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After solving the inequality we get the value of x as x ∈ (₋5,3)

Given the inequality is 2 |x + 1|  < 8

Divide both sides of the inequality by the coefficient of variable.

|x + 1| < 8/2

Reduce the fraction

|x + 1| < 4

Now convert the absolute inequality to standard inequality.

₋4 < x₊1 < 4

separate compound inequalities into system of inequalities.

x ₊ 1 > ₋4  (1)

x ₊ 1 < 4 (2)

for (1) x ₊ 1 > ₋4

rearrange variables to the left side of the equation.

x > ₋4 ₋1

calculate the sum.

x > ₋5

for (2) x ₊ 1 < 4  (2)

rearrange the terms.

x < 4 ₋ 1

x < 3

therefore ₋5 < x < 3

Hence we get the value ranging from (₋5 , 3)

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thirty-seven billion nine hundred five million

Answer:

hskekndndndokn jskjskiwijsnjskjskiwijsn kkskskskjd kdkdkdndndn

Step-by-step explanation:

Julie is correct because:

[tex]\frac{\sin A}{\tan A}=\frac{a/c}{b/c}=a/b=\tan A \\ \\ \frac{\sin B}{\cos B}=\frac{b/c}{a/c}=b/a =\tan B[/tex]

Answer:

{(5,1),(5,0),(1,0),(0,-3),(-3,0),(-4,-3),(2,5)}

Step-by-step explanation:

This is all I could get from the cropped out picture of the graph

The coordinate of point C that is 7/8 of the distance is 14

The given parameters are

C =7/8 from m to j

While the points are

M = 2

J = 18

The coordinate of point C that is 7/8 of the distance is calculated as

C = 7/8 * (J - M)

This gives

C = 7/8 * (18 - 2)

Evaluate

C = 14

Hence, the coordinate of point C that is 7/8 of the distance is 14

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For the given triangle ABC, the value of angle A = 64°.

For the given ΔABC;

∠A = 4x

∠B = 90

∠C = x + 10

By the sum of angles of triangle property;

∠A + ∠B +∠C = 180

Substitute the values;

4x + 90 + x + 10 = 180

Simplifying the equation;

5x = 180 - 100

5x = 80

x = 16

Put the value of x in angle A.

∠A = 4x

∠A = 4×16

∠A = 64°

Therefore, the value of angle A is found as 64°.

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hi

f(a+7)

f(x) =x²+5

by remplacing X by (a+7) :

then  f(a+7) = (a+7)²+5

                  =   a² +2*a*7 +49 +5

                  = a² +14a +54

Answer:

10°C

Step-by-step explanation:

c = [tex]\frac{F - 32}{1.8}[/tex]  Plug in 50 for F and solve for C

c = [tex]\frac{50-32}{1.8}[/tex]

C = [tex]\frac{18}{1.8}[/tex] Divide

c = 10

Answer:

the slope intercept form is 5y= -x+12

Answer:

(x+3)(x-3)

Step-by-step explanation:

When factoring x^2-9 you'd look for square multiples of -9.

Because 3×3 is 9, 3 is your square. You can't just use (x+3) because your outcome is a -9. Which is why your answer would be (x+3)(x-3)

Answer:

Step-by-step explanation:

First I would begin by dividing both sides by 4

4(x+y) = 48     4/4 = 1      48/4 = 12

x + y = 12

next I'm going to assume this is needed in y = mx+b format so I will solve for y by subtracting the x:

y = -x + 12

this line has a slope of -1 and has a y-intercept at 12.

Answer:

Step-by-step explanation:

Whats 21 - 20 x 2?

21 - 20 x 2 =

21 - 40 =

-19

Answer: 24

A hyperbola is the locus of a point in a plane which moves in the plane in such a way that the ratio of its distance from a fixed point in the same plane to its distance from a fixed line is always constant, which is always greater than unity.

the fixed point is called the focus and the fixed line is directrix and the ratio is the eccentricity.

The general equation for the vertical hyperbola is

            [ (y-k)^2 / a^2 ] – [ (x-h)^2 / b^2 ] = 1

The conjugate axis of the vertical hyperbola is y = k

Length of the conjugate axis  = 2b

According to the question k = 2, h = -1, a = 4, b = 12

Length of the conjugate axis = 2b = 2 * 12  = 24

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This sequence's explicit formula is [tex]a_n=-5+(n-1)*10[/tex]

What is a sequence?

The common distinction is equal to:

10

The sequence's total is equal to:

40

This sequence's explicit formula is:

[tex]a_n=-5+(n-1)*10[/tex]

This sequence's recursive formula is:

[tex]a_n=a_((n-1))+10[/tex]

Next terms:

-5,5,15,25,35,45,55,65,75,85,95...

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There are a total of 36 possible answers in digit .

