Expression of the given interval (-4,-1) in inequality notation is -4< x <-1.
As given,
Given interval:
( -4 , -1 )
Let us consider x variable belongs to given interval x ∈ ( -4 , -1 ).
Given interval ( -4 , -1 ) is open interval.
In open interval when we plot it on the real number line , we are not including upper limit and the lower limit of the given interval.
-4 and -1 are exclusive values for the given variable.
Symbol representing open interval is sign of < or >.
Interval (-4,-1) in inequality notation is given by -4 < x < -1.
All values are included between -4 and -1 except -4 and -1.
Therefore, the expression of the given interval (-4,-1) in inequality notation is -4 < x < -1.
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A stand at the farmers market sells different types of apples, as shown in the table.
Apple A Apple B Apple C
Cost ($)4.90 1.00 0.45
Weight 4 lb 10 oz 1/2 lb
Which type of apple costs the least per pound?
The apple that costs the least per pound is Apple B.
What is the least cost?The cost per pound for each apple will be calculated as:
= Cost / Weight
Apple A:
= Cost / Weight
= 4.90 / 4
= $1.25 per pound
Apple B:
= Cost / Weight
= $1 / 10
= $0.1 per pound
Apple C:
Cost / Weight
= $0.45 / 0.5
= $0.9 per pound
Therefore, apple B is the cheapest
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College Algebra
A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 5 hours, while the outlet pipe can empty it in 8 hours. How long will it take to fill the vat if both pipes are left open?
It will take__ hours.
(Simplify your answer. Do not round.)
Answer:
3 1/13
Step-by-step explanation:
rate(time) of one pipe + rate(time) of the other pipe = 1 job
The rate would be the the number of jobs over the time
The rate of the first pipe is 1/5 and the rate of the second pipe is 1/8.
Together:
1/5t + 1/8t = I job
t(1/5 + 1/8) = 1
t(8/40 + 5/40) = 1
t(13/40) = 1 multiply each side by 40/13
t(40/13)(13/40) = 1(40/13)
t = 40/13
t = 3 1/13
Find the slope of a line parallel to the line whose equation is x-y = 4
Answer: Slope of 1.
Step-by-step explanation:
First, we will put the equation into slope-intercept form.
x - y = 4
x = y + 4
y = x - 4
Our slope, when the line is written as y = mx + b, is the m value. Our m value here is one, so the slope of a line parallel to the line whose equation is x - y = 4 is 1.
Given the scatter plot on the graph below. What is the slope of the line of fit
Hello there. To solve this question, we'll have to remember some properties about scatter plots and slope of a line.
Given the scatter plot of the data information, we have to determine the slope of the line.
For this, we could determine it numerically using the least squares method, if we knew the data (the coordinates of the points we're plotting the best fit).
In this case, we simply need to find, by inspection, two points contained in the line and use the slope formula.
Given two points (x0, y0) and (x1, y1) that a line L passes through, then the slope m of this line is given by:
[tex]m=\frac{y_1-y_0}{x_1-x_0}[/tex]By inspection, we can easily spot the points (16, 12) and (28, 20).
Plugging these coordinates in the formula, we get:
[tex]m=\frac{20-12}{28-16}[/tex]Add the numbers and simplify the fraction
[tex]m=\frac{8}{12}\overset{:4}{=}\frac{2}{3}[/tex]This is the slope of this line.
Use trigonometric identities and algebraic methods, as necessary, to solve the following trigonometric equation. Please identify all possible solutions by including allanswers in [0, 2x) and indicating the remaining answers by using n to represent any integer. Round your answer to four decimal places, if necessary. If there is nosolution, indicate "No Solution."cos(x) + cos(x) = 4cos(x) + 4
The solutions to the quadratic trigonometric equation are given as follows:
x = kπ, k = ± 1, ± 3, ± 5, ± 7.
How to solve the quadratic trigonometric equation?The quadratic trigonometric equation is defined as follows:
cos²(x) + cos(x) = 4cos(x) + 4.
Then the following transformation is applied to solve the equation:
y = cos(x).
