Receive 99 points if answered correctly with steps!

Point E is the midpoint of side BC of parallelogram ABCD (labeled counterclockwise) and AE ∩ BD =F. Find the area of ABCD if the area of △BEF is 3 cm2.

c - the number

The sum of 7 times a number and 9 is 5:

[tex]7c+9=5[/tex]     subtract 9 from both sides

[tex]7c=-4[/tex]          divide both sides by 7

[tex]\boxed{c=-\dfrac{4}{7}}[/tex]

[tex]\left\{\begin{array}{ccc}2x+3y=5&|\text{multiply both sides ny 3}\\3x+4y=4&|\text{multiply both sides by (-2)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}6x+9y=15\\-6x-8y=-8\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad \boxed{y=7}\\\\\text{put the value of y to the first equation}\\\\2x+3(7)=5\\\\2x+21=5\qquad\text{subtract 21 from both sides}\\\\2x=-16\qquad\text{divide both sides by 2}\\\\\boxed{x=-8}\\\\Answer:\ \boxed{x=-8\ and\ y=7}[/tex]

Answer:

9 days.

Step-by-step explanation:

If the company produced 20 more items than 40 items each day, then it must have produced 60 items each day.

Though you're probably expected to write an equation, it's easiest to solve this through educated guess and check.

If there were 120 items to be produced, the company would be required to do it in 3 days (120 items, 40 items/day) but completed it in 2 days (120 items, 60 items/day). In this case, they finished their order 1 day early. But the problem states that they finished 3 days early. So we guess 3 times 120 items, or 360 items. Checking this, they should have finished their order in 9 days (360 items, 40 items/day) but they finished in 6 days (360 items, 60 items/day). 6 is three less than 9, so our guess of 360 items was correct. We have shown that the company should have finished the order in 9 days.

If you had to use an equation:

Let the desired number of days be x. Then, the company finished its order in x - 3 days. Since number of items produced is the number of days times items per day, and it doesn't change:

number of items = 40 items/day * x days = 60 items/day * (x - 3) days

40x = 60(x - 3) = 60x - 180

180 = 20x

x = 9

9 days is the desired answer.

Answer:

9

Step-by-step explanation:

Answer:

The equation of the line would be y = -3/7x - 20/7

Step-by-step explanation:

To start finding the line of this equation, you need to find the slope. You can do this using the slope equation.

m(slope) = (y2 - y1)/(x2 - x1)

m = (-2 - -5)/(-2 - 5)

m = (-2 + 5)/(-2 - 5)

m = 3/-7

m = -3/7

Now that we have the slope, we can use that and either point in point-slope form to get the equation.

y - y1 = m(x - x1)

y + 5 = -3/7(x - 5)

y + 5 = -3/7x + 15/7

y = -3/7x - 20/7

To find the equation of the line that passes through (-2, -2) and (5, -5), calculate the slope, apply it to the point-slope form using one of the points, then simplify to slope-intercept form, resulting in y = (-3/7)x - 20/7.

To find the equation of the line that passes through the points (-2,-2) and (5,-5), we first need to calculate the slope of the line. The slope (m) can be found using the formula:

m = (y_{2} - y_{1}) / (x_{2}  - x_{1})

Substituting our points into the formula:

m = (-5 - (-2)) / (5 - (-2)) = (-5 + 2) / (5 + 2) = -3 / 7

Next, we use the point-slope form of a line's equation which is y - y1 = m(x - x1). Let's use the first point (-2, -2):

y - (-2) = (-3/7)(x - (-2))

Now we simplify and write the equation in slope-intercept form (y = mx + b):

y + 2 = (-3/7)x - 6/7

Subtract 2 from both sides of the equation to solve for y:

y = (-3/7)x - 6/7 - 14/7

y = (-3/7)x - 20/7

The equation of the line that passes through the points (-2,-2) and (5,-5) is y = (-3/7)x - 20/7.

