The value of the numbers 'x' and 'y' will be 6 and 17, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
One number is 5 more than twice another and their sum is 23.
Let the two numbers be 'x' and 'y'. Then the equations are given as,
y = 2x + 5 ...1
x + y = 23 ...2
From equations 1 and 2, then we have
x + 2x + 5 = 23
3x + 5 = 23
3x = 23 - 5
3x = 18
x = 6
Then the value of the variable 'y' will be given as,
6 + y = 23
y = 23 - 6
y = 17
The value of the numbers 'x' and 'y' will be 6 and 17, respectively.
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Solve the systems and please show all work using substitution.
The value of x = -84/17, y= 24/17 and z = 9/17
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
x -2y + z= -6
x- 5z= -12
-x+ 6y + 4z = 3
Put x= -12+ 5z in equation 1 and 3
-12+ 5z - 2y + z= -6
6z - 2y = 6
3z - y= 3............(a)
and, 12 - 5z + 6y + 4z = 3
6y - z = -9.......(b)
Solving a and b we get
6(3z- 3) - z = -9
18z - 18 - z= -9
17z = 9
z= 9/17
and, y= 3(9/17) - 3 = 24/17
and, x = -12 + 120/17= -84/17
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The length of a rectangle is 3 m less than twice the width, and the area of the rectangle is 27 m. Find the dimensions of the rectangle.
Answer:
4.5 m and 6 m---------------------------
Let the length be l and width be w.
Given:
l = 2w - 3,A = lw = 27.Substitute l and solve for w:
lw = 27w(2w - 3) = 272w² - 3w = 272w² - 3w - 27 = 02w² - 9w + 6w - 27 = 0w(2w - 9) + 3(2w - 9) = 0(2w - 9)(w + 3) = 02w - 9 = 0 and w + 3 = 02w = 9 and w = - 3 (discarded as distance can't be negative)w = 4.5Find the value of l:
l = 2*4.5 - 3 = 9 - 3 = 6Solve the equation. .35(x+4)=.25(X-6)
What is the constant of proportionality, k, for the data in the table above? Enter answer
Enter just the numeric answer.
Answer:
you really just click on peoples questions and just be like sorry im just here for the points so im doing it to you
Step-by-step explanation:
which relation is a function
Answer:
top right :)
Step-by-step explanation:
you can use the ruler trick! if you drag a ruler across the math problem and it crosses two lines at the same time then it's not a function. same goes for points. and as you can see if I were to drag a ruler across this one you won't pass two points at once!
The graph of the line with equation Y equals 2/3 X is shown. What is the product of 2/3 and -3
Answer:
-2
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] * -3
= [tex]\frac{2}{3}[/tex] * [tex]-\frac{3}{1}[/tex]
= [tex]-\frac{6}{3}[/tex]
= [tex]-\frac{2}{1}[/tex]
= -2
I need help pls someone I’ll give brainliest and tons of points
Answer: rotation 90 degrees counterclockwise about the origin I believe. lmk
Step-by-step explanation: counterclockwise is the key word. im jus using common sense cuz counterclock wise is from the left, and there is a rotation. lmk if it wrong tho
Which statement is correct about the product of
3
2
3
and
10
9
?
Because
10
9
is greater than 1, the product of
3
2
3
and
10
9
is greater than
3
2
3
.
Because
10
9
is less than 1, the product of
3
2
3
and
10
9
is greater than
3
2
3
.
Because
10
9
is less than 1, the product of
3
2
3
and
10
9
is less than
3
2
3
.
Because
10
9
is greater than 1, the product of
3
2
3
and
10
9
is less than
3
2
3
.
option B is correct. 10/9 is greater than 1, the product of [tex]3\frac{2}{3}[/tex] and 10/9 is greater than 3 is the statement,
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
We need to find the product of [tex]3\frac{2}{3}[/tex] and 10/9.
Firstly let us convert the mixed fraction [tex]3\frac{2}{3}[/tex] to the improper fraction.
