Step-by-step explanation:
To solve the inequality |2x + 5| < 2 - x, we need to split it into two cases:
When 2x + 5 > 0:
In this case, the absolute value is positive, so we can simplify the inequality as follows:
2x + 5 < 2 - x
Expanding the left side:
3x + 5 < 2
Subtracting 5 from both sides:
3x < -3
Dividing both sides by 3:
x < -1
So the solution for this case is x < -1.
When 2x + 5 < 0:
In this case, the absolute value is negative, so we can simplify the inequality as follows:
(2x + 5) < 2 - x
Expanding the left side:
-2x - 5 < 2 - x
Adding x to both sides:
-2x - 5 + x < 2
Combining like terms:
-x - 5 < 2
Adding 5 to both sides:
-x < 7
Dividing both sides by -1:
x > -7
So the solution for this case is x > -7.
Taking the union of the two solutions, we get:
-7 < x < -1.
This means that x is between -7 and -1, excluding -7 and -1.
R if R={x|||xis an odd, negative integer andx>−16} .
The number of subsets for R { -15 , -13 , -11 , -9 , -7 , -5 , -3 , -1 } is given by the equation A = 255 subsets
What is union and intersection of sets?The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets
The intersection of two sets is a new set that contains all of the elements that are in both sets
Given data ,
Let the relation set be represented as R
Now , the set R = { x|||xis an odd, negative integer and x>−16 }
The number of elements in the set R is given by
R = { -15 , -13 , -11 , -9 , -7 , -5 , -3 , -1 }
So , the number of elements n = 8 elements
The number of subsets of any arbitrary set is equal to 2ⁿ
This means that the number of proper subsets (which is the number of subset minus the set itself, for finite subsets) is equal to 2ⁿ-1
So , the number of subsets for R = 2⁸ - 1 = 255 subsets
Hence , the solution set is { -15 , -13 , -11 , -9 , -7 , -5 , -3 , -1 }
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StartFraction 32 Over 8 EndFraction = StartFraction 28 Over x EndFraction
a.
x = 4
c.
x = 8
b.
x = 28
d.
x = 7
Answer:
d. x = 7
Step-by-step explanation:
To find the value of x, you can cross multiply the fractions to get 32 * x = 8 * 28, then simplify:
32x = 224
x = 7.
The hypotenuse of a 30°–60°–90° triangle measures 10 inches. Which could be the length of a leg of the triangle? Select all that apply.
A. 6
B. 8
C. 5
D. 53–√
Answer:
C. 5
D. 5√3*
*Check the last one - choice D - make sure it is 5√3 not 53–√ before marking it correct.
Otherwise only choice C is the correct answer
Step-by-step explanation:
The sides of a 30-60-90 triangle are always in the ratio of 1 : √3 : 2.
If the side opposite the 90° angle(the hypotenuse) = a
If the side opposite the 30° angle: PQ = a
Then the side opposite the 90° angle = 2a
The side opposite the 60° angle = √3a
Since here we are given the hypotenuse = 10
Side opposite the 30° angle = 2a/2 = 10/2 = 5
Side opposite the 60° angle = √3a = √3 · 5 = 5√3
I believe in your choice for D it should be 5√3 but not sure about that so check if it is before marking it correct
Answer:
Options C) and D) are correct
Step-by-step explanation:
Given: The hypotenuse of a 30°-60°-90° triangle measures 10 inches.
To choose: the correct option
Solution:
ΔKBO is a right-angled triangle.
