Triangular pyramid: volume 56 cubic centimeters, base edge 8 centimeters, base height 7 centimeters

Answer:

(t, t -1, t)

Step-by-step explanation:

You have three unknowns but only 2 equations, so you can't really SOLVE this...you can get a solution with a variable still in it (I forget what this is called.  I think it refers to infinite many solutions).  Here's how it works:

Set up your matrix:

[tex]\left[\begin{array}{ccc}1&-2&1\\2&-1&-1\\\end{array}\right] \left[\begin{array}{ccc}2\\1\\\end{array}\right][/tex]

You want to change the number in position 21 (the 2 in the scond row) to a 0 so you have y and z left.  Do this by multiplying the top row by -2 then adding it to the second row to get that 2 to become a 0.  Multiplying in a -2 to the top row gives you:

[tex]\left[\begin{array}{ccc}-2&4&-2\\2&-1&-1\\\end{array}\right]\left[\begin{array}{ccc}-4\\1\\\end{array}\right][/tex]

Then add, keeping the first row the same and changing the second to reflect the addition:

[tex]\left[\begin{array}{ccc}-2&4&-2\\0&3&-3\\\end{array}\right] \left[\begin{array}{ccc}-4\\-3\\\end{array}\right][/tex]

The second equation is this now:

3y - 3z = -3.  Solving for y gives you y = z - 1.  Let's let z = t (some random real number that will make the system true.  Any number will work.  I'll show you at the end.  Just bear with me...)

lf z = t, and if y = z - 1, then y = t - 1.  So far we have that y = t - 1 and z = t.  Now we solve for x:

From the first equation in the original system,

x - 2y + z = 2.  Subbing in t - 1 for y and t for z:

x - 2(t - 1) + t = 2.  Simplify to get

x - 2t + 2 + t = 2  and  x - t = 0, and x = t.  So the solution set is (t, t - 1, t).  Picking a random value for t of, let's say 2, sub that in and make sure it works.  If:

x - 2y + z = 2, then t - 2(t - 1) + t = 2 becomes t - 2t + 2 + t = 2, and with t = 2, 2 - 2(2) + 2 + 2 = 2.    Check it:  2 - 4 + 4 = 2 and 2 = 2.  You could pick any value for t and it will work.

Answer: B Scientific Method

Answer:

B

Step-by-step explanation:

The exponential function [tex]y=a^x[/tex] shows the exponential growth if [tex]a>1.[/tex]

Consider choice B.

If x=1, then [tex]y=2=2^1;[/tex]

if x=2, then [tex]y=4=2^2;[/tex]

if x=3, then [tex]y=8=2^3;[/tex]

if x=4, then [tex]y=16=2^4.[/tex]

This means that the function [tex]y=2^x[/tex] represents the table B.

ANSWER

See attachment

EXPLANATION

The table that represent a geometric sequence is the one shown in the attachment with y-values

[tex]2,4,8,16,...[/tex]

We can see that, the subsequent term is obtained by multiplying the previous term by 2.

In other words, there is a bit ratio of 2.

Here the table represents a geometric sequence.

Check the picture below.

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=&area~of\\ &its~base\\ h=&height\\ \cline{1-2} B=&\stackrel{4\times 4}{16}\\ h=&4 \end{cases}\implies V=\cfrac{1}{3}(16)(4)\implies V=\cfrac{64}{3}\implies V=21.\overline{3}[/tex]

Answer:

21.03^3  this is the answer.

Answer:

D

Step-by-step explanation:

C is also possible but it is not purely random and it is not mentioned the mall is in her district.

Answer:  D) Mail a questionnaire to random households.

Step-by-step explanation:

A) You are limited to only listeners of the radio show

B) You are limited to only those that are wiling and able to attend the meeting.

C) You are limited to only shoppers at that particular mall.

D) Randomly selecting households is the least biased method of responses from the district.

Answer:

12-5.5=h

12-5.5=6.5

Kyle needs to volunteer 6.5 more hours.

Step-by-step explanation:

Answer:

5.5 + h = 12

Step-by-step explanation:

Here, h represents the number of hours, Kyle still needs to volunteer this week,

Given,

He volunteered 5.5 hours at the library this week.

Since, the total number of hours he needs to volunteer = 5.5 + h

According to the question,

5.5 + h = 12

Which is the required equation.

[tex]

\frac{\frac{9}{10}}{\frac{-3}{5}}=\frac{45}{-30}=-\frac{9}{6}=\boxed{\frac{3}{2}}

[/tex]

Hope this helps.

r3t40

The number of runners run at most 2 miles per day is 13.

