a team played 42 games and won 5/14 of them. how many games were lost?

[tex]\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{7})~\hspace{10em} slope = m\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-7=-2(x-4)[/tex]

Answer:

The equation in point-slope is [tex]y-7=-2(x-4)[/tex].

Step-by-step explanation:

Point-slope is a specific form of linear equations in two variables:

[tex]y-b=m(x-a)[/tex]

When an equation is written in this form, m gives the slope of the line and (a, b) is a point the line passes through.

We want to find the equation of the line that passes through (4, 7) and whose slope is -2. Well, we simply plug m = -2, a = 4, and b = 7 into point-slope form.

[tex]y-7=-2(x-4)[/tex]

false

under the given translation

the point (1, 6 ) → (1 - 7, 6 + 3 ) → (- 6, 9 )

19

evaluate the parenthesis, noting that + ( - ) = -

(19 + 9 ) + ( - 9) = 28 - 9 = 19

[tex]Solution, \left(19+9\right)+\left(-9\right)=19[/tex]

[tex]Steps:[/tex]

[tex]\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}[/tex]

[tex]\mathrm{Calculate\:within\:parentheses}\:\left(19+9\right)\::\quad 28, =28+\left(-9\right)[/tex]

[tex]\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:28+\left(-9\right)\::\quad 19, =19[/tex]

The correct answer is 19

Hope this helps!!!

The distance formula is:  Distance = Rate x Time.

We know the distance: 2000 miles.

We know the rates: 560 and 500 mph.

We need to solve for time:

2000 = (560 + 500) * T

2000 = 1060 *T

T = 2000 / 1060

T = 1.89 hours ( 1 hour 53 minutes)

They left at noon:

12:00 pm + 1 hour and 53 minutes = 1:53 pm.

The two planes are [tex]2000[/tex] miles apart at [tex]1:53[/tex] p.m.

Distance [tex]= 2000[/tex] miles

When both are traveling in opposite directions, speeds are added.

So, net speed [tex]= (560+500) = 1060[/tex] mph.

[tex]Speed = \frac{Distance}{Time}[/tex]

[tex]Time = \frac{Distance}{Speed}[/tex]

[tex]Time = \frac{2000}{1060}[/tex]

[tex]Time = 1.89[/tex] hour  

or  

Time [tex]= 1[/tex] hour [tex]53[/tex] minutes.

They leave at noon:

[tex]12:00[/tex] p.m [tex]+ 1[/tex] hour [tex]53[/tex] minutes [tex]= 1:53[/tex] p.m

So, the two planes are [tex]2000[/tex] miles apart at [tex]1:53[/tex] p.m.

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Answer:

The Answer is B

Step-by-step explanation:

Subtract f-g

4x + 1 - x^2 - 5

Distribute the - sign

4x + 1 - x^2 + 5

Combine like terms

-x^2 + 4x + 1 + 5

-x^2 + 4x + 6

To use the AA postulate directly, you need to show that two corresponding angles are congruent. In order to show that here, you must calculate the value of one of the missing angle measures. Either of the missing angles can be found by invoking the fact that the sum of angles in a triangle is 180°.

After finding either missing angle, you can show that the measures of two angles in one triangle are identical to the measures of two angles in the other triangle, hence the triangles are similar by the AA postulate.

Answer:

I wrote the answer below :)  hope it makes sense

Step-by-step explanation:

The Angle-Angle Similarity postulate can be used to prove that these two triangles are similar. To demonstrate I will use an example, and try to make sense to the reader. on triangle ABC, the 2 angles that are given to us are 32 degrees and 49 degrees. Since all triangles have an angle sum of 180 degrees, the missing degree would have to be 99 degrees. Same for the triangle A'B'C'. The 2 angles given are 99 degrees and 49 degrees, which means the missing angle has to be 32 degrees. Therefore, the triangles are similar.

I just took the test and this is correct.

Happy Holidays!

