The base of a triangle is one half of its height. If the area of the triangle is 196 square millimeters,
find its base and height.

Answer:

Step-by-step explanation:

Yes, you did it right.

Answer: 2 ft.

Step-by-step explanation:
|-20| = 20, |-22| = 22
22 - 20 = 2

Answer:

Use AAA congurency rule

Step-by-step explanation:

1 angle=52

2 angle=58

3 angle=78

The sale price including tax for the refrigerator is $520.

From the information, the following can be deduced:

Refrigerator = $595

Discount = 20%

Tax = 9.25%

The sales price will be:

= Refrigerator price + Tax - Discount

= $595 + (9.25% × $595) - (20% × 650)

= $595 + $55 - $130

= $520

The price is $520.

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The square root of √-36 is 0.

So, √-36:
Calculate the square root as follows:

Therefore, the square root of √-36 is 0.

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The percentage of students in the tutor group that have attended at least one tutorial is 71%

The percentage of students who have attended at least a single tutorial in the tutor group can be found by the formula:

= Number of students who attended at least one tutorial / Total number of students in tutor group x 100%

Number of students who attended at least one tutorial = 21 students

Total number of students in tutor group = 15 students

The percentage is therefore:

= 15 / 21 x 100%

= 0.7142857 x 100%

= 71.42%

= 71%

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Answer:

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

If a person deposits $8,000 into a savings account at 6.5% interest compounded quarterly for 12 years, the balance (future value) will be $17,342.70.

The future value is the compounded present value of an investment for a future period.

The future value can be computed using the FV formula, table, or an online finance calculator as below.

N (# of periods) = 48 quarters (12 years x 4)

I/Y (Interest per year) = 6.5%

PV (Present Value) = $8,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $17,342.70

Total Interest = $9,342.70

Thus, the future value of a present investment of $8,000 at 6.5% interest compounded quarterly for 12 years is $17,342.70.

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Answer:

y = x^2 + 6       given equation

y = m x + b        equation of straight line required

dy/dx = 2 x       tangent to given curve

dy/dx = slope = 2 * 5 = 10

Thus our line must be of the form

y = 10 x + b

31 = 10 * 5 + b       at the point required

b = 31 - 50 = -19

Then our final equation becomes

y = 10 x - 19

Answer: 4/5 or 0.8

Step-by-step explanation:

[tex]1\frac{1}{4}[/tex] * [tex]\frac{4}{5}[/tex] = [tex]\frac{1}{1}[/tex] = 1

[tex]1\frac{1}{4}[/tex] is also equal to 1.25.

1.25 * 0.8 = 1

Answer:

4/5

Step-by-step explanation:

because 4 is half of a half two fourths are a half and 4/4 are 1 whole

x = 5/2 and x = -25/2 are the solutions to the equation 4x (x + 10) + 55 = 180.

Given the equation in the question;

4x (x + 10) + 55 = 180

To solve for x, apply distributive property to eliminate the parenthesis.

4x (x + 10) + 55 = 180

4x(x) + 4x(10) + 55 = 180

4x² + 40x + 55 = 180

4x² + 40x + 55 - 180 = 0

4x² + 40x - 125 = 0

Now, we use the quadratic formula to solve the quadratic equation.

x = (-b±√(b² - 4ac)) / (2a)

From 4x² + 40x - 125 = 0

Plug these into the formula and solve for x.

x = (-b±√(b² - 4ac)) / (2a)

x = ( -40 ± √( (40)² - ( 4 × 4 × -125))) / ( 2 × 4 )

x = ( -40 ± √( 1600 - ( -2000) )) / ( 8 )

x = ( -40 ± √( 1600 + 2000 )) / ( 8 )

x = ( -40 ± √( 3600 )) / ( 8 )

x = ( -40 ± 60) / ( 8 )

x = ( -40 - 60) / ( 8 ), ( -40 + 60) / ( 8 )

x = ( -100 )/( 8 ), ( 20 )/( 8 )

x = -25/2, 5/2

Therefore, the solution to the quadratic equation is x = -25/2, 5/2.

