Solve the compound inequality for x and identify the graph of its solution.
x+7>3 and x-5≤-1
O A. Solution: x<-4 or x ≥ 4
-5-4-3 -2 -1 0 1 2 3 4 5
OB. Solution: x>-4 and x≤ 4
-5-4-3 -2 -1 0 1 2 3 4 5
O C. Solution: x>-4 and x≤ 4
-5 -4 -3 -2 -1 0 1 2 3 4 5
OD. Solution: x²-4 and x < 4

The solution for the given inequality will be x≤ -3 or x≥ 5. Thus, the correct option is B.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

For the given inequality the solution can be found as,

         3|x-1| ≥ 12

         x-1 ≥ 4

         x ≥ 5

         3|x-1| ≥ 12

         - x + 1 ≥ 4

         -x ≥ 3

         x ≤ -3

Hence, the solution for the given inequality will be x≤ -3 or x≥ 5. Thus, the correct option is B.

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[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's evaluate ~

[tex]\qquad \sf  \dashrightarrow \: 2 {x}^{2} - 1[/tex]

plug in the value of x :

[tex]\qquad \sf  \dashrightarrow \: 2(3) {}^{2} - 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2(9) - 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: 18 - 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: 17[/tex]

The required value is 17

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Answer:  [tex]\textsf{Option B, 17}[/tex]

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Given:  [tex]\textsf{2x}^2\textsf{ - 1}[/tex]

Find: [tex]\textsf{When x = 3}[/tex]

Solution: In order to find the value when x is equal to 3 we just need to equate any x to the value of 3 and simplify.

Plug in the values

Simplify the expression

Therefore, the answer that would make most sense would be option B, 17.

The correct option is Option A: [tex]16^{3x/4}[/tex] is equivalent to the expression  [tex](\sqrt[4]{16})^{3x[/tex].

The rules of the exponent are

(a) [tex]a^m*a^n=a^{m+n[/tex]

(b)[tex]a^m/a^n=a^{m-n[/tex]

(c)[tex](a^b)^c=a^{bc}[/tex]

(d) [tex]\sqrt[n]{a}=a^{1/n[/tex]

here the given expression is [tex]16^{3x/4}[/tex]

we can rewrite the expression as

[tex]16^{3x/4}[/tex]

as we know by the rule of the exponent that    [tex](a^b)^c=a^{bc}[/tex]

=[tex](16^{1/4})^{3x[/tex]

as we know by the rule of the exponent  [tex]\sqrt[n]{a}=a^{1/n[/tex]

=[tex](\sqrt[4]{16})^{3x[/tex]

Therefore the correct option is Option A: [tex](\sqrt[4]{16})^{3x[/tex]

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Answer:

11

Step-by-step explanation:

The distance Leah would have to walk home is 1.5 miles

From the question, we are to determine the distance Leah will have to walk home

From the given information,

Price of journey in pounds = 3 + 2 × distance in miles

Let the distance be d

Then,

Price of journey in pounds = 3 + 2d

Since Leah has £5, we can write that

5 = 3 + 2d

5 - 3 = 2d

2 = 2d

∴ d = 2/2

d = 1 mile

This means her money can only cover 1 mile

But the journey to her home is 2.5 miles

Therefore, she will have to walk

2.5 mile - 1 mile  = 1.5 miles

Hence, the distance Leah would have to walk home is 1.5 miles

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Answer:

Angles G and H are congruent.

Step-by-step explanation:

Answer:

7/9

Step-by-step explanation:

Divide the numerator and denominator by 4.

28/36 = 7/9

Answer:

7/9

Step-by-step explanation:

28 and 36 are both divisible by 4.

28÷4 is 7 and

36÷4 is 9

28/36 = 7/9

Answer:

6

Explanation:

[tex]\textsf {The range of a data representation refers to difference of the smallest and }\\\textsf {greatest possible values. }[/tex]

[tex]\textsf {Here :}[/tex]

[tex]\textsf {smallest value = 5}\\\textsf {greatest value = 11}[/tex]

[tex]\textsf {Then the range will be :}\\\implies \textsf {greatest value - smallest value}\\\implies \mathsf {11 - 5}\\\implies \mathsf {6}[/tex]

Answer:

R

H

S

=  cos

2

x

Step-by-step explanation:

Hope this helped!

Answer:

Inequality would be the answer

Answer:

The first statement is true so Shannon is incorrect.

Step-by-step explanation:

Volume of the pyramid with base  20 and h = 6

= 1/3 * base area * height

= 1/3 * 20 * 6

= 40 unit^3.

Answer: In between the red and yellow ribbons

Step-by-step explanation:

When something is rotated 180 degrees, you basically just mirror it. Since this pinwheel has an uneven amount of ribbons, there isn't a ribbon opposite of it, so it would be between red and yellow.

The function that best models the scenario is as follows;

x < 5 :  C(x) = 3.45x + 1

x ≥ 5  : C(x) = 3x + 1

A local candy shop sells boxes of chocolate for $3.45 each.

This is when the consumer purchase less than 5 boxes of chocolates.

