The solid curve shows that the points on the curve are part of the inequality solution set, and the shade inside the parabola indicates that the points below the curve are part of the solution set as well.
What is inequality?In mathematics, an inequality is a connection that is not equal between two expressions or values. Consequently, imbalance leads to inequity. In mathematics, an inequality connects two unrelated values. Inequality is separate from equality. When two values are not equal, the not equal sign is most usually used (). Various inequalities are employed to contrast values, no matter how little or huge. Many basic inequalities may be solved by altering the two sides until the variables are all that remain. Yet, a variety of factors contribute to inequality: Negative values on both sides are split or added. Trade off the left and right.
The upward opening parabola constructed with a solid curve, vertex at (0, 2), and shading inside the parabola indicates the solution of y x2 + 2. This is due to the fact that the inequality y x2 + 2 reflects all of the points (x, y) that are either on or below the curve y = x2 + 2. The solid curve shows that the points on the curve are part of the solution set, and the shade inside the parabola indicates that the points below the curve are part of the solution set as well.
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Find the value of the indicated trigonometric ratio.
cosβ
The value of the indicated trigonometric ratio.
cosβ is equal to 0.9167
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
the side CA = 22 is adjacent to the angle β while BA = 24 is the hypotenuse, so:
cosβ = 22/24 {adjacent/hypotenuse}
cosβ = 11/12
cosβ = 0.9167
Therefore, the cosine of the angle β is equal to 0.9167 using the trigonometric ratio.
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If you have the right answer I will give you brainilest!!!
Solve by Elimination:
5x+2y=−3
2x+3y=−10
Answer:
Multiplying the second equation by 2, we get:
4x + 6y = -20
Now we can subtract the first equation from this to eliminate x:
4x + 6y = -20
-(5x + 2y = -3)
-x + 4y = -17
Now we have one equation with only y. Solving for y:
-x + 4y = -17
4y = x - 17
y = (1/4)x - 17/4
Now we can substitute this expression for y into either equation to solve for x. Let's use the first equation:
5x + 2y = -3
5x + 2((1/4)x - 17/4) = -3
5x + (1/2)x - 17 = -3
(11/2)x = 14
x = 28/11
So the solution is (x,y) = (28/11, -17/11).
Step-by-step explanation:
Please help me with this question. Thanks :)
Answer:
26
Step-by-step explanation:
Total pupils 60
32 boys and girls will be 28 (60-32)
Cola 12 boys
Water 4 boys 9 girls
Milk 21 pupils
Total results 12 + 4 +9+ 21 = 46
Outstanding girls will be 60 - 46
Girls who like coke 14
If 14 girls liked cola and 12 boys liked cola, total will be 14 + 12
Find possible roots
The answer of the given question based on finding roots are roots of the equation are -3, 3/2, and 1.
What is Synthetic division?Synthetic division is shortcut method used to divide polynomial by linear factor of form (x-a), where "a" is a constant. It is simplified method of polynomial long division, and it is especially useful when dividing by linear factor, as it avoids the need to write out all powers of x.
We list the factors of the leading coefficient 2 and the constant term 9:
Factors of 2: ±1, ±2
Factors of 9: ±1, ±3, ±9
Possible rational roots are: ±1, ±2, ±3, ±9
Using synthetic division with x = -1, we get:
-1 | 2 1 -12 9
-2 1 11
2 -1 -1 20
The remainder is not zero, so x = -1 is not a root of the equation.
Using synthetic division with x = -2, we get:
-2 | 2 1 -12 9
-4 6 -88
2 -3 -6 -79
The remainder is not zero, so x = -2 is not a root of the equation.
Using synthetic division with x = -3, we get:
-3 | 2 1 -12 9
-6 15 -9
2 -5 3 0
The remainder is zero, so x = -3 is a root of the equation. This means that (x + 3) is a factor of the equation.
Using polynomial long division, we get:
2x³ + x² - 12x + 9 = (x + 3)(2x² - 5x + 3)
quadratic factor can factored further we get:
2x² - 5x + 3 = (2x - 3)(x - 1)
Therefore, roots of given equation is:
x = -3 (root obtained earlier)
x = 3/2 (from 2x - 3 = 0)
x = 1(from x -1=0)
For the given equation 2x³ + x² - 12x + 9 = 0, the factors of the leading coefficient 2 are ±1, ±2, and the factors of the constant term 9 are ±1, ±3, ±9. Therefore, possible rational roots of equation are:
±1/1, ±3/1, ±1/2, ±3/2, ±9/2, ±1/9, ±3/9, ±9/9
Using synthetic division or other methods, we can check that the real rational roots of the equation are -3, 3/2, and 1.which we found in part (a).