[tex]sinO=\frac{side opposite to angle}{sideadjacent to angle}[/tex]
[tex]= \frac{BK}{KO} \\= \frac{BK}{10}[/tex]
⇒ sin 60°= [tex]\frac{BK}{10}[/tex]
[tex]\frac{\sqrt{3} }{2} = \frac{BK}{10}[/tex]
BK = [tex]\frac{\sqrt{3} }{2} (10) = 5\sqrt{3}[/tex]
CosO = [tex]\frac{side adjacent to angle}{side opposite to angle}[/tex]
[tex]= \frac{BK}{KO} \\= \frac{BO}{10}[/tex]
⇒ cos 60° = [tex]\frac{BO}{10}[/tex]
[tex]\frac{1}{2}= \frac{BO}{10} \\BO = \frac{10}{2} = 5[/tex]
Melissa bought a comic book for $2.17. The cashier gave Melissa $2.91 in change. How much money did Melissa give the cashier?
Answer:
5.08
Step-by-step explanation:
2.17+2.91 = 5.08
Help me asap pls i need it quick
Answer: 0.5km per hour
Step-by-step explanation:
Yo = 10 mg; The half-life is 100 days.
Answer:
After 100 days, the amount of the substance will decrease to half its original value, so Yo/2 = 5 mg. The half-life of a substance is the time it takes for half of it to decay or disappear. So, every 100 days, the amount of the substance will be halved until there is none left.
Question is not clear.
In parallelogram LMNP if PQ=21 find QM.
The length of the line segment QM which is half the diagonal MP is equal to 21 in the parallelogram LMNP.
Diagonals of a parallelogramA parallelogram is a quadrilateral, and the diagonals always bisect each other. However, diagonals only form right angles if the parallelogram is a rhombus or a square.
For the parallelogram LMNP; the lines MP and LN are its diagonals, and the both bisect each other, that is they cut each other to form two equal parts.
So QM and PQ are equal halves of the line MP
Therefore, since PQ = 21 then QM = 21 because they form a diagonal of the parallelogram LMNP bisected by the diagonal LN.
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The base of a triangular pyramid is an equilateral triangle. Each side of the base measures 12 in. The area of the base is 62.4 in². The slant height of the pyramid is 6 in.
What is the surface area of the pyramid?
Enter your answer in the box.
The surface area of the pyramid is given by the equation A = 170.4 inches²
What is the surface area of the pyramid?The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid
Surface Area of Pyramid = B + ( 1/2 ) ( P x h )
Given data ,
Let the surface area of the pyramid be represented as A
Now , the equation will be
The slant height of the pyramid h = 6 inches
The side of the equilateral triangle = 12 inches
So , the perimeter of the triangle = 3 x side length
Substituting the values in the equation , we get
The perimeter of the triangle = 36 inches
The area of the base = 62.4 inches²
So , Surface Area of Pyramid = B + ( 1/2 ) ( P x h )
Substituting the values in the equation , we get
Surface Area of Pyramid = 62.4 + ( 1/2 ) ( 36 x 6 )
On simplifying the equation , we get
Surface Area of Pyramid = 62.4 + ( 108 )
Surface Area of Pyramid = 170.4 inches²
Hence , the surface area of pyramid is 170.4 inches²
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Where does runoff end up?
A
ponds
B
streams
C
rivers
D
all of the above
Answer:
D all of the above is the answer
Answer:
D) All of the above
Runoff can end up in ponds, streams, and rivers.
Step-by-step explanation:
Hope it helps! =D
Which expression is equivalent to − 3 +t-6
The equivalent expression is t - 9
How to determine the equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
− 3 +t-6
Collect the like terms
So, we have the following representation
t - 3 - 6
Evaluate the like terms
This gives
t - 9
Hence, the expression is t - 9
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If posts are spaced 5 feet apart, how many posts are needed for 40 feet of straight-line fence?
Answer:
the answer is 8 just divide
Answer:
8 is the answer just divide
51. Rewrite each equation in expanded form. Then, give the x- and y-intercepts, the coordinates of the maximum or minimum point, and the line of symmetry for the graph of each equation.
a. y = (x − 3)(x + 3) =
X-intercepts: Y-intercepts:
Coordinates of the maximum or minimum point: Line of symmetry:
The correct form of the expression is x² -9
How to find the rewrite the expression?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is y = (x − 3)(x + 3) =
This can be done by opening the brackets
x²+3x-3x-9
⇒x²-9
Therefore, the correct form of the equation is x²-9
The x-intercept = 1 and the y intercept is -9
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Given f(x) = log x, what transformations are needed to produce g(x) = log (x) - 3?
