The values of x and y on solving the two simultaneous equations are x = 1 and y = 3.
The simultaneous equations to be solved are 4x + 2y = 10 and x + 2y = 7.
Rearranging the above equations, we have,
- 4x - 2y = - 10 -----(A)
x + 2y = 7 -------(B)
Solving them, we have, -3x = -3
x = 1 ------(C)
Substituting (C) in (B), we have,
1 + 2y = 7
2y = 6
y = 3 ------(D)
Now, let us substitute the x and y values in (A) and (B) and then check.
4x + 2y = 10
4 + 2(3) = 10
A is checked.
x + 2y = 7
1 + 2(3) = 7
B is checked.
Thus, the values of x and y are checked to be correct.
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a shade allows light to pass through from a lamp, but reduces the intensity of the light. the intensity of the light is reduced by 15% if the fabric is 1mm thick. each additional millimetre of fabric reduces the intensity by another 15%
a) write an expression that gives percent P, of light which penetrates x mm of fabric. b) use the equation to determine the percentage of light that will pass through a cloth, that is 2.75mm thick
a) The exponential function that gives the percent P is: P = (0.85)^x.
b) The percentage of light that will pass through a cloth that is 2.75mm thick is given as follows: 63.96%.
How to define the exponential function?A decaying exponential function is defined as follows:
y = a(1 - r)^x.
In which the parameters are given as follows:
a is the initial value.r is the decay rate, as a decimal.The parameter values for this problem are given as follows:
a = 1, r = 0.15.
Hence the function is:
y = (0.85)^x.
The percentage passing through a cloth that is 2.75 mm thick is given as follows:
y = (0.85)^2.75
y = 0.6396.
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PLEASE HELP I WILL GIVE BRAINLIEST
For the set of triangle vertices, find the coordinates of the vertices of the image after a dilation by the given scale
factor and center of dilation.
D(2,-2), E(4, -2), F(1, -4)
k = 1.5,, E(4,-2), centered at E
The coordinates of vertices after dilation by scale factor of 1.5 with center of dilation is D'(3,-3), E'(6,-3) and F'(1.5,-6).
What is the vertices after dilation?A dilation is just a transformation which enlarges or contracts the size of a figure. This means that the preimage and image are similar and are scaled up or down using a factor.
The vertices of the triangle are D(2,-2), E(4,-2), F(1,-4).
The origin-centered dilation with a scale factor of k is defined as,
(x,y) → (kx,ky)
As a result, dilation with a scale factor of 1.5 centered at the origin is defined as,
(x,y) → (1.5x,1.5y)
The image's vertices are
D(2,-2) → D'(3,-3)
E(4,-2) → E'(6,-3)
F(1,-4) → F'(1.5,-6)
Therefore the coordinates of vertices after the dilation by the given scale factor 1.5 is D'(3,-3), E'(6,-3) and F'(1.5,-6).
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Adding and subtracting fractions with unlike denominators Find the sum.
1. 1/3+2/3 = 2. 1/2 + 1/3 = 3. 2/5+1/2
Find the difference.
1. 1/2-1/3 = 2. 4/5-2/3 = 3. 4/15-1/10 =
the sum is 1) 5/3, 2) 5/6 , 3) 7/10 and the difference is 1) 1/6 , 2)2/15, 3) 1/30. When adding or subtracting fractions with unlike denominators, the first step is to convert the fractions so that they have a common denominator.
1. 1/3+2/3 = 5/3
2. 1/2 + 1/3 = 5/6
3. 2/5+1/2 = 7/10
1. 1/2-1/3 = 1/6
2. 4/5-2/3 = 2/15
3. 4/15-1/10 = 1/30
When adding or subtracting fractions with unlike denominators, the first step is to convert the fractions so that they have a common denominator. To do this, you can use the lowest common denominator, which is the least common multiple of the denominators. For example, in the first problem, the least common multiple of 3 and 2 is 6, so you can convert the fractions to 2/6 and 4/6, or 1/3 and 2/3. Then, you can add or subtract the fractions as normal. For example, 1/3+2/3 would equal 3/3 or 1.
For subtracting fractions with unlike denominators, the same process is used. For example, in the second problem, the least common multiple of 5 and 3 is 15, so you can convert the fractions to 4/15 and 2/15. Then, you can subtract the fractions as normal. For example, 4/15-2/15 would equal 2/15.
