Answer:
a. FALSE
b. FALSE
c. FALSE
d. TRUE
Step-by-step explanation:
Statement a.
2 (3 - 4 y) = 6 - 4 y
use distributive property on the left:
6 - 8 y which is NOT 6 - 4 y then, FALSE statement
Statement b.
3 + 5 (9 + 2 n) = 48 + 5 n
apply distributive property on the left:
3 + 45 + 10 n = 48 + 10 n which is NOT 48 + 5 n then , FALSE statement
Statement c.
9 - 3 (y - 2) = 3 - 3 y
apply distributive property on the left:
9 - 3 y + 6 = 15 - 3 y which is NOT 3 - 3 y then, FALSE statement
Statement d.
3 (6 x - 2) - 7 = 18 x - 13
apply distributive property on the left:
18 x - 6 - 7 = 18 x - 13 which IS the same as 18 x - 13 then , TRUE statement
How many pounds of walnuts that cost $6.50 per pound must be mixed with 7 pounds of cashews that cost $11 per pound to make a mixture of nuts that costs $8.60 per pound?
I need help with this question.
Answer:You will need to buy 1/2 a pound of cashews and 1/2 a pound of peanuts
Write an equation in standard form for the line, where the points (-2, -1) and (0, 4) are on the line
Answer:
An equation in standard form for the line is:
[tex]\frac{5}{2}x-y=-4[/tex]
Step-by-step explanation:
Given the points
(-2, -1) and (0, 4)The slope between two points
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-2,\:-1\right),\:\left(x_2,\:y_2\right)=\left(0,\:4\right)[/tex]
[tex]m=\frac{4-\left(-1\right)}{0-\left(-2\right)}[/tex]
[tex]m=\frac{5}{2}[/tex]
Writing the equation in point-slope form
As the point-slope form of the line equation is defined by
[tex]y-y_1=m\left(x-x_1\right)[/tex]
Putting the point (-2, -1) and the slope m=1 in the line equation
[tex]y-\left(-1\right)=\frac{5}{2}\left(x-\left(-2\right)\right)[/tex]
[tex]y+1=\frac{5}{2}\left(x+2\right)[/tex]
[tex]y=\frac{5}{2}x+4[/tex]
Writing the equation in the standard form form
As we know that the equation in the standard form is
[tex]Ax+By=C[/tex]
where x and y are variables and A, B and C are constants
so
[tex]y=\frac{5}{2}x+4[/tex]
[tex]\frac{5}{2}x-y=-4[/tex]
Therefore, an equation in standard form for the line is:
[tex]\frac{5}{2}x-y=-4[/tex]
What is the angle of elevation?
Answer:
Step-by-step explanation:
tan x° = [tex]\frac{3}{4}[/tex] ⇒ x° ≈ 36.87° ≈ 36.9°
please help it’s due soon ): Find the slope of the line represented
by the data below.
Help please this is so hard!!
Answer:
use it to help you
See the explanation for a 'tip'
Explanation:
Quotient means 'the answer after dividing'.
If you get really stuck this is one (bit long) way of dealing with it.
Firstly lets for the moment forget about the negative and just deal with
-96÷12
Write as 96 12
Notice that both numbers are even so we can divide by 2
96÷2=48
12÷2=6
Again they are both even
48÷2=24
6÷2=3
The two digits of 24 are such that
2+4=6
and 6 is exactly divisible by 3 so 24 is also exactly divisible by 3. So now we can do this:
24÷3=8
3÷3=1
Now we put the negative back in giving −8
The table below represents a linear function. Determine the missing values in the table using the function rule.
Answer: In order: 25, 15, 67.
Step-by-step explanation:
In picture
Simplify the expression using order of operations.
5×2+32
Answer:
42
Step-by-step explanation:
start with the first 5x2 then add
Answer:
42
Step-by-step explanation:
5×2+32
10+32
42
A rocket is launched from a tower. The height of the rocket , y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot.
Y=-16x^2+147x+118
========================================================
Explanation:
The general equation
y = ax^2 + bx + c
has the vertex (h,k) such that
h = -b/(2a)
In this case, a = -16 and b = 147. This means,
h = -b/(2a)
h = -147/(2*(-16))
h = 4.59375
The x coordinate of the vertex is x = 4.59375
Plug this into the original equation to find the y coordinate of the vertex.
y = -16x^2+147x+118
y = -16(4.59375)^2+147(4.59375)+118
y = 455.640625
The vertex is located at (h,k) = (4.59375, 455.640625)
The max height of the rocket occurs at the vertex point. Therefore, the max height is y = 455.640625 feet which rounds to y = 455.6 feet
Find PM pls help fast
Answer:
I think it is 4 but, im not sure
Como es la fórmula del perímetro de un hexágono?
