Which expression represents the area of the triangle drawn below (4x-3) (2x-1) (4x-2) (3x-3)?

For this case we must resolve the following expression:[tex]log_ {0.5} (16)[/tex]

We have to:

[tex]log_ {a} (x) = \frac {log_ {b} (x)} {log_ {b} (a)}[/tex]

The base change rule can be used if a and b are greater than 1 and are not equal to x.

We substitute the values in the base change formula, using [tex]b = 10[/tex]

[tex]\frac {log (16)} {log (0.5)} = - 4[/tex]

Answer:

-4

Option A

Answer:

The sine function is y = 4 sin (4 x) - 3

Step-by-step explanation:

The explanation in the attached file

Answer:

  f(-1) = 7

Step-by-step explanation:

Put -1 where x is and do the arithmetic.

  f(-1) = 2(-1) +9 = 7

Answer:

3u - 2v + w = 69i + 19j.

8u - 6v = 184i + 60j.

7v - 4w = -128i + 62j.

u - 5w = -9i + 37j.

Step-by-step explanation:

Note that there are multiple ways to denote a vector. For example, vector u can be written either in bold typeface "u" or with an arrow above it [tex]\vec{u}[/tex]. This explanation uses both representations.

[tex]\displaystyle \vec{u} = \langle 11, 12\rangle =\left(\begin{array}{c}11 \\12\end{array}\right)[/tex].

[tex]\displaystyle \vec{v} = \langle -16, 6\rangle= \left(\begin{array}{c}-16 \\6\end{array}\right)[/tex].

[tex]\displaystyle \vec{w} = \langle 4, -5\rangle=\left(\begin{array}{c}4 \\-5\end{array}\right)[/tex].

There are two components in each of the three vectors. For example, in vector u, the first component is 11 and the second is 12. When multiplying a vector with a constant, multiply each component by the constant. For example,

[tex]3\;\vec{v} = 3\;\left(\begin{array}{c}11 \\12\end{array}\right) = \left(\begin{array}{c}3\times 11 \\3 \times 12\end{array}\right) = \left(\begin{array}{c}33 \\36\end{array}\right)[/tex].

So is the case when the constant is negative:

[tex]-2\;\vec{v} = (-2)\; \left(\begin{array}{c}-16 \\6\end{array}\right) =\left(\begin{array}{c}(-2) \times (-16) \\(-2)\times(-6)\end{array}\right) = \left(\begin{array}{c}32 \\12\end{array}\right)[/tex].

When adding two vectors, add the corresponding components (this phrase comes from Wolfram Mathworld) of each vector. In other words, add the number on the same row to each other. For example, when adding 3u to (-2)v,

[tex]3\;\vec{u} + (-2)\;\vec{v} = \left(\begin{array}{c}33 \\36\end{array}\right) + \left(\begin{array}{c}32 \\12\end{array}\right) = \left(\begin{array}{c}33 + 32 \\36+12\end{array}\right) = \left(\begin{array}{c}65\\48\end{array}\right)[/tex].

Apply the two rules for the four vector operations.

[tex]\displaystyle \begin{aligned}3\;\vec{u} - 2\;\vec{v} + \vec{w} &= 3\;\left(\begin{array}{c}11 \\12\end{array}\right) + (-2)\;\left(\begin{array}{c}-16 \\6\end{array}\right) + \left(\begin{array}{c}4 \\-5\end{array}\right)\\&= \left(\begin{array}{c}3\times 11 + (-2)\times (-16) + 4\\ 3\times 12 + (-2)\times 6 + (-5) \end{array}\right)\\&=\left(\begin{array}{c}69\\19\end{array}\right) = \langle 69, 19\rangle\end{aligned}[/tex]

Rewrite this vector as a linear combination of two unit vectors. The first component 69 will be the coefficient in front of the first unit vector, i. The second component 19 will be the coefficient in front of the second unit vector, j.

[tex]\displaystyle \left(\begin{array}{c}69\\19\end{array}\right) = \langle 69, 19\rangle = 69\;\vec{i} + 19\;\vec{j}[/tex].

[tex]\displaystyle \begin{aligned}8\;\vec{u} - 6\;\vec{v} &= 8\;\left(\begin{array}{c}11\\12\end{array}\right) + (-6) \;\left(\begin{array}{c}-16\\6\end{array}\right)\\&=\left(\begin{array}{c}88+96\\96 - 36\end{array}\right)\\&= \left(\begin{array}{c}184\\60\end{array}\right)= \langle 184, 60\rangle\\&=184\;\vec{i} + 60\;\vec{j} \end{aligned}[/tex].

