2x + 16 = 5
2x = -11
x = -5.5
y = 5
(-5.5,5)
Final answer:
The solution to the system of equations y=5 and y=2x+16 is found using substitution, yielding the solution (-5.5, 5).
Explanation:
To solve the system of equations y=5 and y=2x+16, we can use the method of substitution. Since the first equation directly gives us the value of y, we can substitute y = 5 into the second equation to find the corresponding value of x. Doing so, we have 5 = 2x + 16. To solve for x, we subtract 16 from both sides to get -11 = 2x, and then divide both sides by 2 to find that x = -5.5. Thus, the solution to the system is (-5.5, 5).
Two lines intersect to form a linear pair with equal measures. One angle has the measure 3x° and the other angle has the measure (9y − 18)°. Find the values of x and y.
3x + 9y - 18 = 180
3x = 9y - 18
Which means
3x = 90
9y - 18 = 90
Solving for each:
x = 90/ 3
x = 30
And
9y = 108
y = 108/9
y = 12
Answer: x = 30 , y = 12
The values of x and y are 33 and 13, respectively. To find these, we used the properties of a linear pair of angles being equal and supplementary, which led us to a system of equations that we solved for both variables.
When two angles form a linear pair with equal measures, they are supplementary and equal to each other. Therefore, the sum of their measures is 180 degrees. Since both angles in the linear pair are equal, we can set them equal to each other to find the values of x and y.
The first angle is given as 3x degrees and the second angle is given as (9y - 18) degrees. Since they are equal, we can set up the equation:
3x = 9y - 18
To find the value of x and y, we also need to use the fact that angles in a linear pair add up to 180 degrees. Thus:
3x + (9y - 18) = 180
Substituting the value of 3x from the first equation into the second:
3x + 3x = 180 + 18
6x = 198
x = 33
Now substituting the value of x back into the first equation to find the value of y:
3(33) = 9y - 18
99 = 9y - 18
9y = 117
y = 13
The values of x and y are therefore 33 and 13, respectively.
is a fraction a numerical or algebraic
[tex] \frac{n}{4} [/tex]
Algebraic is your answer
In a numerical fraction, there can only be numbers and the operation that is connected with the numbers
In an Algebraic fraction, not only can you have numbers and operation, you can also have variables.
~Rise Above the Ordinary, Senpai
Locating Zeros of Polynomial Function:
Describe how you find an upper bound and a lower bound for the zeros of a polynomial function
The value p is an upper bound on the real roots of the polynomial if division of the polynomial by (x-p) results in quotient terms that all have positive coefficients.
The value q is a lower bound on the real roots of the polynomial if division of the polynomial by (x-q) results in quotient terms that alternate signs.
_____
The division can be either synthetic division or long division.
_____ ______
An upper bound on the magnitude of the roots can be found this way:
Divide all coefficients by that of the highest-degree termFind the absolute value of the resultChoose the maximum of those results and increase it by 1There are various refinements, including finding the sum of the ratios of successive coefficients, or taking increasing roots of the ratios found above, then doubling the maximum of those.
Use synthetic division to find the values of the polynomial function for consecutive integers. An integer that produces no sign change in the quotient and the remainder is an upper bound. To find a lower bound of a function, find an upper bound for the function of -x. The lower bound is the negative of the upper bound for the function of -x.
That is the right answer as I just finished the 10 practice problems on E2020
if a cd can store 700,000,000 bytes of data express, in scientific notation the number of bytes of data which can be store on 2 such cd
700,000,000 = 7.00E8 bytes of data. Then, 2 such cd's will hold 2(7.00E8 bytes of data) = 1.4E9 byes of data (answer)
HELP PLEASE!!!! 8TH GRADE MATH
1. 12 pages per minute
Jennifer is making costumes for the school play she has 70 M of Ribbon if she beeds 54 percent of the ribbon for the costumes. how much ribbon does she need Will mark brainiest show your work
70 m * .54=37.8 METERS
Solve for x.
