On a given day, the temperature in a pool increases with both the work of a heater modeled by the function h(t) and the sun, s(t), depending on the amount of time that passes,t, in minutes.

Which graph best shows the combination of both functions, c(t)?

Answer:

m = -2

b = -3

Step-by-step explanation:

Point slope formula of a line = [tex]y-y_{1} = M(x-x_{1} )[/tex]

Where x1 and y1 are the coordinates of the point and M is the slope.

Given slope = -2

Point = (-7,11)

So x1 = -7 and y1 = 11

Substituting the values in the point-slope formula, we get:

[tex]y-11 = -2(x - (-7))[/tex]

[tex]= > y = -2x -14 + 11[/tex]

Or

[tex]y = -2x -3[/tex]

Thus, m = -2 and b = -3

The ratio of the CosA will be 12 / 37 for the right-angle triangle.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry. The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that there is a right angle triangle having the Hypotenuse = 37, Base = 12, and Height = 35.

The value of CosA will be calculated as:-

CosA = Base / Hypotenuse

CosA = 12 / 37

Therefore, the ratio of the CosA will be 12 / 37 for the right-angle triangle.

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Answer:

Step-by-step explanation:

1/10 = 0.1

4/5 = 0.8

What's halfway between 1 and 8?

Let's show it on a number line:

             ¬                                                                                        ¬

_0____1____2_____3______4_____5____6_____7_____8__________

It's 4 and 5, therefore it's 4.5

0.45 comes halfway through 1/10 and 4/5

Expressed as a fraction: 45/100 = 9/20

Hope that helps! Please make me brainliest!

Answer: 0.45

Step-by-step explanation:

The sum of the 1st and three-term of the GP is 87.75.

What is geometric progression?

A geometric progression often referred to as a geometric sequence, is a series of non-zero values where each term following the first is obtained by multiplying the preceding value by a constant, non-zero number known as the common ratio.

Here, we have

Given:  3rd term is 27 and whose 6th term is 8​

Let the GP terms are a, ar, ar², ar³, ar⁴ and ar⁵,

Given ar² = 27 and ar⁵ = 8

Take the ratio of the sixth term to the third term:

ar⁵ / ar² = 8/27 => r³ = (2/3)³

r = 2/3

We know that

ar² = a(2/3)² = 27

=> a(4/9) = 27

=> a = 27*9/4 = 243/4

So, the terms are 243/4, 243/4*(2/3), 243/4*(4/9), 243/4*(8/27), 243/4*(16/81), 243/4*(32/243)

= 243/4 + 27

= 60.75 + 27

= 87.75

Hence, the sum of the 1st and three-term of the GP is 87.75.

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The numerical value of x in the expression 3x + 6 is 3.

The diagonals of a rectangle bisects each other and are equal.

Given that;

Since the diagonals of a rectangle bisects each other and are equal.

DG = CG

Plug in the given values and simplify.

15 = 3x + 6

Solve for x

Subtract 6 from both sides

15 - 6 = 3x + 6 - 6

9 = 3x

Divide both sides by 3

9/3 = 3x/3

9/3 = x

3 = x

x = 3

Therefore, the value of x is 3.

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Answer:

y=4,x= -1

Step-by-step explanation:

2y-3 =y+1

2y-y=1+3

y=4

∆CBD

2x+7=2y-3

2x+7=5

2x= 5-7

2x= -2

x= -1

Answer:

$27/month

Step-by-step explanation:

300-220=80

100%= 300

1%= 300÷100

= 3

10%= 3×10

= 30

300-30=270

270÷10= $27

Answer:

Step-by-step explanation:

root of -48 is equal to 4iroot3, so plus/neg 4iroot3

Answer:

Step-by-step explanation:

What is Joey's total distance run on the first day?

Joey runs 5 laps around the track, which we can assume is 1 mile per lap. So, she runs 5 miles. Additionally, she runs 1.5 miles, so her total distance run on the first day is 5 + 1.5 = 6.5 miles.

What is Joey's total distance run on the second day?

Joey runs 3 laps around the track, which we can assume is 1 mile per lap. So, she runs 3 miles. Additionally, she runs 4 miles, so her total distance run on the second day is 3 + 4 = 7 miles.

Answer:

E

Step-by-step explanation:

Answer: figure 1 is 9

figure 2 is 81

figure 3 is 72

= 162

Step-by-step explanation:

Answer: Given that a, b, and c form an arithmetic sequence, so they are equally spaced, meaning the difference between each of them is constant. Let's denote the common difference between a, b, and c as d.

So, we have:

a = b - d

c = b + d

Using these two equations, we can prove that 2^a, 2^b, and 2^c form a geometric sequence.

