Answer:
The ordered pair that is a solution to the equation (5, 2)
Step-by-step explanation:
It is given that,
2x + 5y = 20
To find the ordered pairs
Multiples of 2 are,
2, 4, 6, 8, 10, 12....
Multiples of 5 are,
5, 10, 15, 20,...
20 can be written as,
20 = 2x + 5y
2x is the multiple of 2 and 5y is the multiple of 5
From the above data we get, 20 = 10 + 10
2x = 10 then x = 5
5y = 10 then y = 2
Therefore the ordered pair that is a solution to the equation (5, 2)
Final answer:
To determine if an ordered pair is a solution to the equation 2x + 5y = 20, substitute the values into the equation and check if the simplified result equals 20.
Explanation:
To find an ordered pair that is a solution to the equation 2x + 5y = 20, we need to check which pair (x, y) satisfies the equation when we substitute the values of x and y into it. This involves basic algebraic skills, including substitution and simplification.
Step-by-Step Explanation
Select a potential ordered pair solution.Substitute the x-value and the y-value into the equation.Simplify to see if the values satisfy the equation and make it true.If the left side of the equation equals the right side after substitution, then the ordered pair is a solution to the equation. For example, if we substitute x = 2 and y = 4, we get 2(2) + 5(4) = 20 which simplifies to 4 + 20 = 24, not equal to 20. Thus, (2,4) is not a solution. Find an ordered pair where, after the substitution and simplification, the equation is satisfied.
If A • B*2 = 1.8 x 10*-7, and C•B/D = 7.2 x 10*-4, find the value of A•D*2/C*2
Answer:
-7.2
Step-by-step explanation:
The value of expression A•D²/C² is 1.8 x 10⁻⁷ / D².
To find the value of A•D²/C², we can first rearrange the given equations and then manipulate them to get the desired expression.
Given equations:
A • B² = 1.8 x 10⁻⁷
C • B/D = 7.2 x 10⁻⁴
Let's manipulate the second equation to get C by itself:
C • B/D = 7.2 x 10⁻⁴
C = (7.2 x 10⁻⁴) • (D/B)
Now, substitute the expression for C from the second equation into the first equation:
A • B² = 1.8 x 10⁻⁷
A = (1.8 x 10⁻⁷) / B²
Now, we have expressions for both A and C:
A = (1.8 x 10⁻⁷) / B²
C = (7.2 x 10⁻⁴) • (D/B)
Now, let's find the value of A•D²/C²:
A•D²/C² = ((1.8 x 10⁻⁷) / B²) • (B/D)²
Since (B/D)² = B²/D²:
A•D²/C² = ((1.8 x 10⁻⁷) / B²) • (B²/D²)
Now, B² in the numerator and denominator cancel out:
A•D²/C² = 1.8 x 10⁻⁷ / D²
Thus, the value of A•D²/C² is 1.8 x 10⁻⁷ / D².
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Carla is cutting pieces of string that are exactly 24 3/8 in long how many pieces can she cut from a ball of string that is 100 ft
Answer:
4 1/8 pieces
Step-by-step explanation:
Since you are using a string that is 100 ft. long then and you need exactly 24 3/8 ft. sections, you would do these calculations:
3/8 = 0.375
100/24.375 = 4.1026
.1026 = 1/8
4 1/8 ft long pieces
Answer:
The string is cut into 4.1025 pieces.
Step-by-step explanation:
We are given the following information:
Length of the string = 100 feet
Length of one piece = [tex]24\displaystyle\frac{3}{8} = \displaystyle\frac{195}{8} ~feet[/tex]
Number of pieces =
Formula:
[tex]\text{Number of pieces} = \displaystyle\frac{\text{Length of string}}{\text{Length of one piece}}[/tex]
Number of pieces =
[tex]\displaystyle\frac{100}{\frac{195}{8} } = \displaystyle\frac{100\times 8}{195}\\\\=\displaystyle\frac{800}{195} = 4\displaystyle\frac{4}{39} = 4.1025[/tex]
Thus, the string is cut into 4.1025 pieces.
Raymond can paint 5/8 of a wall in 16minutes. How long would it take him to paint 1/3 of a wall?
Answer:
128/15 min or 8.5 min
Step-by-step explanation:
By using unitary method,
Time required to paint 5/8 of wall = 16 min.