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which graph shows different numbers of tickets that ellena can sell to raise more than 180$
how to go from slope intercept form to standard form
To go from slope intercept form of line to standard form Ax + By + C = 0, collect all terms on the left side of the equation and multiply by the denominator B.
We know that the standard form of equation of line is Ax + By + C = 0. And the slope intercept form of line is y = mx +b, where m is the slope of the line, and b is the y-intercept i.e., the value of y when x = 0.
Converting from slope intercept form to standard form:
⇒ y = mx + b
⇒ y - mx = (mx - mx) + b .........(subtract mx from each side)
⇒ y - mx = b
⇒ y - mx - b = b -b .........(subtract b from each side)
⇒ y - mx - b = 0
⇒ - mx + y - b = 0
Above equation is of the form Ax + By + C = 0
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HELP ASAP PLS!!
PLSS
Answer:
Step-by-step explanation:
6. XZY
7. YX
Amanda explains to a classmate how to find the growth factor of an exponential function, given a table of values. She tells her classmate to choose a f ( x ) f(x) value from the table and divide it by the previous f ( x ) f(x) value.
Analyze Amanda's explanation.
If she is correct, choose one of the following ways to respond.
Create a function and explain how to use Amanda's method.
Create a function, in function notation, and explain how to tell what the growth factor is.
If she is incorrect, respond to the following statement.
Explain what Amanda did wrong and what should be done to correct her explanation
Amanda's explanation is not correct. The growth factor of an exponential function is the constant value that the function is multiplied by for each expansion in the information variable.
It is not determined by dividing one value in the table by the previous value.
To find the growth factor of an exponential function, one ought to take the proportion of any two consecutive f(x) values and distinguish the normal proportion. The growth factor is equivalent to this normal proportion.
For instance, assuming the function is [tex]f(x) = 2^x[/tex], and the table of values is:
x f(x)
0 1
1 2
2 4
3 8
The growth factor can be tracked down by taking the proportion of f(x) values for consecutive x:
f(1)/f(0) = 2/1 = 2
f(2)/f(1) = 4/2 = 2
f(3)/f(2) = 8/4 = 2
For this situation, the growth factor is 2, meaning that the function is multiplied by 2 for each increase in x.
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It takes 2 cups of water to cook 1 cup of rice.
How much rice can you cook with 0.5 cups of water?
How much water does it take to cook 6.5 cups of rice?
Answer:
0.25 cup of rice; 13 cup of water
Step-by-step explanation:
2 cup of water: 1 cup of rice = 2:1 ratio
I’m kinda slow can someone help
Answer:
60
Step-by-step explanation:
You're not slow.
So given was the formula for perimeter
12x + 1/2 - 4x - 8.5 + 2x + 8
They want you to find perimeter is x = 6, so this is a matter of plug and play. so everywhere you see an x, you'll replace it with the number 6
And we will start simplifying what we can
P = 12(6) + 1/2 - 4(6) - 8.5 + 2(6) + 8
P = 72 + 0.5 - 24 - 8.5 + 12 + 8
P = 72 - 24 - 8 + 12 + 8
P = 72 - 12
P = 60
what is the value of x in 12 ( x + 10 ) = 24
also explain
Answer: x = -8
Step-by-step explanation:
12 ( x + 10 ) = 24
First we divide the two sides of the exercise by 12.
[tex]\boldsymbol{\sf{x+10=\dfrac{24}{12} }}[/tex]
We divide 24 by 12..
x + 10 = 2
Subtract 10 from both sides.
x = 2 - 10
Subtract 10 from 2 to get. Since the number 10 is greater than 2, the result will be negative.
x = -8
Answer:
[tex] \sf \: x = - 8[/tex]
Step-by-step explanation:
Given equation,
→ 12(x + 10) = 24
Now the value of x will be,
→ 12(x + 10) = 24
→ 12(x) + 12(10) = 24
→ 12x + 120 = 24
→ 12x = 24 - 120
→ 12x = -96
→ x = -96 ÷ 12
→ [ x = -8 ]
Hence, the value of x is -8.
alex earns a $35,000 salary in the first year of his career. each year, he gets a 3% percent raise. which expression gives the total amount alex has earned in his first n years of his career?