What is digits in math?

Let's assign three blanks for each digit of the unknown number. But let's fill in the tens digit because it is already specified.

_ 4 _

The last digit should be even to make it even. The possible digits for this are 2, 4, 6, and 8. The first digit could be any digit from 1 to 9. Therefore, the possible answers are

142  242  342  442  542  642  742  842  942

144  244  344  444  544  644  744  844  944

146  246  346  446  546  646  746  846  946

148  248  348  448  548  648  748  848  948

Therefore, there are a total of 36 possible answers.

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Answer:

principle (p)= $200

interest (I) =$9

Rate (R) = 6%

time (T)= ?

we know,

Time(T) = I×100÷P×R

= 9×100÷ 200×6

= 3÷4 years

The 5.1 cubic ft of water weighs 317.77 pounds

The weight of 5.1 cubic ft of water in tons is 0.16 tons

From the question, we are to calculate how much 5.1 cubic ft of water weigh in pounds

From the given information,

"one cubic foot holds 7.48 gallons of water"

Therefore,

5.1 cubic ft of water = 5.1 × 7.48 gallons of water

= 38.148 gallons of water

Also,

"one gallon of water 8.33 pounds"

That  is,

38.148 gallons of water = 38.148 × 8.33 pounds

= 317.77 pounds

Thus, 5.1 cubic ft of water weigh 317.77 pounds

For the weight in tons

NOTE: 1 pounds = 0.0005 tons

∴ 317.77 pounds = 0.0005 × 317.77 tons

= 0.158886 tons

≈ 0.16 tons

Hence, the weight of 5.1 cubic ft of water in tons is 0.16 tons

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Amelia went on a walk that was, She stopped to have lunch [tex]\frac{15}{4}[/tex] miles

when she had walked of the way [tex]\frac{12}{25}[/tex] miles. Amelia walk before lunch in

[tex]\frac{3}{25}[/tex] miles.

The mile is a customary unit of measurement in the United States and the United Kingdom that is based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. It is often referred to as the international mile or statute mile to distinguish it from other miles. In 1959, the statute mile was formally redefined with respect to SI units as precisely 1,609.344 meters. This resulted in a standardization of the statute mile between the British Commonwealth and the United States.

The unqualified term "mile" is typically understood to refer to the current international mile. The international mile may also be referred to as a land mile or a statute mile when it has to be distinguished from nautical mile.

The term "statute mile" in British English can apply to either the current international mile or any other variation of the English mile since the 1593 Act of Parliament, which established it as 1,760 yards. However, in American law, a statute mile is equivalent to a US survey mile. If it is obvious from the context, as in a discussion of the 2nd-century Antonine Itinerary that the distances are described in terms of miles rather than Roman miles, the qualifier to describe the type of mile being used may be omitted. Foreign and historical units that are translated into English as miles typically employ a qualifier to describe the kind of mile being used.

Now from the above given question:

She stopped to have lunch in [tex]\frac{15}{4}[/tex] miles

She had walked of the way in [tex]\frac{12}{25}[/tex] miles

[tex]\frac{15}{4}-\frac{12}{25} = \frac{60}{100}- \frac{48}{100} = \frac{12}{100}[/tex][tex]=\frac{3}{25}[/tex].

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[tex](\frac{-4}{5} )[/tex] in the form of Equivalent Fraction can be written as [tex]\frac{-4x}{15x}[/tex], where "x" is any integer.

As per the question statement, we are provided with a fraction, [tex](\frac{-4}{5} )[/tex].

We are required to rewrite the above mentioned fraction in the form of a general Equivalent Fraction.

To solve this question, we need to know what an equivalent fraction is.

Equivalent fractions are those fractions that have different numerators and denominators but are equal to the same value, when simplified.

For example, [tex](\frac{1}{2}, \frac{2}{4}, \frac{3}{6}, \frac{4}{8})[/tex] all equate to [tex]\frac{1}{2}[/tex] when simplified.

Now, for this case, equivalent fractions of [tex](\frac{-4}{5} )[/tex] are [tex](\frac{-8}{30}, \frac{-12}{45}, \frac{-16}{60},...)[/tex], where

[tex]\frac{-8}{30}=\frac{(-4)*2}{15*2}\\\frac{-12}{45}=\frac{(-4)*3}{15*3}\\ \frac{-16}{60}=\frac{(-4)*4}{15*4}[/tex]

i.e., the equivalent fractions of [tex](\frac{-4}{5} )[/tex] are in the form of  [tex]\frac{-4x}{15x}[/tex], where "x" can be any integer, (...-6, -5, -4, -3, -2, -1, 2, 3, 4, 5, 6...)

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This problem is related to the formation of a function. We need to know how an function is formed. Here it is given that there is a function which is affected by the value of t. Which means the value of t in  the function decides the value of that function.

