x = -1 is the solution to the given inequality |x| - 2 ≤ -3.
The five steps to resolving inequalities are as follows?
When addressing an inequality, we can:
Equal numbers are added to both sides.Take the same amount away from both sides.Add the same positive number to both sides.Subtract the same positive value from both sides.Reverse the sign and multiply both sides by the same negative value.Isolate the variable on one side of the inequality and place all other constants on the other. To achieve this, alter the inequality by performing opposing procedures. First, multiply each side by two to isolate the x. Any action you take toward one side must also be taken toward the other.
C) If x = -1,
|x| - 2 ≤ -3
|-1| - 2 ≤ -3.
1 - 2 ≤ -3.
-1 ≤ -3 which is true.
Hence, x = -1 is the solution to the given inequality |x| - 2 ≤ -3.
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in the figure, h II o find the value of x and y
Answer:
y = 119
30 =x
Step-by-step explanation:
61 and y are same side interior angles and they add to 180
61+y = 180
y = 180-61
y = 119
y and 6x-61 are vertical angles and they are equal
y = 6x-61
119 = 6x-61
Add 61 to each side
119 + 61 = 6x
180 = 6x
Divide each side by 6
180/6 = x
30 =x
Answer:
y = 119°
x = 30°
Step-by-step explanation:
We know that if two lines are parallel, the co - interior angles are added up to 180°°.
Accordingly,
y + 61 = 180
y = 180 - 61
y = 119°
Also, we know that, vertically opposite angles are equal to each other.
y = 6x - 61
119 = 6x - 61
Now, we have to make x the subject.
For that, first, add 61 for both sides.
119 + 61 = 6x
180 = 6x
Now, divide both sides by 6.
30° = x
dave is making a rectangular garden bed. after assembling it, he finds that the bed has a width of three-fourths of a foot and a length of nine and one-third feet. what is the area of the garden in square feet
The area of the garden is 7 square feet.
Define area.The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth. An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions. A rectangle's area (A) is calculated by multiplying its length ('a') by its breadth ('b'). Area of Rectangle is therefore equal to (a× b) square units.
Given,
Width = 3/4
Length = 9 + 1/3
Length = 28/3
Area:
Length × Width
3/4 × 28/3
84/12
7
The area of the garden is 7 square feet.
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Please help thanks, Which postulate can be used to prove the two triangles are congruent?
The postulate that can be used to prove the two triangles are congruent is the HL this is the last option
What is HL?HL is an acronym that means Hypotenuse Leg. The Hypotenuse leg theorem is used in proving angle congruency in right angle triangle.
The theorem says that, two angles of a right angle triangle that have equal
hypotenuse andany one legthen two triangles are congruent
The figure in the problem is a right angle triangle that is sharing same hypotenuse hence the hypotenuse is equal. and one other leg is marked to be equal
Therefore, this theorem says that the two triangle are congruent
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PLEASE HELP ASAP I NEED TO GET THIS DONE!!
Answer:
B and D
Step-by-step explanation:
A is wrong because x has a negative exponent
C is wrong because x is a denominator
In triangle ABC, m angle A=45 degrees. The altitude divides side AB into two parts of 20 and 21 units. Find BC
The 20 and 21 unit leg lengths of the right triangles ΔACD and ΔBCD formed by the altitude CD indicates, by using Pythagorean theorem that the length of BC is 29 units
What is a right triangle?A right triangle is a triangle that has two perpendicular sides. The altitude of a triangle is perpendicular to the base of the triangle, forming two right triangles in acute triangle.
Angle ∠A = 45°
The length of the segment the altitude CD divides AB into = 20 and 21 units
Please find attached a drawing created using MS Word based on the question parameters.
[tex]tan(\angle A) = \dfrac{CD}{AD}[/tex]
AD = 20
Therefore;
[tex]tan(45^{\circ}) = \dfrac{CD}{20}[/tex]
CD = 20 × tan(45) = 20
Pythagorean theorem applied to right triangle ΔCBD, indicates that;
[tex]\overline{BC}^2[/tex] = [tex]\overline{CD}^2[/tex] + [tex]\overline{DB}^2[/tex]
DB = 21 units, which gives;
[tex]\overline{BC}^2[/tex] = 20² + 21² = 841
BC = √(841) = 29
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Find the x- and y-intercepts of the graph of 4x - 9y = 20. State each answer as an
integer or an improper fraction in simplest form.