After n years Alex will earn salary which can be expressed as $(1 + 0.03)^n * 35,000.
The total amount Alex has earned in his first year of his career is $35,000.
In the second year of his career, he gets a 3% raise, which is an increase of 3/100 * $35,000 = $1,050.
So his salary for the second year is $35,000 + $1,050 = $36,050.
In the third year of his career, he again gets a 3% raise, which is 3/100 * $36,050 = $1,081.50
So his salary for the third year is $36,050 + $1,081.50 = $37,131.50
We can see that for each year, his salary is increasing by a fixed percentage of the previous year's salary.
This pattern can be represented by the expression:
(1 + 0.03)^n * 35,000
Where n is the number of years since the start of his career. This expression gives the total amount Alex has earned in his first n years of his career.
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Can u solve and show me the steps pls
Answer:
[tex]\dfrac{-8y}{y-3}[/tex]
Step-by-step explanation:
[tex]\sf \dfrac{49 - y^2}{6y^2 +42y}=\dfrac{7^2-y^3}{6y^2 +6*7y}\\\\[/tex]
[tex]\sf =\dfrac{(7+y)(7-y)}{6y(y + 7)}=\dfrac{(7+y)(7-y)}{6y(7+y)}\\\\\\=\dfrac{7-y}{6y}[/tex]
y² - 10y + 21
sum = -10
Product = 21
Factors = (-7) , (-3) {(-7)*(-3) = 21 & (-7)+ (-3) = -10}
y² - 10y + 21 = y² - 7y - 3y + 21
= y(y - 7) - 3(y - 7)
= (y - 7) ( y - 3)
[tex]\sf \dfrac{49 -y^2}{6y^2 + 42y}*\dfrac{48y^3}{y^2 - 10y + 21}=\dfrac{7-y}{6y}*\dfrac{48y^3}{(y-7)(y-3)}\\\\\\[/tex]
[tex]\sf = \dfrac{(-1)(y-7)}{6y}*\dfrac{48y^3}{(y-7)(y-3)}\\\\\\=\dfrac{(-1)*8y^2}{y-3}\\\\\\=\dfrac{-8y^}{y-3}[/tex]
Robert Wadlow was 8’11” tall. He Pingping was 2’4.7”. what is the difference between their heights in feet and inches?
The difference between their heights in feet and inches is 6'6.3"
How to determine the difference between their heights in feet and inches?From the question, we have the following parameters that can be used in our computation:
Robert Wadlow was 8’11” tall.
Pingping was 2’4.7" tall
The difference in their heights can be calculated by subtracting the smaller height from the larger
So, we have
Difference = 8’11” - 2’4.7"
Evaluate the difference
Difference = 6'6.3"
Hence, the difference is 6'6.3"
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what is the volume? please please PLEASE help T0T
The volume of the cuboid is 16 cubic yards.
What is cuboid?A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.
Given:
A cuboid with height 2 yards, length 2 yards and width 4 yards.
The volume of the cuboid,
= length x width x height
= 4 x 2 x 2
= 16 cubic yards.
Therefore, the volume is 16 cubic yards.
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Use substitution to solve the system
4x+3y = 2
x-2y = -5
X=
Y=
The solution for linear equations given will be x=-1 and y=2 using substitution method.
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now
Given 4x+3y=2 -->1
x-2y=-5 --->2
Using substitution method, In this method, first, solve the equation for one variable, and substitute the value of the variable in the other equation.
From 2, x=2y-5
Put x=2y-5 in 1
4(2y-5)+3y=2
11y-20=2
y=22/11
y=2
Hence,
x=2*2-5
x= -1
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we have 20 cards including 10 a, 5 b and 5 c. we randomly take a card. if it is not a, what is the probability that it is b?
We randomly take a card, if it is not a, then the probability that it is b, is 1/4.
We have to find the the probability that it is a card of b, if it is not a.
We have total number of cards = 20
The cards of a = 10
The cards of b = 5
The cards of c = 5
We don't select the card a, then;
The probability of choosing card b = The total number of card b/total number of cards
The probability of choosing card b = 5/20
The probability of choosing card b = 1/4
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Please help someone with this additional gcse maths 'surds and indices' question :)
The simplest form of the expression is given as 12 + 6√3.
