Victoria needs to order some new supplies for the restaurant where she works. The restaurant needs at least 673 glasses. There are currently 368 glasses. If each set on sale contains 10 glasses, write and solve an inequality which can be used to determine x, the number of sets of glasses Victoria could buy for the restaurant to have enough glasses.
Answers
Using a linear function, we have that:
The inequality is: [tex]368 + 10x \geq 673[/tex].The solution is: [tex]x \geq 31[/tex].What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Since there are currently 368 glasses(y-intercept), and each set on sale comes with 10 glasses(slope), the number of glasses after x sales is given by:
y = 368 + 10x.
She needs at least 673 glasses, hence the inequality is:
[tex]y \geq 673[/tex]
[tex]368 + 10x \geq 673[/tex].
Now we solve the inequality to find the number of sets needed:
[tex]10x \geq 305[/tex]
[tex]x \geq 30.5[/tex]
As the number of sets is an integer number, the solution is:
[tex]x \geq 31[/tex].
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Related Questions
A cylindral drill with radius 5 cm is used to bore a hole through the center of a sphere with radius 9 cm. Find the volume of the ring-shaped solid that remains.
Answers
The volume of the ring-shaped remaining solid is 1797 cm³.
The volume is the total space occupied by an object.
The volume of a sphere of radius r units is given as (4/3)πr³.
The volume of a cylinder with radius r units and height h units is given as πr²h.
In the question, we are asked to find the volume of the remaining solid when a sphere of radius 9cm is drilled by a cylindrical driller of radius 5cm.
The volume will be equal to the difference in the volumes of the sphere and cylinder, where the height of the cylinder will be taken as the diameter of the sphere (two times radius = 2*9 = 18) as it is drilled through the center.
Therefore, the volume of the ring-shaped remaining solid is given as,
= (4/3)π(9)³ - π(5)²(18) cm³,
= π{972 - 400} cm³,
= 572π cm³,
= 1796.99 cm³ ≈ 1797 cm³.
Therefore, the volume of the ring-shaped remaining solid is 1797 cm³.
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Construct a square matrix A of order 3
Answers
[tex]A_{ij}[/tex] refers to the entry of [tex]A[/tex] in row [tex]i[/tex] and column [tex]j[/tex].
When [tex]i=j[/tex], the entry in question lies on the diagonal. In this case, [tex]A_{ij}=0[/tex] so
[tex]A = \begin{bmatrix} 0 & \square & \square \\ \square & 0 & \square \\ \square & \square & 0 \end{bmatrix}[/tex]
When [tex]i<j[/tex], the row number is smaller than the column number, which happens for each [tex]A_{ij}[/tex] in the upper half of [tex]A[/tex].
[tex]A = \begin{bmatrix} 0 & -1 & -1 \\ \square & 0 & -1 \\ \square & \square & 0 \end{bmatrix}[/tex]
When [tex]i>j[/tex], the row number is larger, which happens everywhere else in the matrix.
[tex]A = \begin{bmatrix} 0 & -1 & -1 \\ 1 & 0 & -1 \\ 1 & 1 & 0 \end{bmatrix}[/tex]
A website advertises job openings on its website, but job seekers have to pay to access the list of job openings. The website recently completed a survey to estimate the number of days it takes to find a new job using its service. It took the last 31 customers an average of 40 days to find a job. Assume the population standard deviation is 10 days. Calculate a 99% confidence interval of the population mean number of days it takes to find a job.
Answers
Using the z-distribution, the 99% confidence interval of the population mean number of days it takes to find a job is (35.38, 44.62).
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
The other parameters are:
[tex]\overline{x} = 40, \sigma = 10, n = 31[/tex]
Hence the bounds of the interval are:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 40 - 2.575\frac{10}{\sqrt{31}} = 35.38[/tex]
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 40 + 2.575\frac{10}{\sqrt{31}} = 44.62[/tex]
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Use matrix method to find the point of intersection between the lines:
5x+3y-35=0 and 3x-4y=-8
Answers
Hello !