Use the definition of conditional probability:

[tex]P(\text{sports}\mid\text{senior})=\dfrac{P(\text{sports AND senior})}{P(\text{senior})}[/tex]

We know that 0.10 of students belong to both categories, and that 0.25 of students are seniors, so

[tex]P(\text{sports}\mid\text{senior})=\dfrac{0.10}{0.25}=0.40[/tex]

Answer:

0.40

Step-by-step explanation:

The simplest form of 38 multiplied by 45 equals  to 1710.

To multiply 38 and 45, we'll use the long multiplication method:

  38

x 45

------

 190   (38 * 5)

+1520  (38 * 40, shift one position to the left)

------

1710

So, 38 multiplied by 45 equals 1710.

Another method is to break down 38 into its factors to simplify the multiplication:

38 = 2 * 19

Now, we can rewrite 38 * 45 as (2 * 19) * 45:

(2 * 19) * 45 = (2 * 45) * 19

             = 90 * 19

Now, we can multiply 90 by 19:

90

x 19

-----

180  (90 * 9, shift one position to the left)

+ 0   (90 * 1, with a zero placeholder)

-----

1710

Again, we get the result as 1710.

So, whether we use long multiplication directly or break down the numbers into factors, the result remains the same: 38 * 45 = 1710.

Answer:

The answer is: 8km - 4

Step-by-step explanation:

Given: (4k4m - 8)1/2 =

Simplify then multiply 1/2 by each term:

4k4m/2 - 8*1/2 =

16km/2 - 4

8km - 4

Hope this helps! Have an Awesome day!! :-)

48 1/8

As written, it is evaluated as ...

... 47 + 9/8 . . . . . . . . parentheses are evaluated first

... = 47 + 1 1/8 . . . . . . then division

... = 48 1/8 . . . . . . . . then addition

_____

A decent calculator will evaluate this for you according to the order of operations. A Google or Bing search box will do that, too.

I like to use a little X diagram to work mixture problems like this. The constituent concentrations are on the left; the desired mix is in the middle, and the right legs of the X show the differences along the diagonal. These are the ratio numbers for the constituents. Reducing the ratio 32:8 gives 4:1, which totals 5 "ratio units". We need a total of 100 kg of alloy, so each "ratio unit" stands for 100 kg/5 = 20 kg of constituent.

That is, we need 80 kg of 60% alloy and 20 kg of 20% alloy for the product.

_____

Using an equation

If you want to write an equation for the amount of contributing alloy, it works best to let a variable represent the quantity of the highest-concentration contributor, the 60% alloy. Using x for the quantity of that (in kg), the amount of copper in the final alloy is ...

... 0.60x + 0.20(100 -x) = 0.52·100

... 0.40x = 32 . . . . . . . . . . .collect terms, subtract 20

... x = 32/0.40 = 80 . . . . . kg of 60% alloy

... (100 -80) = 20 . . . . . . . .kg of 20% alloy

Answer:

what do i do if my math skills are bad

Step-by-step explanation:

Let the Salary of Mr. O'Conell be : S

Given : Mr. O'Conell spends 15% of his Salary on Food

[tex]\mathsf{\implies 15\%\;of\;Salary(S) = (\frac{15}{100} \times S) = 0.15 \times S}[/tex]

Given : Mr. O'Conell spends 24% of his Salary on Transportation

[tex]\mathsf{\implies 24\%\;of\;Salary(S) = (\frac{24}{100} \times S) = 0.24 \times S}[/tex]

Given : After Spending on Food and Transportation, He saves $1830

Money Spent on Food + Money spent on Transportation + Remaining Money should be Equal to his Total Salary

[tex]\mathsf{\implies 0.15S + 0.24S + 1830 = S}[/tex]

[tex]\mathsf{\implies 0.39S + 1830 = S}[/tex]

[tex]\mathsf{\implies S - 0.39S = 1830}[/tex]

[tex]\mathsf{\implies 0.61S = 1830}[/tex]

[tex]\mathsf{\implies S = \frac{1830}{0.61} }[/tex]

[tex]\mathsf{\implies S = 3000}[/tex]

Mr. O'Conell's Salary is $3000

Answer:

k = -2

Step-by-step explanation:

The graph clearly shows the y-intercept of f(x) as being 4, and that of g(x) as being 2. Thus, g(x) = f(x) -2 = f(x) +k.

