Answer: The required solution in interval notation is [tex](0,\infty)U(-\infty,-5].[/tex]
Step-by-step explanation: We are given to find the solution to the following compound inequality in interval notation :
[tex]2(x+3)>6~or~2x+3\leq -7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the solution to (i), we must solve both the parts separately.
The inequality (i) can be solved as follows :
[tex]2(x+3)>6\\\\\Rightarrow x+3>\dfrac{6}{2}\\\\\Rightarrow x+3>3\\\\\Rightarrow x>3-3\\\\\Rightarrow x>0\\\\\Rightarrow x\epsilon (0,\infty)[/tex]
or
[tex]2x+3\leq-7\\\\\Rightarrow 2x\leq-7-3\\\\\Rightarrow 2x\leq -10\\\\\Rightarrow x\leq -\dfrac{10}{2}\\\\\Rightarrow x\leq-5\\\\\Rightarrow x\epsilon(-\infty,-5].[/tex]
Thus, the required solution in interval notation is [tex](0,\infty)U(-\infty,-5].[/tex]
A mountain climber ascends 800 feet per hour from his original position. After 6 hours, his final position is 11,600 feet above sea level. Find the climber's position.
Look at the diagram. Which angle is complementary to < EOD
A. < EOD
B. < EOC
C. < AOC
D. < AOB
Answer:
D. [tex]\angle AOB[/tex]
Step-by-step explanation:
Since we know that complementary angles add up-to 90 degrees.
We can see from our given diagram that angle EOA and angle EOC is a linear pair of angles. The measure of angle EOA is 90 degrees, so EOC will be 90 degrees as well (Linear pair of angles must add up to 180 degrees).
We can also see that [tex]\angle EOC=\angle EOD+\angle COD[/tex].
Upon substituting value of angle EOC we will get,
[tex]90^o=\angle EOD+\angle COD[/tex]
We can see from our given diagram that angle COD and angle AOB are vertical angles.
[tex]\angle COD=\angle AOB[/tex]
Since vertical angles are equal, so by substitution property of equality we will get,
[tex]90^o=\angle EOD+\angle AOB[/tex]
Therefore, [tex]\angle AOB[/tex] is complementary to [tex]\angle EOD[/tex] and option D is the correct choice.
Find the common ratio for the following sequence
27,9,3,1
Answer:
The common ratio is [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Given sequence,
27, 9, 3, 1
Since,
[tex]\frac{9}{27}=\frac{3}{9}=\frac{1}{3}[/tex]
Hence, in the given sequence the ratio of a term to its previous term is [tex]\frac{1}{3}[/tex]
Therefore, we can say that,
The common ratio of the given sequence is [tex]\frac{1}{3}[/tex]
What what are the rules for addition and subtraction with numbers in scientific notation?
A box of crackers weighs 11 1/4 ounces. kaden estimates that one serving is 3/4 ounces. How many servings are in the box?
ivied 11 1/4 by 3/4
11 1/4 = 45/4
45/4 / 3/4 =
45/4 *4/3 = 180/12 = 15
there are 15 servings
Answer:
there are 11 servings in all
An animal shelter spends $2.35 per day for each cat and $5.50 per day to care for each dog. Pat noticed that the shelter spent $89.50 caring for cats and dogs on Wednesday. (A) write an equation to represent the possible numbers of cats and dogs that could have been at the shelter on Wednesday. (b) pat said that there might have been 8 cats and 14 dogs at the shelter on Wednesday. Are pats numbers possible? Use your equation to verify your answer
An angle is exactly half its complement. what is the angle
let x = angle
x = 1/2(90-x)
2x = 90-x
3x=90
x = 90/3 = 30
x = 30 degrees
What you s 50 percent of 2.98
Answer:
1.49
Step-by-step explanation:
50% of 2.98 is 1.49
How do i solve this for x
Jacob is ordering custom T-shirts for his soccer team. Long-sleeved shirts cost $15 each and short-sleeved shirts cost $10 each. Jacob can spend at most $250 and he wants to order at least 20 shirts.