Espero respuesta
Gracias
Answer:
El Perímetro de un hexágono es igual a la suma de todos sus lados.
Step-by-step explanation:
el perimetro siempre es la suma de los lados de cualquier figura
A rectangle is constructed with its base on the x-axis and two of its vertices on the parabola yx. What are the dimensions of the rectangle with the maximum area? What is that area?
Answer:
The answer is below
Step-by-step explanation:
The question is not complete, the complete question is:
A rectangle is constructed with its base on the x-axis and two of its vertices on the parabola y 81-x², what are the dimensions of the rectangle with the maximum area? what is the area?
Solution:
Given the parabola:
y = 81 - x²
Let the points (a,0) and (-a, 0) be points on the axis, this points touch the parabola at (a, 81 - a²) and (-a, 81 - a²).
Points (a,0), (-a, 0), (a, 81 - a²), (-a, 81 - a²) form the rectangle.
The length of rectangle = distance between (a,0) and (-a, 0) or between (a, 81 - a²) and (-a, 81 - a²) = 2a
The breadth of rectangle = distance between (a,0) and (a, 81 - a²) or between (-a, 0) and (-a, 81 - a²) = 81 - a²
Area of rectangle (A) = length × breadth = 2a × (81 - a²) = 162a - 2a³
A = 162a - 2a³
The maximum area is at dA / da = 0
dA / da = 162 - 8a² = 0
162 - 6a² = 0
6a² = 162
a² = 27
a = 5.2 units
Length = 2a = 2(5.2) = 10.4 units
Breadth = 81 - a² = 81 - 5.2² = 54 unit
Area = length × breadth = 54 × 10.4 = 561 unit²
What is the difference between a tax credit and a tax deduction?
Answer:
A deduction can only lower your taxable income and the tax rate that is used to calculate your tax. This can result in a larger refund of your withholding. A credit reduces your tax giving you a larger refund of your withholding, but certain tax credits can give you a refund even if you have no withholding.
Step-by-step explanation:
9a + 8 - 20-3-50
Answer
Answer:
9a-65
Step-by-step explanation:
simply write 9a+(add the remaining numbers all together)
3044 in base 5 to base 10
Houses can be either domed or octagonal.
True
False
Answer:
true
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
Houses can be either domed or octagonal: True
Hadley paddled a canoe 2 miles in 1/9 of
an hour How far could Hadley paddle in
1 hour?
Answer: 18 miles
explanation: set up a proportion. (2 over 1/9 = x over 1). cross multiply, 2x1=2, then divide 2/(1/9)=18.
Which of the following is parallel to the line
Answer:
1
Step-by-step explanation:
h
Answer:
I know it is 1
Step-by-step explanation:
plisss helppppppppppñp
Answer:
The value of x is 37.36
Step-by-step explanation:
The given triangle is a right-angled triangle where
Base = 25
Angle = 48°
Hypotenuse = x
As the triangle is a right angled triangle, trigonometric ratios can be used to find the missing value. We can use a ratio which uses base and hypotenuse.
[tex]cos\ 48 = \frac{base}{hypotenuse}\\cos\ 48 = \frac{25}{x}\\0.6691 = \frac{25}{x}\\x = \frac{25}{0.6691}\\x = 37.36[/tex]
Hence ,
The value of x is 37.36
Which of the following expressions is equivalent to 18 m - 12?
A. 021-9 m+6)
B. -1(18 m +12)
C. 6(3 m - 2)
D. -3(-6 m - 4)
Answer:
C and D
multiply the 6 and -3 to the numbers inside the parenthesis
There are a total of 120 bicycles and tricycles in a shop. There are 302 wheels in allmany bicycles and how many tricycles are in the shop?
Answer: There are 62 tricycles in the shop.
Step-by-step explanation:
Given: Number of wheels in a bicycle = 2
Number of wheels in a tricycle = 3
Let x = Number of bicycles , y = Number of tricycles.
As per given , we have
x+y =120 (i)
2x+3y=302 (ii)
Multiplying 2 on both sides of (i)
2x+2y=240 (iii)
Subtract (iii) from (ii) , we get
y= 62
Put value of y in (i) , we get
[tex]x+62=120\\\\\Rightarrow\ x=120-62\\\\\Rightarrow\ x= 58[/tex]
Hence, there are 58 bicycles and 62 tricycles in the shop.
please helppp! and thank you
Answer:53
Step-by-step explanation:
What is the slope of the line?
