The system of equations for the given conditions in question includes equation: 3.40 = 0.05x + 0.1y + 0.25z, and 2x = z. and we have 2 nickels, 23 dimes, and 4 quarters.
What is system of equations?
A system of equations is a collection of some equations with one or more numbers of variables. Systems of equations have solutions that are either the variable mappings that satisfy each component equation or the intersections of all of these equations.
Let the quantities of nickels, dimes, and quarters are x, y, and z respectively.
We know that, 1 nickel = $0.05, 1 dime = $0.1, and 1 quarter = $0.25
So, the values of nickels, dimes, and quarters would be value of one times total quantity.
Nickels = 0.05x, dimes = 0.1y, and quarters = 0.25z
As given in the question, the total value is 3.40
So, we get equation:
3.40 = 0.05x + 0.1y + 0.25z
Also it is given that there are twice as many nickels than quarters.
2x = z
Combining above two equations
3.40 = 0.05x + 0.1y + 0.25(2x)
3.40 = 0.05x + 0.1y + 0.5x
3.40 = 0.55x + 0.1y
Lets put 2 in place of x, we get y
(3.40 - 1.1)0.1 = y
y = 23.
Now, putting values of x, y in equation to get value of z
3.40 = 0.05(2) + 0.1(23) + 0.25z
3.40 = 0.1 + 2.3 + 0.25z
(3.40 - 2.4)/0.25 = z
z = 4
Therefore, we have 2 nickels, 23 dimes, and 4 quarters.
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Find the equation of the line passing through points (6,0) and (-1,14).
Oy = 6x
y = -2x + 12
y = -2x + 14
y = 2x + 10
Answer:
y = - 2x + 12
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (6, 0 ) and (x₂, y₂ ) = (- 1, 14 )
m = [tex]\frac{14-0}{-1-6}[/tex] = [tex]\frac{14}{-7}[/tex] = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (6, 0 )
0 = - 12 + c ⇒ c = 0 + 12 = 12
y = - 2x + 12 ← equation of line
lim
x→ pi/4
(sec x)/(4x^2 -5x)
The correct answer for the limit expression is √2 (π/4)(π - 5).
What is limit?
In mathematics, the value of the limit of a function always approaches as input and finally it approach to some value. It is used for the calculation of the continuity function, derivatives or calculus.
According to the question, the value of the variable 'x' should be substituted in the limit expression.
Now, the required expression will be:
[tex]\lim_{x \to \\pi /4} (secx)(4x^{2} -5x) = sec(\pi/4)(4(\pi /4)^{2} -5(\pi /4))[/tex]
Now, the value of the sec(pi/4) is √2
⇒ √2((π²/4)-5(π/4)) = √2 (π/4)(π - 5)
Hence, the correct answer for the limit expression is √2 (π/4)(π - 5).
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The point (-3,-2) is rotated 180 degrees about the origin. The coordinates of its image are:A. (−3,2)B. (3,2)C. (−2,−3)D. (2,3)
Given point :
(-3, -2)
When the rotation is about 180 degree about the origin then a point M(h, k)
will become M'(-h, -k)
So, the point (-3, -2) will become (-(-3), -(-2)) that is (3, 2)
Answer : Option (B)
Think about your answers to these questions. Then write a summary of your findings below.1. How do you decide which of two numbers is greater when...a. both numbers are positive?b. both numbers are negative?c. one number is positive and one number is negative?
1. a)
Given:
Both numbers are positive.
Aim:
We need to find which one of the two numbers is greater than the other.
Explanation:
On a number line, numbers always increase so numbers to the right are greater than numbers to the left.
Mark the given points on the number line and find which number is right of another. numbers to the right are greater than numbers to the left.
For example.
The positive numbers are 17 and 20.
20 to the right are greater than 17 to the left
20 is greater than 17.
1. b)
Given:
Both numbers are negative.
Aim:
We need to find which one of the two numbers is greater than the other.
Explanation:
On a number line, numbers always increase so numbers to the right are greater than numbers to the left.
If both numbers are negative, the number closer to zero is the bigger number.
For example.
The negative numbers are -10 and -5.
-5 is closer to zero.
-5 is greater than -10.
1, c).
Given:
one number is positive and one number is negative
Aim:
We need to find which one of the two numbers is greater than the other.
Explanation:
On a number line, numbers always increase so numbers to the right are greater than numbers to the left.
The positive numbers are always to the right are greater than the negative numbers to the left.
Positive numbers are greater than negative numbers.
For example.
The positive number is 5 and the negative number is -8.
5 is greater than -8.
If ABC is reflected across the z-axis to get the AA'B'C', what is the y-coordinate of C'? Enter the answer in the box.
The horizontal and vertical axes are the two axes of the coordinate plane.