Let x represent the number of long-sleeved shirts. Let y represent the number of short-sleeved shirts.
Which inequalities are among the constraints for this situation?
Select each correct answer.
⋅ 15x + 10y ≥ 20
⋅ x + y ≤ 250
⋅ x + y ≥ 20
⋅ 15x + 10y ≥ 250
⋅ 15x + 10y ≤ 250
⋅ x + y ≤ 20
x + y ≥ 20 ( total number of shirts at least 20)
15x + 10y ≤ 250 ( total amount spent no more than $250)
These are the answers.
3. x + y ≥ 20
5. 15x + 10y ≤ 250
Hope this helps and have a wonderful day!
During summer vacation, you charge people $8 per hour for swimming lessons and a $20 registration fee. If you make $52 one day, how many hours did you spend teaching lessons?
Sari has a bag containing 6 half dollars. What is the mass of half dollars in Sari's bag when half dollars weighs 11.34 grams?
Find the equation of the line passing through the points (-3 5) and parallel to the y axis
A fabric store sells two types of ribbon. One customer buys 3 rolls of the lace ribbon and 2 rolls of the satin ribbon and has a total of 120 yards of ribbon. Another customer buys 2 rolls of the lace ribbon and 4 rolls of the satin ribbon and has a total of 160 yards of ribbon. How many yards are on one roll of lace ribbon and one roll of satin ribbon?
Answer:
20 and 30. that's your answer.
Step-by-step explanation:
Julie started solving the equation 3x=4+2(3−x). which is a correct next step?
Answer:
Distribute 2 inside the parenthesis
Step-by-step explanation:
Julie started solving the equation
3x=4+2(3−x)
To simplify any expression we use order of opeation PEMDAS
Always start simplifying the parenthesis
To remove parenthesis we apply distributive property
Distribute 2 inside th4e parenthesis
3x=4+2(3−x)
3x=4+6-2x
So next step is distributing 2 inside the parenthesis
3x=4+6-2x
Which number(s) below belong to the solution set of the inequality?
Check all that apply. x/8<10
A.80
B.96
C.64
D.40
E.32
F.88
Divide x 4 + 7 by x - 3. 3x 3 + 3x 2 + 9x - 27 R88 3x 3 + 3x 2 + 9x + 27 R88 x 3 + 3x 2 + 9x + 27 R88
x + y = 0 x - y = 8 What is the solution of the system shown?
A; (-8, 12)
B; (8, -12)
C; (8, 12)
the two solutions of 2x squared +1 =5x are j and k. What is the value of (j-1)(1-k)
Final answer:
The two solutions of the quadratic equation 2x squared + 1 = 5x are j = 1 and k = 1/2. The value of (j-1)(1-k) with these solutions is 0.
Explanation:
To solve the equation 2x squared + 1 = 5x, we first bring all terms to one side to get a quadratic equation:
2x2 - 5x + 1 = 0
Using the quadratic formula, x = [-b ± √(b2 - 4ac)]/(2a), where a = 2, b = -5, and c = 1, we find that the two solutions (j and k) of the equation are j = 1 and k = 1/2.
The value of (j-1)(1-k) with these values is:
(j - 1)(1 - k) = (1 - 1)(1 - 1/2) = (0)(1/2) = 0
Therefore, the value of (j-1)(1-k) is 0.
Select all of the answers that apply. What type of information do scientist use to determine the approximate age of the earth? water layers of rock fossils atmospheric pressure
Answer:
Layers of rock
Fossils
Step-by-step explanation:
Layers of rock and fossils are types of information the scientists use to determine the approximate age of the earth.
Fossils found in rocks and the layering in rock formations play a vital role for the scientists to determine the approximate age of the earth.
One side of a triangle is 4 inches longer than the side that is the base of the triangle. the third side is 6 inches longer than the base. of the perimeter is 34 inches, find the length of each side.
