5(x - 3) +6 = 5x - 9 has infinitely many solutions
Solution:Given equation is 5(x - 3) +6 = 5x - 9
We have to find whether the given equation has one, zero, or infinitely many solutions
Let us solve the given equation
5(x - 3) + 6 = 5x - 9
Let us use BODMAS rule to solve the given equation
According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right
So let us first solve for brackets in given equation
5x - 15 + 6 = 5x - 9
5x - 9 = 5x - 9
0 = 0
Since the statement is true, there are infinitely many solutions
Three different ways to put 6(3x + 8) + 32 + 12x
Answer:
Writing 6(3x + 8) + 32 + 12x in 3 different ways:
w₁ = 18x + 48 + 32 + 12x∵ 6(3x + 8) = 18x +48 as distribute law suggests that a(b + c) = ab + ac
w₂ = 18x + 80 + 12x ∵ 48 + 32 = 80 w₂ = 30x + 80 ∵ 18x + 12x = 30xStep-by-step explanation:
As the expression is 6(3x + 8) + 32 + 12x, and we have to write it in three different ways. Using the properties of operations we can write it in three different ways,
Let way one be denoted as w₁
Let way two be denoted as w₂
Let way three be denoted as w₃
So, lets write 6(3x + 8) + 32 + 12x in 3 different ways:
w₁ = 18x + 48 + 32 + 12x∵ 6(3x + 8) = 18x +48 as distribute law suggests that a(b + c) = ab + ac
w₂ = 18x + 80 + 12x ∵ 48 + 32 = 80 w₂ = 30x + 80 ∵ 18x + 12x = 30xKeywords: operation properties, distributive law
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3. What is the y-intercept in the equation y= -2x + 5
a) -2
I c) 5
b)3
d) Cannot be Determined
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Equations are generally in the form of:
y = mx + c
where m is the gradient and c is the y intercept
As you can see, in this equation, the y intercept is 5
Thus, your answer is C. 5
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The variable X varies directly with Z the constant variation is -6 write an equation of a direct variation modeling the situation
Answer:
x = - 6z
Step-by-step explanation:
The equation of quantities in direct variation is
y = kx ← k is the constant of variation
Here k = - 6, thus
x = - 6z ← equation of variation
What is the sum of the digits in 18
Answer:
9
Step-by-step explanation:
1+8=9
Answer:
9
Step-by-step explanation:
1+8=9
PLs, help! VVVVVVVVVVVV
Answer:
see explaination
Step-by-step explanation:
the diagram shows two equal parts being the divided by two in the equations. The parts are worth 8 meaning if you divide 16 by 8 it is 2 because there are two parts.
Answer:
8x2 = 16
Step-by-step explanation:
8x2 = 16
16/2 = 8
Stretch thinking Rewrite this sentence using the word fewer. Carey reads 10more pages than Lucey.
Answer:
Lucey reads 10 pages fewer than Carey.
HELP
How would I find C? would I have to subtract 180 from 50??
Answer:
m∠C = 115°
Step-by-step explanation:
DE≈DF
ΔDEF is an isosceles triangle ∴ m∠DEF = m∠DFE = 1/2 (180-50) = 65
∴ m∠DFB = 180 -65 = 115
∵ DCBF is a parallelogram m∠DFB = m∠DCB = 115°
Chiquita planned to do the same thing as Rhonda, but she misunderstood what Rhonda meant when she
said "...20% smaller than the one below it." Chiquita made her first ball the same size as Rhonda but
then decreased the volume by 20% for each subsequent ball. How much taller is Chiquita's completed v
snowman than Rhonda's completed snowman? Express your answer as a decimal to the nearest tenth.
Plz show full work
Answer:
to find how much taller Chiquita’s completed snowman is than Rhonda's completed Snowman
We divide the Height of the Chiquita’s snowman by the height of Rhonda’s Snowman
i.e. 7.456/8.532 = 0.87
Step-by-step explanation:
Let Vr1 be the volume of Rhonda’s first ball, and Vc1 be the volume of Chiquita’s first ball. Since the balls are spheres the formula for obtaining their Volume value is given as V= (4/3) x ∏ r3
Since from the question we were told that the first snowball for Rhonda and Chiquita’s Snowman are the same.