The origin is the location where these two axes come together. What is the y-coordinate of C' if ABC is mirrored across the z-axis to produce AA'B'C'?
Answer :
(-3,2)
Detailed explanation:
The right response is C (-3,2). The bold line moving up and down in the middle of the page is the y axis. If you could take up the triangle and turn it on its side, you could. In Point C's landing zone (-3,2).
Point C is situated two spaces to the right of the y-axis, as you can also see. The x axis is still three spaces below it.
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A system of inequalities is shown.Which system is represented in the graph? y > –x2 – x + 1y < 2x2 + 3 y ≤ x2 – x + 1y < 2x2 + 3 y ≥ x2 – x + 1y ≤ 2x2 + 3 y ≥ –x2 – x + 1y > 2x2 + 3
The system of inequatilies that is represented in the graph is:
y ≥ –x² – x + 1
y > 2x² + 3
We can confirm this statement since the first equation implies that the system doesn't include any point bellow the parabola y = -x² - x + 1, and the second equation implies that the system must include only points above the parabola y = 2x² + 3
I have to find out at which points the lines intersectY= .5x+3 & Y= 2x-9
SOLUTION
We want to find out at which points the lines
[tex]\begin{gathered} y=0.5x+3\text{ and } \\ y=2x-9 \end{gathered}[/tex]intersect.
To do this, we have to solve the equations simultaneously and look for the values of x and y.
This becomes
[tex]\begin{gathered} y=0.5x+3\ldots\ldots\ldots\text{.}\mathrm{}eq\text{ 1} \\ y=2x-9\ldots\ldots\ldots\ldots\text{.}\mathrm{}eq\text{ 2} \\ \text{subtracting equation 2 from 1, we have } \\ y-y=(0.5x-2x)+(3-(-9) \\ 0=-1.5x+(3+9) \\ 1.5x=(3+9) \\ 1.5x=12 \end{gathered}[/tex]Dividing both sides by 1.5, we get x, this becomes
[tex]\begin{gathered} \frac{1.5x}{1.5}=\frac{12}{1.5} \\ x=8 \end{gathered}[/tex]To get y, we substitute the x for 8 into equation 1 or 2. Let us use equation 1, we have
[tex]undefined[/tex]Select all the intervals where h is increasing A:-1.5< x < -0.5B: 0 < x <1c: 3.5 < x <4D none of the above
So,
We can identify that the function is increasing when it goes up.
In this graph, we can notice that the graph goes up in the intervals:
[tex]-1.5As the function increases in that whole interval, the correct answers are A and B.Please help me with my calculus homework :)
Given
Answer
Let the side of square be s
s = 10 ft
[tex]\Delta s=\pm0.1ft[/tex][tex]\begin{gathered} A=s^2 \\ \frac{dA}{ds}=2s \\ \text{ now error in area is} \\ dA=\frac{dA}{ds}\Delta s \\ dA=(2s)\pm0.1 \\ dA=2(10)(\pm0.1)=\pm2ft^2 \end{gathered}[/tex]PLEASE CAN SOMEONE HELP ME PLEASE !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Fill in the gap in the equation below by
completing the square.
2
x² +14x+55= (x + 7)² +
The correct value of the equation that's illustrated will be x² + 14x + 55= (x + 7)² + 6
How to illustrate the information?It should be noted that an equation can be used in order to show the relationship between the variables.
It should be noted that (x + 7)² will be:
= (x + 7)(x + 7)
= x² + 7x + 7x + 49
= x² + 14x + 49
Therefore, x² 14x + 55 - (x² + 14x + 49) = 6
In conclusion, the answer in the box is 6.
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Write the following expression using a single exponent. 7^(4))^(3) x7^(7)
Answer:
7⁷¹
Step-by-step explanation:
Let's do it this way
7⁴^³ × 7⁷
Let's firstly apply indices since the base is the same
7⁴^³+ (⁷)
(4³ = 4×4×4 can be rewrite)
7⁴×⁴×⁴ + ⁷
7⁶⁴+⁷
= 7⁷¹
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Answer:
Raise 7 to the power of 4
Step-by-step explanation:
2401
the volume of a volleyball is 288 cubic inches. What is the radius of the volleyball, to the nearest tenth of an inch?
The radius of the volleyball to the nearest tenth of an inch is 8.3
How to calculate the radius of the volleyball ?The formula is
= √ 3v/4π
volume(v) = 288
π = 3.142
= √ 3×288/4×3.142
= √ 864/12.6
Next step is to get the square root of 68.6
= √ 68.6
= 8.29
Hence the radius of the volley ball is 8.3 inches
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Use the rate and the amount of water pumped after 13 minutes to find how much will have been pumped into pool after 14.5 minutes? The unit rate is 24 gal/min so 1.5 minutes after 13 minutes, an additional gallons will be pumped in
An additional 36 gallons of water will be pumped into the pool past 13 minutes
Constant rate of flow: The definition of a constant rate of flow rate shows how fluid of a certain volume moves through a segment in a specified amount of time. Instead of measuring how quickly a fluid moves from point A to point B, the motion of fluids is examined by figuring out its flow rate. Specifically, how much fluid volume moves from point A to point B in a given amount of time.
