expand 321 five using exponent ​

The following ages combination is possible -

[A] = 17 and [B] = 6

or

[A] = 6 and [B] = 17

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is sum of the ages of A and B as 23 years and their product is 102 years.

Assume that the age of A is [x] years and of B is [y] years. So, we can write -

x + y = 23

xy = 102

Refer to the graph attached. It shows two points of intersection as -

(17, 6)  and  (6, 17).

Therefore, the following ages combination is possible -

[A] = 17 and [B] = 6

or

[A] = 6 and [B] = 17

To solve more questions on equation modelling, visit the link below-

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[Question translation in english -

The sum of the ages of A and B is 23 years and the product is 102 years. find both ages.]

Answer:

1

Step-by-step explanation:

Use your [tex]\frac{rise}{run}[/tex] knowledge. To get to the point above a whole number starting from your y-intercept, you would go up 1 and left one. [tex]\frac{1}{1} = 1[/tex], so that's your answer.

Answer:

1

Step-by-step explanation:

Let m the slope of our function and f the function :

m = [f(0)-f(-1)]/0-(-1) = (1-0)/1= 1

Answer: The points of the images are  (9,10), (15,6), (6,4)  and the image is not a rigid motion because the shape changes in side.

Step-by-step explanation:

Since it gives you the scale factor then find they coordinates by multiplying the coordinates by the scare factor.

A(3,5) → (3*3,5*2) → (9,10)

B( 5,3) → (5*3, 3*2) → (15,6)

C ( 2,3)→ (2*3, 2*2)→ ( 6,4)

Answer:

In this problem, there is multiple choice for every question. The trick is to exclude the answer that unlikely true.

To solve this easier, you need to find the distance of AB first. After that try to match the answer coordinate with the midpoint of AB. 

1.  Answer: Point C(-3.6, -3.4) divides AB in the ratio 2:3

A (-2,-1) and B(-6, -7)The distance between A and B would be:

x= x2-x1 = -6 - (-2)= -4

y= y2-y1 = -7 - (-1)= -6

Since both x and y coordinate of A and B is minus, let's try answer with x and y minus value.

Point C(-3.6, -3.4) divides AB in the ratio 2:3

x3= x1 + AB ratio* AB distance

x3= -2 + (2/2+3)*(-4)= -3.6

y3= y1 + AB ratio* AB distance

y3= -1 + (2/2+3)*(-6)= -1 - 12/5= -3.4

2.  Point C(0, 1) divides AB in the ratio 4:7

A(4,-3) and B(-7,8)

The distance between A and B would be:

x= x2-x1 = -7 - (4)= -11

y= y2-y1 = 8 - (-3)= 11

Since both x and y distance is 11, let's try answer with total ratio 11

Point C(0, 1) divides AB in the ratio 4:7

x3= x1 + AB ratio* AB distance

x3= 4 + (4/4+7)*(-11)= 4- 4=0

y3= y1 + AB ratio* AB distance

y3= -3 + (4/4+7)*(11)= -3 +4= 1

3. Answer: Point C(8, 9) divides AB in the ratio 5:3

A(3,4) and B(11,12)The distance between A and B would be:

x= x2-x1 = 11 - (3)= 8

y= y2-y1 = 12 - (4)= 8

Since both x and y distance is 8, let's try answer with the total ratio 8. Both of x and y also plus, so focus on coordinate with both x and y plus too.

Point C(3.5, -2.5) divides AB in the ratio 1:7-----> total ratio 8,y minus

Point C(-2, 5) divides AB in the ratio 2:6  -----> total ratio 8, x minus

Point C(8, 9) divides AB in the ratio 5:3   -----> total ratio 8, both x and y plus

x3= x1 + AB ratio* AB distance

x3= 3 + (5/5+3)*(8)= 3+ 5=8

y3= y1 + AB ratio* AB distance

y3= 4 + (5/5+3)*(8)= 4 +5= 9

4. Point C(-2, 5) divides AB in the ratio 2:6  

A(-5,2)and B(7, 14)

The distance between A and B would be:

x= x2-x1 = 7 - (-5)= 12

y= y2-y1 = 14 - (2)= 12

Since both x and y distance is 12, it will be hard to use it since 12 has many factors. Both y coordinate is plus, so focus on coordinate with y more than x and plus.