3x / 6 + 1 = 7
3x/6 +1 = 7
Subtract 1 from each side:
3x/6 = 6
Multiply both sides by 6:
3x = 36
Divide both sides by 3:
X = 36 / 3
X = 12
x = 12
given [tex]\frac{3x}{6}[/tex] + 1 = 7 ( subtract 1 from both sides )
[tex]\frac{3x}{6}[/tex] = 6 ( multiply both sides by 6 )
3x = 36 ( divide both sides by 3 )
x = 12
In a usually right-angled (x, y, z)-coordinate system, three planes are given by the following system of linear equations:
[tex]\alpha_1: x-y+(a-1)z=a\\\alpha_2: x+(a-1)y=0 \\\alpha_3: ax+ay+(a-1)z=0[/tex]
a ∈ R
a) Solve the equation system for [tex]a=2[/tex]
b) Find the value of [tex]a[/tex] for which the three planes intersection is a straight line and specify a parametric equation for the line.
c) Find the value of [tex]a[/tex] for which the three plans have no common point.
d) Is there a value of [tex]a[/tex] for which the three plans have the common intersection [tex](1, -\frac{1}{69}, \frac{4624}{4761})[/tex]?
Please, explain how you found the solutions :-)
Extra:
e) Illustrate questions a) and b) with Maple software.
Hint: The [tex]implicitplot3d[/tex] command can sure to be helpful. Also note that the argument [tex]orientation[/tex] can lock your plot in a favorable position for inspection.
Answer:
a) (x, y, z) = (1, -1, 0)
b) a = 0; L = {t, t, 0}
c) a = 1 . . or . . a = 3
d) No
Step-by-step explanation:
a) The solution using row-reduction techniques is shown in the first attachment, part (a). The generic solution is shown evaluated for a=2, the result being (1, -1, 0).
You will note that the solution gives indeterminate values for a=1 and a=3, which make the denominators zero.
b) For this, we use the point solution of part (a) together with the cross product of the normal vectors of planes 1 and 2. Said cross product will be in the direction of their line of intersection. We substitute the parametric equation for that line into the equation for plane 3 and solve for a. The result is a = 0.
The simplification of the resulting equation also gives a=1 and a=3, but we treat those as extraneous solutions because the corresponding common point of intersection of the planes does not exist.
c) The values a = 1 and a = 3 were found in part (a). These are values of a that make the common point indeterminate.
d) Substituting the given values for (x, y, z) gives three equations for a that have 3 different solutions. Hence there cannot be a value of a that makes this be a common point of intersection.
e) The second attachment illustrates part (a), with a=2. The third attachment illustrates part (b) with a=0.
The fourth attachment illustrates part (c). The first picture has the triangular tunnel between the planes in a vertical orientation (a=1). The second picture has the triangular tunnel extending from lower front to upper back (a=3).
if you miss a payment for a bill, how do you compute the interest due on the next bill?
To calculate the interest due after missing a payment, add any late fees to the unpaid bill and apply the monthly interest rate to the outstanding balance. Interest compounds monthly, so it's crucial to pay off the debt quickly to prevent the balance from growing.
Explanation:To compute the interest due on the next bill after missing a payment for a bill, you need to consider any late fees in addition to the compounded interest. For a credit card company that charges a flat rate of $10 for a late payment and a daily rate of $5 for each day the payment remains unpaid, you would add these fees to the subtotal of the unpaid bill. Additionally, most creditors use a formula to calculate minimum payments and interest on the outstanding balance, typically on a monthly basis.
The interest on the next bill is calculated by multiplying the balance you owe by the interest rate that is applied each month. If you continue to carry a balance from month to month, this interest will be added to your outstanding balance, which will increase the amount you owe. It is important to pay off credit card debt as promptly as possible to avoid accruing additional interest.
The expanded form of a number is (6 × 1) + (2 × 0.1) + (7 × 0.01). How should the number be written in word form? six and twenty-seven six and twenty-seven tenths six and twenty-seven hundredths six and twenty-seven thousandths
All choices agree that it is "six and (something)".