Let’s assume that the Vr1 =Vc1=10m²
So to find the radius we make r the subject of formula so r =∛(3V/4∏) where V is equal to 10 for the first spheres and ∏ is a constant with value 3.142 so
r1 = ∛(3×10/4)×3.142 = 1.337m
For the Second Snow ball of Rhonda’s Snowman
Given from the question that first Snow ball is 20% less than the Second Snow Ball
Let Vr2 Denote the volume of the second Rhonda’s Snowball
Vr2 = 20% of Vr1 + Vr1
= 20% of 10 + 10
= (20/100) x 10 + 10
= 12m²
So to find the radius of the second ball for Rhonda’s Snowman
Let r2 denote the radius of the second ball
r2 = ∛(3×12/4)×3.142 = 1.420m
For the Third Snow ball of Rhonda’s Snowman
Given from the question that Second Snow ball is 20% less than the Third Snow Ball
Let Vr3 denote the volume of the third Rhonda’s Snowball
Vr3 = 20% of Vr2 +Vr2
= (20/100) x 12 +12
= 14.4m²
So to find radius of the Third ball for Rhonda’s Snowman
Let r3 denote the radius of the second ball
r3 = ∛(3×14.4/4)×3.142 = 1.509m
For the Second Snow ball of Chiquita’s Snowman
Given from the question that first Snow ball is 20% greater than the Second Snow Ball
Let Vc2 denote the volume of the second Chiquita’s Snowball
For Vc2 = Vc1 - 20% of Vc1
= 10 – (20/100) x 10
= 8m²
So to find the radius of the second ball for Chiquita
Let c2 denote the radius of the second ball
c2 = ∛(3×8/4)×3.142 =1.240m
For the Third Snow ball of Chiquita’s Snowman
Given from the question that Second Snow ball is 20% greater than the third Snow Ball
Let Vc3 denote the volume of the third Chiquita’s Snowball
For Vc3 = Vc2 - 20% of Vc2
= 8 – (20/100) x 8
= 6.4m²
So to find the radius of the second ball for Chiquita
Let c3 denote the radius of the second ball
c3 =∛((3×6.4/4)×3.142) = 1.151m
Therefore Height of Rhonda’s Snowman = Dr1 + Dr2 + Dr3
= 2×r1 +2×r2 +2×r3
= (2×1.337) + (2×1.420) + (2×1.509)
= 8.532m
Therefore the Height of Chiquita’s Snowman = Dc1 + Dc2 +Dc3
= 2×c1 +2×c2 +2×c3
= (2×1.337) + (2×1.240) + (2×1.151)
= 7.456m
No to find how much taller Chiquita’s completed snowman is than Rhonda's completed Snowman
We divide the Height of the Chiquita’s snowman by the height of Rhonda’s Snowman
i.e. 7.456/8.532 = 0.87
Note: if we assume another value for Vr1 = Vc1 we will still get the same ratio.
Evaluate 6x + 3y - 4, if x = 20 and y= 2.
O D.
8
Answer:
122
Step-by-step explanation:
6x+3y-4=6(20)+3(2)-4=120+6-4=126-4=122
y = -x + 8
y= 5/2x - 6
Plot two lines by clicking the graph.
Click a line to delete it.
Answer:
Step-by-step explanation:
Discussion for Applications of Linear Systems
When solving a system of equations, how do you determine which method to use?
Step-by-step explanation:
There are certain methods for solving a system of equations. Some of which are:
Substitution MethodElimination MethodGraphing MethodSubstitution Method
Substitution method to solve a system of equations is suitable if a variable of a any equation seems isolated or could comfortably be isolated without any ration/fraction resulting.
For example, for the following system of equations
x - 2y = 11....[A]
x = 5 - y....[B]
substituting the value of x = 5 - y from equation [B] into equation [A], so that
(5 - y) - 2y = 11
5 - y - 2y = 11
3y = -6
y = -2
Elimination Method
Elimination method to solve a system of equations is suitable if both equation are in standard form, and just adding or subtracting the equations to determine an equation in one variable.
For example, for the following system of equations
2x + 7y = -5....[C]
5x - 7y = 12....[D]
Adding Equation [C] and Equation [D].
7x + 0 = 7
x = 1
Graphing Method
Sometimes graphing method may be used to solve the system of the equation and visualize the solution.
For example,
y = -2....[E]
y = 3x + 1....[F]
The solution for this system of equation is the point of intersection of both the lines, which is shown in attached figure. The point of intersection is (-1, -2).
Hence, the solution of this system of equations is (-1, -2), as shown in attached figure.
