Answer:
Slope = - ⅖
Y-intercept = (0, 4), where b = 4
Step-by-step explanation:
Given the linear equation in standard form, 2x + 5y = 20, where A = 2, B = 5, and C = 20:
Start by transforming the standard equation into its slope-intercept form, y = mx + b, where m = slope, and b = y-intercept.
Subtract 2x from both sides:
2x -2x + 5y = - 2x + 20
5y = -2x + 20
Divide both sides by 5 to isolate y:
[tex]\frac{5y}{5} = \frac{-2x + 20}{5}[/tex]
y = - ⅖x + 4 ⇒ This is the slope-intercept form where the slope, m = -⅖, and the y-intercept, b = 4. The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b). The y-coordinate is the value of b in the slope-intercept form. Therefore, the y-intercept is (0, 4).
What is the geometric mean of
1. 16 and 27
2. 24 and 32
3. 5 and 36
4. 8 and 48
Answer:
1. 12√3
2. 16√3
3. 6√5
4. 8√6
Step-by-step explanation:
To find the geometric mean of n numbers multiply the numbers and then take the nth root.
For two numbers n = 2
it's the square root of the product
√(16 * 27)
√432
12√3
√(24 * 32)
√768
16√3
√(5 * 36)
√180
6√5
√(8 * 48)
√384
8√6
2x-y=4
-2x+y=7
is there a solution
[tex] \text{Given : 2x - y = 4 and x + 2y = 7}[/tex]
[tex] \text{Solution : according to the question here we are provided with} \\ \text{two equations separately. So, let's name them as eq(1) and eq(2).} \\ \text{ The rest is followed as we continue to get to our goal} \\ \\ \sf {1}^{st} \: equation : \\ \quad\dashrightarrow \frak{2x - y = 4} \\ \\ \quad \dashrightarrow \frak{ \red{x = \frac{y + 4}{2} }} \qquad \sf ...eq(1) \\ \rm{ now \: \: as \:per \: our \: plan \: we \: need \: to \: get \: eq(2) } \\ \\ \sf{ {2}^{nd} \:equation} : \\ \quad\dashrightarrow \frak{ x + 2y = 7} \\ \\ \quad\dashrightarrow \frak{ \red{y = \frac{7 - x}{2}}} \qquad \sf ...eq(2) \\ \\ \text{Now, finding x and y} \\ \\ \underline{ \frak{Finding \: x}}\\ \\ \quad \hookrightarrow \frak{x = \frac{y + 4}{2}} \\ \\ \quad \hookrightarrow \frak{2x = \frac{7 - x}{2} + 4} \\ \\ \quad \hookrightarrow \frak{2x = \frac{7 - x + 8}{2}} \\ \\ \quad \hookrightarrow \frak{2x = \frac{1 - x}{2}} \\ \\\quad \hookrightarrow \frak{4x = 1 - x} \\ \\ \quad \hookrightarrow \frak{5x = 1} \\ \\\quad \star \qquad \underline{ \boxed{ \green{ \frak{x = \frac{1}{5}}}}} \\ \\ \underline{ \frak{Finding \: y}} \\ \\ \quad \hookrightarrow \frak{y = \frac{7 - x}{2}} \\ \\ \hookrightarrow \frak{2y = 7 - \frac{1}{5} } \\ \\ \hookrightarrow \frak{2y = \frac{35 - 1}{5} } \\ \\ \hookrightarrow \frak{2y = \frac{34}{5}} \\ \\ \hookrightarrow \frak{y = \frac{34}{5} \times \frac{1}{2}} \\ \\ \hookrightarrow \frak{y = \frac{17}{5} } \\ \\ \star \qquad \underline{ \boxed{ \frak{ \green{y = 3 \frac{2}{5} }}}}[/tex]
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x - 5)?
-
o
-5
-4
-3
-1
0
1
2
3
4
5
f
.
-5
-4
-3
-2.
-1
o
3
o
1
2
4
5
+
+
-4
-5
-3
-2
-1
+
1
o
+
2.
+
3
+
4
5
Ол
O
3
-5
-4
-3
-2
-1
o
1
2.