Time required to paint 1/1 of wall = 16×8/5
Hence, Time required to paint 1/3 of wall = 16×8/5×1/3
Answer:
8 8/15
Step-by-step explanation:
simplify the two fractions you have to make them have the same denominater
enthen you can determine the answer.
In the expression 6^8 what does the exponent show
Answer:
6^8=6*6*6*6*6*6*6*6
=1679616
Step-by-step explanation:
In this expression the exponent shows that how many times 6 will be multiplied.
6^8=6*6*6*6*6*6*6*6
=1679616
Two rigid transformations are used to map JKL To MNQ-
The first is a translation of vertex L to vertex Q. What is the
second transformation?
a reflection across the line containing LK
a reflection across the line containing jk
a rotation about point l
a rotation about point k
Answer:
Step-by-step explanation: it’s c
Answer:
C. a rotation about point L
Step-by-step explanation:
Geometry please help
Check the picture below.
Answer:
x=6.9 inches
Step-by-step explanation:
If a tangent and a secant are draw to a circle from the same exterior point, the square of the length of the tangent is equal to the product of the total length of the secant and the length of the external segment of the secant.
From the given diagram,
(8+4)×4=x²
12×4=x²
x²=48
x=6.9 inches
Your baseball team has won 6 games and lost 4 games. If the team
does not lose any more games, how many games must the team win
to have a win : loss ratio of 2:1? Explain your answer.
Answer:
2
Step-by-step explanation:
2:1 win / loss ratio
1 = 4 loses
4 x 2 = 8
the team has 6 wins it would need to win a total of 8 to have a 2:1 ratio
The baseball team must win 2 more games to achieve a win:loss ratio of 2:1, assuming they have no additional losses.
The student's baseball team currently has a record of 6 wins to 4 losses. The question asks how many more games the team must win to achieve a win:loss ratio of 2:1, assuming no more losses occur. To achieve a 2:1 win:loss ratio, the number of wins must be twice the number of losses. Since the losses are fixed at 4, the team needs 2 times 4 (which equals 8) wins to attain this ratio. The team has already won 6 games, so they need 8 - 6, which equals 2 more wins to reach a 2:1 ratio.
Someone please help me
Answer:
1 mi/1.61 km
Step-by-step explanation:
we know that
1 mile= 1.61 kilometers
To convert 1 kilometer to miles
use proportion
so
1/1.61 mi/km=x/1 mi/km
x=1 mi/1.61 km
Answer:
[tex]\frac{1 mi}{1.61km}[/tex]
Step-by-step explanation:
We are given the unit values of inch, foot and mile to convert into centimeters.
Using these conversion units, we are to determine whether which expression in the answer options can be used as the conversion factor to convert kilometers to miles.
So using the given conversion units, we can see that the following is the conversion factor to convert kilometers to miles.
[tex]\frac{1 mi}{1.61km}[/tex]
math help please its just one question
Use the law of sines:
Sin(angle) = Opposite Leg / Hypotenuse
Sin(30) = 14 / x
x = 14/sin(30)
x = 28
Circle O has a circumference of 367 cm
What is the length of the radius, /?
6 cm
18 cm
36 cm
72 cm
To find the length of the radius, use the formula for the circumference of a circle. Divide the circumference by 2π to get the radius. In this case, the radius is approximately 59 cm.
Explanation:In order to find the length of the radius, we can use the formula for the circumference of a circle: C = 2πr, where C is the circumference and r is the radius. We are given that the circumference is 367 cm, so we can plug in the values to solve for r.
367 = 2πr
To isolate r, divide both sides of the equation by 2π: r = 367 / (2π)
Using a calculator to approximate π as 3.14, we can calculate the radius: r ≈ 367 / (2 * 3.14) ≈ 58.598
Therefore, the length of the radius, rounded to the nearest centimeter, is approximately 59 cm.
