To use the substitution method to solve the system, we need to solve one of the equations for x or y in terms of the other variable, and then substitute that expression into the other equation to get an equation in one variable that we can solve.
Let's solve the first equation for x in terms of y:
x + 4y = -9
x = -4y - 9
Now we substitute this expression for x into the second equation:
2x + 5y = -6
2(-4y - 9) + 5y = -6
Simplifying this expression, we get:
-8y - 18 + 5y = -6
-3y = 12
y = -4
Now we can substitute this value of y into either of the original equations to find x. Let's use the first equation:
x + 4y = -9
x + 4(-4) = -9
x - 16 = -9
x = 7
Therefore, the solution to the system is x = 7, y = -4.
Now let's look at the answer choices and see which one matches the equation we got by substituting x = -4y - 9 into the second equation:
A) 2(4-9)+ 5y-6 = -10 + 5y - 6 = 5y - 16
B) 21-4y-9)+5% -6 = -4y + 6
C) 2x+5(4-9)=-6 = 2x - 25 = -6
D) 2x+5(-4y-9)=-6 = 2x - 20y - 45 = -6
The answer choice that matches our equation is D), 2x + 5(-4y - 9) = -6.
construction worker cuts a pace of electrical wires that is 7/8 of an inch in the length heat and cuts and other piece that is 5/8 of an inch in length what is the combined length of the pieces of wire
The combined length of the two pieces of wire is 3/2 inches or 1 and 1/2 inches.
To find the combined length of the pieces of wire, we need to add the lengths of the two pieces of wire together.
The first piece of wire is 7/8 of an inch long.
The second piece of wire is 5/8 of an inch long.
To add the two fractions, we need to find a common denominator. The smallest number that both 8 and 5 will divide into is 40.
7/8 can be rewritten as 35/40 (multiply the numerator and denominator by 5)
5/8 can be rewritten as 25/40 (multiply the numerator and denominator by 5)
Now we can add the two fractions:
35/40 + 25/40 = 60/40
Simplifying the fraction:
60/40 = 3/2
Therefore, the combined length of the two pieces of wire is 3/2 inches or 1 and 1/2 inches.
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HELP ASAP/ Given line `t` on the graph provided, choose all points that lie on the line that passes through point `P` and is perpendicular to line ' t'
(choose all that apply)
All points that lie on the line that passes through point `P` and is perpendicular to line ' t' are: (4, -1) and (6, -5)
What is the equation of the line?The equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
Using two coordinates on line t as: (-4, 1) and (2, 4), the slope of the line t is:
Slope = (4 - 1)/(2 + 4)
Slope = 3/6
Slope = 1/2
Equation of line t is:
(y - 1)/(x + 4) = 1/2
y - 1 = x/2 + 2
y = ¹/₂x + 3
Thus, slope of line passing through P and perpendicular to t is: -1/(1/2) = -2
Now, coordinates of point P is (3, 1). Thus:
Equation passing through point P and perpendicular to line t is:
(y - 1)/(x - 3) = -2
y - 1 = -2x + 6
y = -2x + 7
The only coordinates that fits into this are (4, -1) and (6, -5)
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What is the area of the composite figure
Answer:
34 units²
Step-by-step explanation:
triangle=1/2×5×2=5
other triangle at the right=5
square 6 ×5= 30
unshaded square= 3×2=6
30-6=24
total=5+5+24=34units²
Use the drawing tool(s) to form correct answer on the provided plot
Shawna oversees tour guides at a community college.each week she selects one day to record the number of tours each guide leads for prospective students. The results from last week are presented in the box plot below.
The data for this week is shown below and gives the number of tours led by each tour guide
{ 3,5,3,4,9,7,10,7,3,6,2,5}
Complete the box plot based on the data given above.
A construction of the box-and-whisker plot based on the data is shown below.
What is a box-and-whisker plot?In Mathematics and Statistics, a box plot is also known as a box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the data (information) provided above, the five-number summary for the given data set include the following:
Minimum (Min) = 2.First quartile (Q₁) = 3.Median (Med) = 5.Third quartile (Q₃) = 7.Maximum (Max) = 10.In conclusion, we can reasonably infer and logically deduce that the maximum number is 10 while the minimum number is 2, and the median is equal to 5.
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a. If this trend continues, predict the percent of U.S.house- holds with an Internet subscription in 2025. graph it
b.Explain any issues with your answer to part c.