[tex]\begin{cases} 5x+3y - 35&=0 \\ 3x - 4y &= - 8 \end{cases}[/tex]
[tex]\Leftrightarrow\begin{cases} 5x+3y &=35 \\ 3x - 4y &= - 8 \end{cases}[/tex]
[tex]\Leftrightarrow AX = B [/tex]
With
[tex]A=\left[\begin{array}{ccc}5&3\\3& - 4\end{array}\right] [/tex]
[tex]X=\left[\begin{array}{ccc}x\\y\\\end{array}\right] [/tex]
[tex]B=\left[\begin{array}{ccc}35\\ - 8\\\end{array}\right] [/tex]
The solution is given by [tex]X=A^{-1}B[/tex].
[tex]X= {\left[\begin{array}{ccc}5&3\\3& - 4\end{array}\right] }^{ - 1} \left[\begin{array}{ccc}35\\ - 8\\\end{array}\right] [/tex]
[tex]X=\left[\begin{array}{ccc}4\\ 5\\\end{array}\right] [/tex]
The point of intersection between the lines is (4;5).
Have a nice day
Answer:
Point of intersection (4,5)
Step-by-step explanation:
5x + 3y - 35 = 0
3x - 4y = -8
⇒ 5x + 3y = 35
3x - 4y = -8
Matrix A will be formed by the coefficient of x and y. Matrix B will be formed by the constants.
[tex]\sf A = \left[\begin{array}{cc}5&3\\3&-4\end{array}\right][/tex]
[tex]\sf B = \left[\begin{array}{c}35&-8\end{array}\right][/tex]
AX = B
[tex]\sf X =A^{-1}B[/tex]
[tex]Now ,\ we \ have \ to \ find \ A^{-1}[/tex],
Find the workout in the document attached.
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 8 meters cubed. Yolanda found the volume of the sphere.
A sphere with height h and radius r. A cylinder with height h and radius r.
Her work is shown below.
V = four-thirds (8) cubed. V = four-thirds (512). V = StartFraction 2,048 Over 3 EndFraction meters cubed.
What is Yolanda’s error?
Yolanda should have found the volume by multiplying 8 by Two-thirds.
Yolanda should have found the volume by multiplying 8 by Four-thirds.
Yolanda should have found the volume with the formula V = two-thirds pi (8) cubed.
Yolanda should have found the volume with the formula V = two-thirds (8) cubed.
Answers
Yolanda’s error during the calculation of the volume is that A. Yolanda should have found the volume by multiplying 8 by Two-thirds.
How to illustrate the volume?It should be noted that the volume of a sphere is simply 4/3πr³.
In this case, the sphere and a cylinder have the same radius and height and the volume of the cylinder is 8 meters cubed.
Based on the information given, Yolanda’s error during the calculation of the volume is that she should have found the volume by multiplying 8 by two-thirds.
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The expression (x+5)(x+8)+(x+5)(2x-3) can be written as the product of (x+5) and
Answers
B(x+8)+B(2x-3)
B(3x+5)
(x+5)(3x+5)
Please help and explain! :( I really need this
Select the correct answer.
Consider the absolute value functions c and d
An absolute value function where red line d intercepts d of x at (0, 4) and vertex at (minus 1, 2)
Which statement correctly describes these functions?
A.
The maximum value of d is 5 less than the minimum value of c.
B.
The maximum value of d is 3 less than the minimum value of c.
C.
The minimum value of d is 3 more than the maximum value of c.
D.
The minimum value of d is 5 more than the maximum value of c.
Answers
Answer:
d - the minimum value of d is 5 more than the maximum value of c
Step-by-step explanation:
we can see from the graph that d has a minimum value
that value is at (-1, 2) and the minimum is 2
for c the vertex is where the graph reflects itself
that point is (-4, -3) and the maximum is -3
that means that the minimum value of d is 5 more than the maximum value of c because 2 - (-3) = 5
Alice is playing a game in which she will roll 4 6-sided dice at the same time. She gets 5 points for each die that shows an even result. Let x represent the total number of points awarded on any given toss of the dice. What is the expected value of x
Answers
The expected value of x is 10.
