To solve the inequality |x| + 3 > 8, we can start by isolating the absolute value term.
Subtracting 3 from both sides, we get:
|x| > 5
This inequality means that the distance of x from 0 on the number line is greater than 5 units. So, x can be either less than -5 or greater than 5.
Therefore, the solution to the inequality |x| + 3 > 8 is:
x < -5 or x > 5
We can represent this solution on a number line by placing open circles at -5 and 5, and shading the regions to the left of -5 and to the right of 5.
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A line with a slope of – 6/7 passes through the points (v, – 9) and ( – 2, – 3). What is the value of v?
V has a value of -20.
What exactly is slope?The slope of a line determines its steepness. Slope is defined in mathematics as "rise over run" (change in y divided by change in x). A linear equation is one in which each term has a maximum of one degree. Linear equations with x and y variables can be represented as y = mx + c.
We know that the slope of the line passing through the two given points is equal to -6/7. Therefore, we can use the slope formula to find the value of v.
The slope formula is given by:
slope = (y² - y¹) / (x² - x¹)
where (x¹, y¹) and (x², y²) are the coordinates of the two given points.
Plugging in the values, we get:
-6/7 = (-3 - (-9)) / (-2 - v)
Simplifying this equation, we get:
-6/7 = 6 / (v + 2)
Multiplying both sides by (v + 2), we get:
-6(v + 2) / 7 = 6
Solving for v, we get:
v = -20
Therefore, the value of v is -20.
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Answer must be in simplest form and can not be an improper fraction. Explain your steps.
[tex]3 \frac{1}{15} + 0.4[/tex]
The simplification of the given value in simplest form and can not be an improper fraction is 52/15.
What is fraction?An object's portion of the total or group is represented by a fraction. The fractional bar is a horizontal bar that divides a fraction's numerator (the top number) and denominator (the bottom number). The total number of items in a group or the number of equally divided equal pieces of the whole is represented by the denominator.
The given value is 3 1/15 + 0.4 , then we can convert to proper fraction as :
3 1/15 = 46/15
Then we can convert as;
0.4 = 4/10 =2/5
Then add together; 46/15 + 2/5
= 52/15
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Question 15(Multiple Choice Worth 1 points)
(05.05 LC)
Which graph matches the inequality y 2-x+1?
-6 -5
-4 -3
-2
-1
5
4
3
-2
-3
2
A
0
2
3
Answer:
3-x
Step-by-step explanation:
2-x+1
collect like terms
=2+1-x=3-x
Daniel is building a “learning tower.” A learning tower is a small structure that allows small children to help in the kitchen. The design plans that Daniel is using requires 12 boards of high quality lumber. At the local home improvement store, about 88% of the lumber would be high quality, meaning it would be free of defects and usable in this project. To account for lumber that may be discarded, Daniel purchases 15 boards of lumber from this store. (Assume that Daniel is in a hurry and does not have time to closely inspect the boards while at the store.)
What is the probability that Daniel is able to complete the project without purchasing more boards? (Remember, the project requires 12 usable boards.) Round answer to 4 decimal places.
The probability that Daniel is able to complete the project without purchasing more boards is given as follows:
0.9041 = 90.41%.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The parameter values for this problem are given as follows:
n = 15, p = 0.88.
The probability that at least 12 work is given as follows:
P(X >= 12) = P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15).
Using a calculator with these parameters and obtaining these values, the probability is given as follows:
0.9041 = 90.41%.
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Among the ledger accounts used by Rapid speedway are the following: Pre p aid Rent, Rent Expense, Unearned Admissions Revenue, Admissions Revenue, Prep aid Printing, Printing Expense, Concessions Receivable, and Concessions Revenue. For each of the following items, provide the journal entr y ( if one is needed ) to record the initial transaction and provide the adjusting entry, if any, required on Ma y 31, assuming the company makes adjusting entries monthly.
The ledger account for the information is provided in the image below:
What is a Ledger Account?A ledger is an accounting book or group of books where account transactions are noted.
Each account has a beginning or carry-forward balance, as well as the ending or closing balance, and would record each transaction as either a debit or credit in distinct columns.
The three types of ledgers are:
General ledger.Sales ledger or debtor's ledger.Purchase ledger or creditor's ledger.The Sales Ledger serves as a record of your sales, as well as whether you have received payment and how much is still outstanding.