The requried, predicted percentage of U.S. households with an Internet subscription in 2020 is approximately 88.3%.
To find the number of subscriptions in the year 2020, we need to find the value of y when x = 10 (since x is the number of years after 2010).
Substituting x = 10 into the equation y = 1.56x + 72.7, we get:
y = 1.56(10) + 72.7
y = 15.6 + 72.7
y = 88.3
Therefore, the predicted percentage of U.S. households with an Internet subscription in 2020 is approximately 88.3%.
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Solids Applied Problem
Find the volume of 1 coin from the stack below. Each coin has a radius of 0.5 in and the coins
are offset by 1 in. The slant is 7in long. Show your work.
The amount of volume of 1 coin in the stack underneath is 0.433 cm³. The distance between the coins is 1 in, and each coin having a radius approximately 0.5 in. 7 inches make up the tilt.
Any three-dimensional solid's volume is the area it takes up. The volume of these solids include cubes, cuboids, cones, cylinders, and spheres. Different shapes have different volumes. We have looked at a variety of three-dimensional solids and shapes, including cubes, cuboids, cylindrical objects, cones, and and more.
V= πD²×h/4
=π0.5²×7/4
= 0.433 cm³
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The position of a particle on the x-axis at time t, t >0, is ln(t). The average velocity of the particle for 1 <= t <= e is.
A. (1/e) - 1
B. 1/(e - 1)
C. e
D. e - 1
Please show work
Answer:
Perdón no te puedo ayudar no entiendo
Step-by-step explanation:
To find the average velocity of the particle over the interval [1, e], we need to calculate the net displacement divided by the time interval.
Given the position function x(t) = ln(t), let's find the displacement by evaluating x(e) and x(1):
x(e) = ln(e) = 1
x(1) = ln(1) = 0
So, the net displacement is 1 - 0 = 1.
The time interval is e - 1.
Therefore, the average velocity is:
average velocity = (net displacement) / (time interval)
average velocity = 1 / (e - 1)
The correct answer is B. 1/(e - 1).
1.what is the cost of three 5kg bags of Rice at ¢2 par kg.
2.how many 2km price can I cut off a string of one meter long.
3. what fraction of a litre is 259 ml?
4.write 60ps as a decimal of ¢240.
5. how many groups of 4 mark 20.
6.an orange ¢150 .how much do 9 orange coast.
7. find the product of 35 and 12 .
8.how many 180g could be obtained from kg?
1. Using mathematical operations, the cost of three 5kg bags of rice at ¢2 per kg is ¢30.
2. From the 2km piece, you can cut 2,000 pieces with each one meter long.
3. The fraction of a liter that is 259 ml can be written as ²⁵⁹/₁₀₀₀.
4. 60ps expressed as a decimal of ¢240 is 0.25.
5. The groups of 4 marks in 20, based on a division operation, is 5.
6. If an orange costs ¢150, by multiplication, 9 oranges will cost ¢1,350.
7. The product of 35 and 12, which is a multiplication operation, is 420.
8. Using division operation, from 1 kg, one could obtain 5.55 units of 180g each.
What are mathematical operations?The four basic mathematical operations are addition, subtraction, division, and multiplication.
In this situation, the mathematical operations involved are division and multiplication.
1) The cost of price per kg = ¢2
The number of bags bought = 3
The weight per bag = 5kg
The total weight of 3 bags = 15kg (5 x 3)
The total cost = ¢30 (¢2 x 15)
2) The total length of the piece = 2km
1 km = 1,000 meters
2km = 2,000 meters
The length of each string = 1 meter
The number of strings = 2,000 (2,000 ÷ 1)
3) 1 liter = 1,000 ml
259 ml/1,000 ml = 259/1,000
= ²⁵⁹/₁₀₀₀
4) 60p as a decimal of ¢240
= 0.25 (60 ÷ 240)
5) 20 ÷ 4 = 5
4 x 5 = 20
6) The cost per orange = ¢150
The number of oranges bought = 9
The total cost of 9 oranges = ¢1,350 (¢150 x 9)
7) The product of 35 and 12 = 420 (35 x 12)
8) The quantity of each unit = 180g
The total quantity = 1 kg
1 kg = 1,000 g
5.55 (1,000 ÷ 180)
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what is the radius of the circle shown below x^2+y^2-8x-10y-8=0
Answer:
r = 7
Step-by-step explanation:
equation of circle is (x - a)² + (y - b)² = r²
where a is x-coordinate of centre of circle, b is y-coordinate of centre of circle, r is the radius. radius = half of diameter.
x² - 8x + y² - 10y = 8
we need to complete the sqaure for both x and y
x² - 8x = (x - 4)² = x² - 8x + 16, which is 16 more than x² - 8x. so we need to subtract that 16.
we now have (x - 4)² - 16.
now do the same with y
(y - 5)² = y² - 10y + 25, which is 25 more than y² - 10y. so we need to subtract 25.
we now have (y - 5)² - 25.
back to our full equation.
