Solve the following inequality: -3x - 8 > -32

Given:

f(x) = 2x - 5

g(x) = 4x + 3

(f + g)(x) can be found as,

Therefore, (f + g)(x)=6x-2.

Answer:

80% chance of winning$100

Step-by-step explanation:

50/1000 , 10/1000

=> 0.05, 0.01

0.05 - 0.01

0.04 ÷ 0.05

0.8 × 100

=> 80%

Answer:

the sine of the angle of one corner equals the opposite side divided by the hypotenuse.

the cosine of the angle of one corner equals the adjacent side divided by the hypotenuse.

the tangent of the angle of one corner equals the opposite side divided by the adjacent side.

Answer:

what he said is right! didnt let me comment so I just wanted to let yall know thats right!

sin(70)cos(25) - cos(70)sin(25) simplifies to approximately 0.7071.

To calculate the expression sin(70)cos(25) - cos(70)sin(25), we can use the trigonometric identities:

sin(A - B) = sin(A)cos(B) - cos(A)sin(B)

Applying this identity to the given expression, we have:

sin(70)cos(25) - cos(70)sin(25) = sin(70 - 25)

The angle 70 - 25 = 45 degrees, so we can rewrite the expression as:

sin(45)

The value of sin(45) is equal to 1/√2 or approximately 0.7071.

sin(70)cos(25) - cos(70)sin(25) simplifies to approximately 0.7071.

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Answer:

94.2 ft of fencing

Step-by-step explanation:

To answer this, find the circumference, C, of the garden, using the circumference formula C = 2(pi)r.

Here, with r = 15 ft, we get C = 2(3.14)(15 ft) = 94.2 ft of fencing will enclose this garden.

Answer:

73 and 15

Step-by-step explanation:

I made two variables for this:

x = larger number

y = smaller number

Write an equation for "the sum of two number is 88" and you get:

x + y = 88

Write an equation for "four times the smaller number is subtracted from the larger number" and you get:

x - 4y = 13

I do not want an equation with both x and y in it, so I will rewrite the first one and use substitution in the second one:

x + y = 88   -- move the x to the other side

y = 88 - x

x - 4y = 13 -- substitute for y

x - 4(88 - x) = 13 -- multiply by 4

x - 352 + 4x = 13 -- move -352 to the other side, combine x's

5x = 365 -- divide by 5

x = 73

Now that I know x is 73, I go back to my first equation (x + y = 88) and I get:

73 + y = 88 -- subtract 73 from both sides

y = 88 - 73

y = 15

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer:

x equals 73

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

the . means times and 5 times 3 is 15

Answer:

x5+3x3-2x2-2x+7x-1

Step-by-step explanation:

x5+3x3-2x2-2x+7x-1

The given series is convergent and the first term is 4 and the common ratio is -0.5 and the sum of the series is 8/3 .

The given series is 4 - 4/2+ 4/4 - 4/8 +...

We can see that the first term of the geometric series is 4

Hence a = 4

The second term is  -4/2 and the third term is 4/4

Hence r = 4 ÷ (-4/2) = -4/2 ÷ 4/4 = - 1/2 or -0.5

Since the common ratio is less than 1 we can say that the series is convergent.

Now for a convergent series we know that the sum of the terms of the series is equal to

S = a / (1-r)

or, S = 4 / (1-(-0.5))

or, S = 4 / 1.5

or, S = 8/3

Hence the sum of the convergent series is 8/3 .

Both the ratio test and the root test are based on a comparison with a geometric series and hence function in comparable scenarios.

In fact, if the ratio test works (that is, if the limit exists and is not equal to 1), then so does the root test; the contrary is not true. The root test is thus more broad, although in practise, determining the limit for regularly encountered kinds of series is frequently challenging.

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Using common factor method, sum of the given expressions is 17.14m + 9.37

what is common factor ?

In mathematics, a common factor is a factor that two or more numbers have in common. For example, the numbers 12 and 18 have common factors of 1, 2, 3, and 6. The greatest common factor (GCF) is the largest number that divides evenly into two or more numbers.

In algebra, we often use the term "common factor" when referring to expressions. When two or more algebraic expressions have a factor in common, we can use the distributive property to factor out the common factor.

