[02.05] Solve for x: 3 − (2x − 5) < −4(x + 2) x < −8 x > −8 x < −3 x > −3

Answer:

Step-by-step explanation:

(LOOK AT THE PICTURE)

ΔADC and ΔCDB are similar (AAA). Therefore the corresponding sides are in proportion:

[tex]\dfrac{AD}{CD}=\dfrac{CD}{DB}[/tex]

We have

[tex]AD=16,\ CD=x,\ DB=9[/tex]

Substitute:

[tex]\dfrac{16}{x}=\dfrac{x}{9}[/tex]          cross multiply

[tex]x^2=(9)(16)\to x=\sqrt{(9)(16)}\\\\x=(\sqrt9)(\sqrt{16})\\\\x=(3)(4)\\\\x=12[/tex]

bear in mind that, a perpendicular line stemming from the right-angle like so, creates three similar triangles, a large one, containing the other two smaller ones, a medium and a small.

so.. .we can just use the medium and small proportions.

Check the picture below.

Answer:

9

Step-by-step explanation:

namely, how many times does 2/3 go in 6?

[tex]\bf 6\div\cfrac{2}{3}\implies \cfrac{6}{1}\div\cfrac{2}{3}\implies \cfrac{6}{1}\cdot \cfrac{3}{2}\implies \cfrac{3}{1}\cdot \cfrac{6}{2}\implies 3\cdot 3\implies 9[/tex]

Answer:  [tex]24\sqrt{3}in^2[/tex] or  [tex]41.56in^2[/tex]

Step-by-step explanation:

You can find the area of a regular hexagon with the following formula:

[tex]A_{(hexagon)}=\frac{3\sqrt{3}s^2}{2}[/tex]

Where "s" is any side of the regular hexagon.

For this hexagon you know that the length of each side is 4 inches. Then, you must substitute [tex]s=4in[/tex] into the formula  [tex]A_{(hexagon)}=\frac{3\sqrt{3}s^2}{2}[/tex].

Therefore, the area of this regular hexagon is:

 [tex]A_{(hexagon)}=\frac{3\sqrt{3}(4in)^2}{2}[/tex]

 [tex]A_{(hexagon)}=24\sqrt{3}in^2[/tex] or [tex]A_{(hexagon)}=41.56in^2[/tex]

Answer:

the answer is 24 square root 3

Step-by-step explanation:

What is the question?

I would say there would be 5 blue pencils, 4 green pencils, and 2 red pencils. I say this because the chance of grabbing a green pencil is smaller than the blue, and the chance of grabbing a red one is smaller than the green one, as a result, we are left wit 5 blue pencils, 4 green pencils, and 2 red pencils.

For this case we have that by definition, the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

A: It is the radius of the cylinder

h: It's the height

We have according to the data that:

[tex]r = \frac {34} {2} = 17 \ m\\h = 27 \ m[/tex]

Substituting in the equation we have:

[tex]V = \pi * (17) ^ 2 * 27\\V = \pi * 289 * 27\\V = 24501.42\ m^3[/tex]

ANswer:

[tex]V = 24501.42\ m^3[/tex]

Answer:

a=4

Step-by-step explanation:

6.97a = 27.88

Divide 6.97a on both sides

6.97a/6.97a = 27.88/6.97a

a=4

6.97a = 27.88

Divide both sides by 6.97.

6.97a/6.97 = 27.88/6.97

a = 4

For this case, to find the roots of the function, we equate to zero.

[tex]x ^ 3 + 2x ^ 2-x-2 = 0[/tex]

We rewrite how:

[tex]x ^ 3 + 2x ^ 2- (x + 2) = 0[/tex]

We factor the maximum common denominator of each group:

[tex]x ^ 2 (x + 2) -1 (x + 2) = 0[/tex]

We factor the polynomial, factoring the maximum common denominator[tex](x + 2):[/tex]

[tex](x + 2) (x ^ 2-1) = 0[/tex]

By definition of perfect squares we have to:

[tex]a ^ 2-b ^ 2 = (a + b) (a-b)[/tex]

ON the expression[tex](x ^ 2-1):[/tex]

[tex]a = x\\b = 1[/tex]

So:

[tex](x ^ 2-1) = (x + 1) (x-1)[/tex]

Thus, the factorization of the polynomial is:

[tex](x + 2) (x + 1) (x-1) = 0[/tex]

[tex]x_ {1} = - 2\\x_ {2} = - 1\\x_ {3} = 1[/tex]

ANswer:[tex]x_ {1} = - 2\\x_ {2} = - 1\\x_ {3} = 1[/tex]

Answer:

1536 in²

Step-by-step explanation:

S = 6s²

We are told that s = 16 inches, so plugging in:

S = 6 (16)²

S = 1536 in²

Answer:

Step-by-step explanation:

The formula of a circumference of a circle:

[tex]C=2\pi r[/tex]

r - radius

We have r = 11. Substitute:

[tex]C=2\pi(11)=22\pi[/tex]

[tex]\pi\approx3.14\to C\approx(22)(3.14)=69.08[/tex]

The answer is B.

