Given:
There are given that the two points:
[tex]A(5,7),and,B(8,12)[/tex]Explanation:
According to the question:
We need to find the equation of the line:
Then,
To find the equation of the line, first, we need to find the slope of the line.
So,
From the formula of the slope of the line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]x_1=5,y_1=7,x_2=8,y_2=12[/tex]Then,
Put all the values into the given formula:
So,
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{12-7}{8-5} \\ m=\frac{5}{3} \end{gathered}[/tex]Then,
From the formula of the equation of the line:
[tex]y-y_1=m(x-x_1)[/tex]Then,
Put the value of m into the above equation:
So,
[tex]\begin{gathered} y-y_{1}=m(x-x_{1}) \\ y-7=\frac{5}{3}(x-5) \\ 3y-21=5(x-5) \\ 3y-21=5x-25 \end{gathered}[/tex]Then,
[tex]\begin{gathered} 3y-21=5x-25 \\ 3y-21+21=5x-25+21 \\ 3y=5x-4 \\ y=\frac{5}{3}x-\frac{4}{3} \end{gathered}[/tex]Final answer:
Hence, the equation of line is shown below:
[tex]y=\frac{5}{3}x-\frac{4}{3}[/tex]Combinatorics is a branch of math focused on arrangements of objects. Jorge is an event organizer who must seat 102 guests. He has circular tables that seat 10 people each and square tables that seat 4 people each. He wants to use as many circular tables as possible but have no empty seats. Explain how he could arrange the tables he will need.
Explain how Jorge could arrange the tables he will need
To maximize the number of circular tables, he must thus employ 9 circular tables and 3 square tables.
What is Combinatorics?Combinatorics is a branch of math focused on the arrangements of objects.
Estimates of the number of operations needed by a computer algorithm can be created using combinatorial approaches.
It is given that the number of persons in each circular table and the square table will be 10 and 4 respectively.
We now need to determine the largest multiple of 10 in order to maximize the number of circular tables.
Now, if we take 100, there will only be 2 seats left. However, 4 people are needed for square tables. Therefore, 100 is incorrect.
The circular tables utilized would be if we choose 90 as a multiple of 10 is,
= 90 / 9
= 10
Number of guests left,
=102 - 90
= 12
12 is a multiple of 4 as a result 3 square tables may therefore fit 12 people,
=4 × 3
=12
Thus, to maximize the number of circular tables, he must thus employ 9 circular tables and 3 square tables.
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The area of a bulletin board is 55 square feet. The length is
four feet more than three times the width. Find the length
and width of the bulletin board.
Step-by-step explanation:
it is a rectangle.
the area is a rectangle is
length × width
in our case
length × width = 55 ft²
length = 3×width + 4
we use that in the first equation :
(3×width + 4)×width = 55
3×width² + 4×width - 55 = 0
the general solution to a quadratic equation like
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
so,
width = (-4 ± sqrt(4² - 4×3×-55))/(2×3) =
= (-4 ± sqrt(16 + 660))/6 = (-4 ± sqrt(676))/6 =
= (-4 ± 26))/6
width1 = (-4 + 26)/6 = 22/6 = 11/3 = 3 2/3 ft
width2 = (-4 - 26)/6 = -30/6 = -5
negative numbers for the size of a physical object don't make sense, so
11/3 = 3 2/3 ft is our solution.
length = 3×width + 4 = 3×11/3 + 4 = 11 + 4 = 15 ft
so,
the length = 15 ft
the width = 3 2/3 ft (or 11/3 ft)
Find a point-slope form for the line with slope 1/5 and passing through the point (-4,-5).
The Point-slop form for X is X = 5Y+15, and the Point-slop form for Y is [tex]\frac{X-5}{5}[/tex], for the line with a slope 1/5 and passing through the point (-4, -5).
Finding the slop form using the formula [tex]m=\frac{Y_{1} - Y_{2} }{X_{1} -x_{2} }[/tex]
The equation for x.
Here m=1/5.
∴ [tex]\frac{1}{5}=\frac{Y-(-4)}{X-(-5)}[/tex]
[tex]\frac{1}{5}[/tex] × X-(-5) = Y-(-4)
[tex]\frac{1}{5}[/tex] × X+5 = Y+4
X+5= 5Y+2O
X=5Y+20-5
X=5Y+15
∴Point-slop for X is X=5Y+15.
Solving for Y.