Subtracting f(x) from that equation, you get k = -2.

_____

Check

g(x) is displaced 3 units to the right of f(x). The slopes of both f(x) and g(x) are 2/3, so a displacement of 3 units right is equivalent to a displacement of 2 units down. k represents the vertical translation, so is -2.

The value of k is found by examining the vertical distance between the graphs of y=f(x) and y=g(x) at the same x-coordinate. Without the visual graphs or specific points, the exact value of k cannot be provided.

The student is asking about the relationship between two functions, where g(x) is related to f(x) by the addition of a constant k.

To find the value of k, one would typically examine the vertical distance between the two function graphs at any given x-coordinate, since g(x) = f(x) + k. Without the graphical information provided, it is not possible to determine the exact value of k.

However, typically if you have two functions with graphs that are vertically shifted versions of each other, and you know two corresponding points on each graph with integer coordinates, you can subtract the y-values of these points to find k.

Answer:

f(x) = 60 + 15n

Step-by-step explanation:

if the start off amount is 60, so we can simply start it with 60 + ...

If she gets 15 for each customer, and the amount of customers is equal to n, then this can be written by 15n ( 12 * n )

Simply put these two parts together:

60 + 15n

So in a function:

f(x) = 60 + 15n

Answer:

19 yards

Step-by-step explanation:

A square has 4 equal sides, thus its area is given by the formula below.

[tex]\boxed{\text{Area of square}=\text{side}^2}[/tex]

Substitute the area of the square into the formula:

361= side²

Square root both sides:

Length of each side

= [tex]\sqrt{361}[/tex]

= 19 yards

To learn more about area of square, check out: https://brainly.com/question/4988011

Answer:

77° or 103°

Step-by-step explanation:

All of the angles are either the given angle or its supplement. Corresponding angles are congruent, as are vertical angles. Any linear pair of angles will add to 180°.

Answer:

77° and 103°

Step-by-step explanation:

77° because it says one of the angles is 77°

103° because two parallel lines are equal to 180°

180°-77° is 103°

Answer:

2 km/h

Step-by-step explanation:

Let c represent the speed of the current of the river in km/h. Then the speed of the boat upstream is (10-c). In 3/4 hour, the distance traveled upstream is ...

... distance upstream = (3/4)·(10 -c)

The time taken to travel the same distance downstream is given as 3 hours. The speed in that direction is c, so we have ...

... 3 = distance upstream/c = (3/4)(10 -c)/c

Multiplying this equation by 4c, we get ...

... 12c = 3(10 -c)

... 15c = 30 . . . . . . . . add 3c

... c = 2 . . . . . . . . . . . divide by 15

The speed of the river current is 2 km/h.

Answer:

2km/h

Step-by-step explanation:

D. R(x) = 850x +9600

Selling 10 more machines increased revenue from $18100 to $26600, an increase of ...

... $26,600 -18,100 = $8,500

That is, the revenue increased by $8500/10 = $850 per machine.

Only one answer choice has this number in it:

... D. R(x) = 850x+9600

_____

Check

R(10) = 850·10 +9600 = 8500 +9600 = 18,100 . . . . OK

R(20) = 850·20 +9600 = 17000 +9600 = 26,600 . . . . OK

_____

Comment on answer selection

On multiple-choice questions, it is rarely necessary to work out the solution to the problem completely. Usually, it is sufficient to find the one number that discriminates between correct and incorrect answers.

In real life, answers are rarely multiple-choice. You are required to work the problem completely and to figure out how to tell if your answer is correct.

Here, we have worked the problem far enough to find the slope, the amount by which revenue increases when sales increases by 1 unit. The intercept can be found different ways. One of them is to see what number makes the revenue match for one of the "x" values:

... R(10) = 850·10 +b = 18100

... b = 18100 -8500 = 9600

so ...

... R(x) = 850x +9600

We can check this answer by computing R(20), as we have above.

Answer:

R(x)=850x+9600

Step-by-step explanation:

:⊃

Answer:

30

Step-by-step explanation:

These are generally easier to evaluate by hand if they are simplified first.

