Triangle SBA has coordinate S(15,-8), B(-2,21), A(0,0). If the height of the triangle for the corresponding base sb is 8.89 units, then determine the perimeter and area of SBA.

To factor the expression 5ac + 10ab - 2c^2 - 4bc, we first factor out common factors from the pairs of terms which results in 5a(c + 2b) - 2c(c + 2b). Then, we factor out the common binomial (c + 2b) to get the fully factored form: (5a - 2c)(c + 2b).

The expression given is 5ac + 10ab - 2c^2 - 4bc. To factor this expression, we need to look for common factors in the terms. Let's take each pair of terms and factor it.

For the first two terms (5ac and 10ab), the common factor is 5a. Factoring these gives: 5a(c + 2b).

The last two terms (-2c^2 and -4bc), -2c is the common factor. Factoring these gives: -2c(c + 2b).

So our expression becomes 5a(c + 2b) - 2c(c + 2b). Finally, we factor out the common binomial term (c + 2b) to get the fully factored form: (5a - 2c)(c + 2b).

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its d to check answer use symbolab its a great sight

2 hours and 13 mins hope this helps

7.25 u need to add 2.25+5=7.25

This is a right triangle (you can confirm by using Pythagorean Theorem: 15² + 36² = 39²)

A = [tex]\frac{1}{2} b * h[/tex]

A = [tex]\frac{1}{2} 15 * 36[/tex]

   = 15 * 18

   = 270

Answer: 270 cm²

Solution-

The table shows the number of touchdowns Luis scored during his football games.

Touchdowns scored (X) 0 1 2 3

Number of games (f)             6 10 7 5

Total games played = 6+10+7+5=28

1.

[tex]Probability\ of\ an\ event=\frac{Number\ of\ Favorable\ Outcomes}{Total\ Number\ of\ Possible\ Outcomes}[/tex]

[tex]P(X=0)=\frac{6}{28} \\ P(X=1)=\frac{10}{28} \\ P(X=2)=\frac{7}{28} \\ P(X=3)=\frac{5}{28}[/tex]

Probability Distribution Table,

Touchdowns scored (X) 0      1           2      3

Probability P(X)                      6/28    10/28  7/28    5/28

2.

The probability of Luis scoring 2 touchdowns(i.e when X=2),

P(scoring 2 touchdowns) = P(X=2)

[tex]=\frac{7}{28}=0.25[/tex]

3.

The probability of Luis scoring more than 1 touchdown(i.e when X>1)

P(scoring more than 1 touchdowns) = P(X>1) = P(X=2) + P(X=3)

[tex]=\frac{7}{28}+\frac{5}{28}=0.42[/tex]

4.

Estimated number of touchdowns is calculated by multiplying the number of touchdowns by their respective probabilities and adding the result.  

Estimated number of touchdowns is,

[tex]=0\times \frac{6}{28}+1\times \frac{10}{28}+2\times \frac{7}{28}+3\times \frac{5}{28}[/tex]

[tex]=0+\frac{10}{28}+\frac{14}{28}+\frac{15}{28}[/tex]

[tex]=\frac{39}{28}=1.39[/tex]

The graph which  represents the equation y = -2x+3 is Option (B)

A straight line , say y = mx + c can be plotted on the graph by checking its y intercept (c), slope of the following curve (m) and satisfying the points on the x and y coordinates of the following graph.

Following these simple steps, we can easily plot the graph for any straight line.

The equation given is y = -2x + 3 .

First of all the graph will have a negative slope as the slope of the straight line is -2 .

Checking the graph in Option (B), we have

Slope of the curve = -2

Putting the points (0,3) and (1,1) in the following equation of curve ,  

y = -2x + 3 , both satisfies.

Thus the graph in Option (B) represents the equation of the straight line.

To learn more about plotting graph of a straight line, refer -

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1 1/3 cups of raisins are needed to make 1/2 of a recipe

To find the quantity of raisins for half of the recipe, which originally called for 2 2/3 cups, you'd divide 2 2/3 cups by 2, which equals 1 1/3 cups.

This is a question about fractions and division. If a full recipe requires 2 2/3 cups of raisins and you want to make just 1/2 of the recipe, you need to divide the quantity of the raisins by 2.

In fraction form, 2 2/3 is equivalent to 8/3 (as 2*3 + 2 = 8). Then, to find half of this amount, we divide 8/3 by 2. We can do this by multiplying 8/3 by 1/2, which gives us 4/3. Therefore, 1/2 of the recipe requires 4/3, or 1 1/3 cups of raisins.

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-12x - 0.4 > 0.2(36.5x + 80) - 55    Remove the brackets.