(x - 4)² -16 + (y - 5)² - 25 = 8
(x - 4)² + (y - 5)² - 41 = 8
(x - 4)² + (y + 5)² = 49 = r²
radius r = √49 = 7
If Richard's monthly deposit fee is R69, 95 per R100 what would be the total bank charges for R4200?
Joe wondered whether the days of the week of health clinic appointments at his clinic had an even distribution from Monday through Friday, so he took a random sample of
500
500500 health clinic appointments and recorded their days of the week. Here are his results:
Day Monday Tuesday Wednesday Thursday Friday
Appointments
115
115115
100
100100
115
115115
100
100100
70
7070
He wants to use these results to carry out a
�
2
χ
2
\chi, squared goodness-of-fit test to determine if the distribution of days of the week of the appointments disagrees with an even distribution.
What are the values of the test statistic and P-value for Joe's test?
The test statistic is 14.5 and the P-value is less than 0.05. Therefore, we have evidence to suggest that the distribution of days of the week of the appointments disagrees with an Even distribution.
To carry out the chi-squared goodness-of-fit test, we need to calculate the expected number of appointments for each day if there were an even distribution. Since there are 5 days of the week, each day would have an expected value of 100 (i.e., 500 appointments / 5 days = 100 appointments per day).
Day | Monday | Tuesday | Wednesday | Thursday | Friday
Observed | 115 | 100 | 115 | 100 | 70
Expected | 100 | 100 | 100 | 100 | 100
To calculate the chi-squared test statistic, we use the formula:
χ2= ∑ (observed − expected)^2 / expected
Plugging in the observed and expected values, we get:
χ2= [(115 - 100)^2/100] + [(100 - 100)^2/100] + [(115 - 100)^2/100] + [(100 - 100)^2/100] + [(70 - 100)^2/100]
= 2.75 + 0 + 2.75 + 0 + 9
= 14.5
To find the P-value, we need to use the chi-squared distribution table with 4 degrees of freedom (5 days of the week minus 1 for the expected value). Using the table, we find that the P-value for a chi-squared statistic of 14.5 with 4 degrees of freedom is less than 0.05. Therefore, we reject the null hypothesis that the appointments have an even distribution from Monday through Friday.the test statistic is 14.5 and the P-value is less than 0.05. Therefore, we have evidence to suggest that the distribution of days of the week of the appointments disagrees with an even distribution.
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Perform the indicated operation:
(4 + 2i) (1 + 5i)
-6 +22i
6-221
-14 + 18i
6+22i
Answer:
-235+84i
Step-by-step explanation:
I hope this is what you were looking for.
Question 1
Find the volume of the prism, Round your answer to the nearest tenth, if necessary.
13 m
3m
5m
Need help with this question?
The volume of the prism is 195 cubic meters.
To find the volume of the prism, we need to multiply the length, width, and height of the prism.
Length = 13 m
Width = 3 m
Height = 5 m
Volume = Length x Width x Height
Volume = 13 m x 3 m x 5 m
Volume = 195 cubic meters
find the median of each of the following scores
x f fc
300-309 9 9
310-319 20 29
320-329 24 53
330-339 38 91
340-349 48 139
350-359 27 166
160-169 17 183
170-179 6 189
The median score, considering the frequency distribution in this problem, is given as follows:
334.5.
How to obtain the median of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.
The total number of observations in the data-set is given as follows:
189.
Hence the position in the cumulative frequency table of the median element is given as follows:
0.5 x (189 + 1) = 95.
Which is in the following interval:
330-339.
Hence the median is of 334.5, as it is the middle value of the interval.
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Tanya has captured many purple-footed bog frogs. She weighs each one and
then counts the number of yellow spots on its back. This trend line is a. fit for these data.
