First, we need to solve the equation 4x+5y=7 to make it slope intercept form and find the slope of the line, because parallel lines have the same slope.
4x+5y=7
Subtract 4x from both sides.
5y=-4x+7
Divide both sides by 5.
y=-4/5x+7/5
The slope of the line is -4/5x. Plug that in to the blank slope intercept form equation, y=mx+b, with m being the slope and b being the y-intercept.
y=-4/5x+b
Now, we need to solve for the y-intercept. We can do this by plugging in the given coordinates (4,-3) into the above equation for x and y respectively:
-3=-4/5(4)+b
-3=-16/5+b
Add -16/5 to both sides.
1/5=b
The y-intercept is 1/5, plug this into the equation:
[tex]y=-\frac{4}{5}x+\frac{1}{5}[/tex]
Your equation is the above equation.
I hope this helps :)
Final answer:
To find the slope-intercept form of a line parallel to 4x + 5y = 7 and passing through (4, -3), first find the slope of the given line, then use the point-slope form with the given point to derive the final slope-intercept form, which is y = (-4/5)x + 1/5.
Explanation:
The student is asking for the slope-intercept equation of a line parallel to another line. Since parallel lines have the same slope, we first need to find the slope of the given line, 4x + 5y = 7. To do this, we solve for y to get it into the slope-intercept form, y = mx + b, where m is the slope.
To convert 4x + 5y = 7 into slope-intercept form, we subtract 4x from both sides to get 5y = -4x + 7, and then divide by 5, resulting in y = (-4/5)x + 7/5. The slope of this line is -4/5. Hence, our new line must have the same slope of -4/5 to be parallel.
We use the point-slope form of the equation, which is y - y1 = m(x - x1), to get the equation of the line passing through the point (4, -3). Plugging in the values, we have y - (-3) = (-4/5)(x - 4), which simplifies to y + 3 = (-4/5)x + 16/5. To get the slope-intercept form, we subtract 3 from each side and get y = (-4/5)x + 16/5 - 15/5, leading to y = (-4/5)x + 1/5.
[tex] \pi x^{2} [/tex] = a
The formule is about area of a circle.
[tex]\pi x^{2} = a[/tex]
We need to solve the equation for x. Where x is the radius of the circle.
In order to solve it for x, we need isolate it for x on left side.
So, first we need to get rid pi from left side.
On dividing both sides by pi, we get
[tex]\frac{\pi x^2}\pi}=\frac{a}{\pi}[/tex]
[tex]x^2=\frac{a}{\pi}[/tex]
Taking square root on both sides, we get
[tex]\sqrt{x^2}=\sqrt{\frac{a}{\pi}}[/tex]
[tex]x=\sqrt{\frac{a}{\pi}}[/tex]
what is the solution to this equation?
-6x+3=21
if g=8, what is the value of the expression
[tex] \frac{g}{2} + 3[/tex]
A.
[tex] \frac{8}{5?} [/tex]
B.
[tex] \frac{11}{2} [/tex]
C.
[tex]7[/tex]
D.
[tex]19[/tex]
this afternoon,sara noticed that the number of the page assigned for homework is divisble by both 12 and 2.what is the smallest possible page number tha
t could have been assigned
Answer:
The smallest possible page number that would have been assigned is 12.
Step-by-step explanation:
Number of pages assigned for homework = x
The 'x' is the number which divisible by both 2 and 12.
2 = 1 × 2 (prime number)
12 = 1 × 2 × 2 × 3 (Composite number)
The smallest possible page number that could have been assigned will be equal to lowest common multiple of 1, 1, 2, 2 and 3.
X = 1 × 1 × 2 × 2 × 3 = 12
liquid A has a density of 1.4 g/mL , liquid B has a density of 5.9 g/mL and liquid c has a density of 3.2 g/ mL. arrange the three liquids ina density column ( explain your answer)
Liquid B
Liquid C
Liquid A
Because the denser layers sink and the less dense layers float to the top, just like oil and water, the water is more dense than the oil, that is why the oil floats to the top and the water remains at the bottom:))
At the bottom of the density column there is liquid B with a density of 5.9 g/ml, in the middle liquid C with a density of 3.2 g/ml and in the middle liquid A with a density of 1.4 g/ml be at the top.
Explanation:
To arrange liquids A, B, and C in a density column, you must consider their respective densities, since the highest density liquid stays at the bottom and the lowest density liquid floats at the top. Liquid B has the highest density (5.9 g/ml), then liquid C with a density of 3.2 g/ml, then liquid A with the lowest density, 1.4 g/ml. Therefore, when arranging these liquids in a density column, place liquid B at the bottom, liquid C in the middle, and liquid A at the top.
