we have the following:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]replacing:
17. (1, 0) and (5, 5)
[tex]m=\frac{5-0}{5-1}=\frac{5}{4}[/tex]therefore,
[tex]\begin{gathered} y=mx+b \\ y=\frac{5}{4}\cdot x-\frac{5}{4} \end{gathered}[/tex]19. (0, -1) and (3, -5)
[tex]m=\frac{-5-(-1)}{3-0}=\frac{-4}{3}=-\frac{4}{3}[/tex]therefore,
[tex]\begin{gathered} y=mx+b \\ y=-\frac{4}{3}\cdot x-1 \end{gathered}[/tex]21. (1, 9) and (6, 2)
[tex]m=\frac{2-9}{6-1}=\frac{-7}{5}=-\frac{7}{5}[/tex]therefore,
[tex]\begin{gathered} y=mx+b \\ y=-\frac{7}{5}\cdot x+10.4 \end{gathered}[/tex]$825 due in 3 years at 10% compounded annually.
Given: Principal, P=$825
Rate, R=10% compounded annually
Time, t=3 years.
Required: To find the amount after 3 years.
Explanation: The amount, A after t years at r% rate is given by
[tex]A=P(1+\frac{r}{100})^t[/tex]Putting the values we get
[tex]\begin{gathered} A=825(1+\frac{10}{100})^3 \\ A=1098.075\text{ \$} \end{gathered}[/tex]Final Answer: The amount after 3 years is $1098.075.
Change the proper fraction below to a decimal.
31/200
31/200 converted from a proper fraction to a decimal is 0.155.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
We can convert this proper fraction 31/200 into a decimal by first eliminating the zeroes and moving a decimal point from right to left to as many places as zeroes.
∴ 31/200.
= 0.31/2.
Now, we know that 30/2 is 15 and 32/2 is 16.
So, 31/2 must be 15.5.
∴ 0.31/2.
= 0.155.
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A shopkeeper wants to sell a shirt originally priced at $120. Which deal will result in the greatest sale price of the shirt?A. 20% offB. $30 couponC. 15% off and then a $15 rebateD. 10% off and then a $20 rebate
Let's determine which sale is better.
20% means that the shirt will cost:
[tex]120(0.8)=96[/tex]$30 coupon means that the shirt will cost $90
15% off and $15 rebate means:
[tex]120(0.85)-15=87[/tex]10% off and $20 rebate means:
[tex]120(0.9)-20=88[/tex]Comparing the prices we conclude that the best deal is C
Consider the equations 3(−2)(+3)=0 and (2−4)(3+9)=0.Do they have the same solutions? Justify your answer.
First equation
3(x−2)(x+3)=0
3 is multiplying on the left, then it will divide on the right.
(x−2)(x+3) = 0/3
(x−2)(x+3) = 0
The solutions are:
x - 2 = 0 or x + 3 = 0
that is, x = 2 and x = -3
Second equation
(2x−4)(3x+9) = 0
The solutions are:
2x − 4 = 0
x = 4/2
x = 2
or 3x+9 = 0
x = -9/3
x = -3
Then, they have the same solutions.
A helicopter hovers 1075 feet above a small island. The figure shows that the angle of depression from the helicopter to point P on the coast is 35". How far off the coast, to the nearest
foot, is the island?
The situation forms a right angle triangle. The distance form the coast to the helicopter is 1535.25910 ft.
What is meant by Right angle triangles?Right angle triangles exists triangle that contains one of its angles as 90 degrees. The height of the helicopter exists the opposite side of the triangle formed.
How far off the coast to the helicopter is the adjacent side.
The situation forms a right angle triangle.
