8) There are 2116 students in a school .In how many equal rows and columns can they be arranged for a drill display?

Answer:

A 2 by 2 inch square has an area of 4 square inches.

If its area is increased by 21 inches, then its area equals 25 square inches.

To find the length of the side we take the square root of 25 square inches which is 5 inches.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

So we have the equation:

[tex]-15=5a+12-2a+6[/tex]

On the right combine like terms:

[tex]-15=5a-2a+12+6\\-15=3a+18[/tex]

Subtract 18 from both sides. The right cancels:

[tex](-15)-18=(3a+18)-18\\-33=3a[/tex]

Divide both sides by 3:

[tex](-33)/3=(3a)/3\\a=-11[/tex]

The answer is A, -11.

Answer:

a = -11

Step-by-step explanation:

-15 = 5a +12- 2a + 6

Combine like terms

-15 = 3a +18

Subtract 18 from each side

-15-18 = 3a+18-18

-33 = 3a

Divide each side by 3

-33/3 = 3a/3

-11 =a

Answer:

[tex]5 \frac{1}{9}[/tex]

[tex]6 \frac{2}{5}[/tex]

Step-by-step explanation:

We can convert these improper fractions into mixed numbers by seeing how many times the denominator goes into the numerator.

In [tex]\frac{46}{9}[/tex], 9 goes into 46 5 times, with a remainder of 1. So:

[tex]5 \frac{1}{9}[/tex].

In [tex]\frac{32}{5}[/tex], 5 goes into 32 6 times with a remainder of 2, so:

[tex]6 \frac{2}{5}[/tex].

Hope this helped!

Answer:

5 1/9 and 6 2/5

Step-by-step explanation:

The simplest way to convert improper fractions into mixed fractions is by long division (see attached).

Answer:

5x(25)

Step-by-step explanation:

Answer: 96

Step-by-step explanation:

Ok, lines a and b are parallel.

We can separate this problem in two cases:

Case 1: 2 vertex in line a, and one vertex in line b.

Here we use the relation:

"In a group of N elements, the total combinations of sets of K elements is given by"

[tex]C = \frac{N!}{(N - K)!*K!}[/tex]

Here, the total number of points in the line is N, and K is the ones that we select to make the vertices of the triangle.

Then if we have two vertices in line a, we have:

N = 6, K = 2

[tex]C = \frac{6!}{4!*2!} = \frac{6*5}{2} = 3*5 = 15[/tex]

And the other vertex can be on any of the four points on the line b, so the total number of triangles is:

C = 15*4 = 60.

But we still have the case 2, where we have 2 vertices on line b, and one on line a.

First, the combination for the two vertices in line b is:

We use N = 4 and K = 2.

[tex]C = \frac{4!}{2!*2!} = \frac{4*3}{2} = 6[/tex]

And the other vertice of the triangle can be on any of the 6 points in line a, so the total number of triangles that we can make in this case is:

C = 6*6 = 36

Then, putting together the two cases, we have a total of:

60 + 36 = 96 different triangles

Answer:2 c^2 - 10c

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

First equation: the coefficients of x and y are 3 and -2, and the constant is 4.

So the first row should be [3 -2 4].

Second equation: the coefficients of x and y are 6 and -1, and the constant is 10. Hence, the second row should be [6 -1 10].

Answer:

g = 1

Step-by-step explanation:

-3 + 5 + 6g = 11 - 3g

Move the variables to one side and the numbers to the other:

9g = 9

Simplify:

g = 1

Answer:

g=1

Step-by-step explanation:

-3+5=2

2+6g=8

11-3g=8

makes sense that g will have to be 1

Hi there! Hopefully this helps!

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Answer: 14.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

First we calculate 3 to the power of 2 and get 9.

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9 + 9 - [tex]\frac{8}{2}[/tex] = 14.

Now we add 9 + 9 to get 18.

18 - [tex]\frac{8}{2}[/tex] = 14.

Then, we divide 8 by 2 to get 4.

18 - 4 = 14.

Then we subtract 4 from 18 to get.....You guessed it, 14!

