Question 4(Multiple Choice Worth 5 points)
(04.03 MC)
What is the slope of the line joining (8, 1) and (24, 9)?
1 H
&
M
Answer:
1/2
Step-by-step explanation:
The slope between two points is found by
m = (y2-y1)/(x2-x1)
= (9-1)/(24-8)
= 8/16
= 1/2
Answer:
1/2.
Step-by-step explanation:
The slope = rise / run
= difference in y coordinates / corresponding differences in x coordinates
= (9 - 1) / (24 - 8)
= 8 / 16
= 1/2.
What is the length of line segment BC?
Answer:
24
Step-by-step explanation:
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Let f(x) = x^2-6 and g(x) =10x . Find (g ° f)(x)
Answer:
[tex](g \circ f)(x)=10x^2-60[/tex]
Answer:[tex]10x^2-60[/tex]
Step-by-step explanation:
[tex](g \circ f)(x)=g(f(x))[/tex]
Replace [tex]f(x)[/tex] with [tex]x^2-6[/tex].
This gives us:
[tex](g \circ f)(x)=g(f(x))[/tex]
[tex](g \circ f)(x)=g(x^2-6)[/tex]
This means to replace the old input variable with new input, [tex](x^2-6)[/tex].
Let's do that:
[tex](g \circ f)(x)=10(x^2-6)[/tex]
They probably want you to distribute:
[tex](g \circ f)(x)=10x^2-60[/tex]
Answer:
10x^2-60
Step-by-step explanation:
(G o F)(x) is the same as g(f(x)). We know that f(x)=x^2-6. So now you have to find g(x^2-6). To solve for that plug in x^2-6 in for x in the original equation for g(x). You get 10(x^2-6) or 10x^2-60
The volume of a rectangular prism is (x^4+4x^3+3x^2+8x+4), and the area of its base is (x^3+ 3x^2+8). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism
Answer:
height of prism = [tex]x+1-\frac{4}{x^3+3x^2+8}[/tex]
Step-by-step explanation:
Volume of rectangular prism = (x^4+4x^3+3x^2+8x+4)
Area of its bases = (x^3+ 3x^2+8)
Height of prism = ?
Volume of rectangular Prism = Area of its bases * Height of prism
(x^4+4x^3+3x^2+8x+4) = (x^3+ 3x^2+8) * height of prism
=> height of prism = (x^4+4x^3+3x^2+8x+4) /(x^3+ 3x^2+8)
=> height of prism = [tex]x+1-\frac{4}{x^3+3x^2+8}[/tex]
The division of (x^4+4x^3+3x^2+8x+4) /(x^3+ 3x^2+8) is shown in the attached figure.
Answer:
Step-by-step explanation:
The price of pebbles are 4.50/kg.
A) How many kilograms of pebbles can be bought with $10?
Answer:
2.222222222222222222222222222222222222222222222222222222kg
or 2.2kg rounded :)
Step-by-step explanation:
10/4.50 = 2.2222222222222222222222222222222222222222222222222
so if you multiply both sides by 2.22222 you get (4.50 *2.222222 = 10)(kg*2.222222 = 2.222222222kg)
Which angle is included between MP and PN?
Answer:
MPN
Step-by-step explanation:
According to an informal poll in Glenview 1/3
of the men and 2/3 of the women said they
would vote for John Smith. On election day,
one and a half times as many men as women
voted. What fraction of the total vote,
according to the poll, should be cast for John
Smith?
Answer:
Percent form: 41.65%
Fraction form: [tex]\frac{833}{2000}[/tex]
Step-by-step explanation:
33% of men support John Smith.
67% of women support John Smith.
Lets say, for instance, that there are 20 polled individuals -- 10 women and 10 men.
However, since 1.5 times as many men voted as women, we have to apply our poll to 15 men and 5 women.
33% of the 15 men makes 5 men who voted for Smith and 10 who did not.
67% of the 5 women makes 3.33 women who voted for Smith and 1.67 who did not.
Add these numbers together.
8.33 total voters were cast for John Smith, while 11.67 were not.
Now, divide 8.33 by 20 and multiply by 100 to obtain a percentage.