Hence:
y² + y = 4y + 4
y² - 3y - 4 = 0
(y - 4)(y + 1) = 0.
Applying the Factor Theorem, the solutions are given as follows:
y - 4 = 0 -> y = 4.y + 1 = 0 -> y = -1.However, we want the solutions for x, hence they are obtained as follows:
cos(x) = 4.
x = arccos(4), which has no solution, as there are no angles with a cosine of four.
cos(x) = -1.
x = arccos(-1)
x = kπ, k = ± 1, ± 3, ± 5, ± 7
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Point (-3,2) Line x + y = 3 (Question parts in the photo, sorry)
a)
The slope intercept equation of a line is expressed as
y = mx + c
where
m is the slope
c is the y intercept
The given equation is
x + y = 3
y = - x + 3
By comparing both equations,
m = - 1
If two equations are parallel, it means that they have the same slope. Thus, the slope of the parallel line passing through the point (- 3, 2) is - 1
We would find the y intercept by substituting x = - 3, y = 2 and m = - 1 into the slope intercept equation. It becomes
2 = - 1 * - 3 + c
2 = 3 + c
c = 2 - 3
c = - 1
By substituting m = - 1 and c = - 1 into the slope intercept equation, the equation of the line is
y = - x - 1
b) If two equations are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line Thus, the slope of the perpendicular line passing through the point (- 3, 2) is - - 1/1 = 1
We would find the y intercept by substituting x = - 3, y = 2 and m = 1 into the slope intercept equation. It becomes
2 = 1 * - 3 + c
2 = - 3 + c
c = 2 + 5
c = 5
By substituting m = 1 and c = 5 into the slope intercept equation, the equation of the line is
y = x + 5
a) y = - x - 1
b) y = x + 5
I need help with statistical problem I have got the answer of 0.3354 because I subtracted 0.9991 - 0.146 I wanted to know if that was correct I kept getting the answer wrong
Data:
• Cumulative probability of -2.18 ,: 0.0146
• Cumulative probability of 3.74 ,:, ,0.9999
Procedure:
0. Using the following formula we can get our probability.
[tex]P(-2.182. Replacing the values previously got from a Standard Normal Table.[tex]P(-2.18Answer: 0.9853
solve the equations and verify the answer
The value of m is -6/5.
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.
Given:
2m -3 = 3/10 (5m - 12)
Now, cross multiplying
10( 2m -3)= 3( 5m -12)
20m -30 = 15m - 36
20m- 15m= -36 + 30
5m = -6
Divide both side by 5
m= -6/5
Verification:
LHS = 2m-3
=2(-6/5)-3
=-12/5-3
=-27/5
and, RHS
= 3/10( 5m -12)
=3/10(5 x (-6/5) -12)
=3/10 (-6 - 12)
=3/10 x -18
= -54/10
= -27/5
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8y=5x-15;y=10 which is the answer
Since we have that y = 10, then:
[tex]8\cdot(10)=5x-15[/tex][tex]80=5x-15\Rightarrow80+15=5x-15+15\Rightarrow95=5x+0[/tex]Then
[tex]5x=95\Rightarrow\frac{5}{5}x=\frac{95}{5}\Rightarrow x=19[/tex]In the first part, we need to sum 15 to both sides of the equation.
In the second part, we divide both sides by 5.
Then, x = 19.
A building floor plan is shaped like a trapezoid, with two right angle corners. If the third corner is a 40° angle, what is the measure of the fourth angle?
Recall that the interior angles of a regular quadrilateral add up to 360 degrees, and a right angle has a measure of 90 degrees.