It is given that the number of dice that are showing an even number is a binomial random variable with n = 4, and p = 1/2 (because half the faces on the die are even and half are odd).
The expected value of this random variable is n*p = 4*1/2 = 2.
The number of points is simply 5 times this random variable, and by the rules of expected value, E(C*Y) = C*E(Y), where C is a constant and Y is a random variable.
Thus E(X) = 5*2 = 10.
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Terry runs a snowplowing business. income from snowplowing is given by the function f(x) = 35.5x 6, where f(x) is the income in dollars and x is the snowfall in inches received during a winter. if during the years 2006 to 2011, terry’s town received 53, 42, 55, 63, 58, and 47 inches of snowfall, what was his income (in dollars) during those years?
Answers
If the function is f(x)=35.5x+6 and snowfall in inches are 53,42,55,63,58,47 then the income received will be $1887.5,$1497,$1958.5,$2242.5,$2065$1674.5.
Given Snowfall received during the years:53,42,55,63,58,47 and f(x)=35.5x+6
We have to find the income in dollars received if f(x) shows the income.
Function is a relationship between variables and it have each value of y for each value of x.
To find the income we have to just put the values of x=53,42,55,63,58,47one by one and we will get income.
f(53)=35.5*53+6=1887.5
f(42)=35.5*42+6=1497
f(55)=35.5*55+6=1958.5
f(63)=35.5*63+6=2242.5
f(58)=35.5*58+6=2065
f(47)=35.5847+6=1674.5
Hence the income for snowfall 53,42,55,63,58,47 inches are 1887.5,1497,1958.5,2242.5,2065,2674.5.
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Eden just bought a trough in the shape of a rectangular prism for her horses. She needs to know what volume of water to add to the trough. She knows that the height of the trough is 13 inches shorter than the width, and that the length is 33 inches longer than the width.
The volume of the trough, V(w), can be modeled by a polynomial function, where w is the width of the trough. Which of the following correctly models the situation and gives the rate of change of the volume over a width of 38 inches to 53 inches?
A. V(w)= w^3 + 20w^2 - 429w
Rate of Change: 2167 cubic inches per inch
B. V(w)= w^3 + 20w^2 - 429w
Rate of Change: 7658 cubic inches per inch
C. V(w)=w^2 + 429w
Rate of Change: 520 cubic inches per inch
D. v(w) = w^2 + 20w - 429
Rate of Change: 111 cubic inches per inch
Answers
The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let w represent the width, hence:
length = w + 33, height = w - 13
Volume (V) = w(w + 33)(w - 13) = w³ + 20w² - 429w
V(w) = w³ + 20w² - 429w
Rate of change = dV/dw = 3w² + 40w - 429
When w = 38, dV/dw = 3(38)² + 40(38) - 429 = 5423
When w = 53, dV/dw = 3(53)² + 40(53) - 429 = 10118
Rate = 10118 - 5423 = 4695 in³/in
The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in
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The product of 1.3 times 10 Superscript negative 4 and a number n results in 2.6 times 10 Superscript 12. What is the value of n?
2 times 10 Superscript negative 8
2 times 10 Superscript negative 3
2 times 10 Superscript 16
2 times 10 Superscript 48
Answers
The value of n is calculated as n = 2 times 10 superscript 16.
The product of 1.3 times 10 Superscript negative 4 and a number n results in 2.6 times 10 Superscript 12.
What is simplification?Simplification, in mathematics, is to solve the equation through mathematical operations
1.3 x 10^-4 x n = 2.3 x 10^12
n = 2 x 10^ 16
Thus the value of n is calculated as n = 2 times 10 superscript 16.
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What is the domain of the function y= 2√x-6?
0-00
O 0
O 3
O 6≤x<∞
Answers
Given f(x)=2−∣x−5∣
Domain of f(x) is defined for all real values of x.
