Answer:
4.5 cups of lettuce for 1 cup of tomatoes
Step-by-step explanation:
If A is an obtuse angle in a triangle and sin A is 5/13, calculate the exact value of sin 2A
One year there was a total of 73 commercial and noncommercial orbital launches worldwide. In addition, the number of noncommercial orbital launches was one more than three times the number of commercial orbital launches. Determine the number of commercial and noncommercial orbital launches.
Final answer:
The number of commercial orbital launches is 18, and the number of noncommercial orbital launches is 55.
Explanation:
Let's assume that the number of commercial orbital launches is represented by x. According to the problem statement, the number of noncommercial orbital launches is more than three times the number of commercial orbital launches. So, the number of noncommercial orbital launches would be 3x + 1.
Given that the total number of commercial and noncommercial orbital launches is 73, we can set up the equation:
x + (3x + 1) = 73
Combining like terms, we get:
4x + 1 = 73
Subtracting 1 from both sides, we get:
4x = 72
Dividing both sides by 4, we get:
x = 18
Therefore, there were 18 commercial orbital launches and 55 noncommercial orbital launches.
The number of commercial orbital launches is 24, and the number of noncommercial orbital launches is 49.
Explanation:Let's assume that the number of commercial orbital launches is represented by 'x'. According to the question, the number of noncommercial orbital launches is one more than three times the number of commercial orbital launches. So, the number of noncommercial orbital launches can be represented by '3x + 1'.
Given that the total number of commercial and noncommercial orbital launches is 73, we can set up the equation 'x + (3x + 1) = 73' to represent the total launches. Solving this equation will give us the values of 'x' and '3x + 1', which represent the number of commercial and noncommercial orbital launches, respectively.
By solving the equation, we find that 'x = 24' and '3x + 1 = 73 - 24 = 49'.
What is the decimal expansion of the following fraction?
1/4
1.4
0.14
___
0.25
0.25
Solve and graph the absolute value inequality: |2x + 4| > 8. number line with open circles on negative 6 and 2, shading in between. number line with closed circles on negative 6 and 2, shading going in the opposite directions. number line with open circles on negative 6 and 2, shading going in the opposite directions. number line with open circles on negative 2 and 2, shading going in the opposite directions.
Final answer:
The inequality |2x + 4| > 8 is resolved by considering the inside expression being greater than 8 and less than -8, which leads to x > 2 and x < -6. The proper representation on a number line is with open circles on -6 and 2, shading away from these points, indicating the range of solutions.
Explanation:
To solve the absolute value inequality |2x + 4| > 8, we must consider the two scenarios that could make the inequality true: when (2x + 4) is greater than 8 and when -(2x + 4) is less than -8. Absolute values denote the distance from zero, so they are never negative. Since the inequality is strict (indicated by '>'), we will use open circles in the graph.
First, let's consider when the expression inside the absolute value is positive:
2x + 4 > 8
2x > 4
x > 2
This scenario corresponds to all x-values greater than 2.
Now for the negative scenario:
-(2x + 4) > 8
-2x - 4 > 8
-2x > 12
x < -6
This scenario corresponds to all x-values less than -6.
The correct graph of the solution set on a number line would have open circles on -6 and 2, with shading going in opposite directions away from these points, indicating all the numbers greater than 2 and all the numbers less than -6 satisfy the original inequality.
Based on this, the third choice is correct: A number line with open circles on negative 6 and 2, shading going in the opposite directions.
For any given rational function, differentiate between a function’s vertical and horizontal asymptotes. In two or more complete sentences, make a connection between the asymptotes and the function’s domain and range.
Consider the function
f(x) = [tex]\frac{x-3}{x-4}[/tex]
Domain of the function = All real numbers except , x≠4 .
[tex]y=\frac{x-3}{x-4} \\\\ xy - 4y = x-3 \\\\ x y -x= 4 y-3\\\\ x=\frac{4 y-3}{y-1}[/tex]
Range = All real numbers except , y≠1 .
Horizontal Asymptote= Since the degree of numerator and denominator of rational function is same , So Divide coefficient of x in numerator by divide coefficient of x in denominator.
So Horizontal Asymptote , is : y=1
To get vertical asymptote, put
Denominator =0
x-4=0
x=4 , is vertical asymptote.
Domain = All real numbers except vertical Asymptote
Range = All real numbers except Horizontal Asymptote
Final answer:
The vertical asymptotes of a rational function can be found by determining the roots of the polynomial in the denominator, while the horizontal asymptotes can be determined by analyzing the behavior of the function as x approaches infinity. The asymptotes are closely related to the function's domain and range.