O A weak
B. strong
C. parabolic
D. negative
Answer:
B) strong
Step-by-step explanation:
The correlation coefficient is close to 1, meaning it is both a strong correlation and a positive correlation.
name the leading coefficient and degree of the polynomial 4xy^8
(a) The leading coefficient is 4
(b) The degree is 8
How to determine the leading coefficient and the degree of the expressionFrom the question, we have the following parameters that can be used in our computation:
4xy⁸
Consider an expression ax where the variable is x
The leading coefficient of the variable in the expression is a
Using the above as a guide, we have the following:
The leading coefficient is 4
Consider an expression axⁿ where the variable is x
The degree of the variable in the expression is n
Using the above as a guide, we have the following:
The degree is 8
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Srekar needs to increase the length, width, and height of the prism below by 2 inches. The original prism has a length of 3 inches, a width of 2 inches, and a height of 1 inch. A prism has a length of 3, height of 1, and width of 2. Which statements about the new prism are true? Select three correct answers. The new prism will have a length of 5 because 3 + 2 = 5. The new prism will have a width of 4 because 2 + 2 = 4. The new prism will have a height of 2 because 1 times 2 = 2. The volume will increase by 6 because 2 times 3 = 6 and each of the 3 dimensions is increased by 2. Srekar could increase the volume by the same amount by just adding 6 to the height instead of 2 to each side. The volume of the new prism will be 20 times 3 = 60 because there will be 20 cubes in each layer and the height will be 3 so there will be 3 layers of 20 cubes each.
The three accurate statements concerning the new prism are as follows:
The new prism will possess a length of 5, which can be derived from the addition of 3 and 2 resulting in 5.The new prism will possess a width of 4, obtained by adding 2 and 2, yielding 4.The volume will experience a growth of 6 units, as each of the three dimensions is increased by 2.
This can be calculated by multiplying 2 by 3, resulting in an increase of 6.
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Help with te question pls.P.S. got reward
The amount of water that flows into the tank each minute is given as follows:
0.56 cm.
How to obtain the volume of a rectangular prism?The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:
Volume = length x width x height.
The dimensions for this problem are given as follows:
45 cm, 50 cm and 38 cm.
Hence the volume of the tank is given as follows:
V = 45 x 50 x 38
V = 85,500 cm³.
Three-fifths of the volume is given as follows:
3 x 85500/5 = 51300 cm³.
The height associated with 3/5 of the volume is given as follows:
50 x 38 x h = 51300
h = 51300/(50 x 38)
h = 27 cm.
This means that 27 - 13 = 14 cm flew into the tank in 25 minutes, hence the minute rate is given as follows:
14/25 = 0.56 cm.
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HELP ME QUICK. paul is thinking of a number. ⅖ of this number is 14 what is the number??
Answer:
Step-by-step explanation:
If we know that 2/5 of the number is 14, 5/5 must be the answer Paul is thinking of.
= (14/2) x 5 <---- This is 1/5 of the number
= 35
∴, the number Paul is thinking of if 35
How many multiples of both 2 and 5 are there in between 34 and 417?
The number of multiples of both 2 and 5 that are there between 34 and 417 is given as follows:
39.
How to obtain the multiples?The rules for the multiples of 2 and 5 are given as follows:
Multiples of 2: numbers finished in 0, 2, 4, 6, 8.Multiples of 5: numbers finished in 0 and 5.Hence the numbers that are multiples of both 2 and 5 finish in zero, which are the multiples of 10.
Then the divisions are given as follows:
417/10 = 41. -> integer part.34/10 = 3 -> integer part.Hence the number of multiples is given as follows:
41 - 3 + 1 = 39.
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sphere a has a radius of r feet. sphere b has a radius of 2r feet. sphere c has a radius of 3r feet. write the appropriate values to complete the statements.
The volume of Sphere A is __ the volume of Sphere B.
The volume of Sphere C is __ times the volume of Sphere A.
1/27 1/9 1/8 1/4 2 8 9 27
Answer: 3r
Step-by-step explanation: because 2r+1r=3r
6th grade of a school with a total of 90 students. In the year-end summary, the number of good students is equal to 1/6 of the students in the whole grade, the number of good students is equal to 40 of the students in the whole block, the average number of students is equal to 1/3 of the number of students in the whole grade. is the weak student again, calculate the number of students in each category
There are a total of 15 good students, 35 weak and 40 in bad shape if number of good students are fraction of 1/6th of total students.
As we know that the total number of students are 90.
Good students are fraction of 1/6th of total students.