Answer: 14

PEMDAS

P: Parentheses

E: Exponets

M: Multiplcaction

D: Divison

A: Addition

S: Subtraction

PEMDAS can also be known as Please Excuse My Dear Aunt Sally

P: [tex](9-8/2)[/tex]

E: [tex]3^2[/tex]

M: [tex]3*3[/tex]

D: [tex]8/2[/tex]

A: [tex]9+5[/tex]

S: [tex]9-8/2[/tex]

Multiply

E: [tex]3^2=3*3=9[/tex]

M: [tex]3*3=9[/tex]

Divide

D: [tex]8/2=4[/tex]

Subtract

S: [tex]9-4=5[/tex]

Add

A: [tex]9+5=14[/tex]

Answer: [tex]14[/tex]

The reason why we didn't use P to get our answer because it would of messed up the steps. So instead we separated it by dividing 8/2 in D and 9-4-5 for S.

Answer:

No, it does not matter.

Step-by-step explanation:

In prime factorization there is only one way to be factored. Once these numbers are broken down, into prime numbers you will get the same result no matter what list of prime numbers you use and what order you use them in.

Answer:

-19

Step-by-step explanation:

(-14)

-5

-------

14+5=19

add the negative

-19

Answer:

TRUE

Step-by-step explanation:

Length of other leg [tex]= \sqrt {12^2 - 8^2} \\

= \sqrt {144 -64} \\

= \sqrt {80} \\

= 4\sqrt {5} \\[/tex]

Since, [tex] \sqrt 5[/tex] is an irrational number, hence Perimeter of triangle will also be irrational.

TRUE

Answer:

True.

Step-by-step explanation:

The length of the other side = sqrt ( 12^2 - 8^2)

= sqrt (144 - 64)

= sqrt ( 80) which is irrational so the perimeter is also irrational.

(The sum of a rational number and an irrational is irrational).

Supplementary angles are those which sum upto 180°

[tex] \angle 1+\angle2=180^{\circ}[/tex]

Complementary are those which sum to 90°

[tex] \angle 1+\angle2=90^{\circ}[/tex]

so if you know one angle, you can find other.

Answer:Look at my explaination

Step-by-step explanation:The complement of 50 is 90-50 giving us 40degrees

The supplement of 145 is 180-145=35 degrees

The compliment of 27 degrees is 90-27=63 degrees

The supplement of 50 degrees is 180-50=130 degrees

Answer:

32

Step-by-step explanation:

the country would need 30 to 33 trees

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]6x^2-8x+k=0\\\\\text{We compute the discriminant.}\\\\\Delta = b^2-4ac=8^2-4*6*k=8*8-8*3*k=8*(8-3k)[/tex]

And the we know that if the discriminant is

***** [tex]\Delta[/tex] < 0, meaning 8-3k<0, meaning

[tex]\boxed{k>\dfrac{8}{3}}[/tex]

then, there is no real solution.

***** [tex]\Delta = 0[/tex], meaning

[tex]\boxed{k=\dfrac{8}{3}}[/tex]

There is 1 solution.

***** [tex]\Delta[/tex] > 0, meaning

[tex]\boxed{k<\dfrac{8}{3}}[/tex]

There are 2 solutions.

Thank you

PS: To give more details...

[tex]8-3k=0\\\\\text{Add 3k}\\\\8=3k\\\\\text{Divide by 3}\\\\k=\dfrac{8}{3}[/tex]

Answer:

8

Step-by-step explanation:

x+37+x+37+90 = 180

2x + 74 = 90

2x = 16

x = 8

Answer:

x=8°

Step-by-step explanation:

JI is a diameter and K is on the circumference of a circle.

∴∠JKI=90°

also KJ=KI=x(say)

tan (x+37)=y/y=1=tan 45

so x+37=45

x=45-37=8°

Step-by-step explanation:

[tex]\huge{\purple{\underline{\underline{\bf{\pink{Answer}}}}}}[/tex]

in this we have given the value of f(x) = 15

[tex]f(x) = x + 7[/tex]

[tex]f(15) = 15 + 7[/tex]

[tex]f(15) = 22[/tex]

so this is ur answer

hope it helps .