Similarly we have to write the function as the variable r so that the value of function is related to the value of r.

h(r)=6-18r ; where 6 is the constant and 18r is the variable in the function.

Hence, the required function is  h(r)=6-18r.

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Step-by-step explanation:

good job then !

the first thing I see in the graphic is that

BG is half of BD (as a major definition of diagonals in a parallelogram).

BD on the other hand is the Hypotenuse (the side opposite of the 90° angle at A) of the triangle ABD.

to be able to use Pythagoras to get BD, I need to find the length of AB.

this I get from the triangle ABE. this is also a right-angled triangle. AE = 4cm. the angle B1 = 50°. the angle A = 90°.

so, the angle E1 = 180 - 90 - 50 = 40° (remember, the sum of all angles in a triangle is always 180°).

now we use the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

with a, b, c being the sides of the triangle, and A, B, C being the corresponding opposite angles.

so, we have here

AE / sin(50) = AB / sin(40)

4 / sin(50) = AB / sin(40)

AB = 4×sin(40) / sin(50) = 3.356398525... cm

so (Pythagoras),

BD² = AB² + AD² = 3.356398525...² + 9² =

= 11.26541106... + 81 = 92.26541106...

BD = 9.60548859... cm

BG = BD/2 = 4.802744295... cm

and now look at that.

because of the fact that I did not have to go through the other points, I chose the first approach that went through my mind.

and it showed that your teacher created an impossible (contradicting) scenario :

the angle of B1 does not fit to the ratios of the various line segments.

as you correctly calculated CD as 3 cm, that must mean that AB is also 3 cm.

that makes

BD² = 9² + 3² = 81 + 9 = 90

BD = 9.486832981... cm

BG = BD/2 = 4.74341649... cm

PLEASE, USE THIS VALUE.

there is a difference to my previous calculation. and the reason for this is : the 50° for B1 are not correct.

with AE = 4, AB = 3 and then BE = 5, we get

AE / sin(B1) = BE / sin(A)

4 / sin(B1) = 5 / sin(90) = 5

sin(B1) = 4/5 = 0.8

B1 = 53.13010235...°

and not 50° !!!!

Answer:

The last digit you multiplied by.

Step-by-step explanation:

It's not that hard, but here you go  :)

If you multiplied 12 by 11 you would get 2 as your last digit, because 2 is the last digit of 12. (12x11=132)

So for 123 by 11, following this pattern, 3  is the last digit of 123 so the answer must end in 3. (123x11=1353)

If you still don't get the pattern I'll give you a few more examples here:

If you multiply 1234 by 11 you would get a number ending in 4 because the last digit of 1234 is 4! (1234x11=13574)

So what would be the last digit of 12345?

Hope this was helpful!

(The answer was 5 btw)

Answer:13

Step-by-step explanation:(2)²+3(3)=4+9=13

Answer:

2a^n+ 3b

Differentiate w.r.t a

2na^n - 1

= 13

Concluding that m∠ J K L = m ∠ Q R S is an example of: substitution property of equality

The substitution property of equality states that 'If a variable x is equal to another variable y, then x can be substituted in place of y in any equation/expression and y can be substituted in place of x in any equation/expression.

Now, we are told that m ∠ J K L = m ∠ X Y Z and m ∠ X Y Z = m ∠ Q R S.

Thus, concluding that m ∠ J K L = m ∠ Q R S is an example of: substitution property of equality

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Explanation:

The given sequence is 5, 12, 33, 96, 285, ...

The sequence of increases is: 7, 21, 63, 189

Then notice,

Assuming this pattern keeps up, the next increment will be 189*3 = 567

We add this increment to the last term of the original sequence

285+567 = 852

The sequence is now 5, 12, 33, 96, 285, 852, ...

Work Shown:

9+15 = 24 students total

9 have glasses, so 9/24 = 0.375 = 37.5% of the class wears glasses.

(A∩B)∪(A∩C) using roster method is as follows:

(A∩B)∪(A∩C)  = {a, e, f}

Sets are an organized collection of objects that can be represented in set-builder form or roster form.

Therefore,

The universal sets is as follows:

U = {a, b, c, d, e, f, g, h}

The subsets are as follows:

A = {c, e, f}

B = {a, e, f}

C = {a, b, d, g, h}

Therefore, let's find (A∩B)∪(A∩C) using roster method.

The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.

Hence,

(A∩B) = {e, f}

(A∩C) = {a}

Finally,

(A∩B)∪(A∩C) = {a, e, f}

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Answer:

0.01

Step-by-step explanation:

Nearest hundredth is the second digit after the decimal point.

If the digit after hundredth is greater than or equal to 5, add 1 to hundredth. Else remove the digit.