2 miles = 6

3 miles = 4

4 miles = 2

5 miles = 1

Now if we add this,

So,

= 6 + 4 + 2 + 1

= 13

Learn more: brainly.com/question/17429689

Answer:

13

Step-by-step explanation:

Its easy, but its a trick question into getting you to click 6

A = 0.5 x 10.4 x 16.9

A = 87.88

The area of the triangle is 87.88 ft²

Answer:

Step-by-step explanation:

I(x)=P(13x) = 2(13x)²+3(13x) +4

I(x)=P(13x).= 338x²+39x+4

Answer: The required function would be [tex]x^2+3x-40[/tex]

Step-by-step explanation:

Since we have given that

There are two real zeroes :

x = -8 and x = 5

So, we need to find the function satisfying the above two zeroes:

Let α = -8 and β = 5

So, it means it is a quadratic equation :

[tex]x^2-(\alpha +\beta)x+\alpha \beta \\\\=x^2-(-8+5)x+-8\times 5\\\\=x^2+3x-40[/tex]

Hence, the required function would be [tex]x^2+3x-40[/tex]

Answer:

The answer is A

Step-by-step explanation:

Answer:

The answer would be the large album has 54 more stamps than the small album.

Step-by-step explanation:

... 92 - 38 = 54

Do you need a drawing done though?

Answer:

12

Step-by-step explanation:

96 / 8

Answer:

12 Cups are needed!

Step-by-step explanation:

You find the answer by dividing 96 milkshakes by 8 Milkshakes and find that 12 cups are needed.

:)

Answer:

1 is my answer but I could be wrong

Answer:

1

Step-by-step explanation:

y = mx + b

y = 1/2 x - 1

y = 1/2 (4) - 1

y = 2 - 1

y = 1

When x = 4, the function y = (1/2)x - 1 evaluates to y = 1. This linear equation has a slope of 1/2 and a y-intercept of -1.

To find the value of the function y = (1/2)x - 1 when x = 4, you simply need to substitute x = 4 into the equation and solve for y:

y = (1/2)(4) - 1

y = 2 - 1

y = 1

So, when x = 4, the value of the function y is 1.

In a more general sense, this equation represents a linear function with a slope of 1/2 and a y-intercept of -1. The slope (1/2) represents the rate of change, meaning that for every unit increase in x, y increases by 1/2. The y-intercept (-1) is the value of y when x is 0.

When x = 4, as calculated above, y is 1. This means that if you were to plot this function on a coordinate plane, the point (4, 1) would lie on the graph.

For more question on slope visit:

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Answer:  B) -6x³ + 4x²

Step-by-step explanation:

         f(x): -3x⁴ - 2x³ + 3x²

     + g(x): 3x⁴ - 4x³ +   x²

f(x) + g(x):        - 6x³ + 4x²

Answer:

  (x +2)(x -4)(x -5)

Step-by-step explanation:

When you divide the cubic by (x +2), the factor that has -2 as a root, you get a quadratic with roots 4 and 5. Thus the factors are ...

  (x +2)(x -4)(x -5)

___

In the attachment, we have done the division using a graphing calculator. You can also do it by polynomial long division or by synthetic division. The resulting quadratic is ...

  x^2 -9x +20 = (x -4)(x -5) . . . . . factor the quadratic

19/50 of the baseball caps in the store are blue and on sale.

Let's say there are a total of 100 baseball caps in the store. Then, 2/3 of them are blue, which is:

2/3 x 100 = 66.67 (approximately 67)

So, there are approximately 67 blue baseball caps in the store. Out of these, 4/7 are on sale, which is:

4/7 x 67 = 38 (rounded to the nearest whole number)

Therefore, there are approximately 38 blue baseball caps that are on sale in the store.

The fraction of baseball caps in the store that are blue and on sale is:

38/100 = 19/50

So, 19/50 of the baseball caps in the store are blue and on sale.

for such more question on word problem

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To find the fraction of baseball caps in the store that are blue and on sale, multiply the fractions representing the proportion of blue caps and the proportion of blue caps that are on sale.

To find the fraction of baseball caps in the store that are blue and on sale, we need to multiply the fractions representing the proportion of blue caps and the proportion of blue caps that are on sale.

Given that 2/3 of the caps are blue and 4/7 of the blue caps are on sale, we can calculate the fraction of blue caps that are on sale by multiplying 2/3 and 4/7:

2/3 * 4/7 = 8/21

Therefore, 8/21 of the baseball caps in the store are blue and on sale.

https://brainly.com/question/12656995

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Answer:

B. f -1(x) = x + 2 / 5

[tex]f^{-1}(x)=\frac{x+2}{5}[/tex]

Step-by-step explanation:

To find the inverse of a function we need to interchange x and y an solve for y.

Since [tex]f(x)=y[/tex], then

[tex]f(x)=5x-2[/tex]

[tex]y=5x-2[/tex]

[tex]x=5y-2[/tex]

Add 2 to both sides

[tex]x+2=5y-2+2[/tex]

[tex]x+2=5y[/tex]

Divide both sides by 5

[tex]\frac{x+2}{5}=\frac{5y}{5}[/tex]

[tex]\frac{x+2}{5}=y[/tex]

[tex]y=\frac{x+2}{5}[/tex]

[tex]f^{-1}(x)=\frac{x+2}{5}[/tex]

We can conclude that the correct answer is B. f -1(x) = x + 2 / 5

Answer:

The T-shirts cost $10 and the jeans cost $20.

Step-by-step explanation:

I guess you want to find the cost of the T-shirts and jeans at his first buy,

Let the cost be  $t and $j for T-shirts and jeans respectively.

Then we have the system:

2t + j = 40...................(1)

and a month later:

0.5*2t  + 0.5*5j = 60

t + 2.5j = 60................(2)

Multiply by - 2:

-2t - 5j = -120.............(3)

Adding equations (1) and (3):

-4j = -80

j = -80 /  -4

j =  $20.

Substituting j = 20 into equation (2):

t + 2.5(20) = 60

t = 60 - 50

t = $10.

t = $55

Answer:

  3, -8, 11

Step-by-step explanation:

The first factor is zero when x=3.

The second factor is zero when x=-8.

The third factor is zero when x=11.

Whenever any factor is zero, the polynomial is zero.

The zeros are 3, -8, 11.

Answer:

Step-by-step explanation:

So the table means that there are 20 1's, 120 2's, 40 3's, and 20 4's.

The total number is 20+120+40+20 = 200.

So the probability of each is:

1: 20/200 = 0.10

2: 120/200 = 0.60

3: 40/200 = 0.20

4: 20/200 = 0.10

A bar graph that represents the probability distribution of each card is shown in the image below.

In Mathematics and Statistics, a frequency table can be used for the graphical representation of the frequencies or relative frequencies that are associated with a categorical variable or data set.

Based on the frequency, the total number of deck of cards can be calculated as follows;

Total number of deck of cards = 20 + 120 + 40 + 20

Total number of deck of cards = 200 cards.

Next, we would determine the probability distribution of each card as follows:

P(X = 1) = 20/200 = 0.10.

P(X = 2) = 120/200 = 0.60.

P(X = 3) = 40/200 = 0.20.

P(X = 4) = 20/200 = 0.10.

Answer:

1 m 79 cm

Step-by-step explanation:

Subtract 1.46 m from 3.25 cm:  1.79 cm, or 1 m 79 cm

Answer:

  $388.16

Step-by-step explanation:

Her monthly interest rate is 3.8%/12, so the amount of interest due on the first payment is ...

  $260,000 × 0.038/12 ≈ $823.33

Then the amount applied to the principal is ...

  $1211.49 -823.33 = $388.16

[tex]f(x)=2\sqrt x[/tex] is continuous on [0, 4] and differentiable on (0, 4), so the MVT holds. We have

[tex]f'(x)=\dfrac1{\sqrt x}[/tex]

so that by the MVT, there is some [tex]c\in(0,4)[/tex] such that

[tex]f'(c)=\dfrac{f(4)-f(0)}{4-0}\implies\dfrac1{\sqrt c}=\dfrac{2\sqrt4}4=1[/tex]

[tex]\implies1=\sqrt c\implies \boxed{c=1}[/tex]

Answer:

x= 16/9

Step-by-step explanation:

[tex]f(x) = 2\sqrt{x}[/tex] is differentiable on [0,4] so the Mean Value Theorem For Integrals applies.

