A square pyramid has the sides of the base of 4 cm and a height of 10 cm, what is its surface area?

Answer:

Step-by-step explanation:

x^2 - 36 is the difference of two squares and factors as follows:

        (x - 6)(x + 6)

x^2 - 16 is the difference of two squares and factors as follows:

        (x - 4)(x + 4)

x^2 - 7x + 12 is an easily factored quadratic; the factors are

         (x - 3)(x - 4)

x^2 - x - 20 is an easily factored quadratic; the factors are

         (x - 5)(x + 4)

I conclude that none of the four expressions is prime.

Answer:

B. [tex]x^2+16[/tex]

Step-by-step explanation:

We are asked to find the prime polynomial from our given choices.

We know that a polynomial is prime, when it has only two factors that are 1 and polynomial itself.

Upon looking at our given choices, we can see that each polynomial can be factored except [tex]x^2+16[/tex].

We can see that [tex]x^2+16[/tex] is sum of squares and sum of squares cannot be factored, therefore, polynomial [tex]x^2+16[/tex] is a prime polynomial.

Check the picture below.

Answer:

(1,12) is correct if you meant [tex]3 \cdot 4^x[/tex].

Please correct if I'm wrong about your expression.  

Step-by-step explanation:

I think you mean [tex]f(x)=3 \cdot 4^x[/tex].

Let's test the point and see.

A. (0,12)?

(0,12)=(x,y)

What happens when x equals 0? Is the result 12?

[tex]3 \cdot 4^0[/tex]

[tex]3 \cdot 1[/tex]

[tex]3(1)[/tex]

[tex]3[/tex]

Yep that isn't 12 so (0,12) is not on the graph of f.

B. (0,0)?

(0,0)=(x,y)

What happens when x equals 0? Is the result 0?

[tex]3 \cdot 4^0[/tex]

We already this and got 3 so (0,0) is not on the graph of f.

C.  (1,12)?

(1,12)=(1,12)

What happens when x equals 1? Is the result 12?

[tex]3 \cdot 4^1[/tex]

[tex]3 \cdot 4[/tex]

[tex]12[/tex]

The result is 12 so (1,12) is on the graph of f.

C.  (12,1)

(12,1)=(x,y)

What happens when x equals 12? Is the result 1?

[tex]3 \cdot 4^{12}[/tex]

This will result in a really big number that isn't 1 so (12,1) is not on the graph of f.

(1,12) is correct if you meant [tex]3 \cdot 4^x[/tex].

Answer:

(1,12)

Step-by-step explanation:

ape x

Answer:

6^(32)

Also I don't see your choices.

Step-by-step explanation:

I'm going to apply this law of exponents: (x^a)^b=x^(a*b).

It justs says to multiply the exponents in this case so we have 6^(-8*-4)=6^(32).

Answer:

It would be 1/6^32

Step-by-step explanation:

Answer:

93

Step-by-step explanation:

A quadrilateral's 4 angles add to 360 degrees

70 + 92+<1 + 105 = 360

Combine like terms

267 + <1 = 360

Subtract 267 from each side

267-267 + <1 = 360-267

<1 = 93

Answer:

93

Step-by-step explanation:

OK it's simple...

The interior angles of ANY quadrilateral (a shape with 4 sides) add up to 360.

So all you have to do is add up the angles you already know (70+92+105=267) and subtract that from 360. (360-267).

Answer:

Step-by-step explanation:

We have a triangle 45° - 45° - 90°.

Sides are in the ratio 1 : 1 : √2 (look at the picture).

If [tex]BC=12\sqrt2[/tex] then [tex]AB=(12\sqrt2)(\sqrt2)=(12)(2)=24[/tex]

Used [tex](\sqrt{a})(\sqrt{a})=a[/tex]

Answer: y=-16

Step-by-step explanation:

Y/-2+5=13

Y/-2=8

Y=-16

Answer:

Yes.

Step-by-step explanation:

If we add a fixed number to each term of an arithmetic sequence, we are still going to be having an arithmetic sequence.

For example, given the following sequence:

1, 3, 5, 7, 9, 11...

The difference between consecutive terms  is 2, therefore the pattern is adding two to the previous term.

If we add a fix number, let's say '3':

1+3, 3+3, 5+3, 7+3, 9+3, 11+3...

4, 6, 8, 10, 12, 14...

We notice that the pattern is the same, and it's still an arithmetic sequence.

[tex]\bf \stackrel{\textit{y-intercept}}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-1})}\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-1)}{1-0}\implies \cfrac{1+1}{1}\implies \cfrac{2}{1}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-1)=2(x-0) \\\\\\ y+1=2x\implies \stackrel{\textit{general form}}{-2x+y+1=0}[/tex]

To find the equation of the line with a y-intercept of -1 and passing through the point (1,1), you first determine the slope (which is 2), leading to the slope-intercept form: y = 2x - 1. Then convert this to the general form: -2x + y + 1 = 0.

The general form of the equation of a line is Ax + By + C = 0 where A, B, and C are constants.

To write the equation of a line with a given point (1,1) and a y-intercept of -1, we'll start with the slope-intercept form of the equation, which is y = mx + b. We know that the y-intercept b is -1.

Next, we need to find the slope m, which is the change in y over the change in x. Using the point (1,1), we calculate the slope as (1 - (-1)) / (1 - 0) which equals 2.

Therefore, the slope-intercept form of our line is y = 2x - 1.

To convert this to general form, rearrange the terms and change the equation to have a 0 on one side: -2x + y + 1 = 0.

This is the general form of the equation of the line with the given conditions.

Answer:

60,000/ -30,000 (read explanation)

Step-by-step explanation:

8% of 10,000 is 800, 800 x 50(years) = 40,000, 100,000 -40,000 = 60,000, I believe you meant 100,000, cause if not, the answer is -30,000

Hope this helped

Answer:

Given a function f(x), the function f(x) + k will be translated k units down if k<0. In this case, if we want to produce a vertical translation by 4 units down of the function f(x) = 2x, therefore the new function is:

f(x) = 2x - 4.

Now, we can graph the function like we normally do. Attached you will find the graph made with the help of a graphing calculator.

Answer: B. It would be shifted up.

Step-by-step explanation: We are changing the last number only. This number determines where the y-intercept is, which is on the vertical axis. Since the number increases by 4, the y-intercept would be shifted up by 4, without changing the slope. Therefore, the answer would be B. It would be shifted up.

Answer:

The radius C) of a circle centered at the origin measures the distance from the origin to any point on the circle

Final answer:

The radius of a circle centered at the origin is the distance from the origin to any point on the circle, represented by the equation x² + y² = r².

Explanation:

The radius of a circle centered at the origin measures the distance from the origin to any point on the circle. When we consider the set of all points (x, y) at a fixed distance r from the origin, the equation x² + y² = r² represents a circle of radius r.

This equation is derived using the Pythagorean theorem. The radius is not to be confused with the circumference, which is the distance around the circle, or the y-coordinate, which is simply the vertical position of a point. The radius squared (r²) refers to the square of the length of the radius.

Answer:

16 un.

Step-by-step explanation:

In right triangle ABC:

m∠C = 90°;

m∠BAC = 2m∠ABC;

BC = 24;

AL is a bisector of angle A.

The sum of the measures of all interior angles in triangle  is always 180°, then

In right triangle the leg that is opposite to tha angle 30° is half of the hypotenuse. This means that

By the Pythagorean theorem,

Let AL be the angle A bisector. By bisector property,

Use the Pythagorean theorem for the right triangle ACL:

Read more on Brainly.com - https://brainly.com/question/7723556#readmore

Answer:

AL=24 cm

Step-by-step explanation:

We are given that a triangle ABC,

[tex]m\angle C=90^{circ}[/tex]

[tex]m\angle BAC=2m\angle ABC[/tex]

BC=24 cm

AL is angle bisector

We have to find the value of AL

Let [tex]m\angle ABC=x[/tex]

In triangle ABC

[tex]m\angle BAC+m\angle ABC+m\angle ACB=180^{\circ}[/tex]

[tex]2x+90+x=180[/tex]

[tex]3x=180-90[/tex]

[tex]3x=90[/tex]

[tex]x=\frac{90}{3}=30[/tex]

[tex]m\angle ABC=30^{\circ}[/tex]

[tex]m\angle BAC=2\times 30=60^{\circ}[/tex]

AL is a bisector of angle A

Then [tex]m\angle CAL=30^{\circ}[/tex]

BL=LC=12 cm

In triangle ACL

[tex]sin\theta =\frac{perpendicular side }{hypotenuse}[/tex]

[tex]sin30^{\circ}=\frac{12}{AL}[/tex]

[tex]\frac{12}{AL}=\frac{1}{2}[/tex]

[tex]AL=12\times 2=24 cm[/tex]

Hence, AL=24 cm

Answer:

The Solution set is (x,y){(2,5)}

Step-by-step explanation:

The given equation is:

  6x+4y=32

 -6x+4y=8

We will use the elimination method:

By this method we will eliminate the variable x.