[tex]\displaystyle \begin{aligned}7\;\vec{v} - 4\;\vec{w} &= 7\;\left(\begin{array}{c}-16\\6\end{array}\right) + (-4) \;\left(\begin{array}{c}4\\-5\end{array}\right)\\&=\left(\begin{array}{c}-112 - 16\\42+20\end{array}\right)\\&= \left(\begin{array}{c}-128\\62\end{array}\right)= \langle -128, 62\rangle\\&=-128\;\vec{i} + 62\;\vec{j} \end{aligned}[/tex].

[tex]\displaystyle \begin{aligned}\;\vec{u} - 5\;\vec{w} &= \left(\begin{array}{c}11\\12\end{array}\right) + (-5) \;\left(\begin{array}{c}4\\-5\end{array}\right)\\&=\left(\begin{array}{c}11-20\\12+25\end{array}\right)\\&= \left(\begin{array}{c}-9\\37\end{array}\right)= \langle -9, 37\rangle\\&=-9\;\vec{i} + 37\;\vec{j} \end{aligned}[/tex].

Answer:

(a, 0)

Step-by-step explanation:

Point S has the same x-coordinate as does Point R:  a.

Point S has the y-coordinate 0, as Point S lies on the x-axis.

Correct final answer:  (a, 0) represents Point S.

Answer:

Step-by-step explanation:

36.7

Applying the Heron's formula, the area of the parallelogram = 36.7 square units.

Heron's Formula = √[s(s - a)(s - b)(s - c)], where:

A diagonal of a parallelogram cuts a parallelogram into two equal triangles.

Thus, we have two equal triangles in the parallelogram given.

Area of the parallelogram = 2(area of triangle)

Find the area of one triangle using the Heron's formula:

a = 5

b = 8

c = 11

s = (5 + 8 + 11)/2 = 12

Area of one triangle = √[12(12 - 5)(12 - 8)(12 - 11)]

= √[12(7)(4)(1)]

= √336

= 18.33 sq. units.

Therefore, area of the parallelogram = 2(18.33) = 36.7 square units.

Learn more about the Heron's formula on:

https://brainly.com/question/9476574

Answer:

2264 students

Step-by-step explanation:

3330/100=33.3

100-32=68

33.3 x 68=2264.4

Hope This Helps! :D

Answer:

2264 students get 8 or more hours of sleep.

Step-by-step explanation:

We are given that 32% of students say they get less than the recommended eight hours of sleep per night.

We are to find the number of students who get 8 or more hours of sleep.

Percentage of students who get 8+ hours of sleep = 100 - 32 = 68%

Number of students who get 8 or more hours = 68/100 - 3330 = 2264

Answer:

[tex]|5+13i|=\sqrt{194}[/tex]

Step-by-step explanation:

The given expression is [tex]|5+13i|[/tex].

This is a complex number expression.

The absolute value of the complex number means the magnitude of the complex number.

Recall that;

[tex]|a+bi|=\sqrt{a^2+b^2}[/tex]

This implies that:

[tex]|5+13i|=\sqrt{5^2+13^2}[/tex]

[tex]|5+13i|=\sqrt{25+169}[/tex]

[tex]|5+13i|=\sqrt{194}[/tex]

Answer:

B. [tex]\frac{x\sqrt{2}}{2y}[/tex]

Step-by-step explanation:

We want to divide [tex]\sqrt{9x^2}[/tex] by[tex]\sqrt{18y^2}[/tex].

This becomes:

[tex]\frac{\sqrt{9x^2}}{\sqrt{18y^2}}[/tex]

[tex]\frac{\sqrt{(3x)^2}}{\sqrt{2(3y)^2}}[/tex]

We remove the perfect squares to obtain

[tex]\frac{3x}{3y\sqrt{2}}[/tex]

Cancel out the common factors to get;

[tex]\frac{x}{y\sqrt{2}}[/tex]

Rationalize the denominator to get:

[tex]\frac{x}{y\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}[/tex]

[tex]\frac{x\sqrt{2}}{2y}[/tex]

The correct answer is B

Answer:

[tex]\large\boxed{B.\ \dfrac{x\sqrt2}{2y}}[/tex]

Step-by-step explanation:

[tex]\sqrt{9x^2}:\sqrt{18y^2}=\dfrac{\sqrt{9x^2}}{\sqrt{18y^2}}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{\sqrt9\cdot\sqrt{x^2}}{\sqrt{18}\cdot\sqrt{y^2}}\qquad\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=\dfrac{3\cdot x}{\sqrt{9\cdot2}\cdot y}=\dfrac{3x}{\sqrt9\cdot\sqrt2\cdot y}=\dfrac{3x}{3y\sqrt2}\qquad\text{cancel 3}\\\\=\dfrac{x}{y\sqrt2}\cdot\dfrac{\sqrt2}{\sqrt2}\qquad\text{use}\ \sqrt{a}\cdot\sqrt{a}=a\\\\=\dfrac{x\sqrt2}{2y}[/tex]

Answer:

50

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

Substitute 7 for x into the expression 8x−6 and then simplify using order of operations.

