Identify the initial value and rate of change for the graph shown. (4 points) A coordinate plane is shown. A line passes through the y-axis at 2 and passes through the point 2 comma 4. a Initial value: 1, rate of change: 2 b Initial value: 2, rate of change: 1 over 2. c Initial value: 2, rate of change: 1 d Initial value: 1 over 2., rate of change: 2

Answer: 4/D

Step-by-step explanation: going through the options one by one.

for the first point, the first statement is true since both lines intersect at (4,5)

for the second point, this is also true because since (4,5) is on both functions, x=4 and y=5 will be a solution for both

for the third point, this is also true since the point of intersection is (4,5), this is the solution for the system

for the fourth point, this is untrue. since we don't know what f and g are and the only solution to the system is (4,5), what works for f may not necessarily work for g. so 4/d is the answer.

ps. you got this :) you'll be done before you know it

A grain of rice contains about 0.029 milliliters of volume.

A grain of rice is a tiny, ingestible seed that comes from either Oryza sativa (Asian rice) or Oryza glaberrima, two types of grass (African rice). A single grain of rice is round or oval in shape and measures about 3–4 millimeters in length. A grain of rice has a volume of 0.029 milliliters and a mass of approximately 0.05 grams. The type of rice and the method of processing affect the size and form of a single grain of rice. Over half of the world's population relies heavily on rice as a source of nutrition and as a staple food in many different cultures. Sushi, risotto, rice pudding, and many more recipes all use rice as an ingredient.

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Answer:

0.64

Step-by-step explanation:

16/25 = 0.64

If -8x + 2y = -10 and 7x + 6y = -3 are true equations what would be the value of 15x + 4y is Cross out the common factor: 7.

Verify your math to ensure that the values on either side of the equals sign are the same in order to create a genuine equation. To create a genuine equation, ensure sure the numbers on both sides of the "=" symbol are equal. For instance, the equation 9 = 9 is real. The equation 5 + 4 = 9 is accurate. The formula 6 + 3 = 9 is accurate.

Multiplying both side of a equation by a coefficient:{3(-8x + 2y) = -10 × 3, 7x + 6y = -3}

apply the distributive property {-24x + 6y = -30, 7x +6y -3}

Subtract the two equations: -24x + 6y - (7x +6y) = -30 - (-3)

Remove parentheses: -24x + 6y - 7x - 6y = -27

Cancel one variable : -24x - 7x = -27

Solve the equation: x = 27/31

Substitute into one of the equations: 7 × 27/31 + 6y = -3

Solve the equation: y = -47/31

The solution of the system is {x = 27/31, y = -47/31}

Substitute { x = 27/31 , y = -47/31  into 15x + 4y :: 15 × 27/31 + 4 × (-47/31)

Determine the sign of multiplication or division: 15 × 27/31 - 4 × 47/31

Write as a single fraction: 15 × 27 /31 - 4 × 47 /31

calculate the product or quotient: 405/31 - 188/31

Write the numerators over common denominators: 405 - 188/31

calculate the sum or difference: 217/31

Cross out the common factor: 7

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0.96×10⁴ is the quotient of 7.584×10⁶ and 7.9×10²

A division is a process of splitting a specific amount into equal parts.

We need to find the quotient of

7.584×10⁶ and 7.9×10²

Dividend is the number that is to be divided by the divisor.

Divisor is the number by which the dividend is to be divided is called the divisor.

The resultant of the division is called the quotient.

7.584×10⁶/7.9×10²

0.96×10⁶⁻²

0.96×10⁴

Hence, 0.96×10⁴ is the quotient of 7.584×10⁶ and 7.9×10²

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Divide the principal by the time, interest rate, and time period to calculate simple interest.Annual interest rate is 0.02.

Divide the principal by the time, interest rate, and time period to calculate simple interest.The equation is expressed as "Simple Interest = Principal x Interest Rate x Time."It is easiest to calculate interest using this equation.

I, or the interest earned or charged on a loan, can be calculated using the straightforward interest formula.

I = Prt, where P is the principal, r is the yearly interest rate stated in decimal form, and t is the loan term expressed in years, gives the amount of interest.

It is necessary to transform the rate r from percentage to decimal form.

