By using algebra properties and given that the linear equation 4 · x + 2 · y = 20, the value of (8 · x + 4 · y) / 5 is equal to 8.
How to determine the value associated to a linear equation
Herein we find a linear equation equal to a given number and we are asked to find a number associated with a modified form of the formula, this can be done by using algebra properties. The complete procedure is shown below:
4 · x + 2 · y = 20 Given
2 · (4 · x + 2 · y) = 20 · 2 Compatibility with multiplication
8 · x + 4 · y = 40 Associative and distributive properties
(1 / 5) · (8 · x + 4 · y) = (1 / 5) · 40 Compatibility with multiplication
(8 · x + 4 · y) / 5 = 8 Multiplication of fractions / Result
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Three squares have been used to form a right triangle. What is the area of the third square if the area of the first two squares are 8 square units and 16 square units respectively?
The area of the third square is 24 units square.
How to find the area of a square?The squares forms a right angle triangle.
The side length of a square are equal.
Therefore, the side length of each square contribute to the three sides of the right triangle formed. The unknown length of the right triangle is the hypotenuse side of the triangle. That unknown length is the side length of the square.
area of a square = l²
where
l = side lengtharea of the first square = l²
√8 = l
l = 2√2 units
area of the second square = l²
√16 = l
l = 4 units
The length of the squares are the legs and hypotenuse of the right triangle formed.
using Pythagoras theorem,
a² + b² = c²Therefore,
a = 2√2 unitsb = 4 unitsc = ?(2√2)² + 4² = c²
16 + 8 = c²
c = √24
c = 2√6 units
area of the third square = (2√6)² = 24 unit²
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18=2(4+x) ughhhh? omg
Step-by-step explanation:
linear
8+2x=18
2x=10
x=5
Help me with number 59 and 60 :)
Answer:
59. a₁ = 4
60. a₁ = 10
Step-by-step explanation:
The general equation for the sum of the first n terms Sₙ of a geometric sequence with common ratio r and first term a₁ is
[tex]S_n = a_1 \dfrac{1-r^n}{1-r}[/tex]
Problem 59
Here we are given
[tex]S_n = \dfrac{31}{4}\\\\r = \dfrac{1}{2}[/tex]
So we can plug these values into the above equation and get [tex]a_1[/tex]
Let's first compute [tex]1 - r^n[/tex]
[tex]1 - r^n = 1 - \left(\dfrac{1}{2}\right)^5\\\\\left(\dfrac{1}{2}\right)^5 = \dfrac{1}{32}\\\\1 - r^n = 1 - \left(\dfrac{1}{2}\right)^5 = 1-\dfrac{1}{32} = \dfrac{32}{32}-\dfrac{1}{32} = \dfrac{31}{32}[/tex]
[tex]1- r = 1 - \dfrac{1}{2} = \dfrac{1}{2}[/tex]
So
[tex]\dfrac{1-r^n}{1-r} = \dfrac{31}{32} \div \dfrac{1}{2} = \dfrac{31}{32} \times \dfrac{2}{1} = \dfrac{31}{16}[/tex]
Substituting this value into [tex]S_n = a_1 \dfrac{1-r^n}{1-r}[/tex] we get
[tex]\dfrac{31}{4} = a_1\dfrac{31}{16}[/tex]
Multiplying both sides by [tex]\dfrac{16}{31}[/tex]
[tex]\dfrac{31}{4} \times\dfrac{16}{31} = a_1\dfrac{31}{16} \times\dfrac{16}{31}\\\\4 = a_1 \textrm{or alternatively }\\ \\\boxed{a_1 = 4}[/tex]
Problem 60
Use the same technique as above
[tex]S_8 = 2550, r = 2\\\\S_8 = a_1 \times \dfrac{1-r^8}{1-r}\\\\\\2550 = a_1 \times \dfrac{1-2^8}{1-2}\\\\2550 = a_1 \times \dfrac{1 - 256}{1-2}\\\\2550 = a_1 \times \dfrac{-255}{-1}\\\\2550 = a_1 \times255\\\\== > a_1 = \dfrac{2550}{255}\\\\\boxed{a_1=10}[/tex]
Find the equation of the linear function represented by the table below in slope-intercept form.