So, you're asked to figure out whether 0.2 + 0.07 = 0.27 is
twenty-seventwenty-seven tenthstwenty-seven hundredthstwenty-seven thousandthsYou can start with the original expanded form to decide
... (2 × 0.1) + (7 × 0.01) = (20 × 0.01) + (7 × 0.01)
... = (20+7) × 0.01 = (27 × 0.01)
Since you know 0.01 is 1 hundredth, you know the correct choice is ...
... six and twenty-seven hundredths
the answer would be -six and twenty-seven hundredths
Terence owes $5.00 to his mother and his father. Write the integer problem and determine the total amount he owes his parents. (50 PTS SUPER EASY)
$5 + $5 = $10
Terence owes both his parents a total of $10
Hope this helps you
-AaronWiseIsBae
4- is there any price for which there are. I data
5-
4. There are no data for prices other than integer values in the range $11 to $16. For example, there is no data for a price of $11.50, or for a price of $17.
5. insufficient information
Part 1: Create an equation of a line in point-slope form. Be sure to identify all parts of the equation before writing the equation.
Part 2: Using the equation of the line you wrote in part 1, write an equation of a line that is perpendicular to this line.
Part--1:
We know that a equation in point-slope form is represented by:
[tex]y-y_1=m(x-x_1)[/tex]
where m is the slope of the line and [tex](x_,y_1)[/tex] is a point through which the line passes.
Consider a equation in a point-slope form as:
[tex]y-5=2(x-1)[/tex]
This means that the slope of the line is: 5
and the line passes through the point (1,5).
Part--2:
Now as we know that if a line has a slope as m then the perpendicular line has a slope: -1/m
Since,
[tex]m\times \text{Slope\ of\ second\ line}=-1\\\\i.e.\\\\\text{Slope\ of\ second\ line}=\dfrac{-1}{m}[/tex]
Let this perpendicular line passes through (2,6)
Hence, the equation of a line in point slope form is given by:
[tex]y-6=\dfrac{-1}{2}(x-2)[/tex]
Answer:
Equation:
y-y1=m(x-x1)
y-2=4(x-1)
Part 2:
y=-1/4x +b
Step-by-step explanation:
One coin weighs 11 grams. How many grams do 10 coins weigh?
Answer:
110
Step-by-step explanation:
8. When hired at a new job a a salesperson you are given two pay options:
A base salary of $17,000 per year with a commission of 12% of your sales
A base salary of $20,000 per year with a commission of 5% of your sales
How much you need to sell for option A to pay more?
9. When hired at a new job as a salesperson you are given two pay options:
A base salary of $20,000 per year with a commission of 9% of your sales
A base salary of $25,000 per year with a commission of 3% of your sales
How much you need to sell for option A to pay more?
You can write equations for total pay, but in the end, you want to find the amount of sales that makes the difference in commission make up for the difference in base pay.
... (commission rate difference) × sales = (base pay difference)
To find the sales, divide by its coefficient:
... sales = (base pay difference)/(commission rate difference)
8.Sales = (20,000 -17,000)/(.12 -0.05) = 3000/0.07 ≈ 42,857.14
You need to sell more than $42,857.14 for option A to pay more.
9.Sales = (25,000 -20,000)/(.09 -.03) = 5000/0.06 ≈ 83,333.33
You need to sell more than $83,333.33 for option A to pay more.
_____
In each case, total pay is ...
... total pay = (base pay) + (commission rate) × sales
For the two options to give the same total pay, the difference in total pay is zero. That occurs when ...
... 0 = (base pay₁) + (commission rate₁) × sales -((base pay₂) + (commission rate₂) × sales)
... 0 = (base pay₁) - (base pay₂) - sales × ((commission rate₁) -(commission rate₂))
Solving for sales, we get the above result:
... sales = ((base pay₂) -(base pay₁))/((commission rate₁) -(commission rate₂))
Solution 8:
We are given base salary of 17000 and 12% of sales.
Les us say salesperson does sales of x amount.
