The equations of the line are:
y – 2 = 2(x – 5)
y + 16 = 2(x + 4)
y = 2x – 8
How to Find the Equation of a Line that Passes through two Points?The equation of a line, in point-slope form, that passes through two points can be expressed as y - b = m(x - a).
To find the equation, first, we will need to find the slope of the line. Next, we will use a point and the slope to write the equation by simply substitute their values in y - b = m(x - a), where the slope is m and a point is (a, b).
Given the points:
(–4, –16) (5, 2)Find the slope of the line (m):
Slope of the line (m) = change in y / change in x = (-16 - 2)/(-4 - 5)
Slope of the line (m) = -18/-9
Slope of the line (m) = 2
Substitute m = 2 and (a, b) = (5, 2) into y - b = m(x - a):
y - 2 = 2(x - 5)
Or, substitute m = 2 and (a, b) = (-4, -16) into y - b = m(x - a):
y + 16 = 2(x + 4)
Any of the above equations can be rewritten in slope-intercept form as:
y = 2x - 8.
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Solve N = 2st- 3sv
solve for x=?
Find the union of A and B.Select the correct answer below:{2.5,b,4,f,1/2,c,4.1,a,3,1/3}{2.5,4,1/2,4.1,3,1/3}{b,f,c,a}{2.5,b,1/2,c,4.1,a,3,1/3}
EXPLANATION:
Given;
We are given two sets A and B with the elements as indicated in the attached image.
Required;
We are required to find the union of sets A and B.
Solution;
The union of two sets is given as the elements contained in set A, in set B and the intersection of both.
The elements of set A are;
[tex]A=\lbrace2.5,b,4,f,\frac{1}{2},4.1,c\rbrace[/tex]The elements of set B are;
[tex]B=\lbrace a,3,\frac{1}{3},\frac{1}{2},4.1,c\rbrace[/tex]The intersection of both sets are:
[tex]A\cap B=\lbrace\frac{1}{2},4.1,c\rbrace[/tex]Taking all elements common to both sets A and B including the intersection, we now have the union of both sets;
ANSWER:
[tex]A\cup B=\lbrace2.5,b,4,f,\frac{1}{2},c,4.1,a,3,\frac{1}{3}\rbrace[/tex]The first option is the correct answer.
6#Suppose that IQ scores in one region are normally distributed with a standard deviation of 17. Suppose also that exactly 58% of the individuals from this region have IQ scores of greater than 100 (and that 42% do not). What is the mean IQ score for this region? Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.
ANSWER:
103.4
STEP-BY-STEP EXPLANATION:
Given:
Standard deviation (σ) = 17
x = 100
The probability is 42%, that is 0.42, we look for this value in the normal table to determine the value of z as follows:
z = -0.2
Knowing that value we can calculate the mean, just like this:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \\ \text{ We replacing:} \\ \\ -0.2=\frac{100-\mu}{17} \\ \\ 100-\mu=-0.2\cdot17 \\ \\ \mu=100+0.2\cdot17 \\ \\ μ=103.4 \end{gathered}[/tex]The mean is equal to 103.4
If UV = 9 and WX = 14, what is the length of the diameter of circle X?
Given:
[tex]UV=9\text{ ; WX=14}[/tex][tex]\begin{gathered} UW=2(UV) \\ UW=2(9) \\ UW=18 \end{gathered}[/tex][tex]\text{Diameter of the circle X}=2(UW+WX)[/tex][tex]\text{Diameter of the circle X}=2(18+14)[/tex][tex]\text{Diameter of the circle X}=2(32)[/tex][tex]\text{Diameter of the circle X}=64[/tex]Write a recursive formula and an explicit formula for the following arithmetic sequence.
-5, 1, 7, 13, 19, ...
A recursive formula is a₁ = a₁ = ₁
(Simplify your answers.)
The recursive formula is aₙ₊₁ = aₙ + 6 and the explicit formula is aₙ = -5 + (n-1)6 for the given sequence.
What is the recursive formula of an arithmetic sequence?The recursive formula to find the nth term of an arithmetic sequence is:
aₙ = aₙ₋₁ + d for n ≥ 2
where aₙ is the nth term of an A.P.
In arithmetic, sequence d represents the common difference.