Time for which water has been pumped into the pool = 13 minutes
Rate of flow of water = 24 gal/min
So, water pumped in 1.5 minutes = 24*1.5 = 36 gallons
Total water pumped in the pool in 14.5 minutes = 24*14.5 = 348 gallons
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Use your calculator on the following data X1=3, Y1=7, X2=4, Y2=8, X3=5, Y3=10.
Determine (1) correlation, (2) slope of the regression line, (3) y-intercept of the regression line:
From the given data-set, we have that:
The correlation coefficient is of: r = 0.982.The slope of the regression line is of: 1.5.The intercept of the regression line is of: 2.33. How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.
To find the correlation coefficient, we find the same strategy, inserting these points into a calculator of correlation coefficients.
From the data, the points are given as follows:
(3, 7), (4, 8), (5, 10).
Hence the correlation coefficient is of:
r = 0.982.
The line of best-fit is given by:
y = 1.5x + 2.33.
Which has a slope of 1.5 and an intercept of 2.33.
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PLEASE HURRY!
Write the following expression using the fewest possible terms.
(−4x − 15) + (17 + 7x)
3x + (−2)
3x + 2
11x + (−2)
11x + 32
The simplified expression of (−4x − 15) + (17 + 7x) is - 11x + 2.
How to simplify expression?The expression can be simplified as follows:
(−4x − 15) + (17 + 7x)
we have to open the brackets of the expression
(−4x − 15) + (17 + 7x)
−4x − 15 + 17 + 7x
Combine like terms
−4x − 15 + 17 + 7x
- 4x + 7x - 15 + 17
Do the arithmetic of the like terms
- 4x + 7x - 15 + 17
Therefore, the simplified expression is as follows:
- 11x + 2
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Answer: 3x+2
Ex:
(-4x-15)+(17+7x)
-4x-15+17+7x Remove unnecessary parentheses
3x-15+17 Add like terms
3x+2
On a piece of paper, graph y ≥ 2x – 3. Then determine which answer choice matches the graph you drew.
Answer:
Step-by-step explanation:
We are asked to graph an inequality . y≥2x - 3
The boundary line of our given inequality will be a solid line as we have greater than or equal to ≥ sign.
The boundary line of our given inequality would be .y=2x - 3
Now, we will test point (0,0) to shade in the correct region as:
0≥2(0)-3
0≥0-3
0≥-3
It should look something like this:
help meeeeeee
Write the verbal sentence as an equation or an inequality:
Four is greater than six times a number t.
Answer:
four is greater than six times a number t in an inequality sentence is 4 › 6 * t
About 2% of the population has a particular genetic mutation. 500 people are randomly selected.
Find the standard deviation for the number of people with the genetic mutation in such groups of 500
The standard deviation for the number of people with the genetic mutation in such groups is 3.1305.
Standard DeviationIn statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Let X be the number of people with genetic mutation is a group of 500,
The formula of standard deviation is given as
[tex]SD=\sqrt{n*p(1-p)} \\SD=\sqrt{500*0.02*0.98} \\SD=3.1305[/tex]
The standard deviation of the given sample is 3.1305
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I will give brainliest, like and rating if u solve this right
Which of the following statements is not true?
Answer:
Answer C
This statement is not true
Step-by-step explanation:
Logarithms result in real values only for positive values of the argument i.e. log(x) results in a real value only for x > 0 So A is correct
Range is set of all real numbers -∞ < x < ∞ So B is correct
D is also correct. At x = 0, log is not defined
Only C is incorrect. If 0 < a < 1 the graph actually shows a downward trend ie logarithmic decline instead of growth
Please help me with all I’ll mark you brainly
Answer:
am pretty sure am correct i hope it helps you
There are 5 more girls than boys in MS, Rabu's class of 31 students, What is the ratio of number of girls to the number of boys in her class?
Answer: The answer is 18 Girls and 13 Boys. (18 + 13 = 31)
The ratio for girls to boys would 18:13
Step-by-step explanation: Confirmed correct.
A wheel on Amanda's bicycle is 0.3 m in diameter. Amanda races the bicycle for 35 m. How many times does the wheel turn as the bicycle travels this distance?
Use the value 3.14 for π. Round your answer to the nearest tenth. Do not round any intermediate steps.
Answer: 37.2
Step-by-step explanation:
The circumference of the bike is [tex]0.3\pi \approx 0.3(3.14)=0.942[/tex] m.
