admin

2 months ago

Guest #1966

2 months ago

Y=mx+b

m=0.5

b is value of y in y-intercept, b=-2

The equation of this line is

y=0.5x-2

When x=4

y=0.5x-2=y=0.5*4-2=2-2 = 0

When x=4, y=0.

m=0.5

b is value of y in y-intercept, b=-2

The equation of this line is

y=0.5x-2

When x=4

y=0.5x-2=y=0.5*4-2=2-2 = 0

When x=4, y=0.

Question

The axis of symmetry for the graph of the function f(X)=3x^2+bx+4 is X=3/2. What is the value of b?

Solution 1

Remember that the axis of symetry is x=value of how far it is from the origin

also remember that the vertex formula is -b/(2a) so

a=3

3/2=-b/(2(3))

3/2=-b/(6)

mutiply both sides by 6

18/2=-b

9=-b

multily both sides by -1

-9=b

so the equation is

f(x)=3x^2-9x+4

b=-9

also remember that the vertex formula is -b/(2a) so

a=3

3/2=-b/(2(3))

3/2=-b/(6)

mutiply both sides by 6

18/2=-b

9=-b

multily both sides by -1

-9=b

so the equation is

f(x)=3x^2-9x+4

b=-9

Solution 2

Answer:

-9

Step-by-step explanation:

Question

Jackson mows lawns to make money. It costs him $7 each week to advertise his business. It costs him $1.50 in gas to mow each lawn, and he charges $10.00 for each lawn he mows. Write an equation to model the amount of profit, P, he makes from mowing x lawns in one week.

Solution 1

Lawns = L

Money he gets from mowing = M

M - $7 - (L * $1.50) = P for 1 Week

Hope this helped :D

Money he gets from mowing = M

M - $7 - (L * $1.50) = P for 1 Week

Hope this helped :D

Question

A quality control officer is randomly checking the weights of pumpkin seed bags being filled by an automatic filling machine. Each bag is advertised as weighing 400 grams. A bag must weigh within 2.1 grams in order to be accepted. What is the range of rejected bags, x, for the bags of pumpkin seeds?

Solution 1

If a bag of pumpkin seeds must weigh within 2.1 grams in order to be accepted, each bags must weigh between (400-2.1) grams and (400+2.1) grams. This means that if a bag weighs less than 397.9 grams (x<397.9) or more than 402.1 grams (x>402.1) it will be rejected. Therefore, 397.9>x>402.1 is the range of rejected bags.

Solution 2

**Answer:**

**Step-by-step explanation:**

The range of rejected bags is found by summing and subtracting the 400 grams to 2.1 grams, because the second one represent the acceptable margin.

So, we have:

However, this interval represents the accepted range. The rejected range would be the opposite. Therefore, the asked range is:

Question

Jason incorrectly simplified the expression (4.7*10^2)*(6.2*10^4). Circle each step that shows an error. Then correct each of those steps so that the expression is correctly simplified. A Step 1. 4.7*6.2*10^2*10^4 ______________
B Step 2. (4.7*6.2)*(10^2*10^4) ______________
C Step 3. 29.14*10^8 _____________
D Step 4. 2.914*10^6 _______________

Solution 1

**Answer:**

Step C is incorrect: When you simplify exponents the rules are: for adding or subtracting, the base and the exponent must be equal; when multiplying the base must be the same, and the exponents will add; when dividing the base must be the same and the exponent will subtract.

Step D is incorrect: The last division is wrong, you could treat it with the general rule of exponents, subtracting the exponents of the base *10*.

The correct procedure of each step is:

**C.**

**D.**

Solution 2

So sum means add

difference means subtract

represent as x and y

x+y=55 times (x-y)

find ratio of numbers

solve for one placeholder and simplify

solve for y

distributiver property a(b-c)=ab-ac

55(x-y)=55x-55y

difference means subtract

represent as x and y

x+y=55 times (x-y)

find ratio of numbers

solve for one placeholder and simplify

solve for y

distributiver property a(b-c)=ab-ac

55(x-y)=55x-55y

Question

25.6% of what # is 21.12

Solution 1

To solve this problem, we are going to use the percent proportion, a/b = p/100, where a is the part of a number b, the whole, and p is the percentage out of 100.

When we fill in our known integers into this equation, we get

21.12 / b = 25.6 / 100

Next, to simplify this equation, we should use cross products (means - extremes products theorem). This means multiplying the numerator of one fraction and the denominator of the other fraction and setting them equal to one another.

21.12(100)=25.6(b)

When we multiply, you get

2112 = 25.6b

Finally, we divide both sides by 25.6, to get our variable b, alone, and without a coefficient.

82.5 = b

Therefore, 25.6%**of the number 82.5 **is 21.12.

When we fill in our known integers into this equation, we get

21.12 / b = 25.6 / 100

Next, to simplify this equation, we should use cross products (means - extremes products theorem). This means multiplying the numerator of one fraction and the denominator of the other fraction and setting them equal to one another.