So 12% of x is 0.12x
Total salary = 17000+0.12x
In second case base salary is $20000 and commission of 5% of sales.
Total salay=20000+0.05x
Now for option A to pay more we have:
[tex]17000+0.12x>20000+0.05x[/tex]
Solving we get:
[tex]0.07x>3000[/tex]
x>42,857
Answer: Option A need to make sales of $42,857 more.
Solution 9:
We are given base salary of 20000 and 9% of sales.
Les us say salesperson does sales of x amount.
So 9% of x is 0.09x
Total salary = 20000+0.09x
In second case base salary is $25000 and commission of 3% of sales.
Total salay=25000+0.03x
Now for option A to pay more we have:
[tex]20000+0.09x>25000+0.03x[/tex]
Solving we get:
[tex]0.06x>5000[/tex]
x>83,333.33
Answer: Option A need to make sales of $83,333.33 more.
evaluate this expression
[tex]2^{-2}[/tex]
Answer:
0.25
Step-by-step explanation:
we have to use the following formula here-
[tex]a^{-m}= \frac{1}{a^{m}}[/tex]
Now, here we get,
[tex]2^{-2}[/tex]
So, applying the formula we get
[tex]2^{-2}= \frac{1}{2^{2}}= \frac{1}{4} =0.25[/tex]
So, the answer is 0.25
[tex]2^{-2}[/tex] = [tex]\frac{1}{4}[/tex]
using the law of exponents
[tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{}a^{m}[/tex]
[tex]2^{-2}[/tex] = [tex]\frac{1}{}2^{2}[/tex] = [tex]\frac{1}{4}[/tex]
Which is a translation of the shaded figure?
A.) D
B.) A
C.) B
D.) C
The answer is D. because they are the same shape and have the same dimensions.
The solution is Option A.) D
What is Translation?
A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
Given data ,
From the given figure , we can see that only figure represents the same exact figure as per the pre-image
Now , a translation moves a figure only up , down or from side to side
The figure in the image is only translated by a scale factor and no other changes are happening or no other transformations occur.
So , it is clear from the options that the image D is the only possible outcome where a translation of the shaded figure takes place.
Hence , the solution is figure D
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Solve the formula for the specified variable
N=(1/6)rm what is r
N=(1/6)rm
Solve for r
[tex]N = \frac{1}{6} rm[/tex]
[tex]N = \frac{1}{6}*r*m[/tex]
To remove the fraction 1/6, we multiply both side by reciprocal 6/1
[tex]N\frac{6}{1}= \frac{1}{6}*r*m\frac{6}{1}[/tex]
6N = rm
Now divide by m on both sides
[tex]\frac{6N}{m}= \frac{r}{m}[/tex]
[tex]\frac{6N}{m}= r[/tex]
We solved for r
[tex]r = \frac{6N}{m}[/tex]
Answer:
r = [tex]\frac{6N}{m}[/tex]
Step-by-step explanation:
Given an equation in terms of N on the left side and r, m variables on the right side.
Instead of N on left side we have to bring r on left side alone and other terms on right side to get formula for r.
For this multiply the given equation first by 6.
6N = rm
Now divide by m
r = [tex]\frac{6N}{m}[/tex]
This is the formula for r in terms of N, m.
A bucket holds c liters of water, but a jar holds d liters more. How much water do they hold together?
The total volume of water that the bucket and jar hold together is found by adding the liters the bucket holds (c) and the liters the jar holds more than the bucket (d). Therefore, the expression for total volume is c + d.
Explanation:The subject of the question is simple addition in Mathematics. To solve this, we need to add the liters of water the bucket holds (represented by c) and the liters of water the jar holds (represented by d liters more than the bucket). On this basis, the equation is as follows: total liters = c + (c + d).
However, as the question states that the jar holds d liters more than the bucket, not that it holds d liters more than the total amount in the bucket, the correct equation to find out the total volume of water in both the bucket and the jar together is: total liters = c + d.