The equation of the linear function represented by the table below in slope-intercept form is y = 7x + 4
Linear equationsThe equation of a line in point-slope form is expressed as y = mx + b
where
m is the slope
b is the intercept
Using the coordinate points (0,4) and (1, 11)
Slope = 11-4/1-0
slope = 7
The y-intercept is at the point (0,4)
Determine the equation
y = mx + b
y = 7x + 4
Hence the equation of the linear function represented by the table below in slope-intercept form is y = 7x + 4
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The perimeter is 26. How much bigger is the longest side than the shortest side?
Answer:
8
Step-by-step explanation:
the perimeter is the sum of the 3 sides of the triangle.
Given perimeter = 26 , then
2a - 3 + 2a + 3a + 1 = 26 , that is
7a - 2 = 26 ( add 2 to both sides )
7a = 28 ( divide both sides by 7 )
a = 4
then
shortest side = 2a - 3 = 2(4) - 3 = 8 - 3 = 5
longest side = 3a + 1 = 3(4) + 1 = 12 + 1 = 13
the difference between the 2 sides is 13 - 5 = 8
the longer side is 8 units bigger than the shortest side
Monica reads 7 ½ pages of a mystery book in 5 minutes. What is her average reading rate in pages per minute?
Answer:
1.5 or 1 ½ pages per min
Step-by-step explanation:
7.5/5=1.5
She reads 1 ½ pages per min
Answer: 1.5 pages per minute
Step-by-step explanation:
Divide the total number of pages she read by 5, the amount of time it took her. So it should look like this: 7.5/5
The answer is 1.5 pages per minute.
alexio has $100$ cards numbered $1$-$100$, inclusive, and places them in a box. alexio then chooses a card from the box at random. what is the probability that the number on the card he chooses is a multiple of $2$, $3$ or $5$? express your answer as a common fraction.
Answer:
37/50
Step-by-step explanation:
You want the fraction of integers in the range [1, 100] that are divisible by 2, 3, or 5.
DivisibilityAttached is a Venn diagram showing how the divisibility of numbers from 1 to 100 stacks up. Circle A includes all 50 numbers divisible by 2; Circle B counts all 33 numbers divisible by 3; and Circle C counts the 20 numbers divisible by 5.
Where the circles overlap, there are counts of the numbers divisible by the relevant combination of factors. For example, there are 3 numbers divisible by 2, 3, and 5. (They are 30, 60, 90.)
ProbabilityIn all, there are 74 numbers in the range 1–100 that are divisible by 2, 3, or 5.
The probability that a card chosen at random will have a number divisible by 2, 3, or 5 is 74/100 = 37/50.
P( 2, 3, or 5 divides N) = 37/50.
__
Additional comment
Roughly, the number of numbers in range [A, B] divisible by n is (B -A)/n. This is how we arrived at the counts shown in the attachment. For example, There are 100/(2·5) = 10 numbers divisible by both 2 and 5. Of those, there are 10/3 = 3 divisible also by 3. So, the number 3 is found in the area ABC, and the number 10-3=7 is found in the area AB'C.
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if you have a mixture of 10 lb. sunflower seeds which cost 32c per pound and 16 lb. of cracked corn which cost 18¢per pound, how much would this mixture cost per pound?
By unitary method, we get that the total cost of mixture per pound = 50 cents.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Given:
Cost of 1 pound sunflower seeds = 32 cents.
Cost of 1 pound cracked corn = 18 cents.
Available sunflower seeds = 10lb = 10 pounds
Available cracked corn = 16lb = 16 pounds
To find: Cost of the mixture per pound
Finding:
By unitary method, Cost of 1 pound sunflower seeds = 32 cents.
Cost of 10 pounds sunflower seeds = 32(10) = 320 cents.
Again, by unitary method,
Cost of 1 pound cracked corn = 18 cents.
Cost of 16 pound cracked corn
= 18(16) cents
= 288 cents.
Therefore, total cost of mixture per pound
= 32 + 18 = 50 cents.
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home prices in a neighborhood vary every year. in 2021, the following nine home prices were listed. (in thousands)
H 120 166 173 H H H 123 127 L
Where L indicates a Home below $110 and H indicates a Home above $190. The median home price is:
A) 166
B) 169.5
C) 170
D) 173
E) Cannot be determined
Based on the prices of the homes in the neighborhood, the median home price is A) 166
What is the median home price?