According to the question:
To add the expressions (5.19+4m)+(4.18+3.95m), we can first group the like terms:

(5.19 + 4.18) + (4m + 3.95m)

9.37 + 7.95m

So, the sum of the expressions is:

(5.19+4m)+(4.18+3.95m) = 9.37 + 7.95m

Now, we can use the distributive property to factor out a common factor of m from 7.95m:

9.37 + 7.95m = 4m + (5.19 + 7.95)m

We can factor out a common factor of 1 from (5.19 + 7.95)m:

4m + (5.19 + 7.95)m = (4 + 5.19 + 7.95)m

Adding the coefficients, we get:

4 + 5.19 + 7.95 = 17.14

Therefore, the sum of the expressions is:

(5.19+4m)+(4.18+3.95m) = (4m+5.19)+(3.95m+4.18)= 17.14m + 9.37.

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Given:

Total No. of students in the travel club = 61

Students visited Country A = 21

Students visited Country B = 29

Students visited Country C = 25

Students visited Country A and B = 8

Students visited Country C only = 14

Students visited Country A only = 11

No. of members who have not been to any country = No. of members who have been to all 3 countries ( *let's call the two of them x since they are equal)

Required:

a. No. of students whho have been to all 3 countries

b. No. of studens who have been to Country B only

Solution:

Total Number of Students = A + B + C - AB - AC -BC + ABC + NONE

61 = 21 + 29 + 25 - 8 - AC - BC + X + X

61 = 67 - AC - BC + 2X

AC + BC = 67 - 61 + 2X

AC + BC = 6 + 2X

Only in Country A = A - AB - AC + ABC

11 = 21 - 8 - AC + X

11 = 13 - AC + X

AC = 13 -11 + X

AC = 2 + X

Only in Country C = C - AC - BC + X ( but, AC = 2 + X )

14 = 25 - ( 2 + X ) - BC + X

14 = 25 - 2 - X - BC + X

BC = 25 - 2 -14 -X + X

BC = 9

Only in Country B = B - AB - BC + ABC

Only in Country B = 29 - 8 - 9 + X

Only in Country B = 12+ X

Also, we know that AC + BC = 6 + 2X ( but, AC = 2 + X and BC = 9 )

Thus,

AC + BC = 6 + 2X

( 2 + X ) + 9 = 6 + 2X

2 + X + 9 = 6 + 2X

11 + X = 6 + 2X

11 - 6 = 2X - X

5 = X

If X = 5 then,

Only in Country B = 12+ X = 12 + 5 = 17

and AC = 2 + X = 2 + 5 = 7

Answer:

a. No. of students whho have been to all 3 countries = 5

b. No. of studens who have been to Country B only = 17

Part A: There are 28 green beans in the garden. Part B: There are 80 plants that are either pumpkin or tomato. Part C: There are 52 more corn plants than cucumber plants.

A circle graph, often called a pie chart, is a circular graph with sectors on it, each representing a particular category or set of data. Each sector's area or angle is proportionate to the amount it stands for. In data visualisation, circle graphs are frequently used to show the relative sizes or proportions of several categories or groups within a dataset. They can instantly convey the distribution of data without the need for laborious numerical calculations, which makes them effective for presenting data that is divided into discrete groups. However, if the data is not presented in a clear and simple manner or if the sectors are not precisely drawn to scale, circle graphs may be deceiving.

Part A: The percentage of green beans in the circle graph is 14%.

14% of 200 = 0.14 x 200 = 28

Part B: The circle graph shows:

pumpkin plants and tomato plants is 20% + 20% = 40%.

40% of 200 = 0.40 x 200 = 80

Part C: The corn plants is 36% and the percentage of cucumber plants is 10%.

36% of 200 - 10% of 200 = (0.36 x 200) - (0.10 x 200) = 72 - 20 = 52

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Answer:

There's no question-

Step-by-step explanation:

If my bowl of easter candy has colorful foil-wrapped chocolate eggs. there are 5 gold, 7 blue, and 10 pink. The probability that she reaches in without looking and gets a chocolate candy wrapped in pink foil is 0.45.

Total color = 5 gold + 7 blue + 10 pink

Total color = 22

Now let find the probability that she reaches in without looking and gets a chocolate candy wrapped in pink foil

Probability (pink) = 10/22

Probability (pink) = 0.45

Therefore the  probability of Callie Brooke getting a pink foil-wrapped chocolate egg is 10/22, or approximately 0.45.

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Answer:

Scale factor is .25.

Step-by-step explanation:

Side A is .25 times 35 which is 8.75. Side b is .25 (25)= 6.25

Answer:

B: The scale factor is 0.25.

C: The length of side A is 8.75 cm.