What is the simplest form of the expression?
We know that when we are asked to simplify in mathematics, they are asking us to write the expression in the simplest form that the expression can be in. In this case, we are to simplify 6/2 - √3.
Then we would now have to multiply the numerator and the denominator by the conjugate of the denominator such that we have;
6/2 - √3 * 2 + √3/2 + √3
12 + 6√3/4 +2√3 - 2√3 - 3
12 + 6√3/1
12 + 6√3
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which of the functions in this command can help them determine how strongly related their variables are?
The cor() returns the correlation between two variables.
Correlation shows us how strong the relationship is between two variables.
Hence, option (c) is the correct choice.
Correlation quantifies the intensity of a link between two variables and is symmetrical, meaning that the correlation between A and B is the same as the correlation between B and A.
Correlation is a statistical term that describes the degree to which two variables are linearly connected (meaning they change together at a constant rate). It's a common way of explaining simple interactions without stating a cause and effect relationship.
In R, the cor() function is used to calculate the correlation coefficient between two vectors. Correlations may be generated using the cor() function, while covariances can be generated using the cov() function. The type of correlation is specified.
There are three options: Pearson, Spearman, and Kendall.
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The complete questions should be like:
A data analyst is using statistical measures to get a better understanding of their data. What function can they use to determine how strongly related are two of the variables?
A sd()
B mean()
C cor()
D bias()
It entered the wrong thing so i js took a picture ….. :)
Mary ran 1 3/5 miles on Monday and 7 1/5 miles on Tuesday. How many times her Monday’s distance was her Tuesday’s distance?
Mary's Tuesday distance is 1/8 times her Monday distance
How to calculate the number of Mary's Tuesday distance that is her Monday's distance?
On Monday Mary ran 1 3/5 miles
= 8/5
On Tuesday Mary ran 1/5 miles
Therefore the number of times her Tuesday distance was her Monday distance can be calculated as follows
1/5 ÷ 8/5
= 1/5 ×5/8
= 1/8
Hence her Tuesday distance was 1/8 times her Monday distance
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Which of the reasons to network is most important for recent culinary program graduates?
A. Developing friendships that may lead to business referrals
B. Learning best practices from experienced professionals
C. Recommending extensive contacts that can help others
D. Sharing their favorite recipes and stories from their program
Answer:
C. gaining confidence
find the value of X.
1. x ÷ 5/6 = 1 and 4/5
2. x ÷ 2 and 1/10 = 1 and 2/3
The value of X are 5/6,1/5
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given;
x ÷ 5/6 = 1....1
x ÷ 2 = 1/10....2
Equation.1
(x/5)*6=1
6x/5=1
x=5/6
Equation.2
x/2=1/10
x=2/10
x=1/5
Therefore, the value of x in equations will be 5/6 and 1/5
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Angela wants to learn how to rock climb. The Rocky Climbing gym has a special where 5 climbs cost $52.50.
Select the equation that represents the total cost, t, of c climbs. Assume the relationship is proportional.
Answer: t = 10.50c
Step-by-step explanation: The relationship between the number of climbs, c, and the total cost, t, is proportional. This means that the ratio of t to c is constant. One way to represent this relationship is through an equation of the form:
t = kc
where k is a constant of proportionality. In this case, we know that 5 climbs cost $52.50, so we can use this information to find the value of k:
52.50 = k(5)
k = 52.50/5 = 10.50
So the equation that represents the total cost, t, of c climbs is:
t = 10.50c
Where t is the total cost, c is the number of climbs and 10.50 is the constant of proportionality.
How to plot the function-2x+1 on a graph
Answer:
Start at 1 on y-intercept and go down 2 units and right 1 unit
Step-by-step explanation:
First you have to graph your y-intercept (1) *which is the red dot in the graph I made for you*
Then you must use your slope (-2) to graph the rest
Since your slope is negative you have to go down from your y-intercept. In your case you are going down 2 units from your intercept. And since your slope is a whole number instead of a fraction you just go to the right 1 unit to make the coordinate (1,-1).
That is how you graph your equation.