Calculation
Find the dependent variable by itself: [tex]y= \frac{4x}{9} -\frac{20}{9}[/tex]
Find the function's x-intercept: x= 5
Find the dependent variable by itself: [tex]y= \frac{4x}{9} -\frac{20}{9}[/tex]
Find the function's y-intercept: y = [tex]-\frac{20}{9}[/tex]
The chart for : 4x-9y = 20
see the attachment
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The x- and y-intercepts of the graph 4x - 9y = 20 In the simplest form, state each answer as an integer or an improper fraction. x = 20 + 9y /4
What is meant by fraction?A fraction is a portion of a whole. In arithmetic, the number is expressed as a quotient, which is the numerator divided by the denominator. In a simple fraction, both are integers.A complex fraction has a fraction in either the numerator or denominator. In a proper fraction, the top number is less than the lowest common.A fraction pretty much tells us how many parts of a whole we have. A fraction is identified by the slash that is written between the two numbers. Designers have a top number, the quaternion, and a bottom number, the denominator. For instance, 1/2 is a fraction.Given
x, 4x - 9y = 20
x = 20 + 9 /4 y
Steps
4x - 9y = 20
Add 9 y to both sides
4x - 9y + 9y = 20 + 9y
Simplify
4x = 20 + 9y
Divide both sides by 4
4x/4 = 20/4 + 9y/4
Simplify
x = 20 + 9y /4
Hence, The x- and y-intercepts of the graph 4x - 9y = 20 In the simplest form, state each answer as an integer or an improper fraction.
x = 20 + 9y /4
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maths enlargements calculations of lines in shapes help pls
The length of the line segment BD is 3 centimeters.
How to find the missing length of triangle proportional to another triangle
Herein we find two triangles proportional to each other. According to Thales's theorem, two triangles are proportional when both have congruent angles. The geometric system is represented by the following expression:
AB / AD = BC / DE = AC / AE
By direct inspection we notice that the two triangles are proportional as they have congruent angles. If we know that DE = 10 cm, BC = 8 cm and AB = 12 cm, then the side AD has the following measure:
12 cm / AD = 8 cm / 10 cm
AD = (10 cm / 8 cm) × 12 cm
AD = 15 cm
And the length of the line segment BD is:
BD = AD - AB
BD = 15 cm - 12 cm
BD = 3 cm
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32. what proportion of the 30 sampled bottles are more than 12 ounces? a. 0.20 b. 0.60 c. 0.50 d. 0.30 33. in the sample of 30 bottles, the lowest recorded fill is 11.3 ounces, however, originally this value was mistakenly entered as 1.3 ounces. suppose the error is left uncorrected and the lowest value remains 1.3 ounces. which value is most affected by the error? a. the median. b. the interquartile range. c. the mean. d. all measurements would be affected the same.
The proportion of the 30 sampled bottles are more than 12 ounces is 0.30. The value is most affected by the error will be mean.
What is mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency. A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set. When a data set is ranked from least to greatest, the median is the midpoint.
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people enter a gambling casino at a rate of 1 every 2 minutes. (a) what is the probability that no one enters between 12:00 and 12:05? (b) what is the probability that at least 4 people enter the casino during that time?
The probability that no one enters between 12:00 and 12:05 is 0.082.
The probability that at least 4 people enter the casino during that time is 0.242
Given that people enter the casino at the rate of 1 every 2 minutes. A random variable X is defined as the number of people entering the casino between the time period of 12:00 and 12:05. Since we are given in the question that people enter the casino at the rate of 1 every minute, hence in the given time period they enter at the rate of 2.5.
P(X=0) = [tex]e^{-2.5}[/tex] = 0.082
Hence the probability that no one enters between 12:00 and 12:05 is 0.082.
The required probability is simply
P(X≥4) = 1 - P(X=0) - P(X=1) - P(X=2) - P(X=3)
= 1 - [tex]e^{-2.5}[/tex] - 2.5[tex]e^{-2.5}[/tex] - (((2.5)² / 2)[tex]e^{-2.5}[/tex] ) - (((2.5³)/3!)[tex]e^{-2.5}[/tex])
= 0.242
Hence, the probability that at least 4 people enter the casino during that time is 0.242
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How much of a radioactive kind of bismuth will be left after 8 minutes if the half-life is 2
minutes and you start with 79,360 grams?
grams
help asap, ill give
The greatest number of bags Caesar can make is 16 bags. Each of these bags will have 5 boxes of pasta and 8 jars of sauce.