Then, 2,000 = 1,000 * r * 10 ;

Finally, r = 2 ÷ 10 = 20 ÷ 100 = 0.02

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Step-by-step explanation:

it says it in the headline : the cube root function.

1.

it goes through (0, 0) and (1, 1) and (-1, -1).

so,

f(x) = cubic root(x)

domain = (-infinity, +infinity)

range = (-infinity, +infinity)

x-intercept = 0

y-intercept = 0

2.

the function is y = cubic root(x + 2)

compared to

y = cubic root(x)

the domain is x >= -2

wrong !

this is not a square root. for the square root that domain would be correct (there are no real number square roots for negative values). but cubic roots are possible also for negative values. this function has the same domain and range as the basic y = cubic root(x) : (-infinity, +infinity).

the function is a vertical translation of g(x) = cubic root(x).

wrong !

vertical means up/down.

but it is a horizontal (left/right) translation of that g(x). by 2 units to the left, actually.

3.

for 1 <= x <= 4 we have already the average rate of change :

about 0.197

for 4 <= x <= 7 we get

(f(7) - f(4))/(7 - 4) ≈ (1.91 - 1.59)/3 ≈ 0.109

so, the interval [1, 4] has a greater average of change.

which is also clear when looking at the graph : the function increases stronger for the lower x-values than for the larger x-values.

Answer:

0.125 miles

Explanation:

1/4 of a mile is 440 yards and 1/8 of a mile is 220. 440-220=220.

Therefore , the solution of the given problem of equation comes out to be cost of one pair of pants is $40.

The similar symbol (=) is used in mathematical equations to variables denote equality between two propositions. Mathematical formulae, which are abstractions of reality, are used to demonstrate how different numerical factors can be compared. For instance, the equal sign splits the integer 12 or perhaps the equation y + 6 = 12 to two separate halves. One can compute how so many characters each side of the a character has. Contradictory meanings are common in symbols.

Here,

Given :

Mathew bought 5 shirts and 2 pairs of pairs is $165.

Toby bought 3 shirts and 5 pairs of pants for $251.

x is the shirt of price ,

y is the pants of price .

Thus,

=> 5x + 2y = 165

=> 3x + 5y = 251

So,

=> x = 165 -2y/5

=> 3(165 - 2y/5) + 5y = 251

=> 3(165 - 2y /5) + 5y = 251

=>  495 - 6y  + 25y = 251 *5

=>  495 + 19y = 1255

=> 19y = 1255 - 495

=> 19 y =  760

=> y =760/19

=> y = 40

and

=> x = 165 - 2*40 /5

=> x = 165-80/5

=> x = 85/5

=> x =17

Thus , cost of one pair of pants is $40.

Therefore , the solution of the given problem of equation comes out to be cost of one pair of pants is $40.

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The given graph represents a quadratic function with negative leading coefficient, hence it opens down.

c) Its vertex is its maximum and the function is increasing before reaching vertex and decreasing after it.

The vertex is at (-2, 8) so the domain on which the function is increasing is:

d) The x-intercepts of the graph are x = - 6 and x = 2. The function is positive between the x-intercepts and negative outside, so:

The slope of the line that passes through the points (9,8) and (2,3) is 5/7.

The slope of a line in a graph is a measure of its steepness or slant. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. In mathematical terms, the slope of a line can be represented as the difference in the y-coordinates of two points on the line divided by the difference in the x-coordinates of the same two points.

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

Plugging in the given points, we get:

slope = (3 - 8) / (2 - 9) = -5 / -7 = 5/7

So, the slope of the line that passes through the points (9,8) and (2,3) is 5/7.

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The value of the trigonometric relation tan θ = 0.25819889

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin (-θ) = -sin (θ)

csc (-θ) = -csc (θ)

cos (-θ) = cos (θ)

sec (-θ) = sec (θ)

tan (-θ) = -tan (θ)

cot (-θ) = -cot (θ)

In the first quadrant, sin, cos and tan are all positive.

In the second quadrant going anti-clockwise, only sin is positive.

In the third quadrant going anti-clockwise, only tan is positive.