[tex]\frac{8.33}{20} \\.4165\\41.65[/tex]
41.65% of voters voted for John Smith according to the results of the poll.
According to an informal poll, with 1/3 of men and 2/3 of women supporting John Smith, and 1.5 times more men than women voting, 2/3 of the total vote should be cast for John Smith.
We need to calculate the fraction of the total vote that would be cast for John Smith according to the informal poll. Let's denote the number of women voters as w and the number of men as m. According to the poll, 1/3 of men and 2/3 of women will vote for John Smith. On election day, 1.5 times as many men as women voted, which means m = 1.5w.
The total votes for John Smith would be (1/3)m + (2/3)w. Substituting m with 1.5w, we get:
Total votes for John Smith = (1/3)(1.5w) + (2/3)w
This simplifies to:
Total votes for John Smith = 0.5w + (2/3)w = (1.5/3)w + (2/3)w = (1.5/3 + 2/3)w = (3/3 + 2/3)w = (5/3)w
The total votes cast would be m + w, substituting again we get 1.5w + w = 2.5w.
To find the fraction of total votes that would be for John Smith, we divide the total votes for John Smith by the total votes cast:
Fraction for John Smith = (5/3)w / (2.5)w
Since w is in both the numerator and denominator, it cancels out, and we're left with:
Fraction for John Smith = (5/3) / (2.5)
Converting 2.5 to a fraction gives us 5/2, so:
Fraction for John Smith = (5/3) / (5/2)
By dividing fractions, we invert and multiply:
Fraction for John Smith = (5/3) * (2/5) = 2/3
Therefore, according to the poll, 2/3 of the total vote should be cast for John Smith.
(02.05)The figure shows three quadrilaterals on a coordinate grid:
A coordinate plane is shown. Figure Q is a quadrilateral with sides measuring 5 and 2. Figure S is a quadrilateral with sides measuring 5 and 2. Figure W is a quadrilateral with sides measuring 10 and 4.
Which of the following statements is true about the three quadrilaterals?
Q and W are similar but not congruent.
W and S are similar and congruent.
W and Q are similar and congruent.
Q and S are similar but not congruent.
Answer:
The correct option is A) Q and W are similar but not congruent.
Step-by-step explanation:
Consider the provided graph.
Figure Q is a quadrilateral with sides measuring 5 and 2
Figure S is a quadrilateral with sides measuring 5 and 2.
Figure W is a quadrilateral with sides measuring 10 and 4.
Two figures are similar if the shape of the figures are same but not necessarily same size.
Two figures are congruent if the size and shape of the figure are same.
Note: If two figures are congruent, then they are also similar, but converse is not true.
The dimensions of Q is equals to the corresponding dimensions of the rectangle S. Thus, Q and S are similar and congruent as they have the same shape and the same size.
The dimension of quadrilateral W is 2 times of quadrilateral Q and S. Thus the dimensions of W is proportional to dimensions of Q.
That means quadrilateral W is similar to Q and S but not congruent.
Thus, the correct option is A) Q and W are similar but not congruent.
the number that is x more than 2x+1
Answer:-1
Step-by-step explanation:x>2x+1=x-2x>1
-x>1,x<- 1
Answer:
-1
Step-by-step explanation:
The u-drive rent-a-truck company plans to spend $8 million on 280 new vehicles. Each commercial van will cost $25,000 , each small truck $30,000 , and large truck $40,000. Past experience shows that they need twice as many vans as small truck. How many of each type of vehicle can they buy?
Answer:
They can buy 160 commercial vans, 80 small trucks and 40 large trucks.
Step-by-step explanation:
The company plans to spend $8 million on 280 new vehicles.
Commercial van = $25,000
Small truck = $30,000
Large Truck = $40,000
Let 'x' be commercial van, 'y' small truck and 'z' large truck. Therefore:
x + y + z = 280
Also, we know that x = 2y
Therefore: 3y + z = 280
Also we know that:
25,000x + 30,000y + 40,000z = 8,000,000
50,000y + 30,000y + 40,000z = 8,000,000
80,000y + 40,000z = 8,000,000
Therefore, we need to solve the following system of equation:
3y + z = 280 [1]
80,000y + 40,000z = 8,000,000 [2]
We have that the results are: y=80, z=40 and x=160.