E: The length of side B is 6.25 cm.

Step-by-step explanation:

To find the answer of 8.75 in C multiply 35 x .25

To find E multiply 25 by .25.

And the scale factor is .25 becuase the original is 1/4 the new perimeter.

To find the equation of a line that passes through the points (5, -3) and (-2, -4) in standard form, we can use the point-slope form of a linear equation and then convert it to standard form.

Determine the slope (m) of the line using the formula:

   m = (y2 - y1) / (x2 - x1)

For the given points (5, -3) and (-2, -4), we have:

   m = (-4 - (-3)) / (-2 - 5) = (-4 + 3) / (-2 - 5) = -1 / (-7) = 1/7

Use the point-slope form of a linear equation:

   y - y1 = m(x - x1)

Using the point (5, -3), we have:

   y - (-3) = (1/7)(x - 5)

Simplifying:

   y + 3 = (1/7)(x - 5)

Convert the equation to standard form:

Multiply both sides of the equation by 7 to eliminate the fraction:

   7y + 21 = x - 5

Rearrange the equation to have the x and y terms on the same side:

   x - 7y = 26

The equation of the line in standard form that passes through the points (5, -3) and (-2, -4) is x - 7y = 26.

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Projectile B begins its descent 1 seconds before Projectile A does.

In Mathematics and Geometry, the y-intercept of any graph or table such as a quadratic equation or function, generally occurs at the point where the value of "x" is equal to zero (x = 0).

By critically observing the table shown in the image attached above, we can reasonably infer and logically deduce the following y-intercept of Projectile A:

y-intercept = (0, 44).

Maximum height = (4, 300).

When t = 0, the y-intercept of Projectile B can be calculated as follows;

h(t) = -16t² + 96t

h(0) = -16(0)² + 96(0)

h(0) = 0.

For the maximum height, we have:

h(t) = -16t² + 96t

h'(t) = -32t + 96

32t = 96

t = 96/32

t = 3

Difference in time = 4 - 3

Difference in time = 1 seconds.

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Now we know PR∥QX , according to construction with transversal line TX.

∠PTS=∠QXS (Alternate angle)

In △PTS and △QSX

∠PTS=∠QXS (Alternate angle)

∠PST=∠QSX(vertically opposite angles)

PS=SQ(S is mid point of PQ)

△PTS≅△QSX(AAS rule)

So, TP=QX(CPCT)

As we know, TP=TR (T is midpoint)

Hence, TR=QX

Now, in quadrilateral TSQR

TS∥QR

Hence proved.

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Step-by-step explanation:

for such simple equations and only 2- dimensional problems, a request like this (which of the following points is a solution for the system ?) can be solved (often) the fastest by just putting the point coordinates in, calculate and see, if the equations hold or not.

the formal way to solve the system is usually done, when there are no solution options, and we need to find them ourselves.

to be sure you understand what I mean, I am demonstrating here both for the first 2 systems :

2x - y = 7

3x + y = 3

(2, -3)

1. the formal method. with experience I see immediately that when just adding the 2 equations, y is eliminated, and we can solve only for x.

this looks like

2x - y = 7

3x + y = 3

----------------

5x 0 = 10

so,

5x = 10

x = 2

and we get from e.g. the first equation

2×2 - y = 7

-y = 3

y = -3

2. the trial method. often accompanied with the mentioned experience factor that helps what option to try first.

but I am picking a wrong one first to show you what happens in that case.

let's pick (-2, -3) :

2×-2 - -3 = 7

-4 + 3 = 7

-1 = 7

no, the equation does not hold, -1 is definitely not equal to 7. so, that cannot be the answer.

mostly we find that already after trying the first equation, but sometimes only after the second equation (both need to hold for an actual solution).

so, when we pick (2, -3) we get

2×2 - -3 = 7

4 + 3 = 7

7 = 7 OK

3×2 + -3 = 3

6 - 3 = 3

3 = 3 OK

yeah, (2, -3) is the solution.

now for the second system.

