MATHEMATICS HIGH SCHOOL

g(p)=(p-2 )and g(x)=(p^3+4p^2-2) evaluate g(p)*h(p) by modeling or by using the distributive property.

Answers

Answer 1

Answer:

Given that g(p)=p-2 and

$h(p)=p^3+4p^2-2$

Now we have to evaluate g(p)*h(p) by modeling or by using the distributive property.

We know that g(p)*h(p) means just multiply expressions of g(p) with h(p)

which can be shown as following:

$g(p)*h(p)=(p^3+4p^2-2)(p-2)$

Apply distributive property

$g(p)*h(p)=p(p^3+4p^2-2)-2(p^3+4p^2-2)$

$g(p)*h(p)=p^4+4p^3-2p-2p^3-8p^2+4$

$g(p)*h(p)=p^4+2p^3-2p-8p^2+4$

$g(p)*h(p)=p^4+2p^3-8p^2-2p+4$

Hence final answer is $g(p)*h(p)=p^4+2p^3-8p^2-2p+4$

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Which would be appropriate compatible numbers to use to estimate (19 4/5)(4/6)

Answers

Answer:

Approximately 10

Step-by-step explanation:

19 / 5 Approximately 4

4 * 4 = 16

16 * 4 / 64

64 / 6 * = Approximately 10 / 10.6 ish

Actual Answer is 10.133

Angle D is a circumscribed angle of circle O.Circle O is shown. Triangle A C B is inscribed within circle O. Side A B goes through point O. The length of A C is 15 and the length of C B is 8. Angle A C B is a right angle. Line segment O E is a radius. Tangents B D and E D intersect at point D outside of the circle to form kite O B D E. Angles O B D and D E O are right angles. The length of E D is 5.

What is the perimeter of kite OBDE?

17 units
23 units
27 units
60 units

Answers

Since angle D is a circumscribed angle of circle O, the perimeter of kite OBDE is equal to 27 units in accordance with Pythagorean's Theorem.

How to calculate the perimeter of kite OBDE.

In order to determine the perimeter of kite OBDE, we would apply Pythagorean's Theorem because angles OBD and DEO are right angles.

Mathematically, Pythagorean Theorem is given by this formula:

c² = a² + b²

Where:

h is the hypotenuse.

a is the adjacent side.

b is the opposite side.

Given the following data:

Length of AC = 15 units.

Length of CB = 8 units.

Length of ED = 5 units.

Substituting the given parameters into the formula, we have;

c² = 15² + 8²

c² = 225+64

c =√289

c = 17 units.

Since a kite is a quadrilateral with four (4) equal sides and two (2) congruent sides, we can deduce the following:

Side OB = OE = 1/2 × 17 = 8.5 units.

Side BD = ED = 5 units.

Therefore, the perimeter of kite OBDE is given by:

Perimeter = 17 + (5 + 5)

Perimeter = 17 + 10

Perimeter = 27 units.

Read more on Pythagorean Theorem here: brainly.com/question/16176867

Answer:

Step-by-step explanation:

How many gallons of pure water should be evaporated from 160 gallons of a solution containing 12% salt so that the remaining solution contains 20% salt?

Answers

The quantity of pure water is 64 gallons which are to be evaporated.

What is an expression?

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The total amount of salt must be equal before and after evaporation.

Multiply the percent of salt in the solution before evaporation by the total gallons of solution

= 12% x 160 gallons convert 12% to decimal form (12% ÷ 100)

= 0.12 * 60

Subtract the number of gallons of pure water that should be evaporated from the total number of gallons of the solution and multiply by the percent of salt in the solution after evaporation

= 20% * (160 - x)convert 20% to decimal form (20% ÷ 100)

= 0.20(160 - x)

Set the before & after evaporation equations equal to one another to solve for x.

0.12 x 160 = 0.20(160 - x)

19.2 = (0.20 * 160) + (0.20 * -x)

19.2 = 32 - 0.20x

-12.8 = -0.20x

64 gallons = x

Therefore, the quantity of pure water is 64 gallons which are to be evaporated.

To know more about an expression follow

brainly.com/question/7265649

#SPJ2

x= # gallons of pure water that should be evaporated

The total amount of salt must be equal before and after evaporation.
STEP 1
BEFORE EVAPORATION: multiply the percent of salt in the solution before evaporation by the total gallons of solution
= 12% * 160 gallonsconvert 12% to decimal form (12% ÷ 100)
= 0.12 * 60

STEP 2
AFTER EVAPORATION: subtract the number of gallons of pure water that should be evaporated from the total number of gallons of the solution and multiply by the percent of salt in the solution after evaporation

= 20% * (160 - x)convert 20% to decimal form (20% ÷ 100)
= 0.20(160 - x)

STEP 3
Set the before & after evaporation equations equal to one another to solve for x.
0.12 * 160= 0.20(160 - x)multiply 0.20 by each term in parentheses
19.2= (0.20 * 160) + (0.20 * -x)multiply in parentheses
19.2 = 32 - 0.20xsubtract 32 from both sides
-12.8= -0.20xdivide both sides by -0.20
64 gallons= x

CHECK:substitute x= 64 into the step 3 equation
0.12 * 160= 0.20(160 - x)19.2= 0.20(160 - 64)subtract in parentheses19.2= 0.20(96)19.2= 19.2

ANSWER: 64 gallons of pure water should be evaporated.
Hope this helps! :)

Five eighths added to Q number is 4. Determine the number.

Answers

Yes five eights added to Q is 4!

Solve, using the substitution method.4x + 2y = 11
x – 2 = – 2y

A.

B.

C.

D.

Answers

$4x+2y=11 \nx-2=-2y \n \n\hbox{from the 2nd equation:} \nx-2=-2y \nx=-2y+2 \n \n\hbox{substitute -2y+2 for x in the 1st equation:} \n4(-2y+2)+2y=11 \n-8y+8+2y=11 \n-8y+2y=11-8 \n-6y=3 \ny=-(3)/(6)=-(1)/(2) \n \n\hbox{solve one of the equations for x:} \nx=-2 \cdot (-(1)/(2)) +2=1+2=3 \n \n \hbox{the answer:} \n x=3 \n y=-(1)/(2)$

4x + 2y = 11
x - 2 = -2y
First you have to get a variable alone in one of the equations.

x - 2 = -2y
+2 +2
--------------
x = -2y + 2
Next you substitute -2y +2 for x in the second equation.

4(-2y + 2) + 2y = 11
Distribute.

-8y + 8 + 2y = 11
Combine like terms.

-6y + 8 = 11
Get the variable (y) by itself.

-6y + 8 = 11
-8 -8
--------------------
-6y = 3
Finally get y by itself.

-6y = 3
----- ------
-6 -6

Y = 0.5

Now to get x you plugin the answer for y.

x - 2 = -2y
x - 2 = -2(0.5)
x - 2 = -1
+2 +2
x = 1

(1, 0.5) Is your ordered pair. :D

A car salesperson sells cars at prices ranging from $5,000 to $45,000. the histogram shows the distribution of the numbers of cars he expects to sell over the next 10 years. the median of the car is ___.

- $20,000
- $25,000
- $30,000
- $40,000

the distribution exhibits ___.

- a negative skew
- a positive skew
- symmetry
- uniformity throughout