Therefore, they can buy 160 commercial vans, 80 small trucks and 40 large trucks.
Write an equation for a line parallel to y=−4x+5 and passing through the point (4,-21)
Answer:
Y=-4x-5
Step-by-step explanation:
-21=-4(4)+b
-21=-16+b
b=-5
y=-4x-5
Answer:
y = - 4x - 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 4x + 5 is in this form with slope m = - 4
• Parallel lines have equal slopes, hence
y = - 4x + c ← is the partial equation of the parallel line
To find c substitute (4, - 21) into the partial equation
- 21 = - 16 + c ⇒ c = - 21 + 16 = - 5
y = - 4x - 5 ← equation of parallel line
what is the purpose of graphing linear equations? and how can we use it in everyday life?
variable costs, rates, marketing and budgeting are completely dependant on linear graphs it can be used to display a steady flow of something, or even and increase of a specific subject over time. if you were a market manager or banker, you'd probably deal with them.
Eli had $10 but he lost some of it. He mom doubled the money he had left. Eli wrote the expression 2(10-k) how much money he has now, where k is the amount of money he lost. Aisha wrote another correct expression , 20-2k, to also how much money Eli has now
Answer:
Step-by-step explanation:
According to the first expression:
2(10-k): where,
2:shows the double amount of money which ELI has
10:shows the amount of money which ELI had at the starting.
k:shows the amount of money which is lost.
10-k:shows the amount of money which ELI has after losing some amount.
According to the second expression:
20-2k where,
20:shows the twice of initial amount.
k: is the amount of money which is lost
2k:s hows the twice of amount which is lost
20-2k: shows the amount of money which is left with ELI after his mom gave him some money....
The area of a circle is 16π m2. What is the radius of the circle?
Answer:
the radius of the circle= 4m
Step-by-step explanation:
Given:
Area of circle=16π m2
radius,r of circle=?
Formula of area of circle is given as
Area=πr^2
Putting values we get
16π=πr^2
r^2=16
r=4
the radius of the circle= 4m !
Given the area [tex]A=\pi r^2=16\pi[/tex] we can solve the formula for radius.
[tex]A=\pi r^2\Longrightarrow r=\sqrt{\dfrac{A}{\pi}}[/tex]
So,
[tex]r=\sqrt{\dfrac{16\cdot\not{\pi}}{\not{\pi}}}=\sqrt{16}=4[/tex]
The radius is 4m.
Hope this helps.
r3t40
Enter the explicit rule for the geometric sequence. 60,12,12/5,12/25,12/125,...
Answer:
60(1/5)^(n-1).
Step-by-step explanation:
The common ratio r is 12/60 = 12/5 / 12 = 12/25 / 12/5 = 1/5.
The first term a1 = 60 so the explicit rule is
a1 * r^(n-1)
= 60(1/5)^(n-1).
aₙ=60(1/5)ⁿ⁻¹ is the explicit rule for the geometric sequence 60,12,12/5, 12/25,12/125,... .This can be obtained by using the formula of geometric sequence.
What is a geometric sequence?Sequence is s collection of objects in a particular order and repetitions are allowed.
Geometric Sequence:
a, ar, ar¹, ..., arⁿ⁻¹ is a geometric sequence, where a is the first term, r is the common ratio and arⁿ⁻¹ is the nth term.Common ratio, r = aₙ/aₙ₋₁In the given question, first term a=60
Common ratio r = a₂/a₁ = 12/60 = 1/5 ⇒ r = 1/5
By definition, arⁿ⁻¹ = (60)(1/5)ⁿ⁻¹ is the required explicit rule for the geometric sequence.
Hence aₙ=60(1/5)ⁿ⁻¹ is the explicit rule for the geometric sequence 60,12,12/5, 12/25,12/125,... .
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What is the median of the data set given below?
42, 20, 12, 15, 18, 15, 29, 33
ОА. 19
с. 15
Answer:
19
Step-by-step explanation:
Hey diddle diddle the medians in the middle you add then divide for the mean. the mode is the one that appears the most and the range is the difference in between.