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Brittany is sell car magnets. She purchases them for $7.50 each and marks up the price by 30%. How much is Brittany planning to charge?
Considering that 30% of $7.50 is the same as 0.3/7.5, you would get $2.25 as the markup price. So by adding $7.50 with $2.25, Brittany would charge $9.75 per car magnet.
help Asp please it's do tomorrow
Hello!
To answer your question we need to follow these steps:
First we will need to subtract the $6 tip from the total of the meal, as a tip is added AFTER tax is applied.Once we subtract 6 from 45.42 we are given 39.42 as our price with tax.The next step is divide 39.42 by 1.08 , or 8% This gives us the total of $36.50 before tax.We will then subtract the price of the fries from out total before tax, giving us the equation $36.50 - $5.00 which gives us a total of $31.50Our last step, is to divide this amount by 3 to find the cost of 1 sandwich. $31.50/3= $10.50If you have followed these steps correctly you will find that the cost of one sandwich is $10.50!
If the opposite of g(x) is –g(x), then –g(x) = ?
Answer:
if you are looking for g(x)=x-6 the opp is....... -g(x)=-x+6
Step-by-step explanation:
Answer: -g(x)=-x+6
Step-by-step explanation:
Determine the x- and y-intercepts of the graph of y=−13x+3 . Then plot the intercepts to graph the equation.
To find the x-intercept of the equation y = -13x + 3, set y to zero and solve for x to get (3/13, 0). For the y-intercept, set x to zero and solve for y, resulting in (0, 3). These intercepts are then plotted and connected to graph the equation.
Determining X and Y Intercepts
To determine the x-intercept of the linear equation y = -13x + 3, we need to set y to zero and solve for x:
0 = -13x + 3
13x = 3
x = 3/13
So, the x-intercept is (3/13, 0).
To determine the y-intercept, we set x to zero and solve for y:
y = -13(0) + 3
y = 3
Thus, the y-intercept is (0, 3).
Plotting the Intercepts
On graph paper, mark the x-intercept at (3/13, 0) and the y-intercept at (0, 3). Then use a ruler to draw a straight line that passes through these points; this line represents the equation y = -13x + 3.
The slope is the rate of change along a line. However, in this scenario, the slope is not required to plot the line since we already have the intercepts. Nonetheless, for your reference, the slope (m) in the equation y = mx + b corresponds to -13, indicating a decline of 13 units in the y-direction for each single unit increase in the x-direction.
Olympic swimming pools are rectangles measuring 164.042 feet in length and 82.021 feet in width. What is the perimeter of an Olympic pool pls help i have no clue how to do this
To find the perimeter of a rectangle, you use the equation 2(lxw) so 2(164.042+82.021)
2(246.063) which is 492.126
The perimeter of an Olympic pool is 492.126 feet if the Olympic swimming pools are rectangles measuring 164.042 feet in length and 82.021 feet in width.
What is a rectangle?It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.
It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is given that:
Olympic swimming pools are rectangles measuring 164.042 feet in length and 82.021 feet in width.
Perimeter = 2(length + width)
Perimeter = 2(164.042 + 82.021)
Perimeter = 2(246.063)
Perimeter = 492.126 feet
Thus, the perimeter of an Olympic pool is 492.126 feet if the Olympic swimming pools are rectangles measuring 164.042 feet in length and 82.021 feet in width.
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You are remodeling your kitchen. You’ve contacted two tiling companies who gladly told you how long it took their workers to tile a floor of a similar size. Jim completed half the floor in 12 hours . Pete completed the other half in 10 hours. If Pete can lay 25 more tiles per hour than Jim, what equation would you use to find the rate that Jim can lay tiles. Let x represent Jim’s rate
As given, let Jim's rate = x
Let Pete's rate =y
Jim completed half the floor in 12 hours so it's [tex]12\times rate[/tex]= 12x
Pete completed the other half of the floor in 10 hours so its [tex]10\times rate[/tex]=10y
As floor area is equal so,
[tex]12x=10y[/tex] .............(1)
Now, given is that Pete can lay 25 more tiles per hour than Jim, this gives=
[tex]y=x+25[/tex] ...... (2)
Putting the value of y from equation (2) in equation (1) , we get
[tex]12x=10(x+25)[/tex]
So, the equation is : [tex]12x=10(x+25)[/tex]
If you want to solve it, it becomes:
[tex]12x=10x+250[/tex]
[tex]2x=250[/tex]
[tex]x=125[/tex]
Hence, Jim can lay 125 tiles and Pete can lay 25 more so 125+25=150 tiles.