So, if the bucket holds 5 liters of water (c=5) and the jar holds 2 liters more (d=2), then together, they hold 5 + 2 = 7 liters of water.
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What is the solution of sqrt x+12=x ? x = –3 x = 4 x = –3 or x = 4 no solution
x = 4 is the solution
given [tex]\sqrt{x+12}[/tex] = x ( square both sides )
x + 12 = x² ( rearrange into standard form )
x² - x - 12 = 0 ← in standard form
(x - 4 )(x + 3 ) = 0 ← in factored form
equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 3 = 0 ⇒ x = - 3
substitute these values into the original equation and if both sides are equal then they are the solutions
x = 4 : [tex]\sqrt{4+12}[/tex] = [tex]\sqrt{16}[/tex] = 4 = x ← correct
x = - 3 : [tex]\sqrt{-3+12}[/tex] = [tex]\sqrt{9}[/tex] = 3 ≠ - 3 ← false
the solution is x = 4
Answer: x= 4
Step-by-step explanation:
Write a word problem for this inequality
72-12a<24
A ball rolling down a hill was displaced 19.6 m while uniformly accelerating from the rest. If the final velocity was 5.00m/s, what was rate of acceleration?
we are given
A ball rolling down a hill was displaced 19.6 m
so,
[tex]h=19.6m[/tex]
the final velocity was 5.00m/s
so, [tex]v=5m/s[/tex]
Since, a ball rolling down a hill was displaced
so, we get
[tex]u=0m/s[/tex]
we can use kinematic equation formula
[tex]v^2-u^2=2ah[/tex]
Here ,
v is final velocity
u is initial velocity
a is acceleration
h is height from which ball is dropped
now, we can plug our values
[tex]5^2-0^2=2a(19.6)[/tex]
[tex]2a\left(19.6\right)=5^2[/tex]
[tex]2a\left(19.6\right)=25[/tex]
[tex]a=0.63776m/s^2[/tex]................Answer
Using the equation of Motion, the rate of acceleration of the ball is 0.638 m/s²
Using the 2nd equation of Motion :
Height, h = 19.6 meters Final velocity, v = 5 m/sInitial Velocity, u = 0v² = u² - 2gh (downward motion)
5² = 0 - 2(19.6)a
25 = 0 - 39.2a
39.2a = 25
a = 25/39.2
a = 0.638 m/s²
Therefore, the rate of acceleration is 0.638 m/s²
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Find the value of the expression 2x^4–5x^3+x^2+3x+2 for x=−5
Answer:
1887
Step-by-step explanation:
You can do this by putting the value -5 where x is in the expression, using synthetic division, or letting a calculator evaluate the function. (Likely a calculator is involved, regardless.)
Shown in the attachments are a couple of these methods.
1 .Which statement correctly describes the relationship between the graph of f(x)=2x
and the graph of g(x)=f(x)−4 ?
A. The graph of g(x) is the graph of f(x) translated 4 units right.
B. The graph of g(x) is the graph of f(x) translated 4 units left.
C. The graph of g(x) is the graph of f(x) translated 4 units up.
D. The graph of g(x) is the graph of f(x) translated 4 units down.
2. Which statement correctly describes the relationship between the graph of f(x) and g(x)=f(x−7) ?
A. The graph of g(x) is the graph of f(x) translated 7 units down.
B. The graph of g(x) is the graph of f(x) translated 7 units left.
C. The graph of g(x) is the graph of f(x) translated 7 units right.
D. The graph of g(x) is the graph of f(x) translated 7 units up.
3. The graph of g(x) is the graph of f(x)=x+6 reflected across the x-axis.
Which equation describes the function g?
A. g(x)=−x−6
B. g(x)=x−6
C. g(x)=−x+6
D. g(x)=−6x−6
4. The graph of g(x) is the graph of f(x)=12x+6 compressed vertically by a factor of
1/3 .
Which equation describes the function g?