[tex]\frac{1}{5}=\frac{Y-(-4)}{X-(-5)}[/tex]
Simplifying and Solving.
[tex]\frac{1}{5}[/tex] × X-(-5) = Y-(-4), Taken 0n X-(-5) the right side.
[tex]\frac{1}{5}[/tex] × X+5 = Y+4
X+5= 5Y+2O
X+5-20=5Y
X-15=5Y
Taking 5 0n the right side.
[tex]\frac{X-15}{5}[/tex] = Y
∴ Point-slop form for Y is [tex]\frac{X-5}{5}[/tex]
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2) Are the triangles similar? If so, what is the scale factor which converts ARPQ to AVAQ?
A)NO
B)YES;1/2
C)YES;2/3
D)YES;2/1
1/2 is the factor which converts right angled triangles ΔRPQ to ΔVAQ
What is a Triangle?Triangle: A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane
Both the triangles are right angled triangles at ΔVAQ and ΔRPQ
side AV=3 units and AQ=4 units
side RP=6 units and PQ=8 units
AV is half of RP and AQ is half of PQ
AV=1/2(RP) and AQ=1/2(PQ)
1/2 factor converts ΔRPQ to ΔVAQ
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Solve the system of equations.
Answer:
b
Step-by-step explanation:
because you need ti 2x +
Given the translation T(3, -1), translate the ordered pairs (-3, 6) and (9, -8).
Answer:
(-3,6)----> (0,5)
(9,-8)----> (6,-9)
Step-by-step explanation:
The translation T(3,-1) shows that we need to add three units to the x-coordinates and -1 unit to the y-coordinates, as follows in the answer above.
The graph below shows the solution to which system of inequalities?
A.y > –3 and y ≤ –x
B.y ≥ –3 and y ≤ –x
C.x ≥ –3 and y > –x
D.x > –3 and y ≥ –x
The correct option is A, the system of inequalities is:
y > -3y ≤ –xWhich is the system of inequalities graphed?On the graph, we can see two lines.
One is a dashed line (so we need to use the symbols > or < ) and it is horizontal, such that the line is:
y = -3
And the shaded region is above that line, so the inequality is:
y > -3.
The other inequality is below a line y = -x, and we can see that the line is solid (so we use the symbols ≤ or ≥).
Then here the inequality is.
y ≤ -x
Then the system of inequalities is:
y > -3.
y ≤ -x
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Need help finding the perimeter
Answer:
Perimeter
P = 24.2
Step-by-step explanation:
Perimeter
P = 9 + √(6^2 + 6^2) + √(3^2 + 6^2) = 24.2
Find the simple interest and the total amount after three years.Principal = 11,750 rupeesAnnual rate of interest = 7.5%Total interest = (rupees)Total amount=(rupees)
The formula for calculating simple interest is expressed as
I = PRT
where
I represents the interest
P represents the principal or initial amount invested
R represents the interest rate
T represents the time in years
From the information given,
P = 11750
R = 7.5%
Recall, percentage is expressed in terms of 100. Thus,
R = 7.5/100 = 0.075
T = 3
By substituting these values into the formula,
I = 11750 x 0.075 x 3
I = 2643.75
Total interest = 2643.75 rupees
Total amount = principal + total interest
By substituting the values,
Total amount = 11750 + 2643.75
Total amount =
Answer: 11750 + 2643.75
Step-by-step explanation:
The formula for calculating simple interest is expressed as
I = PRT
where
I represents the interest
P represents the principal or initial amount invested
R represents the interest rate
T represents the time in years
From the information given,
P = 11750
R = 7.5%
Recall, percentage is expressed in terms of 100. Thus,
R = 7.5/100 = 0.075
T = 3
By substituting these values into the formula,
I = 11750 x 0.075 x 3
I = 2643.75
Total interest = 2643.75 rupees
Total amount = principal + total interest
By substituting the values,
Total amount = 11750 + 2643.75
50 POINTS!
David borrowed money from a credit union for 5 years and was charged simple interest of 6%. The total interest that he paid was $2,100. How much money did he borrow?
[tex]5 \div 6 \times 2100 = 1750[/tex]
A store owner mixes 2 lb of candy that cost x dollars per pound with 3 lb of candy that costs $1.50 per pound. She sells the mix for $2.50 per pound.