Answer:
12x=10(x+25)
Step-by-step explanation:
apex
True or False: For any two integers a and b, (a-b)^2 = a^2-b^2
Expanding the expression, it is found that the statement is false.
---------------------------
The statement given is: [tex](a - b)^2 = a^2 - b^2[/tex]Expanding the left side, we get:[tex](a - b)^2 = (a - b)(a - b) = a^2 - ab - ab + b^2 = a^2 - 2ab + b^2[/tex]
Which is different than the statement, and thus, the statement is false.The expression is also known as a notable product, the perfect square binomial.A similar problem is given by: https://brainly.com/question/17202374
The statement is false. The square of difference of two quantities is not equal to the difference of their squares. The correct expression for [tex](a-b)^2 is a^2 - 2ab + b^2, not a^2 - b^2.[/tex]
Explanation:The statement For any two integers a and b,[tex](a-b)^2 = a^2-b^2[/tex] is false. Let's illustrate why this is incorrect with an example. If we let a = 2 and b = 1, then the left-hand side of the equation [tex](a-b)^2[/tex] would give us [tex](2-1)^2[/tex] = 1 and the right-hand side of the equation [tex]a^2 - b^2[/tex] would give us 2² - 1² = 3 which are not equal.
It's important to note that (a - b)² can be expanded to a² - 2ab + b² in accordance with the square of a binomial formula, which is definitely not equal to [tex]a^2 - b^2[/tex]. A common mistake is to drop the middle term in the expansion (-2ab), which leads to this incorrect equation.
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Find three consecutive integers whose sum is 35.
5, 10, and 20. (This is your answer.)
5 + 10 + 20 = 35.
These numbers are also consecutive, meaning each comes after the other on a number-line.
Hope this helps!
The area of a rectangular vegetable garden is 200ft^2 . The width is 10 ft. What is the lenght of the vegetable garden?
The length of the rectangular vegetable garden will be 20 feet.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be
Area of the rectangle = L × W square units
The region of a rectangular vegetable nursery is 200 square feet. The width is 10 feet.
The length of the rectangle will be given as,
200 = 10 L
L = 200 / 10
L = 20 feet
The length of the rectangular vegetable garden will be 20 feet.
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The population of a city can be modeled with a linear equation, y = –80x + 3,450, where x is the number of years after 2000 and y is the city’s population. Write a description of the city’s population based on the equation.
Answer:
Initial population is 3450 in the year 2000 and it decreases 80 every year.
Step-by-step explanation:
We are given with y=-80x+3450 where y is city's population and x is the number of years after 2000.
That is x=0 means the year 2000.
Hence y-intercept will represent the initial population which is nothing but 3450.
Since our equation slope =-80 which is negative means y is decreasing as x increases.
For x raises by 1, y decreases by 80.
That means population decreases by 80 for every year.
Answer:
The y-intercept indicates the population in the year 2000, so 3,450 people lived in the city in 2000. The negative slope indicates that the city is losing population. It loses 80 people each year.
Step-by-step explanation:
i just did the assignment
Write
10/17 as a decimal and round to the nearest hundredth.
the answer to that is 0.59
Answer:
0,900 or 0,9
Step-by-step explanation:
10/17 = 10 ÷ 17 = 0,588235
Hope it helped,
BioTeacher101
30 + (.0825 x 30) + (15% x 30) =
30×·15=4.50
then subtract 30 by 4.50 to get 25.50
.0825×30=2.475
now add 2.475+25.50+30= 57.975 round to 57.98
The final answer is 36.975. The expression simplifies to 36.975 when all calculations are completed.
1. 30 + (.0825 x 30):
To calculate this part, we first multiply 0.0825 (which is 8.25% written as a decimal) by 30. This gives us:
0.0825 x 30 = 2.475
Next, we add 30 to the result:
30 + 2.475 = 32.475
2. (15% x 30):
To calculate this part, we first convert 15% to a decimal by dividing it by 100:
15% = 15/100 = 0.15
Next, we multiply 0.15 by 30:
0.15 x 30 = 4.5
Now that we have the results from both parts, we add them together:
30 + (.0825 x 30) + (15% x 30) = 30 + 2.475 + 4.5 = 36.975
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Complete question is:
Solve the given expression: 30 + (.0825 x 30) + (15% x 30) =
Convert the decimal 0.6333… to a fraction and classify it as either rational or irrational.