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Answer: The answer is D bc i did the test before hope you have a great day:]

Step-by-step explanation:

8

x

5

−

6

x

4

+

12

x

3

Answer:add 5 to both sides

Step-by-step explanation:

The magnitude of the boats resultant vector is 314.1 mi

A vector is a physical quantity that has both magnitude and direction.

A resultant vector is the sum of two or more vectors.

Since the boat sails 285 miles south and then 132 miles west, we have that its first direction vector is r = (285 mi)j. Also, its direction vector west is r' = -(132 mi)i

So, the resultant vector R = r + r'

=  (285 mi)j + (132 mi)i

=  (132 mi)i + (285 mi)j

So, the magnitude of the resultant vector is R = √(r² + r'²)

So, substituting thevalues of the variables into the equation, we have

R = √(r² + r'²)

R = √((285 mi)² + (132 mi)²)

R = √(81225 mi² + 17424 mi²)

R = √(98649 mi²)

R = 314.08 mi

R ≅ 314.1 mi

So, the resultant vector is 314.1 mi

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The quadratic function whose only zero is -13 is h(x) = x² + 26x + 169

From the question, we are to write a quadratic function whole only zero is -13.

Since -13 is the only zero of the function,

Then,

x = -13 twice

This means that (x + 13) is a factor of the function

Since x = -13 twice,

Then,

The quadratic function h is

h(x) = (x + 13)(x + 13)

Expand the quadratic function by distributing

h(x) = x(x + 13) + 13(x + 13)

h(x) = x² + 13x + 13x + 169

h(x) = x² + 26x + 169

Hence, the function is h(x) = x² + 26x + 169

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The least number of balls we require to take out to be sure that we have two green or two red balls is 14.

In the bag, there are a total number of balls of;

Total number of balls = 12 + 7 = 19 balls

Inside the bag, we have 12 red balls and 7 green balls.

The balls are selected without replacement, and this means that they are removed from the bag, and replaced back.

In theory, we could pick 12 balls, and all 12 being red, while also 13, with 12 red and 1 green e.t.c

Therefore, at least 14 balls are needed to guarantee that there are at least 2 green or two red balls

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Answer:

A: Independent contractor

Step-by-step explanation:

1) Option 3 had the least amount invested. The investment plan was to invest a certain amount in the beginning and let it grow at an interest of 6.25% APR compounded monthly for 30 years.

2) Option 2 yielded the highest amount at the end of 30 years. The plan was to invest $75/quarterly i.e, $25/monthly at an interest of 4.00% APR compounded monthly for 30 years.

3) Difference in principle is $8000 and the difference is interest is $2976.83

4) It is better to invest more at the end of 30 years.

Define interest.

When you borrow money, you must pay interest, and when you lend money, you must charge interest. The most common way to represent interest is as a percentage of a loan's total amount per year. The loan's interest rate is denoted by this proportion.

Solution Explained:

First, let's calculate the amount after adding the compound interest using

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex], where P is principal, r = interest rate, n = number of times interest is compounded monthly, and t = time

After calculation (For Op 1 and 2, the principal is $9000 and 3 is $1000)

Option 1 has $15275.50
Option 2 has $17467
Option 3 has $6489.17

Interest for Option 1 = $6275.50
Interest for Option 2 = $8466
Interest for Option 3 = $5489.17

After this solving the questions will be easy to understand.

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Answer:

contributions:
1 $25/ month at a rate of 3.25% APR
2 $75/ quarter at a rate of 4.00%
3 $1,000 at a rate of 6.25% APR

total interest rate:

1 $6275.50

2 $8466

3 $5489.17

final balances:

1 $15275.50

2 $17467

3 $6489.17

questions 1-4

1: Option 3 had the least amount invested

2: option 2
3: Difference is $8000 – and interest difference in $2976.83

4: it’s better to invest more at the end of 30 years

Step-by-step explanation:

i did the assignment

The simplest polynomial form of  f(x)×g(x) is x³ - 16x² + 69x - 90.