Average Value of the Integral:

[tex]\frac{1}{b-a} \int\limits^b_a {f(x)} \, dx = \frac{1}{4-0} \int\limits^4_0 {2\sqrt{x} } \, dx[/tex]

After evaluating you will get  [tex]\frac{8}{3}[/tex]

Now, this is the average value so you still need to find the x-value using the original equation:

[tex]\frac{8}{3} =2\sqrt{x}\\\\\frac{4}{3} = \sqrt{x}\\\\\frac{16}{9} =x[/tex]

Answer:

the answer is the letter a) -sin x

Step-by-step explanation:

Simplify the expression.

sine of x to the second power minus one divided by cosine of negative x

(1−sin2(x))/(sin(x)−csc(x))

sin2x+cos2x=11−sin2x=cos2x

cos2(x)/(sin(x)−csc(x))csc(x)=1/sin(x)cos2(x)/(sin(x)− 1/sin(x))= cos2(x)/((sin2(x)− 1)/sin(x))sin2(x)− 1=-cos2(x)cos2(x)/(( -cos2(x))/sin(x))

=-sin(x)

Answer:

[tex]-cos \ x[/tex]

Step-by-step explanation:

First of all, we must have to understand what is the described expression in the paragraph

"sine of x to the second power minus one divided by cosine of negative x"

In this sentence, we need to identify what are the elements and operations involved in the expression.

In the sentence appears ""to the second power", "minus" and "divided by" (highlighted)

"sine of x to the second power minus one divided by cosine of negative x"

Therefore, the expression must has three operations:

Now, we can identify what are the elements: "sine of x", "one" and "cosine of negative x"

Therefore, the expression is:

[tex]\frac{(sin\ x)^{2}-1}{cos(-x)}[/tex]

In order to find the simplified expression, we must have to apply these trigonometric identities:

Applying the first and third identities, we have:

[tex]\frac{(sin\ x)^{2}-1}{cos(-x)}=\frac{sin\x^{2}x-1}{cos\ x}[/tex]

From the second trigonometric identity, we have:

[tex]cos\x^{2}x=\ 1-sin\x^{2}x[/tex]

Now, multiplying by -1 in both sides:

[tex](-1)(cos\x^{2}x)=(-1)(1-\ sin\x^{2}x)[/tex]

In the left side, multiplying by -1 the sign of the expression changes:

[tex](-1)(cos\x^{2}x)=-cos\x^{2}x[/tex]

In the right side, multiplying by -1 changes the order of the substraction:

[tex](-1)(1-\ sin\x^{2}x)=\ sin\x^{2}x-1[/tex]

Putting all together:

[tex]-cos\x^{2}x=\ sin\x^{2}x-1[/tex]

Now, replacing values we have:

[tex]\frac{sin\x^{2}x-1}{cos\ x}=\frac{-cos\x^{2}x}{cos\ x}=-\frac{cos\x^{2}x}{cos\ x}[/tex]

Finally, the property of the first trigonometric identity (property of exponentiation) can be apply in this case:

[tex]-\frac{cos\x^{2}x}{cos\ x}=-\frac{(cos\ x)^{2}}{cos\ x}=-cos\ x[/tex]

Answer:

Option B) $122,140

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=5\ years\\ P=\$100,000\\ r=0.04[/tex]  

substitute in the formula above  

[tex]A=\$100,000(e)^{0.04*5}=\$122,140.28[/tex]  

Round to the nearest dollar

[tex]\$122,140.28=\$122,140[/tex]  

Answer:

[tex]x=10, NL=8, NP=12[/tex]

Step-by-step explanation:

we know that

Applying the Intersecting secant Theorem

[tex]NL*NM=NP*NO[/tex]

substitute the given values and solve for x

[tex](3+5)*3=(2+x)*2[/tex]

[tex](8)*3=(2+x)*2[/tex]

[tex]24=(2+x)*2[/tex]

[tex]12=(2+x)[/tex]

[tex]x=12-2=10[/tex]

Find the value of NP

[tex]NP=(2+x)=2+10=12[/tex]

therefore

[tex]x=10, NL=8, NP=12[/tex]

Answer:

x = 7; NL = 12; NP = 20

Step-by-step explanation:

ur welcome

Answer:

A. $4397.9

Explanation:

We are given that Kendra sold 200 shares and that the price per share was $22.1

This means that:

Total value = 200 * 22.1 = $4420

Now, we know that the broker charged 0.5% commission on the total value

This means that:

Broker's charge = 0.5% * 4420 = 0.005 * 4420 = $22.1

Therefore,

Kendra's return = Total value - broker's charge

Kendra's return = 4420 - 22.1 = $4397.9

Hope this helps :)

Answer:

$4,397.90

Step-by-step explanation:

Answer: 12800m^2

This shape is made up of a rectangle and a triangle.

Rectangle

= 120 x 60

= 7200

Triangle

= (200 - 60) x (120 - 40) x 0.5

= 140 x 80 x 0.5

= 5600

Total Shape

= 7200 + 5600

= 12800m^2