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Calculate the money you will have in the following accounts after 5 years assuming you earn simple interest,
51. you deposit $700 in an account with an annual interest rate of 4%
54. you deposit $1800 in an account with an annual interest rate of 3.8%
We will have $840 and $2142 respectively. The solution has been obtained by using simple interest.
What is simple interest?
Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest.
We know that amount after simple interest is given by
A = P (1 + rt)
We are given that $700 are deposited in an account with an annual interest rate of 4%.
Here,
P = $700
r = 4%
t = 5 years
On substitution, we get
⇒A = 700 (1 + (0.04 * 5))
⇒A = 700 (1 + 0.2)
⇒A = 700 (1.2)
⇒A = $840
Similarly, in the second case,
P = $1800
r = 3.8%
t = 5 years
On substitution, we get
⇒A = 1800 (1 + (0.038 * 5))
⇒A = 1800 (1 + 0.19)
⇒A = 1800 (1.19)
⇒A = $2142
Hence, we will have $840 and $2142 respectively.
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Lisa walked from south Pier to the North Pier along the beachfront. Deanna walked from the South Pier to the North Pier along Harbor Drive and Park Street. Which statement best describes the distances the two women walked?
Answer:
2
Step-by-step explanation:
Find the area of the parallelogram below:
What is the area?
Answer:
The area of the parallelogram is 630.4 square units, to the nearest tenth.
Step-by-step explanation:
The formula to find the area of a parallelogram is:
[tex]A=bh[/tex]
where b is the base and h is the height.
For the given parallelogram ABCD, BC and AD are the bases and h is the height. Therefore, we need to calculate the height, h, before we can calculate the area of the parallelogram.
The height of the parallelogram is also the side opposite angle 62° in the right triangle of the given diagram. As we also know the hypotenuse of this triangle, we can use the sine trigonometric ratio to find "h".
[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
Given:
θ = 62°O = hH = 21Therefore, the expression for h is:
[tex]\implies \sin 62^{\circ}=\dfrac{h}{21}[/tex]
[tex]\implies h=21\sin 62^{\circ}[/tex]
Given the base of the parallelogram is 34 units, substitute b = 34 and the expression for h into the formula for the area:
[tex]\begin{aligned}\implies \textsf{Area}&=34 \cdot 21\sin 62^{\circ}\\&=630.424581...\\&=630.4\; \sf square\;units\;(nearest\;tenth) \end{aligned}[/tex]
Therefore, the area of the parallelogram is 630.4 square units, to the nearest tenth.
Gretchen is refinishing her gazebo that is in the shape of a regular octagon. The length of one side is 3 feet and the apothem is 3. 5 feet. What
is the area that Gretchen will be refinishing?
Answer:
10.5
Step-by-step explanation:
you just have to multiply 3 feet by 3.5 feet.
14. Find the measures of all the angles in the rectangle. 1 2 3 5 32 4
[tex]90^{0} - 32^{0} = 58^{0}[/tex]
1 = 4 = 90°
2 = 32°
3 = 5 = 58°
Answer:
∠1 = ∠4 = 90°∠2 = 32°∠3 = ∠5 = 58°Step-by-step explanation:
You want the measures of the marked angles in the rectangle, given one of the acute angles is 32°.
Complementary anglesThe corner angles of a rectangle are all 90°. That's part of the definition of a rectangle:
∠1 = ∠4 = 90°
That make angles 5 and 32° be complementary angles:
∠5 = 90° -32° = 58°
The angles at the opposite end of the diagonal are complementary to these, as the sum of angles in a triangle is 180°.
∠2 = 90° -58° = 32°
∠3 = 90° -32° = 58°
__
Additional comment
You may have noticed that angles on opposite sides and opposite ends of the diagonal have the same measure. This is no coincidence. These are called "alternate interior angles". As such, they are always congruent where a diagonal meets parallel lines. (The sides of a rectangle are parallel.)
What two criteria must a graph meet to show a proportional relationship?
A graph shοws a prοpοrtiοnal relatiοnship if it meets the fοllοwing twο criteria Linearity and Cοnstant ratiο.
