x + 3y = 1 ; 7x + 8y = 11 solve by substitution.
Step-by-step explanation:
x + 3y = 1
x = 1 - 3y-(i)
7x + 8y = 11
x= 11-8y/7-(ii)
substituting eqn (i) in eqn (ii)
11-8y/7= 1-3y
11-8y=7-21y
13y=-4
y=-4/13
putting the value of y in eqn (i)
x=1-(-12/13)
x=25/13
Evelyn sells beauty supplies. She gets 5% commission for selling beauty products. How much commission will she receive if she sells 1,648 worth of beauty products?
Given:
Evelyn sells beauty supplies. She gets 5% commission for selling beauty products.
Required:
To find the commission she receive if she sells $1,648 worth of beauty products.
Explanation:
The commission she receive if she sells $1,648 worth of beauty products is
[tex]\begin{gathered} =\frac{5}{100}\times1648 \\ \\ =82.4 \end{gathered}[/tex]Final Answer:
$82.4
What is 4x + y = -3?
Answer:x=
−1/4y+ −3/4
Step-by-step explanation
As the sample size becomes larger, the sampling distribution of the sample mean approaches a _____ distribution.
The sampling distribution of the sample mean approaches a Normal Distribution when the sample size becomes larger.
According to the central limit theorem for samples, if we keep drawing larger .And larger samples and calculating their means, then the sample forms its . Own normal distribution (the sampling distribution). The mean of normal distribution has the same the original distribution and a variance that is equal to the original variance divided by the sample size. The variable p is the number of values whose average is taken together ,and not the number of times we do the experiments.
Thus, for a large random sample, the sample does not resemble the regular curve but for a large random sample it will closely resemble the normal curve.
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A bag contains:• 3 red marbles• 2 2 orange marbles• 1 yellow marble• 4 green marblesA marble is drawn from the bag and replaced 150times. How many times can you predict that a greenmarble or yellow marble will be drawn?
The probability of getting a green of a yellow marble can be determined like this:
Probability = (yellow marbles + green marbles) / total number of marbles
Probability = (1 + 4) / 10
Probability = 5 / 10
Probability = 1/2
By multiplying the given probability by the number of times a marble will be drawn, we get how many times we can predict that a green or a yellow marble will be picked, then we get:
Number of predictions = 150 × 1/2
Number of predictions = 75
Then, the answer is 75 times
Answer:
75 times.
Step-by-step explanation:
There are a total of 10 marbles in the bag.
Probability a green marble is drawn (in 1 draw) = 4/10 = 2/5.
In 150 draws you can expect to draw 150* 2/5 = 60 green marbles.
Probability a yellow marble is drawn (in 1 draw) = 1/10.
In 150 draws you can expect to draw 150* 1/10 = 15 yellow marbles.
So, the number of times for a green or yellow marble
= 60+15= 75.
Find the value of x in each case. Please put statement reasons.
Answer:
x = 10°
Step-by-step explanation:
Given the figure with angles 2x, 4x, 5x, and 50° marked, you want to find the value of x.
Development∠HAC = ∠HCA . . . . base angles of isosceles triangle HAC
2(∠HAC) = 4x . . . . . exterior angle 4x is equal to the sum of the equal remote interior angles HAC and HCA
∠HAC = 2x . . . . . . . divide by 2
∠AED = 180° -2x -2x = 180° -4x . . . . sum of angles in ∆AED is 180°
∠AHC = 180° -4x . . . . angles at H are a linear pair
HC ║ ED . . . . converse of corresponding angles theorem
∠FEG = ∠FCH = 50° . . . . . corresponding angles theorem
5x = 50° . . . . . substitute value of ∠FEG
x = 10° . . . . . divide by 5
Using this value for the marked angles, we get the measures shown in the attachment.
Jodi bough a new car with 14 gallon gas tank. Around the town she is able to drive 336 miles on one tank of gas. on her first trip traveling on highways, she drives 448 on one tank of gas.A: Write a compound inequality in compact from the represents how many miles Jodi can drive on a tank of gas. Let m represent the number of miles per gallon.B: Rewrite the compound inequality as two simply inequalities separate by either and or, or.C: Solve each simple inequality. Then write the solution in compact form.
We have the following:
A.
