The three consecutive odd integers are [tex]-11, -9,[/tex] and [tex]-7[/tex].
To find three consecutive odd integers whose sum is -27, let's define the three integers as follows:
Let the first consecutive odd integer be [tex]x[/tex].The second consecutive odd integer will be [tex]x + 2[/tex].The third consecutive odd integer will be [tex]x + 4[/tex].According to the problem, the sum of these integers is -27. We can write this as an equation:
[tex]x + (x + 2) + (x + 4) = -27[/tex]
Now, let's simplify and solve the equation step-by-step:
Combine like terms on the left-hand side of the equation:
[tex]x + x + 2 + x + 4 = -27[/tex]
[tex]3x + 6 = -27[/tex]
Subtract 6 from both sides to isolate the term with [tex]x[/tex]:
[tex]3x + 6 - 6 = -27 - 6[/tex]
[tex]3x = -33[/tex]
Divide both sides by 3 to solve for [tex]x[/tex]:
[tex]x = \frac{-33}{3}[/tex]
[tex]x = -11[/tex]
So, the first consecutive odd integer is [tex]-11[/tex].
Find the second consecutive odd integer:
[tex]-11 + 2 = -9[/tex]
Find the third consecutive odd integer:
[tex]-11 + 4 = -7[/tex]
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.
What is the simplified form of (x – 2)(2x +3)? Use the Distributive Property.
2x2 – x – 6
2x2 – 6
2x2 – 7x – 6
2x2 + x – 6
2. What is the simplified form of (3x + 2)(4x – 3)? Use a table.
12x2 + 18x + 6
12x2 + x – 6
12x2 + 18x – 6
12x2 – x – 6
3. What is the simplified form of (4p – 2)(p – 4)?
4p2 + 6p – 16
4p2 – 18p + 8
4p2 – 14p – 6
4p2 – 6p + 16
4. The radius of a cylinder is 3x – 2 cm. The height of the cylinder is x + 3 cm. What is the surface area of the cylinder? Use the formula A = 2r2 + 2rh.
Answer:
Step-by-step explanation:
A. The given equation is:
[tex](x-2)(2x+3)[/tex]
simplifying this,
[tex]2x^{2}-4x+3x-6[/tex]
[tex]2x^{2}-x-6[/tex]
Option A is correct
B. The given equation is:
[tex](3x+2)(4x-3)[/tex]
simplifying this,
[tex]12x^{2}+8x-9x-6[/tex]
[tex]12x^{2}-x-6[/tex]
Option D is correct.
C. The given equation is:
[tex](4p-2)(p-4)[/tex]
simplifying this,
[tex]4p^2-2p-16p+8[/tex]
[tex]4p^2-18p+8[/tex]
Option B is correct.
D. The radius of a cylinder is 3x – 2 cm. The height of the cylinder is x + 3 cm. Then,
Surface area of cylinder=[tex]2r^{2}+2rh[/tex]
=[tex]2r(r+h)[/tex]
=[tex]2(3x-2)(3x-2+x+3)[/tex]
=[tex]2(3x-2)(4x+1)[/tex]
=[tex]2(12x^{2}-8x+3x-2)[/tex]
=[tex]24x^{2}-10x-4[/tex]
Therefore, Surface area of cylinder=[tex]24x^{2}-10x-4[/tex] sq units
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 .
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)?)
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 are the two types of exponential functions?
The two types of exponential functions are:
Exponential Growth: exponential growth function is [tex]y = a^x[/tex], where "a" is the base and "x" is the exponent.
Exponential Decay: exponential decay function is [tex]y = a^{(-x)[/tex], where "a" is the base and "x" is the exponent.
The two types of exponential functions are:
Exponential Growth: In an exponential growth function, the base (often denoted by "a") is greater than 1.
As the input (x) increases, the output (y) grows at an increasing rate, creating a steep upward curve on the graph.
The general form of an exponential growth function is [tex]y = a^x[/tex], where "a" is the base and "x" is the exponent.
Exponential Decay: In an exponential decay function, the base (often denoted by "a") is between 0 and 1 (exclusive).
As the input (x) increases, the output (y) decreases at an increasing rate, creating a steep downward curve on the graph.
The general form of an exponential decay function is [tex]y = a^{(-x)[/tex], where "a" is the base and "x" is the exponent.
Both types of exponential functions show rapid growth or decay patterns, and their graphs exhibit a characteristic curve that is continuous and smooth.
The difference lies in the behavior of the output (y) concerning the input (x).
In exponential growth, the output increases exponentially with increasing input, while in exponential decay, the output decreases exponentially as the input increases.
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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
You want to put $2,500 in a simple interest account. It has a 4% annual interest rate. How long will it take you to earn $200 in interest? 2nd question of the day. See if you can answer it.
If A is an obtuse angle in a triangle and sin A is 5/13, calculate the exact value of sin 2A
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.
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What are prime numbers of 50?
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
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:
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.
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.
what does it mean for an equation to be balanced and why must you keep an equation in balance?
If $2500 is invested at an interest rate of 2.5% per year, compouded daily, find the value of the inevestment after 2 years
What is 324 divided by 6??
The price of a gallon of milk is 3.75. circle the price of milk rounded to the nearest dollar
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
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:
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
Where is the dependent variable plotted on a line graph?
What is the lateral area of a pyramid with base edges 5ft and surface area 55ft^2? ...?
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'.
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.
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
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:
What is one half plus one fifth?