Write the equation for 5x + 2y = 3 in slope-intercept form.
Answer:
Slope-Intercept Form states that in the equation of a straight line y=mx+b the slope is the number represented by m that is multiplied on the x, and b is the y intercept i.,e the point where line cut the vertical y-axis.
Given equation: 5x+2y=3 ......[1]
To convert this equation into slope intercept form;
Subtraction Property of equality states that you subtract the same number from both sides of an equation.
Subtract 5x from both sides in equation [1];
[tex]5x+2y-5x=3-5x[/tex]
Simplify:
[tex]2y=3-5x[/tex] or we can write this as;
[tex]2y=-5x+3[/tex] ......[2]
Division property of equality states that you divide the same number from both sides of an equation:
Divide by 2 from both sides of an equation in [2]
[tex]\frac{2y}{2} =\frac{-5x+3}{2}[/tex]
On simplify:
[tex]y=-\frac{5}{2}x+\frac{3}{2}[/tex]
Therefore, the given equation in slope intercept form is: [tex]y=-\frac{5}{2}x +\frac{3}{2}[/tex]
making 10 pounds of Apple Jam requires five pounds of Apple how many pounds of Apple are needed to make eight pounds of apple jam
Which shows the correct substitution of the values a, b, and c from the equation –2 = –x + x2 – 4 into the quadratic formula?
Quadratic formula: x =
Answer:
D on edge
Step-by-step explanation:
A number close to its actual value is a(n)
A room has 3 lamps. From a collection of 12 light bulbs of which 5 are not working, Richard selects 3 at random and puts them in the sockets. What is the probability that he will have light? ...?
Can someone help me?
In the circles shown, Line AC is congruent and equal to Line RT and Line AB is congruent and equal to Line RS. Which shaded region has a larger area?
what is 5√28 + √63 in simplest radical form
The simplest radical form of the expression 5√28 + √63 will be 29√7.
How do convert the exponent into the simplest radical form?If the power of the variable "a" is b/c.
Then the simplest radical form of the expression will be
[tex]\rm \left ( a \right )^{\rm \frac{b}{c}} = \rm \sqrt[\rm c]{\rm a^b}[/tex]
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ 5√28 + √63
Simplify the expression, then we have
⇒ 5√28 + √63
⇒ 5√(4 x 7) + √(9 x 7)
⇒ 5 x 4√7 + 9√7
⇒ 20√7 + 9√7
⇒ 29√7
The simplest radical form of the expression 5√28 + √63 will be 29√7.
More about the simplest radical form link is given below.
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A group of children, 6 to 10 years old, were asked how many video games they owned. The scatter plot shows the results.
What is the range of video games owned for the cluster?
Answer:
8 to 10
Step-by-step explanation:
Solve for c.
3abc + b = 5
c = (5 - b)/(3ab)
c = -5/3ab
c = 2 - ab\
how does one work this out
Transversal CD←→ cuts parallel lines PQ←→ and RS←→ at points X and Y, respectively. Points P and R lie on one side of CD←→, while Q and S lie on the other side. If
m∠PXY = 64.36°, what is m∠XYS?
Answer: [tex]64.36^{\circ}[/tex]
Step-by-step explanation:
According to the question,
PQ ║ RS
And, PQ and RS are cut by the same transversal CD.
Then, By the alternative interior angle theorem,
The alternative interior angles made by the transversal CD on parallel lines PQ and RS must be congruent.
Thus, [tex]\angle PXY\cong \angle XYS[/tex]
⇒ [tex]m\angle PXY = m\angle XYS[/tex] ( by the property of congruent angles )
Here [tex]m\angle PXY = 64.36^{\circ}[/tex]
⇒ [tex]m\angle XYS = 64.36^{\circ}[/tex]
Find the missing angle measures. The diagram is not to scale
If 100 envelopes cost 70 cents, how much would 250 cost?
To find out how much 250 envelopes would cost, set up a proportion using the given information that 100 envelopes cost 70 cents. Cross-multiply and solve for the unknown cost, which is $1.75.
Explanation:To find out how much 250 envelopes would cost, you can use the concept of proportions. Since 100 envelopes cost 70 cents, you can set up a proportion to find the cost of 250 envelopes: 100/70 = 250/x, where 'x' represents the unknown cost. Cross-multiplying, you get 100x = 70 * 250. Dividing both sides by 100, you find that x = 175.
Therefore, 250 envelopes would cost 175 cents.