Therefore, tan 35° = opposite / adjacent
tan 35° = 1075 / a
Multiply both sides by a,
tan (35°) a = (1075 / a) a
Simplifying the above equation, we get
[tex]$\tan \left(35^{\circ}\right) a=1075$$[/tex]
Divide both sides by [tex]$\tan \left(35^{\circ}\right)$[/tex]
tan (35°) a / tan (35°) = 1075 / tan (35°)
Simplifying the above equation, we get
a = 1075 / tan (35°)
singularity points: a = 0
Combine undefined points with solutions:
a = 1075 / tan (35°)
a = 1535.25910 ft
Therefore, the distance form the coast to the helicopter exists 1535.25910 ft.
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help me pleasee!!
thank you
Step-by-step explanation:
so, we need to get the slope-intercept form
f(x) = y = ax + b
"a" is as always the slope, "b" is the y-intercept (the y-value when x = 0).
as we have the slope and a point, we can start with the point-slope form and transform it :
y - y1 = a(x - x1)
with (x1, y1) being a point on the line.
y - 7 = -9(x - 2) = -9x + 18
y = -9x + 25
therefore, the functional equation is
f(x) = -9x + 25
Help please show your work please
Using Subtraction, At least 15 more people are required to register for the swimming class to held.
What does math subtraction mean?To remove anything from a set or a group of items in mathematics is to take that item away. The total number of elements in the group decreases or decreases when we subtract from it.
What different types of subtraction are there?There are actually three methods to understand subtraction: taking away. Part-whole. Comparison.
Given:
No. of people required to start the class = 24
no. of people registered = 9
Therefore no. of people required = 24 - 9
= 15 people
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mrs.bells daughter has 3.5 baskets of towels that need to be folded.if she gets 1.5 baskets folded per hour,how many hours will it take her daughter to fold all of the towels
mrs.bells daughter has 3.5 baskets of towels that need to be folded.if she gets 1.5 baskets folded per hour,how many hours will it take her daughter to fold all of the towels
we know that
The unit rate is 1.5 baskets per hour
To find out the number of hours , divide the total baskets by the unit rate
so
3.5/1.5=2.33 hours
2.33 hours=2 1/3 hours or 2 hours 20 minutes
therefore
the answer is
2 1/3 hours or 2 hours 20 minutesFind the nth term of this quadratic sequence
3, 11, 25, 45, …
Using the principle of mathematical induction, the [tex]n^{th }[/tex] term of the given quadratic sequence is found to be 3n² - n + 1.
What exactly is mathematical induction?Mathematical induction is a technique for proving the truth of a statement, theorem, or formula for each and every natural number n. This is generalized as the 'Principle of Mathematical Induction,' which we would use to prove any mathematical statement.Given sequence: 3, 11, 25, 45,...
The first term of the sequence is 3, the second term is 11, the third term is 25, and the fourth term is 45.
The difference between the first and second terms can be calculated as follows:
11-3 = 8
The difference between the second and third terms can be calculated as follows:
25-11 = 14
The difference between the third and fourth terms can be calculated as follows:
45-25 = 20
The sequence is expressed as follows:
3,3+8,11+11,25+20,...
The difference between consecutive terms expands by 6.
Use the principle of mathematical induction.
[tex]6(\frac{n(n+1)}{2})[/tex]
= 3n(n+1)
The sequence's nth term can be calculated as follows:
[tex]n^{th }[/tex] term = 3n(n+1) - 4n + 1
= 3n² - n + 1
Therefore, the [tex]n^{th }[/tex] term of the given quadratic sequence is found to be 3n² - n + 1 using the principle of mathematical induction.
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Hello, I need help with task 3 which has 3question as it is part of one big question. Therefore 30 for a question for each. These questions are connected to previous ones so, I will send an image of the other two task
Task 3 (of 3)
Part 1: In this case the probabilitie that a person saw resould and receive the power pill is 0.65, so in order to have a trustable resould should be more than 95% to be certan. How ever I think that with a probabiliti of more that the 70% could wor. So in this case a probabilitie of 65% is not enogh to produce or dristribute.
Part 2: We can compare the resoulds of group A and group B and the resoulds of group C vs the resould in group D so we check if telling the subject affect anything.