8(7)−6

56−6

50

Subtract 6 from both sides

-x > -1 - 6

Simplify -1 - 6 to -7

-x > -7

Multiply both sides by -1

= A. x < 7

Answer:

a. x<7 is the correct choice.

Step-by-step explanation:

The question is telling that the equation 6-x is larger than 1, so the last three choices are eliminated.

Answer:

4.4 in

Step-by-step explanation:

If a radius is perpendicular to a chord, it bisects that chord. You can use Pythagorean theorem here

[tex] {3.7}^{2} + {2.4}^{2} = {x}^{2} [/tex]

Once solved you'll find x to be roughly 4.4 in

Answer:

x = 4.4 in

Step-by-step explanation:

The segment from the centre of the circle to the chord is a perpendicular bisector, hence

7.4 ÷ 2 = 3.7

Consider the right triangle with legs 3.7 and 2.4 and hypotenuse x

Using Pythagoras' identity in the right triangle, then

x² = 2.4² + 3.7² = 5.76 + 13.69 = 19.45

Take the square root of both sides

x = [tex]\sqrt{19.45}[/tex] ≈ 4.4 in

Answer:

  -12

Step-by-step explanation:

To put the equation into vertex form, you can factor out the leading coefficient, then add and subtract a value equal to the square of half the x-coefficient (inside parentheses).

  = 4(x^2 +2x) -8

  = 4(x^2 +2x +1) -8 -4

  = 4(x +1)^2 -12

The y-value of the vertex is -12.

The answer would be -12

Answer:

neither

Step-by-step explanation:

The second and 3rd one can be modeled by by y = 100/x but the first one and the fourth one do not follow that, so the answer is neither. The first and fourth are y = 80/x

Put the values in and you will see the equations for yourself.

One

y = 80/2

y = 40

The 80 came from looking at this as an indirect variation. y = k/x

y = 40

x = 2

y = k/x

40 = k/2  Multiply both sides by 2

40 * 2 = k

k = 80

Two

y = k/x

20 = k/5

k = 20 * 5

k = 100

Answer:

A

Step-by-step explanation:

Group the 4 terms into groups of 2 without changing their order.  That looks like this:

[tex](2x^3+6x^2)+(5x+15)[/tex]

Now within each group pull out what's common:

[tex]2x^2(x+3)+5(x+3)[/tex]

Now we have (x + 3) common between the 2 terms, so let's pull that out.  With grouping, you know that it "works" if what's in the parenthesis are both exactly the same term.  Ours are both (x + 3).  What's "left over" are the things we originally pulled out, so group those together and you're done!

[tex](x+3)(2x^2+5)[/tex]

Answer:

Sn = ∑ 4(-6)^n, from n = 0 to n = n

Step-by-step explanation:

* Lets study the geometric pattern

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)  

- The sum of n terms is Sn = [tex]\frac{a(1-r^{n})}{(1-r)}[/tex], where

 a is the first term , r is the common ratio between each two

 consecutive terms and n is the numbers of terms

- The summation notation is ∑ a r^n, from n = 0 to n = n

* Now lets solve the problem

∵ The terms if the sequence are:

  4 , -24 , 144 , -864 , ........

∵ [tex]\frac{-24}{4}=-6[/tex]

∵ [tex]\frac{144}{-24}=-6[/tex]

∴ There is a constant ratio between each two consecutive terms

∴ The pattern is geometric

- The first term is a

∴ a = 4

- The constant ratio is r

∴ r = -6

∵ Sn = [tex]\frac{a(1-r^{n})}{(1-r)}[/tex]

∴ Sn = [tex]\frac{4(1-(-6)^{n})}{(1-(-6))}=\frac{4(1-(-6)^{n})}{(1+6)}=\frac{4}{7}[1-(-6)^{n}][/tex]

- By using summation notation

∵ Sn = ∑ a r^n , from n = 0 to n = n

∴ Sn = ∑ 4(-6)^n

Answer:

[tex] a_n = (4)(-6)^{n-1}, n =1,2,3,4,.... [/tex]

And we can verify:

[tex] n=1 , a_1 = 4 (-6)^{1-1}= 4[/tex]

[tex] n=2 , a_2 = 4 (-6)^{2-1}= -24[/tex]

[tex] n=3 , a_3 = 4 (-6)^{3-1}= 144[/tex]

[tex] n=4 , a_4 = 4 (-6)^{4-1}= -864[/tex]

And finally we can write the summation like this:

[tex] S_n = \sum_{i=1}^n 4 (-6)^{n-1} , n =1,2,3,... [/tex]

Step-by-step explanation:

For this case we have the following pattern of numbers :

4-24+144-864+...