Let m represent the number of miles per gallon, the inequality would be as follows
[tex]\frac{336}{14}\leq m\leq\frac{448}{12}[/tex]B. In two simple inequalities we have this
[tex]m\ge\frac{336}{14}\text{ or }m\leq\frac{448}{14}[/tex]C.
[tex]\begin{gathered} m\ge24\text{ or }m\leq32 \\ 24\leq m\leq32 \end{gathered}[/tex]PLEASE HELP GIVE BRAINLIST Exterior Angle
Theorem
On a triangle ABC
Why is A+B=D
Not D=A+B I wrote it backwards
Angle d is exterior angle . and an exterior angle is equal to addition of two interior angles .
What is the formula for the exterior angle theorem?
The exterior angle that results from the creation of a triangle side is equal to the product of the two opposite internal angles.Two inside opposite angles that are not adjacent add up to the external angle. A triangle's outer angle is the product of its two inner, diagonally opposing angles.In this figure,
Angle d is exterior angle . and an exterior angle is equal to addition of two interior angles .
So, According to Exterior Angle Theorem,
∠D = ∠A + ∠B
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Answer:
See explanation below.
Step-by-step explanation:
There is a theorem about the sum of the measures of the angles of a triangle.
In this case, with the interior angle measures called a, b, and c, the theorem states:
Theorem:
The sum of the measures of the interior angles of a triangle is 180°.
a + b + c = 180°
Now we will prove the theorem and answer why a + b = d.
Look at angles c and d. They form a linear pair. Angles that form a linear pair are supplementary angles. By the definition of supplementary angles, the sum of the measures of angles c and d is 180°.
We have
c + d = 180° Eq. 1
By the theorem above, we have
a + b + c = 180° Eq. 2
Let's subtract Eq. 1 from Eq. 2:
a + b + c = 180°
- c + d = 180°
------------------------------
a + b - d = 0
a + b - d = 0
Add d to both sides.
a + b = d
That is a proof of the Exterior Angle Theorem.
The log flume ride lasts 8 minutes. This amount of time is one minute more than twice the length of time for the teacup ride.
How long does the teacup ride last?
The time for the teacup to last is D. m = 3.5 minutes.
What is an expression?An expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the number of minutes be m.
The amount of time is one minute more than twice the length of time for the teacup ride. This will be:
= (2 × m ) + 1 = 8
2m - 1 = 8
Collect like terms
2m = 8 - 1
2m = 7
Divide
m = 7/2
m = 3.5
The correct option is D.
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Answer:
d) m = 3.5 minutes
Step-by-step explanation:
Now we have to,
→ find the time the teacup ride last.
Forming the equation,
→ 2m + 1 = 8
Then the value of m will be,
→ 2m + 1 = 8
→ 2m = 8 - 1
→ m = 7/2
→ [ m = 3.5 min ]
Hence, ride lasts for 3.5 min.
What is the solution to the inequality? 3(x+5)>12
Answer:
x>-2
Step-by-step explanation:
3 times five is fifteen, which is larger than 12, so all x needs to be is be bigger negative 2.
Tell whether the data in the table can be modeled by a linear equation. Explain. A table listing pairs of x and y values. First pair. Negative 3 and 16. Second pair. Negative 1 and 10. Third pair. 1 and 4. Fourth pair. 3 and negative 2. Fifth pair. 5 and negative 8. The data be modeled by a linear equation because the rate of change constant. Question 2 If possible, write a linear equation that represents y as a function of x. If not possible, leave blank.
The table is a linear function and the equation is y = -3(x - 1) + 4
How to determine if the table represents a linear equation?From the question, we have the pairs to be
First pair = (-3, 16)Second pair.= (-1, 10)Third pair = (1, 4)Fourth pair = (3, -2)Fifth pair = (5, -8)From the above representations, we can see that:
As the values of x increase by +2, the values of y constantly increase by -6
This means that the table has a constant rate
By the definition of a linear function, the table represents a linear function
The linear equation of the functionIn (a), we have
x = +2
y = -6
The slope is calculated as
Slope = y/x
So, we have
Slope = -6/2
Evaluate
Slope = -3
The equation is then calculated as
Y = Slope * (X - x) + y
Where
(x, y) = (1, 4)
So, we have
y = -3(x - 1) + 4
Hence, the linear function is y = -3(x - 1) + 4
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Consider the line whose equation is y=-1/2x+3
any line that is perpendicular to this line is
Answer:
positive
Step-by-step explanation:
for a line to be perpendicular to another line, the slope must be reciprocaled and if its positive it becomes negative (vice versa)
y = -1/2x+3 = Line A
y = 2x+3 = PERPENDICULAR to Line A
(2x-3)²=4x solved using the equator formula
After solving the given equation using quadratic formula we gat solutions as 0.83 and 0.169
What is quadratic formula?
Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b±√(b²-4ac))/(2a).
On simplifying the given equation we get,
(2x-3)²=4x
4x²+9-12x = 4x
4x²-16x+9 = 0
Comparing with ax²+bx+c = 0
a = 4, b = -16, c = 9
Quadratic formula is:
[tex]\frac{-b +- \sqrt{b^2-4ac} }{2a}[/tex]
putting the values from question we get,
[tex]\frac{16 +- \sqrt{16^2-4(4)(9)} }{216}[/tex]
[tex]\frac{16 +- \sqrt{256-144} }{32}[/tex]
[tex]\frac{16 +- \sqrt{112} }{32}[/tex]
[tex]Solution 1 = \frac{ 16+ 10.58 }{32} = 0.83[/tex]
[tex]Solution 2 = \frac{16 - 10.58}{32} = 0.169[/tex]
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Complete question
(2x-3)²=4x solve using quadratic formula
Points A(-1, 2) and B(5,8) are the endpoints of AB. What are the coordinates of point C on AB such that AC is 2/3 the length of AB
The coordinates of point C on AB such that AC is 2/3 the length of AB is (2,0)
What is Pythagoras' Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are the rest of the two sides of that triangle ABC, AC being the hypotenuse).
To find out how long AC is, we must first find the length of AB.
According to Pythagoras’ theorem,
[tex]a^2 + b^2 = c^2[/tex].
Thus [tex]4^2 + 6^2 = c^2[/tex].
[tex]16 + 36 = c^2[/tex].
The square root of this is;
c = √52.
AB is 7.21 units long.
2/3 of 7.21 is 4.8
The coordinate that fits this is (2,0).
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please answer this following question.
on the triangle on the left, on the bottom left of that triangle it says,
[4(x +2)]
The two triangles are not similar to each other.
What is perimeter?The perimeter of the triangle is the sum of the lengths of all its sides.
The angle of triangle = 62
The two equal angles = [4(x +2)] and (5x - 7)
According to the question,
The Perimeter of triangle are;
[4(x +2)] + (5x - 7) + 62 = 180
4x + 8 + 5x - 7 + 62 = 180
9x + 63 = 180
9x = 117
x = 13
The other triangle is
6x + 62 + 6x + 6 = 180
12x + 68 = 180
12x = 112
x = 9.33
Hence, the two triangles are not similar to each other.
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Find the distance between the two points rounding to the nearest tenth (if necessary).
(6,7) and (4,−1)
Answer:
8.2 units (nearest tenth)
Step-by-step explanation:
Distance between two points
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where (x₁, y₁) and (x₂, y₂) are the two points.
Given points:
(x₁, y₁) = (6, 7)(x₂, y₂) = (4, -1)Substitute the given points into the distance formula and solve for d:
[tex]\implies d=\sqrt{(4-6)^2+(-1-7)^2}[/tex]
[tex]\implies d=\sqrt{(-2)^2+(-8)^2}[/tex]
[tex]\implies d=\sqrt{4+64}[/tex]
[tex]\implies d=\sqrt{68}[/tex]
[tex]\implies d=8.2 \; \sf (nearest\;tenth)[/tex]
Therefore, the distance between the two given points is 8.2 units to the nearest tenth.
Suppose a golf ball bounces off a wall at a point P, and that
line mis perpendicular to the wall at point P.
What is the measure of the angle of reflection?
A. 50°
B. 40°
C. 140°
D. 90°
The graph shows g(x), which is a transformation of f(x)= 1x1. Write the function rule for
g(x).
The most appropriate choice for function will be given by -
g(x) = -|x| is the correct function
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
f(x) = |x| is the given function.
f(x) has been transformed to g(x) according to the graph given in the figure
In the figure, the range is negative real number.