In the fourth quadrant going anti-clockwise, only cos is positive

Given data ,

Let the angle be represented as θ

Now , the measure of sin θ = - ( 1/4 )

So , the value of θ lies in the 3rd quadrant

Taking inverse on both sides of the equation , we get

θ = sin⁻¹ ( - ( 1/4 ) )

θ = 194.47751218° + 2πn

Now , In the third quadrant going anti-clockwise, only tan is positive.

So , tan θ = tan ( 194.47751218 )

On simplifying the equation , we get

tan ( 194.47751218 ) = 0.25819889

Hence , the value of tan ( 194.47751218 ) is 0.25819889

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Francisco uses the method of similar triangles to find the distance across the river, and the distance across the river is 372 feet.

A triangle is a polygon with three sides and three vertices. The triangle's total number of angles comes to 180°. The distances between the formed the sight-lines are;

RB = 210 feet

OC = 275 feet

The distance between the point close to the river and the next point further from the river = is 115 feet

In triangles ΔPRB and ΔPOC,

we have;

∠PRE = ∠POC = 90°

Given;

∠PER ≅ ∠PCO

By the corresponding angle formed between two parallel lines and a common transversal.

Using angle-angle similarity theorem;

ΔPRE is similar to ΔPOC Which gives;

PR / PO = RE / OC

Let x represent the distance across the river,

we have;

PR = x

PO = 115 + x

Which gives;

x / (115+x) = 210 / 275

275x = 210 × (115 + x)

275x = 24150 + 210x

275x - 210x = 24150

65x = 24150

x = 371. 54

Therefore, the distance across the river is 372 feet.

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The slope of the red line is -1/2

What is a slope?

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Here, we have

Two lines are parallel. Two lines are shown by the color green and red line.

As we know if lines are parallel then their slope is equal.

W are given a green line parallel to the red line.

The slope of the green line is -1/2

But The slope of the red line = slope of the green line.

The slope of the red line = -1/2

Hence, The slope of the red line is -1/2.

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Angle A is congruent to angle c because they are both right angles. By the angle sum theorem, angle ADB is congruent to angle CBD.

A triangle is a closed polygon with three-line segments that intersect at each of its three angles. When the sides and angles of two triangles match, the triangles are said to be congruent. Thus, two triangles can be placed side by side and angle by angle on top of one another.

Line AB is parallel to line DC and cut by transversal DB. So angles CDB and ABD are alternate interior angles and must be congruent.

Side DB is congruent to side BD because they are the same segment.

Angle A is congruent to angle c because they are both right angles.

By the angle sum theorem, angle ADB is congruent to angle CBD.

By angle- side triangle congruence theorem, triangle BCD is congruent to triangle DAB.

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The volume of the solid under the cone z = x2y2 and above the disk x2y2 ≤ 36 is 7056π. This was found by using polar coordinates and integrating the equation V = ∫∫∫r2sin(θ)dzdθdr with the limits of integration r = 0 to 6, θ = 0 to 2π, and z = 0 to x2y2.

The volume of the solid can be found by integrating the equation:

V = ∫∫∫r2sin(θ)dzdθdr

where r is the radius and θ is the angle of the polar coordinates.

The limits of integration are as follows:

r = 0 to 6

θ = 0 to 2π

z = 0 to x2y2

The integral is then:

V = ∫0 to 2π∫0 to 6∫0 to r2sin(θ)dr dθ

V = ∫0 to 2π∫0 to 6 r3sin(θ)θdr

V = ∫0 to 2π [r4sin(θ)]0 to 6 dθ

V = ∫0 to 2π 644sin(θ)dθ

V = 7056π

The volume of the solid under the cone z = x2y2 and above the disk x2y2 ≤ 36 is 7056π. This was found by using polar coordinates and integrating the equation V = ∫∫∫r2sin(θ)dzdθdr with the limits of integration r = 0 to 6, θ = 0 to 2π, and z = 0 to x2y2.

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The value of a is 12 and b is 10.39, for the given special right triangle.

A special right triangle is a right triangle with a regular feature that facilitates calculations on the triangle or for which straightforward formulas are available. Angles in a right triangle, for instance, could form straightforward relationships like 45°-45°-90°. Right triangle that is "angle-based" is what this is. When the side lengths of a right triangle form ratios of whole numbers, like 3:4:5, or of other unusual numbers, like the golden ratio, the triangle is said to be "side-based." Without using more complex techniques, one can quickly calculate different lengths in geometric problems by understanding the relationships between the angles or side ratios of these special right triangles.

