Equations/Rules 2
What is the zero of the function f(x)=3 x-9 ? Explain how you know.
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What is the zero of the function f(x)=-x+4 ? Explain how you know.
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Answer:

  d = 23 1/3

Step-by-step explanation:

You want to solve the proportion (0.3d -1)/(3 1/3) = (0.84)/(7/15).

  [tex]\dfrac{0.3d-1}{3\dfrac{1}{3}}=\dfrac{0.84}{\dfrac{7}{15}}\qquad\text{given}\\\\\\\dfrac{3(0.3d-1)}{10}=\dfrac{15(0.84)}{7}\qquad\text{invert and multiply}\\\\0.09d -0.3=1.8\qquad\text{simplify}\\\\0.09d = 2.1\qquad\text{add 0.1}\\\\d=\dfrac{2.10}{0.09}=\dfrac{70}{3}\qquad\text{divide by 0.09}\\\\\boxed{d=23\dfrac{1}{3}}[/tex]

__

Check

  (0.3·(70/3) -1)/(3 1/3) = 0.84/(7/15)

  (7 -1)/(10/3) = 1.8

  6(3/10) = 1.8 . . . . . . true

Answer: 23 1/3

Step-by-step explanation:

Answer:

A bar notation

Step-by-step explanation:

the line is called a bar notation

Answer:

If you have a line over a number (let's say there is a line over 0.2):

0.2, then it means that it is a repeating number.

So, a line over 0.2 would mean it is actually 0.2222222222 etc. They just don't want to right it out because it is way to long, and it is infinite.

Step-by-step explanation:

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Answer:

22m+16

Step-by-step explanation:

4(6m+4)-2m

4(6m)+4(4)-2m

24m+16-2m

24m-2m+16

22m+16

Hopes this helps please mark brainliest

Answer:

24 : 15 : 20

Step-by-step explanation:

express ratios in fractional form and express b and c in terms of a

[tex]\frac{a}{b}[/tex] = [tex]\frac{8}{5}[/tex] ( cross- multiply )

8b = 5a ( divide both sides by 8 )

b = [tex]\frac{5}{8}[/tex] a

also

[tex]\frac{b}{c}[/tex] = [tex]\frac{3}{4}[/tex] ( cross- multiply )

3c = 4b ( divide both sides by 3 )

c = [tex]\frac{4}{3}[/tex] b = [tex]\frac{4}{3}[/tex] × [tex]\frac{5}{8}[/tex] a = [tex]\frac{5}{6}[/tex] a

Then

a : b : c

= a : [tex]\frac{5}{8}[/tex] a : [tex]\frac{5}{6}[/tex] a ( multiply each part by 24, the LCM of 8 and 6 )

= 24a : 15a : 20a ( divide each part by a )

= 24 : 15 : 20 ← in simplest form

Step-by-step explanation:

[tex] \frac{dy}{dx} ( \sqrt{x} ) = \frac{1}{2 \sqrt{x} } [/tex]

The slope of the line at x=1 is

[tex] \frac{1}{2(1)} = \frac{1}{2} [/tex]

so our equation is

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

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

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

The time taken for the money to grow to $8670 at compound interest is approximately 9.24 years.

Given the amount of money that is the principal = $6000

Rate = 4% compounded quarterly.

Time = t

Amount = $8670

Now we know that the amount is calculated by the formula:

A = P(1+r/4)ⁿ

8670 = 6000(1+0.01)ⁿ

Hence

log 1.445 = n log 1.01

or, n = 36.99

Number of years = 36.99 / 4 = 9.24 years.

The interest that is added to a loan or deposit is referred to as compound interest. Compound interest is computed for a sum utilizing both the principal and interest already paid. The main distinction between compound interest and simple interest is this.

If we look at our bank statements, interest is usually credited to our account once a year. While the principle remains constant, the interest changes annually.

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The kilograms of sugar that were used for cherry jam is 9kg.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

Since there are 40 kg of sugar in the bag. Strawberry jam was used which was 4 kg. The remaining kilograms will be:

= 40kg - 4kg

= 36 kg

Since 1/4 of the remaining sugar was used, the amount used will be:

= Fraction × Total amount

= 1/4 × 36

= 9kg.

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The distance around the given triangle is [tex]\cfrac{13x}{12}[/tex].

We are asked to calculate the distance around the triangle, commonly known as the perimeter.

The perimeter is the sum of all side lengths in any shape. For a triangle, you add up all the side lengths and that is your perimeter.

Now we need to add up all these side lengths.

[tex]\cfrac{x}{2} +\cfrac{x}{3} +\cfrac{x}{4}[/tex]

We have fractions with unlike denominators. We need to get common denominators in order to solve. To do this, we need to obtain the GCF (Greatest Common Factor) of the numbers 2, 3, and 4.

This number is 12.