6x+4y=32

-6x+4y=8

________

      8y=40

Divide both the sides by 8

8y/8=40/8

y=5

Now substitute the value of y in equation 2:

-6x+4y=8

-6x+4(5)=8

-6x+20=8

Move the constant value to the R.H.S

-6x=8-20

-6x= -12

Divide both the terms by -6

-6x/-6 = -12/-6

x= 2

The Solution set is (x,y){(2,5)}....

Answer:

[tex]\large\boxed{-1\dfrac{1}{2}}[/tex]

Step-by-step explanation:

The points on the graph are collinear (they lie on one straight line).

Therefore, average of change is the same as a slope.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We choose two points and put the coordinates to the formula

[tex](1, 4), (3, 1)\\\\\dfrac{1-4}{3-1}=\dfrac{-3}{2}=-1\dfrac{1}{2}[/tex]

The average rate of change for the sequence given is [tex]-1\frac{1}{2}[/tex].

The average rate of change formula is used to find the slope of a graphed function. To find the average rate of change, divide the change in y-values by the change in x-values.

The points on the graph are collinear (they lie on one straight line).

Therefore, average of change is the same as a slope.

The formula of a slope:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

We choose two points and put the coordinates to the formula

(1, 4), (3, 1)

[tex]\frac{1-4}{3-1} =\frac{-3}{2} =-1\frac{1}{2}[/tex]

The average rate of change for the sequence given is [tex]-1\frac{1}{2}[/tex].

Find out more information about average rate of change here

https://brainly.com/question/12531344

#SPJ2

Answer:

$2322.59

Step-by-step explanation:

Given

mortgage amount=$470,000

Interest rate annually=4.6%

Time=30 years

Monthly payments=?

Formula to apply

[tex]M=\frac{P(1+r)^n*r}{(1+r)^n-1}[/tex]

where

M=monthly payment for the mortgage

P=Principal amount =$470,000

i=rate per month=4.6÷12=0.3833%

n=30×12=360

Applying the formula

[tex]M=\frac{P(1+r)^n*r}{(1+r)^n-1} \\\\\\M=\frac{470000(1+0.004)^{360}*0.004 }{(1+0.004)^{360} -1} \\\\\\M=\frac{7452.235}{3.209} =2322.59[/tex]

Answer:

[tex]y=\frac{1}{30}(x-7)+1.5[/tex]

2.8 million is what we get in 2047

Step-by-step explanation:

Ok I see the following given in 2007, the medium salary is 1.5 million and in 2013 the medium salary is 1.7 million.

It says let x=7 represent 2007 so that means x=13 would represent 2013.

It also says y is in millions so y=1.5 means 1.5 million and y=1.7 means 1.7 million.

So we have these points that we need to find a line for:  (7,1.5) and (13,1.7).

The slope can be found by using the slope formula given two points.  This looks like this (y2-y1)/(x2-x1).

I like to line the points up and subtract then put 2nd difference over 1st difference.

Let's do that.

(13, 1.7)

-(7, 1.5)

-----------

6       .2

The slope is .2/6 or 2/60 (after multiplying top and bottom by 10) or 1/30 (after dividing top and bottom by 2)

So point slope form for this line is [tex]y-1.5=\frac{1}{30}(x-7)[/tex].

To get the point slope form for this line I just entered my m (the slope) and point (x1,y1) I knew on the line (like (7,1.5) ). Point slope form is [tex]y-y_1=m(x-x_1)[/tex].

So adding 1.5 on both sides of  [tex]y-1.5=\frac{1}{30}(x-7)[/tex] gives me  [tex]y=\frac{1}{30}(x-7)+1.5[/tex]

So now it says what is the medium salary in 2047 I believe. So we are going to plug in 47.