If Caesar made fewer bags, he would have boxes of pasta and jars of sauce remaining.He could use 8 bags but this is not the greatest number he could use.What is the number of pasta and sauce in each bag?Boxes of pasta = 32Jars of sauce = 48Find the greatest common factor of 32 and 48
32 = 1, 2, 4, 8, 16, 3248 = 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.The greatest common factor of 32 and 48 is 16
So, the greatest number of bags Caesar can make is 16 bags
Number of pasta in each bag = 32/16
= 5 boxes of pasta per bag
Number of sauce in each bag = 48/16
= 8 jars of sauce per bag
If Caesar made fewer bags, he would have boxes of pasta and jars of sauce remaining.
He could use 8 bags but this is not the greatest number he could use.
Therefore, Caesar can use the greatest common factor to determine the highest number of bags he could use.
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you have 600 ft of fencing material to construct a rectangular pen for cattle. what are the dimensions (in feet) of the pen that maximize the area (enter number only)?
The dimension of pen that maximize the area is 150 ft by 150 ft.
What is the dimension of a area?
In mathematics, a dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, width, and height.
Given the perimeter of the rectangular is 600 ft.
Assume that the length of the rectangular be l and the breadth be b.
The perimeter of the rectangular is 2(l+b).
According the question:
2(l+b) = 600
Divide both sides by 2:
(l+b) = 300
l = 300 - b
The area of rectangular is A = lb
Substitute the value of l in the above equation:
A = (300 - b) b
A = 300b - b^2
The maximum value of a quadratic polynomial Ax^2+BX+C is at x = - B/(2A).
Compare Ax^2+BX+C with 300b - b^2:
A = -1 and B = 300.
Putting A = -1 and B = 300 in b= - B/(2A).
b= - 300/(2×(-1))
b = 150.
Putting b =150 in l = 300 - b
l = 300 - 150
l = 150
The dimension is 150 ft × 150 ft.
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"the difference of a number cubed and 10" translated expression
Answer:
[tex]x^3-10[/tex]
Step-by-step explanation:
Let the number be x.
"A number cubed" refers to x³.
"Difference" means to subtract, so the answer is [tex]x^3-10[/tex].
1. (2ab^5)^4/ab^3
2. (x^3y^5/ab^7)^2
3. 5mn^7-1
ANSWER :
[tex] \rm{1.)16a {}^{3}b {}^{17} }[/tex]
= (2ab^5)^4
= 2ab^5×2ab^5×2ab^5×2ab^5
= 16a^4b^9
= 16a^4b^9/ab^3
= 16a^3b^17
[tex] \rm2.) \frac{x {}^{6} y {}^{10} }{a {}^{2}b {}^{14} } [/tex]
= (x^3y^5)^2
= (x^6y^10)
= (ab^7)^2
= (ab^14)
= (x^6y^10)/ab^14
[tex] \rm3.)4mn {}^{7} [/tex]
= 5mn^7 - 1
= 4mn^7
15÷(3+13)2
A 2
B 5
C p
D 2 over 5
Answer: D.
Step-by-step explanation:
Answer 3,4,5,6 Thank you
B) The missing angle at the intersection point of both triangles is; x = 15°
C) The missing angle is gotten as; x = 61°
How to find the missing angles?B) In the second image given, we can see two angles;
Now, we know that sum of angles in a triangle is 180 degrees. Thus, for the interior angles, we have;
90 + 5x - 14 + y = 180
where y is the third interior angle
Now, we know that sum of angles on a straight line is equal to 180 degrees. Thus;
y = 180 - (9x + 16)
Put 180 - (9x + 16) for y into the first equation to get;
90 + 5x - 14 + 180 - (9x + 16) = 180
180 will cancel out to get;
90 + 5x - 14 - (9x + 16) = 0
4x = 90 - 14 - 16
4x = 60
x = 60/4
x = 15°
C) The missing angle of the triangle with side of 12y + 3 is an alternate angle to get;
Missing angle = 63°
Sum of angles in a triangle is 180 degrees. Thus;
56 + 63 + 3rd angle = 180
3rd angle = 180 - (56 + 63)
3rd angle = 61°
Thus, x = 61° because they are opposite angles
Also, the two given sides are equal to each other as shown. Thus;
51 = 12y + 3
12y = 51 - 3
12y = 48
y = 48/12
y = 4
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Last year, James earned £2,100 per month.