21.12(100)=25.6(b)

When we multiply, you get

2112 = 25.6b

Finally, we divide both sides by 25.6, to get our variable b, alone, and without a coefficient.

82.5 = b

Therefore, 25.6%

Solution 2

Let

x------> the number

we know that

% is equal to

By using proportion

divide by both sides

therefore

**the answer is**

Question

Expand and simplify: (x + 5y) (x − 3y)

Solution 1

We have the following expression:

(x + 5y) (x - 3y)

Rewriting we have:

x ^ 2 - 3xy + 5xy - 15y ^ 2

Grouping similar terms we have:

x ^ 2 - 15y ^ 2 + 2xy

**Answer:**

**The complete and simplified expression is given by:**

**x ^ 2 - 15y ^ 2 + 2xy**

(x + 5y) (x - 3y)

Rewriting we have:

x ^ 2 - 3xy + 5xy - 15y ^ 2

Grouping similar terms we have:

x ^ 2 - 15y ^ 2 + 2xy

Solution 2

The answer you are looking for is x^2 - 15y^2 + 2xy.

To find this, you must first distribute one set of parenthesis into the other. This will give you "x^2 - 3xy + 5xy - 15y^2. You then combine like terms (-3xy and +5xy), to get "x^2 + 2xy - 15y^2". Finally, you organize the numbers based on their power (highest to lowest). Your final answer would be x^2 - 15y^2 + 2xy.

I hope this helps!

To find this, you must first distribute one set of parenthesis into the other. This will give you "x^2 - 3xy + 5xy - 15y^2. You then combine like terms (-3xy and +5xy), to get "x^2 + 2xy - 15y^2". Finally, you organize the numbers based on their power (highest to lowest). Your final answer would be x^2 - 15y^2 + 2xy.

I hope this helps!

Question

Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of α if α < β. sin(2x − 8) = cos(6x − 6)

Solution 1

We know that

in a right triangle

if sin A= cos B

then

angle A and angle B are complementary angles

so A+B=90

therefore

(2x-8)+(6x-6)=90-------> 8x-14=90----> 8x=104--------> x=13°

(2x-8)-----> 2*13-8----> 18°

(6x-6)-----> 6*13-6----> 72°

if α < β

then

α =18°

β=72°

in a right triangle

if sin A= cos B

then

angle A and angle B are complementary angles

so A+B=90

therefore

(2x-8)+(6x-6)=90-------> 8x-14=90----> 8x=104--------> x=13°

(2x-8)-----> 2*13-8----> 18°

(6x-6)-----> 6*13-6----> 72°

if α < β

then

α =18°

β=72°

Question

Sharon wants to know the difference between the average amount she stacked and the average amount Diane stacked. Which operation would she use to find the difference?

Solution 1

Sharon would subtract the amount that she stacked from Diane to figure out the difference.

Hope this helped :D

Hope this helped :D

Question

The function f(x) = 12x + 50 gives the amount of money a worker earns for working x hours per week. What is the inverse function?

Solution 1

12x + 50 = 62 but you have to multiply x by 12. I don't know what x is so maybe subtract 12 and 50 to get x. 50 - 12 = 38/ 38 x 12 = 456, then divide that by 50. 456 / 50 = 9.12, round up or down and get 9. 9 is your answer!!!

Question

How do you use properties of exponents and logarithms to rewrite functions in equivalent forms and solve equations?

Solution 1

Some of the logarithmic properties most used to solve equations are the following.

1) log (a) ^ b = b * log (a)

2) log (a * b) = log (a) + log (b)

3) log (a / b) = log (a) - log (b)

These logarithmic properties can be used to solve equations.

For example:

2 ^ x = 56

If we apply to this equation the logarithm function on both sides that we have left

log (2) ^ x = log (56)

This function is equivalent to the first.

If we now apply the property 1) of the previous logarithms, we can reveal x of the equation.

x * log (2) = log (56)

x = log (56) / log (2)

**x = 5,807**

Thus, thanks to the properties of the logarithms, this exponential function could be solved

1) log (a) ^ b = b * log (a)

2) log (a * b) = log (a) + log (b)

3) log (a / b) = log (a) - log (b)

These logarithmic properties can be used to solve equations.

For example:

2 ^ x = 56

If we apply to this equation the logarithm function on both sides that we have left

log (2) ^ x = log (56)

This function is equivalent to the first.

If we now apply the property 1) of the previous logarithms, we can reveal x of the equation.

x * log (2) = log (56)

x = log (56) / log (2)

Thus, thanks to the properties of the logarithms, this exponential function could be solved

Mathematics
2647929

History
842281

English
748681

Biology
586256

Social Studies
406852

Chemistry
368373

Business
348603

Physics
324927

Health
199835

Spanish
130075

Geography
112100

Computers and Technology
106146

Arts
77164

Advanced Placement (AP)
23675

World Languages
23213

French
22589

Engineering
19607

Law
17108

Medicine
13966

SAT
10987

German
3389

High School
3423409

Middle School
2092250

College
1518097