Median: you have to organize the numbers from least to greatest then eliminate one by one.
12, 15, 15, 18, 20, 29, 33, 42
eliminate 12, and 42
15, 15, 18, 20, 29, 33
eliminate 15, and 33 ... so on
once you get to the median you end up with two numbers.
18, 20
because you can only have one median you find the number between, which in this case would be 19
Answer:
19
Step-by-step explanation:
The median is the middle value of the data in ascending order. If there is no exact middle then it is the average of the two values either side of the middle.
Arrange in ascending order
12, 15, 15, 18, 20, 29, 33, 42
The middle is between 18 and 20
median = [tex]\frac{18+20}{2}[/tex] = [tex]\frac{38}{2}[/tex] = 19
Use the elimination method to solve the system of equations. Choose the
correct ordered pair.
-3y = x-5
x+ 5y = 7
O A. (-1,2)
O B. (5,0)
O C. (2.1)
O D. (-4,3)
Answer:
C. (2, 1)
Step-by-step explanation:
-3y = x-5
x+ 5y = 7
Subtract x from both sides in the first equation. Write the second equation below it.
-x - 3y = -5
x + 5y = 7
Add the two equations above.
2y = 2
Divide both sides by 2.
y = 1
Substitute y with 1 in the second original equation and solve for x.
x + 5(1) = 7
x + 5 = 7
Subtract 5 from both sides.
x = 2
Answer: C. (2, 1)
Answer:
○ C. (2, 1)
Step-by-step explanation:
{-3y = x - 5 [Move -x to the left of the equivalence symbol]
{x + 5y = 7
{-x - 3y = -5
{x + 5y = 7
____________
2y = 2
__ _
2 2
y = 1 [Plug this back into both equations to get the x-coordinate of 2]; 2 = x
I am joyous to assist you anytime.
Solve 18x + 6 > 12x + 18.
-
The solution of the inequation 18x + 6 [tex]>[/tex] 12x + 18 is x [tex]>[/tex] 2.
An inequation is a mathematical statement that represents an inequality relationship between two expressions. It compares the relative values of the two expressions, indicating whether one is greater than, less than, or not equal to the other.
Solving an inequation involves finding the values of the variables that satisfy the inequality. This can often be done by using algebraic techniques, such as simplifying and rearranging the expressions, isolating the variable, and applying appropriate rules and operations.
To solve the above inequation, let's assume that it is an equation.
Then,
18x + 6 = 12x + 18
18x - 12x = 18 - 6
6x = 12
x = [tex]\frac{12}{6}[/tex]
x = 2.
Thus the inequation in simplifying is x [tex]>[/tex] 2.
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Final answer:
The result to the inequality 18x 6> 12x 18 is x> 2. This is set up by abating 12x from both sides, also abating 6, and also dividing by 6 to insulatex.
Explanation:
To break the inequality 18x 6> 12x 18, we need to insulate the variable x on one side.
Abate 12x from both sides 18x- 12x 6> 18.
Simplify the equation 6x 6> 18.
Abate 6 from both sides 6x> 12.
Divide both sides by 6 to break for x x> 2.
The result to the inequality is x lesser than 2. This gives a range of values for x that will satisfy the original inequality. thus, any number lesser than 2 for x makes the inequality true.
At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree
Answer:
Step-by-step explanation:
This is a question that uses the Pythagorean Theorem.
a = 35 feet
b = x which is the height of the tree.
c = 3*x + 1 so we are trying to find x. Substitute into a b and c
a^2 + b^2 = c^2
35^2 + x^2 = (3x + 1)^2
35^2 + x^2 = 9x^2 + 6x + 1 Subtract x^2 from both sides.
35^2 = 8x^2 + 6x + 1 Subtract 35^2 from both sides.
0 = 8x^2 + 6x + 1 - 35^2
0 = 8x^2 + 6x - 1224
Does this factor?
(x + 12.75)(x - 12)
x - 12 = 0 is the only value that works.
x = 12
The tree is 12 feet high.
Note: I used the quadratic formula to solve this.
Answer:
12 ft
Step-by-step explanation:
Let the height of the tree is h.