The opposite sides of a 30-60-90 special right triangle are always in the ratio of 1:√3: 2.

so opposite of 30deg here is 6

as When opposite side 30deg is 6 then opposite side 90deg is 2(6)

a = 2(6)

a = 12

Now we have base = 6 and hypotenuse = 12

Use Pythagoras theorem

b [tex]= \sqrt{12^2 - 6^2}[/tex]

b = 10.39

Thus, The value of a is 12 and b is 10.39, for the given special right triangle.

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Answer:

1 n) = -2n^2 + 2

2 Let x be the number of chocolate hearts sold. The number of rose bouquets sold is x + 15. The total cost of the chocolate hearts is 3x and the total cost of the rose bouquets is 5(x + 15). The total cost of both products is 3x + 5(x + 15) = 3x + 5x + 75 = 8x + 75 = $339. Solving this equation for x, we get x = (339 - 75) / 8 = 64. So the number of chocolate hearts sold is 64.

3 The price of the ticket is increasing at a constant rate. This suggests that the price of the ticket is following an arithmetic sequence. The formula for the nth term of an arithmetic sequence is t(n) = a + (n-1)d, where a is the first term, d is the common difference, and n is the number of terms.

Using the given information, we can find the common difference, d = t(2) - t(1) = $60.50 - $55 = $5.50.

Now, to find the price of the ticket after 6 years, we can use the formula t(n) = a + (n-1)d where n = 6, a = $50, and d = $5.50.

So t(6) = $50 + (6-1)$5.50 = $50 + 5$5.50 = $50 + $27.50 = $77.50. So, the price of the ticket in 6 years will be $77.50.

The linear regression model is expressed as y = -25.31x + 1017.075.

The best-fit line is given by:

y = bx + a

The slope is as follows:

b = Σ(x - X) ( y - Y)/Σ(x - X)²

After determining the slope using the means for x and y, the coefficient an is calculated.

The means are provided by:

X = (0 + 1 + 2 + 3 + 4 + 5)/ 6 = 2.5

Y= (904 + 924 + 938 + 957 + 977 + 1023)/6

= 953.83

The figures are as follows:

Σ(x - X) = (0 - 2.5) +(1 - 2.5) + ---------+ (5 - 2.5)

Σ( y - Y) = ( 904 - 953.83) + (924 - 953.83) + ---------- + ( 1023 - 953.83)

Making use of a calculator:

Σ(x - X) ( y - Y) = -443

Σ(x - X)² = 17.5

As a result, the slope is:

b = -443/17.5

= -25.31

y = -25.31x + a

Using the means to locate a:

953.83 = -25.31 x 2.5 + a

a = 1017.075

As a result, the linear regression model is:

y = -25.31x + 1017.075

After 2012, the number of cases would reach 1171 in x years, and x is found when y = 1171. Thus:

1171 = -25.31x + 1017.075

1171 - 1017.075 = -25.31x

x = 6

2012 + 6 = 2018

The number of reported cases is expected to reach 1171 by 2018.

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The percent error of the measurement, to the nearest tenth of a percent, is 4.54%

Percent error of the measurement:

Percent error is the difference between the estimated value and the actual value in comparison to the actual value and is expressed as a percentage.

In other words, the percent error is the relative error multiplied by 100.

The formula for percent error is:

PE = (|Estimated value-Actual value|/ Actual value) × 100

Here,

T = True or Actual value

E = Estimated value

Estimated length of a line = 2.1 inches

The actual length of the line = 2.2 inches

Error = 2.2-2.1=0.1inches

Percent error of the measurement = 0.1/2.2(100)=4.54.

PE=4.54%

So, the percent error of the measurement, to the nearest tenth of a percent is 4.54%

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Answer: 4(x + 3)

Step-by-step explanation:

8x + 12

= 4(2x + 3)

Answer: look below :))

Step-by-step explanation: Yes, 8x + 12 can be factored as follows:

8x + 12 = 4x + 6 + 4x + 6

= (4x + 6) + (4x + 6)

= 2(2x + 3) + 2(2x + 3)

= 2(2x + 3) + 2(2x + 3)

= 4(2x + 3)

So the factored form of 8x + 12 is 4(2x + 3).

