A 16-foot piece of string is cut into two pieces so that the longer piece is 1 foot longer than twice the shorter piece.
Find the lengths of both pieces.
Question content area bottom
Part 1
What is the length of the shorter piece?
What is the length of the longer piece?
Answer:
Shorter piece: 5 Longer piece: 11
Step-by-step explanation:
(2x+1)+(x)=16
3x+1=16
3x=15
x=5
(solve each system by graphing. Check your solution) questions 11 and 13
Answer: 10. (2,4) 11. (4,9) 13. (2,-2) 14. (1,2)
Step-by-step explanation:
Just plugged em into desmos & double checked
Answer: 11. (4,0) 13. (2,-2)
Step-by-step explanation:
11.
[tex]\displaystyle\\\left \{ {{y=\frac{1}{2} x+7 } \atop {y=\frac{3}{2}x+3 }} \right. \\\\y=\frac{1}{2}x+7[/tex]
x | 0 | 4 |
y | 7 | 9 |
[tex]\displaystyle\\y=\frac{3}{2}x+3\\[/tex]
x | 0 | 2 |
y | 3 | 6 |
13.
[tex]\displaystyle\\\left \{ {{y=x-4} \atop {y=-x}} \right. \\\\y=x-4[/tex]
x | 0 | 4 |
y | -4 | 0 |
[tex]y=-x[/tex]
x | 0 | 4 |
y | 0 | -4 |
Need help before 10:30
Answer: I will really try to get answers just wait
Step-by-step explanation:
John runs the same number of kilometres each day.write an expression to represent the number of kilometre john ran in june last year
An algebraic expression to represent the number of kilometres John ran in June month last year is 30a.
Given that, John runs the same number of kilometres each day.
We need to find an algebraic expression to represent the number of kilometres John ran in June month last year
What is an algebraic expression?An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.
Let us assume that john is running 'a' kilometres per day.
We know that June month composed of total 30 days
So the algebraic expression for the number of kilometres John ran in June last year = Number of kilometres running per day × Number of days in the month of June
=a × 30=30a
Therefore, an algebraic expression to represent the number of kilometres John ran in June month last year is 30a.
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Mr. Sullivan's employer withheld $19,342.19 in federal income tax. After completing his return, Elsner has determined that his tax is $23,945.22. Will he get a refund, or does he owe the IRS and how much? Use a negative number to represent a refund and a positive amount to represent additional taxes owed. Round to the nearest penny.
HHe will owe the IRS and the amount is $4603.03
In this question, we have been given Mr. Sullivan's employer withheld $19,342.19 in federal income tax.
Elsner has determined that his tax is $23,945.22
We need to find whether he get a refund, or he owes the IRS.
From given information,
Employer withheld in federal taxes last year = $19,342.19
His tax amount is $23,945.22
So by considering the above information, the he owes the additional taxes because the tax amount i.e., $23,945.22 is more than the withheld amount i.e., $19,342.19
So, the additional taxes would be,
$23,945.22 - $19,342.19 = $4603.03
This difference represent the additional taxes owed.
Therefore, he will owe the IRS and the amount is $4603.03
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11) Mike is thinking of two numbers. Their difference is 12. If one of the numbers is 19, what is the other
number? Is there only one answer? If not, what is the other possibility for the second numbe? Explain
your reasoning.
Answer: 7, and 31
Step-by-step explanation:
7 + 12 = 19 or 19 - 12 = 7
19 + 12 = 31
The other number will be - 7.
Yes, There is only one answer.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The difference of two numbers is 12.
And, one of the numbers is 19.
Now,
Let two numbers are x and y.
So, We get;
x + y = 12
Here, one of the numbers is 19.
So, x = 19
We get;
x + y = 12
19 + y = 12
y = 12 - 19
y = - 7
Thus, The other number will be - 7.
Yes, There is only one answer.
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A triangle has angles measuring 45°, 55°, and 80°. It is dilated by a scale factor of 2. What are the angle measures, in order from least to greatest, of the dilated image?
The angle measures, in order from least to greatest, of the dilated image 45°,55° and 80°.
A dilation is a function f from a metric space M into itself that satisfies the identity d=rd for all points x, y \in M, where d is the distance from x to y and r is some positive real number. In Euclidean space, such a dilation is a similarity of the space.