Therefore , the solution of the given problem of function comes out to be g(x) = f(x) - 3 transformed .
Define function.Mathematics includes the study of numbers, various variable, the natural reality, architecture, and both actual and hypothetical locations. A function is a visual representation of the relationship between the number of inputs and the corresponding outputs for each. Simply explained, a function range is a collection of inputs that, whenever combined, result in a different output by each input. Every function is assigned a city, county, or scope, sometimes known as a realm. The letter f is frequently used to denote functions (x).
Here,
Given :
=> f(x) = log x
=> g(x) = log (x) - 3
So , it is transformed as logx = f(x)
it is transformed as :
=> g(x) = f(x) - 3
Therefore , the solution of the given problem of function comes out to be g(x) = f(x) - 3 transformed .
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Help ASAP!
Question 1:
Check attached file for question 1
Question 2:
A new lake was populated with a small number of trout. The number of trout in the lake can be modeled by the function: P(t)=740 / 1+73e^−0.07 where t is the number of months since the population of trout was first introduced. Round all answers to the nearest whole number
A. what is P(0)= I got 10
B. What does the answer from part A tell us about the trout population?
C. How many trout were in the lake after 1 year?
D. How many trout were in the lake after 10 years?
E. lim t→∞P(t)= I got 740
F. What does the answer from part E tell us about the trout population?
The answer from part A tells us that the trout population was 10 in the first month after it was introduced.
How solve the problem?A. P(0) = 740 / (1 + 73e^-0) = 740 / (1 + 73) = 740 / 74 = 10, so the answer is 10.
B. The answer from part A tells us that the trout population was 10 in the first month after it was introduced.
C. To find the number of trout in the lake after 1 year, we need to find P(12): P(12) = 740 / (1 + 73e^-0.07*12) = 740 / (1 + 73e^-0.84) ≈ 490, so the answer is 490.
D. To find the number of trout in the lake after 10 years, we need to find P(120): P(120) = 740 / (1 + 73e^-0.07*120) = 740 / (1 + 73e^-8.4) ≈ 740, so the answer is 740.
E. lim t→∞ P(t) = 740, so the answer is 740.
F. The answer from part E tells us that as the number of months t approaches infinity, the trout population will approach 740. This means that the trout population will eventually stabilize at 740 if no other factors such as predators, disease, or lack of food affect the population.
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Work out the following sheet
Note that in question 28 above:
X = 56° (Alternative Angles)
Y = 124° (Angles in a straight line)
Z = 81° (Sum of angles in an irregular parallelogram).
in Question 29,
x = 126° (Co-interior angles and Bisector theorem).
Question 28: Note that the sum of angles in an irregular parallelogram always equal 360°. Since X and 56° are alternate angles and are therefore congruent, and Y and 56° are on the same line and therefore sum up to 180°, resulting in Y being equal to 124°, then we have three interior angles of an irregular parallelogram:
∠X = 56°
∠Y = 124°; and
∠99° (As given), which is co-interior with ∠Z
Thus whether by the Co-interior principle where two co-interior angels sum up to 180° or by sum of angles in an irregular parallelogram, we will still obtain a result where:
∠Z = 81°. That is
360° = 56 + 124 + 99 + ∠Z
∠Z = 360 - (56 + 124 + 99)
∠Z = 81°
OR
Using the Co-Interior angles theorem, we can state that:
∠Z = 180 - 99
∠Z = 81°
Question 29:
Recall that an angle bisector of a triangle's angle divides the opposing side into two portions that are proportionate to the triangle's other two sides, according to the angle bisector theorem.
Thus, we can state that 27° is half of the angle whose Co-interior is x.
