Find an equation of the line. Write the equation using function notation. Through ;(6,-7) perpendicular to 2y=x-4

The baking powder that they would need if they used 1 teaspoon of salt will be illustrated will be 6 baking Powder.

It should be noted that from the information given, the Shah family's pancake recipe uses 2 teaspoons of baking powder for every 1/3 of a teaspoon of salt.

Therefore, the baking powder that they would need if they used 1 teaspoon of salt will be illustrated thus:

= Pancake recipe ÷ Teaspoon

= 2 ÷ 1/3

= 2 × 3

= 6

Therefore, the baking powder that they would need if they used 1 teaspoon of salt will be illustrated will be 6 baking Powder.

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The answer is most probably to round the the numbers to nearest 10 digits and multiply

697x82 =  56,154

700 x 80 = 56000

A rounded number is less precise but roughly equal to the original number in value.

To the closest hundred, 341 is equivalent to 300. This is due to the fact that 341 is more similar in value to 300 than to 400. Because $1.89 is closer to $2.00 than to $1.00, when rounded off to the nearest dollar, it becomes $2.00.

The standard rounding rule is as follows:

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Round to nearest 10 digits and multiply

697x82=________x________=________

Answer:

9!

Step-by-step explanation:

Answer: 9

Step-by-step explanation:So you look at whatever can be multiplied to get 27 or 36. When you do that 9 is your biggest number

Answer:

These are dividend, divisor, quotient and remainder.

Step-by-step explanation:

Determine the first digit or set of digits your divisor will go into at least once.

Determine the maximum number of times your divisor will go into the said digit or digits.

Place the answer over the corresponding digit. For multiple digits, place it over the last digit.

Multiply the answer from above by your dividend.

Place the result under your dividend starting from the left most digit.

Subtract the result from your dividend. Only subtract the digits that line up. For instance, if you have a five digit dividend, but the result is only two digits, only subtract using the first two digits of your dividend.

Bring down the next digit of your dividend beside the result.

Repeat the process using the new set of digits. Each time, bring down the next digit of your dividend.

The secant line connects two points on a graph's curve:

Point P: (15, 1257)

(a) The secant lines' slopes PQ.

The points are as follows:

The slope (m) is calculated using:

Therefore, the secant line connects two points on a graph's curve:

The slope (m) is calculated as follows:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

So far, we have:

The slope of the secant line for Q = (5,3410) is:

[tex]\begin{aligned}m_1 &=\frac{1275-3410}{15-5} \\m_1 &=\frac{-2135}{10} \\m_1 &=-213.5\end{aligned}[/tex]

The slope of the secant line for Q = (10, 2210) is:

[tex]\begin{aligned}&m_2=\frac{1275-2210}{15-10} \\&m_2=\frac{-935}{5} \\&m_2=-187\end{aligned}[/tex]

The slope of the secant line for Q = (20, 550) is:

[tex]\begin{aligned}&m_3=\frac{1275-550}{15-20} \\&m_3=\frac{725}{-5} \\&m_3=-145\end{aligned}[/tex]

The slope of the secant line for Q = (25, 145) is:

[tex]\begin{aligned}&m_4=\frac{1275-140}{15-25} \\&m_4=\frac{1135}{-10} \\&m_4=-113.5\end{aligned}[/tex]

The slope of the secant line for Q = (30, 0) is:

[tex]\begin{aligned}&m_5=\frac{1275-0}{15-30} \\&m_5=\frac{1275}{-15} \\&m_5=-85\end{aligned}[/tex]

(b) The average slope of the tangent.

The secant lines that are closest to tangent P are:

This is because point P (15, 1275) is located between the two previous points.

The slopes of secant lines at Q = {( 10, 2210), (20, 550)} are:

[tex]\begin{aligned}&m_2=-187 \\&m_3=-145\end{aligned}[/tex]

The average slope (m) is as follows:

[tex]\begin{aligned}&m=\frac{m_2+m_3}{2} \\&m=\frac{-187-145}{2} \\&m=\frac{-332}{2} \\&m=-166\end{aligned}[/tex]

Hence, the average slope is -166.