Answer: rectangle.

Step-by-step explanation:

Given points: K(0,0) I(2,2) T(5,-5) E(7,-3)

Distance formula to find distance between [tex]A(a,b)[/tex] and [tex]B(c,d)[/tex]: [tex]AB=\sqrt{(d-b)^2+((c-a)^2}[/tex]

[tex]KI=\sqrt{(2-0)^2+(2-0)^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}\ units[/tex]

[tex]KT=\sqrt{(5-0)^2+(-5-0)^2}=\sqrt{25+25}=\sqrt{50}=5\sqrt{2}\ units[/tex]

[tex]TE=\sqrt{(7-5)^2+(-3+5)^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}\ units[/tex]

[tex]IE=\sqrt{(7-2)^2+(-3-2)^2}=\sqrt{25+25}=\sqrt{50}=5\sqrt{2}\ units[/tex]

i.e. KI = TE and KT= IE, so opposite sides equal.

It can be a parallelogram or rectangle. [if all sides are equal it would be square or rhombus]

[tex]IT=\sqrt{(5-2)^2+(-5-2)^2}=\sqrt{3^2+7^2}=\sqrt{9+49}=\sqrt{58}\ units[/tex]

[tex]KE=\sqrt{(7-0)^2+(-3-0)^2}=\sqrt{7^2+3^2}=\sqrt{9+49}=\sqrt{58}\ units[/tex]

IT= KE, i.e. diagonals are equal.

It means KIET is  a rectangle.

Answer:

x=25

Step-by-step explanation:

you know that both angles equal the same degrees, so the bottom one is 150° so the other is also 150°. You already have 50° so all you need left is 100°. divide 100 by 4 and you get x=25

Answer:

10a -7b

Step-by-step explanation:

9a-6b+a-b​

Combine like terms

9a+a   -6b-b

10a -7b

Answer:

10a-7b

Step-by-step explanation:

[tex]9a - 6b + a - b \\ 9a + a - 6b - b \\ 10a - 7b[/tex]

Answer:

Step-by-step explanation:

The formula for this is

∠G = 1/2(arcEH - arcHF)

We have angle G (5x - 10) and we have arcEH (195) so we have to solve for x to find the measure of arcEHF so we can add arcEH + arcHF = arcEHF

Filling in the formula with what we have:

[tex]5x-10=\frac{1}{2}(195-(8x+17))[/tex]

which simplifies down a bit to

[tex]5x-10=\frac{1}{2}(195-8x-17)[/tex] which simplifies down a bit more to

[tex]5x-10=\frac{1}{2}(178-8x)[/tex] Multiply both sides by 2 to get rid of the fraction and get:

2(5x - 10) = 178 - 8x which of course simplifies to

10x - 20 = 178 - 8x. Now add 8x to both sides and at the same time add 20 to both sides to get:

18x = 198 so

x = 11. Now we can find the measure of arcHF:

arcHF is 8x + 17, so arcHF is 8(11) + 17 which is 105°.

arcEH + arcHF = arcEHF so

195 + 105 = arcEHF so

arcEHF = 300°

Answer:

  6

Step-by-step explanation:

If x represents the last number, to get zero you must subtract 6 from it:

  x - 6 = 0

  x = 6 . . . . . . add 6 (undo the subtraction)

The last number before zero is 6.

Answer:

466.7 or 42.003 miles

Step-by-step explanation:

subtract 59.99 from 200.00. Then you have 140.01 and divide or multiply it by 0.30.

Answer:

reflection across y = x

Step-by-step explanation:

Transformation is the movement of a point from its initial position to a new position. If a shape is transformed, all its point are also transformed. Types of transformation is reflection, rotation, transformation and dilation.