1. How much did the 2 lb of the first type of candy cost the owner?
2. How much did the 3 lb of the second type of candy cost the owner?
3. How much did the two types of candy cost the store owner in total?
4. How much money will the store owner get if she sells all of the new mixture?
5. Write an equation to find the cost per pound of the first candy
6. Solve the equation to find the owners cost of the first candy per pound
Answer:
1. How much did the 2 lb of the first type of candy cost the owner?
2x
2. How much did the 3 lb of the second type of candy cost the owner?
3*1.5 = 4.5
3. How much did the two types of candy cost the store owner in total?
2x + 4.5
4. How much money will the store owner get if she sells all of the new mixture?
(2 + 3)*2.5 = 12.5
5. Write an equation to find the cost per pound of the first candy
2x + 4.5 = 12.5
6. Solve the equation to find the owners cost of the first candy per pound
2x + 4.5 = 12.5
2x = 8
x = 4
Find the value of the monomial.
-8m^4 n^4 for m = 0.5 and n =2
The value of the given monomial, -8[tex]m^{4}n^{4}[/tex], when m = 0.5 and n = 2 is -8.
According to the question,
We have the following monomial:
-8[tex]m^{4} n^{4}[/tex]
We have m = 0.5 and n = 2.
Now, putting these values of m and n in the monomial:
-8 [tex](0.5)^{4} (2)^{4}[/tex]
(Please note that when a power is there on a number then it means that to solve the expression we have to multiply the base as many times as the given power. For example, in this case, we will multiply 2 four times and the result will be 16. This concept is applicable to every expression we are solving whether the base is in decimal or in fraction or a integer.)
-8*0.0625*16
-128*0.0625
-8
Hence, the value of the given monomial is -8.
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Simplify the expression
(9− 3i) (−6+ 8i) =
[tex] = 9( - 6 + 8i) - 3i( - 6 + 8i) \\ = - 54 + 72i + 15i - 24 {i}^{2} \\ = - 54 + 87i - 24 {i}^{2} [/tex]
ATTACHED IS THE SOLUTION
How many times as great is the value 1.5 than the value of 0.15 Explain
The number of times the value 1.5 exceeds the value 0.15 is 10, which is obtained by dividing both values.
How do you calculate how many times a number is greater?We divide a by b to find how many times greater a number is than b; thus, to calculate how many times greater a number is, we use a division operation.
What exactly is a number comparison?To determine how many times greater a number is than b, we compare them, i.e. divide them.
As an example:
50/10 = 5, indicating that 50 is five times greater than ten.
We must determine how many times the value 1.5 is greater than the value 0.15.
For this , let us divide 1.5 by 0.15
Number of times the value is greater = 1.5/0/15
= 10
Therefore, the number of times the value 1.5 is greater than the value 0.15 is 10.
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determine whether the order pair is a solution 3x-1+2=4
Answer:
x=1
Step-by-step explanation:
3x−1+2=4
Add −1 and 2 to get 1.
3x+1=4
Subtract 1 from both sides.
3x=4−1
Subtract 1 from 4 to get 3.
3x=3
Divide both sides by 3.
x=
3
3
Divide 3 by 3 to get 1.
x=1
Distribute -3\left(7x^{2}+3x\right)
By using distributive property, [tex]-3\left(7x^{2}+3x\right) = -21x^{2} -9x[/tex]
This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.
In order to quickly solve equations, a number is distributed across the integers in the brackets. When using the distributive property of multiplication, for instance, to resolve the expression 4(2 + 4), we would do so as follows: 4(2 + 4) = (4 × 2) + (4 × 4) = 8 + 16 = 24.
We have,
[tex]-3\left(7x^{2}+3x\right)[/tex]
Using Distributive Property, A(B+C) = AB+AC
[tex]-3\left(7x^{2}+3x\right) = -21x^{2} -9x[/tex]
Hence, [tex]-3\left(7x^{2}+3x\right) = -21x^{2} -9x[/tex]
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We poll 550 people and find that 60% favor Candidate S. In order to estimate with 90% confidence the percent of ALL voters would vote for Candidate S, we should use:
We are 90%sure that the interval (0.6036, 0.5963) contains the true population proportion.
Given that, n=550 (Sample size, Number of trials), p=0.6 (Sample proportion) and 1−α=0.9 (Confidence level).
What is confidence interval for a population proportion?The confidence interval is one of the most used for estimating population parameters in statistics. It is common to perform an interval with a known confidence level to find a range of values that show us information about the population.
