Use a trigonometric ratio to find the value of x. Round your answer to the nearest tenth.

3.1
3.4
4.8
2.6

Step-by-step explanation:

Find the Greatest Common Factor (GCF) of a polynomial.

Factor out the GCF of a polynomial.

Factor a polynomial with four terms by grouping.

Factor a trinomial of the form .

Factor a trinomial of the form .

Indicate if a polynomial is a prime polynomial.

Factor a perfect square trinomial.

Factor a difference of squares.

Factor a sum or difference of cubes.

Apply the factoring strategy to factor a polynomial completely

Answer:

See explanation

Step-by-step explanation:

We can factor polynomials by breaking down the expression.

For instance, let's say we have the polynomial [tex]x^2 - 9x + 14[/tex].

We can start solving this because this polynomial is in standard form, meaning that the highest exponents go first. ([tex]ax^2 + bx + c[/tex].)

To factor a polynomial, we are looking for two numbers that:

A. When multiplied, get us [tex]c[/tex] (in this case, 14)

B. When added, get us [tex]b[/tex] (in this case, -9).

If we play around with numbers, looking at the factors of 14, we see that the numbers 7 and 2 might be useful here. They add up to 9 and multiply to be 14.

However, these numbers ADD to be -9, meaning that they both need to be negative.

[tex]-7 + -2 = -9\\-7\cdot-2=14[/tex]

Now that we know our numbers, -7 and -2, we can make these our factors (which are represented by [tex](x + y)[/tex], y being our factor.

So our factors turn out to be [tex](x-7)[/tex] and [tex](x-2)[/tex].

Let me know if you need anything explained more, and I hope this helped!

Answer:

1) Please find attached the graph sowing the line of symmetry

The symmetry line is a vertical line passing through (2, -9)

2) The x-intercept are (5, 0) and (-1, 0)

The y-intercept is (0, -5)

The vertex is (2, -9)

Step-by-step explanation:

The given function is;

f(x) = x² - 4·x - 5

The data values are generated as follows;

x,          f(x)

-1,         0

-0.8,    -1.16

-0.6,    -2.24

-0.4,    -3.24

-0.2,    -4.16

0,         -5

0.2,      -5.76

0.4,      -6.44

0.6,     -7.04

0.8,     -7.56

1,         -8

1.2,      -8.36

1.4,      -8.64

1.6,      -8.84

1.8,      -8.96

2,        -9

2.2,     -8.96

2.4,      -8.84

2.6,     -8.64

2.8,     -8.36

3,        -8

3.2,     -7.56

3.4,     -7.04

3.6,     6.44

3.8,     -5.76

4,        -5

4.2,      -4.16

4.4,     -3.24

4.6,     -2.24

4.8,      -1.16

5,           0

The minimum is found from differentiating the function, f(x), with respect to x and looking for the zeros of the result  as follows;

f'(x) = 2·x -4

f'(x) = 0 = 2·x -4

x = 2

The y-coordinate gives; f(2) = 2² - 4×2 - 5 = -9

Therefore, the symmetry line is a vertical line passing through (2, -9)

The x-intercept is the point at which y = 0, therefore, from f(x) = x² - 4·x - 5, we have;

0 = x² - 4·x - 5 = (x - 5)·(x + 1)  

Therefore, the x-intercept are x = 5 or -1

The x-intercept are (5, 0) and (-1, 0)

The y-intercept occur at the point where the x value = 0, therefore, we have;

The y-intercept occur at y = f(0) = 0² - 4·0 - 5 = -5

The y-intercept is (0, -5)

Re-writing the  equation in vertex form y = a(x - h)² + k gives;

f(x) = x² - 4·x - 5 = 1·(x - 2)² - 9

Therefore, the vertex is (2, -9)

Answer:

see attached graph

The x-intercept are (5, 0) and (-1, 0)

The y-intercept is (0, -5)

The vertex is (2, -9)

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Take the price of each can and multiply by the cost of the cans

.95x

This must be less than or equal to 4.75

.95x ≤ 4.75

They may choose to use an equals sign,  since they asked for an equation

.95x = 4.75

Answer: 0.95x = 4.75

Step-by-step explanation:

Since we do not know how much George can buy, we will put x as 0.95x

If you solve 0.95x=4.75 by dividing 0.95 on both sides you will get the number of cans he can buy which is 5.

Answer:

Step-by-step explanation:

45=3×3×5

60=2×2×3×5

L.C.M=180

2| 180

2|90

3|45

3|15

3|5

180=2×2×3×3×5

third number=2×3=6

or 2×2×3=12

or2×3×3=18

or 2×2×3×3=36

so third number can be one of  6,12,18,36

Answer:

32

Step-by-step explanation:

plug in the values of the variables then simplify

Answer:

[tex]\boxed{32}[/tex]

Step-by-step explanation:

Hey there!