Therefore, the secant line connects two points on a graph's curve:

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The complete question is given below:
a tank holds 5000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallon) after t minutes.a) If P is the point (15,1275) on the graph of V, find the slopes of hte secant lines PQ when Q is the point on the graph with the following values.(5, 3410) -427/2(10, 2210) -187(20, 550) -145(25, 145) -113(30, 0) -85B) estimate the slope of hte tangent line at P by averaging the slopes of two adjacent secant lines. (Round your answer to one decimal places).

Answer:

-61

by both methods

Step-by-step explanation:

Let's first see what the terms direct substitution and synthetic substitution mean.

Direct Substitution

In direct substitution, to find the value of a polynomial f(x) at any point x = k. we simply substitute the value of k into the polynomial function and solve for f(k)

Synthetic Substitution

In synthetic substitution we make use of the Remainder Theorem..
The Remainder Theorem states that when we divide a polynomial [tex]f(x)[/tex] by [tex]x-c[/tex], the remainder [tex]R[/tex] equals [tex]f(c)[/tex]

Solving using direct substitution

The given polynomial is

[tex]f(x) = 3x^5 - x^3 + 6x^2 - x + 1[/tex]
and we are asked to evaluate this function at [tex]x = - 2[/tex]

Using Direct Substitution,
[tex]f(-2) = =3\left(-2\right)^5-\left(-2\right)^3+6\left(-2\right)^2-\left(-2\right)+1\\\\=3\left(-32\right)-\left(-8\right)+6\left(-2\right)^2-\left(-2\right)+1\\\\=- -96 + 8 + 6(4) + 2 + 1\\=-96 + 8 + 24 + 2 + 1\\\\= -61\\\\[/tex]

Using direct substitution we get [tex]\bold{f(-2)= -61}[/tex]

Using Synthetic Substitution
Since the remainder when [tex]f(x)[/tex] is divided by [tex]x - c[/tex] is [tex]f(c)[/tex] , we will divide the polynomial [tex]f(x) = 3x^5 - x^3 + 6x^2 - x + 1[/tex] by [tex]x -(-2) = x + 2[/tex] and find out the remainder which will give f(-2)

This is the technique used in synthetic division
Step 1. Write only the coefficients of [tex]x[/tex]  in the dividend inside an upside-down division symbol. Write -2 as the divisor on the left of this row

[tex]\begin{matrix}\texttt{\:\:-2|\:\:\:3\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\ \;\;\;\;\;\;\;\texttt{\:\:\:\:|\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\;\;\;\;\;\;\;\;\;\;\;\;\;}}\\ \texttt{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]

Step 2
Carry down the leading coefficient as is to below the division symbol

[tex]\begin{matrix}\texttt{\:\:-2|\:\:\:3\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\ \;\;\;\;\;\;\;\texttt{\:\:\:\:|\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\;\;\;\;\;\;\;\;\;\;\;\;\;}}\\ \texttt{\:\:\:\:\;\;\;\;3\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]

Step 3
Multiply the above carry-down value by -2 and carry that result to the next column:
[tex]3\left(-2\right)=-6[/tex]

[tex]\begin{matrix}\texttt{\:\:\:\:\:\:-2|\:\:\:3\:\:\:\:\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\\texttt{\:\:|\ensuremath{\underline{\;\;\;\;\;\:\:\:-6\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}\\\texttt{\:3\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]

Step 4

Add down the column

[tex]\begin{matrix}\texttt{\:\:\:\:\:\:-2|\:\:\:3\:\:\:\:\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\\texttt{\:\:|\ensuremath{\underline{\;\;\;\;\;\:\:\:-6\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}\\\texttt{\:3\:\:\:\:\:\:\:\:-6\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]

Step 5

Multiply the above carry-down value by -2 and carry that result to the next column:
(-6)(-2) = 12

2 | 3     0      -1        6     -1       1
  |        -6      12  
  -------------------------------------------------
     3    -6      

Step 6
Add down the column
-1 + 12 = 11

2 | 3     0      -1        6     -1       1
  |        -6      12    
  -------------------------------------------------
     3    -6      11

Repeat this process for the other two coefficients

The final result is

2 | 3     0      -1        6     -1       1

  |        -6      12    -22   32   -62
  -------------------------------------------------
     3    -6     11       -16   31   -61

The last carry-down value s the remainder and the value of f(-2) = - 61

Answer:

12x-94

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

Hope this helps!