A. g(x)=4x+2
B. g(x)=4x+6
C. g(x)=12x+2
D. g(x)=36x+6
5. Which series of transformations take the graph of f(x)=2x+3 to the graph of g(x)=−2x+4 ?
A. reflect the graph about the y-axis and translate 1 unit up
B. reflect the graph about the y-axis and translate 1 unit down
C. reflect the graph about the x-axis and translate 1 unit up
D. reflect the graph about the x-axis and translate 1 unit down
D
the graph of g(x) is the graph of f(x) translated 4 units down
I looked at them and i'm not sure its d but you should try d.
11.57-n=7.51 write the unknown number for n
n = 4.06
isolate the term in n by subtracting 11.57 from both sides of the equation
- n = 7.51 - 11.57 = - 4.06
multiply both sides by - 1
n = 4.06
please help with7 thru 12
a team played 42 games and won 5/14 of them. how many games were lost?
27 games were lost
fraction of games lost = 1 - [tex]\frac{5}{14}[/tex] = [tex]\frac{14}{14}[/tex] - [tex]\frac{5}{14}[/tex] = [tex]\frac{9}{14}[/tex]
number of games lost = [tex]\frac{9}{14}[/tex] of 42
= [tex]\frac{9}{14}[/tex]× 42 = 27
The team played 42 games and won 5/14 of them, which equals 15 games. Subtracting the number of games won from the total number of games played gives the total number of games lost, which is 27.
Explanation:The team played 42 games and won 5/14 of them. To find out how many games were lost, we first have to find out how many they won. 5/14 of 42 games is 15 games. So, they won 15 games. Now, to find out how many games were lost, we need to subtract the number of games won (15 games) from the total number of games played (42 games). Therefore, 42 games - 15 games = 27 games. So, the team lost 27 games.
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jerome tries to find the value of the expression 3-6+5 by first applying the communtative property. he rewrites the expression as 3-5+6. explain what is wrong with jeromes approach
The commutative property is a property of addition, not of subtraction. It can work in a subtraction problem if you keep the sign with the number, so you're adding positive and negative numbers.
3 - 6 + 5
= (3) + (-6) + (5)
= (3) + (5) + (-6)
= 3 + 5 - 6
why does an angle that is supplementary to an acute angle have to be obtuse
This is because the total needs to be equal to 180 degrees. Since obtuse angles are greater than 90 degrees, then it needs an acute angle (lower than 90 degrees) to supplement it to equal 180
Given: △DMN, DM=10 3 m∠M=75°, m∠N=45° Find: Perimeter of △DMN
Angle D is 180° -75° -45° = 60°. Drawing altitude MX to segment DN divides the triangle into ΔMDX, a 30°-60°-90° triangle, and ΔMNX, a 45°-45°-90° triangle. We know the side ratios of such triangles (shortest-to-longest) are ...
... 30-60-90: 1 : √3 : 2
... 45-45-90: 1 : 1 : √2
The long side of ΔMDX is 10√3, so the other two sides are
... MX = MD(√3/2) = 15
... DX = MD(1/2) = 5√3
The short side of ΔMNX is MX = 15, so the other two sides are
... NX = MX(1) = 15
... MN = MX(√2) = 15√2
Then the perimeter of ΔDMN is ...
... P = DM + MN + NX + XD
... P = 10√3 +15√2 + 15 + 5√3
... P = 15√3 +15√2 +15 . . . . perimeter of ΔDMN
The Perimeter of △DMN is 35.9
First step
sin 45 / 10 = sin 60/ x
x = sin 60 × 10 / sin 45
= √(3)/2 × 10 × 2 / √(2)
= √(3) / 2 × 10 ×√(2)
= 5 × √(6)
Second step
sin 45 / 10 = sin 75 / y
y = sin 75 × 10 / sin 45
= sin 75 × 10 × 2 / √(2)
= sin 75 × 10 ×√(2)
= 13.066054
Now let determine Perimeter of △DMN
Perimeter of △DMN=10 + 5*√(6) + 13.06605425
Perimeter of △DMN= 35.90770275
Perimeter of △DMN=35.9
Inconclusion Perimeter of △DMN is 35.9
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