of years in the job.
By subtracting B(n+1) - Bn, you obtain:
[tex]\begin{gathered} B_{n+1}-B_n=56,000+3,000(n+1)-56,000-3,000n \\ B_{n+1}-B_n=3,000 \end{gathered}[/tex]As you can notice, the difference of the salaries between two consecutive years is constant, which means that Bn is an arithmetic sequence.
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.
PLEASE PLEASE I NEED HELP ANSWERING THIS ITS FOR MY HOMEWORK
In this case the answer is very simple.
We need to write the equation to determine the change in the score.
To find the solution to the exercise we'll have to carry out several steps.
Step 01:
Data
Penalization points = 95
Gained points for each target = 10
Step 02:
Equation
Score change = number of targets* gained points for each target - penalization points
Score change = 4 * 10 - 95
Score change = - 55 points
The answer is:
Sarah's score change = - 55 points
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]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)
Solve the system by substitution.4x – 2y = -4y = 3x
We start by substituting the value of 3x for y in the first equation
We have this as;
[tex]\begin{gathered} 4x-2(3x)\text{ = -4} \\ 4x\text{ - 6x = -4} \\ -2x=\text{ -4} \\ x\text{ = }\frac{-4}{-2} \\ x\text{ =2} \\ \text{From i}i\colon\text{ y = 3x ; y = 3(2) ; y = 6} \end{gathered}[/tex]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 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
learn more on equivalent expression here:https://brainly.com/question/12232348
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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]-\inftyAn 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]Let angle C be congruent to angle C' and POC be congruent to P'O'C'.Let O" be a point on line CO so that CO" is equal to C'O'. Let P" be the point on line CP so that the dilation of P is represented by P".Which statement is true?A. triangle COP is equal to triangle C'O'P'B. line CP is congruent to line CP"C. triangle C'O'P is a glide reflection of triangle COP, whereas triangle CO"P" is congruent to triangle C'O'P'D. triangle CO"P" is a dilation of triangle COP with center C and a scale factor of r = C'O'/CO equals CO/CO
ANSWER
D. Triangle CO''P'' is a dilation of triangle COP with center C and a scale factor of r = C'O'/CO = CO''/CO
EXPLANATION
Given:
• ∠C ≅ ∠C'
,• ∠POC ≅ ∠P'O'C'
,• C'O' = CO''
Triangles COP and C'O'P' are similar triangles, by AA postulate.
Since CO'' and C'O' have the same length - they are congruent, then angle CO''P'' is congruent to angle C'O'P', and we can conclude that segments O''P'' and OP are parallel:
Hence, triangle CO''P'' is a dilation of triangle COP with center C and a scale factor of r = C'O'/CO = CO''/CO
A store has 6 TV Graphic magazines and 8 News time magazines on the counter. If two customers purchased a magazine,find the probability that one each magazine was purchased
SOLUTION:
Case: Probability
Given:
Number of TV Graphic magazines = 6
Number of News time magazines = 8
Total number of magazines on the stand = 14.
*two customers purchased a magazine*
Required: find the probability that one each magazine was purchased
Method:
[tex]\begin{gathered} Pr\left(one\text{ magazine each}\right? \\ =\text{ }\frac{^{n1}C_{x1}\times^{n2}C_{x2}}{^nC_x} \\ n1=\text{ number of TV graphic magazines} \\ x1=\text{ number of TV graphic magazines selected} \\ n2=\text{ number of News time magazines} \\ x2=\text{ number of News time magazines selected} \\ n=\text{ total number of magazines selected} \\ x=\text{ total number sslected} \end{gathered}[/tex][tex]\begin{gathered} \frac{^{n1}C_{x1}\times^{n2}C_{x2}}{^nC_x} \\ \frac{^6C_1\times^8C_1}{^{^14}C_2} \\ \frac{6\times8}{91} \\ \frac{48}{91} \end{gathered}[/tex]Final answer:
The probability that one each magazine was purchased is 48/91
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