The entire amount that Clients still owe you is typically listed as "Trade Debtors" or "Accounts Receivable" on the Balance Sheet.
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Now add all three terms together to get the final quotient.
- 3x5 +18x4-9 divided by
3x²
(Simplify your answer. Use positive exponents only. Do not factor.)
The quotient of -3x⁵ + 18x⁴ - 9 divided by 3x² is -x³ + 6x² and the remainder is -9
How to determine the quotientFrom the question, we have the following parameters that can be used in our computation:
-3x⁵ + 18x⁴ - 9 divided by 3x²
Using the long division method of quotient, we have
3x² | -3x⁵ + 18x⁴ - 9
The division steps are as follows
-x³ + 6x²
3x² | -3x⁵ + 18x⁴ - 9
-3x⁵
------------------------------------------------
18x⁴ - 9
18x⁴
------------------------------------------------
-9
Hence, the quotient is -x³ + 6x² and the remainder is -9
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100 POINTS PLEASE HELPPPPP
WHAT IS THE DOMAIN AND RANGE
Answer:
D(f)=any, R=(-∝;-2].
Step-by-step explanation:
1) the given graph is quadratic parabola with vertex in point [-2;-2]. If to apply the rules of transformation/moving the graph y=x², then it is possible to make up the equation of the given graph, it is y=-(x+2)²-2;
2) according to the equation y=-(x+2)²-2 the required domain is x∈(-∝;+∝), range is (-∞;-2].
PLEAse help And thanks so much if u do the question will be inserted below
The ordered pair of point G is given as follows:
(-3,-4).
How to define the ordered pair?The general format of an ordered pair is given as follows:
(x,y).
In which:
x is the x-coordinate -> horizontal coordinate.y is the y-coordinate -> vertical coordinate.For point G, we have that:
The horizontal coordinate is of x = -3.The vertical coordinate is of y = -4.Hence the ordered pair of point G is given as follows:
(-3,-4).
Meaning that the fourth option is the correct option.
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Find the slope of the line passing through the points (-5, 6) and (-5, -1).
Answer:
(-4, -1)
Thats the answer im sure
Answer:
undefined
Step-by-step explanation:
(-1-6)/(-5+5)
-7/0
undefined
The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
In this case, the two points are (-5, 6) and (-5, -1). The x-coordinates of these two points are the same, which means that the line passing through them is a vertical line.
A vertical line does not have a slope in the traditional sense, as the slope formula involves division by zero (the denominator x2 - x1 would be zero in this case).
Therefore, the slope of the line passing through the points (-5, 6) and (-5, -1) is undefined.
chatGPT
The area of a square is 144 cm^2. Find the length of the diagonal of the square.
Answer:16.97cm
Step-by-step explanation:
d=2A=2·144≈16.97056cm
Distance = 90 miles, Time = 15 hours Speed =
Answer:
Step-by-step explanation:
6 mph
Answer:
6 mph
Step-by-step explanation:
Question 4 (PLEASEEE HELPP)
S
T
W
V
ST = 29 and VU = 2x + 5.
Find the value of x.
U
Answer:
x=2.5
Step-by-step explanation:
so you need to divided five by two the easy you get the answer 2.5.
Compared to last year, the population of Boom Town has increased by 25%.The population is now 6,600. What was the population last year?
A recent high school graduate received $ 600 in gifts of cash from friends and relatives . In addition , he received three scholarships in the amounts of $ 250 , $ 400 , and $ 1400 . If he takes all his gift and scholarship money and invests it in a 36 - month CD paying 1 % interest compounded daily , how much will the graduate have when he cashes in the CD at the end of the 36 - months ?
Answer:
The high school graduate will have $2,787.17 when they cash in the CD at the end of the 36 months.
Step-by-step explanation:
The total amount of money the high school graduate received is:
$600 + $250 + $400 + $1400 = $2650
If this entire amount is invested in a 36-month CD paying 1% interest compounded daily, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money the graduate will have after 36 months
- P is the initial amount invested ($2650)
- r is the annual interest rate (1%)
- n is the number of times the interest is compounded per year (365, since it is compounded daily)
- t is the number of years (3)
Plugging in the values, we get:
A = $2,787.17
Therefore, the high school graduate will have $2,787.17 when they cash in the CD at the end of the 36 months.