So, f(x) × g(x):
Calculate as follows:

Therefore, the simplest polynomial form of  f(x)×g(x) is x³ - 16x² + 69x - 90.

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Answer:

j=24

Step-by-step explanation:

j/8 - 2 = 1

j/8 - 2 + 2 = 1 + 2

j/8 = 3

8 * j/8 = 8 * 3

j=24

Answer:

Ten million, Four hundred eighty-three thousand, one hundred ninety

Step-by-step explanation:

Break it down! into the tens digit, hundreds digit, etc.

Answer:

Step-by-step explanation:

from the figure we understand that it is an isosceles triangle, therefore 2 sides and two congruent angles, BD and CD are congruent, therefore 3x = x + 16.

let's solve

3x = x + 16

2x = 16

x = 8

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

check

3 × 8 = 8 + 16

24 = 24

thee answer is good

The y-intercept of the graph as shown is 2.

The equation of a line can be represented as follows:

y = mx + b

where

The y-intercept is the point where the graph intersects the y-axis. In other words, it is the value of y when x = 0 .

Therefore, let's trace the value of y when x  = 0 on the graph.

Hence, when x = 0, y = 2

Therefore,

b =  y-intercept = 2

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Answer:b=2b

b=−2b

b=−3b

b=3b

Step-by-step explanation: because I tought myself i know

Answer:

see explanation

Step-by-step explanation:

(a)

parallel line segments are indicated by arrows on the segments pointing in the same direction.

from the diagram EA and DC are parallel lines.

(b)

equal lines are indicated by a dash through the lines.

from the diagram AB and BC are equal.

(c)

perpendicular lines are at right angles (90° ) to each other, usually indicated by a small box between them.

from the diagram AE and CD are perpendicular to DE

When it rains at the same rate for 15 more minutes, the fraction of the rain gauge that will be filled is 2/15.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.

From the information, after raining for 3/4 of an hour, a rain gauge 2/5 of the way full. It's important to note that 3/4 is (3 × 1/4).

Therefore, we will divide 2/5 by 3 and this will be:

= 2/5 ÷ 3

= 2/5 × 1/3

= 2/15

This is the value of the rain gauge.

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The percent of change each year is 15%.

How to calculate percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

It is given that The number of carbon atoms in a fossil is given by the function y = [tex]51000(0.85)^t[/tex], where t represents the number of years since being discovered.

Here , y  =  [tex]51000(0.85)^t[/tex]

t = number of years

y = number of carbon atoms in a fossil.

For t = 1 year

y = 51000[tex](0.85)^1= 51000(0.85) = 43350[/tex]

For t = 2 years

y = 51000[tex](0.85)^2= 36847.5[/tex]

For t = 3 years

y = 51000[tex](0.85)^3=31320.375[/tex]

Percentage change in one year = [tex]\frac{36847.5-43350}{43350}[/tex] × 100 = -15%

Percentage change in second year =  [tex]\frac{31320.375-36847.5}{36847.5}[/tex] × 100 = -15%

here, negative sign shows decrement. In this way, every year carbon atom in fossil decreases by 15%.

Therefore, the percent of change each year is 15%.

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In a case where the expression is give as volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P, then the pressure will be 7kg/cm^2.

V = k T/ P

and V= 70 cm^3

T = 420 kelvin

P = 18 kg/cm^2

where K is constant of proportionality,

70 =( k * 420) / 18

k = (70 * 18) / 420

k= 3

Then we were given that the pressure=?

T = 140 kelvin

V = 60 cm^3

then V = k T/ P

P= kT/V

P= (3*140)/60

=7

Then the pressure is 7kg/cm^2

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Answer:

Step-by-step explanation:

Both mentioned sides have equal length as opposite sides of a parallelogram.

Set equation and solve for x: