The table represents a continuous exponential function f(x).


x 2 3 4 5
f(x) 12 24 48 96

Graph f(x) and identify the y-intercept.
0
3
6
12

The special angle pair relationship between ∠2 and ∠3 is same-side interior angles.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.

Therefore, the angle pair relationship between angle 2 and 3 are same side interior angles.

The same-side interior angle theorem states that when two lines that are parallel are intersected by a transversal line, the same-side interior angles that are formed are supplementary.

Supplementary angles are those angles that sum up to 180 degrees. In other words, If the measures of two angles sum up to 180°, they are called supplementary angles.

Therefore, same side interior angles are supplementary angles.

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Answer: 1/6

Step-by-step explanation:

The unknown angles are as follows:

The measures of angle 1 and 2 can be found as follows:

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.

Therefore,

∠1 + ∠2 = 180(sum of angle on a straight line)

∠1 = 118(alternate angles)

118 + ∠2  = 180

∠2 = 180 - 118

∠2 = 62 degrees

Therefore,

∠1 = 118 degrees

∠2 = 62 degrees.

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Answer:

Step-by-step explanation:

Let's solve for x.

x+7y=−39

Step 1: Add -7y to both sides.

x+7y+−7y=−39+−7y

x=−7y−39

Let's solve for y.

x+7y=−39

Step 1: Add -x to both sides.

x+7y+−x=−39+−x

7y=−x−39

Step 2: Divide both sides by 7.

7y/7 = −x−39/7

y= −1/7x+−39/7

Answer:

600000000000000000000000000[tex]x^{2}[/tex]

The given pairs of lines have been identified as parallel, perpendicular lines or neither as explained below.

Two lines are parallel if they have the same slope (m), while they are perpendicular to each other if their slopes are negative reciprocal of each other.

The slope in a given equation of a line that is in slope-intercept form, y = mx + b, is represented as "m" in the equation.

1. y = 3x - 7 and y = 3x + 1 both have the same slope (m) of 3. They are parallel lines.

2. y = -2/5x + 3 and y = 2/5x + 8 both have the different slope (m), which are not negative reciprocal to each other. They are neither parallel nor perpendicular lines.

3. The slope of y = -1/4x is -1/4. The slope of y = 4x - 5 is 4. -1/4 is the negative reciprocal of 4. Therefore, the lines are perpendicular.

4. 2x + 7y = 28 can be rewritten as y = -2/7x + 4, the slope (m) is -2/7.

7x - 2y = 4 can be rewritten as y = 7/2x - 2, the slope (m) is 7/2.

-2/7 and 7/2 are negative reciprocals.

They are perpendicular lines.

5. The slope of y = -5x + 1 is -5.

x - 5y = 30 can be rewritten as y = 1/5x - 6, the slope is 1/5.

The lines are perpendicular.

6.  3x + 2y = 8 can be rewritten as y = -3/2x + 4, the slope (m) is -3/2.

2x + 3y = -12 can be rewritten as y = -2/3x - 4, the slope (m) is -2/3.

The lines are neither.

7. The slope of y = -4x - 1 is -4.

8x + 2y = 14 can be rewritten as y = -4x + 7, the slope is -4.

They are therefore parallel lines.

8. x + y = 7 can be rewritten as y = -x + 7, the slope (m) is -1.

x - y = 9 can be rewritten as y = x - 9, the slope (m) is 1.

The lines are perpendicular.

9. They have the same slope of 1/3. They are parallel lines.

10. They have different slopes that are not negative reciprocals, therefore, they are neither.

11. Their slopes are 1/2 and -2. Therefore, they are perpendicular lines.

12. They have the same slope of 3/4. They are parallel lines.

13. They have the same slope of 1. They are parallel lines.

14. Their slopes are -5/4 and 4/5. Therefore, they are perpendicular lines.

15. Their slopes are not negative reciprocals and are not the same, therefore, they are neither.

16. Their slopes are 1/2 and -2. Therefore, they are perpendicular lines.

17. They are both vertical lines, therefore they are neither.

18. x = 1 is a vertical line while y = -8 is a horizontal line that meets perpendicularly. Therefore, the lines are perpendicular.

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Answer:

Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.

Since slope is 5, equation is y = 5x + c.

Substitute (2,-4) into the equation to find c.