The temperature of Shimla on a winter day at noon was -3°C. If it dropped by 5 degrees at night, what will be the temperature at night?
Answer:
If the temperature at noon was -3°C and it dropped by 5 degrees at night, the temperature at night would be:
-3°C - 5°C = -8°C
Therefore, the temperature at night would be -8°C.
Answer:
If the temperature in Shimla on a winter day at noon was -3°C, and it dropped by 5 degrees at night, we need to subtract 5 from -3 to get the new temperature.
-3°C - 5°C = -8°C
Therefore, the temperature at night in Shimla would be -8°C
PLEASE HELP ASAP THANK YOU!
Answer:
D
Step-by-step explanation:
8.42×1000=8420 which is between 8400 and 8500
Answer:
the answer would be D
Step-by-step explanation:
8.42 x 10^3 = 8420
27
Select the correct answer.
The parent function f(x)=√x is transformed to g(x) = -2f(x). Which is the graph of g?
The graph of g(x) will be a downward facing, steeper version of the square root function f(x).
What is a function ?
Function can be defined in which it relates an input to output.
The parent function f(x) = √x is a square root function that starts at the origin and increases slowly as x gets larger.
When we transform this function to g(x) = -2f(x), we are multiplying the output of f(x) by -2.
This means that the new function g(x) will be a reflection of f(x) about the x-axis, and its outputs will be twice as large (in magnitude) as the outputs of f(x).
Therefore, the graph of g(x) will be a downward facing, steeper version of the square root function f(x).
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21-
3-40
5 > - 6
Daniel invests £2200 into his bank account.
He receives 10% per year simple interest.
How much will Daniel have after 2 years?
Give your answer to the nearest penny where appropriate.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \pounds 2200\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 2200[1+(0.10)(2)] \implies A = 2200(1.2)\implies A = 2640[/tex]
Use the midpoint formula to find the midpoint between H(5,9) and (9,-2). OA. (4, 5.5) O B. (14, 11) O C. (7,3.5) OD. (5.5, 4.5)
[tex] \: [/tex]
[tex] \tt \: J = ( 9 , -2 )[/tex][tex] \: [/tex]
To find:-[tex] \tt \: midpoint \: between \: H \: nd \: J \: = ?[/tex][tex] \: [/tex]
By using formula:-[tex] \red{ \bigstar} \blue{\boxed { \tt \color{green} midpoint = ( \frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} )}}[/tex]
Solution:- [tex] \tt \: midpoint = ( \frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} )[/tex][tex] \: [/tex]
where ,
[tex] \small{\star \underline{ \tt \: H =( x_1 = 5 , y_1 = 9)}}[/tex]
[tex] \: [/tex]
[tex] \small { \star { \underline{ \tt \: J =( x_2 = 9 , y_2 = -2)}}}[/tex]
[tex] \: [/tex]
[tex] \tt \: m= ( \frac{5 + 9 }{2} , \frac{9 + (-2)}{2} )[/tex][tex] \: [/tex]
[tex] \tt \: m = ( \frac{14}{2} , \frac{7}{2})[/tex][tex] \: [/tex]
[tex] \tt \: m = ( \cancel \frac{14}{2} , \cancel\frac{7}{2})[/tex][tex] \: [/tex]
[tex] \underline{ \boxed{ \tt \purple{ \: m = ( 7 , 3.5) \: }}}[/tex][tex] \: [/tex]
The midpoint between H nd J is ( 7 , 3.5 ).
[tex] \color{pink}{━━━━━━━━━━━━━━━━━━━━━━━━━━━}[/tex]
hope it helps! :)
4 in.
If you'd like,
you can use a
calculator.
8 in.
SA = 2πr² + 2πrh
Use 3.14 for π.
Find the surface area of a
cylinder with a height of 8
inches and base radius of
4 inches.
Round to the nearest
hundredth.
SA = [?]in.2
4
The surface region of the cylinder will be 301.44 square inches.
What is the surface area of a right circular cylinder?Let r be the radius and h be the altitude of the cylinder. Then the surface region of the cylinder will be given as,
SA = 2πrh + 2πr² square units
The radius of the cylinder is 4 inches and the height of the cylinder is 8 inches.