Explanation:
Vertical asymptotes of a rational function can be determined by finding the roots of the polynomial in the denominator. Each root corresponds to a vertical asymptote. For example, if the polynomial has a factor of (x - 2), then there is a vertical asymptote at x = 2.
On the other hand, horizontal asymptotes of a rational function can be found by analyzing the behavior of the function as x approaches positive or negative infinity. If the leading terms of the numerator and denominator have the same degree, then the function will have a horizontal asymptote. For instance, if the leading terms are both x^2, then the horizontal asymptote will be y = 0.
The domain of the function is the set of all valid inputs, while the range is the set of possible outputs. The vertical asymptotes and the behavior of the function as x approaches infinity are closely related to the domain, while the horizontal asymptotes are related to the range.
The price of a gallon of milk is 3.75. circle the price of milk rounded to the nearest dollar
What are prime numbers of 50?
can u do this bro 100x7+8-678x56
Answer:
-37260
Step-by-step explanation:
did it in my head
Pleeease help!!
Write an equation in point-slope form of the line that passes through the given point and with the given slope m.
(-2,1);m=7
Which expression is equal to 5/(sqrt)11?
a) 5(sqrt)11/11
b) (sqrt)5/11
c) (sqrt)55/11
d) 25/11
please help, I'm confused.
Answer:
Option A is correct
the expression is equal to [tex]\frac{5}{ \sqrt{11}}[/tex] is [tex]\frac{5\sqrt{11}} {11}[/tex]
Explanation:
Given expression is, [tex]\frac{5}{ \sqrt{11}}[/tex]
Multiply and divide by the denominator by [tex]\sqrt{11}[/tex] in the given expression, we have,
[tex]\frac{5}{\sqrt{11}} \times \frac{\sqrt{11}} { \sqrt{11}}[/tex]
or
[tex]\frac{5 \cdot \sqrt{11}} {\sqrt{11} \cdot \sqrt{11}}[/tex]
use : [tex]\sqrt{a}\cdot\sqrt{a}=(\sqrt{a} )^2 = a[/tex]
then;
[tex]\frac{5\sqrt{11}} { (\sqrt{11})^2} =\frac{5\sqrt{11}} {11}[/tex]
Therefore, the expression is equal to [tex]\frac{5}{ \sqrt{11}}[/tex] is, [tex]\frac{5\sqrt{11}} {11}[/tex]
what does it mean for an equation to be balanced and why must you keep an equation in balance?
Find the greatest common factor of the monomials. 16x, 36x ...?
Final answer:
The greatest common factor of the monomials 16x and 36x is 4x, obtained by finding the common prime factors of 16 and 36 and including the variable x, which is present in both monomials.
Explanation:
To find the greatest common factor of the monomials 16x and 36x, we need to break each monomial into its prime factors and compare them.
Prime factors of 16 are 2 x 2 x 2 x 2.
Prime factors of 36 are 2 x 2 x 3 x 3.
Both 16 and 36 have two 2's in common.
Therefore, the GCF of 16 and 36 is 2 x 2 = 4. Since x is present in both monomials, x is also part of their GCF.
The greatest common factor of the monomials 16x and 36x is therefore 4x.
A circular garden has a radius of 12 feet. what is the approximate circumference of the garden?
a. 1808.6 ft
b. 452.2 ft
c. 75.4 ft
d. 37.7 ft
Answer:
37.7
Step-by-step explanation: K12
Mrs. Curtis wants to buy online tickets for a concert. Two options are given here.
Option 1: $53 for each ticket plus a shipping fee of $10
Option 2: $55 for each ticket and free shipping
What is a system of equations to represent the costs of the tickets?
Express your equations in the form of y=mx+by=mx+b where x is the number of tickets purchased and y is the total cost.
Help Please? Factor Completely: 2x2 − 32
Prime
2(x2 − 16)
2(x + 4)(x + 4)
2(x + 4)(x − 4) ...?
Answer:
Option 4th is correct
[tex]2 \cdot (x-4)(x+4)[/tex]
Step-by-step explanation:
Using difference of square:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
GCF is the largest number that divide the given polynomial or expression.
Given the expression:
[tex]2x^2-32[/tex]
We have to completely factor the expression.
GCF of [tex]2x^2[/tex] and 32 is, 2
then;
[tex]2 \cdot (x^2-16)[/tex]
Using difference of square
[tex]2 \cdot (x-4)(x+4)[/tex]
therefore, the completely factor of [tex]2x^2-32[/tex] is, [tex]2 \cdot (x-4)(x+4)[/tex]
Answer:
D. 2(x + 4)(x − 4)
Step-by-step explanation:
joe is a waiter at a local pizza parlor. he usually gets a tip from the tables he waits on. the bill for one table comes to $34
write a formula that will help joe determine how much of a tip he'll recieve from that table.
p= percent tip
t=tip left for the waiter
What is 324 divided by 6??