Amount needed for down payment = $650

Amount charged by Jordan for mowing 1 lawn = $25

Amount charged by Sharla for 1 necklace = $ 15

Let the number of lawns mowed by Jordan = x

Let the number of necklace made by Sharla = y

Part A:

[tex]25x+15y=650[/tex]

As it is given, Sharla can make 40 necklace so,

[tex]25x+15(40)=650[/tex]

Or it could be 25x=650 and 15y=650

Part B:

No, Sharla cannot afford the down payment because she makes $15 for every necklace and she only has 40 necklaces which is [tex]15*40=600[/tex]

Matrix multiplication is defined for M×K and K×N matrices to give an M×N result. Note that the middle two numbers (K) are the same.

Matrix multiplication of a 2×2 and 2×3 matrix will give a 2×3 matrix result. It is defined.

9 + 5 = x - 11

combine like terms

14 = x - 11

add 11 to both sides

25 = x

or

x = 25

answer

x = 25

9+5=x-11

14=x-11

+11    +11

24=x

Answer:

 PK=8.49m

Explanation:

We have sine formula

     [tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]

By sine formula we have

    [tex]\frac{PS}{sinK} =\frac{PK}{sinS} =\frac{KS}{sinP}[/tex]

    We have PS = 12, ∠P=105° and ∠S=30°, so ∠K=180°-(105°+30°)=45°

 Substituting

        [tex]\frac{12}{sin45} =\frac{PK}{sin30} \\ \\ PK=8.49m[/tex]      

If something goes below sea level, that means the answer is gunna be a negative number. so we have -200 and -130. we have to add the numbers together.

-200 + -130 = -330.

The new depth is -330. Hope this helps. Let me know if you need anymore help!

Let x be the bigger number and y be the smaller number.

One number is 11 more than twice another number. Thus,

x = 2y + 11

The sum of the numbers is twice their difference, thus,

x + y = 2(x-y), which simplifies to:

x + y = 2x - 2y

3y = x  (Now plug this back to the first equation:

3y = 2y + 11, and solve:

y = 11

Plug in y = 11 to the first equation:

x = 2(11) + 11 = 22 + 11 = 33

Thus the numbers are: x = 33, y = 11.

Answer: The value of f is 1.

Step-by-step explanation:

Since we have given that

[tex]-f+2+4f=8-3f[/tex]

We need to find the value of f :

1) First we gather the like terms together:

2) Solving the like terms

3)find the value of f.

[tex]-f+2+4f=8-3f\\\\3f+2=8-3f\\\\3f+3f=8-2\\\\6f=6\\\\f=\dfrac{6}{6}\\\\f=1[/tex]

Hence, the value of f is 1.

The solution to the equation -f + 2 + 4f = 8 - 3f is f = 1.

To solve the equation -f + 2 + 4f = 8 - 3f, we can simplify and solve for f:

Combine like terms on the left side:

-f + 4f + 2 = 8 - 3f

Simplify: 3f + 2 = 8 - 3f

Add 3f to both sides:

3f + 3f + 2 = 8 - 3f + 3f

Simplify: 6f + 2 = 8

Subtract 2 from both sides:

6f + 2 - 2 = 8 - 2

Simplify: 6f = 6

Divide both sides by 6:

6f/6 = 6/6

Simplify: f = 1

Therefore, the solution to the equation -f + 2 + 4f = 8 - 3f is f = 1.

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The associative property allows you to change the grouping of addends or factors without changing the value of the expression.

The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.

Angles on the same side are the same, so angle 1 is 110°.

Angle 1 and 2 are supplementary, so they add up to 180. Since we know angle 1 is 110, angle 2 must be 70°

y=x^2 - 10x +2

Use the form ax^2 + bx + c to find the values of a, b,and c.

a = 1 ( no number in front of the x^2)

b = 10

c = 2

Vertex form is a(x+d)^2 + e

Solve for d using d= b/2a

d = 10 / 2

d = 5

Find e using e = c - b^2/4a

e = 2 - 10^2/4

e = 2 - 25

e = -23

Vertex = d,e

Vertex = (5, -23)

1/2 = 3/6

2/3 = 4/6

2/3 is greater than 1/2, so is to the right of 1/2 on the number line.