Well given the expression,

6p - 2q

and p and q we need to plug them in.

6(3) - 2(-7)

Simplify

18 - -14

18 + 14

= 32

Hope this helps :)

Greetings from Brasil...

As stated in the statement:

HEIGHT = CONSTANT ÷ WIDTH

H = C ÷ W

so, isolating the variable C....

C = H · W

choosing any point on the graph...

(2; 30)  ⇒ W = 2 and H = 30

C = H · W

C = 30 · 2

The value of the constant in the equation shown in the figure would be, 60. Hence option C is true.

Given that,

The graph is the relation between Height and width.

As is given in the graph:

Height = Constant / Width

We observe that the graph passes through (2,30), (5,12), (10,6), (30,2)

So, by using any one point we may get the value of constant( since it is a fixed quantity)

Hence, using the point (2,30)

Width = 2

And, Height = 30

So, we get:

Constant = 2 × 30

= 60

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Answer:

La profesora debe comprar 8 manzanas para reponer la cesta de frutas.

Step-by-step explanation:

La profesora debe reponer la cesta de frutas por la cantidad de manzanas que se encuentran dañadas. La cantidad de manzanas dañadas es igual a las dos séptimas partes del total de manzanas. Es decir:

[tex]x = \frac{2}{7} \times (28\,manzanas)[/tex]

[tex]x = \frac{56\,manzanas}{7}[/tex]

[tex]x = 8\,manzanas[/tex]

La profesora debe comprar 8 manzanas para reponer la cesta de frutas.

Answer: C) similar, SAS similarity, triangle LQR

==============================================

Explanation:

The vertical angles KLJ and QLR are congruent. This forms the "A" in "SAS". The angles in question are between the marked sides.

KL = 18 is twice that of QL = 9, or put another way, KL/QL = 18/9 = 2. The ratio of the sides is 2. Also, JL/RL = 16/8 = 2 is the same ratio. Because both pairs of sides have the same ratio, the sides are in proportion. This helps form the two "S" letters of "SAS".

The original triangle has LKJ mentioned at the top. Note the order as its important. We start with L and move to K, so LK is the first segment mentioned. LK = 18 pairs up with LQ = 9, meaning that LQ must be the first segment mentioned of the answer triangle. Therefore LQR is the correct letter sequence if we start with point L. Writing QLR is not correct because Q is the first letter here but Q does not pair up with L.

Answer:

Area : 14+10+40=64 square unit

Step-by-step explanation:

the area of the top rectangle with sides  2 and 7

A=2*7=14 square unit

the area of the middle rectangle with sides : (7-5)=2 and side (7-2)=5

Area=5*2=10 square unit

the bottom rectangle : sides 10 and 4

Area=10*4=40

add the areas : 14+10+40=64 square unit

Answer:

it's b :)

Step-by-step explanation:

A number line which represents the solution set for the given inequality is: option B.

A number line refers to a type of graph with a graduated straight line which contains numerical values (both positive and negative numbers) that are placed at equal intervals along its length.

Next, we would solve the given inequality:

-½x ≥ 4

-x ≥ 4 × 2

x ≤ -8.

Therefore, a number line which represents the solution set for the given inequality is a number line from -10 to 10 in increments of 2 with a point at -8 and a bold line starts at -8 while pointing to the left.

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Getting each exercise correct gets you 8.3(recurring)%. Therefore if you answer 10 exercises correctly you get 83.3%, and if you answer 9 exercises correctly you get 75%, this means that the minimal exercises you need to get correct is 10.

Answer:

110 feet per second

Step-by-step explanation:

You would mutiply your speed in miles per hour by 5,280. That's the number of feet in a mile and your result is your speed in feet per hour.

75 x 5,280 = 396,000 feet per hour

Then you would divide your speed by 60 and that result is your speed in feet per minute.

396,000 / 60 = 6,600 feet per minute

Lastly, you would divide that speed by 60 and the result is your speed in feet per second.

6,600 / 60 = 110 feet per second

The conversion of 75 miles per hour to feet per second is approximately 110 feet per second.

We can do this by using conversion factors that relate the two units. Specifically, we can use the fact that 1 mile equals 5,280 feet and 1 hour equals 3,600 seconds.

To convert miles per hour to feet per second, we need to multiply the value in miles per hour by a conversion factor that will cancel out the "miles" unit and replace it with "feet," and another conversion factor that will cancel out the "hours" unit and replace it with "seconds."

So, first we convert miles per hour to feet per hour by multiplying 75 miles/hour by 5,280 feet/mile.

This gives us:

= 75 miles/hour x 5,280 feet/mile

= 396,000 feet/hour

Next, we convert feet per hour to feet per second by dividing by 3,600 seconds/hour.