Let x° be the measure of the fourth angle, then we can set the following equation:
[tex]40^{\circ}+90^{\circ}+90^{\circ}+x^{\circ}=360^{\circ}.[/tex]Adding like terms we get:
[tex]220^{\circ}+x^{\circ}=360^{\circ}.[/tex]Subtracting 220 degrees from the above result we get:
[tex]\begin{gathered} 220^{\circ}+x^{\circ}-220^{\circ}=360^{\circ}-220^{\circ}, \\ x^\circ=140^\circ. \end{gathered}[/tex]Answer:
[tex]140^{\circ}.[/tex]2 × 4/3, but the answer as a fraction
The given expression is : 2 × 4/3
[tex]\begin{gathered} 2\times\frac{4}{3}=\frac{2\times4}{3} \\ 2\times\frac{4}{3}=\frac{8}{3} \end{gathered}[/tex]Answer :
[tex]2\times\frac{4}{3}=\frac{8}{3}[/tex]
Dialate about the origin using a scale factor of 1/3
To determine the post image coordinates after a dilation centered about the origin, we will simply multiply each of the coordinates by the given scale factor of 1/3.
Let's start with Point A.
[tex](-12\times\frac{1}{3},24\times\frac{1}{3})\Rightarrow(-4,8)[/tex]The post image coordinate of A is at (-4, 8).
Moving on to Point B.
[tex](-30\times\frac{1}{3},0\times\frac{1}{3})\Rightarrow(-10,0)[/tex]The post image coordinate of B is at (-10, 0).
Lastly to Point C.
[tex](-36\times\frac{1}{3},36\times\frac{1}{3})\Rightarrow(-12,12)[/tex]The post image coordinate of C is at (-12, 12).
The decimal equivalent Of 5/8 is a terminating decimal true or false
Answer:
This statement is True.
Step-by-step explanation:
5/8 is equal to 0.625 in decimal form. Use our fraction to decimal calculator to convert any fraction to a decimal and to know if it is a terminating or a recurring (repeating) decimal. It is, a so called, 'terminating' decimal. To convert this fraction to a decimal, just divide the numerator (5) by the denominator (8).
Consider the two expressions (6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)/(2x + 3 - 7x - 11) and 4x^2 - 7 + 1/(2x + 3 - 7x - 11)
a) Show that the two expressions represent equal numbers when x = 10
b) Explain why these two expressions do not represent equal numbers when x = -3/2
c) Show that these two expressions represent equal numbers for all x other than -3/2.
Step-by-step explanation:
a)
(6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)(2x + 3 - 7x - 11)
[tex] \sf \frac{(6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)}{(2x + 3 - 7x - 11)}[/tex]
[tex] \sf = \frac{(6(10)^3 + 9(10)^2 + 4(10) + 7 - 17(10)^2 - 8(10) + 8)}{(2(10) + 3 - 7(10) - 11)}[/tex]
[tex] = \frac{ - 5175}{58}[/tex]
4x^2 - 7 + 1/(2x + 3 - 7x - 11)
[tex] \sf{ 4x^2 - 7 + \frac{1}{(2x + 3 - 7x - 11)}}[/tex]
[tex] \sf{ 4(10)^2 - 7 + \frac{1}{(2(10) + 3 - 7(10) - 11)}}[/tex]
[tex] = \sf \frac{22793}{58}[/tex]
I can’t seem to understand this. I need 2 solutions and the work. If you could explain the work so I can do it in the future that would be great!!
Given:
Ethan is 23 years older than Evan
So, let Ethan is (x) years old
And Evan is (y) years old
So, the difference between them is 23 years old
so, x - y = 23
And the sum of Ethan and Evan's age is 43
so, x + y = 43
So, we have the following system of equations:
[tex]\begin{gathered} x-y=23 \\ x+y=43 \end{gathered}[/tex]add the equations to eliminate (y):
[tex]\begin{gathered} (x-y)+(x+y)=23+43 \\ 2x=66 \\ x=\frac{66}{2}=33 \end{gathered}[/tex]Now, substitute with (x) into the second equation to find (y):
[tex]\begin{gathered} 33+y=43 \\ y=43-33=10 \end{gathered}[/tex]So, the answer will be:
Ethan's age = x = 33
Evan's age = y = 10
evaluate the expression, given the functions f and h: f(x)=3x-1, h(x)=-2x^2+3x-9. f(7/3)-h(-2)
The value of the function f(7/3)-h(-2) is 30
What are functions?Functions are simply defined as theorems, laws, equation or rules that holds true for the relationship between two variables in a given expression.
The variables are known as;
Independent variableDependent variableGiven the functions as;
f(x)=3x-1 h(x)=-2x^2+3x-9To determine f(73), substitute the value as x in the function, we have;
f(7/3) = 3(7/3) - 1
expand the bracket
f(7/3) = 7 -1
f(7/3) = 6
For h(-2), substitute the value as x in the function, we have;
h(-2) = -2(-2)² + 3(-2) - 9
expand the bracket
h(-2) = -8 -6 - 9
Subtract the values
h(-2) = -23
Now, f(7/3)-h(-2) = 7 --23
f(7/3)-h(-2) = 30
Hence, the value is 30
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I need help with finding the area and the perimeter for a trapezoid thank you
From the figure given in the question, we are asked to find the area and perimeter.
(a) Area:
Since the figure is a trapezoid, the formula for the area of a trapezoid is:
Area = (a + b)h
2
Where:
a = 2
b = 5
h = 4
Area = (2 + 5)4
2
Area = 7/2 * 4
Area = 3.5 * 4
Area = 14 cm²
(b) Perimeter:
To get the perimeter, we will have to add all the side length.
But we will have to find the missin side length first.
Using pythagoras:
a² + b² = c²
Where:
a = 4
b = 3
c² = 4² + 3²
c² = 16 + 9
c² = 25
Taking square of both sides:
c = √25
c = 5
Since we have gotten the missing side length as 5cm, we can now add all the given side length to get the perimeter.
Perimeter = 4 + 2 + 5 + 5
Perimeter = 16 cm
Write the coordinates of the vertex after a dilation with a scale factor of 5, centered at the origin.T(-1, 5)T' (___,___)Write your answer as a pair of numbers separated by a comma and space, like this: 4, -9
Multiply the coordinates by the scale factor (5)
T'= (-1 x 5 , 5x5) = (-5,25)
T' = (-5,25)
The pentagons ABCDE and PQRST are similar.
Find the length x of TP.
Yo bro, I'm just doing this for the rewards for my homework. please don't read this or take it serious
Fill in the blanks so the left side is a perfect square trinomial. That is, complete the square.x² - 6x +__ = (x -__)^2
Given:
[tex]x^2-6x+__{-----}=(x\text{ -}\_\_\_\_\rparen^2[/tex]Find: fill in the blanks.
Explanation:
[tex]x^2-6x+9=(x-3)^2[/tex]Isabel will rent a car for a day. The rental company offers two pricing options: Option A and Option B. For each pricing option, cost (in dollars) depends on miles driven, as shown below.
(a) Option B, 30
At 180 miles, Option B costs $50, but Option A costs $80.(b) 60, Option A
The cost is the same when the graphs intersect.Before 60 miles, the graph for Option A is lower than the graph of Option B, meaning Option A will cost less money.Can you please help me out with a question
Note:
For similar shapes, the ratio of their areas is equal to the square of the ratio of sides.
That is:
[tex]\text{ ratio of areas of similar shapes = (ratio of sides )}^2[/tex][tex]\begin{gathered} \frac{846}{376}\text{ = (}\frac{X}{24})^2 \\ \frac{846}{376}\text{ = }\frac{x^2}{576} \\ \text{cross multiply} \\ 376X^2=\text{ 576 x 846} \\ 376X^2=487296 \\ X^2=\frac{487296}{376} \\ X^2=1296 \\ X=\sqrt[]{1296}\text{ = 36} \end{gathered}[/tex]The value of X is 36
The outside temperature decreases 7*f in 3 1/2 hours.
How would you represent the temperature as unit
A temperature drop of 7 degrees Fahrenheit in 3.5 hours is represented by 2 f/hour.
What is the definition of Fahrenheit?Fahrenheit temperature scale, based on the freezing point of water at 32° and the boiling point of water at 212°, with the interval between the two divided into 180 equal parts.
Given: The outside temperature drops by 7 degrees Fahrenheit in 3 1/2 hours.
We need to represent the temperature as a unit.
To do so, we must represent the temperature change per hour.
7f/3.5 hours = 2 f/hour
Therefore, the temperature that decreases by 7 degrees Fahrenheit in 3.5 hours can be represented as 2 f/hour.