L is for a home below $110 and H is for a home above $190. The distribution of home prices can therefore be shown as:
190, 120, 166, 173, 190, 190, 190, 123, 127, 110
In an ordered list, this becomes:
= 110, 120, 123, 127, 166, 173, 190, 190, 190
The median is the price in the middle and we can see this price is $166
In conclusion, the median home price is $166.
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Please answer I need help
Answer:
What's the wildflowers trails current length so I can help
a sequence is constructed by listing all the possible numbers that contain no digit greater than 3 in ascending order. what is the 2021st term of this sequence?
The 2021st term of the sequence is (- n - 2017).
Given,
A sequence is constructed by listing all the possible numbers that contain no digit greater than 3 in ascending order.
We need to find out what is the 2021st term of this sequence.
What is an arithmetic sequence?An arithmetic sequence is a sequence where the difference between the consecutive terms is the same.
Example: 2, 4, 6, 8, 10
4 - 2 = 2
6 - 4 = 2
8 - 6 = 2
The nth term of an arithmetic sequence is given by:
= a + ( n - 1 ) d
Where a = the first term
d = common difference
Let the sequence that contains no digit less than 3 in ascending order be:
3 - n, 3 - (n + 1), 3 - (n+2), 3 - (n+3), 3 - (n+4),......
Where n = any real number from 1.
We see that the common difference is -1.
3 - (n+1) - (3 - n)
= 3 - n - 1 - 3 + n
= -1
3 - (n+2) - [3-(n+1)]
= 3 - n - 2 - 3 + n + 1
= -1
Find the 2021st term.
We have,
a = 3 - n
d = -1
n = 2021
= a + ( n - 1 ) d
= (3 - n) + ( 2021 - 1 ) (-1)
= 3 - n - 2020
= - n - 2017
Thus the 2021st term of the sequence is - n - 2017.
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two cards are dealt at random from a standard deck of $52$ cards ($13$ hearts, $13$ clubs, $13$ spades, and $13$ diamonds). what is the probability that the first card is a $6$ and the second card is a queen?
The probability of getting a number 6 as the first card and a queen as the second card is 4/663.
Probability is mathematically defined as the ratio of the number of outcomes of a particular event or occurrence to the total number of outcomes.
For a standard deck, there are 52 total outcomes since there are 52 cards. A standard deck is divided into four suits - hearts, clubs, spades, and diamonds - with 13 cards each. Each suit has nine numbered cards from 2 to 10, three face cards (king, queen, and jack), and an ace.
The probability of having a numbered 6 card is 4/52. The probability is the same for getting a queen. Although, the probability of getting 6 as the first card and the queen as the second is different. This kind of probability requires the multiplication rule.
First card probability = 4/52
Second card probability = 4/51
The total number of outcomes for the second card is reduced since the first card is not replaced.
Probability (6 then queen) = (4/52)(4/51)
Probability (6 then queen) = 4/663
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6.018 to 1 decimal place
Answer:
6.0
Step-by-step explanation:
Answer:
Step-by-step explanation:
1.00
terra writes the following proof for the theorem: if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram: terra's proof ao
Vertical angles or contrary angles are the statement that Terra's proof is still absent. The angles formed opposite to each other when two lines cross each other are equal.
The missing word in Terra's proof is described as :Terra describes the parallelogram nature of the diagram. Because they are vertical or opposite angles, these angles are equal.
The angles formed opposite to each other when two lines cross each other are equal. As a result, we have discovered that either vertical angles or opposite angles make up Terra's proof.
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define the points p(−4,−2) and q(3,−4). carry out the following calculation. find two vectors parallel to qp with length 4.