This year, he's had a 6% increase in his monthly pay.
He worked 35 hours per week for 46 weeks in the year.
What is James' average pay per hour this year?
Give your answer to 2 dp.
James average pay per hour is $17.40
How to find James average pay per hour
information given in the problem are
Last year, James earned £2,100 per month
This year, he's had a 6% increase in his monthly pay
35 hours per week for 46 weeks in the year
The question is a percentage problem
6% increase a factor of 1.16
2100 * 1.16 = 2436
number of hours in a month
35 hours = 1 week
? hours = 4 weeks
? = 4 * 35
? = 140 hours in 4 weeks = 1 month
James average pay per hour is gotten form the calculation below
if 140 hours pays 2436 then1 hour will pay ?
140 = 2346
1 = ?
cross multiplying
? * 140 = 2436 * 1
? = 2436 / 140
? = $17.40
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Write the following numbers in words form 1. 126.042 2. 64.1027 3. 67,421.004 4. 621.4021 5. 2.4826 6. 372.6218 7. 87.1648 8. 0.4806 9. 1.2761
Need help
The equation of the line L1 is y = 3x - 2
The equation of the line L2 is 3y - 9x + 5 = 0
Show that these two lines are parallel
Bert keeps honeybees on his farm. When he first started he used a six frame beehive that held 40 pounds of honey. now he uses a 30 frame beehive. It has the same ratios of frames to honey as a smaller beehive.
How much honey does Bert’s new beehive hold?
If now he uses a 30 frame beehive. It has the same ratios of frames to honey as a smaller beehive. The amount of honey that Bert’s new beehive hold is 200.
How to find the number of honey?Given data:
Number of frame beehive = 6
Pound of honey = 40
Current Frame beehive = 30
First step is to formulate an equation and then use the formulated equation to find the number of honey
40 × 30 ÷ 6
Hence,
40 × 5
= 200 honey
Therefore the number of honey is 200.
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A satellite dish has the shape of a parabola when viewed from the side. the dish is 48 inches wide and 36 inches deep. how far is the receiver from the bottom of the dish if the receiver is placed at the focus?
If the receiver is placed at the focus, it is 4 inches from the bottom of the dish. The result is obtained by using the equation of parabola with the vertex is at (0,0).
What is the equation of a parabola?With the vertex at (0,0), the equation of a parabola can be expressed as
x² = 4ay
Where
x = half of the diameter of parabola a = the y-axis of the focus of parabolay = the depth of parabolaGiven
Diameter of the dish = 48 inchesy = 36 inchesHow far is the receiver from the bottom of the dish if it is placed at the focus?
Suppose that the vertex is at (0,0).
x = 1/2 × diameter
x = 1/2 × 48
x = 24
Now, we got two points (-24, 36) and (24,36). See the picture in the attachment!
By using the x and y value, the value of a is
x² = 4ay
24² = 4a(36)
576 = 144a
a = 576/144
a = 4 inches
Hence, the receiver is placed at 4 inches from the bottom of the dish.
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Nicole has $40 in a savings account. The account earns 5% simple interest. She wants to determine the amount in her account after 1 year if she makes no deposits or withdrawals.
Answer:
16
Step-by-step explanation:
40/5 then x the answer by 2 and you get 16 with now deposits or withdraws
Which statement justifies the given ordered pair as a solution to the system of equations? (−1, −13) {y=3x−10y=−2x−15
x = -1 and y = -13, (-1,-13) is the solution to the system of equation y = 3x - 10 and y = -2x - 15.
What is the solution to the given system of equation?Given the system of equation in the question;
y = 3x - 10 y = -2x - 15Is (-1,-13) the correct ordered pair?To find the solution to the system of equation, replace the occurrence of y in the second equation with y = 3x - 10 and solve for x.
y = -2x - 15
3x - 10 = -2x - 15
Add 10 to both sides
3x - 10 + 10 = -2x - 15 + 10
3x = -2x - 15 + 10
Add 2x to both sides
3x + 2x = -2x + 2x - 15 + 10
3x + 2x = - 15 + 10
Add like terms
5x = -5
x = -5/5
x = -1
Now, to solve for y, replace all occurrence of x with -1 in the first equation and solve for y.
y = 3x - 10
y = 3( -1 ) - 10
y = -3 - 10
y = -13
Therefore, the solution to the system of equation is (-1,-13).