Look at the factors of 24 and 32.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 32: 1, 2, 4, 8, 16, 32
The GCE of 24 and 32 is
Answer: 8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
i need help with this plz i have no idea what to do
Answer:
When Item Price * (%) is < or > to $ Off
Step-by-step explanation:
A line passes through the point (-6,7) and has a slope of -4/3. Write an equation in slope-intercept form for this line.
Answer:
Step-by-step explanation:
y-7= -4/3 (x+6)
y-7= -4/3x-8
add 7 to both sides
y= -4/3x-1
The equation in slope-intercept form for the given line is 3y = -4x -3
What is Equation?The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that a line passes through the point (-6,7) and has a slope of -4/3.
Standard equation of a line = y = mx + c where m is the slope,
Therefore, putting values of x and y to get the value of c
7 = -6*-4/3 + c
c = 7 - 8
c = -1
Equation = y = -4x/3 -1
Or, 3y = -4x -1
Hence, the equation of a line passing through the point (-6,7) and has a slope of -4/3 is 3y = -4x -1
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Log2(x-3)+log2x-log2(x+2)=2
We are given the equation:
log₂(x-3) + log₂x - log₂(x+2) = 2
When is it defined:
in this equation, log₂(x-3) and log₂(x+2) can only be defined when
x-3 >0 and x+2 > 0
solving for the values of x, we get:
x > 3 and x > -2
which basically means x > 3
Because we are looking for an inequality which is true for both x>-2 and x>3
Hence, x will have a value greater than 3
Solving for x:
using the product rule [logₐb + logₐc = logₐ(bc)]
log₂[(x-3)(x)] - log₂(x+2) = 2
using the quotient rule [logₐb - logₐc = logₐ(b/c)]
log₂[(x-3)(x) / (x+2)] = 2
from the property [ aˣ = b ⇒ logₐb = x]
(x² - 3x) / (x+2) = 2²
x² - 3x = 4x + 8
x² - 7x - 8 = 0
x² + x - 8x - 8 = 0
x(x+1) - 8(x+1) = 0
(x-8)(x+1) = 0
(x-8) = 0 OR (x+1) = 0
x = 8 OR x = -1
We know that the equation is defined only for x > 3
We can see that x = 8 satisfies that inequality
Therefore, x = 8
Please answer this correctly without making mistakes
Answer:
The answer is $0.07 cents per inch
Step-by-step explanation:
If you take 6 feet into inches (72)
and divide the total cost by the amount of inches (5.04 / 72)
You get the answer
Wait so add 25.50 +25.50
By selling a book for Rs.400 a student got two successive profits of 12% and 40% respectively. Then his total profit is
a.62%
b.50%
c.55%
d.56.8%
The total profit made by the student is 56.8%
The correct answer is D
Given parameters:
final price in which he book was sold = Rs.400
the first profit made by the student = 12% = 0.12
the final profit made by the student = 40% = 0.4
To find:
the total profit of the studentTo find the total profit made by the student, we have to find the initial cost price of the book.
The cost price of the book before the student made the profit of 40%.
Let this cost price = y
100%y + 40%y = 400
140%y = 400
1.4y = 400
[tex]y = \frac{400}{1.4} \\\\y = 285.71[/tex]
This cost price become the new selling price before the student made the profit of 12%.
The cost price of the book before the student made the profit of 12%.
Let this cost price = x
100%x + 12%x = 285.71
112%x = 285.71
1.12x = 285.71
[tex]x = \frac{285.71}{1.12} \\\\x = 255.1[/tex]
This is the initial cost price of the book
The total profit made by the student is calculated as;
[tex]Profit \ \%= \frac{selling \ price - cost \ price }{cost \ price} \times 100\%\\\\Profit \ \%=(\frac{400 - 255.1}{255.1} )\times 100\%\\\\Profit \ \%= 56.8\%[/tex]
Thus, the total profit made by the student is 56.8%
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Plant A is 18 inches tall after one week, 36 inches tall after two weeks, 56 inches tall after three weeks. Plant B is 18 inches tall after one week, 36 inches tall after two weeks, 54 inches tall after three weeks. Which situation represents a proportional relationship between the plants?
Height and number of weeks?
Answer:
There are 2 given situations:
Plant A and Plant B growing in 3 weeks. Find which plant grows proportional
Plant A
=> 1st week = 18 inches
=> 2nd week = 36 inches
=> 3rd week = 56 inches
=> 18 + 18 = 36 + 20 = 56
Thus, this is not proportional
Plant B
=> 1st week = 18 inches
=> 2nd week = 36 inches
=> 3rd week = 54 inches
=> 18 + 18 = 36 + 18 = 54 inches
thus, the growth of this plant is proportional