Where aₙ is the nth term of the sequence and a₁ is the first term
Given the sequence -5, 1, 7, 13, 19, ...
The first term (a₁) = -5
a₂ = 1
a₃ = 7
a₄ = 13
a₅ = 19
The common difference (d) = a₅ - a₄= a₄ - a₃= a₃ - a₂ = 6
So, aₙ₊₁ - aₙ = 6
aₙ₊₁ = aₙ + 6
The explicit formula of the given sequence is given by,
aₙ = a₁ + (n-1)d
aₙ = -5 + (n-1)6
Hence, the recursive formula is aₙ₊₁ = aₙ + 6 and the explicit formula is aₙ = -5 + (n-1)6 for the given sequence.
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consider triangles MNP and TUV which statement must be true?answer questions and the question to the problem is in the image
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
From the question, we can see that triangle MNP has three angles
which are:
[tex]\begin{gathered} 88^{0\text{ }},61^{0\text{ }}and^{} \\ 31^0 \end{gathered}[/tex]while Triangle TUV has three angles which are:
[tex]\begin{gathered} 79^0,40^{0\text{ }}and^{} \\ 61^0 \end{gathered}[/tex]Hence, it is easy to see that the correct option is:
[tex]\Delta\text{ MNP is not similar to }\Delta\text{ TUV ( OPTION A)}[/tex]
y = 3x - 4
m=?
b= ?
Answer:
m = 3 , b = - 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx b ( m is the slope and b the y- intercept )
y = 3x - 4 ← is in slope- intercept form
with m = 3 and b = - 4
Order the expressions by choosing <, >, or =.
The expression is
[tex]6^{-2}[/tex] < [tex]\frac{1}{6} ^{-2}[/tex] , [tex]6^{-1}[/tex]< [tex]\frac{1}{6} ^{-1}[/tex], [tex]6^{-2}[/tex]< [tex]6^{-1}[/tex]
Here we have to find the expression
a) [tex]6^{-2}[/tex] and [tex]\frac{1}{6}^{-2} }[/tex]
= 1/6² and 6²
= 1/ 36 and 36
= 1/36 < 36
So [tex]6^{-2}[/tex]< [tex]\frac{1}{6} ^{-2}[/tex]
b) [tex]6^{-1}[/tex] and [tex]\frac{1}{6} ^{-1}[/tex]
= 1/6 and 6
= 1/6 < 6
So [tex]6^{-1}[/tex] < [tex]\frac{1}{6} ^{-1}[/tex]
c) [tex]6^{-2}[/tex] and [tex]6^{-1}[/tex]
= 1/36 and 1/6
= 1/36 < 1/6
So [tex]6^{-2}[/tex] < [tex]6^{-1}[/tex]
Therefore the expression is [tex]6^{-2}[/tex]< [tex]\frac{1}{6} ^{-2}[/tex] , [tex]6^{-1}[/tex] < [tex]\frac{1}{6} ^{-1}[/tex] , [tex]6^{-2}[/tex] < [tex]6^{-1}[/tex].
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Lisa and Susan are driving to college together. They look at a map to find out how far they have to drive. On the map, Lisa measures the distance to be 4.5 inches. How many miles do they have to drive if the map scale is 1 in. = 35 mi?
Answer:157.5
Step-by-step explanation:becuase mutilpy 4.5x35 that equals 157.5
what is the measure of ZXY in the figure below
we get that
[tex]5x+3x=180\rightarrow8x=180\rightarrow x=\frac{180}{8}=22.5[/tex]so the angle ZXY is:
[tex]\angle ZXY=3\cdot22.5=67.5^{\circ}[/tex]Here is the probability model for the blood type of a randomly chosen person in the United States.Blood typeoАBABProbability 0.42 0.21 0.07 0.3What is the probability that a randomly chosen American does not have type o blood?% Round to the nearest 0.01%
The total probability = 0.4 + 0.21 + 0.07 + 0.3 = 1
Given that the probability that a randomly chosen American has a type O blood is 0.42, then, the probabillity that a randomly chosen American does not have a type O blood is
1 - 0.42 = 0.58
= 58 x 100 = 58%
Find AB if (-9,2) and B(5,-4)
Given:
A(-9, 2) and B(5, -4)
Here,
(x1, y1) ==> (-9, 2)
(x2, y2) ==> (5, -4)
To find AB, use the distance formula below:
[tex]undefined[/tex]A sculptor is planning to order a rectangular of composite stone to sculpt a lion. The sculptor anticipated that the lion will be 5 feet long, about 2 feet wide and at the tallest part of the lions body, have a height of 3.5 feet. The composite stone weighs 40 pounds per cubic foot. To the nearest cubic foot, estimate the weight of the smallest rectangular block that the sculptor must purchase in order to create his statue
In order to sculpt the lion, the scupltor must have, at least, a rectangular composite that has the maximum dimensions of the final sculpture.