Therefore,

x = number of boxes

when x < 5

C(x) = 3.45x + 1

If a customer purchases five or more boxes, the cost is only $3 per box. Therefore,

when x ≥ 5

C(x) = 3x + 1

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Answer:

Domain: All real numbers

Range: y≤4

Step-by-step explanation:

x=66°

180-118=62°

180-52+62=66°

hope this helps

The domain and the range of an exponential parent function, that is, y = eˣ are equal to all real numbers and non-negative numbers, respectively. (Correct choice: C)

In this problem we should determine what an exponential parent function is. The most common exponential functions have the following form:

[tex]y = A\cdot e^{B\cdot x} + C[/tex]     (1)

(1) is an exponential parent function for A = 1, B = 1 and C = 0.

All functions are relations with a domain and range, the domain is an input set related to the range, that is, an output set. In the case of an exponential parent function, the domain and the range of the expression are [tex]\mathbb{R}[/tex] and y ≥ 0, respectively. (Correct choice: C)

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Answer:

Step-by-step explanation:

given

cos(30°) = [tex]\frac{adjacent}{hypotenuse} \\[/tex]

cos(30°) = [tex]\frac{b}{c} \\[/tex]

cos(30°)=[tex]\frac{b}{16}[/tex]

b = 16cos(30°)

b [tex]16(\frac{\sqrt{3} }{2})\\ = 8\sqrt{3}[/tex]

Answer:

26 gm

Step-by-step explanation:

Tin is   1   out of (9+1)   = 1/10 th

1/10th * 260 gm  =   26 gm

Answer:

a. 1/3pi+kpi and 2/3pi+kpi

Step-by-step explanation:

2Sec²x

=2+2tan²x-(tan²x)²=-1

Let tan²x=u

-u²+2u+2=-1

-u²+2u+3=0

u²-2u-3=0

(u+1)(u-3)=0

u=-1,u=3

(tan x)²=-1(No solution)

(tan x)²=3

>>tan x=±sqrt(3)

I) tan x=sqrt(3)

>>tan(pi/3)=sqrt 3

Tan(pi+A) =tanA

Tan(pi+pi/3)=tan(pi/3)

>>tan(4/3pi)=sqrt(3)

>>x=4/3pi and 1/3pi

General solution: 1/3pi+kpi

ii) tan x=-sqrt(3)

x=2/3pi(At 2nd quadrant)

x=5/3pi(at 4th quadrant)

General solution: 2/3pi+kpi

Answer:

83 x 391 - 83 x 15 = 83 x (391 - 15)

Step-by-step explanation:

BODMAS is stands for Bracket Of Division Multiplication Addition and Subtraction.

left hand side:

83 × 391 - 83 × ____   = 32453 - 83 × ____

right hand side:

83  × (391 - 15) = 83 × 376 = 31208

equating both sides

32453 - 83 × ____ = 31208

32453 - 31208 = 83 × ____

1245 ÷ 83 = 15

hence the answer is 15.

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Answer:

Divide the shape in two pieces:

A rectangle and a triangle

Find area of rectangle:

A=length*width=5*4=20m^2

Find area of triangle:

base of triangle=5-2=3m

height of triangle=8-4=4m

Area=(1/2)*base*height

=(1/2)(4)(3)=6m^2

Total area=6+20=26m^2

Hope it helps!

Answer:

A, B and E

Step-by-step explanation:

Answer: A,B and E i did the test

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

the conversion is:

0.50 sen /g = 5 RM/kg

First, we know that

1sen = 0.01RM

Then we can change:

0.50 sen /g = 0.50*(0.01 RM) /g = 0.005 RM/g

Now we use the relation:

1g = 0.001kg

So we can rewrite:

0.005 RM/g = 0.005 RM/(0.001kg) = 5 RM/kg

So the conversion is:

0.50 sen /g = 5 RM/kg

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Answer:

19-73 19-73 and a very nice little

Step-by-step explanation:

19-73 19-73 and he changed

Answer:

From the graph in the attachment, it is clear that Option A is correct.

Step-by-step explanation:

The given inequalities are x - 4y ≤ 4 and y < x + 1.

Let us take the first line x - 4y ≤ 4 and remove the inequality and add equality, x - 4y = 4.

Now, we will find the intercept points. Putting y = 0 we will get x = 4 and putting x = 0 we will get y = -1. So, the points are (4,0) and (0,-1).

When we will solve the inequality, we find that portion above the graph satisfies this inequality.

Let us take the second line y < x + 1 and remove the inequality and add equality, y = x + 1.

Now, we will find the intercept points. Putting y = 0 we will get x = -1 and putting x = 0 we will get y = 1. So, the points are (-1,0) and (0,1).

When we will solve the inequality, we find that portion below the graph satisfies this inequality.

All these conditions satisfy the Option A.

The diagram is in the attachment.

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[tex]\log_7(x+9)-\log_710=\log_77\qquad(x > -9)\\\log_7\dfrac{x+9}{10}=1\\\dfrac{x+9}{10}=7\\x+9=70\\x=61[/tex]

Answer:

None of the options are correct

О E. 289.2 cm

Step-by-step explanation:

Volume of a cylinder = v = л r² h

л = 3.1416     (aprox)

r = radius

h = height

8177 = 3.1416 * 3² * h

8177 = 3.1416 * 9 * h

8177 = 28.2744 * h

8177/282744 = h

h = 289.2 cm