The difference is (4/6) -(3/6) = (4-3)/6 = 1/6.

2/3 is 4/3 times 1/2.

16. Vertical angles are the ones bounded by the same lines and have the same vertex, but that have no sides in common. Pairs 1 and 3 or 2 and 4 are vertical angles.

17. The diagram shows the sum of the three angles makes a right angle (90°). Write that as an equation:

... x° + 2x° + 15° = 90°

Solve the equation in the usual manner: collect terms, add the opposite of the unwanted constant on the left, divide by the coefficient of x.

... 3x° +15° = 90°

... 3x° = 75°

... x = 25

18. You may notice that this problem follows the same pattern as the one of 17. We add the constituent angles to make the whole right angle. Here, you have some follow-on effort to find ∠BDC after you find x.

... (-3x+20)° + (-2x+55)° = 90°

... -5x +75 = 90 . . . . . . . collect terms, divide by °

... -5x = 15 . . . . . . . . . . . subtract 75

... x = -3 . . . . . . . . . . . . . divide by the coefficient of x

Now we can find ∠BDC.

... ∠BDC = (-3x+20)° = (-3(-3)+20)°

... ∠BDC = 29°

A number added to its opposite is zero (0). No exponent is needed.

7^4 - 7^4 = 0

y = - [tex]\frac{1}{4}[/tex] x + [tex]\frac{15}{2}[/tex]

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = 4x + 5 is in this form with slope m - 4

Given the slope of a line m, then the slope ([tex]m_{2}[/tex]) of a line perpendicular to it is

[tex]m_{2}[/tex] = - (1 / m ) = - [tex]\frac{1}{4}[/tex]

y = - [tex]\frac{1}{4}[/tex] x + c is the partial equation of the perpendicular line

to find c, substitute ( 2, 7 ) into the partial equation

7 = - [tex]\frac{1}{2}[/tex] + c ⇒ c = [tex]\frac{15}{2}[/tex]

y = - [tex]\frac{1}{4}[/tex] x + [tex]\frac{15}{2}[/tex] ← equation of perp. line

Answer: Procedure are given below :

Step-by-step explanation:

Since we have given that

Pay rate = $21.00

if he marked up by 78.7% , then

[tex]78.7\%\text{ of }21\\\\=\frac{78.7}{100}\times 21\\\\=16.527[/tex]

So, our pay rate becomes

[tex]\$21+\$16.527=\$37.527[/tex]

Now, he made a 10% profit,

[tex]10\%\text{ of }37.527\\\\=\frac{10}{100}\times 37.527\\\\=\$3.7527[/tex]

So, pay rate becomes

[tex]\$37.527+\$3.7527\\\\=\$41.2797[/tex]

which approximately $41.28

The city has an initial population of 75,000.

Grows at a constant rate of 2,500 per year for five years

a) We must find a linear function that models the P population of the city according to the years.

This function has the following form:

[tex]P=P_{0}+ at\\[/tex]

Where

P is the population as a function of time

[tex]P_{0}[/tex] is the initial population

"a" is the constant rate of growth of the function.

"t" is the time elapsed in units of years.

Then the function is:

 [tex]P=75,000+2500t[/tex]

b) Before plotting the function, let's find its intercepts with the "t" and "P" axes

To find the intercept of the function with the t axis we do P = 0

 [tex]0 =75000+2500t[/tex]

 [tex]t=\frac{-75 000}{2500}[/tex]

 [tex]t = -30[/tex]

Now we make t = 0 to find the intercept with the P axis

[tex]P =75000[/tex]

The intercept with the P axis at P = 75 000 means that this is the initial population, therefore, for a period of 0 to 5 years, the population can not be less than 75,000.