Thereby,
[tex]5ft\cdot2ft\cdot3.5ft=35ft^3[/tex]The rectangular composite would need to have a volume of 35 cubic feet.
Now, let's use a rule of three to calculate the weight of the composite, since we're given its density:
This way,
[tex]x=\frac{35\cdot40}{1}\rightarrow1400lbs[/tex]We can conclude that the weight of the smallest rectangular block that the sculptor must purchase in order to create his statue is 1400 lbs
2x - 8 = 6 what is the equation
Answer:
Step-by-step explanation:
x = 7
Find the length of the sides of a triangle with vertices at (0,-4), (-2,5) and (10,7).
The side lengths of the triangle with vertices at (0,-4), (-2,5) and (10,7). are √85, √148 and √221
How to calculate the side lengths of the triangle?From the question, we have
The triangle with vertices at (0,-4), (-2,5) and (10,7).
The side lengths of the triangle is then calculated using the following distance formula
d = √[(x₁ - x₂)²+ (y₁ - y₂)²]
Where x and y are the coordinates of the triangle
For vertices at (0,-4) and (-2,5), we have
d = √[(0 + 2)²+ (-4 - 5)²]
Evaluate
d = √85
For vertices at (-2,5) and (10,7). we have
d = √[(-2 - 10)²+ (5 - 7)²]
Evaluate
d = √148
For vertices at (0, -4) and (10,7). we have
d = √[(0 - 10)²+ (-4 - 7)²]
Evaluate
d = √221
Hence, the side lengths are √85, √148 and √221
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As shown in the diagram below, ABC || EFG andBF EF.
Now:
[tex]\begin{gathered} BF\cong EF \\ \angle BEF=\angle EFB=42.5 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \angle EBF=180-\angle BEF-\angle EFB \\ \angle EBF=180-42.5-42.5 \\ \angle EBF=180-85 \\ \angle EFB=95 \end{gathered}[/tex]Which set of fractions is ordered from greatest to least? 11/12, 7/10, 5/6 11/12 7/10
Answer:
11/12 11/12 7/10 7/10 5/6
Step-by-step explanation:
I did smallest to largest. still answer your question so 5/6 is the greatest (it's bigger) and 11/12 is the least (it's the smallest) think of it like a cookie would you rather have 11/12 of a cookie or 5/6 of a cookie which is the bigger piece? the bigger piece is the greater number.
Hi, my son just started virtual learning and school not providing much help so far. Need help with step by step (show work) with these 4 problems to double check homework…x= (guess I can only ask one per time?! New to this…
Solution
Step 1
Use the secant and tangent theorem to a circle.
Step 2
AC = 30 + x
BC = x
CD = 20
Step 3
Substitute into the theorem
[tex]\begin{gathered} (30+x)\times x\text{ = 20}^2 \\ \\ x^2+30x\text{ = 400} \\ \\ x^2+30x-400=0 \end{gathered}[/tex]Step 4
Use the factorization method to solve for x.
[tex]\begin{gathered} x^2+30x-400=0 \\ \\ x^2-10x+40x-400=0 \\ \\ x(x-10)+40(x-10)=0 \\ \\ (x+40)(x-10)=0 \\ \\ x-10=0,\text{ x+40=0} \\ \\ x\text{ = 10, x = -40} \end{gathered}[/tex]Step 5
The value of x cannot be negative, hence x = 10
Final answer
x = 10
HELP ASAP
Easy math, for old review notes.
Consider the expression:
8f – 5g + 6h – 10j + 2
How many terms does the expression have?
What is the constant of the expression?
What is the fourth term in the expression?
What is the coefficient of the third term?
In the given expression, the number of terms is 5, the constants are 8, -5 6, -10 and 2. The fourth term is j and the coefficient of the third term is 6
What are Mathematical ExpressionsIn mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. An algebraic expression consists of unknown variables, numbers and arithmetic operators. It does not contain any equality or inequality symbols. An expression in math is a statement involving at least two different numbers (known or unknown) and at least one operation.
In the given expression, we have to answer some questions here;
a) The number of terms in the expression is 5
b) The constant of the expression are 8, -5, 6, -10 and 2
c) The fourth term in the expression is j
d) The coefficient of the third term is 6
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Sharpe Razor Company has total assets of $1,870,000 and current assets of $667,000. It turns over its capital assets one times a year and has $335,000 of total debt. Its return on sales is 5 percent. What is Sharpe’s return on shareholders' equity?
If Its return on sales is 5 percent. Sharpe’s return on shareholders' equity is 8.26%.
How to find the return on shareholders' equity?First step is to find the fixed asset
Fixed asset = $1,870,000 + $667,000
Fixed asset = $2,537,000
Second step is to find the sales
Sales = Total assets × Fixed asset turnover
Sales = $2,537,000 × 1
Sales = $2,537,000
Third step is to find the stockholder equity
Stockholder equity = $1,870,000 - $335,000
Stockholder equity = $1,535,000
Fourth step is to find the net income
Net income = $2,537,000 × 5%
Net income = $126,850
Now let find the return on shareholders' equity
Return on shareholders' equity = Net income / Shareholders' equity
Return on shareholders' equity = $126,850 /$1,535,000
Return on shareholders' equity = 8.26%
Therefore 8.26% is the return on shareholders' equity.
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Given the following geometric sequence, find the common ratio.33,99,297,891,2673,…Give your answer as a reduced fraction, if necessary.
SOLUTION:
From the given geometric sequence gives
The common ratio. reduce
[tex]r=\frac{99}{33},r=\frac{297}{99},r=\frac{891}{297}[/tex]Simplifying this gives
[tex]r=3[/tex]Therefore the common ratio is r=3
Please help! Create a scatterplot for the data in the table. Let English scores be X and History Scores be Y.
Part 2: draw line of fit
Part 3: choose two points, find slope, and record slope decimal
For the given question.
x-axis contains the independent variables "English score."
y-axis contains the dependent variables "History score."
The graph for the given table is plotted with the scattered points.
Let us take two points from the graph,
(x₁,y₁) = (60, 65)
(x₂, y₂) = (61, 61)
Then the slope will be;
slope = m = (y₂ - y₁)/(x₂ - x₁)
Put the values.
m = (61 - 65)/(61 - 60)
m = -4
Thus, the slope of the line is found as -4.
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in the figure above what is the value of X what is the measure is side WZ
Based on the diagram, we have two right triangles. These are triangle WYT and triangle WYZ.
Since both legs of each triangle is congruent to each other, we can also say that their hypotenuse are congruent too.
Thus, TW = WZ or 2x = 3x - 5.
From this, we can now solve for x.
[tex]\begin{gathered} 2x=3x-5 \\ \text{Subtract 3x on both sides.} \\ 2x-3x=3x-3x-5 \\ -x=-5 \\ \text{Divide by -1 on both sides.} \\ x=5 \end{gathered}[/tex]Therefore, the value of x = 5.
To solve for WZ, let's plug in x = 5 to 3x - 5.
[tex]\begin{gathered} WZ=3x-5 \\ WZ=3(5)-5 \\ WZ=15-5 \\ WZ=10 \end{gathered}[/tex]Therefore, WZ = 10.
To summarize, x = 5 and WZ = 10. (Option A)
Sam starts travelling at 4 km/h from a campsite 2 hours ahead of Sue, who travels 6 km/h in the same direction. How many hours will it take for Sue to catch up to Sam?
Sue take 4 hours to catch up Sam. The question is about speed, distance and time
So for this, the formula is given
speed (s) = distance(d) / time(t)
According to question,
Speed of Sam is = 4 km/h
Distance covered by Sam = 4 * 2
= 8 km
Speed of Sue = 6 km/hr
Now, Sam and Sue are in same direction so minus the speed
speed = 6 - 4
= 2 km/hr
Now, we have speed = 2km/hr and
distance = 8km find the time,
put the values in formula, s = d/t
2 = 8/t
t = 8/2
t = 4 hours
Therefore, Sue take 4 hours to catch up Sam.