Hope this helps :)

Answer:

d = 576

Step-by-step explanation

Think of the two different speeds as belonging to 2 different cars going to the same place, taking the same route and going to the same place.

Let the time traveled by the fast car = t

Let the time traveled by the slower car = t+4

Let the rate of travel of the slow car = 36 mph

Let the rate of travel of the fast car = 48 mph

===========

d = 36*(t + 4)

d = 48 * t

Since the distance is the same, they can be equated.

48t = 36(t + 4)           Remove the brackets.

48t = 36t + 144          Subtract 36t from both sides.

48t - 36t = 144           Combine

12t = 144                     Divide by 12

t = 144/12

t = 12

Therefore the faster car takes 12 hours to get where it is going.

d = 48 * t

d = 48 * 12

d = 576

Answer:

1. 48.5÷7

Step-by-step explanation:

4.85÷0.7

We can multiply both terms by 10 without changing the division problem

4.85 * 10 = 48.5

.7 * 10 = 7

48.5 ÷ 7 is the same as 4.85 ÷ .7

Answer:

is it a right triangle or no ?

Step-by-step explanation:

Answer:

the answer is 42.93

Step-by-step explanation:

just did it

Answer:

28

Step-by-step explanation:

3+5^2

3+25

28

Answer:

28

Step-by-step explanation:

5^2=5*5

5*5=25

25+3=28

Answer:

The answer is 40(1.25 – t) C.

Step-by-step explanation:

That's the answer for e2020 students!!

Answer:

c

Step-by-step explanation:

big brain

Answer:

i think its -2

because the object increased in size but nothing else changed the slope stays the same the slope is the same as the original shape

if i am wrong i apologize  

Step-by-step explanation:

The slope of the rectangle will be the same as ABCD option (B) -2 is correct, which is the slope of the ABCD.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We have:

Rectangle ABCD is dilated by a scale factor of 2 with the origin as the center of dilation, resulting in the image A′B′C′D′.

As we know, if dilate the rectangle by factor 2 the slope of the sides will not change.

Thus, the slope of the rectangle will be the same as ABCD option (C) -2 is correct, which is the slope of the ABCD.

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Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Compare the ratio of the measure of corresponding sides, that is

AB = 6 and A'B' = 2

BC = 3 and B'C' = 1

Calculate the ratio of A'B'C' to ABC, then

scale factor = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

Answer:

44 and 46

Step-by-step explanation:

Let

x,x+2-----> the  two consecutive positive even integers

we know that

[tex](x+x+2)^{2}=x^{2}+(x+2)^{2} +4,048[/tex]

Solve for x

[tex](x+x+2)^{2}=x^{2}+(x+2)^{2} +4,048\\ \\4x^{2} +8x+4=x^{2}+x^{2} +4x+4+4,048\\ \\2x^{2} +4x-4,048=0[/tex]

Solve the quadratic equation by graphing

The solution is x=44

see the attached figure

therefore

the numbers are

x=44

x+2=46

Answer:

The first example: a · (b · c) = (a · b) · c

Step-by-step explanation:

The associative property regroups values by changing the location of parentheses. If you notice, the order of the values is not changed. Both sides have a x b x c, only the parentheses have been moved. Moving the parentheses changes the progression of what is multiplied (whatever is in the parentheses is multiplied together first) but doesn't change the final answer.

The statement a. (b . c)  =  ( a . b ) . c describes the correct property.

Associative property for multiplication states that rearranging the terms and brackets places in a multiplication of two or more than two terms does not change the result of the multiplication.

There are more properties multiplication is commutative also for example a×b = b×a

a . ( b . c ) = ( a . b) . c is the right answer here brackets have been changed according to the statement.

