What is the length of the indicated side?

​

Susan has 875 grams of grapes left.

1. Susan bought a 1 kilogram bag of grapes, which is equivalent to 1000 grams (since there are 1000 grams in a kilogram).

2. Susan ate 125 grams of the grapes on her way home.

3. To find out how many grams of grapes Susan has left, we need to subtract the amount she ate from the initial weight of the bag. Therefore, we subtract 125 grams from 1000 grams.

  1000 grams - 125 grams = 875 grams

4. Thus, Susan has 875 grams of grapes left.

measurement units:

In this problem, we used grams as the measurement unit. Grams are commonly used to measure the weight of small objects like grapes. Since the problem stated that Susan bought a 1 kilogram bag of grapes, it was necessary to convert the kilogram measurement to grams.

This conversion was done by multiplying the kilogram value by 1000 (1 kilogram = 1000 grams). By using the correct measurement units, we were able to accurately calculate the amount of grapes Susan had left after eating a portion.

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Answer:

subtract 2 (- 2)

Step-by-step explanation:

the term to term rule is the change between each term in this series.

from 15 to 13, we subtract 2 (-2)

from 13 to 11, we subtract 2 (-2)

from 11 to 9, we subtract 2 (-2)

from 9 to 7, we subtract 2 (-2)

So, this is the term to term rule: subtract 2

Next term as per term rule of arithmetic progression is 5.

" Arithmetic progression is defined as the difference between two consecutive term is constant. Difference is known as common difference."

General form of Arithmetic progression

a, a + d, a + 2d , ........, a + nd

Common difference 'd' = \(a_{n} -a_{n-1}\)

According to the question,

Given terms are,

15, 13, 11, 9, 7

\(a_{1} =15\\\\a_{2} = 13\\\\a_{3} = 11\\\\a_{4} = 9\\\\a_{5} = 7\)

Common difference = \(a_{2} -a_{1}\)

                                 = 13 - 15

                                 = -2

Common difference = \(a_{3} -a_{2}\)

                                  = 11 - 13

                                  = -2

Given sequence is arithmetic progression with common difference -2

Next term after 7 as per term rule of arithmetic progression is

\(a_{6} = 7-2\)

   = 5

Hence, Next term as per term rule of arithmetic progression is 5.

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In mathematical modelling, we take a real-world problem and write it as an equivalent mathematical problem.

We then solve the mathematical problem, and interpret its solution in terms of the real-world problem.

After this we see to what extent the solution is valid in the context of the real-world problem.

Mathematical modeling is one of the bases of mathematics education. Mathematical modeling is described as conversion activity of a real problem in a mathematical form. Modeling involves to formulate the real-life situations or to convert the problems in mathematical explanations to a real or believable situation.

It's extremely precise, since it's math-based, which allows you to develop accurate ideas and assumptions. It's concise, with clear and established rules. It gives you direction when trying to solve a problem.

characters of modeling;

It may be changed or manipulated with relative ease.

It is simplification/Idealization. Mathematical modeling has many benefits related to real-world problems, but the main disadvantages are process simplification, specific rules of the model, and lack of information or data monitoring.

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Answer:

An object balances itself when a perpendicular line drawn through its Centre of Gravity (CG), passes through its base.

See the picture of a popular toy given below. The horse, the rider and the ball are all joined together as one single unit. This entire unit is balanced on the thin black rod shown. At which of the indicated positions, could the Centre of Gravity (CG) of the horse, rider and ball unit be?

July 10 book Science up55 down8

AA BB

CC DD

Step-by-step explanation:

The missing angle is <B= 40 degree and missing side length is AB = 12.25 and AC = 19.068.

To find the missing angle and side measures of ΔABC, we can use the properties of a triangle.

Given:

∠A = 50°

∠C = 90°

CB = 16

We can start by finding the measure of ∠B:

∠A + ∠B + ∠C = 180° (Sum of angles in a triangle)

50° + ∠B + 90° = 180°

∠B + 140° = 180°

∠B = 180° - 140°

∠B = 40°

Now, using Sine law

CB/ sin A = AB / sin C

16 / sin 50 = AB / sin 90

16 / 0.766044 = AB

AB = 12.25

Again 12.25 = AC/ sin B

12.25 = AC / sin 40

AC = 19.068

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Step-by-step explanation:

Step 1 :Equation at the end of step 1

 (((x3) +  7x2) +  4x) -  12

Step 2 :Checking for a perfect cube

2.1    x3+7x2+4x-12  is not a perfect cube

Trying to factor by pulling out :

2.2      Factoring:  x3+7x2+4x-12

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  x3+7x2

Group 2:  4x-12

Pull out from each group separately :

Group 1:   (x+7) • (x2)

Group 2:   (x-3) • (4)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

2.3    Find roots (zeroes) of :       F(x) = x3+7x2+4x-12

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -12.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,3 ,4 ,6 ,12

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -10.00    

     -2       1        -2.00        0.00      x+2

     -3       1        -3.00        12.00    

     -4       1        -4.00        20.00    

     -6       1        -6.00        0.00      x+6

     -12       1       -12.00        -780.00    

     1       1        1.00        0.00      x-1

     2       1        2.00        32.00    

     3       1        3.00        90.00    

     4       1        4.00        180.00    

     6       1        6.00        480.00    

     12       1        12.00        2772.00    

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that

  x3+7x2+4x-12

can be divided by 3 different polynomials,including by  x-1

Polynomial Long Division :

2.4    Polynomial Long Division

Dividing :  x3+7x2+4x-12

                             ("Dividend")

By         :    x-1    ("Divisor")

dividend     x3  +  7x2  +  4x  -  12

- divisor  * x2     x3  -  x2        

remainder         8x2  +  4x  -  12

- divisor  * 8x1         8x2  -  8x    

remainder             12x  -  12

- divisor  * 12x0             12x  -  12

remainder                0

Quotient :  x2+8x+12  Remainder:  0

Trying to factor by splitting the middle term

2.5     Factoring  x2+8x+12

The first term is,  x2  its coefficient is  1 .

The middle term is,  +8x  its coefficient is  8 .

The last term, "the constant", is  +12

Step-1 : Multiply the coefficient of the first term by the constant   1 • 12 = 12

Step-2 : Find two factors of  12  whose sum equals the coefficient of the middle term, which is   8 .

     -12    +    -1    =    -13

     -6    +    -2    =    -8

     -4    +    -3    =    -7

     -3    +    -4    =    -7

     -2    +    -6    =    -8

     -1    +    -12    =    -13

     1    +    12    =    13

     2    +    6    =    8    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  6

                    x2 + 2x + 6x + 12

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x+2)

             Add up the last 2 terms, pulling out common factors :

                   6 • (x+2)

Step-5 : Add up the four terms of step 4 :

                   (x+6)  •  (x+2)

            Which is the desired factorization

Final result :

 (x + 6) • (x + 2) • (x - 1)

Answer:

0.4

Step-by-step explanation:

Divide 2 by 5 you'll get 0.4

Answer:

huuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuh

Answer:

When we multiply two number with the same base but different power, the power gets added.

So, the answer is:

5^17*5^2

=5^(17+2)

=5^19

Answer:

A) trapezoid a=141 b=69

Step-by-step explanation:

It must be a trapezoid because two of the sids are not parallel.  The interior angles of any quadrilateral must equal 360, and each side of a trapezoid  must equal 180, so:

A) trapezoid a=141 b=69

Answer:

a

Step-by-step explanation:

Hello!

-5(x+2)=35

-5x-10=35

-5x=35+10

-5x=45

x=-9

Hope it helps!

~Just a determined gal

#CarryOnGainingKnowledge

\(MysteriousNature\)

Answer:

x = -9

Step-by-step explanation:

-5(x + 2) = 35

~Distribute

(-5 * x) + (-5 * 2) = 35

~Simplify

-5x - 10 = 35

~Add 10 to both sides

-5x = 45

~Divide -5 to both sides

x = -9

Best of Luck!

The point which could represent the player catching the ball is: C. (4, 25).

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect, meet, or cross each other, which is typically represented as an ordered pair containing the point, x-axis and y-axis.

By critically observing the graph (see attachment) which models the given data, we can reasonably infer and logically deduce that the point (4, 45) where the "Distance from Goal" on the y-axis intersect with the "Time after Throw" on the x-axis represents the player catching the ball.

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Answer: 4, 25

Step-by-step explanation:

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Answer:

35

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

Don't swear to god jeez

Answer:

19

Step-by-step explanation:

Unless you're referring to the vine, then 9+10= 19.

If you are referring to the vine of 9+10, then its 21

Answer:

34 tickets

Step-by-step explanation:

323424

The ratio, in simplest form, of the number of tickets Doug sold to the number of tickets Dave sold is 3/4.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Dave and Doug sold some tickets to the school fair.

Number of tickets that Dave sold = 32 tickets

Number of tickets that Doug sold = 24 tickets

Ratio of the number of tickets Doug sold to the number of tickets Dave sold is,

Ratio = 24 / 32

In order to make it simplest, factor out the common factors and cancel it.

Ratio = (8 × 3) / (8 × 4)

         = 3/4

Hence the required ratio is 3/4.

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The Spanish club raised $138 from the slushies sale. First, we found the total number of slushies sold by subtracting 3/4 of the total items from the total items. Then, we multiplied the number of slushies by the price per slushie.