11/3 is the simplified form of [tex]3\frac{2}{3}[/tex]
11/3×10/9
110/27
4.1
As we observe the 10/9 is greater than 1, the product of [tex]3\frac{2}{3}[/tex] and 10/9 is greater than 3.
Hence, the statement 10/9 is greater than 1, the product of [tex]3\frac{2}{3}[/tex] and 10/9 is greater than 3.
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To simplify 8.3-4 1/5 (6.1+1/2) which operation must be performed first? Which is second and which is third?
the answer to the expression 8.3-4 1/5 (6.1+1/2)is -19.42
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
The given expression
8.3-4 1/5 (6.1+1/2)
=8.3-4 1/5 (6.6)
=8.3-(6.6*21/5)
=-19.42
Hence the answer is -19.42
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Help would be appreciated
The correct reason for the similarity of triangles ADC and CBA is given as follows:
SSA.
What are the similarity theorems?The similarity theorems are listed as follows:
SAS: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent by the SAS theorem.ASA: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent by the ASA theorem.SSS: If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are congruent by the SSS theorem.SSA: If two sides and an angle not include between them are respectively equal to two sides and an angle of the other then the two triangles are congruent by the SSA theorem.In this problem, we have that:
Sides AB and DC are equal.Angles BAC and DCA are equal.Sides AC are equal.Two sides and an angle not between them, hence they are congruent by the SSA theorem.
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what is 2 4/5+ 4/6 equivalent to?
Answer:
To find the equivalent of 2 4/5 + 4/6, we first need to convert the mixed numbers to improper fractions. To do this, we multiply the whole number part of the mixed number by the denominator of the fraction part, and add the result to the numerator of the fraction part. So 2 4/5 becomes 2 * 5 + 4 = 14/5. Similarly, 4/6 becomes 4 * 1 + 6 = 10/6.
Next, we need to find a common denominator for the two fractions so that we can add them. A common denominator for 14/5 and 10/6 is 30, so we convert both fractions to have a denominator of 30. To convert 14/5 to have a denominator of 30, we multiply the numerator and denominator by 6, which gives us 14 * 6 / 5 * 6 = 84/30. Similarly, we multiply the numerator and denominator of 10/6 by 5 to get 10 * 5 / 6 * 5 = 50/30.
Now that both fractions have a denominator of 30, we can add them to get the equivalent of 2 4/5 + 4/6. This gives us 84/30 + 50/30 = 134/30. Finally, we simplify the fraction to get the final answer, which is 134/30 = 4 8/30 = 4 4/15. So, the equivalent of 2 4/5 + 4/6 is 4 4/15.
The table shows the total amount D in dollars that Dave charges to clean windows in r rooms he charges the same amount per room to clean windows complete the table to show the amount that each person charges to clean our rooms
The individual charges of Nikki and Dave are mentioned in the table -
Nikki Dave
$20 $12.5
$40 $25
$60 $37.5
$80 $50
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.The complete question is shown in the image attached in the end.
For Nikki, the charge function is given as -
n = 20r
We can write the charge function for Dave as follows.
We have the following points -
(1, 12.50) and (4, 50)
The charge function is equivalent to -
n = {(50 - 12.5)/(4 - 1)}r
n = (37.5/3)r
n = 12.5r
We can write the table for both Nikki and Dave as -
Nikki Dave
$20 $12.5
$40 $25
$60 $37.5
$80 $50
Therefore, the complete table representing the individual charges of Nikki and Dave are -
Nikki Dave
$20 $12.5
$40 $25
$60 $37.5
$80 $50
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I’ll give BRAINLIEST if correct question is in the photo
Explain how to solve the question in the photo f(x)=5x+3
Solve the inequality 4x≥60. Then describe how the graph of the solution would look on a number line.
The inequality of the solution is x > 15.
How to solve inequality?Make use of the following procedures to solve an inequality:
Step 1: Remove fractions by multiplying all terms by the fractions' lowest common denominator.Step 2 Combine like terms on both sides of the inequality to simplify.Step 3 Obtain the unknown on one side and the integers on the other by adding or subtracting amounts.We need to eliminate the coefficient that multiplies the variable in this linear inequality in order to isolate it.
By dividing both sides by 4, this may be done.
The inequality of the solution is
4x≥60.
=[tex]\frac{4x}{4} \geq\frac{60}{4} \\\\= \frac{x}{1} \geq 15\\\\x\geq 15[/tex]
The inequality of the solution is x > 15.
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what table does not represent a function please help!!
Answer:
A,C
Step-by-step explanation:
A,C
Functions have only one output for every input
Chloe runs a farm stand that sells apples and peaches. Each pound of apples sells for
$3 and each pound of peaches sells for $4. Chloe sold 3 times as many pounds of
peaches as pounds of apples and she made $240 altogether. Graphically solve a
system of equations in order to determine the number of pounds of apples sold, x,
and the number of pounds of peaches sold, y.
pls help! plot on a line
Answer:
3x+4y=240; y=3x16 pounds of apples48 pounds of peachesStep-by-step explanation:
You want a system of equations and a graphical solution for the scenario that the weight of peaches sold (y) is 3 times the weight of apples sold (x), and the revenue from sales of apples at $3/lb and peaches at $4/lb was a total of $240.
EquationsThe revenue equation can be ...
3x +4y = 240
The relation between pounds of each fruit sold can be ...
y = 3x
GraphThe graph is attached. The solution is (x, y) = (16, 48).
16 pounds of apples and 48 pounds of peaches were sold.
__
Additional comment
We note that the 3x in the first equation can be substituted by y using the second equation. This gives 5y=240, or y = 48. Then 3x=48, so x=16. This agrees with the graphical solution, as it should.
If JK = 31, KI = 40, and NL = 12, find the length of MN. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale. 95⁰ 34° K N 34° M 950 51° L
please help i need this soon!!
The length of the MN is 9.4.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Triangle NML.
NL = 12
Sin 51 = NM / NL
0.78 = NM / NL
MN = 0.78 x NL
MN = 0.78 x 12
MN = 9.36
Rounding to the nearest tenth.
MN = 9.4
Thus,
MN is equal to 9.4.
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8) Micaela and Sumalee each improved their yards by planting hostas and shrubs. They bought their
supplies from the same store. Micaela spent $33 on 3 hostas and 6 shrubs. Sumalee spent $42 on 6
hostas and 6 shrubs. What is the cost of one hosta and the cost of one shrub?
Cost of shrub is $4 and Cost of hosta is $3. Cost is the value of money that was spent on producing or providing a service and is therefore no longer available for use.
How to calculate cost ?The term "cost" can refer to the amount of money or other resources that are required to produce, acquire, or obtain something. In business and economics, cost is often used to refer to the total expense associated with a product or service, including materials, labor, and other expenses.
Micaela spent a total of $33 on 3 hostas and 6 shrubs. Since the cost of the hostas is H x 3 and the cost of the shrubs is S x 6, we can write the following equation:
H * 3 + S * 6 = 33
Similarly, Sumalee spent a total of $42 on 6 hostas and 6 shrubs, so we can write the following equation:
H * 6 + S * 6 = 42
cost 3 hostas and 6 shrubs = $33
cost 6 hostas and 6 shrubs = $42
Cost difference 33 - 42 = 9
So, cost of 3 hostas = $9
Cost of one hosta = $9/3 = $3
$9 + cost of 6 shrubs = $33
cost of 6 shrubs = $33- $9 = $24
Cost of one shrub = $24/6 = $4
Cost of shrub is $4 and Cost of hosta is $3.
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Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The equation that is a quadratic is 2(x + 5)4 + 2x² + 5 = 0
Option C is the correct answer.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
A quadratic equation is an equation with a second degree in x.
Now,
[tex]x^4[/tex] – 6x² – 27 = 0
This is not second-degree in x.
3[tex]x^4[/tex] = 2x
3x³ = 2
This is not the second degree in z.
2(x + 5)4 + 2x² + 5 = 0
8x + 40 + 2x² + 5 = 0
2x² + 8x + 45 = 0
This is in the second degree in x.
6(2x + 4)2 = (2x + 4) + 2
24x + 48 = 2x + 4 + 2
22x + 42 = 0
This is not in the second degree of x.
6[tex]x^4[/tex] = -x² + 5
This is not in the second degree of x.
8[tex]x^4[/tex] + 2x² – 4x = 0
This is not in the second degree of x.
Thus,
The quadratic equation is 2(x + 5)4 + 2x² + 5 = 0
Option C is the correct answer.
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can someone please help
Step-by-step explanation: When you divide the 2 by 9, you get like 0.222222 (and it repeats forever), then since the 2 is less than 5, you round down, so it would be 0.22 after rounding. I hoped this helped!
Write as a mixed number & simplify, if possible. 4 1/3 divided by 3 1/6
Answer:
1 7/19
Step-by-step explanation:
First, to solve this problem, you change the mixed fraction to improper fractions:
13/3 / 19/6
Now, you make it into a multiplication problem by multiplying the first number by the reciprocal of the second number.
13/3 x 6/19
Simplify :
13/1 x 2/19
Multiply the numerators by denominators to get the total:
26/19 or simplified: 1 7/19
Given the equation cosx = x^2 prove that it has at least one root in the [0, pi] interval. Justify answer by indicating the theorem used.
1 is the root of the equation cosx = x² in the interval [0, pi]/
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given equation is cosx = x²
cosx-x²=0
y(x)=cosx-x²
y(0)=1
y(π)=-1-π²
y(π)<0<y(0) and y is continuous, there must be a value of x in [0, pi]
where
cosx−x²=0.
Hence, 1 is the root of the equation cosx = x² in the interval [0, pi].
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Express the radical using the imaginary unit, i.
Express your answer in simplified form.
±√-27 = ±
Answer:
±3i√3
= -3i√3 or 3i√3
Step-by-step explanation:
Simplify the complex radical
From 2010 to 2012, the average selling price of tablets decreased by 20%. This percent
reduction amounted in a decrease of $140. Find the average selling price of tablets in 2010
and in 2012.
In 2010, the average selling price was $, and in 2012, the average selling price was $[
Answer:
In 2010, the average selling price was $700, and in 2012, the average selling price was $560.
special Right triangles I just need the values of x,z, and y
Answer:
x = 17√3 ; y = 34√2 ; z = 34
Step-by-step explanation:
angle 30° = hypotenuse double of leg
hypotenuse = 17 · 2 = 34
x = 17 · √3 = 17√3
Angle of 45 degrees = two equal legs
z = 34
For the Pythagorean theorem
y = [tex]\sqrt{34^2 + 34^2} = \sqrt{2 (34)^2} = 34\sqrt{2}[/tex]
Answer:
Your answer is: x = 17√3 ; y = 34√2 ; z = 34. Hope it helps.
Step-by-step explanation:
The assets and liabilities of a doctor are listed below.
Home Value $475,732
Mortgage $105,678
Credit Card Balance $7,264
Owned Work Equipment $45,798
Car Value $50,761
Investments $75,283
Personal Loan $32,187
What is the total value of the doctor's capital assets?
$45,798
$50,761
$572,291
$647,574
Answer: $647,574
Step-by-step explanation:
Capital assets are significant pieces of property such as homes, cars, investment properties, stocks, bonds, and collectibles or art. For businesses, a capital asset is an asset with a useful life longer than a year that is not intended for sale in the regular course of the business's operation.
The capital asset is recorded as its value regardless of any loan that may have been used to purchase it.
Capital assets here are: Home value, work equipment, car, and investments.