Point C(4, 1.6) divides AB in the ratio 3:2  ----->  x more than y

Point C(-2, 5) divides AB in the ratio 2:6  -------> y plus, y more than xx3= x1 + AB ratio* AB distance

x3= -5 + (2/2+6)*(12)= -5+ 3=-2

y3= y1 + AB ratio* AB distance

y3= 2 + (2/2+6)*(12)= 2 +3= 5

Step-by-step explanation:

Answer:

Hey there!

We have the equation: y2-y1/x2-x1.

So, we have: 8-2/8-6.

6/2, or 3.

Hope this helps!

Answer:

x=17

sinD = [tex]\frac{8}{17}[/tex]

cos D would be 15 / 17

tan D would be 8/15

sin F is 15/17

cos F is 8/17

tan F is 15/8

Step-by-step explanation:

To solve for x, use the pythagorean theorem - [tex]a^{2} + b^{2} = c^{2}[/tex].

[tex]8^2 + 15^2 = x^2\\289 = x^2\\17 = x[/tex]

For the Sin of D, you put the opposite side over the hypotenuse:

8 / 17

To find Cos, you do adjacent side over hypotenuse and for Tan you do opposite side over adjacent.

cos D would be 15 / 17

tan D would be 8/15

sin F is 15/17

cos F is 8/17

tan F is 15/8

Answer:

Attachment 1:- x = 17

sin D = EF/DF = 8/17

Attachment 2:- sin D = 8/17

cos D = ED/DF = 15/17

tan D = sin D / cos D = 8/15

sin F = DE/DF = 15/17

cos F = EF /DF = 8/17

tan F = sin F / cos F = 15/8

sin = opposite / hypotenuse

cos = adjacent / hypotenuse

tan = sin / cos (or) opposite / adjacent

The first book you select can be any one of 700.

. . . For each of those ...

The second book can be any one of the other 699.

. . . For each of those ...

The third book can be any one of the remining 698.

The total number of ways to gather three books from the shelves into your hands is  (700 · 699 · 698)  =  341,531,400 ways .

BUT ...

When you bring three books to the check-out counter, Marian the Librarian doesn't know in which order you took them down off the shelves.  You could have gathered the same three books in (3 · 2 · 1) = 6 different ways.

So, even though there are 341,531,400 ways to gather up three books, there are only (341,531,400 / 6) = 56,921,900 different GROUPS of three books that you can choose to take home.

Answer:

Below.

Step-by-step explanation:

This is a parabola.

As the coefficient of x^2 is positive it will open upwards ( shaped like a 'U').

If we convert to vertex form we can find the line of symmetry  and the coordinates of the vertex:

f(x) = 3x^2 - 2x + 1

f(x) = 3(x^2 - 2/3 x) + 1

f(x) = 3[(x - 1/3)^2 - (1/3)^2] + 1

f(x) = 3(x - 1/3)^2 - 1/3 + 1

f(x) = 3(x - 1/3)^2 + 2/3

So the line of symmetry is  x = 1/3 and

the vertex ( the minimum of the curve) is at (1/3, 2/3).

Answer:

x = 63

Step-by-step explanation:

We can find the value of x by multiplying the difference of large arc to small arc with 1/2

if a = 117° then the large arc would be 243

1/2 × (243 - 117) = 63

Answer:

x=12

Step-by-step explanation:

Intersecting Chords Formula:

(segment piece) x (segment piece) =  (segment piece) x (segment piece)

10 * x =  ( 3+x) *8

10x = 24+8x

Subtract 8x

10x-8x = 24+8x-8x

2x= 24

Divide by 2

2x/2 =24/2

x = 12

Answer:

X = 0, Y= -2

Step-by-step explanation:

Compare the x and y coordinate values

3x + 2y =-4_______(1)

2x - y = 2 ________(2)

Multiply the (2) with 2

4x - 2y = 4

and add the new equation to (1)

3x + 2y =-4

4x - 2y = 4

____________

7x = 0

X = 0

Substitute x value into (1)

3 *0 + 2y = -4

0 + 2y =-4

2y =-4

Y= -2

Answer:

540 ft^2.

Step-by-step explanation:

The area of the trapezoid = h/2 (10 + 18) = 14h.

By Pythagoras the height h = √(5^2 - 4^2) = 3.

So the area of the 2 trapezoidal bases = 2 * 14*3

= 84 ft^2.

Now we calculate the area of the four lateral rectangular sides:

= 10*12 + 18*12 + 2*5*12

= 456 ft^2.

Total area =  456 + 54

= 540 ft^2.

Answer:

2. -3, 1.

3. -2, 0.

4. 6, 8.

5. 20.