This gives us

[tex]y=\frac{1}{30}(47-7)+1.5[/tex]

[tex]y=\frac{1}{30}(40)+1.5[/tex]

[tex]y=\frac{4}{3}+1.5[/tex]

[tex]y=2.833333333333333333333333[/tex]

So 2.8 million

[tex]\huge{\boxed{y=-3x+4}}[/tex]

Slope-intercept form is [tex]y=mx+b[/tex], where [tex]m[/tex] represents the slope and [tex]b[/tex] represents the y-intercept.

Substitute in the values. [tex]\boxed{y=-3x+4}[/tex]

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

In this case the slope (m) is -3 and the y-intercept (b) is 4

Your equation is:

y = -3x + 4

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

[tex]x_{1=} \frac{-1+i\sqrt{35} }{6} \\\\x_{2=} \frac{-1-i\sqrt{35} }{6}[/tex]

Step-by-step explanation:

Using the quadratic formula:

[tex]x=\frac{-b+-\sqrt{b^{2}-4*a*c} }{2*a}[/tex]

We will have two solutions:

[tex]x_{1}\\ x_{2}[/tex]

-3x^2-x-3=0     a=-3    b=-1   c=-3

We have:

[tex]x_{1}=\frac{1+\sqrt{-35} }{-6}\\\\x_{2}=\frac{1-\sqrt{-35} }{-6}\\[/tex]

we can write:

[tex]x_{1}=\frac{-1+\sqrt{-35} }{6}\\\\x_{2}=\frac{-1-\sqrt{-35} }{6}\\[/tex]

The solutions are not real numbers.

So, we know: [tex]i=\sqrt{-1}[/tex]

Finally we have:

[tex]x_{1}=\frac{-1+i\sqrt{35} }{6}\\\\x_{2}=\frac{-1-i\sqrt{35} }{6}\\[/tex]

Answer:

360

Step-by-step explanation:

Set up an equation:

Numerator is the top number and denominator is the bottom number in a fraction.

(6x)^5 / d = 36

(6x)^5 can be rewritten as 6^5x^5

6^5x^5 / d = 36

Raise 6 tot he power of 5:

7776x^5 /d = 36

Multiply both sides by d:

7776x^5 = 36d

Divide both sides by 36:

d = 7776x^5 / 36

d = 216x^5

Answer:

1. D y = 8

2. C y = −8

Step-by-step explanation:

1.

Both points have y-coordinate 8, so the line is horizontal.

A horizontal line has equation

y = k

where k is the y-coordinate of all of its points.

The y-coordinate of all points on this line is 8.

Answer: y = 8

2.

A line with 0 slope is a horizontal line. All points on a horizontal line have the same y-coordinate.

A horizontal line has equation

y = k

where k is the y-coordinate of all of its points.

The y-coordinate of the given point is -8, so all points must have -8 as the y-coordinate.

Answer: y = -8

The equation of a line through two given points can be found using the point-slope form. A slope of 0 indicates a horizontal line.

To find the equation of a line that contains the points (0, 8) and (8, 8), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1). Here, (x1, y1) represents one of the points and m represents the slope. Since the y-coordinates of both points are 8, we can see that the line is horizontal. Therefore, the equation of the line is y = 8.

For the second question, a slope of 0 indicates a horizontal line. The equation of a horizontal line is y = b, where b is the y-coordinate of any point on the line. Since our point is (0, -8), the equation of the line is y = -8.

https://brainly.com/question/30200878

#SPJ2

Answer:

(a + b)(a + b - 2c)

Step-by-step explanation:

Note that

(a + b)² = a² + b² + 2ab

Given

a² + b² + 2(ab - ac - bc) ← distribute parenthesis

= a² + b² + 2ab - 2ac - 2bc

= (a + b)² - 2ac - 2bc ← factor out - 2c from each term

= (a + b)² - 2c (a + b) ← factor out (a + b) from each term

= (a + b) [ a + b - 2c ]

= (a + b)(a + b - 2c) ← in factored form

The expression a² + b² + 2(ab - ac - bc) cannot be factorized using standard factorization techniques over real numbers, as a² + b² is not factorizable over the reals and there's no common factor for all terms.

To factorize the expression a² + b²+ 2(ab - ac - bc). To factorize this, we will look for a common factor and regroup the terms. Let's see if there's a way to rearrange the terms to resemble a known pattern or factor by grouping.

First, let's rewrite the expression by grouping terms with a common factor:

a² + 2ab - 2ac

b² - 2bc

However, we notice that the expression does not fit into a perfect square or any other easily factorizable form like (a + b)² or (a - b)² due to the nature of the terms a², b², and 2(ab - ac - bc). The expression is already in its simplest factored form as it stands because a²+ b² is not factorizable over the real numbers, and there's no common factor for all terms.