-4 = 5(2) + c

c = -14

Hence equation of line is y = 5x - 14

From the given linear function, we have that:

A. The function is constant on the following interval: B.2 ≤ x ≤ 5.

B. The function is increasing on the following interval: A.0 ≤ x ≤ 2.

C. The function is decreasing the fastest on the following interval: D.5 ≤ x ≤ 6.

D. The justification for the previous item is: D.5 ≤ x ≤ 6 is the interval where the slope is the steepest.

A function is constant when it's graph is an horizontal line, hence in this problem the function is constant for two intervals.

Hence, in item A, option B is correct.

A function is increasing on the intervals that y is increasing while x increases, that is, the function is moving right and up.

Hence, in item B, option A is correct.

A function is decreasing on the intervals that y is decreasing while x increases, that is, the function is moving right and down.

The decrease is faster when the division of the change in the output by the change in the input has the lower value(greater absolute negative).

Hence:

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If this year, Reba hands out the same number of buckets to each of the 12 teams in the contest. Each team gets 6 buckets. the total number of buckets Reba delivers is 72 buckets.

Let x represent the total number of buckets Reba delivers.

The equation to find the total number is:

x / 6  = 12

Let solve for x, to get the total number of buckets Reba delivers.

x = 12 × 6

x = 72 buckets

Therefore the  total number of buckets is 72.

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The $150 monthly payment on the $3,482.46 credit card loan at 1.55% monthly interest rate gives the number of fewer months it would take to repay the loan if the monthly payment is $200 as 10 months

A monthly interest rate is obtained from an annual interest rate by dividing it by 12.

The monthly payment formula is presented as follows;

[tex] \displaystyle{M = \frac{P \cdot r \cdot (1 + r)^{n} }{ (1 + r)^{n} - 1}} [/tex]

Where;

M = The monthly payments = $150

P = The loan amount = $3,482.46

r = The monthly interest rate = 1.55% = 0.0155

n = The number of periods (monthly payments) = 30

When the monthly payment, M = $150, it takes the career councilor approximately 30 months for the debt to be repaid.

When the monthly payment, M = $200, we have;

[tex]\displaystyle{200 \approx \frac{3482.46 \times 0.0155 \times (1 + 0.0155)^{n} }{ (1 + 0.0155)^{n} - 1}} [/tex]

Which gives;

[tex] \displaystyle{200 \times ((1 + 0.0155)^{n} - 1)= 3482.76 \times 0.0155 \times (1 + 0.0155)^{n}} [/tex]

[tex] \displaystyle{200 \times (1.0155)^{n} - 200 = 53.98278 \times (1.0155)^{n}} [/tex]

[tex]\displaystyle{ 146.017 \times (1.0155)^{n} = 200 }[/tex]

n•ln(1.0155) ≈ ln(1.3697)

[tex] n = \frac{ln(1.3697)}{ln(1.0155)} \approx 20.45[/tex]

The number of months it will take to pay back the loan using a monthly payment of $200 is therefore approximately 20 months

The number of fewer months it takes to repay the loan is therefore;

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Answer:

[tex]x=-1[/tex]

Step-by-step explanation:

[tex]\textsf{Given equation}:[/tex]

[tex]5x-6=3x-8[/tex]

[tex]\textsf{Subtract $3x$ from both sides}:[/tex]

[tex]\implies 5x-6-3x=3x-8-3x[/tex]

[tex]\implies 2x-6=-8[/tex]

[tex]\textsf{Add $6$ to both sides}:[/tex]

[tex]\implies 2x-6+6=-8+6[/tex]

[tex]\implies 2x=-2[/tex]

[tex]\textsf{Divide both sides by $2$}:[/tex]

[tex]\implies \dfrac{2x}{2}=\dfrac{-2}{2}[/tex]

[tex]\implies x=-1[/tex]

Answer:

0.003, 0.03, 0.303, 0.383, 3.03, 33.03

Step-by-step explanation:

Answer: 11.78

Step-by-step explanation:

It will take 11 days to place all of the 100 tiles needed to finish the floor.

The slope of a line and any points it contains determine the point-slope form of the line. When a point on the line and the slope are provided, the form's objective is to represent the equation of the complete line.

Given Data

She had a tough time at first and placed only 5 tiles the first day. She started to go faster, and by the end of day 4, she had placed 35 tiles.