Thus ∠x = 180 - (27*2)
∠x = 180 -54
∠x = 126°
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Drag and drop numbers into the boxes to complete the expanded form of 706.039.
The expanded form of the given decimal number is 706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009
What is expanded form?We break up a number according to its place value and expand it to show the value of each digit.
Given that to write expanded form of 706.039
Expanded Factors Form:
706.039 = 7 × 100 + 0 × 10 + 6 × 1 + 0 × 0.1 + 3 × 0.01 + 9 × 0.001
Expanded Notation Form:
706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009
Hence, the expanded form of the given decimal number is 706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009
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You buy a house for $230,000. It depreciates 3% per year. How much is it worth in 5 years?
a. Write the equation.
b. Solve the problem.
The equation is $230,000 x 0.97^5.
The worth of the house in five years is $197,508.83.
What is the worth of the house?
Depreciation is the decline in the carrying value of an asset. Depreciation occurs as a result of wear and tear.
The equation that would be used to determine the worth of the house in 5 years is
Worth of the house = cost of the house x (1 - depreciation/100)^number of years
= $230,000 x (1 - 3/100)^5
$230,000 x (1 - 0.03)^5
$230,000 x 0.97^5 = $197,508.83
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At what rate of interest will Rs 2500 amo- unt 10 Rs.3200 in. 7yrs?
Answer:
The rate of interest required to make Rs. 2500 amount to Rs. 3200 in 7 years is 8.5%. This can be determined by using the information from pa01000192.schoolwires.net, which states that the formula for finding the rate of interest is: Rate of Interest = (Future Value - Present Value) / (Present Value * Time). Applying this formula to the given values gives a rate of interest of 8.5%.
Step-by-step explanation:
Julia had a bag filled with gumballs. There were 1 watermelon, 2 lemon-lime, and 3 grape gumballs. What is the correct sample space for the gumballs in her bag?
Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape
Sample space = lemon-lime, watermelon, grape
Sample space = 1, 2, 3, 4, 5, 6
Sample space = 1, 2, 3
The correct sample space for the gumballs in her bag is;
A: Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape
How to find the sample space?The sample space of an experiment is defined as the set of all the possible outcomes. For example, when we toss a coin, the sample space is; {head, tail}.
Now, the parameters for the bag filled with gumballs are;
1 watermelon.
2 lemon-lime.
3 grape gumballs.
Therefore the sample space is the different types of gumballs there and it is; {Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape}
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The bedroom of our house is 1,200 cubic meters. We know there are 3.4 x 10⁹ particles of dust per cubic meter. Write how many particles of dust are present in the bedroom of our house.
Answer:
4,080,000,000,000
Step-by-step explanation:
1,200 * 3.4*10⁹
=4080*10⁹
=4,080,000,000,000
3 friends share
5/6 of a pizza
What fraction of a pizza does each person get?
Answer:
5/18
Step-by-step explanation:
We assume they share equally.
5/6 ÷ 3 = 5/6 × 1/3 = 5/18
Hey does anyone know how to do this
The required equation is y = -9x - 65.
What is a slope intercept form?
One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills.
Here, we have
Given: the equation of a line parallel to y =-9x + 8, that passes through the point P(-8, 7).
The slope of y = -9x+8.... (1)
can be found as
compare with the standard equation
y = mx+c.... (2)
where m is the slope so
Comparing (1) and (2)
slope = m = -9
So the slope of the parallel line will also be -9
So in order to find the equation we need a point and a slope to put in the point-slope formula
y-y₁ = m(x-x₁)
Point (x,y) = (-8,7) slope m = -9
y-7 = -9(x+8)
y = -9x - 72 + 7
y = -9x - 65
Hence, the required equation is y = -9x - 65.
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Trei correctly spelled 60% of the words on her last spelling test! how many words did she spell correctly for each word that she spelled wrong?
Let's call the number of words Trei spelled correctly "x". Then, the number of words she spelled incorrectly is 100 - 60 = 40 words.