-12x - 0.4 > 7.3x + 16 - 55               Combine the like terms on the right

-12x - 0.4 > 7.3x - 39                      Add 12x to both sides

- 0.4 > 7.3x + 12x - 39    

- 0.4 > 19.3x - 39                            Add 39 to both sides.

-0.4 + 39 > 19.3x                              Combine like terms on the left

38.6 > 19.3x                                    Divide by 19.3

38.6 / 19.3 > x

2 > x

-x-3y=-26

6x+3y=21

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

3y cancels out.

-x=-26

6x=21

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

5x=-5

x=-1

The question in English

A small farmer in the interior of Par, when measuring his rectangular terrain, realized that his dimension is in reason 5/7. If the terrain area is 2240 m2, then its largest dimension in meters is

Let

x--------> the smallest dimension of the rectangular terrain

y--------> the largest dimension of the rectangular terrain

we know that

the area of the rectangular terrain is

[tex]A=x*y[/tex]

[tex]A=2,240\ m^{2}[/tex]

so

[tex]2,240=x*y[/tex] -------> equation A

[tex]\frac{x}{y}=\frac{5}{7}[/tex]

[tex]x=\frac{5}{7}y[/tex] -------> equation B

substitute the equation B in equation A

[tex]2,240=[\frac{5}{7}y]*y\\\\5y^{2}= 15,680\\ \\y^{2}=3,136\\ \\y=56\ m[/tex]

therefore

the answer is the option D

[tex]56\ m[/tex]

Answer:

Point B

Step-by-step explanation:

(X,Y)

(-3,2) If you first look on the x line, all the way to the negative section. You'll find -3, starting there you will go up to 2. Following the y line.

Answer:

B

Step-by-step explanation:

Answer: 684 divided by 57=12

Step-by-step explanation:(with reference to the figure)

To find  684 divided by 57 by partial quotients .

Here dividend= 684 and divisor =57

Step 1: Write easy factors of divisor that is nearest to the dividend as follows

57×2=114

57×3=171

57×5=285

57×10=570(nearest easy factor)

Step 2: Now subtract 570 from 684 ,we get 114 then subtract 114=57×2 from it we get 0.

Step 3: Adding the factors we have used in step 1 and 2 ,it will give required quotient=10+2=12

i.e. 684=57(10)+57(2)

The denominator of a fractional exponent represents the degree of root.

For example

[tex]x^{\frac{1}{3}} = \sqrt[3]{x}\\x^{\frac{1}{4}} = \sqrt[4]{x}\\x^{\frac{1}{5}} = \sqrt[5]{x}[/tex]

The denominator of a rational exponent represents the root or nth root of the base number. It is expressed in the form of a fraction where the numerator represents the power and the denominator represents the root or nth root. Rational exponents are used in simplifying expressions and performing calculations involving roots and powers.

The denominator of a rational exponent represents the root or nth root of the base number. A rational exponent is expressed in the form of a fraction, where the numerator represents the power to which the base is raised, and the denominator represents the root or nth root. For example, in the rational exponent 3/2, the base number is raised to the power of 3 and then the cube root is taken.

When the numerator of the rational exponent is 0, it signifies that the number is raised to the power of 0, which always results in 1. On the other hand, when the denominator is 1, it signifies that there is no root involved, and the number is simply raised to the power indicated by the numerator.

Understanding rational exponents is essential in simplifying expressions, solving equations, and performing calculations involving roots and powers.

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You're basically looking for the square root of 49. In fact, if a number [tex] x [/tex] gives [tex] y [/tex] when multiplied by itself two times, then you have [tex] x^2 = y [/tex], which also means that [tex] x [/tex] is the square root of [tex] y [/tex], i.e. [tex] x = \sqrt{y} [/tex]

In your case, the answer is 7, because you have

[tex] \sqrt{49}=7 \iff 7^2 = 49 [/tex]

which is indeed true

Answer:

Step-by-step explanation:

You want the square root of 49, which is 7

Hi there!

To find the average speed of a moving object all you need to do is divide the distance traveled by the object by amount of time it took the object to reach its final destination. So for this problem it would go like this:

325 ÷ 5 = 65

So for this problem in particular the answer is 65 MPH was the average speed of the train.

Your friend, ASIAX

To round 17,509 to the nearest thousand, you look at the hundreds digit. If it's 5 or above, you round up. Therefore, 17,509 rounded to the nearest thousand is 18,000.

To round the number 17,509 to the nearest thousand, we first need to look at the digit in the hundreds place; in this case, it's 5. In rounding, if this digit is 5 or above, we round up the preceding number. Since the digit in the hundreds place is 5, we round up the number in the thousand's place from 7 to 8 making the number 18,000. On the other hand, if the digit in the hundreds place was 4 or lower, we would keep the number in the thousands place the same. So, 17,509 rounded to the nearest thousand is 18,000.