3
4
5
Answer:
3 8-4× less than 6 ×-5 and then you solve the equation
Jack and Jill, trying to do math and chill, when they ran into a problem. They can't agree on what the answers should be, so now it's up to you to solve them.
In class, Jack thought as Jill she sought solve an absolute value... she removed the sign from her negative nine and said "the problem should be just about through".
But Jack he said, "no Jill you misread, the negative is on the outside". Still Jill didn't budge, so you be the judge, does this mean that the teacher lied?
Here's the problem Jack and Jill are trying to solve: -|9| = ?Jack thinks the answer is -9, because the negative is outside the absolute value signs. Jill thinks the answer is 9, because the teacher said absolute value is always positive.
Who is right and why? Explain your steps using sentences.
Answer:
-9
Step-by-step explanation:
the teacher was right
40
X
5. A health-food business would like to create a high-potassium blend of dried fruit in the form
of a box of fruit bars. It decides to use dried apricots, which have 407 mg of potassium per
serving, and dried dates, which have 271 mg of potassium per serving.
4
y
The company can purchase its fruit through www.driedfruitbaskets.com in bulk for a
reasonable price. Dried apricots cost $3.33/serving and dried dates cost $2/serving. The company
would like the box of bars to have at least the recommended daily potassium intake of about
4700 mg, but would like to keep it under twice the recommended daily intake. In order to
minimize cost, how many servings of each dried fruit should go into the box of bars?
5
Objective Function:
Constraints:
Corner Points & Answer:
Thus, the values corresponding to the function and constraints will be:
Objective Function:[tex]C=3.33X+2.00Y[/tex]
Constraints:[tex]407X+271Y\geq 4700\\407X+271Y\leq 9400[/tex]
We begin by defining the variables. Let call:
X = of servings of dried apricots
Y= of servings of dried dates
For apricots, there are 3 servings in one pound. This means that the cost per serving is $9.99/3 = $3.33. The cost for X:
[tex]3.33X[/tex]
For dates, there are 4 servings per pound. This means that the cost per serving is $7.99/4=$2.00. The cost for Y:
[tex]2.00Y[/tex]
The total cost would be:
[tex]C=3.33X+2.00Y[/tex]
Product must contain at least 4700mg of potassium
[tex]407X+271Y\geq 4700\\407X+271Y\leq 9400[/tex]
So now with the equations set it is possible to see that the desired values are between 9400 and 4700. Then using the critical points X=0, Y=0 for the two given equations. This will inform the points of interest for X and Y if this analysis is needed for the exercise.
Learn more: brainly.com/question/16173741
One thousand families were surveyed to
determine the distribution of families by size. The
results follow.
Family Size 2
3
4
5 6 7 8
Frequency
350
200 245 125
66
10
To the nearest percent, the probability that a given
family has 3 people is [? ]%.
Answer:
Step-by-step explanation:
probability of an event: number of events that satisfy the criteria/ total number of events
number of events that satisfy the criteria (in this case the number of families with three people)= 200
total number of events= 1000
200/1000= 20%
En una panadería, con 80 kg de harina hacen 120 kg de pan. ¿Cuántos kilos de harina serían necesarios para hacer 360 Kg de pan?
Answer:
240 kg
multiplica 360 con 80 y luego dividelo por 120. Que equivale a 240, o divide 120 por 80 que te da 1.5 y multiplicalo por 240 que equivale a el total 360 Kg
Events A and B are disjoint. Find P(AorB) when P(A) = 0.55 and P(B) = 0.2
P (A or B)=
Answer:
0.75 = P(A or B)
Step-by-step explanation:
Since the events are disjoint, we can find the probability of one or the other occurring merely by adding P(A) and P(B): 0.55 + 0.2 = 0.75 = P(A or B)
Louise spins the spinner twice. Which probabilities are correct? Check all that apply.
Keith wants to buy an IPad for $500. He wants to earn enough money delivering pizzas to cover at least two-fifths of the cost.
Part A.
If he earns $12.50 per hour at work, write an inequality that represents how many hours Keith's needs to work
Part B
Solve your inequality? Justify your answer.