So the distance of top of the tree = 3 h + 1
Distance of base of tree = 35 ft
So, by use of Pythagoras theorem
[tex]\left ( 3h+1 \right )^{2}=h^{2}+35^{2}[/tex]
[tex]8h^{2}+6h-1224=0[/tex]
[tex]4h^{2}+3h-612=0[/tex]
[tex]h=\frac{-3\pm \sqrt{9+4\times 4\times 612}}{8}[/tex]
[tex]h=\frac{-3\pm 99}{8}[/tex]
Take positive sign
h = 12 ft
Thus, the height of tree is 12 ft.
d – 10 – 2d + 7 = 8 + d – 10 – 3d
Answer:
d=1
Step-by-step explanation:
Let's start by combining like terms.
-3-d=-2-2d
+d. +d
-3= -2-d
+2 +2
-1= -d
/-1. /-1
d=1
Solve the proportion.8/d = -12/30
A. -45
B. -20
C. -3.2
Answer:
B. -20
Step-by-step explanation:
8/d = -12/30
We can use cross products to solve
8 * 30 = d* -12
240 = -12 d
Divide each side by -12
240/-12 = -12d/-12
-20 = d
The dishes have been sorted into cups and plates. The number of plates is four less than two times the number of cups. The dishes are 60% plates. How many cups are there?
a) 3
b) 6
c) 8
d) 9
Answer:
Option C) 8 cups
Step-by-step explanation:
Let
x----> the number of cups
y ---> the number of plates
we know that
y=2x-4 -----> equation A
60%=60/100=0.60
y=0.60(x+y) ----> equation B
Substitute equation A in equation B and solve for x
2x-4=0.60(x+2x-4)
2x-4=0.6x+1.2x-2.4
2x-4=1.8x-2.4
2x-1.8x=4-2.4
0.2x=1.6
x=1.6/0.2
x= 8 cups
From looking at the question, the answer is C. 8
PLEASE BE QUICK AND ACCURATE
After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the rainbow is the shape of a parabola.
The equation for this parabola is y = -x2 + 36.
1. In the distance, an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. Create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow.
2. Analyze the two functions. Answer the following reflection questions in complete sentences. What is the domain and range of the rainbow? Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not? What are the x- and y-intercepts of the rainbow? Explain what each intercept represents. Is the linear function you created with your table positive or negative? Explain. What are the solutions or solution to the system of equations created? Explain what it or they represent.
3. Create your own piecewise function with at least two functions. Explain, using complete sentences, the steps for graphing the function. Graph the function by hand or using a graphing software of your choice (remember to submit the graph).
We know that after a dreary day of rain, the sun peeks through the clouds and a rainbow forms. So you notice the rainbow is the shape of a parabola as shown in the first figure. This parabola has the following equation:
[tex]y=-x^2+36[/tex]
On the other hand, in the distance you notice that an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. So let's choose two points on the graph of the parabola to build up the equation of the line:
[tex]\bullet \ If \ x=-5, then: \\ \\ y=-(-5)^2+36=11 \\ \\ So: \\ \\ P_{1}(-5,11) \\ \\ \\ \bullet \ If \ x=4, then: \\ \\ y=-(4)^2+36=20 \\ \\ So: \\ \\ P_{2}(4,20)[/tex]
Therefore, the equation of the line using these two points is:
[tex]y-20=\frac{20-11}{4-(-5)}(x-4) \\ \\ y-20=\frac{9}{9}(x-4) \\ \\ y-20=x-4 \\ \\ y=x+20-4 \\ \\ y=x+16[/tex]
FOR THE PARABOLA, THE TABLE IS:
[tex]Other \ two \ points: \\ \\ \bullet \ If \ x=0, then: \\ \\ y=-(0)^2+36=36 \\ \\ So: \\ \\ P_{3}(0,36) \\ \\ \\ \bullet \ If \ x=1, then: \\ \\ y=-(1)^2+36=35 \\ \\ So: \\ \\ P_{4}(1,35)[/tex]
So the table is:
[tex]\left[\begin{array}{cc}x & y\\-5 & 11\\4 & 20\\0 & 36\\1 & 35\end{array}\right][/tex]
FOR THE LINE, THE TABLE IS:
[tex]Other \ two \ points: \\ \\ \bullet \ If \ x=0, then: \\ \\ y=x+16=0+16=16 \\ \\ So: \\ \\ P_{3}(0,16) \\ \\ \\ \bullet \ If \ x=1, then: \\ \\ y=x+16=1+17=17 \\ \\ So: \\ \\ P_{4}(1,17)[/tex]
So the table is:
[tex]\left[\begin{array}{cc}x & y\\-5 & 11\\4 & 20\\0 & 16\\1 & 17\end{array}\right][/tex]
2. Analyzing the functions:2.1 Domain and Range:The Domain of both the quadratic function and the linear function is the set of all real numbers. The range of the quadratic function is [tex](-\infty,36)[/tex] while the range of the linear function is the set of all real numbers.The domain represents the horizontal distance while the range represents the height. In this situation, all values don't make sense. First, the rainbow starts in a point on the earth's crust. Also, the airplane starts at a point on the runway, so this doesn't include all the real numbers. A similar thing happens to the height since the airplane turns into an horizontal way at a moment of its trip and this doesn't include all the real numbers.