Since, ∣x−5∣≥0⟹−∣x−5∣≤0
⟹2−∣x−5∣≤2⟹f(x)≤2
Hence, range of f(x) is (−∞,2].
The domain of the function y= 2√x-6 is [6, ∞).
What is a function?A relation is a function if it has only One y-value for each x-value.
In the given function, we have a square root of x-6 which means that the value inside the square root must be non-negative, otherwise the function will not be real.
Therefore, we have x - 6 ≥ 0
Adding 6 to both sides, we get:
x ≥ 6
So, the domain of the function y = 2√(x-6) is all real numbers greater than or equal to 6.
In interval notation, we can write the domain as:
Domain: [6, ∞)
Hence, the domain of the function y= 2√x-6 is [6, ∞).
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What is the completely factored form of 6 x squared minus 13 x minus 5? (2x - 5)(3x 1) (2x 5)(3x - 1) (2x - 1)(3x - 5) (2x 1)(3x 5)
Answers
Answer:
(2x - 5)(3x + 1)
Step-by-step explanation:
6x² - 13x - 5
ax² + bx + c
ac = 6 × (-5) = -30
-30 = -15 × 2
-13 = -15 + 2
6x² - 13x - 5 =
= 6x² - 15x + 2x - 5
= 3x(2x - 5) + 1(2x - 5)
= (2x - 5)(3x + 1)
Answer: its a.) (2x-5)(3x+1)
Step-by-step explanation:
6x² - 13x - 5ax² + bx + cac = 6 × (-5) = -30-30 = -15 × 2-13 = -15 + 26x² - 13x - 5 == 6x² - 15x + 2x - 5= 3x(2x - 5) + 1(2x - 5)= (2x - 5)(3x + 1)
and got it right on the test review.
The first five terms of a sequence are
7. 10, 13, 16, 19.... (a) what is the nth term of the sequence? (b) workout the 1000th term of the sequence.
Answers
Answer:
(a) 7 + 3( n - 1 )
(b) 1006
Step-by-step explanation:
ARITHMETIC SEQUENCE.
The number of term of an Arithmetic progression has the formular :
nth term = a + ( n - 1 ) d
a = 7
d = 10 - 7 = 3
nth term = 7 + ( n - 1 ) 3
= 7 + 3n - 3
= 7 + 3( n - 1 )
Therefore,
the nth term of the sequence
= 7 + 3( n - 1 )
(b) For the 1000th term
= 7 + 3 ( 1000-1 )
= 7 + ( 999 )
7 + 999 = 1006
Therefore,
the 1000th term = 1006
Suppose the length of each sude of a square is decreased by 4 ft if the perimeter of the square is now 32 feet what was the original length of each side
Answers
Answer:
12ft
Step-by-step explanation:
length of one side of the square now
32ft / 4 = 8ft
length of one side of the square before decreasing the length
(original lenght)
8ft +4ft = 12ft
EG is a tangent to the circle below at point F.
Calculate the size of angle x.
Give reasons for your answer.
Answers
[tex]\angle FHD=74^{\circ}[/tex] (alternate segment theorem)
[tex]x=77^{\circ}[/tex] (angles in a triangle add to 180 degrees)
You enter a room. 2 dogs, 4 horses, 1 giraffe and a duck lie on the bed. 3 hens fly over a chair. How many legs are there on the floor?.
Answers
Answer:
4 legs from the bed and 4 from the chair im guessing since not all have 4
Hope This Help
Answer:
4 legs from the bed and 4 from the chair
Step-by-step explanation:
im a math wizard fr
Which phrase best describes the translation from the graph y = 6x2 to the graph of y = 6(x + 1)2?
Answers
The statement which best describes the translation from the graph y= 6x² to the graph of y = 6(x+1)² is; The translation represents a unit shift rightward.
Which phrase best describes the translation from the graph?The translation involved in the transformation of the graph as given in the task content represents a rightward shift of the graph y = 6x² by 1 unit.
On this note, it follows that the translation involved between the two graphs is; a unit shift to the right.