Then the surface area of the cylinder is calculated as,
SA = 2πrh + 2πr²
SA = 2 x 3.14 x 4 x 8 + 2 x 3.14 x 4²
SA = 200.96 + 100.48
SA = 301.44 square inches
The surface region of the cylinder will be 301.44 square inches.
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Peter has $100 to spend on drinks for his party. Bottles of lemonade
cost $2 each, and juice boxes cost $0.50 each.
Ifx is the number of bottles of lemonade and y is the number of juice
boxes, which inequality models this situation?
(1) 0.50x + 2y ≤ 100
(3) 2x +0.50y≤ 100
(4) 2x + 0.50y≥ 100
(2) 0.50x + 2y ≥ 100
Answer: Let x be the number of bottles of lemonade and y be the number of juice boxes.
The cost of x bottles of lemonade is 2x dollars.
The cost of y juice boxes is 0.5y dollars.
The total cost of the drinks is the sum of the cost of the bottles of lemonade and the cost of the juice boxes:
2x + 0.5y ≤ 100
So the correct inequality that models this situation is:
(3) 2x + 0.50y ≤ 100
Therefore, Peter can spend no more than $100 on drinks, which includes the cost of the bottles of lemonade and the juice boxes.
Step-by-step explanation:
Graph the line by plotting any two ordered pairs with integer value coordinates that satisfy the equation.4x = 12
The two ordered pairs of coordinates that satisfy the given equation are (3, 1) and (3, 2)
What is an equation of a line?The equation of a straight line is y=mx+c y = m x + c m is the gradient and c is the height at which the line crosses the y-axis, also known as the y -intercept.
Given that, an equation, 4x = 12, we need to find two coordinates and plot its graph,
4x = 12
x = 3
Since, there is no y-intercept in the given equation, we will a straight line parallel to the y-axis. [see the graph attached]
The x-intercept for the coordinates of this line will be 3 always, and we can change the value of y-intercept value.
Therefore,
The coordinates can be = (3, 1), (3, 2), (3, 3), (3, 4), (3, 5)....
Hence, the two ordered pairs of coordinates that satisfy the given equation are (3, 1) and (3, 2)
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help
Which of the following is not a dimension of a 3-D shape?
area
height
length
width
Answer:
Area
Step-by-step explanation:
height length and width help you calculate the volume of a 3d shape such as a cube. Area is not something you can measure via rulers
Graph the function f(x)=sin(πx/4) use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
The graph of the function f ( x ) = sin ( πx/4 ) is plotted
What is Equation of Graph of Polynomials?Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Identify the even and odd multiplicities of the polynomial functions' zeros.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is given as
f ( x ) = sin ( πx/4 )
The periodicity of the function is 8 where the domain and range is
The domain of function = ( -∝ , ∝ )
The range of the function is = [ -1 , 1 ]
The graph of the function is plotted below
Hence , the equation of graph is plotted
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Sergey is solving 5x2 + 20x – 7 = 0. Which steps could he use to solve the quadratic equation by completing the square? Select three options. 5(x2 + 4x + 4) = –7 + 20 x + 2 = Plus or minus StartRoot StartFraction 27 Over 5 EndFraction EndRoot 5(x2 + 4x) = 7 5(x2 + 4x + 4) = 7 + 20 5(x2 + 4x) = –7
The three steps that Sergey could use to solve the quadratic equation by completing the square are:
[tex]5(x^2 + 4x + 4) = -4 + 7 x^2 + 4x = 7/5\s(x + 2)^2 = 27/5[/tex]
Sergey can use the procedures below to solve the quadratic equation [tex]5x2 + 20x - 7 = 0[/tex] by completing the square:
[tex]5x2 + 20x = 7[/tex]; move the constant word to the right.