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Joe is taking an amortized loan for 85,000 to open a small business, and it's deciding between the offers if two lenders. He wants to know which one would be the better deal over the life of the small business loan, and by how much. a) His credit union had offered him a 9- year small business loan at an annual interest rate of 14.4% find the monthly payment $_b) a bank has offered him a 10-year small business loan at an annual interest rate of 12.8% find the monthly payment c) suppose Joe pays the monthly payment each month for the full term. which lender small business loan would have the lowest total amount to pay off, and how much? Credit UnionThe total amount paid would be $ less than the bank. BankThe total amount paid would be $ less than the credit union.
An agent lists a sellers house for 6% commission. The final agreed sales price is $205,000. How much commission did the seller pay?
Out of $205000, the total commission earned by the agent will be $12300.
What is Commission?
A commission is a fee paid to a salesperson in exchange for services in facilitating or completing a sale transaction. Mathematically -
Commission [C] = Sales revenue [R] x commission rate [rc]
Given is an agent who lists a sellers house for 6% commission. The final agreed sales price is $205,000.
The total sales price = [P] = $205000
The commission on house = [C] = 6%
Now, the money agent gets as a commission will be = [M] -
[M] = 6% of 205000
[M] = (6/100) x 205000
[M] = 6 x 2050
[M] = 12300
Therefore, out of $205000, the total commission of the agent will be $12300.
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I need help solving for x and y
[tex]\cos \theta=\frac{x}{16} \implies x=16 \cos \theta \\ \\ \sin \theta=\frac{y}{16} \implies y=16 \sin \theta[/tex]
A bicycle has a listed price of 803.98 before tax. If the sales tax is 9.5%, fins the total cost of the bicycle with sales tax included. Round to the nearest cent its necessary.
The total cost with taxes included is given by
[tex]803.98+803.98\times\frac{9.5}{100}[/tex]which is equal to
[tex]803.98(1+\frac{9.5}{100})[/tex]which gives
[tex]\begin{gathered} 803.98(1+0.095) \\ 803.98(1.095) \end{gathered}[/tex]then, we have $880.3581. By rounding to the nearest cent, the answer is $880.36
The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a
followed by a
A 90 degree counterclockwise rotation about point A, a reflection across the y-axis, and a translation 20 units down may be used on quadrilateral ABCD to demonstrate that it is congruent to quadrilateral GHIJ.
A quadrilateral in geometry is a four-sided polygon with four edges and four corners. A polygon with four sides, four angles, and four vertices is called a quadrilateral. The Latin words quadri, which means four, and latus, which means side, were combined to create the English term quadrilateral. A four-sided polygon with four angles is known as a quadrilateral. Parallelogram, rhombus, kite, rectangle, trapezoid, square, and isosceles trapezoid are the seven different forms of quadrilaterals.
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If $16,000 is invested at 8% for 12 years, find the future value if the interest is compounded
semiannually.
Please round the answer to the nearest cent.
The future value is $
t - the number of years the money is invested for
P = $16,000
m =2
t = 12 yr
r = 8% or .08
FV = 16,000* ( 1+ .08/2) 2*12 = 16000 (1.04) 24 = 16000* (2.5633041) = $41012.8656
FV - the future value of the investment = $41012.87 is answer
Question 4 of 10
Solve 2x + 6 8 or 2x + 8 > 12.
A. x2 or x > 6
B. x
1 or x > 6
C.
2 and x > 2
1 ora > 2
OD. x
SU
The value is x≤1 or x>2
What is inequalities?Equations don't always need to have a "equal to" symbol on both sides to be balanced. Sometimes it can be about a "not equal to" relationship, meaning that something is superior to or inferior to another. In mathematics, an inequality is a relationship between two numbers or other mathematical expressions that results in an unequal comparison. Inequalities are the name given to certain algebraic mathematical expressions.
2x +6≤8 or 2x + 8 > 12
2x +6≤8
2x ≤2
x≤1
2x +8>12
2x>4
x>2
The value is x≤1 or x>2
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