So for group A and B are 0.15 and 0.175 so there is no significant difference and for C and the are 0.125 and 0.1 so there is again not significant effect.
Part 3: In this case maybe a better way to made the experiment is to take a bigger poblation, becuase each group has to low participants. if we have more particiants we can have better resoulds. Also we can calculate a standart deviation to be sure of the difference between the groups.
Find the equation of the line through the point (1,-1) with
slope 4?
Answer:
4x - y - 5 = 0
Step-by-step explanation:
Given:
Slope = m = 4
(x1,y1) = (1,-1)
Solution:
y - y1 = m (x - x1)
y - (-1) = 4 (x - 1)
y + 1 = 4x - 4
y = 4x - 4 - 1
y = 4x - 5
4x - y - 5 = 0
A line has a slope of -8 and passes through the point (0,5)
A line has a slope of -8 and passes through the point (0,5)
Find out the equation of the line in slope-intercept form
y=mx+b
where
m is the slope
b is the y-coordinate of the y-intercept
in this problem
m=-8
b=5
therefore
y=-8x+5 -----> equation of the line in slope-intercept form4x + 7 = 23 S = {3, 4, 5, 6}
[tex]4x = 23- 7 \\ 4x = 16 \\ \frac{4x}{4} = \frac{16}{4} \\ x = 4[/tex]
I HOPE THIS IS WHAT YOU WANT SINCE YOU WERE NOT STRAIGHTFORWARD.
DM ME IF YOU HAVE ANY QUERIES.
Please help I would appreciate it. Solve 4x^2-4x-8 needs to be factored.
Given
[tex]4x^2-4x-8[/tex]This can be written as:
[tex]4(x-2)(x+1)[/tex]
Find the coordinates of the midpoint of a segment with the endpoints ( 22 , 4 ) and ( 15 , 7 ) .
The coordinates of the midpoint of a segment with two endpoints ( 22, 4 ) and ( 15, 7 ) is ( 37/2, 11/2 ).
The center of a line segment is known as the midpoint. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
Consider the two endpoints of the segments as:
A( 22, 4 ) and B( 15, 7 )
Let M( x, y ) be the midpoint of the line segment.
Then AM = MB = ( 1/2 )AB
Therefore, the points will also the halfway from the midpoint.
Therefore,
M( x, y ) = ( 1/2 )A + ( 1/2 )B
M( x, y ) = 1/2( 22, 4 ) + ( 1/2 )( 15, 7 )
M( x, y ) = ( 11, 2 ) + ( 15/2, 7/2 )
M( x, y ) = ( 11 + 15/2, 2 + 7/2 )
M( x, y ) = ( 37/2, 11/2 )
Therefore, the coordinate of the midpoint of the line segment is ( 37/2, 11/2 ).
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c. (a²-5a + 3)(a −2)-¹
Long devision
The most appropriate choice for division will be given by-
Quotient = [tex]a - 3[/tex] and remainder = -3
What is division?
For finding the value of single unit from the value of multiple unit, division is used.
Division can be used for integers as well as for algebraic polynomials.
The expression which is divided is known as dividend.
The expression by which the dividend is divided is known as divisor.
The result obtained on division is called the quotient and the part which is remaining is called the remainder.
There is a well known formula in case of division.
Divisor [tex]\times[/tex] Quotient + Remainder = Dividend
The long division has been shown here-
[tex]\begin{array}{r}a-3\phantom{)} \\a-2{\overline{\smash{\big)}\,a^2-5a+3\phantom{)}}}\\\underline{-~\phantom{(}(a^2-2a)\phantom{-b)}}\\-3a+3\phantom{)}\\ \underline{-~\phantom{()}(-3a+6)}\\ -3\phantom{)}\end{array}[/tex]
Here Quotient = [tex]a - 3[/tex] and remainder = -3
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At a restaurant, the bill comes to $40. You decide to leave a 15% tip. How much did you leave for the tip?