And we want to express the sum in terms of a summation.

We can use the fact the the general term for the sum can be expressed as:

[tex] a_n = a_1 r^{n-1}[/tex]

And for this case we can identify the value of r dividing successive terms like this:

[tex] r = \frac{|24|}{|4|}= \frac{|144|}{|24|}=\frac{|864|}{|144|}= 6[/tex]

So for this case we know that the value of r =6 and the initial value 4 would represent [tex] a_1 = 4[/tex]

Since the sequence is alternating with + and - signs we can express the general term like this:

[tex] a_n = (4)(-6)^{n-1}, n =1,2,3,4,.... [/tex]

And we can verify:

[tex] n=1 , a_1 = 4 (-6)^{1-1}= 4[/tex]

[tex] n=2 , a_2 = 4 (-6)^{2-1}= -24[/tex]

[tex] n=3 , a_3 = 4 (-6)^{3-1}= 144[/tex]

[tex] n=4 , a_4 = 4 (-6)^{4-1}= -864[/tex]

And finally we can write the summation like this:

[tex] S_n = \sum_{i=1}^n 4 (-6)^{n-1} , n =1,2,3,... [/tex]

Answer:

$18.750

Step-by-step explanation:

Answer:  B) $11,093

Step-by-step explanation:

[tex]\text{The formula for depreciation is: }\\EV=P(1-r)^t\\\\\bullet EV=expected\ value\\\bullet P=principal\ \text{(original value)}\\\bullet r=rate\ of\ depreciation\\\bullet t=time\ \text{(in years)}\\\\\\\text{The given values are: }\\\bullet P=\$25,000\\\bullet r=15\%\quad (0.15)\\\bullet t=5\\\\\\EV=25,5000(1-0.15)^5\\.\quad =25,000(0.85)^5\\.\quad =25,000(0.443705)\\.\quad =\large\boxed{11,092.63}[/tex]

Answer:

The area of the rhombus is [tex]72\ m^{2}[/tex]

Step-by-step explanation:

we know that

To find the area of a rhombus, multiply the lengths of the two diagonals and divide by 2

[tex]A=\frac{1}{2}(6+6)(6+6)=72\ m^{2}[/tex]

B. The graph that best represents the equation y =  |x| - 1 is the option B.

To solve this problem we have to try with some values, the symbol |x| is the absolute value which means any number either positive or negative always is positive |-5| = 5 and |5| = 5.

Let's take x = -3, -2, -1, 0, 1, 2, 3.

For x = -3

y = |-3| - 1 = 3 - 1

y = 2

For x = -2

y =  |−2| - 1 = 2 - 1

y = 1

For x = -1

y =  |−1| - 1 = 1 - 1

y = 0

For x = 0

y =  |0| - 1 = 0 - 1

y = -1

For x = 1

y =  |1| - 1 = 1 - 1

y = 0

For x = 2

y =  |2| - 1 = 2 - 1

y = 1

For x = 3

y =  |3| - 1 = 3 - 1

y = 2

y  ║  x

2      -3

1       -2

0       -1

-1       0

0       1

1        2

2       3

If we graph the points obtain in the table above, the result is a graph with the characteristics of the option B.

Answer:

[tex]x^{\frac{21}{4} }[/tex]

Step-by-step explanation:

Given expression is:

[tex](\sqrt[8]{x^7} )^{6}[/tex]

First we will use the rule:

[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex]

So for the given expression:

[tex]\sqrt[8]{x^{7}}=(x^{7} )^{\frac{1}{8} }[/tex]

We will use tha property of multiplication on powers:

[tex]=x^{7*\frac{1}{8} }[/tex]

[tex]= x^{\frac{7}{8} }[/tex]

Applying the outer exponent now

[tex](x^{\frac{7}{8} })^6[/tex]

[tex]= x^{\frac{7}{8}*6 } \\= x^{\frac{42}{8} }\\= x^{\frac{21}{4} }[/tex]

Answer:

y = 105°

Step-by-step explanation:

In an isosceles trapezoid

• Any lower base angle is supplementary to any upper base angle

• The lower base angles are congruent

75 and x are supplementary, thus

x = 180° - 75° = 105°

x and y are lower base angles and congruent, so

y = x = 105°

Answer:

zero

Step-by-step explanation:

Given a rational function then the denominator cannot be zero as this would make the function undefined.

