4. Arthur invests $5,000 in a savings account that earns 3% interest per year. Egn:​

Answer:

  (a)  ∠1 and ∠5

Step-by-step explanation:

Complementary angles are angles whose measures total 90°. The angles do not have to be adjacent.

__

In this geometry, we can see that angles 1 and 2 are complementary, as are angles 4 and 5, since their respective sums are right angles. Angles 2 and 5 are vertical angles, so have the same measure.

  ∠1 + ∠2 = 90° . . . . . . adjacent angles that total a right angle

  ∠1 +∠5 = 90° . . . . . substitute ∠5 for ∠2, since measures are equal

This means angles 1 and 5 are complementary.

Answer:

Cubic centimetres

Step-by-step explanation:

Cubic centimetres is perfect

As

Answer:

7 inches

Step-by-step explanation:

The area of a parallelogram is Base x Height.

Area = 28 in^2 = (4 in)*(Height)

Height = 7 inches

Answer:

$2.25

Step-by-step explanation:

You have to set up a proportion to show how much the cost of milk is when discounted per gallon. 0% off, the milk would be $3.75. 40% off, the milk would be x. Now I flipped the percents because that is how much you are actually paying.

Proportion would look something like this:

3.75/100 = x/60

solve for x:

225 = 100x

x= 2.25

Answer:

4:1

Step-by-step explanation:

Answer:

Round 55.99 to the nearest tenth is: 56.0

Answer:

238

Step-by-step explanation:

Given equation:  [tex]a^2+1=6a[/tex]

Rearrange so that it is equal to zero:

[tex]\implies a^2-6a+1=0[/tex]

Quadratic formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]

Using the quadratic formula to solve the given equation:

[tex]\implies a=\dfrac{-(-6) \pm \sqrt{(-6)^2-4(1)(1)} }{2(1)}[/tex]

[tex]\implies a=\dfrac{6 \pm \sqrt{32}}{2}[/tex]

[tex]\implies a=3 \pm 2\sqrt{2}[/tex]

[tex]\implies a^2=17 \pm 12\sqrt{2}[/tex]

Substituting this into [tex]7\left(a^2+\dfrac{1}{a^2}\right)[/tex]

[tex]\implies 7\left(17 \pm 12\sqrt{2}+\dfrac{1}{17 \pm 12\sqrt{2}}\right)[/tex]

For [tex]17+12\sqrt{2}[/tex]:

[tex]\implies 7\left(17+12\sqrt{2}+\dfrac{1}{17+12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{(17+12\sqrt{2})^2}{17+12\sqrt{2}}+\dfrac{1}{17+12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{(17+12\sqrt{2})^2+1}{17+12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{289+408\sqrt{2}+288+1}{17+12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{578+408\sqrt{2}}{17+12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{34(17+12\sqrt{2})}{17+12\sqrt{2}}\right)[/tex]

[tex]\implies 7(34)[/tex]

[tex]\implies 238[/tex]

For [tex]17-12\sqrt{2}[/tex]:

[tex]\implies 7\left(17-12\sqrt{2}+\dfrac{1}{17-12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{(17-12\sqrt{2})^2}{17-12\sqrt{2}}+\dfrac{1}{17-12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{(17-12\sqrt{2})^2+1}{17-12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{289-408\sqrt{2}+288+1}{17-12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{578-408\sqrt{2}}{17-12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{34(17-12\sqrt{2})}{17-12\sqrt{2}}\right)[/tex]

[tex]\implies 7(34)[/tex]

[tex]\implies 238[/tex]

Answer:

Mean (Average): 21.44444

Median (Middle): 22

Mode (Most Common): 29

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remark

What you want to do is get r on one side of the equal sign and everything else on the other.

Givens

V = pi r^2 h

Solution

Divide by pi

V/pi = pi r^2 h/pi

V/p = r^2 * h

Divide by h

V / h pi = r^2 h / h              Cancel h on the right side. Turn equation around

r^2 =  V / h pi

Take the square root of both sides

√r^2 = √(V / h pi )

r = √ (V / h pi)

Answer r =√ (V / h pi)

Answer:

68 is the perimeter.

Step-by-step explanation:

You can find the perimeter by adding up all of the sides. 13 + 11 + 3 + 7 = 34. To find the other sides of the shape you do 11 + 7 and 13 + 3. 11 + 7 = 18. 13 + 3 = 16. 18 + 16 = 34. 34 + 34 = 68.

Answer:

(4,8)

Step-by-step explanation:

(x,y) on the X line it is at 4 and on the Y it is on 8 so that would be (4,8)

Answer:

The son is 24 and the father is 48

Step-by-step explanation:

If you let x = the age of the child, then the father is 2x old since the father is twice as old as the son. The sum of their ages would be 1x + 2x which simplifies to 3x.

Since the problem gives the total of their ages as 72, we know that 3x = 72.

Dividing both sides by 3, we get x = 24, which we said was the age of the child.

Since the age of the father is 2x, we can say that 2x = 2(24), or 2x = 48 for the age of the father.