All other items are liabilliabilities.
The total value of the doctor's capital assets will be $647,574. Then the correct option is D.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
Significant pieces of property including houses, automobiles, rental properties, stocks, bonds, and collectibles or works of art are referred to as capital assets. An asset having a useful life longer than a year that is not intended for sale during normal company operations is referred to as a capital asset for enterprises.
The assets and liabilities of a doctor are listed below.
Home Value $475,732
Mortgage $105,678
Credit Card Balance $7,264
Owned Work Equipment $45,798
Car Value $50,761
Investments $75,283
Personal Loan $32,187
The total value of the doctor's capital assets will be given as,
⇒ $475,732 + $45,798 + $50,761 + $75,283
⇒ $647,574
The total value of the doctor's capital assets will be $647,574. Then the correct option is D.
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The measure of one of the small angles of a right triangle is 6 more than 3 times the measure of the other small angle. Find the measure of both angles.
Input your answers into the following boxes.
The measures of the two angles in the order from the smallest to the greatest are
degrees and
degrees.
The measures of two angles in the order from the smallest to the greatest are 21° and 69°.
What is a right triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
Given the acute angle of a right triangle is 6 more than 3 times the measure of the other small angle.
Assume that the measurement of smaller angle is x.
Then the mathematical expression of 6 more than 3 times of x is 6 + 3x.
The measure of third angle is 90° since it a right triangle.
The sum of all interior angles of a right triangle is 180°.
The equation is
x + (6 + 3x) + 90 =180
x + 6 + 3x + 90 =180
Combine like terms:
(x + 3x) + (6 + 90) = 180
4x + 96 = 180
Subtract 96 from both sides:
4x = 180 - 96
4x = 84
Divide both sides by 4
x = 21
Putting x = 21 in the expression (6 + 3x) :
6 + 3x = 6 + 63 = 69.
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Simplify the expression 3x(-2x + 5).
O 6x + 5
O 6x + 15
O-6x² +5
O -6x² + 15x
Step-by-step explanation:
3x(-2x + 5) = 3×-2×x×x + 3×5×x =
= -6x² + 15x
so, the 4th answer option is correct.
Turn 584/50 in improper fraction 
You have one type of chocolate that sells for $2.10/lb and another type of chocolate that sells for $9.90/lb. You would like to have 62.4 lbs of a chocolate mixture that sells for $2.40/lb. How much of each chocolate will you need to obtain the desired mixture?
You will need __ lbs of the cheaper chocolate and __ lbs of the expensive chocolate.
Answer:
This is a problem of weighted averages and can be solved with a system of equations.
Let's define:
- `x` as the amount (in lbs) of the cheaper chocolate,
- `y` as the amount (in lbs) of the expensive chocolate.
We can set up the following equations:
1. `x + y = 62.4` (the total amount of chocolate we want)
2. `$2.10x + $9.90y = $2.40 * 62.4` (the total cost of the chocolate mixture)
The second equation represents the total value of the chocolate, while the first represents the total weight.
We can solve this system of equations using substitution or elimination. In this case, it may be simpler to use elimination.
Let's first transform the second equation to get rid of the dollar signs:
2.10x + 9.90y = 2.40 * 62.4
2.10x + 9.90y = 149.76
Let's now multiply the first equation by 2.10 (the price per lb of the cheaper chocolate):
2.10x + 2.10y = 2.10 * 62.4
2.10x + 2.10y = 131.04
Subtracting the second equation (multiplied) from the original second equation, we get:
9.90y - 2.10y = 149.76 - 131.04
7.80y = 18.72
Solving for y, we get:
y = 18.72 / 7.80 = 2.4 lbs
Substituting y = 2.4 into the first equation:
x + 2.4 = 62.4
x = 62.4 - 2.4 = 60 lbs
So, you will need 60 lbs of the cheaper chocolate and 2.4 lbs of the expensive chocolate to obtain the desired mixture.