Answer:

zero

Step-by-step explanation:

We have to fill the correct word in the blank space.

Suppose

[tex]f(x)=\frac{1}{x}[/tex]

Substitute x=0 then we get

[tex]f(x)=\frac{1}{0}=\infty[/tex]

The function is not defined at x=0

Because the denominator of the function at x=0 is zero which makes the function not define.

When the definition of a function involves  a fraction , the function is undefined at any value that would make the denominator of the function zero.

Answer:

19-(-8)-(-14) = 41

Step-by-step explanation:

First, we have to solve what is in parentheses

by law of signs ( - . - = +)

19 + 8 + 14 = ?

Then, we only have to sum the number to obtain the result

19 + 8 + 14 = 41

Answer:

41

Step-by-step explanation:

We must do multiplication before addition or subtraction here.

-(-8) = +8 and -(-14) = +14, and therefore:

19 - (-8) - (-14) becomes 19 + 8 + 14, or 19 + 22, or 41.

Answer:

lets say you mark the dice your answer would be 4.

Step-by-step explanation:

1+4=5, 2+3=5, 3+2=5, 4+1=5

Answer:

4 I got it right on Edmentum

Step-by-step explanation:

Hook me up with a 5 star and a Thanks :)

Answer:

See below in Bold.

Step-by-step explanation:

If he scored 76 points he must have answered 76/4 = 19 questions correctly.

If the total number of questions is q then our equation is q = 10 + 76/4

= 10 + 19 = 29 questions.

Mean: 20.5

Standard Deviation: 11.5

The mean is the total of the numbers divided by the amount of numbers. So, add 36 + 14 + 21 + 39 + 11 + 2 to get 123. Now, divide 123 by 6 to find that the mean is 20.5.

The standard deviation is the mean of the distances from the numbers to the mean. So, find the distance from the mean for each number. You get 15.5, 6.5, 0.5, 18.5, 9.5, and 18.5. Find the mean of these distances. Start by adding them together to get 69, then divide that by 6 to get a standard deviation of 11.5.

Answer with Step-by-step explanation:

Six samples are collected of the number of scanning errors: 36, 14, 21, 39, 11, and 2 errors

Mean=(Sum of all observations)/(Total number of observations)

        =(36+14+21+39+11+2)/6

        = 123/6

        = 20.5

Standard deviation is the square root of mean of squares of deviation around mean

Deviation around mean:

36-20.5, 14-20.5, 21-20.5, 39-20.5, 11-20.5, and 2-20.5

15.5,-6.5,0.5,18.5,-9.5 and -18.5

Square of deviations:

240.25,42.25,0.25,342.25,90.25 and 342.25

Mean of square of deviations

=(240.25+42.25+0.25+342.25+90.25+342.25)/6

=176.25

square root of mean of deviations= [tex]\sqrt{176.25}=13.28[/tex]

Hence, Standard deviation=13.28

and Mean=20.5

Answer:

x= 8.1

Step-by-step explanation:

The given triangle is a right angle triangle.

We cannot use the Pythagoras theorem as the lengths of all sides are not known. We will use triangular ratios here to solve the given problem.  

As it is clear from the diagram that x is the hypotenuse of the triangle and 11 is the length of the base. We will use a ratio in which base and hypotenuse are used.

So,

cos⁡ θ= base/hypotenuse

cos⁡ 36=x/10

0.8090=x/10

8.090=x

x=8.090

Rounding off to nearest 10

x=8.1

Answer:

y=-12/5x+62

Step-by-step explanation:

to solve this i turned two point form, 5,50 and 17 1/2,20, into slope intercept form by using the formula y-y1=(y2-y1/x2-x1)(x-x1), which when input with the data becomes y-50=(20-50/17 1/2-5)(x-5) which then becomes y-50=-12/5(x-5), then y-50=-12/5x+12, and finally y=-12/5x+62

Answer:

Linear

Step-by-step explanation:

It is not quadratic or exponential since the term to term sequence is +2.

- 5 ⇔ -3

( Adding 2 )

- 3 ⇔ -1

( Adding 2 )

- 1 ⇔ 1

( Adding 2 )

f(x)+g(x)

f(x)=3x+2 and g(x)=4x

You have:

3x +2 + 4x

Combine like terms:

3x +4x = 7x

The answer becomes 7x +2