Have a great day and God bless! :)

The expression is simplified to 7(-x + 9)

Algebraic expressions are expressions composed of variables, terms, factors, constants and coefficients.

They are also made up of mathematical or arithmetic operations

Given the expression;

9 – 3(4x – 18) + 6x

expand the bracket

9 - 12x + 54 + 6x

collect like terms, we have;

-12x + 5x + 54 + 9

Add or subtract like terms

-7x + 63

Factor out 7

7(-x + 9)

Thus, the expression is simplified to 7(-x + 9)

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A function g whose graph is a reflection in the x axis of the graph of f(x) = |x| - 5 is g(x) = 5 - |x|

The question asks to find a function g, that is, g(x)

The graph of g(x) is a reflection in the x axis of the graph of  f(x) = |x| - 5

Reflection of a function in the x-axis gives us

y = g(x) = - f(x)

=> g(x) = - ( |x| - 5 )

=> g(x) = - |x| + 5

=> g(x) = 5 - |x|

Therefore, using the concept of reflection of a function in x axis of the graph of the given function, we get a function g whose graph is a reflection in the x axis of the graph of f(x) = |x| - 5 as g(x) = 5 - |x|

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to get the equation of any straight line, we simply need two points off of it, let's use those two points off the table in the picture below.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-22}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-22}-\stackrel{y1}{18}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-4)}}} \implies \cfrac{-40}{6 +4} \implies \cfrac{ -40 }{ 10 }\implies -4[/tex]

[tex]\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-\stackrel{y_1}{18}=\stackrel{m}{-4}(x-\stackrel{x_1}{(-4)})\implies y-18=-4(x+4) \\\\\\ y-18=-4x-16\implies y=-4x+2[/tex]

Using the concept of ratio the number of cups of chips Charlie needs can be found out.

A ratio in mathematics shows how many times one number is contained in another. The ratio symbol is represented by a colon (:).A ratio is still valid if all of the quantities are multiplied by the same number. By dividing each quantity by the sum of all the numbers' common factors, ratios can be lowered (much like fractions are). The simplest version of a fraction is one in which the ratio's numbers are the smallest feasible integers.

Amount of dip required by the recipe be 'a' =[tex]1\frac{1}{4}[/tex] cups=[tex]\frac{5}{4}[/tex]cups

Amount of chips required by the recipe be 'b'= [tex]\frac{1}{5}[/tex]cups

Amount of chips to be used be 'c'= 1 cup

Number of cups of chips Charlie needs

=[tex]\frac{c*a}{b}[/tex]

=[tex]\frac{1*\frac{5}{4} }{\frac{1}{5} }[/tex]

=[tex]\frac{5*5}{4}[/tex]

=[tex]\frac{25}{4}[/tex] cups

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Answer:
Study a Times Tables map each day if you can soon you will get the hang of it

Answer: B

Step-by-step explanation:

4 times 3 times 3 times 3 times 3=108

Answer:

A. 39

Step-by-step explanation:

Given:

Length of a pyramid (lpy ) = 4 cm

Width of a pyramid (wpy ) = 3 cm

Height of a pyramid (hpy ) = 3 cm

It is given that the rectangular pyramid fits exactly on top of the prism, the length and width of the prism are the same for the base of the pyramid.