... (4a^2)b -ab^2 -(3a^2)b +ab^2 -ab +6

... = (a^2)b(4 -3) + ab^2(-1 +1) -ab +6

... = a^2·b -ab +6

... = ab(a -1) +6

... = (-3)(2)(-3-1) +6

... = (-6)(-4)+6

... = 24 +6 = 30

Put the values of a = -3 and b = 2 to the expression

[tex]4a^2b-ab^2-3a^2b+ab^2-ab+6[/tex]

[tex](4)(-3)^2(2)-(-3)(2)^2-(3)(-3)^2(2)+(-3)(2)^2-(-3)(2)+6\\\\=(4)(9)(2)+(3)(4)-(3)(9)(2)-(3)(4)-(-6)+6\\\\=72+12-54-12+6+6\\\\=\boxed{30}[/tex]

Answer:

D. x = 3 1/8

Step-by-step explanation:

x + 7/8 = 4

The first step is to subtract 7/8 from each side

x + 7/8 - 7/8 = 4 - 7/8

x = 4 - 7/8

We need to borrow from the 4. It become 3 8/8

x = 3 8/8 - 7/8

x = 3 1/8

Answer:

I believe the answer would be D.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

a) correct is 3/4.5=4/6; b) correct is 3.2/2.4=4/3; c) correct is 4/3.2=3/2.4; d) this is correct answer.

Answer:

(A) y - 7 = 2(x -2)

(B) y = -x + 6; y - 5 = -1(x + 1)

(C) Consistent independent

(D) (1, 5)

Step-by-step explanation:

(A) Road 1

(a) Slope

The point-slope formula for a straight line is

y₂ - y₁ = m(x₂ - x₁)     Insert the points  

 3 - 7 = m(0 - 2)

     -4 = m(-2)           Divide each side by -2

     m = -4/(-2)          Divide numerator and denominator by-2,

      m = 2

=====

(b) y-intercept

y₂ - y₁ = m(x₂ - x₁)

y₂ - 7 = 2(x₂ -2)

y - 7 = 2(x -2)

===============

(B) Road 2

(a) Slope

y = mx + b

Choose point (3,3)

m = (3 - 5)/(3 - 1)

m = -2/2

m = -1

=====

(b) y-intercept

y = mx +b

Choose point (3,3).

3 = -3 + b      Add 3 to each side

b = 6

=====

(c) Equation of line (point-slope form)

y = mx + b

y = -x + 6

=====

(d) Equation of line (slope-intercept form)

y - 5 = -1(x - 1)

===============

(C) Consistency

The two roads intersect.

There is only one point of intersection, so this is a consistent, independent system of equations

===============

(D) Point of intersection

(1)      y - 7 = 2(x -  2)

(2)          y =   -x + 6     Substitute (2) into (1)

-x + 6 – 7 = 2(x – 2)    Remove parentheses

       -x - 1 = 2x – 4      Add 4 to each side

       -x +3 = 2x            Add x to each side

             3 = 3x            Divide each side by 3

             x = 1               Substitute into 2

=====

            y = -1 + 6

           y = 5

The point of intersection is (1, 5).

Answer:

-x^3+5x^2-8x+1, which is choice A

======================================

Work Shown:

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

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

f(2-x) = (2-x)^3 - (2-x)^2 - 3 ................ see note 1 (below)

f(2-x) = (2-x)(2-x)^2 - (2-x)^2 - 3 ........... see note 2

f(2-x) = (2-x)(4-4x+x^2) - (4-4x+x^2) - 3 ..... see note 3

f(2-x) = -x^3+6x^2-12x+8 - (4-4x+x^2) - 3 ..... see note 4

f(2-x) = -x^3+6x^2-12x+8 - 4+4x-x^2 - 3 ....... see note 5

f(2-x) = -x^3+5x^2-8x+1

----------

note1: I replaced every copy of x with 2-x. Be careful to use parenthesis so that you go from x^3 to (2-x)^3, same for the x^2 term as well.