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a bag contains 14 blue, 6 red, 12 green, and 8 purple marbles. 25 marbles are removed from the bag randomly. how many of the removed marbles were green if the chance of drawing a green marble from the bag is now 3/5?
The number of green marbles removed from the bag is 3.
We will use the Formula of Probability:
In mathematics, the probability is defined as the ratio between the number of favorable outcomes and the total number of outcomes.
p(A) = n(A) / n(S)
p(A) is the probability of event A.
n(A) is the number of outcomes with respect to A.
n(S) is the total number of possible outcomes.
Given in the Question:
A bag contains 14 blue, 6 red, 12 green, and 8 purple marbles.
So the total number of marbles in the bag = 40
It is given that 25 marble are removed from the bag randomly
thus, the remaining marbles in the bag = 40 - 25 = 15
It is given that the probability of drawing a green marble from the bag after removing 25 marbles is 3/5.
So, for finding the number of green marbles in the bag after removing we can write,
n(A) = p(A) × n(S)
here, A is the event of drawing the number of green marbles and p(A) = 3/5 and n(s) = 15 (after removing)
Thus, the number of green marbles in the bag after removing = 3/5 × 15
So, the number of green marbles left in the bag = 9
then, the green marbles removed from the bag = 12 - 9 = 3.
Therefore, only 3 green marbles are removed from the bag.
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HELP MEEEE PLEASEEEE
Answer:
24.4 km
Step-by-step explanation:
The Pythagorean theorem states that a^2 + b^2 = c^2, where c is the hypotenuse of the triangle, and a and b are the legs. Plugging in your values, we get:
20^2 + 14^2 = c^2
Simplify: 400 + 196 = c^2
Simplify again: 596 = c^2
Square root both sides to cancel out the exponent on the right: 24.4131=c
Round: 24.4
Write a rule for g that represents the indicated transformations of the graph of f.
f(x)=2x5−x3+x2+4; reflection in the y-axis and a vertical stretch by a factor of 3, followed by a translation 1 unit down
The rule that represents the transformation is g(x) = -6x⁵ + 3x³ + 3x² + 11
How to determine the transformation of the function?The equation of the function is given as
f(x) = 2x⁵ - x³ + x² + 4
The sequence of transformations is given as follows:
Reflection across the y-axisVertically stretched by a factor of 3Translate down by 1 unitWhen the above transformations are combined, we have:
g(x) = 3f(-x) - 1
So, we have
3f(-x) - 1 = 3[2(-x)⁵ - (-x)³ + (-x)² + 4] - 1
This gives
3f(-x) - 1 = -6x⁵ + 3x³ + 3x² + 12 - 1
Expand
3f(-x) - 1 = -6x⁵ + 3x³ + 3x² + 11
So, we have
g(x) = -6x⁵ + 3x³ + 3x² + 11
Hence, the function is g(x) = -6x⁵ + 3x³ + 3x² + 11
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1) 2 more than 5 times x
2) 9 Multiply n by 6, and then divide the product by 5.
Answer:
1. 5x +2
2. 6x/5
Step-by-step explanation:
jim and craig, working together, can mow the lawn in 5 hours. working alone, craig takes five times as long as jim. how long does it take jim to mow the lawn alone?
In linear equation ,Shirley takes 1.66 hours to paint the deck alone.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."Let Shirley's time = x
Let Craig's time = 5x
(5x + x)/2 = 5
We split up the hours by 2 because we want to find out how much time individually.
6x/2 = 5
6x = 10
x = 1.66
Shirley takes 1.66 hours to paint the deck alone.
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Ben watched 3/8 of his television show. There are still 40 minutes left. How long does the whole program last?
The show is 1 hour 4 minutes long.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Ben watched 3/8 of his television show.
There are still 40 minutes left.
let the show be x long.
So, 3/8x + 40 = x
x- 3/8x= 40
5x/8 = 40
x= 320/5
x= 64 minutes
x= 1 hour 4 minutes
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Which algebraic expression represents “the apples were divided equally into seven boxes”?
Answer:
Step-by-step explanation:
a=apples
a/7