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[tex]3x\geq3\qquad|\text{divide both sides by 3}\\\\x\geq1\\---------------------------------\\\\9x < 54\qquad|\text{divide both sides by 9}\\\\x < 6\\\\Answer:\ 1\leq x < 6\to\ graph\ c)[/tex]

The answer is C. Because A. has the wrong length for its numbers, B. has to much space in between it for negative numbers, and D. is just so wrong I can not even explain it! Hope that this was helpful have an awesome day!

Distance = Speed x Time

Therefore distance = 20 x 3

Grandma's house is 60 km away from where you started.

Answer:

Step-by-step explanation:

500+400+200+10

Answer:   a. The store will make 34 full bags of mulch.

                b.  Considering only the full bags, the total sales price is $76.50

Step-by-step explanation:

The total amount of mulch is [tex]77\frac{1}{2}[/tex] pounds or [tex]\frac{155}{2}[/tex] pounds.

Each bag can hold [tex]2\frac{1}{4}[/tex] pounds or [tex]\frac{9}{4}[/tex] pounds of mulch.

a.  Suppose, the store will make [tex]x[/tex] number of bags of mulch.

So, the equation will be.........

[tex]x*\frac{9}{4}=\frac{155}{2}\\ \\x=\frac{155}{2}*\frac{4}{9}=\frac{310}{9}=34.44... \approx 34[/tex]

So, the store will make 34 full bags of mulch.

b.   The store sells one bag of mulch for $2.25

So, the total sales price of 34 full bags of mulch will be:  [tex](\$2.25*34)=\$76.50[/tex]

Step-by-step explanation:

1.) The equation for the line of least squares regression is given by

[tex]Y=mX+c[/tex]

where Y = Output Variable = Average Cost (in thousands of dollars)

           X = Input Variable = Number of years after 2000

Thus, the given data table transforms as follows:

No. of years after            3             4          5           6          7           8             9          10

after 2000 (X)

Average Cost (Y)         15.505   16.510  17.451   18.471   19.363  20.409  21.093 22.092

To determine the equation precisely, we need to calculate the values of 'm' (Slope) and 'c' (Y-intercept)

Let us take any two random values of X and Y from the above table, so that we have

X₁ = 3; Y₁ = 15.505       and      X₂ = 8; Y₂ = 20.409

Plugging in these two sets of values, we get the following two equations:

15.505 = (3)m + c     and

20.409 = (8)m + c

Let us subtract the upper one from the lower one so that we have

20.409 - 15.505 = 8m + c - 3m - c

4.904 = 5m

Hence, m = 0.9808

Using this value and plugging it in one of the above equations yields the value of c as

20.409 = 8(0.9808) + c

Therefore, c = 12.563

So, the required equation for the line of least squares regression is

Y = (0.9808)X + 12.563

2.) To estimate the cost of tuition at a 4-year institution in 2000, we can put the value of X to be 0.

We have Y = 0 + 12.563

Thus, the cost of tuition in 2000 was $12,563.

3.) To estimate the cost of tuition in 2020, we put the value of X as 20 so that we have

Y = (0.9808)(20) + 12.563 = 32.179

Therefore, we can expect the cost of tuition to be as high as $32,179 by 2020.

4.) The slope tells us the factor by which the tuition increases each year, starting with the base of 12,563 dollars in 2000.

One way to lower the cost of college tuition is by applying for a waiver based on income level. Alternatively, one can also work at the school.

One can join a part-time graduation program while working for the rest of the day so that one may support oneself as well as pay for their courses. Alternatively, one can opt for Online Courses and get some Diploma in their area of interest while working part-times so that they may pursue a degree later on in their life.

The least squares regression equation is Average cost = 14.5 + 1.24 * School year. The best estimate for the average cost of tuition at a 4-year institution starting in 2020 is 33.3 thousand dollars. The slope of the regression line means that the average cost of tuition increases by 1.24 thousand dollars for every year after 2000.

1. To find the least squares regression equation, we can use the following steps:

Calculate the mean of the independent variable (school year) and the dependent variable (average cost).

Calculate the deviations from the mean for both variables.

Calculate the product of the deviations from the mean for both variables.

Calculate the variance of the independent variable.