The vector is -2i+7j and the two parallel vectors with length 4 is u=-8/√53i+28/√53j and u=8/√53i-28/√53j respectively
The points are p(-4,-2) and q(3,-4)
The vector qp = vector p -vector q
qp= <-4+2,3+4>
qp=-2i+7j
|QP|=√(-2)^2+(7)^2
|QP|=√4+49
|QP|=√53
The unit vector in direction of QP is 1/√53(-2i+7j)
To get a unit vector parallel in direction of QP, multiply by 4
u=-8/√53i+28/√53j
Multiplying by -4 to get another parallel vector of length 4, we get
u=8/√53i-28/√53j
The term "parallel vectors" refers to 2 vectors which can be in the identical direction, have the equal attitude, but differ in magnitude.two vectors a and b are said to be parallel vectors if one is a scalar more than one of the opposite, the vectors could be parallel.Learn more about parallel vectors at:
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in rhombus $abcd$, points $e,f,g,$ and $h$ are the midpoints of $\overline{ab},\overline{bc},\overline{cd},$ and $\overline{da},$ respectively. quadrilateral $efgh$ has area 14 and perimeter 16. find the side length for rhombus $abcd$.
Side length of Rhombus ABCD is 8+2√2 unit
EFGH is a rectangle :
We know that ,
E, F , G , H are midpoints of AB, BC, CD , DA respectively
Since ABCD is a rhombus
AB = BC = CD = DA
AB ll CD and BC ll DA
since, E, F , G , H are midpoints of AB, BC, CD , DA respectively
from the figure below we can say that ,
1) AB ll CD ll FH and AB= CD = FH
2) BC ll DA ll GE and BC = DA = GE
Using mid point theorem we can say that ,
GH = EF = 1/2 AC and FG= EH = 1/2 BD
Since for the figure EFGH opposite sides are equal and and parallel , and the diagonals are equal in length we can say that EFGH is a rectangle.
Perimeter of a rectangle = 2(a+b) = 2( GH + EH ) = 2 (EF + GF) = 2 ( 1/2 AC + 1/2 BD )
= 2 x 1/2 ( AC + BD ) = 16
⇒ AC + BD = 16 (1)
now area of a rectangle is given by
A = ab = GH x EH = EF x GF = 1/2 AC x 1/2 BD = 1/4 (AC x BD) = 14
⇒AC x BD = 14 x 4 = 56
from equation (1)
AC ( 16 - AC) = 56
= 16 AC - AC ^2 = 56
⇒ AC^2 - 16 AC + 56 = 0
AC = 8 +/- 2√2
BD = ( 16 - AC) = 8 +/- 2 √2 = side length of rhombus ABCD
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15 Write an expression for the
gradient of the line
perpendicular to the line
segmentjoining
(3p, 6) to (-2p, 10).
5p/6 an expression for the gradient of the line perpendicular to the line segment joining (3p, 6) to (-2p, 10).
Use the slope formula to find the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1), or the change in the y values over the change in the x values. The coordinates of the first point represent x1 and y1
gradient of the line segment joining (3p, 6) to (-2p, 10)
m=(y2-y1)/(x2-x1)
m =( 10 -4)/ ( -2p - 3p)
m= 6/ (-5p)
m= -6/5p
we know that
Gradient of a line perpendicular to a line with a gradient of m = -1/m
Gradient of a line perpendicular to a line with a gradient of -6/5p = 5p/6
Hence 5p/6 an expression for the gradient of the line perpendicular to the line segment joining (3p, 6) to (-2p, 10).
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30 points mathamatics
Answer:
1870
Step-by-step explanation:
Answer:
c) 1,870
Step-by-step explanation:
374 multiplied 5 times, or 374 in a group of 5, equals 1,870.
Have a good day <333
Find the values of x and z (please Help)
The value of x is 6° and value of z is 67°
We know that when two lines intersect then the vertically opposite angles are equal.
So according to the given figure
(11x + 47)° = (6x + 77)°
Solving the above equation for x we get
11x° + 47° = 6x° + 77°
5x° = 30°
x = 6°
Thus the value of x is 6°
Also note that the linear pair of angles make 180°. That is sum of the two angle is 180°. As we can see from the figure ∠z and (6x + 77)° make linear pair of angles, therefore there sum will be equal to 180°.
Thus, ∠z + (6x + 77)° = 180°
∠z + (6*6 + 77)° = 180°
∠z + 113° = 180°
∠z = 67°
Hence the value of z is 67°
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4(5x+3)=14x+30 not sure if i understand
Answer:
x = 3
Step-by-step explanation:
Use the distributive property to multiply 4 by 5x+3. Subtract 14x from both sides. Combine 20x and −14x to get 6x. Subtract 12 from both sides. Subtract 12 from 30 to get 18. Divide both sides by 6. Divide 18 by 6 to get 3.