Euclidean space, In geometry, a two- or three-dimensional space in which the axioms and postulates of Euclidean geometry apply; also, a space in any finite number of dimensions, in which points are designated by coordinates (one for each dimension) and the distance between two points is given by a distance formula.
Dilations preserve angle measures, regardless of the scale factor. Therefore, the angle measures of the image will be the same of that of the pre-image, so our answer is still 45 °, 55 °, and 80 °.
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Answer:45,55,80
Step-by-step explanation: dilations preserve angles measures regardless of the scale factor. Therefore the angle measures of the image will be the same of that of the pre-image ,so our answer is still 4545,5555,8080 .
5) If the sun is out, then it is daytime.
Converse:
Inverse:
Contrapositive:
the 3 statements are:
The converse statement is: If it is daytime, then the sun is out.
The inverse statement is: if the sun is not out, then is not daytime.
The contrapositive statement is: if it is not daytime, then the sun is not out.
How to find the converse, inverse, and contrapositive statements?
If we have two propositions P and Q, then we have a conditional statement:
If P then Q.
The converse statement is: if Q then P
The inverse statement is: if Not P, then Not Q.
The contrapositive statement is: if Not Q, then Not P.
The conditional statement is:
"If the sun is out, then it is daytime"
So we have:
P = the sun is out.
Q = it is daytime.
Then the 3 statements are:
The converse statement is: If it is daytime, then the sun is out.
The inverse statement is: if the sun is not out, then is not daytime.
The contrapositive statement is: if it is not daytime, then the sun is not out.
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The midpoint AB is (1,2). The coordinates of A are (-3,6) Find the coordinates of B
Can someone help me with this exercise and show me the procedure of how to do it??
========================================================
Explanation:
We have these points
A = (-3,6)M = midpoint = (1,2)B = (x,y)Focus on the x coordinates for now.
The x coordinates of A and B are -3 and x in that order. Add them up and divide in half to get the x coordinate of the midpoint M
(-3+x)/2 = 1
-3+x = 2*1
-3+x = 2
x = 2+3
x = 5
Repeat for the y coordinates
(6+y)/2 = 2
6+y = 2*2
6+y = 4
y = 4-6
y = -2
Therefore, the location of point B is (5, -2)
You can use a tool like GeoGebra to check your work.
How will this looks like
Answer:
Step-by-step explanation:
Divide.
(−16)÷(−56)
What is the quotient?
Answer:
Quotient = 0; Remainder = 16
Step-by-step explanation:
The area of a rectangular carpet is given by the quadratic function A(x) = x(x + 30), where A(x) is the area and x is the width of the carpet in feet. What are the restrictions on the domain of the function and its inverse?
The inverse of the function is; f⁻¹(x) = - 15 ± √(x + 225)
What is the Inverse of the Function?We have been given a quadratic function f(x) = x(x + 30) and we need to restrict the domain such that it becomes a one to one function.
Now, the given function can also be written in vertex form as;
f(x) = (x + 15)² - 225
We know that vertex of this quadratic function occurs at (-15, -225).
Further, we know that range of this function is (-225, ∞).
If we restrict the domain of this function to either (-∞, -225) or (-225, ∞) , it will become one to one function.
Let us know find its inverse;
y = (x + 15)² - 225
Upon interchanging x and y, we get:
x = (y + 15)² - 225
Solving for y gives;
y = - 15 ± √(x + 225)
Thus, the inverse of the function is;
f⁻¹(x) = - 15 ± √(x + 225)
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4x+2(x+6)=36 ummm.....what?
Answer:
x = 4
Step-by-step explanation:
4x + 2(x + 6) = 36
4x + 2x + 12 = 36
6x = 36 - 12
6x = 24
x = 24
6
x = 4
Chose the step below that correctly uses the distributive property to begin solving the equation: 2(x + 1) + 4 = 8 O 2x+5=8 Ox+1+2 = 4 O 2x + 2 + 4 = 8 O 2x + 1 + 4 = 8
2(x+1)+4
Distributive property : According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
solve equation by using distributive property we should use laws of this property that are as follows:
Expand the equation. Multiply (distribute) the first numbers of each set, outer numbers of each set, inner numbers of each set, and the last numbers of each set. Combine like terms.