In decimal form, 175 cents is equal to $1.75.
Which ratio forms a proportion with 14/42?
1/4
7/21
12/40
28/80
Answer: 7/12
Explaintion: Write at least 20 characters to explain it well.
for a population of 800000 subway riders, the numbers of subway trips taken per rider last january are approximately normally distributed with a mean of 56 trips and a standard deviation of 13 trips. approximately how many of the riders took between 30 and 43 trips last january??? ...?
Calculating the number of subway riders who took between 30 and 43 trips involves finding z-scores for these trip numbers, looking up the corresponding probabilities in the normal distribution table, and multiplying the difference by the total population of riders.
Explanation:The question relates to normal distribution and requires calculating the number of individuals in a given population that fall within a specific range of values. The population in question is 800,000 subway riders whose number of trips are normally distributed with a mean (μ) of 56 and a standard deviation (σ) of 13. The task is to find out how many riders took between 30 and 43 trips last January.
To solve this, we first find the z-scores for the values 30 and 43. The z-score is calculated by subtracting the mean from the value and dividing the result by the standard deviation. This will give:
Z for 30 = (30 - 56) / 13 = -2Z for 43 = (43 - 56) / 13 = -1Next, we look up these z-scores in a standard normal distribution table to find the probabilities corresponding to these z-scores. The difference between these probabilities will give us the proportion of riders who took between 30 and 43 trips. Finally, we multiply this proportion by the total population of riders (800,000) to get the number of riders. Assume that the probabilities from the z-table are 0.0228 for z = -2 and 0.1587 for z = -1.
The calculation would be approximately:
Number of riders = 800,000 * (0.1587 - 0.0228) = 800,000 * 0.1359 = 108,720 riders
unicorns
Math Help! I NEED IT ASAP!!!! PLEASE!! WILL UPVOTE,LIKE PAGE,LIKE POSTS AND PICS!!
Sorry this took me forever to post, I had to do someting
_________________________________________________
5.What is each number in standard form?
Drag the answers into the boxes to match each number.
1.5.78×10−115.78×10−11
2. 5.078×10−65.078×10−6
3. 5.708×10−85.708×10−8
Answer Choices:
A.0.000005078
B.0.0000000000578
C.0.000000578
D.0.0000000005078
E.0.00000005708
F.0.00000000005708
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You are spreading fertilizer on a golf course at the rate of 40 pounds per 10000 square feet. If the course is 320 acres, how many tons of fertilizer will be needed?
Which value of m will create a system of parallel lines with no solution?
y = mx – 6
8x – 4y = 12
The value of [tex]m[/tex] is [tex]2[/tex].
Given:
The given equations are:
[tex]y=mx-6[/tex] ...(i)
[tex]8x-4y=12[/tex] ...(ii)
To find:
The value of [tex]m[/tex] that will create a system of parallel lines with no solution.
Explanation:
The slope-intercept form of a line is:
[tex]y=mx+b[/tex] ...(iii)
where, [tex]m[/tex] is the slope and [tex]b[/tex] is the [tex]y[/tex]-intercept.
The slope of line (i) is [tex]m[/tex].
Equation (ii) can be rewritten as:
[tex]-4y=-8x+12[/tex]
[tex]y=\dfrac{-8x+12}{-4}[/tex]
[tex]y=2x-3[/tex]
The slope of this line is [tex]2[/tex].
We know that the slopes of parallel lines are equal. So, [tex]m=2[/tex].
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What multiplication fact could you use to find a number that can be divided evenly by 8 and9?
A recipe for oatmeal raisin cookies call for 1 2/3 cups of flour to make 4 dozen cookies. How many cups of flour are needed to make 6 dozen cookis?
Which situation shows a constant rate of change?
A. The height of a monkey swinging from branch to branch over time
B. The height of a bouncing ball over time
C. The number of points scored in a basketball game compared with the number of minutes played
D. The amount a person pays for gas compared with the number of gallons purchased
The correct answer is:
D) The amount a person pays for gas compared with the number of gallons purchased
Explanation:
A constant rate of change means that for every x, y increases the same amount.
In the situation "The amount a person pays for gas compared with the number of gallons purchased ," the independent quantity, or x-value, is the number of gallons, and the dependent quantity, or y-value, is the amount paid. Since gas has a set price per gallon, for every gallon purchased, the total amount paid goes up the same amount. This means it has a constant rate of change.