For the coefficient of the quadratic term to be 1, divide both sides by the leading coefficient as follows:[tex]x2 + 4x = 7/5.[/tex]
On the left side of the equation, multiply and divide by the square of half the x-coefficient: term's
[tex]x^2 + 4x + 4 - 4 = 7/5[/tex]
Factor the perfect square trinomial after simplifying the left half of the equation:
[tex](x + 2)^2 = 27/5[/tex]
Take the square root of both sides, adding the plus/minus sign as necessary:
[tex]x + 2 = +/- sqrt(27/5)[/tex]
Subtracting 2 from both sides, find x, and then:
[tex]x = -2 +/- sqrt(27/5)[/tex]
The three methods that Sergey could employ to solve the quadratic problem by completing the square are as follows:
[tex]x^2 + 4x = 7/5(x + 2)^2 = 27/5[/tex]
[tex]5(x^2 + 4x + 4) = -4 + 7[/tex]
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3
of
?
4. The side lengths of three triangles are
shown. Which of the triangles are
right triangles?
Triangle
1
2
3
Side Lengths
12
14
6
11
V160
21
8
11
4
10
10
11
The triangles which are right triangles in the given three are none.
What is the Pythagoras theorem?
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
|AC|^2 = |AB|^2 + |BC|^2
We are given that;
Sides of the triangles
Now,
For Triangle 1, the side lengths are 12, 14, and 16. To check if it is a right triangle, we can see if the Pythagorean theorem holds for any two sides:
12^2 + 14^2 = 144 + 196 = 340
16^2 = 256
Since 340 is not equal to 256, Triangle 1 is not a right triangle.
For Triangle 2, the side lengths are 6, 11, and [tex]$\sqrt{160}$[/tex]. To check if it is a right triangle, we can see if the Pythagorean theorem holds for any two sides:
6^2 + 11^2 = 36 + 121 = 157
[tex]$\sqrt{160}^2 = 160$[/tex]
Since 157 is not equal to 160, Triangle 2 is not a right triangle.
For Triangle 3, the side lengths are 8, 11, and 15. To check if it is a right triangle, we can see if the Pythagorean theorem holds for any two sides:
8^2 + 11^2 = 64 + 121 = 185
15^2 = 225
Since 185 is not equal to 225, Triangle 3 is not a right triangle.
Therefore, by Pythagoras theorem none of the given triangles are right triangles.
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Find a possible formula
The formula that represents the table is:
y = (5/3)*x - 7
Which formula repersents the values in the table?We have a table that seems to represent a linear relation, remember that the general form is:
y = a*x +b
We can see that when x = 0, y = -7, then:
y = a*x - 7
The next point in the table is (3, -2), replacing that we will get:
-2 = a*3 - 7
-2 + 7= a*3
5 = a*3
5/3 = a
Then the formula is:
y = (5/3)*x - 7
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Urgent!! A bowling ball has an outside layer, and an inner core. One type of bowling ball has a diameter of 8 inches, and the outside layer in an inch thick. What is the volume of the outside layer? ___ in^3
Lyra is designing a model of a solar system with a planet and a comet. The planet has a circular orbit, centered at the origin with a diameter of 120. The comet follows a parabolic path with directrix x = 85 and vertex at (75, 0).
Answer:
Step-by-step explanation:
To design a model of a solar system with a planet and a comet, we need to consider their orbits and their relative positions in space. Here are some steps to create the model:
Draw the planet's orbit: Since the planet's orbit is circular and centered at the origin with a diameter of 120, we can draw a circle with radius 60 and center at (0,0).
Draw the comet's path: The comet follows a parabolic path with directrix x = 85 and vertex at (75, 0). We can draw the directrix as a vertical line at x = 85 and draw the vertex at (75,0). Then, we can sketch the parabola using the vertex and directrix as guides. The axis of symmetry of the parabola is parallel to the directrix, so we can draw a horizontal line through the vertex to find the axis of symmetry. The focus of the parabola is located at (75, 30), which is the same distance from the vertex as the directrix.
Place the planet in its orbit: Since the planet's orbit is circular and centered at the origin, we can place the planet at any point on the circle. For example, we can place it at (60,0) or (-60,0) to create a more interesting dynamic with the comet's path.
Place the comet in its path: The comet will follow its parabolic path and pass by the planet at some point. We can choose a point on the parabola that intersects with the planet's orbit, such as (100,40), and place the comet there.
Add details: To make the model more realistic and visually appealing, we can add details such as stars, moons, and asteroids. We can also add labels and descriptions for the planet and comet.
Overall, the model should show the circular orbit of the planet and the parabolic path of the comet, with their relative positions in space. The model can be created using various materials such as paper, cardboard, or 3D printing.