note2: The (2-x)^3 is like y^3 with y = 2-x. We can break up y^3 into y*y^2, so that means (2-x)^3 = (2-x)(2-x)^2

note3: (2-x)^2 expands out into 4-4x+x^2 as shown in figure 1 (attached image below). I used the box method for this and for note 4 as well. Each inner box or cell is the result of multiplying the outside terms. Example: in row1, column1 we have 2 times 2 = 4. You could use the FOIL rule or distribution property, but the box method is ideal so you don't lose track of terms.

note4: (2-x)(4-4x+x^2) turns into -x^3+6x^2-12x+8 when expanding everything out. See figure 2 (attached image below). Same story as note 3, but it's a bit more complicated.

note5: distribute the negative through to ALL the terms inside the parenthesis of (4-4x+x^2) to end up with -4+4x-x^2

Answer:

–x3 + 5x2 – 8x + 1

–x3 + 7x2 – 16x – 15

x3 + 5x2 + 8x + 1

x3 – 7x2 + 16x – 15

Step-by-step explanation:

–x3 + 5x2 – 8x + 1

–x3 + 7x2 – 16x – 15

x3 + 5x2 + 8x + 1

x3 – 7x2 + 16x – 15

Answer:

The inequality [tex]f>40[/tex] represents the length of the femur for which the woman had a height greater than 160cm.

Step-by-step explanation:

The given equation is

[tex]h=60+2.5f[/tex]

Where, h is woman's height in centimeters and f is length of the femur in centimeters.

If woman's height is greater than 160cm, then

[tex]h>160[/tex]

[tex]60+2.5f>160[/tex]

Substract 60 from both sides.

[tex]2.5f>100[/tex]

Divide both sides by 2.5.

[tex]f>40[/tex]

Therefore the inequality  [tex]f>40[/tex] represents the lengths of the femur for which the woman had a height greater than 160cm.

Answer:

-2

Step-by-step explanation:

3.3÷(0.8−3)−0.5

First think of PEMDAS

So first do parenthese

(0.8-3)=-2.2

3.3÷-2.2-0.5

Now do division

3.3/-2.2=-1.5

and now subtraction

-1.5-0.5=-2

Answer:

9/10

Step-by-step explanation:

In ratio units, the relative lengths of the first, second, and third towels are ...

... 1 : 3/5 : (5/12)·(1 +3/5)

... = 1 : 3/5 : 2/3

Then the fraction the second towel is of the third towel is ...

... (3/5)/(2/3) = (3/5)·(3/2) = 9/10

answer:

the answer is 2/3

Answer:

The amount off the original price is $3.6.

Step-by-step explanation:

The original price of the sweater = $18.00

Amount off on the sweater = 20% of the original price of the sweater

=[tex]18.00\times\frac{20}{100}=$3.6[/tex]

The cost of the sweater on the sale = $18.00 - $3.6 = $14.4

The amount off the original price is $3.6.

QUESTION 1

a)

Let

[tex]s [/tex]

represent the amount Same earned and

[tex]k[/tex]

represent the amount Kevin earned.

We were told that, they earned $425 dollars together.

This implies that,

[tex]k+s= 425---eqn(1)[/tex]

It was also given that, Kevin earned $25 more than Same.

This implies,

[tex]k-s=25---eqn(2)[/tex]

For equation (1), when

[tex]s=0[/tex]

[tex]k=425[/tex]

We plot the point,

[tex](425,0)[/tex]

When

[tex]k=0[/tex]

[tex]s=425[/tex]

We plot the point,

[tex](0,425)[/tex]

Similarly for the second equation when

[tex]s=0[/tex]

[tex]k=25[/tex]

This gives the point,

[tex](25,0)[/tex]

When

[tex]k=0[/tex]

[tex]s=-25[/tex]

We plot

[tex](0,-25)[/tex]

and draw a straight line through them.

We can see from the graph that the two points intersect at  

[tex](225,200)[/tex]

This implies that

[tex]k=225\:and\:s=200[/tex]

Therefore Kevin earned $ 225

and Same earned $ 200

QUESTION 2

The given system is

[tex]6=-4x + y---eqn(1)[/tex]

and

[tex]-5x-y=21---eqn(2)[/tex]

From equation (2),

[tex]y=-5x-21---eqn(3)[/tex]

Put equation (3) into equation (1).