Answer:
20x+12=14x+30
6x=18
x=3
Step-by-step explanation:
First, apply the distributive property:
4(5x+3) = 4 · 5x + 4 · 3 = 20x+12
Now, we have this equation
20x+12=14x+30
We need to group the elements now.
So, to bring all the elements with an "x," we subtract 14x from both sides.
20x-14x+12=14x+30-14x
We have this now
6x+12=30
Now, let's subtract 12 on both sides
6x+12-12=30-12
6x=18
Divide both sides by 6
x=3
What is the slope of the line that passes through the points (6,10) and (6,−2)? Write your answer in simplest form.
The slope of the line passes through the points (6,10) and (6,−2) is undefined.
Here,
The points are (6,10) and (6,−2).
We have to find the slope of the line passes through the points (6,10) and (6,−2).
What is slope of line?
The slope of the line passes through the points (x₁, y₁) and (x₂, y₂) is;
[tex]m = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
Now,
The points are (6,10) and (6,−2).
Hence, The slope of the line passes through the points (6,10) and (6,−2) is;
[tex]m = \frac{-2 -10 }{6-6 }= \frac{-12}{0}[/tex]
Which in undefined.
Therefore, The slope of the line passes through the points (6,10) and (6,−2) is undefined.
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the slope of the line that passes through the points (6,10) and (6,−2) is undefined.
Step-by-step explanation:
Order the following numbers from least to greatest. Put the least number on the left. -0.32 -3.2 2 3|2
The numbers from least to greatest are arranged as -
-3.2, -0.32, 3/2, 2
What is ascending and descending order of arrangement of numbers?Ascending order is the arrangement of numbers from the smallest to the largest. For example, the following numbers are in ascending order: 3, 15, 28, 49. Descending order is an arrangement of numbers from the largest to the smallest. For example, the numbers 45, 32, 26, 12 are arranged in descending order.Given is the sequence of numbers as -
-0.32, - 3.2, 2, 3/2
The given sequence of numbers is -
-0.32, -3.2, 2, 3/2
The numbers from least to greatest are -
-3.2, -0.32, 3/2, 2
Therefore, the numbers from least to greatest are arranged as -
-3.2, -0.32, 3/2, 2.
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Slopes of perpendicular lines are equal. true or false
False, parallel lines have not the same slope whereas perpendicular lines have because of this. Perpendicular lines have equal slopes.
What is a slope in mathematics?The steepness and direction of a line, read from left to right, is referred to as its slope. Finding the ratio of will allow you to determine the slope or gradient. Between two places on the line, either by using the rise (vertical change) to the run (horizontal change). a slope-intercept version of a linear equation (y = mx + b).
based on the facts provided;
Two parallel lines' slopes are always their negative reciprocal of one another. The other has a slope of -3/2 if one has a slope of 2/3.
Therefore, perpendicular lines do not have equal slopes.
The sentence is
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Is the following relation a function? x y 1 4 −1 −2 3 10 5 16 a Yes b No
The relation that is represented in the table is a function. YES.
How to Determine a Relation that is a Function?For every relation that represents a function, the each of the x-value (domain element/input) corresponds to exactly one y-value (range element/output).
In the table given showing a relation, every single x-value (input) has exactly only one possible y-value (output) that it is assigned to. The x-values, 1, -1, 3, and 5, each have a specific y-value they each correspond to.
Thus, based on the definition of a function, the relation that is represented in the table is a function. YES.
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Brandy and mark are selling magazines. Brandy has sold half as many as mark. Together they have sold 747 magazines. How many did each sell? Elimination
Answer 1120.5
Step-by-step explanation:
If 14 inches of wire cost 42 cents how many inches of wire can be bought with 21 cents
If 14 inches of wire cost 42 cents, with 21 cents can be bought 7 inch of wire
Information about the problem:
Inches bought= 14Inches bought cost = 42 centsAmount = 21 centsInches with 21 cents = ?Calculating how much 1 inch cost, we have:
1 inch cost= Inches bought cost / Inches bought
1 inch cost= 42 cents / 14 inches
1 inch cost= 3 cent/inch
Calculating how much can be bought with 21 cents:
Inches of wire= Amount / 1 inch cost
Inches of wire= 21 cent / 3 cent/inch
Inches of wire= 7 inch
What is a fraction?Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.