Step-by-step explanation:

2. x - 3y + 6 = 0

-3y = -x -6

y = 1/3x + 2

y + 4 = -5/4(x - 1)

y + 4 = -5/4x + 5/4

y = -5/4x + 5/4 - 16/4

y = -5/4x - 11/4

If you sketch these two lines on paper (or draw them on a graphing calculator), you will find that they intersect at (-3, 1).

So, the values you enter on the response would be -3, 1.

3. x + 3y = -2

x = -3y - 2

-3x + 5y = 6

-3(-3y - 2) + 5y = 6

9y + 6 + 5y = 6

14y + 6 = 6

14y = 0

y = 0

x + 3 * 0 = -2

x + 0 = -2

x = -2

-3 * -2 + 5 * 0 = 6

Since everything works out, the solution to the two equations is (-2, 0).

So, the values you enter on the response would be -2, 0.

4. 3x - 4y = -14

2x + 5y = 52

2(3x - 4y = -14)

3(2x + 5y = 52)

6x - 8y = -28

6x + 15y = 156

6x + 15y = 156

-6x + 8y = 28

23y = 184

y = 8

3x - 4 * 8 = -14

3x - 32 = -14

3x = 18

x = 6

2 * 6 + 5 * 8 = 12 + 40 = 52

Everything works out, so your solution is (6, 8).

Your answer will be (6, 8).

5. For a system of equations to have no solution, the y's and the x's must have the same coefficients.

5x - Ky - 10 = 0

y = 1/4x + 6

-Ky = -5x + 10

Ky = 5x - 10

1/5Ky = x - 2

1/20Ky = 1/4x - 1/2

1/20K = 1

K = 20

y = 1/4x - 1/2

y = 1/4x + 6

1/4x - 1/2 = 1/4x + 6

1/4x - 1/4x = 6 + 1/2

0 = 6.5

There is no solution, so K = 20.

Hope this helps!!

Answer:

Please refer to the attached image for the graph of given function.

Step-by-step explanation:

Given the equation:

[tex]-x^{2} +4x+12[/tex]

Let us rewrite by letting it equal to [tex]y[/tex].

[tex]y=-x^{2} +4x+12[/tex]

Now, we can see that it is a quadratic equation and it is known that a quadratic equation has a graph of parabola.

Let us compare the given equation with standard quadratic equation:

[tex]y=ax^{2} +bx+c[/tex]

we get:

[tex]a = -1\\b = 4\\c = 12[/tex]

Coefficient of [tex]x^{2}[/tex] is negative 1, so the parabola will open downwards.

Axis of symmetry: It is the line which will divide the parabola in two equal congruent halves.

Formula for axis of symmetry is:

[tex]x = -\dfrac{b}{2a}[/tex]

[tex]x = -\dfrac{4}{2(-1)}\\\Rightarrow x=2[/tex]

It is shown as dotted line in the image attached in the answer area.

Axis of symmetry will also contain the vertex of the parabola.

It is a downward parabola so vertex will be the highest point on this parabola.

Putting x = 2 in the equation of parabola:

[tex]y=-2^{2} +4\times 2+12\\\Rightarrow y =16[/tex]

So, vertex will be at P(2, 16).

Now, let us find points of parabola to sketch graph:

put x = 0, [tex]y=-0^{2} +4\times 0+12=12[/tex]

Another point is Y(0,12)

Now, let us put y = 0, it will give us two points because the equation is quadratic in x.

[tex]0=-x^{2} +4x+12\\\Rightarrow -x^{2} +6x-2x+12=0\\\Rightarrow -x(x -6)-2(x-6)=0\\\Rightarrow (-x-2)(x-6)=0\\\Rightarrow x = -2, 6[/tex]

So, other two points are X1(-2, 0) and X2(6,0).

If we plot the points P, Y, X1 and X2 we get a graph as attached in the image in answer area.

Answer:

A, B and E statements are true

Step-by-step explanation:

Since in the question, it is mentioned that Eli selected two shirts out of pack 5 for a weekend trip

Classify each shirt as A, B, C, D, and E.

Now we have to go through the options

In the first statement it is mentioned that AB and BA are the similar. This is true as it contains in same bag.

Since Eli select two shirts so the second statement is also correct

And, the last statement is also true as he selects shirt B so there are four possible ways to second the second shirt as there are four remaining shirts are left after select one shirt

Hence, A, B and E statements are true

Answer: A, B, and E.

Step-by-step explanation:

A is correct: the combination of AB and BA are the same because they both contain the same letters, just a different order.

B is correct: each shirt can be paired with any one of the other remaining shirts because she will be choosing 2 shirts.

