what is the least common multiple of 9, 17, and 51
1. Select the ordered pair from the choices below that is a solution to the following system of equations:
4y = 2x + 10
8x − 3y = -14
a) (-1, 2)
b) (7, 6)
c) (-3, 2)
d) (5, 5)
2. Which of the following systems of equations has no solution?
a) 9x + 5y = 1; 15y = 18x − 4
b) -7x − 7 = 3y; -14y − 8 = -6x
c) 4x − 3y = 9; 6y = 8x − 18
d) 7y = 5x − 10; 10x − 14y = 8
3. Select the ordered pair from the choices below that satisfies following system of equations:
2x − 10y = -14
-4y = -x − 5
a) (-1/2,1)
b) (-20, 3)
c) (3, 2)
d) (8, -4)
If the length of the rectangle is twice the width and the perimeter of the rectangle is 30 cm what is length and width of the rectangle
The two shorter sides of a triangle are the same length. the length of the longer side is 5 m longer than each of the shorter sides. the perimeter of the triangle is 29 m
There is a line through the origin that divides the region bounded by the parabola y=2x-4x^2 and the x-axis into two regions with equal area. What is the slope of that line? ...?
The slope of the line that divides the region bounded by the parabola y=2x-4x^2 and the x-axis into two regions with equal area is -2.
Explanation:To find the slope of the line that divides the region bounded by the parabola y=2x-4x^2 and the x-axis into two regions with equal area, we need to set up an integral to find the area under the parabola. The equation of the line will be in the form y = mx, where m is the slope we need to find. Setting up the integral, we get:
Solve the integral to find:
Substituting the limits of integration and solving, we get:
Therefore, the slope of the line that divides the region into two equal areas is -2.
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Which is greater 20 5/6 or 20.8?
Rosy has 16 pencils and 24 erasers. She is putting together packets that will have an equal number of pencils and erasers in each packet. If Rosy uses all of the pencils and erasers, what is the maximum number of packets she can make?
Answer:
Maximum number of packets made = 8
Step-by-step explanation:
Number of pencils Rosy has = 16
Number of erasers Rosy has = 24
Now, it is given all the packets made contain equal number of pencils and erasers in each packet.
Therefore, to find the maximum number of packets : We find the HCF of both 16 and 24
16 = 2 × 2 × 2 × 2
24 = 2 × 2 × 2 × 3
Common factors are : 2, 2 and 2
⇒ HCF = 2 × 2 × 2
= 8
So, 8 packets can be made from 16 pencils and 24 erasers so that each packet will contain 2 pencils and 3 erasers each.
Hence, Maximum number of packets made = 8
Bill's Furrier marks up mink coats $3,000. This represents a 50% markup on cost. What is the cost of the coats?
...?
The original cost of the mink coats was $6,000. This is determined by dividing the markup amount of $3,000 by the markup percentage, which is 50% or 0.50 in decimal form.
A 50% markup on cost means that the extra amount added to the cost price of the coats is 50% of that original cost price. Since the markup on the mink coats is given as $3,000, we can set up the equation as follows to find the original cost price (C):
Markup = 50% of Cost
3000 = 0.50 imes C
To find the cost (C), we divide the markup by the percentage, which in decimal form is 0.50:
C = $3,000 / 0.50
C = $6,000
Hence, the original cost of the mink coats was $6,000.
y varies directly with x, and y = 5 when x = 4. What is the value of x when y = 8?
Please help
A school conducts 27 test and 36 weeks assume the school conducts test at a constant rate what is the slope of the line that represents the number of tests on the Y axis and the time in weeks on the X axis
A: 3/4
B: 4/3
C: 3
D: 4
Answer:
3/4
Step-by-step explanation:
I got it right.
Explain how unwrapping a present is used as an analogy for solving an equation. How do you "unwrap" with an equation?
...?
Solving an equation is likened to unwrapping a present because in both cases, you aim to uncover what's within by dealing with the outer layers systematically. Through an inverse process, you isolate the equation's variable and solve for it, just as the step-by-step unwrapping of layers reveals the gift within the package.
Explanation:Unwrapping a present is a great way to understand the process of solving an equation. If you consider the equation itself as being 'wrapped' in different operations such as multiplication, division, addition, and subtraction, you can begin to 'unwrap' it by systematically dealing with these operations in reverse from the order of operations. This would be like when you unpack the present by undoing the tape, then the paper, then the box, or whatever other layers might be present.
To use a direct example, let's consider the equation 3x + 7 = 22. You start unwrapping by isolating for the term with the variable. This means you handle the operation that does not involve the variable first. So, subtract 7 from both sides of the equation to get 3x = 15. Next, you handle the multiplication operation by dividing both sides by 3 and solving for x, which would be 5 in this case. Just like unwrapping a present, we aim to get to the 'inside' or the root of the equation.
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At the beginning of the season, MacDonald had to remove 5 orange trees from his farm. Each of the remaining trees produced 210 oranges for a total harvest of 41790 oranges.
Equations
and
Answer
Answer:
Equations: f(t) = 210(t-5)
Initial number of trees(t) = 204
Step-by-step explanation:
Let t represents the initial number of trees and f(t) represents the total number of oranges.
"Remove 5 orange trees from his farm" means (t-5)
" Each of the remaining trees produced 210 oranges" means [tex]210\cdot (t-5)[/tex]
so, the equation become [tex]f(t) = 210 \cdot (t-5)[/tex]
Also, it is given that total harvest of, 41790 oranges.