Good students= 1/6x90
Good students=15
There are 40 good students in a whole block, so X = 40.
In the whole grade, average number of students is 1/3 of students in whole grade.
Students in each class = 1/3x90
Students in each class = 30
Students who are not good in economics and government = 90-40
Students who are not good in economics and government = 50
As the total number of students is sum of good students and weak students.
15+Weak students =90-40
15+Weak students=50
Weak students=50-15
Weak students=35
So, total of 15 good students, 35 weak and 40 in bad shape.
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For f(x) = √(x+4) , what is the value of the function when x = 8 ? Round to the nearest hundredth.
NEED ANSWER ASAP!!
Answer:
exact form : 2√3
decimal form : 3.46410161… or 3.46
hope this helps you!
Answer:
The value of the function is [tex]\sqrt{12}[/tex]. Rounded to the nearest hundredth, the answer is 3.46
Step-by-step explanation:
We are given the value of x, so we simply have to evaluate the function:
[tex]f(x)=\sqrt{x+4}[/tex]
Substitute 8
[tex]f(8)=\sqrt{8+4}[/tex]
Add in the radical
[tex]\sqrt{12}[/tex]
The value of the function is sqrt(12).
Rounded to the nearest hundredth: [tex]3.46[/tex]
For the following stock investment, find (a) the total
purchase price, (b) the total dividend amount, (c) the
capital gain or loss, (d) the total return, and (e) the
percentage return. Ignore broker and SEC fees.
(a) What is the total purchase price?
4
Number of shares
Purchase price per share
Dividend per share
Sale price per share
60
$40
$2
$87
Answer:
can you be more clear
Step-by-step explanation:
what exactly does question need
Shantae's living room is 20.2 metres long and its width half the size of its length. What is the difference between the length and width of her living room?
Enter a positive value for n that makes this statement true: 1 x n is greater than 1 but less than 2
A positive value for n that makes the statement true is n = 1.5.
We need to find a positive value for n that satisfies the given inequality: 1 < 1 x n < 2.
Step 1: Choose a value of n such that it's greater than 1 when multiplied by 1.
Step 2: Ensure the chosen value also makes the product less than 2 when multiplied by 1.
Let's try n = 1.5:
1 x 1.5 = 1.5
Now, let's check if it satisfies the inequality:
1 < 1.5 < 2
Yes, it does. So, a positive value for n that makes the statement true is n = 1.5.
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(When a side has a measurement that is a mixed number, what do you need to do to use it in the formula: area = length x width?)
The sides of the rectangle should be in improper fractions, to calculate the area.
When a side has a measurement that is a mixed number, it's recommended to convert it to an improper fraction before using it in the formula for area.
To convert a mixed number to an improper fraction, you multiply the whole number by the denominator of the fraction part and add the numerator.
Then, you put the result over the original denominator.
Once you have the sides of the rectangle as improper fractions, you can proceed to calculate the area using the formula: area = length x width.
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el area de la base de un cilindro es de 40 pi m2. expresa el volumen en funcion de la altura
The volume of the cylinder, when expressed as a function of the height of same cylinder, is V ( h ) = 40 h ft ³.
How to express the volume of the cylinder ?The volume V of a cylinder is given by the formula:
V = Area of the base of the cylinder x height of the cylinder
Given that the area of the base A is 40 ft², you can substitute this into the formula to express the volume as a function of height:
V ( h ) = 40 ft ² x h
V ( h ) = 40h ft ³
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#11) Determine the period of the following trigonometric function y =
a) 360 b) 180°
c) 360
c) 120
d) 60*
The solution is: the period for the graph of y = cos (0) is:
c.360
We have the following equation:
y = cos (0)
The first thing you should know is that the period of a function is that value for which the function repeats itself.
We have then:
y = cos (0) = 1
y = cos (360) = 1
Therefore, the period is 360.
Answer:
the period for the graph of y = cos (0) is:
c.360
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complete question:
What is the period for the graph of y=cos(0)? (Sketch a graph to help determine the answer.)
a.180
b.90
c.360
d.270
The First Chicago Bank is reviewing its service charges and interest-paying policies on checking accounts. The daily balance of a checking account is defined to be the balance in the checking account at 2:00pm.
The bank has found that for all personal checking accounts the mean of all the daily balances is $ 900 and the standard deviation is $175.
In addition, the distribution of personal checking account daily balances can be approximated very well with a normal model.