Therefore, the ratio of correctly spelled words to incorrectly spelled words is x to 40.
To find the number of words she spelled correctly for each word she spelled wrong, we can simplify the ratio by dividing both values by the greatest common factor:
x / 40 = x / (2 * 20) = x / 2 * 20 / 2 = x / 20.
So for every word Trei spelled incorrectly, she spelled 20 / 1 = 20 words correctly.
Chantelle works at Mattresses R Us. She had $60,000 in sales and made $1200 in commission. What percent commission does she get?
NEED RESPONSE ASAP
The solution is, she got commission of 2%.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
Chantelle works at Mattresses R Us. She had $60,000 in sales and made $1200 in commission.
so, she got commission = 1200/60000 * 100
=2%
Hence, The solution is, she got commission of 2%.
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Use the definition of continuity and the properties of limits to show that the function
The given function is continuous at x = 3, RHL = LHL = F(2)
What is continuity ?In mathematics, The function is called as continuous at the particular value of x, if right hand limit, left hand limit and the value of function at x all are equal.
RHL = LHL = F(x)
Limit exist and continuous
Given that,
F(x) = (x²-9)/(x² - x -6)(x² + 6x +9)
To check whether it is continuous at x = 2
First taking LHL,
[tex]\lim_{h \to \ 0}[/tex] ((2-h)²-9)/((2-h)² - (2-h) -6)((2-h)² + 6(2-h) +9)
⇒ -5/(-4x25)
⇒ 1/20
Now, taking RHL
[tex]\lim_{h \to \ 0}[/tex] ((2+h)²-9)/((2+h)² - (2+h) -6)((2+h)² + 6(2+h) +9)
⇒ -5/(-4x25)
⇒ 1/20
The value at x = 3
F(3) = ((2)²-9)/((2)² - (2) -6)((2)² + 6(2) +9)
= -5/(-4x25)
= 1/20
Hence Proved, RHL = LHL = F(2)
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A student is solving the equation 2|x-3|=8
Answer:
Student most likely forgot to form 2nd equation.
Step-by-step explanation:
The answers appear to be cut off, but I can clearly see that the other solution isn't considered. When solving an absolute value equation, you form two equations. In this case, we have x-3=4 and x-3=-4 as our equations because |-4|=|4|=4 so this is accounted for. Hence, the two solutions should be x=7 AND x=-1.
You can afford a $250 per month car payment. You've found a 3 year loan at 7% interest. How big of a loan can you afford?
Answer:
630
Step-by-step explanation:
36x250 = 9000 ÷ 7 =630
An angle measures 163.6° less than the measure of its supplementary angle. What is the measure of each angle?
ANSWER QUICK I WILL MARK BRAINLIST
Answer:
Supplementary angles are angles that add up to 180 degrees, or on a straight line. If one angle is 163.6 degrees less than its supplementary, then all you have to do is subtract that number from 180. The angles are
180 - 163.6 = 16.4
180 - 16.4 = 163.6
One angle is 16.4 degrees, the other is 163.6. They both add up to make 180.
In parallelogram EFGH, MLH =
F
Зу
(3x - 15)°
2(y + 1)
H
(7x- 5)°
y + 8
o and HG
＝
The measure of HG is 12
What is a parallelogram?A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides is called a rhombus, and a parallelogram whose angles are all right angles is called a rectangle.
The opposite sides of a parallelogram are equal. This means that 3y = y+8
3y = y+8
3y-y = 8
2y = 8
divide both sides by 2
y = 8/2
y = 4
if y = 4 and HG is y+8
therefore
the measure of HG = 4+8
= 12
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The circle graph represents the jobs at a digital animation company with 1,540
The number of artists that are interns is solved to get 77
How to find the number of artists that are internsFrom the problem, showing circle graph, it can be deduced that the interns occupy 5 percent of the total number
The total number is 1540
5% of 1540 is solved by
= 5/100 * 1540
= 0.05 * 1540
= 77
The number of interns is 77
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