⇒f(t) = 41790
Substitute this in the above equation to get t;
[tex]41790 = 210(t-5)[/tex]
Divide both sides by 210 we get;
[tex]199 = t-5[/tex]
Add 5 both sides of an equation we get;
199 + 5 = t-5 + 5
Simplify:
204 = t
Therefore, there were initially 204 orange trees
Identify the horizontal translation of the parent function. step by step
y=(x-4)^2
5t + 5 = 30 solve for t
Maximum value of (log x)/x
Which expression is equivalent to 6x−2(7x−3)?
a.)17x
b.) 14x
c.)−14x+12
d.)−8x+6
Suppose you note that there are congruent vertical angles in the triangles. Can you now use the ASA Postulate, the AAS Theorem, or both to prove the triangles congruent?
Solve for t. 3/4 t = 1/4
An audience of 450 people is seated in an auditorium. Each row contains the same number of seats and each seat in the auditorium is occupied. With three fewer seats per row, and five extra rows, the same audience could still be seated, occupying all seats. How many rows does the auditorium have? ...?
Answer with Step-by-step explanation:
Let there be r rows and s seats in every row.
An audience of 450 people is seated in an auditorium and each seat is occupied.
i.e. rs=450
or s=450/r
With three fewer seats per row, and five extra rows, the same audience could still be seated, occupying all seats.
i.e. (s-3)(r+5)=450
s(r+5)-3(r+5)=450
rs+5s-3r-15=450
450+5s-3r-15=450
Subtracting both sides by 450,we get
5s-3r-15=0
i.e. 5s-3r=15
5(450/r)-3r=15
Dividing both sides by 3 and multiplying by r, we get
750-r²=5r
r²+5r-750=0
r² + 30r - 25r - 750 = 0
r(r + 30) - 25(r + 30) = 0
(r + 30)(r - 25) = 0
either r+30=0 or r-25=0
either r= -30 or r=25
r can't be negative
Hence, number of rows in auditorium are:
25
#1: Jim, Jane, Ann, and Bill measure an object’s length, density, mass, and volume, respectively. Which student’s measurement might be in centimeters?
A. Bill’s
B. Jane’s
C. Jim’s
D. Ann’s
#2: How many centimeters are in 0.05 kilometers?
A. 50
B. 500
C. 5,000
D. 50,000
Ques 1)
The student whose measurement might be in centimeters is:
Jim
Ques 2)
C. 5,000
Step-by-step explanation:Ques 1)
We know that the standard unit centimeters or meters is used to represent the length of some object.
Here Jim measured an object's length.
Hence, he would represent his measurement in centimeters.
Ques 2)
We know that 1 m=100 cm
and 1 km=1000 m
Hence,
1 km=100000 cm
Hence,
0.05 km=0.05×100000 cm
Hence, we have:
0.05 km=5000 cm.
Hence, the correct answer is: Option: C
Answer:
#1. d. ann's
#2. 5,000
Step-by-step explanation:
A regular 40-sided polygon is rotated with its center of rotation at its center. What is the smallest degree of rotation needed to map the polygon back on to itself?
Answer:
171 degrees
Step-by-step explanation:
40-sided polygon has an interior angle equal to:
(40 - 2) (180) /40 = 171 degrees
Is the number 5 prime composite or neither
Answer:
5
It's easy.
5 has only 2 factors: 1 and itself.
Therefore, it is prime:)
Step-by-step explanation:
Solve this: 9x-3=5x-15
please help@!!!!!!!!!
How many months are equivalent to 4 years?
Which choice is the equation of a line that passes through the point (0, 15) and is parallel to the line represented by this equation? 5x-4y=12
Jeanette wants to tile the floor of a room in her house. The square tiles measure 3/4 ft on each side. The room is 10 ft wide.
a. Write an inequality to describe how many tiles are needed to make one row of tiles across the width of the room.
b. Solve the inequality.
c. How many tiles should Jeanette buy to form one row?
Answer:
a. The inequality will be: [tex]\frac{3}{4}x\geq 10[/tex]
b. Solving the inequality: [tex]x\geq 13.333...[/tex]
c. Jeanette should buy 14 tiles to form one row.
Step-by-step explanation:
Suppose, the number of tiles needed to make one row [tex]=x[/tex]
Each square tiles measure [tex]\frac{3}{4}[/tex] ft on each side.
So, the total length of [tex]x[/tex] number of tiles [tex]=\frac{3}{4}x\ ft[/tex]
Given that, the room is 10 ft wide.
So, the inequality will be: [tex]\frac{3}{4}x\geq 10[/tex]
Solving the above inequality.....
[tex]\frac{3}{4}x\geq 10\\ \\ 3x\geq 4(10)\\ \\ 3x\geq 40\\ \\ x\geq \frac{40}{3}\\ \\ x\geq 13.333...\\ \\ x\approx 14[/tex]
So, Jeanette should buy 14 tiles to form one row.
what is the lcm of 4 and 10
write y=2/3x+7 in standard form,
a) -2x+3y=21
b) -2x-3y=21
c) 3x-2y=21
d) -2x+3y=7
I've been trying to figure this out but for some reason my answers end up slightly off and I stg I'm doing this right. I'm kind of fed up with continually refreshing so I don't get a poor score, so I'd really appreciate the help.
Write an equation in slope-intercept form for the line that passes through (4, -4) and is parallel to 3 + 4x = 2y – 9.