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Sam is driving a distance of 140 miles from his house to visit Melissa. Sam takes city roads, on which he can travel an average of 35 mph for a total of 1.5 hours. Sam also takes the highway, on which he travels an average of 65 mph for a total of x hours. Approximately how long does Sam travel on the highway, to the nearest tenth of an hour?
The hours travelled on the highway is 1.3 hours.
What is the time travelled?The first step is to determine the distance Sam travelled on the city road. The formula that would be used is the average speed formula. The average speed is the ratio of total distance travelled and the total time travelled.
Average speed = distance /time
average speed x time = distance
Distance = 35 x 1.5 = 52.50 miles
The second step is to determine the distance travelled on the highway.
Distance travelled on the high way = 140 - 52.50 = 87.50 miles
Now, determine the total hours travelled:
Hours travelled = distance / average speed
87.50 / 65 = 1.3 hours
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Answer: Sam traveled 1.3 hours.
Step-by-step explanation:
Identify an equation in point slope form for the perpindicular to y=-3x+5 that passes through (4,-1)
Answer:
[tex]\boxed {y = \dfrac{1}{3}x - \dfrac{7}{3}}[/tex]
Step-by-step explanation:
If we have a line y = mx + b where m is the slope and be is the y-intercept then a line perpendicular to this line will have slope -(1/m)
So the slope of the line perpendicular to y = -3x + 5 will be [tex]-\dfrac{1}{3}[/tex] = + 1/3 = 1/3
So the perpendicular line equation is
y = (1/3)x + b where b is the y intercept of this line
Since it passes through the point x = 4, y = -1 we plug in these values for x and y and solve for b
We get
[tex]-1=\dfrac{1}{3}\cdot \:4+b[/tex]
Switch sides
[tex]\dfrac{1}{3}\cdot \:4+b=-1[/tex]
[tex]\dfrac{4}{3}+b=-1[/tex]
Subtract [tex]\dfrac{4}{3}[/tex] from both sides
[tex]b = -1 - \dfrac{4}{3} = -\dfrac{3}{3} -\dfrac{4}{3} = -\dfrac{7}{3}[/tex]
So the equation of the perpendicular line is
[tex]\boxed {y = \dfrac{1}{3}x - \dfrac{7}{3}}[/tex]
1. J(1, 9), K(7, 4), L(8, 13), M(-2, 1)
The image of the points after they are reflected across the x-axis are J'(1, -9), K'(7, -4), L'(8, -13), M'(-2, -1)
How to determine the image of the points?From the question, we have the following parameters that can be used in our computation:
J(1, 9), K(7, 4), L(8, 13), M(-2, 1)
Also from the question we have the transformation to be
Transformation: reflection across the x-axis
The rule of the reflection across the x-axis is represented as
(x, y) = (x, -y)
Substitute the known values J(1, 9), K(7, 4), L(8, 13), M(-2, 1) in the above equation, so, we have the following representation
J'(1, -9), K'(7, -4), L'(8, -13), M'(-2, -1)
Hence, the image of the points are J'(1, -9), K'(7, -4), L'(8, -13), M'(-2, -1)
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What is the quotient of 2 3/4 and 7/8?
Pls help fast
The quotient of the given expression 2 3/4 and 7/8 is 22/7
Quotient of an expressionQuotient refers to a number resulting from the division of one number by another. 12 ÷ 2 = 6 the quotient is 6
Dividend is number or expression that is to be divided by another. 12 ÷ 2 = 6 the dividend is 12
Divisor is the number or expression that is to be divided by another. 12 ÷ 2 = 6 the divisor is 2
Quotient of 2 3/4 and 7/8?
= 2 3/4 ÷ 7/8
= 11/4 ÷ 7/8
multiply by the reciprocal of 7/8= 11/4 × 8/7
= (11 × 8) / (4 × 7)
= 88/28
= 22/7
Therefore, the quotient of the given expression 2 3/4 and 7/8 is 22/7
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