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Write the integer that represents the opposite of the opposite. A temperature rise of 15 degrees Fahrenheit
The given number is 15, which express degrees Fahrenheit.
The opposite of the opposite means the negative of the negative because an opposite number refers to multiply by -1.
[tex]-(-15)[/tex]Hence, the opposite of the opposite of 15 is -(-15).Danny has $2.14 worth of pennies and nickels in his piggy bank. The number of nickels is two more than ten times the number
of pennies. How many nickels and how many pennies does Danny have?
Danny has 42 nickels and 4 pennies.
The total amount of Danny in the piggy bank is $2.14.The money in Danny's bank consists of pennies and nickels.We know that a penny is worth $0.01.We also know that a nickel is worth $0.05.We are given the fact that the number of nickels is two more than ten times the number of pennies.Let the number of pennies be denoted by "x".Then the number of nickels is "10x + 2".The total amount of money because of just the pennies is $0.01*x.The total money because of just the nickels is $0.05*(10x + 2).We know that the total amount is $2.14.We can form an equation with the available data.0.01*x + 0.05*(10x + 2) = 2.140.01x + 0.5x + 0.1 = 2.140.51x = 2.04x = 4The number of pennies is 4.The number of nickels is 42.To learn more about equations, visit :
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Amanda has scored 24,22,27,23 and 30 points in her five basketball games so far. How many points does she need to score in her next game so that her average (mean) is 25 points per game?
To answer this question, we need to remember that the mean of a data is the sum of the data divided by the total number of elements that represent this data.
Therefore, if we need to find the sixth value for which the average (mean) per game is 25 points, we can proceed as follows:
[tex]\frac{24+22+27+23+30+x}{6}=25[/tex]Now, to find the value, x, we need to follow the next steps:
1. Add the values in the numerator of the fraction:
[tex]\frac{126+x}{6}=25[/tex]2. Multiply both sides by 6:
[tex]\begin{gathered} \frac{6\left(126+x\right?}{6}=6\left(25\right? \\ \frac{6}{6}\left(126+x\right?=150 \\ 126+x=150 \end{gathered}[/tex]3. Finally, subtract 126 from both sides of the equation:
[tex]\begin{gathered} 126-126+x=150-126 \\ x=24 \end{gathered}[/tex]Therefore, the value she needs is 24 points.
And we can check this value as follows:
[tex]\frac{24+22+27+23+30+24}{6}=\frac{150}{6}=25[/tex]Therefore, in summary, we have that Amanda needs to score 24 points in the next game so that her average is 25 points per game.
Bryan Joan had 261 dollars to spend on 8 books. After buying them he had 13 dollars. How much did each book cost?
Answer:
8
Step-by-step explanation:
.
find the equation of the line:
parallel to the x-axis passing through the point (-3;4)
Answer:
y=4
Step-by-step explanation:
Since any two parallel lines have the same slope we know the slope of the unknown line is 0 (its from the slope of y=0(x)+0 which is also 0).
Also since the unknown line goes through (3,4), we can find the equation by plugging in this info into the point-slope formula
Point-Slope Formula:
y−y
1
=m(x−x
1
) where m is the slope and (x
1
,y
1
) is the given point.
Now substituting the values:
y−4=0(x−3)
⇒y−4=0
⇒y=4
Hence, the equation of the line is y=4.
To compare two values, first convert the values to the same ____
To compare two values, first convert the values to the same measuring unit.
What is a measuring unit?
The definition of a unit of measurement is a certain magnitude of a quantity that has been defined and acknowledged by law or convention and is used as a standard for measuring other quantities of the same kind.
Any other quantity of that sort can be expressed as a multiple of the unit of measurement. For instance, a length is a physical quantity. Measurement is the process of identifying a number that accurately captures the amount of anything.
A measuring unit is a recognized quantity that is used to represent a physical quantity. Let's examine a few of the common units for measuring physical quantities.
Given that, to compare the values
If we want to compare two values first we have to convert it in same measuring unit.
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