So, Length of a prism (lpr) =3 cm, width of a prism (wpr) = 3cm and height of a prism (hpr) = 3 cm

Volume of Prism (Vpr) = lpr × wpr × hpr

⇒ Vpr = 3 cm × 3 cm × 3 cm

⇒ Vpr = 27 cm³ ....(eq 1)

Volume of Rectangular Pyramid Vpy

= (lpy × wpy × hpy ) / 3

⇒ Vpy = (4 × 3 × 3) ÷ 3

⇒ Vpy = 12 cm³ ....(eq 2)

From 1 and 2, Volume of composite space,

Volume of composite space = Volume of prism + Volume of Pyramid

⇒ V = 27 cm³ + 12 cm³ = 39 cm³

⇒ V = 39cm³

Answer: 24/54

Step-by-step explanation:

[tex]\displaystyle\\\frac{4}{9}=\\\\ \frac{4}{9}*1=\\\\ \frac{4}{9}*\frac{6}{6} =\\\\\frac{4*6}{9*6} =\\\\\frac{24}{54}[/tex]

Using translation concepts, the transformations that are used to map △RST onto △VWX are:

Rotation, then a translation.

The two triangles are given at the end of the answer.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

Looking at the image, we have that:

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Her home is 3km far from the bicycle repair shop;

Her avg speed = 2*6*20/(6+20) = 60/13 km/h

d = r*t = (60/13)*(39/60)

d = 3 km;

What is Avg Speed?

In normal use and in kinematics, the speed (normally known as v) of an object is the significance of the change of its position over time or the value of the change of its role consistent with unit of time; it is for this reason a scalar amount.

The common speed of an item in an c programming language of time is the distance travelled by using the item divided by the length of the c program languageperiod

the instant pace is the restriction of the common speed because the length of the time c program languageperiod methods 0. velocity isn't similar to pace.

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Part a: The size of the game in standard form is 240000 kilobytes

Part b: The game was 5 times larger than the patch file

Part A:

Size of the game downloaded by Ryan on his computer = 2.4 * 10^5

Size of the patch file for the game = 48000 kilobytes

Therefore, converting the size of the game into the standard form:

Size of the game = 2.4 * 10^5

= 2.4 * 100000

= 240000 kilobytes

Therefore, the size of the game is 240000 kilobytes in standard form

Part B:

Size of the game = 240000 kilobytes

Size of the patch file = 48000 kilobytes

Computing the size of the game with respect to the patch file we get:

=240000/48000

= 5

Hence, the game was 5 times larger than the patch file

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The length of the line segment NO is 12 units

The ratios of the line segments are given as:

LM : MN : NO = 5 : 1 : 2

The length of LO is given as:

LO = 48

The above means that

NO = (NO Ratio)/(Total Ratio) * LO

So, we have

NO = 2/(5 + 1 + 2) * 48

Evaluate the product

NO = 12

Hence, the length of NO is 12 units

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the combinations that work are "A" and "B" as they both equal to 80

Answer:

The question states four less than twice its width so we first find twice the width. The width is 6 and twice that is 12. Note that it says four less than, so four less than 12 is 8. so the length of the triangle is 8.

Step-by-step explanation:

Hope it helps! =D

Answer:

It's learn proper English. I'll rewrite your statement. I need help, I do not understand how to solve this. Thank you!

true!!!

school 1 spent 13 hours in the weight room whereas school 2 spent 11 hours in the weight room

Answer:

The other diagonal of the kite is 56 meters

Step-by-step explanation:

To find the length of the other diagonal you find to know the formula for finding the area of a kite which is A = (p×q)/2. It is given that the area is 252m² and one diagonal is 9m.

The least and the greatest amounts are $98 and $112

The food budget is modeled by 0.5|x - 110| = 6

So, we have:

0.5|x - 110| = 6

Divide both sides by 0.5

|x - 110| = 12

Remove the absolute bracket

x - 110 = 12 and x - 110 = -12

Add 110 to both sides

x = 112 and x = 98

Hence, the least and the greatest amounts are $98 and $112

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Answer: y = 5x/4 - 13

Step-by-step explanation:

y=mx+b

7=5/4 *16+b

7=5*16/4 +b

7=80/4+b

7=20+b

b=-13

y = 5x/4 - 13

Answer:

8 milkshakes

Step-by-step explanation:

16 cups in a gallon. 2 cups per milkshake.

16/2=8