What is the ratiο and prοpοrtiοn?A ratiο is an οrdered pair οf numbers a and b, written a / b where b dοes nοt equal 0. A prοpοrtiοn is an equatiοn in which twο ratiοs are set equal tο each οther. Fοr example, if there is 1 bοy and 3 girls yοu cοuld write the ratiο as 1 : 3 (fοr every οne bοy there are 3 girls).
A graph shοws a prοpοrtiοnal relatiοnship if it meets the fοllοwing twο criteria:
Linearity: The graph must shοw a straight line passing thrοugh the οrigin (0,0). This means that as οne variable increases, the οther variable increases in prοpοrtiοn.
Cοnstant ratiο: The slοpe οf the line (i.e., the change in the y-variable divided by the change in the x-variable) must be cοnstant thrοughοut the entire graph.
This cοnstant ratiο represents the prοpοrtiοnality cοnstant between the twο variables.
Hence, A graph shοws a prοpοrtiοnal relatiοnship if it meets the fοllοwing twο criteria Linearity and Cοnstant ratiο.
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I NEED THIS FAST PLEASEEE!!
The population of Cirque City was 43,129 in 1999 and was 56,780 in 2010. If the population was growing exponentially, what was the growth rate?
Answer:
Step-by-step explanation:
If we call 1999 year 0, then 2010 would be year 11. This makes the coordinates for our problem (0, 43129) and (11, 56780). That means that the initial value, a, is 43129 and we can use that to solve for b.
[tex]56780=43129(b)^{11[/tex]
Divide both sides by 43129 to get
[tex]1.31651557=b^{11[/tex] and take the 11th root on your calculator to get that
b = 1.025314051
Not sure how you need to round that.
please help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
3/8
Step-by-step explanation:
Maricarmen le pide un préstamo de $24,000 a su amigo, el cuál le dice que cada mes debe pagarle un 20% del préstamo. ¿Qué cantidad del préstamo habrá pagado Maricarmen a los tres meses?
The amount repaid in the three months of the loan amount $24,000 with a condition of 20% repayment is equal to $11,712.
Percent of amount Maricarmen has to pay = 20% of the loan each month.
This implies Maricarmen pay 0.2 times the loan amount each month.
Amount Maricarmen will pay in the first month is equal to,
0.2 x $24,000 = $4,800
Amount left after the first payment,
$24,000 - $4,800 = $19,200
In the second month, Maricarmen will pay,
0.2 x $19,200 = $3,840
Amount left after the second payment,
$19,200 - $3,840 = $15,360
In the third month, Maricarmen will pay,
0.2 x $15,360 = $3,072
Amount left after the third payment,
$15,360 - $3,072 = $12,288
total amount paid in three months,
$4,800 + $3,840 + $3,072 = $11,712
Therefore, after three months Maricarmen will have repaid a total of $11,712 of the loan.
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Find the first five non-zero terms of Maclaurin series (Taylor series centered at x=0) for the function below as well as radius of convergence.
f(x)=xe^x
Answer:
To find the Maclaurin series for $f(x) = xe^x$, we can use the formula for the Maclaurin series of $e^x$ and differentiate the product term by term:
$$e^x = \sum_{n=0}^\infty \frac{x^n}{n!}$$
$$xe^x = x \sum_{n=0}^\infty \frac{x^n}{n!} = \sum_{n=0}^\infty \frac{x^{n+1}}{n!}$$
So the first few terms of the Maclaurin series for $f(x)$ are:
$$f(x) = xe^x = x + x^2 + \frac{x^3}{2} + \frac{x^4}{3} + \frac{x^5}{24} + \cdots$$
To find the radius of convergence, we can use the ratio test:
$$\lim_{n\to\infty} \left| \frac{a_{n+1}}{a_n} \right| = \lim_{n\to\infty} \left| \frac{x^{n+2}/(n+1)!}{x^{n+1}/n!} \right| = \lim_{n\to\infty} \frac{|x|}{n+1} = 0$$
Since the limit is less than 1 for all values of $x$, the Maclaurin series converges for all values of $x$, and the radius of convergence is infinite.
Use Conditional Probability Notation to Describe Events Question Let M be the event that a randomly chosen student passes a math test. Let S be the event that a randomly chosen student studies every day. Identify the answer which expresses the following with correct notation: The probability that a randomly chosen student studies every day, given that the student passes a math test Select the correct answer below: O P(MS) OPM AND S) O P(S) AND P(M) O P(SM)
Answer:
Step-by-step explanation:
Which statement best compares and contrasts the two formats?
The infographic shows the movement of water visually, while the text describes it.