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Solve for a.
a = 3
a = -3
a = 9
a = -9
Answer:
a=9
Step-by-step explanation:
1/a + 1/(2a) = 1/(a-3)
Get a common denominator for the left hand side
2/(2a) + 1/(2a) = 1/(a-3)
3/(2a) = 1/ (a-3)
Using cross products
3 * (a-3) = 1 * 2a
Distribute
3a -9 = 2a
Subtract 3a from each side
3a-3a-9 = 2a-3a
-9 = -a
Multiply by -1
-1*-9 = -1 *-a
9 = a
Which points represent an approximate solution to this system of equations? y=1/x-3 y=3-x³
A. (1.5, 1)
B. (1.5, -0.7)
C. (1.6, 1.6)
D. (2.9, -22.8)
Answer:
Options B and D
Step-by-step explanation:
we have
[tex]y=\frac{1}{x-3}[/tex] -----> equation A
[tex]y=3-x^{3}[/tex] -----> equation B
Solve the system of equations by graphing
The solution of the system of equations is the intersection point both graphs
The solutions are the points (1.545,-0.687) and (2.956,-22.835)
see the attached figure
The approximate solutions are
(1.5,-0.7) and (2.9,-22.8)
Answer:
Options B and D
Step-by-step explanation:
the ratio of chicken to pigs to horses in a farm is 10:2:3.if there is 120 chickens in the farm then the number of the horses in the farm is
Answer:
36
Step-by-step explanation:
The 10 part of the ratio represents 120 chickens. Divide 120 by 10 to find the value of one part of the ratio.
120 ÷ 10 = 12 ← value of 1 part of the ratio, hence
3 parts = 3 × 12 = 36 ← number of horses
The number of horses on the farm is 36.
Given that, the ratio of chicken to pigs to horses on a farm is 10:2:3 and the number of chickens on the farm is 120.
What is the ratio?Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another.
We can write the given ratio 10:2:3 as 10x: 2x: 3x.
So, 10x=120
⇒x=12
Then, the number of horses=3x=36
Therefore, the number of horses on the farm is 36.
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Given that lines b and c are parallel, select all that apply.
Answer:
C) angle 2 and angle 8
Step-by-step explanation:
The population of a city was 572,000 in 2010. In the 2000 census the population was 607,000. What was the rate of decrease of the population from one census to the next? Round to the nearest percent.
Answer:
6%
Step-by-step explanation:
To solve this you need to subtract 607000 by 572000 to see how many people in the population decreased.
607,000- 572,000= 35,000
Then you put 35,000 over 607,000
also you need x over 100
35000/607,000 x/100
Then do cross product property
35,000*100=3,500,000
607,000* x= 607,000x
3,500,000= 607,000x
Then do 3,500,000 divided by 607,000
You get 5.76%
Round to the nearest percent and get 6%
Final answer:
The rate of decrease of the population from the 2000 census to the 2010 census is 6% when rounded to the nearest percent.
Explanation:
To calculate the rate of decrease of the city's population, we use the population values from the 2000 and 2010 censuses. The population in 2000 was 607,000, and in 2010 it was 572,000. To find the population decrease, subtract the 2010 population from the 2000 population:
Population decrease = Population in 2000 - Population in 2010
Population decrease = 607,000 - 572,000
Population decrease = 35,000
Next, to find the rate of decrease as a percent, we divide the population decrease by the original population (in 2000) and then multiply by 100:
Rate of decrease (%) = (Population decrease / Population in 2000) × 100
Rate of decrease (%) = (35,000 / 607,000) × 100
Rate of decrease (%) = 0.0577 × 100
Rate of decrease (%) = 5.77%
Round this to the nearest percent, and you get a 6% decrease.
Assume that a population of newly discovered small creatures called “porgs” in a remote island lays eggs with three distinct appearances: patterned with dots, white, or dark grey. Last year, the porgs laid 30 dotted eggs, 40 grey eggs, and 15 white eggs. You randomly selected 25 eggs, 10 of which were dotted, 13 were grey and 2 were white. Based on this information, what is the probability that you would only collect 2 white eggs?
you have a 1/12.5 chance of getting a white egg. so the theoretical possibility of getting only two white eggs is 1/156.25. so it is very unlikely to get two white eggs
Answer:
0.029
Step-by-step explanation:
Last year, the porgs laid 30 dotted eggs, 40 grey eggs, and 15 white eggs.
Total eggs = 30+40+15 = 85 eggs
White eggs = 15
So, probability of getting 1 white egg = [tex]\frac{\text{No. of white eggs}}{\text{Total no. of eggs}}[/tex]
= [tex]\frac{15}{85}[/tex]
Remaining white eggs = 14
Total eggs remaining = 84
Probability of getting 1 white egg on second draw = [tex]\frac{14}{84}[/tex]
So, the probability that you would only collect 2 white eggs =[tex]\frac{15}{85} \times \frac{14}{84}[/tex]
=0.029
Hence the probability that you would only collect 2 white eggs is 0.029.