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Answer:
Step-by-step explanation:
one unit to the right
What is the rectangular form of z = 6 (cosine (3 pi/4) +isin(3 pi/4) )?
Answers
Answer:
the answer is C, I got it too from the website, I got the answer from it
A globe company currently manufactures a globe that is 20 inches in diameter. if the dimensions of the globe were reduced by half, what would its volume be? use 3.14 for π and round your answer to the nearest tenth. 166.7 in3 1333.3 in3 523.3 in3 4186.7 in3
Answers
The volume of the modified globe would be 523.3 cubic inches (Option 3)
What is the volume of the globe with modified dimensions?
Information Given
The current diameter of the globe = 20 inches
We know that the radius of a sphere (globe) is half its diameter.
⇒ The radius of the globe = 10 inches
If the dimensions of the globe were reduced by half, the new diameter would be, [tex]\frac{20}{2} = 10[/tex] inches.
⇒ New radius of the globe, [tex]r = 10[/tex] inches
Calculating the Volume of the Modified Globe
The volume of a sphere (globe) is given by,
[tex]V = \frac{4}{3} \pi r^{3}[/tex]
Here, [tex]r[/tex] is the new radius of the globe.
∴ The volume of the new globe would be,
[tex]V = \frac{4}{3} \pi (5)^{3}[/tex]
Use [tex]\pi =3.14[/tex]
⇒ [tex]V = \frac{4}{3} (3.14) (5)^{3}[/tex]
⇒ [tex]V = 523.333..[/tex] cubic inches
Rounding off the result to the nearest tenth, we get,
[tex]V = 523.3[/tex] cubic inches
Thus, if the dimensions of the globe were reduced by half, its volume would be 523.3 cubic inches.
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Which of the following is a fifth root of the given complex number?
Answers
Answer:
D
Step-by-step explanation:
This result is true by De Moivre's theorem.
A rectangular container with a square base, an open top, and a volume of 1,372 cm3 is to be made. What is the minimum surface area for the container
Answers
The minimum surface area for the rectangular container is [tex]588cm^{2}[/tex].
How to find the surface area?A solid object's surface area is a measurement of the overall space that the object's surface takes up. Compared to the definition of the arc length of a one-dimensional curve or the definition of the surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is equal to the sum of the areas of its faces, the mathematical definition of surface area in the presence of curved surfaces is much more complex.
Let s be the side of the square base and h be the height.
Surface Area=[tex]s^{2}+4sh[/tex]
Volume=[tex]s^{2}h[/tex]
According to the question,
[tex]s^{2}h=1372\\ h=\frac{1372}{s^{2} }[/tex]
So, surface area=[tex]s^{2} +4s(\frac{1372}{s^{2} })[/tex]
=[tex]s^{2}+\frac{5488}{s}[/tex]
Differentiate with respect to s,
Surface area=[tex]2s-\frac{5488}{s^{2} }[/tex]
Now, [tex]2s-\frac{5488}{s^{2} }=0[/tex]
[tex]2s=\frac{5488}{s^{2} } \\2s^{3}=5488\\ s^{3}=2744\\ s=14[/tex]
Find the value of h from the volume.
[tex]14*14*h=1372\\h=\frac{1372}{14*14}\\ h=7[/tex]
Thus, the minimum surface area=[tex]14^{2}+4*14*7[/tex]
=[tex]588cm^{2}[/tex]
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Given the following information, determine which lines, if any, are parallel. State the
postulate or theorem that justifies your answer.
Answers
1. Lines a and b are parallel by the converse of alternate interior angles theorem
2. l║m by the converse of consecutive interior angles theorem.
What is the Converse of Alternate Interior Angles Theorem?Given that the interior angles, ∠3 ≅ ∠7, according to the converse of alternate interior angles theorem, the lines they are found on, lines a and b would be parallel.
1. Lines a and b are parallel.
What is the Converse of Consecutive Interior Angles Theorem?Given that the interior angles, m∠5 + m∠12 = 180, according to the converse of consecutive interior angles theorem, the lines they are found on, lines l and m would be parallel.