E is correct: If he chooses shirt B, there are 4 possible outcomes for choosing the 2nd shirt. This is true because there is only one B in a group of 5 shirts, so 5-1 = 4 possible outcomes.

Hope this helped.

Have a nice day. :)

Answer:

  d) 27

Step-by-step explanation:

The expanded form of (a+b)³ is ...

  (a +b)³ = a³ +3a²b +3ab² +b³

When we are expanding (x +3)³, the x-term is ...

  3(x)(3²) = 27x

The coefficient of x in the expansion is 27.

Answer:

Hey there!

They are congruent by AAS, where two angles and one side is congruent.

Hope this helps :)

Answer:

Do you have a photo or some other information to go with this?

Step-by-step explanation:

Answer:

Step-by-step explanation:

8d + 4 = 5d + 28

Group like terms

That's

8d - 5d = 28 - 4

3d = 24

Divide both sides by 3

d = 8

[tex] \frac{7(7g + 8)}{4} = 38.5[/tex]

Cross multiply

we have

7(7g + 8) = 38.5(4)

49g + 56 = 154

49g = 154 - 56

49g = 98

Divide both sides by 49

g = 2

Hope this helps you

Answer:

35cm

Step-by-step explanation:

The net of a regular pentagon has 10 sides.

Since each of the faces are equilateral triangles, the side lengths are equal.

Therefore:

Length of each side of the net = 70/10 =7cm

Therefore, the base is a regular pentagon of side length 7cm.

The perimeter of the base of the pyramid = 5 X 7

=35cm

The perimeter of the base of the pyramid is 35cm.

Answer:

B. 8

Step-by-step explanation:

Step 1: Find g(-2)

g(-2) = (-2)² + 1

g(-2) = 4 + 1

g(-2) = 5

Step 2: Find f(5)

f(5) = 2(5) - 2

f(5) = 10 - 2

f(5) = 8

i got this question too as my homework it so hard ill let you know if i find out the answer.

Complete question:

Dr. Lyte wishes to study speed of Reaction Time to press a button in response to the onset of a lamp. The independent variable (V) is the color of the light produced by the lamp (red, orange, yellow, green, or blue) Since only 10 participants are available, she elects to administer the IV within-subjects with all 10 participants being exposed to all five levels of the color variable. The order of the color of the light presentation is to be counterbalanced. Using concepts from the textbook, why would Dr. Lyte need to use counterbalancing in this scenario?

Answer:

Here,

Independent variable (IV) is: the color of the light produced by the lamp (red, orange, yellow, green, or blue)

We are also told only 10 participants are available.

All 10 participants are being exposed to all five levels of the color variable in the same order.

Counterbalancing is said to be a technique used when establishing task order. It helps prevent introduction if cofounding variables.

Dr. Lyte will need to use counterbalancing technique in this scenario because some of the participants may be unable to understand difference in similar colours. Example some participants may not be able to differentiate between orange and red when the red colour comes after orange.

But using counterbalancing technique, Dr. Lyte can avoid such an error.

Answer:

[tex]4^m[/tex]

Step-by-step explanation:

When you exponent an exponent, you multiply the powers together.

When you divide exponents, you subtract the powers.

Step 1: Convert to same base

log₄64 = 3

Step 2: Rewrite equation

[tex]\frac{(4^3)^{0.5m}}{4^{0.5m}}[/tex]

Step 3: Simplify

[tex]\frac{4^{1.5m}}{4^{0.5m}}[/tex]

Step 4: Simplify

[tex]4^m[/tex]

Step-by-step explanation:

given that

p= "I do my chores"

q= "I get my allowance."

The statement that uses p as hypothesis is, if  "I do my chores",  which leads to the conclusion of  "I get my allowance."

hence the test/ hypothesis is  if  "I do my chores", i get my allowance

Answer:

9.

Step-by-step explanation:

When there is an absolute value, anything within the absolute value becomes positive. Things outside the absolute values stay as they are.

|-12| - |-3| = 12 - 3 = 9.

Hope this helps!

Answer:

The answer is C

Step-by-step explanation:

hope it helps

Answer:

The value of a is 50°.

Step-by-step explanation:

In an isosceles triangle, 2 sides have the same lengths and same angles so we can assume that the other side of the triangle is 65°.

Given that the total angle of a triangle is 180°, so have to subtract it :

[tex]a = 180 - 65 - 65[/tex]

[tex]a = 180 - 130[/tex]

[tex]a = 50[/tex]