Answer:
Step-by-step explanation:
500 / 5 = 100 (that's 1 fifth, so 2 fifths will be 200)
200 / 12.5 = 16 (he will have to work 16 hours to get $200)
the inequality would be:
x * 12.5 >= 500 * 0.4 (something like that)
Write the equation of the line in point-slope form that has slope 3 and passes through (2, -5).
Answer:
y+5=3(x-2).
Step-by-step explanation:
1) according to the condition m=3; x₁=2; y₁= -5, then
2) the required equation is y+5=3(x-2).
use properties of logarithms to condense logc Yc X
please need help answering this
9514 1404 393
Answer:
2
Step-by-step explanation:
Between the points at (x, y) = (-5, 4) and (-4, 6), the graph rises 2 units for a horizontal run of 1 unit. The average rate of change between the two points is ...
m = rise/run = 2/1 = 2
The average rate of change on the interval [-5, -4] is 2.
Nothing, never wanted to post a question on here
The graph f(x)=(x+2)^2-7is translated 5 units left, resulting in the graph g(x). Which equation represents the new function, g(x)?
Answer: G(x)=(x-3)^2-7
Step-by-step explanation: Translated 5 units to the left is a negative change and a change in the X axis
The equation represents the new function, g(x) will be G(x)=(x-3)²-7. The correct option is A.
What is translation?The process of changing the location of the image on the coordinate system will be known as the translation. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
It is given that the graph f(x)=(x+2)²-7 is translated as 5 units left, resulting in the graph g(x).
Translated 5 units to the left are a negative change and a change in the X axis. The graph is also attached with the answer below.
The equation represents the new function, g(x) will be G(x)=(x-3)²-7.
To know more about translation follow
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Which figure best demonstrates the setup for the box method of finding the area of a triangle? On a coordinate plane, a triangle is shown. A rectangular box is drawn around the triangle and share 2 sides with the triangle. On a coordinate plane, a triangle is shown. A rectangular box is drawn around the triangle and the 3 points of the triangle touch the sides of the box. The box is 2 units larger than one side of the triangle. On a coordinate plane, a triangle is shown. A rectangular box is drawn around the triangle and all 3 points of the triangle are on the sides of the box. On a coordinate plane, a triangle is shown. A rectangular box is drawn around the triangle and 2 points of the triangle are on the box.
Answer:
C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
The answer is C in Edge. Just took the assigment. Hope this helps! :)
(x^2+ 6x + 9) / (x-3)
Answer:
Simplify:
[tex]\frac{( {x}^{2} + 6x + 9) }{x - 3} [/tex]
Factoring:
[tex] {x}^{2} + 6x + 9[/tex]
The first term is, x2 its coefficient is 1 .
The middle term is, +6x its coefficient is 6 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 1 • 9 = 9
Step-2 : Find two factors of 9 whose sum equals the coefficient of the middle term, which is 6 .
-9 + -1 = -10
-3 + -3 = -6
-1 + -9 = -10
1 + 9 = 10
3 + 3 = 6 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 3
[tex] {x}^{2} + 3x + 3x + 9[/tex]
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+3)
Add up the last 2 terms, pulling out common factors :
3 • (x+3)
Step-5 : Add up the four terms of step 4 :
(x+3) • (x+3)
Which is the desired factorization.
Multiply (x+3) by (x+3)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+3) and the exponents are :
1 , as (x+3) is the same number as [tex](x+3) {}^{1}[/tex]
and 1 , as (x+3) is the same number as[tex](x + 3) {}^{1} [/tex]
The product is therefore, [tex](x + 3) {}^{(1 + 1)} = (x + 3) {}^{2} [/tex]
What is an equation in point-slope form for the line that passes through the points (4,-1) and (-3,4)?
y-3= (x+4)
y–4= (x+3)
y+4= (x+3)
y+4= (x+3)
(3x+8)(x+4)
Expand and simplify
Answer:
Step-by-step explanation:
(3x+8)(x+4), distribute 3x over the second parenthesis first and then the 8
3x² + 12x + 8x + 32 , combine like terms
3x² + 20x + 32
Answer:
3x^2 + 20x + 32
Step-by-step explanation:
Distribute 3x over the second parenthesis first and then the 8.