2x + 3y = 8

3x - 2y = -14

(-2, 4)

1. formal method.

we can multiply or divide whole equations by a factor before adding them up.

since we have no clear option for elimination (as we had for the previous system), we need to bring them to factors that when added a whole variable disappears. this is similar to bringing fractions to the same denominator.

y still has a + and a - term in the 2 equations. so, I am going to eliminate y.

we multiply the first equation by 2, and the second by 3, and then we add then up.

this looks like

4x + 6y = 16

9x - 6y = -42

----------------------

13x 0 = -26

13x = -26

x = -2

using e.g. the first equation with that x :

2×-2 + 3y = 8

-4 + 3y = 8

3y = 12

y = 4

2. the trial method.

because the equating looked different in their structure compared to the first system, I picked the option to try that I considered the most different to the solution of the 1st system. and that was (-2, 4)

2×-2 + 3×4 = 8

-4 + 12 = 8

8 = 8 OK

3×-2 - 2×4 = -14

-6 - 8 = -14

-14 = -14 OK

yeah, (-2, 4) is the solution.

and now to the other 2 systems that actually do not have a defined solution (as explained) :

3x - 2y = 12

6x - 4y = -24

no solution (because when multiplying the first equation by 2 and then subtracting the second from the first we get 0 = 36, which is impossible, a contradiction, so, there is not a single solution possible).

2x - 3y = 6

-4x + 6y = -12

infinitely many solutions, as the second equation is just the first equation multiplied by -2. so, it is in its core the same equation as the first, and therefore we have only one equation but with 2 variables, and that gives infinitely many solutions.

Answer:

#1 = 25

#2 = -3

#3 = 17

#4 = 5

#5 = -15

Answer:

P(both students passed the exam) = 0.61948

Step-by-step explanation:

From the given information:

P(both students passed the exam) = P(both are science students or both are art major students or one is from each group)

= P (both are science students) + P(both are art students) + P(one from each group)

where;

P (both are science students) = (50/100) (0.9) × (44/99) × (0.9) = 0.18

P(both students are art) = (50/100) (0.7) × (49/99) 0.7 = 0.1213

P(one of the student are from each group) = (50/100) (0.9) ×(50/99) (0.7) + (50/100) (0.7)× (50/99)(0.9) =0.3182

P(both students passed the exam) = 0.18 + 0.1213 + 0.3182

P(both students passed the exam) = 0.61948

Is 9 kg bigger than 4 pounds? Nine kilograms is definitely heavier, as one kilogram is equivalent to 2.2 pounds.

Answer:

5 ft^2

Step-by-step explanation:

5/2 * 3/2 * 4/3 = 60/12

Answer:

3 ft.

Step-by-step explanation:

15:20 and x:4 you can cross multiply or if you reduce 15:20, the answer is 3:4

Answer:

Here's your answer .

hope it helps you

Answer:

I'm pretty sure it's -4

Step-by-step explanation:

If you substitute in -2, you get e(-2)= -(-2)+ -6

which is equal to 2-6

2-6=-4

Answer:

e(-2)=-4

Step-by-step explanation:

e(-2)=-(-2)+-6

=2-6

=-4

Answer:

30

Step-by-step explanation:

Answer:

About -4.286

Step-by-step explanation:

First, let's set up the equation.

(24 + 6)/(3 - 2 [4 + 1])

Now, let us do the parenthesis first. (4 + 1). While we are at it, we can also do 24 + 6.

30/(3 - 2[5)]

Now, -2(5)

30/3 - 10

Let us do 3 - 10

30/-7

Lastly, 30/-7, which unfortunately, is a non-terminating decimal, which is about:

-4.286, rounded to the nearest thousandth.

Hope this helps!

Answer: a coordinate plane is used in order to track the location of the object.

Translations are congruence transformations that move an object, without changing its size or shape

Dilations are transformations that generate an enlargement

Step-by-step explanation:

Check the picture below.

so the bag full of gold is 112Kgs, one quarter of that is 28Kgs, but hold the mayo!! our one quarter of gold only bag is not 28Kgs is really 28Kgs and 252grams extra, well, we know the gold reduced by one quarter, so that'd be the 28Kgs, and the slack is just the red part in the picture, the empty part atop of the bag, the 3/4 of the bag.

Now, we know 3/4 of the bag is 252grams, so if we divide the 252grams by 3, we'll know how much each of those three quarters weight.

Let me put it another way, we have four quarters, four of the same, we have three of the same above in red, we want to know how many grams one of those three of the same weight, well, since all three are 252g, one third of that must be what one weights.

\(\cfrac{252}{3}\implies 84\qquad \begin{array}{llll} \textit{each of the three quarters in red}\\ \textit{weight 84 grams, so the bottom of}\\ \textit{the quarters must also weight 84 grams} \end{array}~\hfill~\underset{ empty~bag }{\stackrel{ 252~~ + ~~84}{\text{\LARGE 336}g}}\)