What is the minimum value of P = x - 2y over the feasibility region defined by the constraints shown?
a) 8
b) -2
c) -16
d) -14
the answer is -14
hope this helps : )
41/18 as a mixed number
Today you deposited $5000 into a savings account paying 12% interest. how much shouldyou have in 15 years
which decimal is equivalent to the fraction 9/11?
Which answer describes the type of sequence? 3, 9, 15, 21, ...
geometric
arithmetic
neither arithmetic nor geometric
Answer:
The sequence is arithmetic
Step-by-step explanation:
we know that
In an arithmetic sequence, the difference between consecutive terms is always the same and is called common difference
In this problem we have
[tex]3,9,15,21,...[/tex]
Let
[tex]a1=3, a2=9,a3=15,a4=21[/tex]
[tex]a4-a3=21-15=6[/tex]
[tex]a3-a2=15-9=6[/tex]
[tex]a2-a1=9-3=6[/tex]
The sequence is arithmetic
The common difference is equal to [tex]6[/tex]
solve 2x+3y=10 and 3x-4y=-2
The solution to the system of equations 2x + 3y = 10 and 3x - 4y = -2 is x = 2 and y = 2.
Given the system of equations in the question:
2x + 3y = 10
3x - 4y = -2
To determine the solution to the system of equations, we can use the elimination method:
2x + 3y = 10
3x - 4y = -2
Multiply the first equation by 4 and the second equation by 3:
We have:
8x + 12y = 40
9x - 12y = -6
Now, we add the two equations.
We have:
17x + 0 = 34
x = 34/17
x = 2
Now, plug x = 2 into the first equation and solve for y:
2x + 3y = 10
2(2) + 3y = 10
4 + 3y = 10
3y = 10 - 4
3y = 6
y = 6/3
y = 2
Therefore, the value of x is 2 and the value of y is 2.
solving system using subsitution
question
a shopper purchased 8 t-shirts and 5 pairs of pants for $220.The next day he purh pair of purchased 5 tshirts and 1 pair of pants for $112.How much does each tshirt and each pair of pants cost? ...?
Find the point on the terminal side of θ = 3pi/4 that has a y coordinate of 1.
Answer:
B
Step-by-step explanation:
hope this helps
find where the slope of the curve is defined:
x^2y-xy^2=4
The slope of the curve x²y-xy²=4 is defined everywhere except for points where x = 2y. This conclusion is reached by using implicit differentiation and the product rule to find the derivative (slope), and then determining where the slope is undefined.
Explanation:To find where the slope of the curve is defined for the equation x²y-xy²=4, we first need to find the derivative of the equation. The derivative will give us the slope of the tangent line at a specific point. This process involves using the Product Rule of differentiation. The Product Rule states that the derivative of two functions multiplied together is the first function times the derivative of the second function plus the second function times the derivative of the first function.
For the given equation, we first need to rewrite it in the form: y = f(x). However, as y cannot be easily expressed solely as a function of x in this case, we will need to use implicit differentiation. Implicit differentiation assumes that y is a function of x, even if it's not explicitly stated. By using the product rule, we get 2xy + x² × (dy/dx) - y² - 2xy × (dy/dx) = 0; simplifying this, we get (x² - 2xy) × (dy/dx) = y² - 2xy. So dy/dx = (y² - 2xy) / (x² - 2xy).
Thus, the slope of the curve is defined wherever the denominator, x² - 2xy, does not equal zero, since division by zero is undefined. Hence, we need to solve x² - 2xy ≠ 0. Solving this inequality, we find that the slope of the curve is defined for all (x,y) except where x = 2y.
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john is building a soccer table and wants it to be similar in size to a real soccer field. a full size soccer field is 336 feet long and 210 feet wide. what will be the area of his soccer table if he wants it to be 2.5 feet wide?
Answer:
[tex]10 ft^2[/tex]
Step-by-step explanation:
We are given that
Length of soccer field=336 feet
Width of soccer field=210 ft
Width of soccer table=2.5 feet
We have to find the area of soccer table which is similar to soccer field in size.
Let x be the length of soccer table.
We know that when two figures are similar then ratio of their corresponding sides are equal.
[tex]\frac{336}{x}=\frac{210}{2.5}[/tex]
[tex]x=\frac{336\times 2.5}{210}=4[/tex]
Length of soccer table=4 ft
Area of soccer table=[tex]length\times breadth[/tex]
Area of soccer table=[tex]4\times 2.5=10 ft^2[/tex]
Hence , the area of soccer table=[tex]10 ft^2[/tex]