By changing the fractions so they all have denominators of 12, we retrieve our new equation:

[tex]\cfrac{6x}{12} +\cfrac{4x}{12} +\cfrac{3x}{12}[/tex]

Now we add them:

[tex]\cfrac{6x+4x+3x}{12}=\cfrac{13x}{12}[/tex]

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According to the solving the value of the Quadratic equation are as follows:

x = 0

x = 2

We can answer any quadratic equation using the quadratic formula. The first step is to change the equation's form to ax2+bx+c=0, where a, b, but instead c are the coefficients. The formula (-b(b2-4ac))/(2a) is then used to enter these coefficients. View instances of the formula being used to solve various equations.

Make a video of the pupils utilizing one technique to solve a quadratic equation. Allowing pupils to pick is an option, but you can also direct them to utilize the quadratic equation, factoring, or square-rooting.

f(x) = 2x² – 3x

x- (2x² – 3x) = 0

x - 2x² + 3x = 0

4x - 2x²= 0

x = 0

x = 2

According to the solving the value of the Quadratic equation are as follows:

x = 0

x = 2

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Step-by-step explanation:

g(7)=

[tex] {7}^{2} + n[/tex]

[tex]49 + n[/tex]

f(g(7))=n

[tex]f(g(7)) = \sqrt{49 + n + 1} [/tex]

[tex]f(g(7)) = \sqrt{n + 50} [/tex]

[tex]9 = \sqrt{n + 50} [/tex]

[tex]81 = n + 50[/tex]

[tex]n = 31[/tex]

So

[tex]g(31) = 31 {}^{2} + 31[/tex]

[tex] = 992[/tex]

The statement that would be true if the data in the data in the stem-and-leaf plot is shown in a line plot is: D. We could calculate the range and median.

A line plot is a graph that shows individual data in a data set with the use of dots. Each dot represents a data plot.

In a line plot, we can easily find the middle of the data distribution which is the median of the data and also we can determine the highest and lowest value which enables us to find the range of the data.

Thus, using the stem-and-leaf plot in the diagram, below, write out each data points given, which are:

68, 70, 80, 86, 88, 88, 96, 96, 97, 97, 98, 98, 99, 100, 100, 100, 100, 100

The line plot for these data would have the following frequency for each data point:

68 - 1 dot

70 - 1 dot

80 - 1 dot

86 1 dot

88 - 2 dots

96 - 2 dots

97 - 2 dots

98 - 2 dots

99 - 1 dot

100 - 5 dots

The line plot is shown in the diagram below.

Range = 100 - 68 = 32

Median = 97

Therefore, the answer is: D. We could calculate the range and median.

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Step-by-step explanation:

(2/5x − 1) − (1/4x + 2)

2/5x − 1 − 1/4x - 2

8/20x - 1  - 5/20x - 2

3/20x - 1 - 2

3/20x - 3

Answer:

The quadratic function has the following sets of values below: (0,8) (2,10) (3,1). The quadratic functions represented as follows: f(x) = ax² + bx + c. using (0,8) 8 = a(0)² + b(0) + c. 8 = c. Therefore, using (2, 10)(3 , 1). f(x) = ax² + bx + c.

The triangle has a hypothenuse 9.21 units and the graph it's attached below

The distance between any two points is the length of the line segment joining the points. There is only one line passing through two points. So, the distance between two points can be calculated by finding the length of this line segment connecting the two points.

The formula of distance between two points is given as

d = √(y₂ - y₁)² + (x₂ - x₁)²

The two points are

Substituting the values into the formula above;

d = √(2 -(-7))² + (-6-(-8))²

d = √85

d = 9.21 units

The hypothenuse of the triangle is 9.21 units

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120 cm² is the surface area of the right triangular prism

The surface area of a right triangular prism can be determined using the formula below:

A = (S₁ + S₂ + h)L + bh    (Check the attached image for the labeling)

Given: S₁ = 3 cm,  S₂ = 5 cm, h = 4 cm, L =  6cm and b = 3 cm

Substitute these values into the formula:

A = (S₁ + S₂ + h)L + bh

A = (3 + 5 + 4)6 + 3(4)

A = (18)6 + 12

A = 120 cm²

Therefore, the surface area of the right triangular prism is 120 cm²

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Answer:

350:3=116.66666....

Step-by-step explanation:

so 1/3 is 116.6 (117)

Ratio of women in company is 117.

Good luck!

Thank me later.

Tadano

Answer:

answer for first one is 8

for 2nd one is [tex]2(x+5)/3x^2-7[/tex]

for 3 rd one is [tex](x-5)/x[/tex]

for 4th one is [tex]3x^{2} n^{2} (7n-9)/7x-9[/tex]

Step-by-step explanation:

Answer:

[tex]x=\pm\sqrt{3i} ,\pm3i[/tex]

Step-by-step explanation:

1) Move all terms to one side.