The tip of 15% is 15% of the total value of the bill, which is $40. So, we need to take 15% of 40.
Taking 15% of 40 is the same as multiplying 15% by 40. 15% can also be written as:
[tex]15\%=\frac{15\%}{100\%}=0.15[/tex]So, we can take 15% of 40 by multiplying 0.15 by 40:
[tex]0.15\cdot40=6[/tex]So, the amount left for the tip is $6.
Which of the following expressions are equivalent to 36x + 24y? Choose ALL that apply.
Notice how the coefficients of 'x' and 'y' are both divisible by 4, therefore:
[tex]36x+24y=4(9x+6y)[/tex]So, the equivalent expression of 36x+24y is 4(9x+6y)
simplify with three algebraic terms
0.3p+0.2p+0.4p
The simplified form of the three algebraic terms 0.3p + 0.2p + 0.4p is 0.9p
The three algebraic terms are
0.3p + 0.2p + 0.4p
The algebraic expression is defined as the expression which is made up of constants and variables with the algebraic operation. The algebraic operations are addition subtraction, division and multiplication
To solve this problem first we have to group the like terms of the given expression and add the like terms of the expression
The three algebraic terms are
= 0.3p + 0.2p + 0.4p
Group the like terms
= (0.3 + 0.2 + 0.4) ×p
Add the terms together
= 0.9p
Hence, the simplified form of the three algebraic terms 0.3p + 0.2p + 0.4p is 0.9p
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What is the equation of the line that is parallel to y=-3x+4 and that passes through (-2,-2)?
0--1-1
I need help question
∫ 4 dt
integrate with respect to t
power rule
(x^n + 1)/(n + 1)
but you dont really need to go through all that for this
answer is 4t + c
because the derivative of 4t + c is just 4
A regular quadrilateral and a regular triangle have the same perimeter. The side length of one of the sides of the quadrilateral is 48. What is the length of a side of the triangle?
The length of a side of the triangle is 16.
Which is a Regular Polygon?A polygon is classified as regular when all sides and angles are equal. Therefore, a regular quadrilateral presents all the four sides and the four angles equal. You can use the same conclusion for a regular triangle, but for a triangle the three sides and the three angles are equal.
The question gives:
The perimeter for the regular quadrilateral = 48. Because of this, it is important that you know the definition for perimeter = sum of the sides of a geometric figure.As the triangle was classified as regular, all its sides (x) are equal. Then,
x+x+x=48
3x=48
x=48/3
x=16
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When Kiran moved into a new house, he planted two trees in his backyard. At the time of planting, Tree A was 33 inches tall and Tree B was 15 inches tall. Each year thereafter, Tree A grew by 4 inches per year and Tree B grew by 7 inches per year. Let AA represent the height of Tree A tt years after being planted and let BB represent the height of Tree B tt years after being planted. Write an equation for each situation, in terms of t,t, and determine the interval of time, t,t, when Tree A is taller than Tree B.
Equation are AA = 33+15tt and BB = 15+7tt. Tree A will remain taller than tree B till 2.25 years.
Size of Tree A in the beginning = 33 inches
Size of Tree B in the beginning = 15 inches
Increase in length of Tree A per year = 4 inches
Increase in length of Tree B per year = 7 inches
Let AA represent the height of Tree A tt years after being planted. Let BB represent the height of Tree B tt years after being planted.
Formulating the equation we get:
For tree A:
Height after tt years = Height in beginning + Increase each year*Number of years
AA = 33 + 15tt-----(1)
For tree B:
Height after tt years = Height in beginning + Increase each year*Number of years
BB = 15 + 7tt------(2)
Equating (1) and (2) we get:
33 + 15tt = 15 + 7tt
18 = -8tt
tt = 2.25 years
So, the trees will be of the same height in 2.25 years
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-4b + 8c + 12 - 8b - 2c + 6What is the value of the expression when b = 2 and c =-3? Enter your answer on the grid.
ANSWER
-24
EXPLANATION
We have the expression and we want to find its value when b is 2 and c is -3.