2(x + 1) + 4 = 8
2(x)+2(1)+4=8
2x+2+4=8
2x+6=8
2x=8-6
2x=2
x=2/2
x=1
so final conclusion is Option A 2(x+1)+4=8 is the right answer
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12÷3×5-4 to the 2nd power
I have two answers depending on the format. I'm not sure if the entire function is to the 2ndpower or not. Either way, it's either 256 or 4.
Givien f (x) = -4x-2 , find f (1).
Answer: -6
Step-by-step explanation:
-4(1)-2=-6
Answer:
f(1) = -6
Step-by-step explanation:
Hello!
Substitute 1 for x in the equation.
Evaluatef(x) = -4x - 2f(1) = -4(1) -2f(1) = -4 - 2f(1) = -6f(1) is -6.
what is the inequality for this?
four times a number decreased by three is at least two
Answer:
gegrgryyrryryryyryryr
Select all the correct locations on the figures.
Select two angles, one from each triangle, that must be congruent for the triangles to be congruent by the SAS criterion.
For the two triangles to be congruent by the side angle side (SAS) criterion, then the angle in between the two marked sides must be congruent.
What are congruent triangles?Two triangles are said to be congruent if they have the same shape and their corresponding sides are also equal. Therefore, their corresponding angles would also be congruent.
For the two triangles to be congruent by the side angle side (SAS) criterion, then the angle in between the two marked sides must be congruent.
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Answer:
as shown on the screen shot
When a three-digit number written in base 10 has its final digit moved to the beginning, the result is the same number written in base 7. find all such numbers
There is no such number that has the result is the same number written in base 7 and base 10.
Decimal and Octal numbers:
Decimal system is most familiar number system to the general public. It is base 10 which has only 10 symbols − 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Whereas octal system is one of the number systems to represent numbers. It is base 8 which has only 8 symbols − 0, 1, 2, 3, 4, 5, 6, and 7.
Given,
When a three-digit number written in base 10 has its final digit moved to the beginning, the result is the same number written in base 7.
Here we need to find all such numbers.
Let abc be the starting number, where the catenated letters represent digits, and not factors like in the product
=> a x b x c
And each of a,b, and c can be elements of the list,
=> {1,2,3,4,5,6,7,8,9,0}
Except a≠0.
Since abc is a base-10 numeral, we can also write it as
=> 10²a + 10¹b + 10⁰c
Which can be expanded as,
=> 100a + 10b + c ----------------------(1)
Moving the last digits to the first slot makes the new number,
=> 100c + 10a + b------------------------(2)
So, here the value c≠0.
We know that, the digits in the base-10 numeral cab are identical to those of the base-7 numeral that is written as cab₇.
In the equation form it is equal to,
=> 7²c + 7¹a + 7⁰b
=> 49c + 7a + b ---------------------(3)
but since we're working in base 7 now, the digits a,b, and c cannot exceed 6.
Now, we want to solve for a, b, and c such that
By equalizing the equations 2 and 3,
=> 100c + 10a + b = 49c + 7a + b
=> 100c + 10a + b - 49c - 7a - b
=> (100 - 49)c + (10 - 7)a
=> 51c + 3a
=> 3 (17c + a)
Both a and c must be positive, but this equation has solution,
=> a = -17c
So there are no positive integers solutions, and hence no such number.
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Translate algebraic words to symbols. Triple the product of ab
Answer:
3ab
Step-by-step explanation:
Triple means multiply by 3.
The product of ab is simply ab.
Answer: 3ab
Cuantos múltiplos de 9 hay entre 60 y 100
Answer: 5 multiples of 9
Step-by-step explanation:
First take the difference between 100 and 60.
100-60=40
Then divide the difference by 9.
40/9=4.44
4.44 rounded up is 5 ==> 5 multiples of 9
Primero toma la diferencia entre 100 y 60.
100-60=40
Luego divide la diferencia entre 9.
40/9=4,44
4.44 redondeado es 5 ==> 5 múltiplos de 9
Answer:
5
Step-by-step explanation:
9*7 = 63
9*8 = 72
9*9 = 81
9*10 = 90
9*11 = 99
Hay 5 múltiplos de 9 entre los números 60 y 100
Multiply. Write the answer in simplest form.