The infographic would be less appealing to visual learners than the text.
It is impossible to understand the infographic without the text.
The text is more accurate than the infographic.
The conditional probability that a randomly chosen student studies every day, given that the student passes a math test is O P(M|S). The correct option is A.
P(M|S) is the probability that a randomly chosen student passes a math test given that the student studies every day. But, the question is asking for the probability that a student studies every day given that the student passes a math test.
Considering an P(M|S) situation,
Option D: P(SM) is incorrect because it means the probability that both events S and M occur simultaneously.
Option C: P(S) and P(M) is incorrect because it shows the probabilities of two individual events, not the probability of one event given that the other event has occurred.
Option B: P(M AND S) is incorrect because it means the probability that both events M and S occur simultaneously.
The given problem is based on Conditional Probability Notation to Describe Events. The notation used for conditional probability is P(A|B). Where A and B are two events, the notation represents the probability of event A occurring, given that event B has occurred. Conditional probability can be described as the probability of one event happening given that another event has already happened.
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Handy Automobiles produces two scooters: Basic and Discord. These scooters are produced by assembling multiple units of two key components C1 and C2. The component usage for the two scooters is given below:
Basic Discord
C1 6 10
C2 10 4
These components are produced within the plant. Marginal production costs for C1 and C2 are $8 and $12 respectively. The selling price of Discord is $500 and that of Basic is $400. The demand for these products are uncertain. Handy has to plan for the following 3 demand scenarios:
Basic Discord Prob
Scenario 1 600 200 30%
Scenario 2 400 400 40%
Scenario 3 300 500 30%
Due to the long lead times associated with production, Handy has to produce the components before they know which of the demand scenarios they need to plan for. However the components can be assembled to produce the two products after demand information is available. Unused components have no value and are discarded.
1. Develop a production plan for Handy
2. Suppose Handy can retool its production system and develop an additional component C3 which can serve as a substitute for both C1 and C2. However, the marginal cost of production of this component is $14. Should they go ahead with the retooling? If so, what is their new production plan?
Handy should produce 5400 units of C1 and 5600 units of C2 and the production plan should remain the same, with 5400 units of C1 and 5600 units of C2 being produced.
1. To develop a production plan for Handy, we need to calculate the expected demand for each component under each scenario. This is done by multiplying the demand for each scooter by the number of components used in its production, and then multiplying by the probability of each scenario occurring.
Expected demand for C1 = (600 x 6 x 0.3) + (400 x 6 x 0.4) + (300 x 6 x 0.3) + (200 x 10 x 0.3) + (400 x 10 x 0.4) + (500 x 10 x 0.3) = 5400
Expected demand for C2 = (600 x 10 x 0.3) + (400 x 10 x 0.4) + (300 x 10 x 0.3) + (200 x 4 x 0.3) + (400 x 4 x 0.4) + (500 x 4 x 0.3) = 5600
Therefore, Handy should produce 5400 units of C1 and 5600 units of C2.
2. To determine whether Handy should retool its production system to develop C3, we need to compare the expected cost of production with and without the new component.
Without C3:
Expected cost = (5400 x $8) + (5600 x $12) = $43,200 + $67,200 = $110,400
With C3:
Expected cost = (5400 x $14) + (5600 x $14) = $75,600 + $78,400 = $154,000
Since the expected cost of production with C3 is higher than without C3, Handy should not retool its production system to develop the new component. The production plan should remain the same, with 5400 units of C1 and 5600 units of C2 being produced.
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Tu is a Tangent to the circle at v. Find the value of x
Answer:2.333...
Step-by-step explanation:
A tangent meets a radius (also works with diameters) at 90°.
This means (98 - 3x) = 90
98 = 90 + 3x
8 = 3x
x = 8 / 3 = 2.3333333......
Step-by-step explanation:
Arc wxv is 360 - 176 = 184 degrees
this makes angle 98-3x = 1/2 (184) = 92°
( 98 -3x )°= 92°
- 3x = -6
x = 3
Please Help!
Drag each label to the correct location on the equation. Not all labels will be used.
Picture is linked below.
After answering the given query, we can state that Expression: A group variable of words, divided by signs for addition or subtraction.
What is a Variable?In the context of a mathematical idea or experiment, a variable is something that can be altered. Frequently, a single symbol is used to symbolize a variable. Variables are frequently represented by the letters x, y, and z as abstract symbols. A wide variety of values can be assigned to characteristics known as variables. These factors include, among others, your size, age, wealth, place of birth, scholastic standing, and type of residence. Both numerical and categorical methods can be used to divide variables into two primary groups.