Calculate the slope of the regression line:

slope = sum of the product of the deviations from the mean / variance of the independent variable

Calculate the y-intercept of the regression line:

y-intercept = mean of the dependent variable - slope * mean of the independent variable

Calculations:

Mean of school year: 5.5

Mean of average cost: 19.0

Deviations from the mean for school year: -1.5, -0.5, 0.5, 1.5, 2.5

Deviations from the mean for average cost: -3.5, -2.5, -1.5, -0.5, 1.5

Product of the deviations from the mean: 5.25, 1.25, -0.75, 0.75, 3.75

Variance of the independent variable: 4.25

Slope of the regression line: 5.25 / 4.25 = 1.24

Y-intercept of the regression line: 19.0 - 1.24 * 5.5 = 14.5

Least squares regression equation:

Average cost = 14.5 + 1.24 * School year

1. 2x³ - 11x² + 13x - 21   ÷   x - 3

x - 3 = 0   ⇒ x = 3

3   |   2   -11   13   -21

    |   ↓    6   -15    -6

        2   -5    -2    -27

1. Answer: 2x² - 5x - 2 - [tex]\frac{27}{x - 3}[/tex]

*************************************************************

2. 3x³ + 7x² - 13x + 10   ÷   x + 2

x + 2 = 0   ⇒   x = -2

-2  |   3    7   -13    10

    |   ↓   -6    -2    30

        3    1    -15    40

2. Answer: 3x² + x - 15 + [tex]\frac{40}{x + 2}[/tex]

3. 2x³ + 13x² - 21x + 9   ÷   x - 1

x - 1 = 0   ⇒   x = 1

1  |   2    13   -21     9

    |   ↓     2    15    -6

        2    15    -6    3

3. Answer: 2x² + 15x - 6 + [tex]\frac{3}{x - 1}[/tex]

4. 7x³ + 0x² - 8x + 16   ÷   x - 2

x - 2 = 0   ⇒   x = 2

2  |   7    0     -8     16

    |   ↓    14    28    40

        7    14    20    56

4. Answer: 7x² + 14x + 20 + [tex]\frac{56}{x - 2}[/tex]

5. 8x⁴ - 14x³ - 71x² - 10x + 24   ÷   x - 4

x - 4 = 0   ⇒   x = 4

4  |   8   -14   -71    -10    24

    |   ↓    32    72     4   -24

        8    18       1     -6     0

5. Answer: 8x³ + 18x² + x - 6

Whenever you add a rational and an irrational number, the result is an irrational number.

So, since 3/4 is rational, if you add any irrational number you will get an irrational number as a result.

The correct answer is y=−1/16

Answer:

A. [tex]y=-\frac{49}{16}[/tex]

Step-by-step explanation:

Since, the directrix of a parabola [tex](x - h)^2 = 4p (y - k)[/tex] is,

y = k - p

Here, the given parabola,

[tex]\frac{1}{4}(y+3)=(x-2)^2[/tex]

By comparing,

We get,

k = - 3,

[tex]4p=\frac{1}{4}\implies p=\frac{1}{16}[/tex]

Hence, the directrix of the given parabola is,

[tex]y=-3-\frac{1}{16}[/tex]

[tex] y=\frac{-48-1}{16}[/tex]

[tex]\implies y = -\frac{49}{16}[/tex]

Option 'A' is correct.

Multiply the first and last term.  Now find two numbers that when you multiply gives you that product and when you add them gives you the middle term.  Replace the middle term with those two numbers and factor using the grouping method.

10w² - 37w + 15

                          10 x 15 = 150 (1 x150, 2 x 75, 3 x 50, 5 x 30, 6 x 25, 10 x 15)

None of those pairs have a sum of -37 so this polynomial is prime.

************************************************************************************

4z² + 4z - 3

                   4 x -3 = -12 ( -1 x 12, -2 x 6, -3 x 4)  ⇒ -2 + 6 = 4

= 4z² - 2z   + 6z - 3

= 2z(2z - 1)   +3(2z - 1)

= (2z + 3)(2z - 1)

************************************************************************************

18v² - 15v - 18

= 3(6v² - 5v - 6)

                            6 x -6 = -36 (1 x -36, 2 x -18, 3 x -12, 4 x -9, 6 x -6) ⇒ 4 x -9 = -5

= 3(6v² + 4v    -9v - 6)

= 3[2v(3v + 2)  -3(3v + 2)]

= 3(2v - 3)(3v + 2)

Answer:

It is midpoint, vertex, and medians in that order.

Hope this helps!

I know these are correct because I got them correct!

Answer:

midpoint, vertex, and medians

Step-by-step explanation:

To prove that the medians of an isosceles triangle meet at a point, show that the

✔ midpoint

 of a side lies on the line containing the opposite

✔ vertex

and the point where the other two

✔ medians

intersect.

Edginuity

Divide the total amount made with the amount of hours worked

Ruth makes $35 working 5 hours

35/5 = 7

Ruth makes $7 an hour

Now multiply 7 with 8

7 x 8 = 56

Ruth makes $56 in 8 hours

~Rise Above the Ordinary