Using the standard error of the sample proportions [tex]ME=z_{\alpha /2}.\sqrt{\frac{p(1-p)}{n} }[/tex]
[tex]=z_{0.9/2}.\sqrt{\frac{0.6(1-0.6)}{550} }[/tex]
[tex]=z_{0.45}.\sqrt{\frac{0.6(0.4)}{550} }[/tex]
= 0.1736 × √(0.24/550)
= 0.1736 × 0.0208
= 0.00361
Confidence interval = 0.6±0.00361
= (0.6+0.00361, 0.6-0.00361)
= (0.6036, 0.5963)
Therefore, we are 90%sure that the interval (0.6036, 0.5963) contains the true population proportion.
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Brainliest For Correct Answer
The approximate height of the door is 84in
What is a rectangle?A rectangle is a polygon with 4 sides and 4 right angles.
It has 2 lines of symmetry and one of that lines is called a diagonal.
Rectangles are cut into two to form right angled triangles.
The rectangle is divided into two right angled triangles
with a diagonal of 94 inches, base = 42 inches.
The height of the rectangle, the base and the diagonal form a right angled triangle.
By Pythagoras,
[tex](94)^{2}[/tex] = [tex](42)^{2}[/tex] + [tex](height)^{2}[/tex]
8836 = 1764 + [tex](height)^{2}[/tex]
[tex](height)^{2}[/tex] = 8836 - 1764 = 7072
height = [tex]\sqrt{7072}[/tex] = 84 inches
In conclusion, the height of the rectangular door is 84 inches approximately.
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Answer: B is the answer to the question
Step-by-step explanation:
Mr tan had 2 kg of sugar. He used 1/4 kg of sugar to make dessert and 3/5 kg of sugar to bake some cakes. What was the total mass of sugar used? How much sugar did he have left?
The total mass of sugar used is 1.7 kg.
The mass of sugar he has left is 0.3 kg.
What are fractions in math?In mathematics, a fraction is a numerical value that represents a portion of a whole. The entire can be any number, a specific value, or an item. Fractions are written as p/q.
Given:
Total mass of sugar Mr tan has = 2 kg
Fraction of sugar used to make dessert = 1/4 kg
Fraction of sugar used to bake some cakes = 3/5 kg
The total mass of sugar used is calculated as,
= Mass of sugar used to make dessert + Mass of sugar used to bake some cakes
Mass of sugar used to make dessert = (1/4 of 2) kg = 1/2 kg
Mass of sugar used to bake some cakes = (3/5 of 2) kg = 6/5 kg
Total mass of sugar used = (1/2 + 6/5) kg = 17/10 = 1.7 kg
Mass of sugar left = Total mass of sugar - Total mass of sugar used
= 2 kg - 1.7 kg = 0.3 kg
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select the correct answer. the endpoints of WX are W(-5,-1) and X(2,6) what is the length of WX
Answer:
[tex]d=7\sqrt{2}\text{ }[/tex]Step-by-step explanation:
The distance between two points is represented by the following equation;
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Therefore, if the endpoints of WX are (-5,-1) and X(2,6):
[tex]\begin{gathered} d=\sqrt{(2+5)^2+(6+1)^2} \\ d=7\sqrt{2} \end{gathered}[/tex]Help it was due yesterday
Answer:
10
Step-by-step explanation:
486-466 = 20
1/2 x 20 = 10
:]
Answer:
an expression that equals 10
Step-by-step explanation:
486 - 466 = 20
1/2 of 20 is 10
You don't list choices.
You need an expression that equals 10.
a^-1 = ?
A. -a
B.√ a
C. 1/a
Answer: C
Step-by-step explanation:
This is the definition of a negative exponent.
compare 7.3 and 12 use <,>, or =.
Answer: 7.3 < 12
Step-by-step explanation:
can someone please help solve this math problem with solution? thank u!
===================================================
Work Shown:
[tex]\frac{n^2+n-6}{n-2}\\\\\frac{(n+3)(n-2)}{n-2}\\\\n+3[/tex]
---------------
Explanation:
Often when simplifying, it's a good idea to factor and see what cancels (if anything does cancel).
To factor the numerator, think of two numbers that
multiply to -6add to 1Through trial and error, you should find the two numbers to be 3 and -2
3 times -2 = -63 plus -2 = 1So that's how [tex]n^2+n-6[/tex] factors to [tex](n+3)(n-2)[/tex].