Here are where the labels should be placed based on the illustration:
Coefficient, label one
2nd label: variable
Label 4: the equals symbol Label 3: constant
5th label: term
Expression 6th label
The definition of each term is broken down as follows:
A integer multiplied by a variable in a term of an algebraic expression is referred to as a coefficient.
Variable: A symbol for a quantity that is subject to shift or variation.
A fixed, unchanging number is referred to as a constant.
The equals sign: Shows that the expressions on the left and right are equivalent.
Term: A grouping of variables multiplied by a coefficient and denoted by addition or subtraction marks.
Expression: A group of words, divided by signs for addition or subtraction.
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Help I do not know how to do this and now I’m stuck
Answer:
okay the answer is b[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
(Worth 20 points, will give brainliest if right)
If (r, s) is the solution to the system of equations, what is the value of r?
−8r − 8s = 100
r − 2s = 10
adian picks apples at the rate of 11 apples every minute. how many apples would he pick in 36 minutes
Answer:
Adian would pick 396 apples in 36 minutes.
Step-by-step explanation:
Therefore, in 1 minute, Adian picks 11 apples.
In 36 minutes, he will pick:
11 apples/minute x 36 minutes = 396 apples.
Therefore, Adian would pick 396 apples in 36 minutes.
Answer:
396 apples
Step-by-step explanation:
adian picks apples at the rate of 11 apples every minute
So in order to find out how many he picks in 36 minutes we just multiply 36 by 11
36 x 11 = 396 apples in 36 minutes
Hope this helps!
Brainliest and a like is much appreciated.
XY and BD are parallel lines. Work out BXC give a reason for each angle you work out
For XY and BD are parallel lines,
a) Complete sentence: Angle XBC = 55 degrees because XB = XC and angles opposite to equal sides of a triangle are equal.
b) The angle XBC is 55 degrees due to the equal sides XB = XC, and angle BXC is 125 degrees as the sum of angles in a straight line is 180 degrees.
Working out angle BXC:
Angle XBC = 55 degrees (given)
Angles XBC and BXC form a straight line, so:
Angle BXC = 180 - 55 = 125 degrees (sum of angles in a straight line)
Reasoning for each angle:
Angle XBC is given as 55 degrees because XB = XC and angles opposite to equal sides of a triangle are equal.
Angle BXC is found by subtracting the given angle XBC from the sum of angles in a straight line (180 degrees).
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The question is -
XY and BD are parallel lines.
X is a point on AB and C is a point on BD.
XB = XC.
a) complete this sentence.
Angle XBC = 55 Degrees Because . . .
b) Work out angle BXC.
give a reason for each angle you work out.
List three sides to a right triangle. Explain how you can use the Pythagorean theorem to know that your three sides will create a right triangle.
Answer: Three sides of a right triangle are the lengths of its legs and the length of its hypotenuse.
To know that three given sides will create a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. Symbolically, if a, b, and c are the lengths of the sides of a right triangle, with c being the hypotenuse, then:
c^2 = a^2 + b^2
Therefore, if we are given the lengths of three sides, we can square the lengths of the legs, add them together, and then take the square root to find the length of the hypotenuse. We can then compare the squared length of the hypotenuse to the sum of the squares of the legs. If they are equal, the three sides form a right triangle. If the squared length of the hypotenuse is greater than the sum of the squares of the legs, the three sides form an obtuse triangle. If the squared length of the hypotenuse is less than the sum of the squares of the legs, the three sides form an acute triangle.
Step-by-step explanation:
The measurement of an angle is 3/4 the measurement of its complement. What is the measure of the angle?
Answer:
270
Step-by-step explanation:
360×3/4=270 as per given information in the qustion a complete circle is 360 so then 3/4 × 360
NO EXPLANATION JUST ANSWER!
Answer: 1456 square yds
Step-by-step explanation: Please mark brainliest and give thanks!
Answer:728
Step-by-step explanation:
V=abc=19*14*c=266c=3724
c=14
S=(19c+14c+14*19)=33c+266=33*14+266=728
What is the probability of a surveyed college student having a hard time falling asleep on 3 or more days in the last week
Answer:
Without more information about the specific survey and population being surveyed, it is difficult to provide a precise answer to this question. However, I can provide some general information on how probabilities can be calculated in surveys.