Answer:

An integer is a WHOLE number. No fractions and no decimals. so it would be... no, yes, yes, no, yes

Step-by-step explanation:

To clarify because they try to be tricky here. 27/3 is actually equal to 9 when simplified. Same thing with 40/8... when simplified it equals 5. Both are whole numbers and therefore integers.

Answer:

-76 is an integer and 27/3 and 40/8 could also be as well

Step-by-step explanation:

27/3 is and integer because if you simplify it, it equals 9, an integer. Same for 40/8, it equals 5.

Perimeter of square

Perimeter of two sides of triangle:-

Perimeter of circle excluding diameter line

Total perimeter

Answer:
I believe it is Option C.

Step-by-step explanation:

There has only been one single tie since the passing of the 12th Amendment. It is a very low chance for a possible tie to take place, so they would have no reason to ensure it doesn't happen as it's already unlikely, ruling out option D. Giving two people the same rank would definitely make a difference as you are basically adding not 1, but two votes. Though it would even the count out, each person would gain 1 point, so it would make a difference. Option B is ruled out. This also potentially explains debunking A as there's no possible way to plan a tie to that extent. Again. ties happen very rarely, so it would be unlikely that voting for both candidates would impact the choice at all.

The correct symbol in between numbers is,

⇒ 4/5 > 1/2

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The numbers are,

⇒ 4/5 and 1/2

Now, We can make denominator equal as;

LCM of 5, 2 = 10

Hence, We get;

⇒ 4/5

⇒ 8/10

⇒ 1/2

⇒ 5/10

Thus, We get;

⇒ 4/5 > 1/2

Therefore, The correct symbol in between numbers is,

⇒ 4/5 > 1/2

Learn more about the inequality visit:

https://brainly.com/question/25944814

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Answer:

The first one is geometric. The second one is gemetric. The last one is arithmetic.

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

the figure is an isosceles trapezium

The legs are congruent , that is

BC = AD = 15 units

The upper base angles are congruent , so

∠ B = ∠ A = 145°

Any lower base angle is supplementary to any upper base angle, that is

∠ C + ∠ B = 180°

∠ C + 145° = 180° ( subtract 145° from both sides )

∠ C = 35°

The lower base angles are congruent , so

∠ D = ∠ C = 35°

Answer:

Equation: 1=1

Length of the road after 16 days: 16 miles (if not adding to 53. if adding to 53, the answer is 69)

Explanation:
If they add one mile of road every day, its 1(mile) = 1(day.
Since its one mile every day, 16 days is 16 miles. Adding 53 + 16 = 69

Answer:

The answer is 25

Step-by-step explanation:

Answer:

14.7÷41.4=0.355

the answer is 0.355

Answer:

a no. is the answer

Step-by-step explanation:

b=a+13

or, 14 = 1+13

or, 14= 14 {True}

Answer:

b=a+13

b=1+13

b=14

again,

b=a+13

b=6+13

b=19

so the relationship between a & b is b=a+13

set : {31, 76, 34, 35, 39, 49, 55}

arrange ascending to descending:

{ 31, 34, 35, 39, 49, 55, 76 }

given,

I.Q.R:

Answer:

21

Step-by-step explanation:

Place the numbers in order from smallest to largest:

31, 34, 35, 39, 49, 55, 76

The median (Q2) is the middle value = 39

Q1 is the middle value of the numbers smaller than the median = 34

Q3 is the middle value of the numbers larger than the median = 55

IQR = Q3 - Q1

      = 55 - 34

      = 21

Answer:

2) 4,2

Step-by-step explanation:

Factor by grouping:

[tex]x^2-6x+8\\\\x^2-4x-2x+8\\\\x(x-4)-2(x-4)\\\\(x-2)(x-4)[/tex]

Setting the expression equal to 0 and using the Zero Product Property, [tex]x=2[/tex] and [tex]x=4[/tex], which are the factors of the original polynomial.

Answer:

The factors are x-2 and x-4.

Step-by-step explanation:

x^2 - 6x + 8

= (x - 2)(x - 4)

Answer:

can you clear more I don't understand

To find this answer, we need to understand how to get the Volume.

We get the volume by the formula: L x W x H

L = Length

W = Width

H = Height

So, we can see that there are 3 units required to know for getting the volume, if that's true, then, to do the inverse operation of finding the volume. That can be done by using thie formula:

[tex]V=a^3[/tex]

a= edge

Solving for a

a=V⅓=216⅓=6

now, let's look at how to find whether our answer is right or wrong

6x6=36

36x6=216

So hence, our answer is right!

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The length of a betta fish tank that has a shape of a cube and volume of 216 cubic inches is 6 inches.

A cube has all its sides equal to each other. Therefore,

volume of cube = L³

where

Therefore,

L = >

volume = 216 cubic inches

volume of cube = L³

216 = L³

cube root both sides

∛216 = ∛L³

L = ∛216

L = 6 inches

learn more on volume here: https://brainly.com/question/10961243

Answer:

sqrt (120)

Step-by-step explanation:

Use pythag theorem

Leg1 ^2 + Leg2^2 = Hypot ^2

 13^2    + Leg2^2  =  17^2

    Leg2^2  =  17^2  -  13^2

    Leg2  =  sqrt (120)