Dividing this by the 35 m traveled, we get the bike turned [tex]\frac{35}{0.942} \approx 37.2[/tex]
Fully factorise w² - 144
Answer:
(w-12)(w+12)
Step-by-step explanation:
Using the identity
a^2-b^2=(a-b)(a+b)
now,
w^2-144=(w)^2-(12)^2=(w-12)(w+12)
Cross out the unnecessary information. Then solve the problem.Pedro had a very busy Saturday. After a 6:00 a.m. tennis match, he hadbreakfast with his grandmother, stopped at the corner store to get an icecream cone, hurried to his Spanish lesson, stopped by the swimming poolfor a quick dip, and then ate lunch with his buddies. At 2:00p.m. he wentto a movie and finally stopped at the soccer match to cheer for the team.Just on time he met his family for pizza. When he arrived home he fell intobed and slept 14 hours. His clock showed 10:00 a.m. when he opened hiseyes the next morning. What time did Pedro fall into his bed?Yes
Pedro went to bed and slept 14 hours, when he woke up next day it was 10 am, it means he went to sleep 14 hours before 10am, it means he went to sleep at 8 pm
Find the slope of the line:
Answer:
20
Step-by-step explanation:
Slope = (y2-y1)/(x2-x1)
Choose any two points on the line. For this, I will use (0, 5) and (1, 25):
[tex]\frac{25-5}{1-0}=\frac{20}{1} = 20[/tex]
40 POINTS!
1. Find the missing angle.
2. What is the measure of Angle 1?
3. What is the measure of Angle 2?
4. Can the measure of an exterior angle of a triangle ever equal the measure of its adjacent interior angle? Explain in 2-3 sentences.
Answer:
43 for the first one
Step-by-step explanation:
108+29=
43
The science club members are using transformations on coordinate grids to track the movement of constellations in the sky. Choose the left side of the constellation depicted by the line passing through (1,7) and (2.5,1), and find the linear functions that correspond to the series of motions of the side given below.
The linear function passing through points (1,7) and (2.5, 1) is given by:
y = -4x + 11.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the rule presented below:
y = mx + b
In which the coefficients are described as follows:
The coefficient m is the slope of the function, representing the rate of change of the function.The coefficient b is the y-intercept of the function, representing the value of y when the function crosses the y-axis(x = 0).For this problem, the two points that form the function are given as follows:
(1,7) and (2.5, 1).
The slope is given by change in y divided by change in x, hence it is given by:
m = (1 - 7)/(2.5 - 1) = -4.
Then:
y = -4x + b.
When x = 1, y = 7, hence we can find the intercept b of the function as follows:
7 = -4(1) + b
b = 7 + 4
b = 11.
Hence the equation is:
y = -4x + 11.
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Convert the measurement as indicated.
11 ft=_yd_ft
Answer:
3 yards, 2 feet
Step-by-step explanation:
Convert the measurement as indicated. 11 ft=_yd_ft
There are 3 feet in a yard so 3 yards (equal to 9 feet) and a remainder of 2 feet equal 11 feet so:
11 feet = 3 yards, 2 feet
which of the following is a weakness of plotting a scatterplot and drawing a regression line?
Answer:
A
Step-by-step explanation:
i just did this one
The weakness of plotting a scatterplot is given below
What is a scatterplot?
A scatterplot (also known as a scatter plot, scatter graph, scatter chart, scattergram, or scatter diagram) is a form of plot or mathematical diagram that uses Cartesian coordinates to represent values for a collection of data for generally two variables. One more variable can be presented if the points are coded (color/shape/size). The data is represented as a collection of dots, with the value of one variable defining the horizontal axis and the value of the other variable determining the vertical axis. A scatterplot can be used when one continuous variable is within the experimenter's control and the other is reliant on it, or when both continuous variables are independent.
The weakness of plotting a scatterplot is:
(A) This provides no indication of whether there is cause and effect relationship.
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What are the coordinates of the point that lies of the way along directed line segment AB with A(2,5) and B(14,9)?
1/4 of the distance between points A(2,5) and B(14,9) is given by the formula:
[tex]\begin{gathered} \frac{1}{4}AB=\frac{1}{4}\sqrt[]{(x_2-x_1)^2+(y_2}-y_1)^2 \\ \frac{1}{4}AB=\frac{1}{4}\sqrt[]{(14-2)^2+(9-5)^2} \\ \frac{1}{4}AB=\frac{1}{4}\sqrt[]{12^2+4^2}\text{ = }\frac{1}{4}\sqrt[]{144+16} \\ \frac{1}{4}AB=\frac{1}{4}\text{ }\sqrt[]{160}=\frac{1}{4}\times12.649=3.162 \end{gathered}[/tex]