To do that, we replace b in the expression with 2 and c with -3.
The expression is:
-4b + 8c + 12 - 8b - 2c + 6
So, we have:
-4(2) + 8(-3) + 12 - 8(2) - 2(-3) + 6
=> -8 - 24 + 12 - 16 + 6 + 6
=> -24
That is the answer.
5m-2 = 12m -16
SOLVE
Answer:
m=2
Step-by-step explanation:
m=2 is the answer hope this helped
Answer:
m=2
Step-by-step explanation:
Follow this step by step solution.
Hope this was helpful.
What number is a reasonable estimate for 39x241 8000 2 14000 3 800 4 1400
In this case, we'll have to carry out several steps to find the solution.
Step 01
Data:
reasonable estimate = ?
39x24
Step 02:
39x24 = 936
reasonable estimate = 800
The answer is:
reasonable estimate = 800
f(x) = -x^2 - 10x - 13 Find f(-2)
Answer: f(-2) = 3
The the below quadratic function
[tex]f(x)=-x^2\text{ - 10x - 13}[/tex]Find f(-2). To find f(-2) let x = -2
[tex]\begin{gathered} f(-2)=-(-2)^2\text{ - 10(-2) - 13} \\ f(-2)\text{ = -(4) -10(-2) - 13} \\ f(-2)\text{ = -4 + 20 - 13} \\ f(-2)\text{ = 16 - 13} \\ f(-2)\text{ = 3} \end{gathered}[/tex]Find the area of this trapezoid. Be sure to include the correct unit in your answer.14 ft16 ft7 ft17 ft
The area of a trapezoid can be found through the formula
[tex]A=\frac{a+b}{2}\cdot h[/tex]where a and b are the bases and h the height, then,
[tex]\begin{gathered} A=\frac{14+7}{2}ft\cdot7ft \\ A=10.5ft\cdot7ft \\ A=73.5ft^2 \end{gathered}[/tex]Arrange the equations in the correct sequence to rewrite the formula for displacement, ,
D=VT-1/2at^2
to find a. In the formula, d is displacement, v is final velocity, a is acceleration, and t is time.
The solution of the equation for a is a = 2(vt - d)/t²
What is subject of formula?Subject of formula involves isolating a variable in an equation different from the initial isolated variable
How to determine the equation for a?The equation is given as
d = vt - 1/2at²
From the question, we have
d is displacementv is final velocitya is accelerationt is time.Subtract vt from both sides of the equation
d - vt = - 1/2at²
Multiply both sides by -2
at² = 2(vt - d)
Divide both sides by t²
So, we have the following equation
a = 2(vt - d)/t²
Hence, the solution is a = 2(vt - d)/t²
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One triangle has a height of 15 feet and a base length of 8 feet. It is proportional to a second triangle that has a height of 375 feet. What is the length of the second triangle's base (Hint: draw a visual and set up a proportion)O A 20OB. 28OC 30O 0.70
Using the data from the question, we draw the following triangles:
The dimensions are in feet.
Now, the two triangles are proportional, so if we compute the ratio between the height and the basis of the first triangle, and then we do the same with the second, we must obtain the same number:
[tex]r=\frac{h_1}{b_1}=\frac{h_2}{b_2}[/tex]Replacing the dimensions of the triangles in the last equation, we get:
[tex]\begin{gathered} \frac{h_1}{b_1}=\frac{h_2}{b_2} \\ \frac{15}{8}=\frac{375}{b_2} \end{gathered}[/tex]From the last equation we can compute b2, the basis of the second triangle, doing that we find that:
[tex]\begin{gathered} \frac{15}{8}=\frac{375}{b_2} \\ 15\cdot b_2=375\cdot8 \\ b_2=\frac{375\cdot8}{15} \\ b_2=200 \end{gathered}[/tex]So the second triangle's base is:
[tex]b_2=200[/tex](in feet)
Answer
A. 200