The intercept at t = -30 does not have an important significance for this problem, since we are evaluating population growth for a period of [tex]0 \leq t \leq 5[/tex].

The graph of the function is shown in the attached figure.

c) To answer this question we must do P = 100 000 and clear t.

[tex]100000=75000+2500t [/tex]

[tex]25 000=2500t [/tex]

[tex]t =10years[/tex].

The second problem is solved in the following way:

The weight of a newborn baby is 7.5 pounds

The baby earns half a pound a month in its first year

a) To find the function that models the weight of the baby we follow the same procedure as in the previous problem.

[tex]W = W_{0} + at[/tex]

Where

W is the baby's weight according to the months

[tex]W_{0}[/tex] is the initial weight in pounds

"a" is the rate of increase

"t" is the time elapsed in months.

So:

[tex]W = 7.5 + 0.5t[/tex]

b) The domain of the function is [tex]0 \leq t \leq 12\\[/tex]

Since the function only applies for the first year of growth of the baby, and one year has 12 months.

The range of the function is [tex]7.5 \leq W\leq 13.5[/tex]

The towns' population and the baby's weight can be modeled by linear functions, which have a constant growth rate and an initial starting value. For the population to reach 100,000, we need to solve for t in our linear equation. Linear relationships are common in population growth, but are often approximations as they ignore limiting factors.

In both scenarios, we're dealing with linear functions. The towns' population, P, can be represented by a linear function as follows: P(t) = 2,500*t + 75,000 where t is the number of years passed. For the baby's weight, use the similar linear function: W(t) = 0.5*t + 7.5, where t is the baby's age in months. Both functions have an initial value (intercept at t=0) and a constant growth rate (the slope of the line). For the town's population to reach 100,000, solve the equation 100,000 = 2,500*t + 75,000 for t. Similarly, the baby's weight will depend on how many months have elapsed.

To graph either function, start at the intercept (t=0) and use the slope to find additional points (i.e., for each year that passes, add 2,500 to the population, or for each month that passes, add 0.5 to the baby's weight).

Linear relationships like these are common in Population Growth and other Population Models but are often approximates as they ignore factors that may limit growth (such as resources).

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Answer:

1. Put the numbers in order.

2. Cross off high/low pairs.

3. Add the leftover numbers.

4. Divide the sum by 2.

Step-by-step explanation:

We know that the median represent the middle value in a data which gives the center of the measure.

Whenever we calculate the median of a data the first step we need to follow is to arrange the a data in either ascending or descending order.

After that choose that center-most data value (in odd number of data value) or calculate the mean of the center-most 2 numbers ( if even) which will be the median of the  data.

Given data: 24, 16, 23, 30, 18, 29

Number of numbers = 6 (even)

1. Put the numbers in order.

16,18,23,24,29,30

2. Cross off high/low pairs., we left with the numbers :-

23,24

3. Add the leftover numbers.

23+24=47

4. Divide the sum by 2.

[tex]\dfrac{47}{2}=23.5[/tex]

Answer:

A.

Step-by-step explanation:

The first quartile (Q1) in a box-and-whisker plot is the value at the left boundary of the box, which represents the median of the lower half of the dataset. According to the information provided, Q1 is 80, but none of the given answer options (A, B, C, D) match this value.

In the context of your question, which examines a box-and-whisker plot, the first quartile (Q1) corresponds to the value at the left boundary of the box. The first quartile represents the median of the lower half of the dataset, excluding the overall median. From the information provided, we can deduce that the first quartile (Q1) is 80, as represented by the left boundary of the box in a box plot provided elsewhere.

Therefore, the correct answer to your question would be the option that most closely matches the value of 80. However, since none of the options (A. 43.5, B. 47.5, C. 41.5, D. 50.0) match this value, there appears to be a discrepancy. It's possible that there is an error in the question options, or there might be a misinterpretation regarding the information provided. Make sure that you are referring to the correct box plot.