A. 57⁄9, irrational
B. 57⁄90, rational
C. 63⁄90, rational
D. 63⁄99, rational
answer B
We assume x= 0.6333
100x = 63.3333
10x= 6.333 33 (subtract it )
----------------------------
90x = 57 ( divide by 90 on both sides)
So x= [tex]\frac{57}{90}[/tex]
Answer : [tex]\frac{57}{90}[/tex]
When we can write a number in fraction form then it is a rational number.
We converted the decimal number into a fraction so it is rational
The answer is B. 57/90, rational.
please explain how to do square roots
The difference of 10 and a number is negative eight
10 - x = -8
x = 10 + 8
x = 18
-----------------------
10 - 18 = -8
The sum of 2 and is less than -29
the larger number is 18 more than twice the smaller. if the sum of. the two numbers is 93, find both numbers.
The larger number is 68 and the smaller number is 25.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the larger number is 18 more than twice the smaller. if the sum of. the two numbers are 93. let the larger number be L and the smaller number be S.
L = 18 + 2S
L + S = 93
18 + 2S + S = 93
18 + 3S = 93
3S = 93 - 18
3S = 75
S = 25
L + S = 93
L + 25 = 93
L = 93 - 25
L = 68
Therefore, the larger number is 68 and the smaller number is 25.
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if amit started work at 6am and left at 1:45 pm how many hours should he record for the day on his time card?
6 hours in the morning (from 6 am to 12 am)
1:45 in the afternoon (from 12 am to 1:45 pm)
sum
6:00 + 1:45 =
7:45 ( 7hours and 45 minutes)
6 am to 12 pm is 6 hours.
12 pm to 1 pm is 1 hour.
So you have 7 hours 45 min.
Since 45 min is 3/4 of an hour you would add it up to get 7.75 hours.
Your answer is 7.75 hours.
Hope this Helps!!
What’s |z-15|+5c+j z=10 c=-2 j=-4
Answer:
-9
Step-by-step explanation:
10-15 = -5 I-5I= 5
5*-2= -10
5+-10+-4 = -9
which algebraic rule describes the 270° counter-clockwise rotation about the origin?
a) (x, y) → (−x, y)
b) (x, y) → (x, −y)
c) (x, y) → (y, −x)
d) (x, y) → (−y, x)
270 degree counter clockwise is the same as 90 degrees clockwise.
If you imagine the (x,y) axes rotating 90 clockwise, you will see that what x becomes y, and what was y becomes negative x (after the rotation).
So x-->y, and y-->-x
So the answer (c) is the correct one.
Answer:
option C
Step-by-step explanation:
the correct answer is option C
when a point (x, y ) means point lies in the first quadrant is rotated counter-clockwise to 270° means now the point will be in the fourth quadrant.
hence, in algebraic notation we interchange x by negative x
and y remains the same and their value interchanges so,
the best-suited answer will be (x, y) → (y, -x)
hence, the answer will be option C
A.) Multiply these numbers the quickest and easiest way possible: 87 x 5 x 2 B.) Explain how you were able to quickly determine the product. Justify your reasoning using a property of multiplication.
It is easy to multiply numbers by 10: you simply have to add an extra zero at the end.
This means that, using associative property, we know that
87 x 5 x 2=(87 x 5) x 2=87 x (5 x 2)
The last expression is the easiest to compute, because we have
87 x (5 x 2) = 87 x 10 = 870
Hope I helped.
Which value below is included in the solution set for the inequality statement?
-3(x - 4) > 6(x - 1)
[tex]-3(x-4) > 6(x-1)\qquad\text{use distributive property}\\\\(-3)(x)+(-3)(-4) > (6)(x) + (6)(-1)\\\\-3x+12 > 6x-6\qquad|\text{subtract 12 from both sides}\\\\-3x > 6x-18\qquad|\text{subtract 6x from both sides}\\\\-9x > -18\qquad|\text{change the signs}\\\\9x < 18\qquad|\text{divide both sides by 9}\\\\x < 2[/tex]
PLEASE HELP ME WITH THIS !!
the top one, use the vertical line test and if their are more than two points on the vertical line when testing the points then the relation is not a function. Which tells you that the last three are not a function.
the arithmetic average of 10 numbers -2, -5,-2, 5, x , -3 10, 3, 8, -10 is 8 find x
AS
Arithmetic average = Sum of all the numbers /Total numbers
SO arithmetic average= {(-2)+(-5)+(-2)+(5)+(x)+(-3)+(10)+(3)+(8)+(-10)} / 10
={4x} /10
=0.4 x
As Given Arithmetic average= 8
so 0.4x =8
Dividing 0.4 Both sides
0.4x/0.4 = 8/0.4
x= 20