The linear function f(x) passes through the points (1,2) and (3,0).
A few values from the exponential function g(x) are shown in the table
What is the positive difference in the y-intercept of f(x) and g(x)?)
What is 788 divided by 14 in a long division model?
A steel plate has the form of a quarter of a circle with a radius of 49 cm. Two 2-cm holes are to be drilled in the plate. Let (X1,Y1) and (X2,Y2) be the coordinates of the centers of the holes. Find the coordinates for both holes.
The task is to determine the coordinates of two 2-cm holes in a quarter-circle steel plate, but there is insufficient information to provide a precise location without additional details or constraints.
Explanation:The question requires us to find the coordinates for the centers of two 2-cm holes to be drilled in a steel plate, which is shaped like a quarter of a circle with a radius of 49 cm. Assuming the plate is positioned with its corner at the origin (0,0), with the circular edge encompassed by the positive x-axis and positive y-axis, the holes should be placed in such a way that their centers within the quarter circle are equidistant from the axes and from the plate's circular edge.
However, the question does not provide sufficient information or constraints about the location of the holes within the quarter-circle plate. To determine the exact coordinates, we need more specifics, such as how far from the edges or any other centering constraints for the holes. Without this additional information, there are infinitely many possible coordinates for the holes that meet the given condition of being within the quarter-circle plate.
If the holes are to be evenly distributed and placed symmetrically, a possible choice could be to align the centers of the holes along the line y = x, which bisects the quarter-circle. Yet, without precise instructions, we cannot provide a definitive answer to the coordinates of the holes.
Learn more about Coordinates Determination here:https://brainly.com/question/20338587
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Goran is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges $93 and allows unlimited mileage. Company B has an initial fee of $65 and charges an additional $0.70 for every mile driven. For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m .
b-4/6=b/2. Solve for b.
2(b−4)=6(b) 2b - 8 = 6b 2b - 6b = 8 -4b = 8 Now you can solve.....
Your car gets 20 miles per gallon of gas. This is 4 more miles per gallon than your friend's car gets. How many miles per gallon does your friend's car get?
Answer:
Answer:
16 miles per gallon
Step-by-step explanation:
What is the lateral area of a pyramid with base edges 5ft and surface area 55ft^2? ...?
Write 0.000045 in scientific notation.
The options are:
A. 4.5 · 10-4
B. 4.5 · 10-6
C. 4.5 · 10-5
D. 4.5 · 105
If $2500 is invested at an interest rate of 2.5% per year, compouded daily, find the value of the inevestment after 2 years
Where is the dependent variable plotted on a line graph?
Which expression gives the distance between the points (2, 5) and (-4, 8)?
The expression for the distance between the points (2, 5) and (-4, 8) is the square root of 45 or 3√5, which is approximately 6.708.
Explanation:The expression that gives the distance between the points (2, 5) and (-4, 8) is found using the distance formula which is derived from the Pythagorean theorem. The formula is √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are coordinates of the two points.
To find the distance between (2, 5) and (-4, 8), substitute x1=2, y1=5, x2=-4, and y2=8 into the formula:
√((-4 - 2)² + (8 - 5)²) = √((-6)² + (3)²) = √(36 + 9) = √45
The distance is therefore the square root of 45, which can be simplified to 3√5 (approximately 6.708).
Final answer:
The distance between the points (2, 5) and (-4, 8) is calculated using the distance formula, resulting in 3√(5) units.
Explanation:
The distance between the points (2, 5) and (-4, 8) can be calculated using the distance formula, which is derived from the Pythagorean theorem. The distance formula is √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the given values, the distance d can be calculated as follows:
√((-4 - 2)² + (8 - 5)²) = √((-6)² + (3)²) = √(36 + 9) = √(45) = 3√(5)
Therefore, the distance between the points (2, 5) and (-4, 8) is 3√(5) units.
Given the trinomial 5x2 - 2x - 3, predict the type of solutions.
Two rational solutions
One rational solution
Two irrational solutions
Two complex solutions
Answer:
Two rational solutions. This is the right answer
Step-by-step explanation:
Solve the system using elimination 4x-7y=3
x-7y=-15
Answer: x=6 and y=3
Step-by-step explanation:
4x - 7y = 3 -------(1)
x - 7y = -15 ------(2)
equation(1) - equation (2)
3x = 18
Divide bothside by 3
x = 18/3
x= 6
also, multiply equation (2) by 4
4x - 28y = -60--------------(3)
subtract equation(3) from equation(1)
21y = 63
divide bothside by 21
y = 63/21
y = 3