So the transformation g(x) = - |x|
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Question is stated in picture. Don’t forget to round to nearest hundreth!!
The volume of a cylinder is given by the following formula:
[tex]V=\pi r^2h[/tex]Where r is the radius and h is the height of the cylinder.
By replacing 8 for r and 6 for h into the above formula, we get:
[tex]V=\pi\times8^2\times6=1205.76[/tex]Then, the volume of the cylinder equals 1205.76 units³
11. The graph models the linear relationship between the cost for cleaning and the number of rooms to clean in a house of two different cleaning companies. 200 180 160 140 Home Helper 120 Cost (In dollars) 100 80 scueaky cleaners 60 40 20 0 1 2 10 3 4 5 6 7 8 9 Number of Rooms to Clean in House What is the cost (in dollars) when Squeaky Cleaners and Home Helpers clean the same number of rooms? A. $60 B. $120 C. $150 D. $210
In the graph you can see two variables: Cost and Number of rooms to clean in house.
You can find the cost when both cleaning companies clean the same number of rooms as the point when the value in the varibles (y-axis and x- axis) are the same in the lines of both companies (the point where the lines cross each other)
Then, the cost when both companies clean the same number of rooms is $150 (the number of rooms to clean is 5 in both companies)how many bit strings of length five either start with two zeros or end with two zeros? how many bit strings of length six either do not start with two zeros or do not end with two zeros? how many bit strings of length seven either start with four ones or end with four ones? how many bit strings of length eight do not start with a one or do not end with a one?
16 bit strings of length five either start with two zeros or end with two zeros are there; 32 bit strings of length six either do not start with two zeros or do not end with two zeros are there; 16 bit strings of length seven either start with four ones or end with four ones are there and 256
bit strings of length eight do not start with a one or do not end with a one are there.
A string is a combination which is made up of only two characters, either 1 or 0.
So, the combinations of the string can be found,
If the length of the bit string is 5, it means it will have 5 characters.
If this string either start with two zeroes or end with two zeroes. It mean there are only three positions are remaining which have two choices available for each place.
So, the total bit strings possible are,
= 2×(1×1×2×2×2)
= 16
16 such bit strings are possible.
If the length of the bit string is 6, it means it will have 6 characters.
If this string either do not start with two zeroes or do not end with two zeroes. It mean there are only four positions are remaining which have two choices available for each place.
So, the total bit strings possible are,
= 2×(1×1×2×2×2×2)
= 32
So, 32 such strings are possible.
Now, If the length of the bit string is 7, it means it will have 7 characters.
If this string either start with four ones or end with four ones. It mean there are only three positions are remaining which have two choices available for each place.
So, the total bit strings possible are,
= 2×(1×1×1×1×2×2×2)
= 16
So, 16 such strings are possible.
If the length of the bit string is 8, it means it will have 8 characters.
If this string either do not start with one and do not end with one. It mean there are only seven positions are remaining which have two choices available for each place.
So, the total bit strings possible are,
= 2×(1×2×2×2×2×2×2×2)
= 256
So, 256 such strings are possible.
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Estimate 70⎯⎯⎯⎯√3 to the nearest integer.
Answer:
Step-by-step explanation:
round up
√3 = √4
70-√4= 70-2
=68
Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint: (9,1) Midpoint: (-4,-6)
Answer:
(-13, - 6)
Step-by-step explanation:
Midpoint =(x₁ + x₂)/2, (y₁ + y₂)/2
(-4,-6) = (9+x)/2, (1+y)/2
9+x= - 4
X= - 13
1+y= - 6
Y= - 7
Ans=
(-13, - 6)
Deb wants to put up a fence around her garden.
The fence costs £3 per metre.
The fencing company charges £200 to install the fence.
What is the total cost of the fence for Deb's garden?
The total cost of fencing the garden will be 3x+200 where x is the perimeter of garden that is variable according to the length and breadth of the garden.
What is length?Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The metre serves as the foundational unit of length in the International System of Units.
What is Perimeter?A closed path that encompasses, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.
Here,
Let x be the perimeter to be fenced.
the cost is 3 rupees per meter.
so the equation will be= 3x+200
The total cost of fencing the garden will be 3x+200, where x is the garden's perimeter and is dependent on the garden's length and width.