#CarryOnLearning
What is the quotient of 4/5÷1/3
The quotient of a division, is the result of the division, for example, 3 divided by 3, the result is 1, that is the quotient.
[tex]\sf \displaystyle \sf \frac{4}{\:5}\div \frac{1}{3}\\\\\\\sf \frac{4}{5}\times \frac{3}{1}\\\\\\\sf \frac{4\times \:3}{5\times \:1}\\\\\\\sf \frac{12}{5\times \:1}\\\\\\\sf \frac{12}{5}\approx\boxed{\sf 2,2\ll Quotient}[/tex]
Okay?!What is the inverse of the function f(x) =√x-2
PLEASE HURRY THIS IS TIMED !!!!
Answer:
c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Between what two whole numbers is 5/6 located on the number line? help please!
Answer:
Hello there!
5/6 is located between 0 and 1.
Step-by-step explanation:
5/6 is less than 1, because 1 = 6/6 in this scenario.
At the same time, it's greater than 0!
5/6 is located between 0 and 1 on the number line!
What is the length of the radius of a circle if the equation for the circle is (x + 2)2 + (y - 9)2 = 22.09?
Answer:
The radius is 4.7 units.
Step-by-step explanation:
To answer this we need only find the square root of 22.09: 4.7
The radius is 4.7 units.
The weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams. What is the weight of each tire in pounds? There are 453.592 grams in one pound. Round answers to 2 decimal places.
800 grams = (How many?)
pounds
700 grams = (How many?)
pounds
Answer:
Here they are unrounded
800 grams = 1.7637
700 grams = 1.54324
Step-by-step explanation:
Hope this helps
kate has $2.95 in quarters and nickels and the total number of ocins is 23 how many quarters and how many nickels does kat have
Answer: 9 quarters and 14 nickels
Step-by-step explanation:
9*25=225
14*5=70
225+70=295
The total number of nickels is 14 and the total number of quarters is 9 and this can be determined by forming the linear equation.
Given :
kate has $2.95 in quarters and nickels and the total number of coins is 23.
The following steps can be used in order to determine the total number of quarters and nickels Kat have:
Step 1 - Let the total number of quarters be 'x' and the total number of nickels be 'y'.
Step 2 - Remember one quarter is equal to $0.25 and one nickel is $0.05.
Step 3 - The total amount of money Kat has:
0.25x + 0.05y = 2.95 --- (1)
Step 4 - Total number of coins is given by:
x + y = 23
x = 23 - y --- (2)
Step 5 - Substitute the value of 'x' in equation (1).
0.25(23 - y) + 0.05y = 2.95
5.75 - 0.25y + 0.05y = 2.95
2.8 = 0.20y
y = 14
Step 6 - Now, substitute the value of 'y' in equation (2).
x = 23 - 14
x = 9
So, the total number of nickels is 14 and the total number of quarters is 9.
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Write the Equation
Equation
X Y
-2 5
-1 3
0 1
1 -1
y=-X+2
y=x+2
y=2x+1
y-2x+1
Answer:
y=-5×+13
Step1 inter change ×gy
A hot air balloon is at an elevation of 425 feet. It descends 110 feet what is the elevation of the balloon?
Answer:
315
425 + -115 = 315 feet
Step-by-step explanation:
Answer:
The balloon will be at an elevation of 315 feet.
Step-by-step explanation:
425-110=315
As Sandra drives, her music player randomly selects music from her playlist. Sandra’s playlist contains:
3 traditional country songs
6 traditional rock songs
4 hip-hop rap songs
5 contemporary country songs'
1 Latin rap song
3 traditional pop songs
What is the probability that the player will select some rap music next?
Answer:
the probability will be 18.18%
"15 is always equal to the product of a number and 5" translates to a mathematical equation.
O True
O False
Answer:
This is True
Step-by-step explanation:
I know this because it is like dividing you just divide 15 by 5 and the it will be equal