Points are:

(1,5) (4,35)

Slope = [tex]\frac{30}{3}[/tex]

Slope = 10

y - y₁ = m(x -x₁)

y - 5 = m(x- 1)

For 100, it will need,

100 - 35 = 10(x-4)

65 = 10x - 40

105 = 10x

x = 10.5

It will take 11 days to place all of the 100 tiles needed to finish the floor.

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The new workshop can produce as many as 180 toys each year compared to the old workshop

The approximation of numbers is the estimates of the said number.

This means that the approximation of a number is close to the said number, but it has a slight different value

The given parameters are:

Old capacity = 22,912,546,992 toys per year

New capacity = 4,134,232,638,937 toys per year

The approximate number of times is calculated as

Number of times = New capacity/Old capacity

Substitute the known values in the above equation

So, we have

Number of times = 4,134,232,638,937 toys per year/22,912,546,992 toys per year

Remove the units

So, we have

Number of times = 4,134,232,638,937/22,912,546,992

Evaluate the quotient

So, we have

Number of times = 180.435315217

Approximate

Number of times = 180

Hence. the approximate number of times is 180

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The reflection of the coordinate (-3, 4) over the y-axis is (3, 4).

The Y-coordinates do not change when a point is reflected across the Y-axis. However, the X-coordinates are changed into their opposite signs.

Given the coordinates of the triangles RST as shown below;

R = (-3, 4)

S = (-1, -4)

T = (-4, -2)

If (x, y) for instance is reflected over the y-axis, the resulting coordinate will be (-x, y). Similarly, if the coordinate R (-3, 4) is reflected over the x-axis, the resulting coordinate point will be (3, 4)

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We may get the same conclusion using either approach, which is that x—5 is a factor of the polynomial.

This will be discussed in further detail below.

Explain, taking into account the fact that, using either method, whether or not we can think of x-5 as a factor in the polynomial based on the given information.

Generally, the equation for the problem is mathematically given as

f(x)=x^3-x^2-17 x-15

Therefore,  If (x-5) is factor of f(x) then at x=5 ,f(x)=0 then apply this

[tex]\begin{aligned}f(x) &=5^3-5^2-17 \times 5-15 \\&=125-25-85-15 \\&=0\end{aligned}[/tex]

In conclusion,Since f(x) is equal to 0 when x = 5, the factor of f is (x-5) (x).

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Answer:

13. x = 3∛2

14 x = ± 4√6 = ± 4√2 √3

15. x =  2∛11

16 x =  -4∛2

17 x = ± 10√3

18. x =   ± 4 √3 √5

Step-by-step explanation:

13. x³ = 54

x = ∛4

Factor 54: 2 x 27

∛54 = ∛2 x ∛27

∛27 = 3

answer: 3∛2

14. x² = 96

x = ±√96

96 = 6 x 16
√16 = 4

√6

√96 = ± 4√6 = ± 4√2√3

15. x³ = 88

x = ∛88
88 = 8 x 11
∛88 = ∛8 x ∛11 = 2∛11

16. x³ = -128 means x has to be negative

x = -∛128

128 = 64 x 2

∛128 = ∛64 x ∛2 = 4∛2

So x = -4∛2

17. x² = 300

=> x = ± √300
300 = 100 x 3
√300 = √100 x √3 = 10√3

x = ± 10√3

18. x² = 240

x = ±√240
240 = 16 x 15

√240 = ± (√16 x √15)

= ± 4 √3 √5

Answer:

z=70    y=98

Step-by-step explanation:

180-110=70=z

70+87+105=262

360-262=98=y

Answer:

 (7 x 10) + (1 x 1) + (0/10) + (4/100)

70 + 1 + 0.04

70 + 1 + 4/100

Step-by-step explanation:

Here are all the expanded forms I can think of off the top of my head, sorry if this didn’t help much!

The probability is given by:

Therefore:

- The probability of spinning blue is:

Favorable outcomes = 1 (blue color)

Total outcomes = 3 (red, blue, and yellow)

- The probability of flipping heads is:

Favorable outcomes = 1 (head)

Total outcomes = 2 (head and tail)

- The probability of spinning a one is:

Favorable outcomes = 1 (number 1)

Total outcomes = 3 (numbers 1, 2 and 3)

Next, the probability of the compound event:

Answer: the probability of the compound event is 1/18

Using algebraic expression and equation, he invested $2000 in fund b.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

Let x = amount he invested in fund b

If both funds together returned a 4% profit, then the sum of the profit in each investment is equal to 4% of the total investment.