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When creating a graph, it is important to _____ the x and y axis?
"When creating a graph, it is important to assign the x and y axis."
Assigning the x and y axes is crucial when making a graph because the x-axis is referred to as the line on a Cartesian coordinate system that runs horizontally. A point or line's separation from the y-axis can be determined using the x-axis. The y-axis displays a point's location on a Cartesian plane in the y (vertical) direction. Additionally, it serves as the origin (zero) point for calculating how far a point is from the x-axis.
What is Graph?A graph is a structure that resembles a set of objects in mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
What is x and y axis?Two parallel lines, known as axes (pronounced AX-eez), that are perpendicular to each other make up a coordinate grid. Typically, the term "x-axis" refers to the horizontal axis. The y-axis is the common name for the vertical axis. The origin is the location where the x- and y-axes intersect.
"When creating a graph, it is important to assign the x and y axis."
Because the x-axis is referred to as the line on a Cartesian coordinate system that runs horizontally, determining the x and y axes is essential when creating a graph. The x-axis can be used to calculate a point or line's distance from the y-axis. A point's position on a Cartesian plane is shown on the y-axis in the y (vertical) direction. It also acts as the origin (zero) point for determining a point's distance from the x-axis.
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after 5 seconds the height of the ballon is 20 feet
What is the equation of the line that passes through the point (-3,1) and has a slope of -3?
Answer:
Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.
Since line has a slope of -3, equation is y = -3x + c.
Substitute (-3,1) into the equation to find c.
1 = -3(-3) + c
c = -8
Hence, equation of line is y = -3x - 8.
determine the measure of angle j.
The measure of the value of ∠j is 10°.
What are a few properties of a triangle considering its angles?
A triangle's outer angle is the sum of its internal angles' two opposite sides.
The sum of two linear angles is supplementary.
Given, the three angles of the triangle are measured as (5x - 3)°,
(4x - 2)° and j°.
Also, the exterior angle of the triangle is (10x - 20)°.
Following the literature established above, considering that a triangle's outer angle is the product of its internal angles' two opposite sides, we have: (5x - 3) + (4x - 2) = 10x - 20 ⇒ 9x - 5 = 10x - 20 ⇒ 10x - 9x = 20 - 5
⇒ x = 15 --(i)
Again, since the sum of two linear angles is supplementary, we have using (i):
j + (10x - 20) = 180 ⇒ j + 150 - 20 = 180 ⇒ j = 10°
Therefore, the measure of the value of ∠j is 10°.
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(3x869)+(19x528)+428(3)(1049)=a
a=
The value of a in the equation (3x869)+(19x528)+428(3)(1049)=a is 1359555
How to evaluate the expression?From the question, the equation to evaluate is given as
(3x869)+(19x528)+428(3)(1049)=a
Rewrite the above equation to make it legible
So, we have the following equation
(3 x 869) + (19 x 528) + 428(3)(1049) = a
Evaluate the products in the expression
So, we have the following equation
2607 + (19 x 528) + 428(3)(1049) = a
Evaluate the other products in the expression
So, we have
2607 + 10032 + 428(3)(1049) = a
Remove the brackets in the equation
So, we have the following equation
2607 + 10032 + 1346916 = a
Evaluate the sum
1359555 = a
Rewrite as
a = 1359555
Hence, the solution to the equation is 1359555
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help me please
help me :>
Based on the graphs and equations given, the simultaneous equations can be solved to give x = 1.5 and y = 5.5.
How to solve the simultaneous equation?To solve the simultaneous equation, come up with the values of y using values of x in the given formulas:
For y = 3x + 1: the values of y will be:
When x = 1, then y will be:
= 3(1) + 1
= 4
When x = 2, then y will be:
= 3(2) + 1
= 7
When x = 3, then y will be:
= 3(3) + 1
= 9
For the equation, x + y = 7:
When x = 1, then y will be:
y = 7 - 1
= 6
When x = 2, then y will be:
= 7 - 2
= 5
When x = 3, then y will be:
= 7 - 3
= 4
When these are plotted on a graph, we find that the value of x is 1.5 and the value of y is 5.5. This is the point where the lines intersect.
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