This implies that,

[tex]6=-4x-5x-21[/tex]

Group like terms,

[tex]6+21=-4x-5x[/tex]

Simplify, to get,

[tex]27=-9x[/tex]

[tex]x=-3[/tex]

We substitute this value into equation (3) to get,

[tex]y=-5(-3)-21[/tex]

[tex]y=15-21[/tex]

[tex]y=-6[/tex]

Therefore the solution is

[tex](-3,-6)[/tex]

QUESTION 3

We want to solve,

[tex]2x+y=20---(1)[/tex]

and

[tex]6x -5y=12---(2)[/tex]

We multiply equation (1) by 3 to get,

[tex]6x+3y=60---(3)[/tex]

Equation (3) minus equation (2) will give us,

[tex]8y=48[/tex]

This means

[tex]y=6[/tex]

Put this value into equation (1) to get,

[tex]2x+6=20[/tex]

[tex]2x=20-6[/tex]

[tex]2x=14[/tex]

[tex]x=7[/tex]

The solution is

[tex](7,6)[/tex]

Answer:

Sam earns $200 and Kevin earns $225.

x , y= -3 , -6 by substitution

x , y= 7, 6 by elimination

Step-by-step explanation:

a) Let the amount earned by Sam = s and the amount earned by Kevin = k

We are given, that they both earn total $425 i.e. s + k = 425

Also, Kevin earns $25 more than Sam i.e. k = s + 25

Hence, the system of equations comes out to be:

s + k = 425

-s + k = 25

b) Take s = x and k = y. See the graph plotted below

c) As the intersection point from the graph comes out to be (s,k) = (200,225)

Therefore, Sam earns $200 and Kevin earns $225.

Now, we have the system

-4x + y = 6

-5x - y = 21

We need to use substitution method.

Take y= -5x - 21 from the 2nd equation and put it in the 1st.

We get, -4x - 5x - 21 = 6  i.e.  -9x = 27  i.e.  x= -3

Now, substitute this value of x in any of the equation to find y.

We get, -5*(-3) - y = 21  i.e.  y = 15 - 21  i.e.  y = -6

Now, we are given the system,

2x + y = 20

6x - 5y = 12

We need to use elimination method.

Multiply 5 by equation 1. We get,

10x + 5y = 100

6x - 5y = 12

Adding the above equations, we get, 16x = 112  i.e. x = 7

Put this value in any of the equation to find the value of y.

We get, y = 20 - 2x  i.e.  y = 20 - 2*7  i.e.  y = 20 - 14  i.e. y = 6

Answer:

Answer is: D. $40

Step-by-step explanation:

20+40=60

100-60=40

Answer:

A 48

Step-by-step explanation:

Answer:

Step-by-step explanation:

I don't know how is to speak it English correctly but is the teoreme of whole probability

P(A1)=0.08*0.4=0,032 is probability to choose defective item line I

P(A2)=0.1*0.6=0.06  is probability to choose defective item line II

P(B)=P(A1)+P(A2)=0,032+0.06=0.092 probability to choose defective item

P(C)=1-P(B)=0.908 the probability that it is not defective

3 seconds

For the given problem conditions, the parameters in your formula are ...

... h = 0

... r = 48

Putting these values into the equation, we can solve for t.

... 0 = 48t -16t²

... 0 = 16t(3 -t) . . . . . factored

This will be true for t=0 and for t=3

The ball will hit the ground after 3 seconds.

_____

Comment on answer choices

For the ball to take 456 seconds (more than 7 1/2 hours) to hit the ground, it would have to  be launched at 7296 ft/s, several times the speed of sound. Its maximum height would be over 157.5 miles, and all of the usual assumptions about a stationary flat Earth with a uniform gravity field and no air resistance could not apply.

So, we know that 456 seconds is an impossible choice (as are the higher values, such as 1863 seconds). Perhaps that should be 4 5/6 seconds. For that to be the answer, the launch speed would need to be 77 1/3 ft/s, not 48 ft/s.

___

If these are the actual answer choices associated with this problem, it would be a good idea to have your teacher show you how to work it.