Keywords: system of equations, elimination method, substitution method, graphing method
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Can somebody please help me with this question?
Answer:
c
Step-by-step explanation: first part of the equations.
[tex]-8x+3\geq 27\\-8x\geq 24\\x\leq -3[/tex]
so first you will subtract 3 from both side of the inequality. The divide by -8 on both side which will flip the inequality sign.
second equation
[tex]-13x+5\geq 57\\-13x\geq 52\\x\leq -4[/tex]
So you subtract 5 from both side then divide by -13 on both side and you need to flip the inequality sign because you divide by a negative.
now you will write the expression for it.
[tex]-4\leq x\leq -3[/tex]
we put x in the middle because it an and statement so that is why you would put x in the middle.
What is the answer ? Please
Answer:
1 1/18 kilograms
Step-by-step explanation:
First add 3/8 + 11/8, which equals to 11/8. Then add 5/8, which equals to 19/8. Change the improper fraction to a mixed number, and the sum is 1 1/18.
ans is 19/8 kilogram.......
Anna is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Anna will earn $30 every time one of her songs is played in a commercial and she will earn $80 every time one of her songs is played in a movie. Anna's songs were played on 3 more commercials than movies, and her total earnings on the royalties from all commercials and movies was $640. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Anna's songs were played. Define the variables that you use to write the system.
x=y+3 and 30x+80y=640 is the system of equations for given statement where x represents the number of commercials and y represent the number of movies on which Anna's songs were played.
Step-by-step explanation:
Given,
Earning for song played in commercial one time= $30
Earning for song played in movie one time = $80
Let,
x represent the number of commercials Anna's song played.
y represent the number of movies Anna's song played.
According to given statement;
Anna's songs were played on 3 more commercials than movies
x=y+3
her total earnings on the royalties from all commercials and movies was $640.
30x+80y=640
x=y+3 and 30x+80y=640 is the system of equations for given statement where x represents the number of commercials and y represent the number of movies on which Anna's songs were played.
Keywords: linear equation, substitution method
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Final answer:
To solve the question, two variables are defined: c for commercials and m for movies. The system of equations is $30c + $80m = $640 and c = m + 3, representing Anna's royalties from commercials and movies.
Explanation:
The student's question involves creating a system of equations to determine the number of commercials and movies on which Anna, a songwriter who collects royalties, had her songs played. We are given that Anna earns $30 from each commercial and $80 from each movie her songs are played in. It is also known that her songs were played in 3 more commercials than movies, and she earned a total of $640. To formulate the system of equations, we introduce two variables: let c represent the number of commercials and m represent the number of movies.
The first equation represents the total earnings based on the number of plays:
$30c + $80m = $640.
The second equation represents the relationship between the number of commercials and movies:
c = m + 3.
Combining these two equations gives us a system that can be solved to find the values of c and m.
By substituting the second equation into the first equation, we can create a system of equations:
30(M + 3) + 80M = 640
30M + 90 + 80M = 640
110M + 90 = 640
110M = 550
M = 5
Now that we have found the number of movies (M = 5), we can substitute this value back into the equation C = M + 3 to find the number of commercials:
C = 5 + 3
C = 8
The surface are of a cylinder is given by the formula SA=2pir^2+2pirh,where r is the radius of the base of the cylinder and h is the height of the cylinder. Solve the formula for h in the space given below.show all the steps.
Answer:
A = 2πr2 + 2πrh is the final answer
Step-by-step explanation:
Answer:
h = (x-2πr²)/2πr
Step-by-step explanation:
Given the surfaces area of a cylinder by the formula
SA = 2πr²+2πrh
To solve for h means making h the subject of the formula from the equation.
Let x be the surface area of the cylinder. The formula can be rewritten as;
x = 2πr²+2πrh
Subtracting 2πr² from both sides of the equation will give;
x-2πr² = 2πr²+2πrh-2πr²
x-2πr²= 2πrh
Dividing both sides by 2πr wikk results into;
(x-2πr²)/2πr = 2πrh/2πr
h = (x-2πr²)/2πr where x is the surface area of the cylinder.
Emily's family loves to work together
in the garden. They have a.
preference for flowers as 80% of
their plants are flowers and the rest
are vegetables. They have 90 plants
in the garden. How many vegetable
plants do they have?
Answer:
They have 18 vegetable plants.
Step-by-step explanation:
Given:
Emily's family loves to work together in the garden.
They have a. preference for flowers as 80% of their plants are flowers and the rest are vegetables.