This gives us:

=396,000 feet/hour ÷ 3,600 seconds/hour

= 110 feet/second

Therefore, 75 miles per hour is approximately equal to 110 feet per second.

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Answer:

£13800

Step-by-step explanation:

1150*12=£13800

Answer:

90

Step-by-step explanation:

Hey there!

Well 90.000 to the nearest tenth is just 90 because there is no decimal places to round.

Hope this helps :)

Answer:

90

Step-by-step explanation:

90 has 0 ones so 90 is just 90, but rounded...

Answer:

perimeter is  4 sqrt(29) + 4pi  cm

area is 40 + 8pi cm^2

Step-by-step explanation:

We have a semicircle and a triangle

First the semicircle with diameter 8

A = 1/2 pi r^2 for a semicircle

r = d/2 = 8/2 =4

A = 1/2 pi ( 4)^2

  =1/2 pi *16

  = 8pi

Now the triangle with base 8 and height 10

A = 1/2 bh

  =1/2 8*10

  = 40

Add the areas together

A = 40 + 8pi cm^2

Now the perimeter

We have 1/2 of the circumference

1/2 C =1/2 pi *d

         = 1/2 pi 8

        = 4pi

Now we need to find the length of the hypotenuse of the right triangles

using the pythagorean theorem

a^2+b^2 = c^2

The base is 4 ( 1/2 of the diameter) and the height is 10

4^2 + 10 ^2 = c^2

16 + 100 = c^2

116 = c^2

sqrt(116) = c

2 sqrt(29) = c

Each hypotenuse is the same so we have

hypotenuse + hypotenuse + 1/2 circumference

2 sqrt(29) + 2 sqrt(29) + 4 pi

4 sqrt(29) + 4pi  cm

Step-by-step explanation:

First we need to deal with the half circle. The radius of this circle is 4, because the diameter is 8. The formula for the circumference of a circle is 2piR.

2pi4 so the perimeter for the half circle would be 8pi/2.

The area of that half circle would be piR^2 so 16pi/2.

Now moving on the triangle part, we need to find the hypotenuse side of AC. We will use the pythagoram theorem. 4^2+10^2=C^2

16+100=C^2

116=C^2

C=sqrt(116)

making the perimeter of this triangle 2×sqrt(116)

The area of this triangle is 8×10=80, than divided by 2 which is equal to 40.

We than just need to add up the perimeters and areas for both the half circle and triangle.

The area would be equal to 8pi+40

The perimeter would be equal to 4pi+4(sqrt(29))

Answer:

About 706.5 square inches.

Step-by-step explanation:

Surface area of a sphere is: [tex]SA=4\pi r^2[/tex]

The radius is half the diameter. So, the radius of the given sphere is 7.5 in.

15/2 = 7.5

Find the surface area:

I use 3.14 for pi.

[tex]SA=4*3.14*7.5^2\\\\SA=4*3.14*56.25\\\\SA=12.56*56.25\\\\\boxed{SA=706.5}[/tex]

The surface area is about 706.5 square inches.

Hope this helps.

Answer:

SA=706.86 in²

Step-by-step explanation:

surface area of a sphere = 4πr²

radius r=d/2=15/2=7.5

SA=4(π)(7.5)²

SA=706.86 in²

Answer:

d. physical features and locations tell historians about the ways people lived.

Step-by-step explanation:

I believe this is the correct answer

Answer:

60 tiles are used

Step-by-step explanation:

1m equals 100 cm.

5m equals 500

3m equals 300

the whole thing is 500 by 300 which when you multiply gives you

150,000. When you multiple 50 by 50 it gives you 2,500. So when you divide 150,000 by 2,500 it gives you a total of 60 tiles. HOPE THIS HELPS

Answer:

60 tiles

Step-by-step explanation:

First, I would convert cm to m to make it easier

50 cm is .5 m

Now we can find how many tiles across it takes to make one row (5m)

.5 goes into 5, 10 times

That means we need 10 tiles across to fill one row

Now we need to find how many tiles it takes to fill up a column (3m)

.5 goes into 3, 6 times

It takes 6 tiles to fill up a column

Now we know it takes 10 tiles across and 6 vertically

10x6=60

60 tiles

Answer:

See explanation

Step-by-step explanation:

a) 200,000 x .0288 x 7 = 40,320 interest

b) 240,320/84 = $2860.95

Answer: 2

Step-by-step explanation:

Given: Shaquira has made 86  chocolate chip cookies and 42 sugar cookies.

Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies.

Now, the greatest number of identical packages that Shaquira can make= GCD of 86 and 42

Prime factorization of 86 and 42:

86 = 2 ×43

42 = 2 × 3 × 7

GCD of 86 and 42 = 2   [GCD = greatest common factor]

Hence, the greatest number of identical packages that Shaquira can make =2

Step-by-step explanation:

[tex]\text{Discriminant} =\Delta = b^2-4ac\\

\implies \Delta = 7^2-4(1)(10)=49-40=9\\

\therefore \Delta >0\\[/tex]

Since the discriminant is greater than zero, there are two real solutions.

Also, the solutions are $x=5$ and $x=2$

Answer:

space is the capacity that an object or shape weigh

Answer:

B. 2.7 g

Step-by-step explanation:

The half life of a substance is the time taken for the substance to reduce to half of its original amount. It is given by:

[tex]A=A_o*(\frac{1}{2})^\frac{t}{t_{1/2}}\\ Where\ A\ is \ the \ amount \ of \ substance\ remaining\ after\ t\ years, \\A_o \ is \ the\ initial\ value\ of \ the\ substance,\ t_{1/2} is\ the\ half\ life\ and\\t\ is\ the\ years\ spent[/tex]

Given that:

Ao = 4 g, t = 3 years, t(1/2) = 5.26 years. Therefore:

[tex]A=A_o*(\frac{1}{2})^\frac{t}{t_{1/2}}\\A=4*(\frac{1}{2} )^\frac{3}{5.26}=4*0.6735=2.7\\ A=2.7\ g[/tex]

Answer:

The 4th term = a+3d = 0,

or a = -3d.

The 25th term = a+24d = -3d+24d = 21d. ...

the 25th term is 3 times the 11th term. Proved.

Answer:

a^25 = 3 x a^11 .

Step-by-step explanation:

Given a^4 = 0

That is (a + 3d) = 0

⇒ a = - 3d ........... (1)

nth term of AP is given by an = a + (n – 1)d

a^11 = a + 10d = – 3d + 10d = 7d  [From (1)]

a^25 = a+ 24d = – 3d + 24d = 21d  [From (1)]

Hence

The answer is a^25=3 x a^11

Answer:

2nd statement

3rd statement

4th statement

Step-by-step explanation:

The 2nd statement we know is true since the container was already described with a rectangular pyramid and a rectangular prism.

The 3rd statement is true since the volume for a rectangular prism is,

V=wlh or V=bh    (b=wl)

The volume of a rectangular pyramid is

V=1/3*wlh or V= 1/3*bh     (b=wl)

The 4th statement is true since the formula for the volume of this container is V=wlh+wlh/3. So substitute the values of the rectangular prism and rectangular pyramid and,

V=10*18*12+(18*10*10)/3

V=2160+1800/3

V=2160+600

V=2760

Answer:

3x(x+8)=0

x=0,-8

This is how to solve for x.

Answer:

number 4 on edge

Step-by-step explanation:

Answer:

a. 92 minutes b. 7:56am

Step-by-step explanation:

He should leave at 7:56 so he gets to the bus at 8:05,

he gets to Coventry at 9:37 with enough time to walk 12 minutes to get to work before 10am.

Answer:Answer and Explanation:

When a number is said to be 'to the fourth power,' that just means that you need to multiply the number by itself four times. For example, 7 to the...

Step-by-step explanation:

Answer:

6.5<3rd side <19.9

Step-by-step explanation:

Extremely easy. All you have to do to get the first answer is minus 13.2-6.7 which is 6.5. Then add 13.2+6.7 to get 19.9 for the other answer. So the two answers would be 6.5 and 19.9.

Your welcome

Answer:

At   90% confidence interval, the estimate of the mean breaking weight is (770.45, 778.15)

Step-by-step explanation:

Given that:

sample size n =43

sample mean x = 774.3

standard deviation = 15.4

confidence interval = 90%

At C.I of  90% , the level of significance ∝ = 1 - C.I

the level of significance ∝ = 1 - 0.90

the level of significance ∝ = 0.10

The critical  value for z at this level of significance is [tex]z_{\alpha/2} = z_{0.10/2}[/tex]

[tex]z_{0.05}[/tex] = 1.64

The margin of error can be computed as follows:

Margin of error = [tex]\mathtt{z_{\alpha/2} \times \dfrac{\sigma}{\sqrt{n}}}[/tex]

Margin of error =  [tex]\mathtt{1.64 \times \dfrac{15.4}{\sqrt{43}}}[/tex]

Margin of error = [tex]\mathtt{1.64 \times \dfrac{15.4}{6.5574}}[/tex]

Margin of error  = [tex]\mathtt{1.64 \times2.3485}[/tex]

Margin of error = 3.8515

The mean breaking weight  for the 90% confidence interval is = [tex]\mathtt{\overline x \pm E < \mu }[/tex]

=  [tex]\mathtt{\overline x - E < \mu < \overline x + E}[/tex]

= ( 774.3 - 3.8515  < μ < 774.3 + 3.8515 )

= (770.4485, 778.1515)

[tex]\simeq[/tex] (770.45, 778.15)