[tex]{x}^{4}+12{x}^{2}+27=0[/tex]

2) Factor [tex]{x}^{4}+12{x}^{2}+27x[/tex].

1) Ask: Which two numbers add up to 12nd multiply to 27?

3 and 9

2) Rewrite the expression using the above.

[tex]({x}^{2}+3)({x}^{2}+9)[/tex]

Outcome: [tex]({x}^{2}+3)({x}^{2}+9)=0[/tex]

2) Solve for x.

1)Ask: When will[tex]({x}^{2}+3)({x}^{2}+9)[/tex] equal zero?

When [tex]{x}^{2}+3=0[/tex]or[tex]{x}^{2}+9=0[/tex]

2) Solve each of the 2 equations above.

[tex]x=\pm\sqrt{3i} ,\pm3i[/tex]

Thanks.

Answer:

C.

Step-by-step explanation:

It can not be a or b because the figure is upside-down.

It cannot be d because the figure would literally fly off the grid shown.

It must be C because the figure rotates 90° counterclockwise and moves 4 units to the right.

Answer:

x=6

Step-by-step explanation:

11x-3=4x+39

-4x     -4x

7x-3=39

   +3  +3

7x=42

______

7      7

x=6

11(6)-3=66-3=63

4(6)+39=63

yw hope it helps

Answer: Though there is not enough information to be sure, a table to complete this ratio could be one include the sets of numbers (5,3) (10,6) and (15, 9)

Step-by-step explanation:

Answer: C

Step-by-step explanation:

[tex]A=\pi (17)^2 \approx 908[/tex]

Answer:

Answer C is correct

Step-by-step explanation:

The formula to find the area of a circle is:

A = πr²

Here,

r => radius = 17cm

Let us find the area of the circle.

A = πr²

A = 3.14 × 17 × 17

A = 907.46 cm²

Approx. = 908 cm²

If top opens at a cross section parallel to the base of  the rectangular pyramid, then the shape of the opening of the base will be rectangle

The shape of the jewelry box = Rectangular pyramid

The top opens at a cross section parallel to the  base

The parallel lines are defined as the  the coplanar straight line  that are equal distance from each other and never meet.

The shape of the base of the rectangular pyramid is rectangle and open at a cross section parallel to the base, then the shape of the opening of the base will be same as the base

The shape  of the opening of the base will be rectangle

Hence, if top opens at a cross section parallel to the base of  the rectangular pyramid, then the shape of the opening of the base will be rectangle

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Answer:

252

Step-by-step explanation:

The second and third smallest factors must add to 5. The only possibility is that these factors are 2 and 3.

The second and third largest factors must add to [tex]462-N[/tex]. These factors are [tex]N/2[/tex] and [tex]N/3[/tex].

[tex]462-N=\frac{N}{2}+\frac{N}{3} \\ \\ 462-N=\frac{5N}{6} \\ \\ 462=\frac{11N}{6} \\ \\ N=252[/tex]

Answer: D

Step-by-step explanation:

Using the formula for the volume of a rectangular prism,

[tex]x(8-2x)(11-2x)\\\\=x(88-38x+4x^2)\\\\=4x^3 -38x^2 +88x[/tex]

43 distance diver descend from the rock to the coral

Two or more expressions with an Equal sign is called as Equation.

Given,

A deep sea driver descended from a rock with an elevation of -45.5 feet to a coral reef with an elevation of -88.5 feet

We need to find the distance between -45.5 ft and -88.5 ft.

So the distance between those numbers is given by:

|-45.5-(-88.5)|

|-45.5+88.5|

|88.5-45.5|

|43.0|

|43|  

43

Hence, 43 distance diver descend from the rock to the coral

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During 30 days of summer, Val will spend $ 73.5 on electricity from the use of his air conditioner.

Any of the following algebraic expressions should be used: addition, subtraction, multiplication, and division. Bring the variable to the left side, then move all of the other values to the right side to determine the value of x. For the outcome, simplify the values.

Since Val's air conditioner uses 3,500 watts when running, and that Val Utilizes it for 7 hours during summer days, spending 10 cents per kilowatt hour, estimating how much money Val will spend during a 30-day summer must be done the following calculation:

3,500 watts = 3.5 kilowatts

3.5 kilowatts per hour = 35 cents

35 cents × 7 hours = 245 cents per day

245 cents per day × 30 days = 7,350 cents per month

7,350/100 = X

73.5 = X

Therefore, during 30 days of summer, Val will spend $ 73.5 on electricity from the use of his air conditioner.

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Answer:

[tex]h=2[/tex]

Step-by-step explanation:

[tex]A=bh \\ \\ 14=7h \\ \\ h=2[/tex]

Answer:

h = 2

Step-by-step explanation:

A = 14; b = 7

A = bh

14 = 7h

7h = 14

Divide both sides by 7.

h = 14/7

h = 2