2. Lines l and m are parallel.
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3. Match the polynomial to it's correct name.
1. Quadratic trinomial
2. Cubic monomial
3. Linear binomial
4. Quartic trinomial
a. h(x) = 15x+2
b. j(x)=x²-3x³ + 9x²
c. f(x)= 3x² - 5x+7
d. 8(x)=-5x³
Answers
Answer:
1. to c.
2. to d.
3. to a.
4. to b.
Step-by-step explanation:
These answers should be right.
Hope this helps!
The matching of the polynomials to their correct names are:
a. h(x) = 15x+2 is a linear binomial
b. j(x)=x²-3x³ + 9x² is a Quartic trinomial
c. f(x)= 3x² - 5x+7 is a Quadratic trinomial
d. 8(x)=-5x³ is a Cubic monomial
How to Identify the Polynomials?A polynomial is an expression having more than one algebraic terms.
1) A quadratic trinomial is a polynomial that is defined as a quadratic expression with all three terms in the form of ax² + bx + c, where a, b, and c are numbers and not a 0.
2) A cubic monomial is defined as a a monomial that has a degree of 3.
3) Linear binomial is defined as a polynomial with two terms whose variable has degree 1. For example, 4x − 5 or 3x + 12 are both linear binomials.
4) A quartic trinomial is defined as a polynomial with three terms having the highest degree 4
Thus:
a. h(x) = 15x+2 is a linear binomial
b. j(x)=x²-3x³ + 9x² is a Quartic trinomial
c. f(x)= 3x² - 5x+7 is a Quadratic trinomial
d. 8(x)=-5x³ is a Cubic monomial
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Not mathematics, but can someone help me, and tell me what grade I deserve?
Answers
Answer:
I am not sure how that works but from the way it look and adding it up it comes to 66.6 but I was thinking around 75 - 85
Step-by-step explanation:
Answers to questions one and two please!
Answers
The inequality shows that the number of texts will be 205.
How to solve the inequality?The carriers charged $59 and 20 cents after. Therefore, the inequality to illustrate the information will be:
Let t be the number of texts.
59 + 0.2t = 100
0.2t = 100 - 59
0.2t = 41
t = 205
The number of texts will be 205.
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anybody can help me?
Answers
The graph that corresponds to the proportional relationship M = 3n is graph vs.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, the relationship is:
M = 3n.
Considering that the montant is the vertical axis, the graph is composed by points (n, 3n), that is, the vertical axis is triple the horizontal axis, having points (100, 300), (200, 600) and so on, the graph is graph vs.
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The ratio of Bananas to Mangoes to Oranges is 3:4;5. If there are 180 mangoes and oranges. How many fruits are there altogether.
Answers
Total fruits will be =x
Total ratio=12
Finding number of bananas =3/12(x)
Total number of fruits = 180+3/12(x)=x
180(12)+3x=12x
2160=12x-3x
2160=9x
X=240
The number of fruits will be 240
C --------------------q ???
Answers
1
Which is the equation of a line that has a slope 1/2 and passes through point (2, -3)?
Oy-x-4
0y=x-2
Oy-x+2
Oy=x+3
Answers
Answer:
[tex]y = \dfrac{1}{2}x-4[/tex]
Step-by-step explanation:
Equation of line in slope y-intercept form:[tex]\sf slope = m =\dfrac{1}{2}\\\\Point (2, -3) ; x_1 = 2 \ \& y_1 = -3\\\\\boxed{\bf y - y_1 =m(x -x_1)}[/tex]
[tex]\sf y - [-3] = \dfrac{1}{2}(x - 2)\\\\y + 3 = \dfrac{1}{2}x - 2*\dfrac{1}{2}\\\\y + 3 = \dfrac{1}{2}x-1\\\\[/tex]
[tex]\sf y = \dfrac{1}{2}x - 1 - 3\\\\ y =\dfrac{1}{2}x-4[/tex]