If a point is reflected across the x axis, the x coordinate is the same but the y coordinates is negated. If X(x, y) is reflected across the x axis the new point is X'(x, -y)

If a point is reflected across the y axis, the y coordinate is the same but the x coordinates is negated. If X(x, y) is reflected across the y axis the new point is X'(-x, y)

If a point is reflected across y = x, the x coordinate and y coordinates are interchanged. If X(x, y) is reflected across the y=x axis the new point is X'(y, x)

If a point is reflected across y = -x, the x coordinate and y coordinates are interchanged and both negated. If X(x, y) is reflected across the y=ix axis the new point is X'(-y, -x)

The vertices of △ABC are A(-1, 3), B(2, 4), and C(-5, 6). The vertices of △A′B′C′ are A′(3, −1), B′(4, 2), and C′(6, −5). The reflection of △ABC to form​​ ​△A′B′C′ shows a reflection across x axis since the x and y coordinates are interchanged

Answer:

reflection across y = x

Step-by-step explanation:

Answer:

y=4

Step-by-step explanation:

An exponential function of the form  has a horizontal asymptote of .

The given function is .

The graph of the given function is shown in the attachment.

From the graph the horizontal asymptote is

Answer:

[tex]\boxed{0.15}[/tex]

Step-by-step explanation:

Part 1: Solve for the total amount of marbles

To solve for the probability of certain events, a population is needed to derive this information from. In order to find this population, add up the amounts of each marble.

8 + 14 + 12 = 34 marbles

Part 2: Determine the probabilities

Now, given the amounts of marbles, simply multiply the ratios of blue marbles to total marbles and the ratio of clear marbles to total marbles to get the combined probability.

[tex]\frac{12}{34}*\frac{14}{33} = \frac{28}{187} \approxeq 0.1497 \approxeq 0.15 * 100 = 15[/tex]

The probability of these events occurring simultaneously is 15%.

the change in x  is 1 and 2 in y respectively

the points are in order from r (x,y)         to     m (9,8)         to   s (10,10

if we take - 1 from x and 2 from y we will get r, or (8,6)

Answer:

its a mnemonic

Oh  Heck  Another  Hour Of  Algebra

(O = opposite side, H = hypotenuse ) = sine

(A = adjacent side,  H = hypotenuse ) = cosine

(O = opposite side,  A = adjacent ) = tangent

Answer:

100m

Step-by-step explanation:

x=the height of the tower

100m=the distance from the tower

45 degrees the angle of elevation

Drawing a diagram allows you to see that you can form a 'right-angled triangle'.

Using trig. :

Tan 45=x/100m

multiply both sides by 100m

100m*tan 45=100m

Answer:

[tex]\Huge \boxed{\mathrm{100 \ meters}}[/tex]

Step-by-step explanation:

The base of the right triangle created is 100 meters.

The angle between the base and the hypotenuse of the right triangle is 45 degrees.

We can use trigonometric functions to solve for the height of the tower.

[tex]\displaystyle \mathrm{tan(\theta)=\frac{opposite}{adjacent} }[/tex]

Let the height be x.

[tex]\displaystyle \mathrm{tan(45)}=\frac{x}{100}[/tex]

Multiplying both sides by 100.

[tex]\displaystyle 100 \cdot \mathrm{tan(45)}=x[/tex]

[tex]100=x[/tex]

The height of the tower is 100 meters.

Answer:

The time it takes the rock to reach the canyon floor is approximately 4 seconds.

Step-by-step explanation:

The equation representing the height h (in feet) of an object t seconds after it is dropped is:

[tex]h=-16t^{2}+h_{0}[/tex]

Here, h₀ is the initial height of the object.

It is provided that a small rock dislodges from a ledge that is 255 ft above a canyon floor.

That is, h₀ = 255 ft.

So, when the rock to reaches the canyon floor the final height will be, h = 0.

Compute the time it takes the rock to reach the canyon floor as follows:

[tex]h=-16t^{2}+h_{0}[/tex]

[tex]0=-16t^{2}+255\\\\16t^{2}=255\\\\t^{2}=\frac{255}{16}\\\\t^{2}=15.9375\\\\t=\sqrt{15.9375}\\\\t=3.99218\\\\t\approx 4[/tex]

Thus, the time it takes the rock to reach the canyon floor is approximately 4 seconds.

Answer:

t=4

Step-by-step explanation:

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