I hope this helped!
geometry - i need help with this problem and it’s pretty easy. i’m just curious on how i would round the square root of 95 within the problem
Step-by-step explanation:
I am not sure what you mean. you don't round the intermediate numbers and results. only the final result.
you keep the irrational terms (like square root) like variable terms as they are and apply operations on them without actually expressing them as numbers.
only at the very last moment (when the final result is calculated) would you express them as actual number. and then you round the final result.
so, this is solved via Pythagoras :
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
in our case we have
BP² = BN² + NP² = 7² + sqrt(95)² = 49 + 95 = 144
you see ?
no need ever to bring the actual result of sqrt(95) into the picture. just keep it at sqrt(95) and do with it, what you would do with any actual number.
BP² = 144
BP = sqrt(144) = 12
so, we never had to deal with the actual irrational number.
we know how it is created, so we keep using that term to represent it.
Triangle congruence proof
Given the information, the triangle congruence prove is explained below.
Properties of congruent triangles?If the corresponding sides or measure of angles of two or more triangles have common properties, then the triangles are said to be congruent. Such that on comparing their sides and internal angles, some have equal values.
With the given information in the question, the prove is explained below:
STATEMENTS REASONS
1. AB ≅ CD Given
2. <ABD ≅<CDB Given
3. AD ≅ BC Equal sides of a parallelogram
4. <ADB ≅ <CBD Alternate angle theorem
5. <A ≅ <C Opposite property of a parallelogram
Therefore, it can be deduced that;
ΔABD ≅ ΔCDB
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IXL: S26 (ALGEBRA 1)
The equation of line k is y=9/8x-9. Line I is perpendicular to line k and passes through (-2,2) What is the equation of line I? write the equation in slope intercept form.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{9}{8}}x-9\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{9}{8}} ~\hfill \stackrel{reciprocal}{\cfrac{8}{9}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{8}{9} }}[/tex]
so we're really looking for the equation of a line whose slope is -8/9 and it passes through (-2 , 2)
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{8}{9} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{8}{9}}(x-\stackrel{x_1}{(-2)}) \implies y -2= -\cfrac{8}{9} (x +2) \\\\\\ y-2=-\cfrac{8}{9}x-\cfrac{16}{9}\implies y=-\cfrac{8}{9}x-\cfrac{16}{9}+2\implies {\Large \begin{array}{llll} y=-\cfrac{8}{9}x+\cfrac{2}{9} \end{array}}[/tex]
Pls help me on this homework question
The graph that passes through the points (4,16) and (6,12) , the equation of trend line is K = -2J + 24 .
What is trend line?A linear relationship is depicted by a trend line. Y = mx + b, where x is the independent variable, y is the dependent variable, m is the slope of the line, and b is the y-intercept, is the equation for a linear relationship.
a graph line indicating the general path that a collection of points appears to take.
When plotting predictions, trendlines, also referred to as lines of best fit or regression lines, are frequently used to graphically represent trends in data series. Typically, a trendline is a line or curve that crosses or links two or more points in a series to indicate a trend.
From the graph that passes through the points (4,16) and (6,12) , the equation of trend line is K = -2J + 24.
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What is the distance between PQ?
P: (1,6)
Q: (7,2)
The distance between PQ : 7
Given points P: (1,6)
Q : (7,2)
distance between two points formula is : √(x2-x1)^2 + (y2-y1)^2
(x1,y1)= (1,6)
(x2,y2) = (7,2)
therefore
= √(7-1)^2 +(2-6)^2
= √36+16
= √52
= 7.211
jamal plans to buy a new laptop which is currently priced at $859. ON saturday the store is giving a 25% discount off all laptops =. he will need to pay 8.5% sales tax on the final purchase. how much will the final cost of the laptop be if jamal buys it on saturday.
The final cost of the laptop be if jamal buys it on saturday is $695.79
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
Given;
The new laptop is currently priced at $859
On saturday the store is giving a 25% discount off all laptops
Sales tax on final purchase=8.5%
Now, the final value on saturday be x
x*100/859=25
x=25*859/100
x=214.75
The value will be 859-214.75=644.25
8% of 644.25
x*100/644.25=8
x=8*644.25/100
x=51.54
Final cost= 644.25+51.54
=695.79
Therefore, the final cost after 8 percent sales tax will be $695.79
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