Assuming that the survey is a representative sample of college students and that the question about difficulty falling asleep is a binary (yes/no) question, we can calculate the probability of a surveyed college student having a hard time falling asleep on 3 or more days in the last week as follows:
1. Determine the total number of surveyed college students who answered the question about difficulty falling asleep.
2. Determine the number of surveyed college students who reported having a hard time falling asleep on 3 or more days in the last week.
3. Divide the number of surveyed college students who reported having a hard time falling asleep on 3 or more days in the last week by the total number of surveyed college students who answered the question about difficulty falling asleep.
For example, if 1,000 college students were surveyed and 800 of them answered the question about difficulty falling asleep, and 200 of those 800 reported having a hard time falling asleep on 3 or more days in the last week, then the probability of a surveyed college student having a hard time falling asleep on 3 or more days in the last week would be 200/800, or 0.25, or 25%.
Algebraic proofs geometry
The method used to prove the values of the variables consists of solving the equations as presented in the following section.
What is an equation?An equation is a statement of equivalence between two expressions which is indicated by joining them with an '=' sign.
8. Statement [tex]{}[/tex] Reasons
(5·y - 1)/2 = 7 [tex]{}[/tex] Given
5·y - 1 = 2 × 7 [tex]{}[/tex] Multiplicative property of equality
5·y = 2 × 7 + 1 = 10 [tex]{}[/tex] Additive property of equality
5 = 10/5 = 2 [tex]{}[/tex] Division property of equality
9. Statement [tex]{}[/tex] Reasons
10·k - 4 = 2·k - 20 [tex]{}[/tex] Given
10·k = 2·k - 20 + 4 = 2·k - 16 [tex]{}[/tex] Additive property of equality
10·k - 2·k = 8·k = -16 [tex]{}[/tex] Subtraction property of equality
k = -16/2 = -8 [tex]{}[/tex] Division property of equality
10. Statement [tex]{}[/tex] Reasons
-8·(w + 1) = -5·(w + 10) [tex]{}[/tex] Given
-8·w - 8 = -5·w - 50 [tex]{}[/tex] Distributive property of equality
-5·w + 8·w = 3·w = 50 - 8 = 42 [tex]{}[/tex] Subtraction property of equality
4 = 42/3 = 14 [tex]{}[/tex] Division property of equality
11. Statement [tex]{}[/tex] Reasons
14 - 2·(x + 8) = 5·x - (3·x - 34) [tex]{}[/tex] Given
14 - 2·x - 16 = 5·x - 3·x + 34 [tex]{}[/tex] Distributive property of equality
2·x + 2·x = 4·x = -2 - 34 = -36 [tex]{}[/tex] Subtraction property of equality
x = -36/4 = -9 [tex]{}[/tex] Division property of equality
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6 A farmer has 2 400 sheep. He loses 32 and a half % due to the drought. After that he loses 15% due to sickness. How many sheep does he have now?
Answer: The farmer has 1377 sheeps.
Step-by-step explanation:
Farmer loses sheeps due to drought = 32½% of 2400
32½% of 2400
= 65 × 2400 × 1
2100
After cutting it will be,
65×12
=780
Number of sheeps that are left with him = 2400 - 780
=1620
After that,
The farmer loses due to sickness = 15% of 1620
15% of 1620
= 15 × 1620
100
After cutting it will be,
3 × 81
= 243
Total amount of sheeps that the farmer loses = 780 + 243
= 1023
Now the number of sheeps he has is 2400-1023
= 1377
The largest marine animal is the blue whale, with an average mass of about 1.7×105 1.7 × 10 5 kg. The largest land animal ever is thought to be a dinosaur that had a mass of about 8×104 8 × 10 4 kg. What is the approximate difference in mass between these two animals
The approximate difference in mass between these two animals is 154,000 kg.
Describe Algebra?Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It is a broad area of study that includes a wide range of topics, such as equations, inequalities, functions, polynomials, matrices, and more.
Algebraic expressions are composed of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and logarithms. Equations, on the other hand, are mathematical statements that assert the equality of two algebraic expressions. Inequalities are mathematical statements that assert the relationship between two algebraic expressions using the symbols "<", ">", "<=", or ">=".
Functions in algebra are mappings from one set of numbers to another set of numbers that obey certain rules. These rules may involve properties such as continuity, differentiability, and invertibility.
The difference in mass between these two animals is:
1.7 x 10⁵ kg - 8 x 10⁴ kg = 1.54 x 10⁵ kg
Therefore, the approximate difference in mass between these two animals is 154,000 kg.
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