$3000(0.02) + x(0.07) = (3000 + x)(0.04)

Solving for x,

$3000(0.02) + x(0.07) = (3000 + x)(0.04)

$60 + 0.07x = $120 + 0.04x

0.07x - 0.04x = $120 - $60

0.03x = $60

x = $2000

amount he invested in fund b = $2000

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The function has a minimum if the x2 coefficient is positive. If it is negative, the function has reached its limit. If you have the function 2x2+3x-5, for example, the function has a minimum because the x2 coefficient, 2, is positive. Divide the x term coefficient by twice the x2 term coefficient.

Hence, The function has a minimum if the x2 coefficient is positive. If it is negative, the function has reached its limit. If you have the function 2x2+3x-5, for example, the function has a minimum because the x2 coefficient, 2, is positive. Divide the x term coefficient by twice the x2 term coefficient.

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For every 500 g of reactants, 3.1 g of catalyst were required. The catalyst that was required for 900 g of reactant was 5.58g

The process of catalysis involves introducing a catalyst to chemical reaction to speed up the process. Catalysts are not destroyed during reaction and are unaffected by it. Very little amounts of catalyst are frequently sufficient when the reaction is swift and the catalyst recycles quickly; the velocity of the reaction is greatly influenced by mixing, surface area, and temperature. In most cases, catalysts interact with one or more reactants to produce intermediates that ultimately lead to the final reaction product, regenerating the catalyst in the process.

Homogeneous catalysis, in which all of the components are dispersed in the same phase as the reactant (often a gas or liquid), and heterogeneous catalysis, in which the components are not. It's common to think of enzymes and other biocatalysts as a a third category.

In all branches of the chemical business, catalysis is commonplace. 90% of all chemical compounds manufactured for commercial purposes are thought to use catalysts at some point during the manufacturing process.

500g of reactants = 3.1g of catalyst

1g of reactants = 3.1g of catalyst / 500g of reactants

900g of reactants = [tex]\frac{3.1}{500} * 900[/tex] = 5.58g

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Answer:

Step-by-step explanation:

855555555555fhhhhhhhhhhhhhhhhg6

Value of x [tex]\frac{36}{5}[/tex]

value of m∠3 = [tex]\frac{462}{5}[/tex]

When two rays meet at a point, they make an angle. An "angle" is the term used to describe the "opening" between these two rays, and it is symbolized by the symbol. Angles are typically expressed as 60°, 90°, etc. and are measured in degrees. A figure made up of two rays meeting at the vertex of the angle can be referred to as an angle.

Given Data

m∠3 = 17x - 30

m∠6 = 12x +6

Angle pair - exterior alternate angle

For the value of x,

17x - 30 = 12x + 6

17x - 12x = 6 + 30

5x = 36

x = [tex]\frac{36}{5}[/tex]

For m∠3,

17x - 30

Equating value of x,

17([tex]\frac{36}{5}[/tex]) - 30

[tex]\frac{612-150}{5}[/tex]

[tex]\frac{462}{5}[/tex]

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method 1.

[tex] {x}^{2} - 7x - 18 = 0[/tex]

simplify:

[tex](x - 9)(x + 2) = 0[/tex]

so the answer is (D) x =9 or x = -2

method 2.

if

[tex] {a}^{2}x+ bx + c = 0[/tex]

[tex]x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} \: or \: \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

so

[tex]x = \frac{ - ( - 7) + \sqrt{ { - 7}^{2} - 4(1)(18)} }{2(1)} or\frac{ - ( - 7) - \sqrt{ { - 7}^{2} - 4(1)(18)} }{2(1)}[/tex]

[tex]x = \frac{ 7 + \sqrt{ 121 } }{2}or\frac{ 7 - \sqrt{ 121 } }{2}[/tex]

[tex]x = 9 \: \: \: \: or - 2[/tex]

Answer:

g(3) = 9

Step-by-step explanation:

replace 3 in x

g(3) = 2(3) +3 = 6 + 3 = 9

Hope this helps