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ANSWER

[tex]y = - \frac{3}{x + 2} [/tex]

EXPLANATION

The given parent function is:

[tex]y = \frac{1}{x} [/tex]

When this function is vertically stretched by a factor of 3, then we have

[tex]y = \frac{3}{x} [/tex]

A reflection across the y-axis transforms the function to;

[tex]y = - \frac{3}{x} [/tex]

When the resulting function is shifted to the left, the transformed function becomes;

[tex]y = - \frac{3}{x + 2} [/tex]

Answer:

The number of students per year increasing

Answer:

13

Step-by-step explanation:

x² = 5²+12²

x² = 25+144

x² = 169

x² = 13²

x = 13

Step-by-step Answer:

There is a total of 10 coins, 5 dimes, 2 quarters and three pennies.

By picking a coin, it could be any that shows up out of the 10, so the probability of picking any coin in particular is 1 / 10.

If there are 5 dimes, the probability of picking ANY one particular dime is 1/10, so with 5, the probability of picking ANY of the five dimes is 5/10 = 1/2.

Going along the same line of thought, the probability of picking any of quarters and pennies would be 2/10+3/10 = 5/10 = 1/2 as well.

Answer:

D. 12 units

Step-by-step explanation:

The distance between two points is found by

d = sqrt( (x2-x1)^2 + (y2-y1)^2)

   sqrt( (4 -4)^2 + (-5-7)^2)

 sqrt((0^2 + (-12)^2)

 sqrt(0+144)

sqrt(144)

12

Final answer:

The coordinates of the y-intercept of 5x − 5y = 4 are (0, -4/5).

Explanation:

The y-intercept of a linear equation represents the point where the line intersects the y-axis. To determine the coordinates of the y-intercept, we set the x-coordinate to 0 and solve for y. In the equation 5x - 5y = 4, To determine the coordinates of the y-intercept of the equation 5x − 5y = 4, we set the x-value to 0 since, by definition, the y-intercept occurs where the line crosses the y-axis (x=0). The equation simplifies to -5y = 4. we substitute x=0 and solve for y:

5(0) - 5y = 4
-5y = 4
y = -4/5

Therefore, the coordinate of the y-intercept is (0, -4/5).

Answer:

34

Step-by-step explanation:

The volume is calculated as approximately 33.5 cubic inches when rounded to the nearest tenth.

The question asks us to calculate the volume of a sphere with a known radius using the value of 3.14 for pi. The formula for the volume of a sphere is V = (4/3)πr³. Given that the radius (r) is 2 inches, we substitute the given values into the formula to find the volume:

V = (4/3)πr³

V = (4/3) × 3.14 × (2 inches)³

V = (4/3) × 3.14 × 8

V ≈ 33.51 cubic inches

We then round the result to the nearest tenth to get the final answer:

The approximate volume of the ornament is 33.5 cubic inches.

Answer:

38: is A

39: is A

Step-by-step explanation:

To express rates in the lowest terms, divide both the numerator and denominator by their greatest common divisor. For unit rates, calculate the rate per single unit of item or time. Example: $7 for 2 kg simplifies to a rate of $3.50 per kg, six teachers for 108 students simplifies to one teacher for 18 students, $20 for 5 T-shirts becomes $4 per T-shirt, and 45 miles in half an hour translates to 90 miles per hour.

Question 38: Our goal is to express the rates in the lowest terms.

Question 39: Here, we will convert the given rates to unit rates.

Answer:

No solution

Step-by-step explanation:

The given equation is [tex]3(x-8)=x+2x+7[/tex].

Kamal expanded first  and simplified the RHS to get: [tex]3x-24=3x+7[/tex]

He then subtracted 3x from both sides of the equation to get: -24=7

Since the last statement is false, it means the given equation is inconsistent.

Hence the equation has no solution.

Answer:Its No Solution i just took the Unit Test.

Step-by-step explanation:

Answer:

7

1

0.1666666667

The following exponents can be simplified as follows:

The exponent of a number says how many times to use the number in a multiplication.

For example: 8 to the Power 2( or 8^2)

In 8^2 the "2" says to use 8 twice in a multiplication,

so 8^2 = 8 × 8 = 64

In words: 8^2 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared".

So coming to the question:

a) 7^1 = 7 times 1 from definition that 7*1=7

b)To prove this one, I will go with the property of exponents:

  [tex]a^{(b-c)}=\dfrac{a^b}{a^c}[/tex]

implies:

[tex]4^0=4^{(2-2)}=\dfrac{4^2}{4^2} =1[/tex]

c)Applying the previous property:

[tex]6^{-1}=6^{0-1}=\dfrac{6^0}{6^1}=\dfrac{1}{6}[/tex]

Therefore, with the help of definitions and property of exponent, we can simplify it.

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