In this problem, we are going to write and solve a system of equations based on a real world situation.
Last week, she did 1 load of laundry and 8 loads of dishes, and her parents paid her $26. The week before, she finished 3 loads of laundry and 8 loads of dishes, earning a total of $30.
To begin, we need to create variables for the unknown cost of each chore.
Let x represent laundry, and let y represent dishes.
From the first equation, we can write the equation:
[tex]x+8y=26[/tex]We can write the second equation as:
[tex]3x+8y=30[/tex]Together, we have the system:
[tex]\begin{cases}x+8y={26} \\ 3x+8y={30}\end{cases}[/tex]Multiply the first equation by -1, then add it to the second equation:
[tex]\begin{gathered} \begin{cases}-1(x+8y={26)} \\ 3x+8y={30}\end{cases} \\ \\ \begin{cases}-x-8y={-26} \\ 3x+8y={30}\end{cases} \\ \\ (-x+3x)+(-8y+8y)=-26+30 \\ 2x=4 \end{gathered}[/tex]We can divide the remaining equation by 2 on both sides:
[tex]\begin{gathered} \frac{2x}{2}=\frac{4}{2} \\ \\ x=2 \end{gathered}[/tex]Lada made $2 per load of laundry.
We can use the value of x in the first equation to find the value of y. Substitute x = 2:
[tex]2+8y=26[/tex]Subtract 2 from both sides:
[tex]8y=24[/tex]Divide by 8 on both sides:
[tex]y=3[/tex]Lada made $3 per load of dishes.
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°
Find the median AM of triangle ABC whose height point has the coordinates: [tex]A(0; 1), B(1; -4), C(5; 2)[/tex]
The value of the coordinates of the median AM is (0.5, -1.5)
How to find the median AM of the triangle?Given: A(0,1), B(1, -4), C(5,2)
Consider the image attached:
The distance AM is the midpoint of the distance AB. So we can use the midpoint formula:
Xm = (Xa + Xb) /2 and Ym = Ya + Yb/2
Where Xm and Ym are the x and y coordinates of the midpoint M
SInce A(0,1): Xa = 0, Ya = 1
Also B(1, -4); Xb = 1, Yb = -4
Xm = 0 + 1/2 = 1/2 = 0.5
Ym = 1 + (- 4)/2 = -3/2 = -1.5
Therefore, the coordinates of the median AM is (0.5, -1.5)
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a student has taken 6 tests and received scores of 88, 73, 81, 80, 79, and 94. the seventh test is coming up and the student wants to know what score is needed on the seventh test to have a mean score of 83. determine the score the student needs. show your work.
Solution:
Let the score for the seventh test be represented below as
[tex]=x[/tex]The mean score t be attained after the sevent tests is
[tex]mean=83[/tex]The scores from the 6 tests are given below as
[tex]88,73,81,80,79,94[/tex]To figure out the seventh score, we will do the calculation below
[tex]\begin{gathered} mean=\frac{additionofthescores}{number\text{ of tests}} \\ 83=\frac{88+73+81+80+79+94+x}{7} \\ 83=\frac{495+x}{7} \\ cross\text{ multpily} \\ 83\times7=495+x \\ 495+x=581 \\ x=581-495 \\ x=86 \end{gathered}[/tex]Hence,
The final asnwer is
[tex]\Rightarrow86[/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.
Do the interior angles of a quadrilteral always add up to the same thing? Explain why you think so.
Graph the image of the figure on the right under the given translation.T(3, -1) (x,y)
Answer:
The only image with edges at the given coordinates is;
Given the figure in the attached image.
we want to identify the image after a translation;
[tex]T(3,-1)(x,y)[/tex]Using one of the edges of the figure;
[tex](x,y)=(-4,0)[/tex]Applying the above translation we have;
[tex](-4,0)\rightarrow(-4+3,0-1)=(-1,-1)[/tex]The edge of the image would be at;
[tex](-1,-1)[/tex]Therefore, the only image with edges at the given coordinates is;
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.
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)
Find the number that makes the ratio equivalent to 3:5
Answer:
6:109:1512:20
Step-by-step explanation:
Find the number that makes the ratio equivalent to 3:5
multiply or divide 3 (numerator) and 5 (denominator) by the same number, the result of the division will be equal, therefore equivalent
6:10
9:15
12:20
the result of all ratios is 0.6, therefore equivalent
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
The manager at the local auto shop has found that the probability that a car brought into the shop requires an oil change is 0.68, the probability that a car brought into the shop requires brake repair is 0.32, and the probability that a car requiresboth anoil change and brake repair is 0.11. For a car brought into the shop, determine the probability that the car will require an oil change or brake repair.The probability that the car requires an oil change or brake repair is
Remember that
P(A or B)=P(A)+P(B)-P(A and B)
In this problem, we have that
Event A and Event B are not independent
we have
P(A)=0.68
P(B)=0.32
P(A and B)=0.11
substitute
P(A or B)=0.68+0.32-0.11
P(A or B)=0.89
The answer is 0.89w + 2 < 24 solve for w and simplify your answer as much as possible
Answer: w<22
1. Group all constants on the right side of the inequality
2. Subtract from both sides
3. Simplify the arithmetic
4. Simplify the arithmetic
Answer:
w < 22
Step-by-step explanation:
w + 2 < 24
Step 1 : Subtract 2 on both sides.
w + 2 - 2 < 24 - 2
w < 22
Hence, simplified
What is 4x + y = -3?
Answer:x=
−1/4y+ −3/4
Step-by-step explanation
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.
after 5 seconds the height of the ballon is 20 feet
(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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Debra makes 26.40 from selling 52.8 ounces of lemonade. Find the unit price in dollars per ounce. If necessary, round your answer to the nearest cent.
The unit price in dollars per ounce is 0.5 dollars per ounce.
According to the question,
We have the following information:
Debra makes 26.40 dollars from selling 52.8 ounces of lemonade.
Now, to convert this into dollars per ounce, we will divide the total amount by the number of ounces of lemonade:
Dollars per ounce = 26.40/52.8
Dollars per ounce of lemonade = 0.5
Now, we can also convert this into cent.
We know that 100 cent make 1 dollar.
So, 0.5 cents will make (0.5*100) cents or in other words, 50 cents.
Now, it will be 50 cents per ounce.
Hence, the units price of lemonade in dollar per ounce is 0.5.
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Every rational number is positive.
A. True
B. False
Answer:
Step-by-step explanation: it is true because when the numerator and denominator both are positive integers both are negative integers it is a positive rational number.
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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How is adding positive and negative integers different from adding only positive integers on a number line?
1) To understand how that works, let me draw a number line:
If we only add positive numbers like 2 +3 = 5, 6+8 =14, etc. we'll only get a positive result (right to the zero) on the number line, we are moving to the right
2) If we add positive and negative numbers, for example:
2 +(-3) =2 -3=-1
0+(-1)= -1
6+(-2)= 4
On the number line, we are starting from one point and moving to the left.
if the ratio of similarity of the figures above is 2/3, then what is the ratio of the perimeters of the two figures?
Perimeter = side 1 + side 2 ´+ side 3.
Triangle 1
Perimeter = 6 + 8 + 10
= 24
Triangle 2
Perimeter = 9 + 12 + 15
= 36
Ratio
24/36 = 2/3
The ratio of the perimeters is also 2/3
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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(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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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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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
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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CAN Someone pleasde help me !!!!!
Answer: It will take 3.5-4 months
Step-by-step explanation:
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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