Write as an algebraic expression and then simplify if possible The distance traveled by a train in three hours with a constant speed of r miles per hour.
Answer:
Distance = 3r
Step-by-step explanation:
We are to write an algebraic expression and then simplify it for the given situation:
The distance traveled by a train in three hours with a constant speed of r miles per hour.
We know the formula of distance linking the speed and the time.
Distance = speed × time
Substituting the given values to get:
Distance = r × 3
Distance = 3r
Wong’s Garage buys quarts of motor oil by the gross (144 units) for $0.75 per quart. When Wong’s changes the oil in customers’ cars, it marks up the oil 175% of the cost. What is the selling price of a quart of oil used in a standard oil change?
Answer:
Each quart is 1.31 to the customer.
Step-by-step explanation:
Cost of 1 quart to Wong = 0.75
Cost to you or I = 0.75 * 175/100 = 1.31
He sells each quart for 1.31 dollars.
a boat is 60% full with 48. What is the maximum carrying capacity?
Answer:
80
Step-by-step explanation:
60%=48
10%=8
8*10=80
Answer:80
Step-by-step explanation:
60/100*x=48
60/100=3/5 so,
3/5*x=48
3x=48*5
x=240/3
x=80
therefore the maximum capacity is 80 people
Which expression is not equivalent to the other three?
A: 2x + 2+ 2x + 3x – 8
B:4 + 7x – 2
C:–2 + 5x + 2x – 4
D:8x – x – 6
Answer:
b. 4+7x-2
Explanation:
when you add like terms for the first equation it becomes 7x-6
the second one becomes 7x+2
the third one becomes 7x-6
and the last one is also 7x-6
which means the second one is not equivalent
Answer:
B. 4 + 7x – 2
Step-by-step explanation:
Does anyone know this ? Please .
Answer:
5/4 hope this helps
Step-by-step explanation:
ANSWER
The correct answer is D.
EXPLANATION
The given exponentiial expression is
[tex] {5}^{ \frac{7}{3} } [/tex]
Recall that:
[tex] {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } [/tex]
We put a=5, n=3 and m=7
This implies that,
[tex]{5}^{ \frac{7}{3} } = \sqrt[3]{ {5}^{7} } [/tex]
The correct answer is D.
The last option is correct.
What is the equation of the line in point-slope form?
Answer:
A
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 4, - 4) and (x₂, y₂ ) = (4, 0) ← 2 points on the line
m = [tex]\frac{0+4}{4+4}[/tex] = [tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex]
Using (a, b) = (- 4, - 4), then
y - (- 4) = [tex]\frac{1}{2}[/tex] (x - (- 4)), that is
y + 4 = [tex]\frac{1}{2}[/tex] (x + 4) → A
If a wheel has 64 spokes, how many spaces are there between the spokes?
Answer:
One
Step-by-step explanation:
It is one because each spoke has one space in the middle. However some people think it's 64 because they read the question wrong.
What is the slope of the line passing through (5, -6) and (4, 3)
Answer:
-9
Step-by-step explanation:
Answer:
slope = - 9
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (5, - 6) and (x₂, y₂ ) = (4, 3)
m = [tex]\frac{3+6}{4-5}[/tex] = [tex]\frac{9}{-1}[/tex] = - 9
When 60% of a number is added to the number, the result is 192
Answer:
the number (x) is 120.
Explanation:
100% + 60% = 160% = 1.6
(just multiply it by 1.6 because it is equal to 60%)
The equation for the problem can be expressed as x + 0.6x = 192. To solve for x, you simplify the equation and isolate x, resulting in the answer of 120.
Explanation:This problem is a simple algebraic problem in which we're trying to find a number that satisfies a given condition. To solve this, we need to express the problem as an equation. Let's assume the number we're looking for is denoted as x. So, according to the problem, we have the following equation:
x + 0.60x = 192
The steps to solve this equation are as follows:
Combine like terms: 1x + 0.60x = 1.60xTo isolate x, divide both sides of the equation by 1.60: x = 192 / 1.60Doing the division on the right side, we find x = 120, which is our number.