Therefore, the expression a² + b² + 2(ab - ac - bc) does not factorize further using real numbers and the usual factorization techniques.

Answer:

Martha and George Washington had no children together, but they raised Martha's two surviving children. In 1773 her daughter Patsy died when she was 16 during an epileptic seizure. John Parke "Jacky" Custis left King's College that fall and married Eleanor Calvert in February 1774.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

Part 1) [tex]b=8.2\ units[/tex]

Part 2) [tex]a=10.1\ units[/tex]

Part 3) [tex]A=51\°[/tex] and [tex]C=90\°[/tex]

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

Find the side b

we know that

In the right triangle ABC

The function sine of angle B is equal to divide the opposite side angle B (AC) by the hypotenuse (AB)

[tex]sin(B)=AC/AB[/tex]

we have

[tex]AB=c=13\ units[/tex]

[tex]AC=b[/tex]

[tex]B=39\°[/tex]

substitute

[tex]sin(39\°)=b/13[/tex]

solve for b

[tex]b=(13)sin(39\°)[/tex]

[tex]b=8.2\ units[/tex]

step 2

Find the side a

we know that

In the right triangle ABC

The function cosine of angle B is equal to divide the adjacent side angle B (BC) by the hypotenuse (AB)

[tex]cos(B)=BC/AB[/tex]

we have

[tex]AB=c=13\ units[/tex]

[tex]BC=a[/tex]

[tex]B=39\°[/tex]

substitute

[tex]cos(39\°)=a/13[/tex]

solve for a

[tex]a=(13)cos(39\°)[/tex]

[tex]a=10.1\ units[/tex]

step 3

Find the measure of angle A

we know that

In the right triangle ABC

[tex]C=90\°[/tex] ----> is a right angle

[tex]B=39\°[/tex]

∠A+∠B=90° ------> by complementary angles

substitute the given value

[tex]A+39\°=90\°[/tex]

[tex]A=90\°-39\°[/tex]

[tex]A=51\°[/tex]

Answer:

R(- 12, 22 )

Step-by-step explanation:

Using the midpoint formula

[tex]\frac{1}{2}[/tex](8 + [tex]x_{R}[/tex] ) = [tex]x_{M}[/tex] = - 2

Multiply both sides by 2

8 + [tex]x_{R}[/tex] = - 4 ( subtract 8 from both sides )

[tex]x_{R}[/tex] = - 12

----------------------------------------------

[tex]\frac{1}{2}[/tex](- 10 + [tex]y_{R}[/tex] ) = [tex]y_{M}[/tex] = 6

Multiply both sides by 2

- 10 + [tex]y_{R}[/tex] = 12 ( add 10 to both sides )

[tex]y_{R}[/tex] = 22

The coordinates of R = (- 12, 22 )

Answer:

[tex]\large\boxed{(n^3)^2\times(n^5)^4=n^{26}}[/tex]

Step-by-step explanation:

[tex](n^3)^2\times(n^5)^4\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=(n^{3\cdot2})\times(n^{5\cdot4})=n^{6}\times n^{20}\qquad\text{use}\ a^n\times a^m=a^{n+m}\\\\=n^{6+20}=n^{26}[/tex]

Answer:

0.5

Step-by-step explanation:

there are 26 black cards

26/52=

0.5

Answer:

0.5

Step-by-step explanation:

A deck of cards has 52 cards. Out of which 26 are red and 26 are black. The black cards are further divided into two suits.

So,

total sample space = n(S) = 52

Let A be the event that the drawn card is a black card

Then,

n(A) = 26

So, the probability of A will be:

[tex]P(A) = \frac{n(A)}{n(S)}\\ = \frac{26}{52}\\ =\frac{1}{2}\\ =0.5[/tex]

Hence the theoretical property of drawing a black card is 0.5 ..

Answer:

39 tables

Step-by-step explanation:

Given:

third grade= 134

fourth grade=167

total=134+167=301

Now no. of students is 7 times no. of adults,

no. of adults= 301/7

                    =43

Total no. of people =301+43

                                 =344

Each picnic table can seat 9 people, so

No. of tables for 344 people= 344/9

                                              =38.222

39 tables picnic tables will need to be set up for the picnic!