To solve this problem, we first need to figure out how many slushies were sold. As the question mentions, 3/4 of the 368 items sold were pizzas, and the rest were slushies. Therefore, the total number of slushies sold is the difference, i.e., 368 - (368 * 3/4).

Calculation: 368 - (368 * 3/4) = 92 slushies sold.

Next, since each slushie was sold for $1.50, the total amount raised from the sale of slushies is 92 (slushies sold) * $1.50 (price per slushie).

Calculation: 92 * $1.50 = $138 raised from the slushies sale.

The Spanish club therefore raised $138 from the slushies sale.

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The fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

The volume of a rectangular prism can be calculated using the formula:

V = l x b x h..........(i)

where,

V ⇒ Volume

l  ⇒ length

b ⇒ width

h ⇒ height

From the question, we are given the values,

l = 8 inches

b = 4 inches

h = 9 inches

Putting these values in equation (i), we get,

V = 8 x 4 x 9

⇒ V = 288 in³

Therefore, the fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

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Answer:

If y and x have a proportional relationship, then we can write an equation of the form y = kx, where k is a constant of proportionality.

To find the value of k, we can use the given values of y and x:

y = kx

24 = k(12)

k = 2

Now that we know k, we can use the equation to find the value of y when x=16:

y = kx

y = 2(16)

y = 32

Therefore, when x=16, y=32.

Answer:2.5

Step-by-step explanation:

tell me if im wrong

The tangent line at that point is:

y = (-3/25)*x + 6/5

so m = -3/25, and b = 6/5

To find the slope at that point, we need to evaluate the derivative at that point.

y = 3/x

The derivative is:

y' = -3/x²

When x = 5, we have:

y' = -3/5² = -3/25

So that is the slope, m.

Now let's find the line.

The line must pass trhough the point (5, 3/5), then:

3/5 = (-3/25)*5 + b

3/5 = -3/5 + b

3/5 + 3/5 = b

6/5 = b

The equation of the line is:

y = (-3/25)*x + 6/5

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Answer: C

Step-by-step explanation:

The rest of the quadrilaterals provided have 2 pairs of parallel lines.

The choice is:

Explanation:

The quadrilateral that has exactly one pair of parallel lines is called a trapezoid.

Here's what a trapezoid looks like :

\(\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\linethickness{0.3mm}\qbezier(0,0)(0,0)(1,3)\qbezier(5,0)(5,0)(4,3)\qbezier(1,3)(1,3)(4,3)\qbezier(3,0)(8.2,0)(0,0)\put(-0.5,-0.3){$\sf A$}\put(5.3,-0.3){$\sf B$}\put(4.2,3.1){$\sf C$}\put(0.6,3.1){$\sf D$}\end{picture}\)

Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

Answer:

the answer to this question is 12 and 12

The slope of a horizontal line is always zero.

What is slope?

The slope of a line is a measure of how steep the line is. It represents the rate at which the y-coordinate of the line changes with respect to the x-coordinate. Symbolically, it is represented by the letter m, and can be calculated using the following formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are any two points on the line.

The slope of a horizontal line is always zero. This is because a horizontal line has the same y-coordinate at every point, and therefore, there is no change in the y-coordinate for any change in the x-coordinate.

By definition, the slope of a line is the change in y divided by the change in x. In the case of a horizontal line, the change in y is always zero, since the y-coordinate does not change. So, no matter what value of x you choose, the slope of a horizontal line will always be:

slope = change in y / change in x = 0 / (any non-zero value of x) = 0

So, the slope of a horizontal line is always zero.

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The equations of the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x

From the question, we have the following equations that can be used in our computation:

h(x) = x² + 3

f(x) = 3/4x

From the above, we have

(h o h)(x) = h(h(x))

So, we have

(h o h)(x) = (x² + 3)² + 3

Also, we have

(f o f)(x) = 3/[4(3/4x)]

Evaluate

(f o f)(x) = x

Hence, the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x

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Answer:

E.

Step-by-step explanation:

Answer:

(2, 5)

Step-by-step explanation:

Given:

To find the components of \(\overrightarrow{RS}\) we need to go from R to O and then O to S.  Remember that \(\overrightarrow{RO}\) is the negative of \(\overrightarrow{OR}\).  Therefore:

\(\begin{aligned} \displaystyle \overrightarrow{RS} & =\overrightarrow{RO}+\overrightarrow{OS}\\& = \overrightarrow{OS}-\overrightarrow{OR}\\& =\binom{-2}{12}-\binom{-4}{7}\\& =\binom{2}{5}\end{aligned}\)

Therefore, the component form (x, y) of the vector \(\overrightarrow{RS}\) is (2, 5)

Answer:

? = 92°

Step-by-step explanation:

the chord- chord angle ? is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is

? = \(\frac{1}{2}\) (LM + AK) = \(\frac{1}{2}\) (120 + 64)° = \(\frac{1}{2}\) × 184° = 92°