They have 90 plants in the garden.
Now, to find the number of vegetable plants.
Total plants in the garden = 90.
80% of the plants are flowers.
So, number of plants which are flowers = 80% of 90.
[tex]=\frac{80}{100} \times 90[/tex]
[tex]=\frac{7200}{100}[/tex]
[tex]=72\ plants.[/tex]
The number of flower plants = 72.
Total plants = 90 (given)
So, to get the number of vegetable plants we subtract:
[tex]90-72=18\ plants.[/tex]
Thus, vegetable plants = 18.
Therefore, they have 18 vegetable plants.
When multiplying polynomials for a math assignment, Pat found the product to be -4x+8x^2-2x^3+5. He then had to state the leading coefficient of this polynomial. Pat wrote down -4. Do you agree with Pat’s answer? Explain your reasoning.
Answer:
I am not agree with him. Because -2 is the leading coefficient of this polynomial.
Step-by-step explanation:
Pat multiplied the polynomials for a math assignment.
Then he found the product is [tex]-4x+8x^2-2x^3+5[/tex]
Now Pat wants to find the leading coefficient to this polynomial.
Pat's answer was -4.
But I am not agree with him.
Because for a given polynomial we can calculate the leading coefficient when comparing with degrees of the polynomial.
Leading coefficient means that the coefficient whose degree is the highest.
When compared with the given polynomial we have [tex]x^3[/tex] is the highest degree, so that -2 is the leading coefficient to this polynomial.
The monthly salary of a show room attendant is the sum of a fixed
salary of $600 plus 8% of all monthly sales. What should the monthly
sales be so that her monthly salary reaches $1,800?
Answer:
Monthly sales = $15000
Step-by-step explanation:
Let x be the monthly sale.
Given:
The monthly salary of a show room attendant is the sum of a fixed salary of $600 plus 8% of all monthly sales.
8% of monthly sale = [tex]\frac{8}{100}\times mothly\ sale[/tex]
8% of monthly sale = [tex]\frac{8}{100}\times x[/tex]
So, the monthly salary of attendant is.
[tex]Monthly\ salary = 600+8\ percent \ of\ monthly\ sales[/tex]
[tex]Monthly\ salary = 600+\frac{8}{100}\times x[/tex]
Monthly salary is given.
[tex]1800 = 600+\frac{8}{100}\times x[/tex]
[tex]1800 - 600 = \frac{8}{100}\times x[/tex]
[tex]1200 = \frac{8}{100}\times x[/tex]
[tex]x=\frac{1200\times 100}{8}[/tex]
[tex]x=\frac{120000}{8}[/tex]
[tex]x=15000[/tex]
Therefore, the monthly sale is $15000
Each story in Will's apartment building is 9 feet tall. There are 10 stories in the building. How tall is the apartment building?
Answer:
the building is 90 feet tall
Step-by-step explanation:
each floor is 9 feet, there are 10 floors,
9 x 10 = 90 feet
A teacher handed out 10 notebooks in packs with 5 notebooks in each pack. How many packs were there?
Answer:
2 packs
Step-by-step explanation:
Since there is 10 packs just divided it by how many notebooks were in the pack.
Oscar project inquiry
The Academy Awards, also known as Oscars, are prestigious awards recognizing achievements in the film industry. The OscarsSoWhite controversy raised concerns about diversity and representation in Hollywood.
Explanation:Academy Awards, commonly known as Oscars, are prestigious awards in the film industry recognizing outstanding achievements in various categories. The controversy surrounding the OscarsSoWhite highlighted issues about diversity and representation in Hollywood.
The base of a 40-foot ladder is 8 feet from the wall. How high is the ladder on the wall (round to the nearest foot)?
Answer:
Around 39.2
Step-by-step explanation:
To do this question, you use the pythag theorem, a^2 + b^2 = c^2. You have the hypotenuse of the triangle, 40 feet in length, and you have a because it's 8 feet from the wall. You now have b^2 = 1600-64. b^2 = 1536. Take the square root, and you have the height of the latter on the wall is equal to 39.1918 or 39.2 rounded
8) What is "7 less than 3 times c" represented as an
algebraic expression?
3c - 7
3 times c = 3c
7 less than is subtraction
Answer:
3c - 7
Step-by-step explanation:
less than = flip the equation
If $650 is invested in a bank account that earns a nominal 2.5% yearly interest, compounded quarterly, then how much is the investment worth after 10 years
Answer:
[tex]\$833.97[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ P=\$650\\ r=2.5\%=2.5/100=0.025\\n=4[/tex]
substitute in the formula above
[tex]A=650(1+\frac{0.025}{4})^{4*10}[/tex]
[tex]A=650(1.00625)^{40}[/tex]
[tex]A=\$833.97[/tex]
A large bottle contains 1.3 liters of olive oil. A medium-sized bottle has 0.8 times the amount of olive oil as the large bottle.
How much more olive oil does the large bottle contain than the medium-sized bottle?
Answer: 0.236 Liters.
Step-by-step explanation:
First you multiply 1.3 and 0.8 you get 1.064.
You subtract 1.3 and 1.064 and you get your answer 0.236 Liters.
What is the slope of the line parallel to the line y = -5/3x + 5?
A) -5/3
B) -3/5
C) 3/5
D) 5/3
Answer:
C
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 )
y = - [tex]\frac{5}{3}[/tex] x + 5 ← is in slope- intercept form
with slope m = - [tex]\frac{5}{3}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular }[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{5}{3} }[/tex] = [tex]\frac{3}{5}[/tex]
Answer:
5/3
Step-by-step explanation:
HELP PLEASEE!!!I DONT UNDERSTAND THIS
Answer:
Median
Step-by-step explanation:
Median, in geometry, is a line segment that is drawn from the vertex or the corner of the shape that extends to the middle or the midpoint of the side opposite of that corner.
When you say opposite the corner, that means it is the one across it. Look at the attached picture for emphasis.
Reasoning A ship is sighted from the top of a lighthouse.
The angle of depression from the lighthouse to the ship is 45°
The distance from the top of the lighthouse directly to the ship is 4 miles.
Calculate the horizontal distance of the ship from the bottom of the lighthouse
Give your answer correct to 2 decimal places.
Answer: Sin45 = x/4
x = 4Sin45
x = 2.83miles
Step-by-step explanation:
Final answer:
The horizontal distance of the ship from the bottom of the lighthouse is equal to the direct distance from the lighthouse to the ship, which is 4.00 miles, because the angle of depression is 45 degrees forming an isosceles right-angled triangle.
Explanation:
The student is asking how to calculate the horizontal distance of a ship from the bottom of a lighthouse when the angle of depression from the top of the lighthouse to the ship is 45° and the direct distance from the lighthouse to the ship is 4 miles. This is a trigonometry problem involving right-angle triangles.
Since the angle of depression is 45°, we can establish that the lighthouse height and the horizontal distance will be equal due to the properties of an isosceles right-angled triangle. Thus, the horizontal distance from the bottom of the lighthouse to the ship is the same as the distance from the top of the lighthouse directly to the ship, which is given as 4 miles. Therefore, the horizontal distance is 4.00 miles.
what is an equation of the line that passes through the points (-4,-1) and (2,8)?
Answer:
y=3/2 x + 5
Step-by-step explanation:
[tex]y = mx + c[/tex]
Firstly, find m (gradient).
m= (y1-y2)/(x1- x2)
m= 8-(-1)/ 2-(-4)
m= 9/ 6
m= 3/2
Please leave gradient in improper fraction if its value is not a whole number.
Now substitute m into the equation:
y= 3/2 x + c
Then substitute a coordinate to find c:
When y= 8, x= 2,
8= 3/2 (2) + c
8= 3 + c
c= 8 - 3 = 5
Thus, the equation of the line is y= 3/2 x + 5.
21. What method can be used to prove the
triangles below are congruent?
A. SSS
B. SAS
C. HL
D. Not Possible
Answer:
there is not a triangle
Step-by-step explanation:
but if is has all 3 sides the same it is sss, if there is two sides and an angle in between them it is sas, and if there is a hypotenuse and then a leg then it is hl, or if it is none it is d
The method that can be used to prove the triangles below are congruent is the SAS (Side-Angle-Side) criterion. To prove that two triangles are congruent using the SAS criterion, you need to show that two pairs of corresponding sides are congruent and the included angles between them are congruent. In the given options, B. SAS is the correct answer.
Explanation:The method that can be used to prove the triangles below are congruent is the SAS (Side-Angle-Side) criterion.
To prove that two triangles are congruent using the SAS criterion, you need to show that two pairs of corresponding sides are congruent and the included angles between them are congruent.
In the given options, B. SAS is the correct answer.
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