After this point, the (n-2) terms cancel leaving n+3 behind
We can say [tex]\frac{n^2+n-6}{n-2}=n+3 \ \ \text{when } n \ne 2[/tex]
The [tex]n \ne 2[/tex] is to avoid a division by zero error.
This is the exercise I have to do to practice for my GED I’m a six year old woman I’m trying to figure this out I know I have inserted in the formula and it says just like example 3 I will insert example 3 in the text hereA survey indicates that for each trip to a supermarket, a shopper spends an average of 43 minutes with a standard deviation of 12 minutes in the store. The lengths of time spent in the store are normally distributed and are represented by the variable X. A shopper enters the store. Find the probability that the shopper will be in the store for each interval of time listed below. a) Find the probability that the shopper will be in the store between 33 and 66 minutes.b)) Find the probability that the shopper will be in the store for more than 39 minutes. Hint: Convert the normal distribution X to Standard normal using Z formula Z=(X-μ)/σ and then look the Z-values from the table and then find the probability.Hint: Convert the normal distribution X to Standard normal using Z formula Z=(X-μ)/σ and then look the Z-values from the table and then find the probability.Please help me answer properly so I can start the exercise so I can be fish prayers for the GED practice course
Given:
The lengths of time spent in the store are normally distributed and are represented by the variable X
The survey indicates that for each trip to a supermarket, a shopper spends an average of 43 minutes with a standard deviation of 12 minutes in the store.
so, the mean = μ = 43
And the standard deviation = σ = 12 minutes
We will find the probability that supermarkets between 31 and 58 minutes
We will use the following formula to convert to the z-scores
[tex]Z=\frac{(X-μ)}{σ}[/tex]So, we will find Z when x = 31 and When x = 58
[tex]\begin{gathered} x=31\rightarrow z=\frac{31-43}{12}=\frac{-12}{12}=-1 \\ \\ x=58\rightarrow z=\frac{58-43}{12}=\frac{15}{12}=1.25 \end{gathered}[/tex]So, we will find the probability of P (-1 < z < 1.25)
From the tables of the z-score:
[tex]P(-1So, the answer will be 0.7357let x be a normally distributed random variable with mean 5 and standard deviation 15. please express your answer as a number between 0 and 100. if you want to write 52%, please enter 52. what is the probability that x is less than or equal to 38?
The probability that x is less than or equal to 38 is 0.9861.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value = 38
μ = mean = 5
σ = standard deviation = 15
z-score = (38 - 5) / 15
z-score = 33 / 15
z-score = 2.2
Find the probability that corresponds to the z-score in the z-table. (see attached images)
z-score = 2.2
probability = 0.9861
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a number is between 26 and 31 it has the prime factors of 2 and 7 what is the number
Answer:
28
Step-by-step explanation:
2 x 7 = 14
Number should be in between 26 and 31
So,
14 x 2 = 28
28 has one of its prime factors as 2 and 7.
Hence,
28 is the number which is in between 26 and 31 it has the prime factors of 2 and 7.
Answer:
Step-by-step explanation: Given prime factors: 2, 7
By multiplying, 2 X 7= 14
Given, number is between 26 and 31
therefore, 14 X 2= 28 (since 2 is a prime factor)
ans: 28
The amount Abigail Frump makes, in dollars, working h hours can be represented by the expression 18h + 8. Abigail hopes to get a raise that
can be represented by the expression 2h + 32. Write an expression that represents how much Abigail will make working h hours if he gets the
raise. How much will he make for working 6 hours?
Hakim drew a scale drawing of a neighborhood park. he used the scale 5 inches : 2 yards. a soccer field in the park is 130 inches wide in the drawing. how wide is the actual field?
Answer:
52 yards across
Step-by-step explanation:
Hakim drew a scale drawing of a neighborhood park. he used the scale 5 inches : 2 yards. a soccer field in the park is 130 inches wide in the drawing. how wide is the actual field?
130/5 = 26
26*2 = 52 yards across
Giselle stars with the two parallel line segments shown. She correctly reflects the segments across
the x-axis and then translates them following the rule (x,y) → (x-2, y + 5).
Line Segment AB has endpoints (2,4) and (-2,-1). Line Segment CD has end points (3,1) and (-1.-4).
(image attached)
Which statements about the reflection and translation of the line segments are true? Select all that
apply.
omg what is the......................