13/18 x 6/7
Answer:
13/21
Step-by-step explanation:
Solving steps
13/18 × 6/7
Simplify the expression
13/3 × 1/7
Multiply
Solution:
13/21
Alternative Form
0.619047
The answer in simplest form 13/18 x 6/7 = 13/21
To find the answer in simplest form 13/18 x 6/7
Simplify this, multiple nominator to nominator and denominator to denominator
(13 × 6)/(18 × 7) = 78/126
Now, reduce the fraction divide by 6,
we get, 78/126 = 13/21
Therefore, the final answer is 13/21.
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5 divided by 555.25
Keenan got 13 /25 for his Mathematics Test write this as a decimal fraction
Answer: Answer is 0.52
Step-by-step explanation:
So we have the fraction 13 Out of 25.
step 1: here we divide numerator(which is 13) by denominator(which is 25).
step 2: first we make denominator 100 by multiplying by 25 with 4 and also 13 with 4.
ie. [tex]\frac{13 * 4}{25 * 4}[/tex]
step 3: we get [tex]\frac{52}{100}[/tex]
step 4: now we can easily write the decimal fraction. ie. 0.52
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in need of some help! rewrite the expression -6x^4y^3z^-7 so that there are no negative exponents
Answer:
[tex]-\frac{6x^4y^3}{z^7}[/tex]
Step-by-step explanation:
[tex]=-6x^4y^3\frac{1}{z^7}[/tex] <- Apply the exponent rule.
[tex]=-\frac{6x^4y^3\cdot \:1}{z^7}[/tex] <- Apply the fraction rule.
[tex]=-\frac{6x^4y^3}{z^7}[/tex]
2r−2p= n solve for p. has to be answered such as n-2r line under (division) equals p.
The solution of the given linear equation 2r−2p= n in two variables for p is r -n/2.
According to the given question.
We have a linear equation in two variables 2r - 2p = n.
Here we have to solve the given linear equation 2r - 2p = n in two variables for p.
So, the solution of the equation 2r - 2p = n for p is given by
2r - 2p = n
⇒ 2(r - p) = n (taking 2 as a common)
⇒ r - p = n/2 (dividing both the sides by 2)
⇒ r - n/2 - p = 0 (subtracting n/2 from both the sides)
⇒ r - n/2 = p (adding p both the sides)
⇒ p = r -n/2
Hence, the solution of the given linear equation 2r−2p= n in two variables for p is r -n/2.
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If the straight-line distance from her home to the university is 10. 3 km in a direction 25. 0° south of east, what was her average velocity in km/h?.
34.3 Km /h was her average velocity in km/h.
What is average velocity?
The change in position or displacement (x) divided by the time intervals (t) during which the displacement happens is the definition of average velocity. Based on the direction of the displacement, the average velocity might either be positive or negative. Meters per second (m/s or ms-1) is the SI measure for average velocity.The displacement of a body, or the shortest distance it must go during a trip, is calculated as the displacement multiplied by the time interval over which it covered that distance.average velocity = Displacement / time taken
V = d/ l
V = 10.3 Km/0.300m = 34.3Km
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A new go-cart track has opened up in your neighborhood. They charge $10 for a license and $3 for each ride . If you paid in total of $22 , how many rides did you take
Answer:
Step-by-step explanation:
4 rides
Answer:
4 rides is the answer to this question
Write an algebraic expression
to represent each verbal expression.
the sum of six times a number and 25
Answer:
6x+25
Step-by-step explanation:
6 times a number. Let x represent that number.
6x
It also says the to add 25 to the expression.
Add 25 to 6x.
6x+25
Hope this helps!
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a traffic study has shown that the probability that 55 cars will pass over a small bridge in a 4-4-minute period is 0.16.0.16. what are the odds against exactly 55 cars passing over the bridge in that time?
4:21 are the odds against exactly 55 cars passing over the bridge in that time.
What is Probability?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Probability is the branch of mathematics concerning the occurrence of a random event, and four main types of probability exist: classical, empirical, subjective and axiomatic.Probability of 0.16, thus, for 100 trials, 16 successes and 84 failures, and the odd is:
16:84, which, simplifying by 4, is 4:21.
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