Answer:

the answer is a. -2

Step-by-step explanation:

i hope that helps you

thanku

The percentage of his income he saved is 44.4%.

Percentage is a way of expressing a number as a fraction of 100. It is commonly used to represent a proportion or share of a whole, such as a percentage of a total amount, a percentage of a target or goal, a percentage of a population, etc.

In mathematical terms, a percentage can be represented as a decimal or a fraction, and is expressed as a symbol, such as "%".

If Ravindra's monthly income is rupee 90000 and saves rupee 40000 per month, then the percentage can be calculated as:

percentage = (40,000/90,000) x 100% = 44.4%

Hence, she saves 44.4% of his income per month.

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The interest earned and the balance of the account 200 at 3 % for 5 years is 30.

percentage, a relative value indicating hundredth parts of any quantity.

Given that an account earns simple intrest

We have to find the interest earned

the balance of the account 200 at 3 % for 5 years

I=PRT

P is the principal amount

t is the time

r is the rate of interest

I=200×0.03×5

I=30

Hence, the interest earned and the balance of the account 200 at 3 % for 5 years is 30.

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Following APA criteria, statistical power should be stated along with effect magnitude, sample size, and alpha level.

Following the recommendations of the American Psychological Association (APA), statistical power should be stated. This includes stating the sample size that was utilised, the estimated effect size, and the alpha level that was chosen for the analysis. The degree of the difference between two groups is measured by the effect size, which should be stated together with the accompanying confidence interval. The sample size, which represents the number of observations used in the study, is also crucial. The degree of significance, commonly known as the alpha level, should also be given. This shows the likelihood of a false-positive finding and can be used to assess the accuracy of the findings. Researchers are able to accurately assess the trustworthiness of the results when statistical power is reported in accordance with APA recommendations.

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A property of an isosceles triangle, which is the base angles of the are equal, can be used to show that ΔBCD us an isosceles triangle.

There are two equal edges and two equivalent angles in an isosceles triangle. The Greek words iso (identical) and Skelos are the source of the name (leg). Equilateral triangles are those in which all of the sides are equal, whereas scalene triangles are those in which none of the sides are equal.

The characteristics of an isosceles triangle are as follows:

Let assume,

∠DAB = ∠A,

∠DCB = ∠C,

∠ABC = ∠B

The steps to show that ΔABD is an isosceles triangle are as follows;

∠ABD = 72° = ∠ADB :- Base angles of the isosceles triangle ΔABD

∠A + ∠ABD + ∠ADB = 180° (angle summation property)

∠A = 180° - (∠ABD + ∠ADB) = 180° - (72° + 72°) = 36°

∠A = ∠C :- Base angles of the isosceles triangle ΔBDC

∠ADB = ∠C + ∠DBC :- Exterior angle of a triangle theorem

72° = ∠C + ∠DBC

∠BDC = 72° + ∠A

∠DBC + ∠BDC + ∠C = 180° (angle summation property)

∠DBC = 180° - (∠BDC + ∠C) = 180° - (72° + 36° + 36°) = 36°

∠DBC = 36° = ∠C

In ΔBCD, ∠DBC = ∠C

ΔBCD is an isosceles triangle :- definition of an isosceles triangle

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The inequality to represent the instances when a vehicle other than a cargo van is used, where x is the distance of a location from the warehouse is given as follows:

x ≤ 8.

The four inequality symbols, along with their meaning, are presented as follows:

Distances of 8 miles or less are of at most 8 miles, hence the inequality is defined as follows:

x ≤ 8.

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The common binomial factor for the given expression is[tex]$x+3$[/tex].

We are given the expression[tex]$x^2+3 x+5 x+15$.[/tex]

We wish to find the common binomial factor for the given expression. So, we have:

Solution:

Factoring by grouping, we have:

[tex]x^2+3 x+5 x+15 & =x(x+3)+5(x+3) \\[/tex]

[tex]& =(x+3)(x+5)[/tex]

Therefore, we can see that the common binomial factor for the given expression is[tex]$x+3$[/tex].

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