Final answer:
The base of the triangle is 8 inches, one side is 12 inches (base + 4), and the other side is 14 inches (base + 6). Hence, the side lengths of the triangle are 8 inches, 12 inches, and 14 inches, with a total perimeter of 34 inches.
Explanation:
The question describes a triangle with sides of varying lengths relative to what is defined as the base of the triangle. To find the length of each side, we'll use algebra and the fact that the perimeter of the triangle is given as 34 inches.
Let's denote the base as b. According to the problem, one side is 4 inches longer than the base, which would be b + 4 inches. The third side is 6 inches longer than the base, which would be b + 6 inches. The perimeter of a triangle is the sum of all its sides, so we have:
b + (b + 4) + (b + 6) = 34
Combining like terms, we get:
3b + 10 = 34
Subtracting 10 from both sides gives us:
3b = 24
Dividing by 3 gives us the length of the base:
b = 8 inches
Now, we can find the lengths of the other two sides:
b + 4 inches is 12 inches and b + 6 inches is 14 inches.
So, the lengths of the sides of the triangle are 8 inches, 12 inches, and 14 inches.
Attempting to use the regression equation to make predictions beyond the range of the data is called _______.
Harriet earns the same amount of money each day. Her gross pay at the end of 7 work days is 35h + 56 dollars. Which expression represents her gross pay each day?
Answer:
Daily Payment = 5h+8
Step-by-step explanation:
Here we are given that in seven days the amount Harriet earned is given as
35h+56
It is also given that the amount earned each day is same.
We have to determine the amount earned each day. Total number of days is 7 . Hence in order to find the daily earning we divide the total earning by 7
Daily earning =
[tex]E=\frac{35h+56}{7}\\E=\frac{7(5h+8)}{7}\\E=5h+8[/tex]
Hence answer is 5h+8
the difference of two numbers is 40. Their sum is 66. Find the numbers.
A soccer player who is 27 feet from a goal attempted to kick the ball in into the goal. the flight of the ball is modeled by a parabola. the ball reached a maximum height of 10 feet when it was 15 feet from the soccer player. the goal has a height of 8 feet. will the soccer ball land in the goal?
Answer:
The ball will land inside the goal.
Step-by-step explanation:
Given : The flight of the ball is modeled by a parabola.
To find : Will the soccer ball land in the goal?
Solution :
Let the equation of the parabola be,
[tex]y=a(x-h)^2+k[/tex]
Where, (h,k) are the vertex of the parabola,
According to question,
A soccer player who is 27 feet from a goal.
Let A be the point where player stand i.e, (27,0)
The height of the goal is 8 feet.
Let B be the point of height of goal i.e, (0,8)
The ball reached a maximum height of 10 feet when it was 15 feet from the soccer player.
The distance from goal to the distance 15 feet away from the player is
27-15=12 feet
Let C be the point with maximum height i.e, (12,10)
C is the vertex of the parabola and A is the point on the parabola.
Then, The equation of parabola is
[tex]y=a(x-12)^2+10[/tex]
Point A satisfy the equation,
[tex]0=a(27-12)^2+10[/tex]
[tex]0=a(15)^2+10[/tex]
[tex]a=-\frac{10}{225}[/tex]
Substitute back in equation,
[tex]y=-\frac{10}{225}(x-12)^2+10[/tex]
Now, we find the y-intercept of the equation i.e, x=0,
[tex]y=-\frac{10}{225}(0-12)^2+10[/tex]
[tex]y=-\frac{10}{225}(144)+10[/tex]
[tex]y=3.6[/tex]
If the y-intercept is greater than 8 then the ball will land outside the goal.
If the y-intercept is less than 8 then the ball will land inside the goal.
As 3.6<8
Therefore, The ball will land inside the goal.
Refer the attached figure below.
Final answer:
The soccer ball will not land in the goal due to its maximum height being above the height of the goal.