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Find the perimeter of a triangle with side lengths of /80
20 and 45
Answer:
145
step by step explanation:
perimeter definition:
perimeter definition:the continuous line forming the boundary of a closed geometrical figure.
add up the length of the sides:
80+20+45=145
Line CD passes through points C(1, 3) and D(4, –3). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?
–5
–2
1
5
Answer:
5
Step-by-step explanation:
First we need to find the slope
m = (y2-y1)/ (x2-x1)
= (-3-3)/(4-1)
=-6/3
= -2
Then we can use point slope form to make the equation
y-y1 = m(x-x1)
y-3 = -2(x-1)
Distribute
y-3 = -2x+2
Add 3 to each side
y-3+3 = -2x+2+3
y = -2x+5
Since this is in slope intercept form, y = mx +b, the y intercept is 5
Answer: D. 5
Step-by-step explanation: First we need to find the slope
m = (y2-y1)/ (x2-x1)
= (-3-3)/(4-1)
=-6/3
= -2
Then we can use point slope form to make the equation
y-y1 = m(x-x1)
y-3 = -2(x-1)
Distribute
y-3 = -2x+2
Add 3 to each side
y-3+3 = -2x+2+3
y = -2x+5
Since this is in slope intercept form, y = mx +b, the y intercept is 5
how many 3/4 pound bags of peanuts can be from 5 pound bag
Final answer:
To determine how many 3/4 pound bags of peanuts can be made from a 5 pound bag, divide the weight of the 5 pound bag by the weight of each 3/4 pound bag.Therefore, 20/3 or 6 and 2/3 3/4 pound bags of peanuts can be made from a 5 pound bag.
Explanation:
To determine how many 3/4 pound bags of peanuts can be made from a 5 pound bag, we need to divide the weight of the 5 pound bag by the weight of each 3/4 pound bag. We can use the division operation to solve this.
5 pounds ÷ 3/4 pounds = 5 ÷ 3/4
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 3/4 is 4/3.
5 ÷ 3/4 = 5 × 4/3 = 20/3
Therefore, 20/3 or 6 and 2/3 3/4 pound bags of peanuts can be made from a 5 pound bag.
HEEEELLLLLLLLLLPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP ME
Answer:
41.79%
Step-by-step explanation:
To be on the swim team, we look at the right most (total) number int he table of "on the swim team" row. That is 28.
The grand total is the bottom-rightmost. That is 67.
Hence, probability of being on swim team is 28/67 = 41.79%
What is true about the completely simplified sum of the polynomials 3x2y2 − 2xy5 and −3x2y2 + 3x4y?
The sum is a trinomial with a degree of 5.
The sum is a trinomial with a degree of 6.
The sum is a binomial with a degree of 5.
The sum is a binomial with a degree of 6.
Answer:
The sum is a binomial with a degree of 6
Step-by-step explanation:
we have
[tex](3x^{2}y^{2}-2xy^{5})+(-3x^{2}y^{2}+3x^{4}y)[/tex]
Group terms that contain the same variable
[tex](3x^{2}y^{2}-3x^{2}y^{2})-2xy^{5}+3x^{4}y[/tex]
[tex]0-2xy^{5}+3x^{4}y[/tex]
[tex]-2xy^{5}+3x^{4}y[/tex]
The sum is a binomial ( two terms) with a degree of 6
[tex]-2xy^{5}[/tex] has a degree of 6 (x has an exponent of 1, y has 5, and 1+5=6)
The sum of the polynomial is a binomial with a degree of 6. The correct option is D) and this can be determined by using arithmetic operations.
Given :
Polynomials -- [tex]3x^2y^2-2xy^5[/tex] and [tex]-3x^2y^2+3x^4y[/tex]
The following steps can be used to determine the sum of the given polynomials:
Step 1 - Write the sum of the given polynomials.
[tex]3x^2y^2-2xy^5-3x^2y^2+3x^4y[/tex]
Step 2 - Subtract [tex]3x^2y^2[/tex] from [tex]3x^2y^2[/tex] in the above expression.
[tex]-2xy^5+3x^4y[/tex]
The above expression cannot be further simplified. Therefore, this is the final expression of the sum of the given polynomials.
The sum of the polynomial is a binomial with a degree of 6. Therefore, the correct option is D).
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