2.2 x and y intercepts of the rainbow.x-intercepts:
The x intercepts are the points at which the graph passes through the x-axis, that is, when [tex]y=0[/tex]. So:
[tex]-x^2 + 36=0 \\ \\ x^2=36 \\ \\ x=\pm\sqrt{36} \\ \\ x=\pm 6[/tex]
So the x intercepts are [tex]x_{1}=6 \ and \ x_{2}=-6[/tex]
y-intercepts:
The y-intercept is the point at which the graph passes through the y-axis, that is, when [tex]x=0[/tex]. So:
[tex]y=-x^2+36 \\ \\ y=-(0)^2+36 \\ \\ y=36[/tex]
So the y-intercept is [tex]b=36[/tex]
In conclusion, if we take the x-axis as the ground, the x-intercepts represent the beginning and the end of the rainbow while the y-intercept represent its maximum height.
2.3 Is the linear function positive or negativeThe equation of this line is:
[tex]y=x+16[/tex]
As you can see, the slope [tex]m=1[/tex] is positive, therefore the line I've created is positive. This means as x increases y increases, but how do x and y increase? Well, they increase as the airplane is taking off, so this means the horizontal distance and the height increase.
2.4 What are the solutions or solution to the system of equations created?The system of equations we created is:
[tex]\left\{ \begin{array}{c}y=x+16\\y=-x^{2}+36\end{array}\right.[/tex]
Remember that in Part 1, chose two points on the graph of the parabola to build up the equation of the line, so the solutions to this system is indeed those two points:
[tex]P_{1}(-5,11) \ and \ P_{2}(4,20)[/tex]
They represents that the airplane cuts through the rainbow at those two points.
3. Create a piecewise function.A piecesewise function is a function defined by two or more equations over a domain. Our piecewise function is shown in the second figure below and is defined by:
[tex]f(x)=\left\{ \begin{array}{c}x+16\quad if\quad-16\le x\le-5\\-x^{2}+36\quad if\quad-5\le x\le4\\x+16\ \quad if\quad4\le x\le24\\40\quad if\quad x\ge24\end{array}\right.[/tex]
To graph this function, let's follows these steps:
STEP 1: Graph [tex]y=x+16[/tex] from -16 to -5. This represents the graph of the trajectory of the airplane before touching the rainbow.
STEP 2: Graph [tex]y=-x^2+36[/tex] from -5 to 4. This is represents the graph of the rainbow as the airplane passes under its path.
STEP 3: Graph [tex]y=x+16[/tex] from 4 to 24. This is represents the graph of the trajectory of the airplane after touching the second point of the rainbow.
STEP 4: Graph [tex]y=x+16[/tex] from 24 and forward. This is represents the graph of the trajectory of the airplane when turning into an horizontal way.
In △ABC,a=34, b=18, and c=17. Find m∠A.