Explanation:
To determine if the soccer ball will land in the goal, we need to analyze its flight path. From the given information, we know that the ball reached a maximum height of 10 feet when it was 15 feet from the soccer player. This indicates that the ball's flight path is modeled by a downward-opening parabola.
Since the soccer player is 27 feet from the goal, we can consider the ball's horizontal distance from the player to the goal as the x-coordinate, and its height above the ground as the y-coordinate.
Based on the given information, the soccer ball will not land in the goal. The ball's maximum height is 10 feet, but the goal has a height of 8 feet. This means that at any point along its flight path, the ball's height will be above the height of the goal.
99 points!!!
Factor each expression completely.
1. x^2-5x-24
2. 13x^2-52
3. Find the equation of a line through (-6, 3) and parallel to 3x-9y=14
4. Solve (5x+4)(3x-7)=0; {rational numbers}
[tex] \sf \: {x}^{2} - 5x - 24 \\ \sf \: {x}^{2} + 3x - 8x - 24 \\ \sf \: x \times (x + 3) - 8(x + 3) \\ \sf \: (x - 8) \times (x + 3)[/tex]
➪Therefore the factors are: (x-8) & (x+3)
[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]
#2[tex] \tt \: {13x}^{2} - 52 \\ \tt13( {x}^{2} - 4) \\ \tt13(x - 2) \times (x + 2)[/tex]
➪ Therefore the factors are: 13(x-2) & (x+2)
[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]
#3To find this we will use the standard form of equation i.e. ax+by+c=0We will substitute the given values of x and y and solve the equation for cx = -6y = 3Substitute the values into 3x-9y=14
[tex] \bf 3( - 6) - 9(3) = c[/tex]
[tex] \bf \: - 3 \times 6 - 9 \times 3 = c[/tex]
[tex] \bf \: 3( - 6 - 9) = c[/tex]
[tex] \bf \: 3( - 15) = c[/tex]
[tex] \bf \: - 45 = c[/tex]
[tex] \boxed{ \bf \: c = - 45}[/tex]
➪ So, the equation parallel to 3x-9y=14 is: 3x-9y=-45
[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]
[tex] \rm \: (5x + 4)(3x - 7) = 0[/tex]
[tex] \rm \: 5x + 4 = 0 \\ \rm \: 3x - 7 = 0[/tex]
[tex] \rm \: 5x = - 4 \\ \rm 3x = 7[/tex]
[tex] \rm \: x_{1} = - \frac{4}{5} , x_{2} = \frac{7}{3} [/tex]
➪ The values of x1 and x2 are: -4/5 & 7/3
Solve the quadratic equation by completing the square. x^2+6x-6=0 First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. If there is more than one solution, separate them with commas.
The measure of ∠BQS is 78°.
What is m∠NQS?
Enter your answer in the box.
m∠NQS = ?°
The required measure of angle ∠NQS = 30°.
Given that,
The measure of ∠QBS is 78°. What is m∠NQS is to be determined?
The angle can be defined as the one line inclined over another line.
In mathematics, it deals with numbers of operations according to the statements.
Here,
∠NQS + ∠BQN = ∠BQS
∠NQS + 48 = 78
∠NQS = 78 - 48
∠NQS = 30
Thus, the required a measure of angle ∠NQS = 30°.
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Pleaeseee help on this probability question
there are 4 eggs total 3 plain and 1 gold
so you have a 1/4 probability of picking the gold egg
The real numbers between 1 and 4 , inclusive
The real numbers between 1 and 4, inclusive, are all the numbers that lie on the interval [1, 4]. In interval notation, this can be represented as [1, 4].
In set-builder notation, the set of real numbers between 1 and 4, inclusive, can be written as:
{x | 1 ≤ x ≤ 4}
This set includes all real numbers greater than or equal to 1 and less than or equal to 4. It includes the numbers 1 and 4 as well. Some examples of numbers in this set are 1, 2, 3, 4, 1.5, 2.718 (approximation of Euler's number), etc.
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