A. 14.1
B. 132.6
C. 152.5
D. 101.5
Answer:
C. m < A = 152.5 degrees.
Step-by-step explanation:
Use the Cosine Rule:
a^2 = b^2 + c^2 - 2.b.c.cos A
34^2 = 18^2 + 17^2 - 2.18.17 cos A
2.18.17 cos A = 18^2 + 17^2 - 34^2
cos A = (18^2 + 17^2 - 34^2) / (2.18.17)
cos A = -0.88725
m < A = 152.5 degrees.
Answer:
C.) 152.5
Step-by-step explanation:
I got it correct on founders edtell
Find the coordinates of P so that P partitions the segment AB in the ratio 6:2 if A(−4,12) and B(9,−4).
A. (13.75, -24)
B. (5.75, 0)
C. (-16, 13)
D. (9.75, -12)
ANSWER
B. (5.75, 0)
EXPLANATION
If the point P(x,y) partitioned
[tex]A(x_1,y_1)[/tex]
and
[tex]B(x_2,y_2)[/tex]
in the ratio m:n, then
[tex]x = \frac{mx_2+nx_1}{m + n} [/tex]
[tex]y=\frac{my_2+ny_1}{m + n} [/tex]
If the coordinates are A(−4,12) and B(9,−4), then:
[tex]x = \frac{6 \times 9+2 \times - 4}{6 + 2} [/tex]
[tex]x = \frac{54 - 8}{8} [/tex]
[tex]x = \frac{46}{8} [/tex]
[tex]x = 5.75[/tex]
[tex]y= \frac{6 \times - 4+2 \times 12}{6 + 2} [/tex]
[tex]y = \frac{24 - 24}{8} [/tex]
[tex]y = \frac{0}{24} = 0[/tex]
The correct choice is
[tex]B. (5.75, 0) [/tex]
The number of lattes sold daily for two coffee shops is shown in the table:
Lattes
55
52
50
47
68
48
53
53
Based on the data, what is the difference between the median of the data, including the possible outlier and excluding the possible outlier?
Answer:
0.5
Step-by-step explanation:
Sort the given data in ascending order:
47, 48, 50, 52, 53, 53, 55, 68
Possible outlier is number 68. Check whether this number is an outlier:
[tex]Q_1=49\\ \\Q_2=52.5 \\ \\Q_3=54[/tex]
The interquartile range is
[tex]Q_3-Q_1=54-49=5[/tex]
Multiply it by 1.5:
[tex]1.5\cdot 5=7.5[/tex]
and add to third quartile:
[tex]7.5+54=61.5[/tex]
Since [tex]68>61.5,[/tex] number 68 is an outlier.
The median of the sample with outlier is [tex]Q_2=\dfrac{52+53}{2}=52.5[/tex]
The median of the sample without outlier is 52
The difference between the median of the data, including the possible outlier and excluding the possible outlier is 52.5-52=0.5
Answer:
0.5
Step-by-step explanation:
i finished the assignment and it was right so yeah it’s 0.5
f(1)=-1.5
f(n+1)=f(n)+0.5
what is f(10)?
Answer:
Step-by-step explanation:
3.
Final answer:
To find f(10) using a recursive formula, we can calculate intermediate values starting from f(1) and applying the given rule to find f(10) as 2.
Explanation:
The function is defined as follows:
f(1)=-1.5
f(n+1)=f(n)+0.5
To find f(10), we can use the given recursive formula to calculate subsequent values:
f(2) = f(1) + 0.5 = -1.5 + 0.5 = -1
f(3) = f(2) + 0.5 = -1 + 0.5 = -0.5
Continuing this pattern, we find f(10) = 2
What is the volume of a sphere with a diameter of 11ft? Round your answer to the nearest cubic foot.
[tex]d=11\text{ ft}\\V=\dfrac{4}{3}\pi r^3\\r=\dfrac{d}{2}=\dfrac{11}{2}=5.5\\\\V=\dfrac{4}{3}\pi \cdot (5.5)^3\approx697\text{ ft}^3[/tex]
A. Figure A
B. Figure B
Answer:
A.) Figure A
Step-by-step explanation:
because the first part "If..." always goes on the inside of the 2 circles
(6x^2-5x+3)+(3x^2+7x-8)
add
Answer:
[tex]9 {x}^{2} + 2x - 5[/tex]
Step-by-step explanation:
I have answered ur question