We have:

2^a = 2^b / 2^d

2^c = 2^b * 2^d

Since the product of two powers of the same base is equivalent to the power of the base with the sum of the exponents, we have:

2^a * 2^c = 2^b * 2^b * 2^d * 2^d = 2^(b+b+d+d) = 2^(2b+2d)

So, we have:

2^a * 2^c = 2^(2b+2d) = 2^(2b) * 2^(2d) = 2^b * 2^b * 2^d * 2^d = 2^b * 2^c

This means that 2^a, 2^b, and 2^c form a geometric sequence, with the common ratio of 2^d.

Step-by-step explanation:

Lauren spent a total of 10 hours on the duties if he spent 1 3/8 hour cleaning, 7/8 hour doing laundry, and 1 5/8 cooking dinner.

A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.

Here,

To find the total time Lauren spent on the tasks, we need to add the time she spent cleaning the house, doing the laundry, and preparing food.

Cleaning the house: 1 3/8 hours

Doing the laundry: 7/8 hours

Preparing food: 1 5/8 hours

Adding these three quantities, we get:

1 3/8 + 7/8 + 1 5/8 = 1 3/8 + 7/8 + (2 3/8)

Next, we simplify each fraction by finding a common denominator of 8:

(18/8) + (7/8) + (28/8) = 1 + 7 + 2 = 10

So, Lauren spent a total of 10 hours on the tasks if he spent 1 3/8 hour cleaning the house, 7/8 hour doing the laundry, and 1 5/8 preparing food.

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The width of the rectangular will be x+4.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees. Quadrilaterals are typically four-sided closed shapes, and there are numerous varieties of them. Square, rectangle, rhombus, kite, and trapezoid are the most typical shapes. Four closed sides make up a quadrilateral. Quadrilaterals are the following figures: a four-sided figure. The form features a single set of parallel sides and no right angles.

Area of the rectangle is A = a*b

Given Length is = x+7

And  the area is x² +11x+28

So the width is = x² +11x+28 / x+7

x² +7x+4x+28/x+7

=(x+7)(x+4)/x+7

=x+4

Hence the width of the rectangular will be x+4.

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(a) The equation to find x is 4x + 22 = 90.

(b) The degree of each angle:

The sum of angle 1 and 2 is equal to right angle.

The value of a right angle is equal to 90°.

In the figure, we have a right angle and one line in it. It makes two angles 1 and 2 with

(a) Find an equation to find x!

(b) Find the degree measure of each angle!

The sum of angle 1 and 2 is equal to 90°. So,

m∠1 + m∠2 = 90

3x + x + 22 = 90

4x + 22 = 90

This is the equation to find x. Then, we find x.

4x + 22 = 90

4x = 90 - 22

4x = 68

x = 68/4

x = 17°

The degree measure of each angle will be

m∠1 = 3x

m∠1 = 3(17)

m∠1 = 51°

m∠2 = x + 22

m∠2 = 17 + 22

m∠2 = 39°

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Answer:

2[tex]\sqrt{13x^{2} }[/tex]

Step-by-step explanation:

To simplify the expression √52x^4, we can break it down as follows:

√(52x^4) = √(4 * 13 * x^4)

Since the square root of a product is equal to the product of the square roots, we can simplify further:

√(4 * 13 * x^4) = √4 * √13 * √(x^4)

The square root of 4 is 2, and the square root of x^4 is x^2:

2 * √13 * x^2

Therefore, the simplified expression is 2√13x^2.

Answer:

[tex]\large\text{$2\sqrt{13}\;x^2$}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sqrt{52x^4}[/tex]

Prime factorization is the process of representing a positive integer as a product of its prime factors.

The prime factorization of 52 is 2² · 13. Therefore, rewrite 52 as 2² · 13:

[tex]\sqrt{2^2 \cdot 13 \cdot x^4}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{abc}=\sqrt{\vphantom{b}a}\sqrt{b}\sqrt{c}[/tex]

[tex]\sqrt{2^2} \sqrt{13} \sqrt{x^4}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]

[tex]2\sqrt{13} \sqrt{x^4}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt[n]{a^m}=a^{\frac{m}{n}},\quad \textsf{assuming} \;a\geq 0[/tex]

[tex]2\sqrt{13} \;x^{\frac{4}{2}}[/tex]

[tex]2\sqrt{13} \;x^2[/tex]

Therefore, the simplified expression is:

[tex]\large\boxed{2\sqrt{13}\;x^2}[/tex]

The sum of a and b is obtained as follows:

a + b = 5.

The function for this problem is defined as follows:

f(x) = ax/[bx - 4]

f(1) = -2 means that when x = 1, y = -2, hence:

-2 = a/(b - 4)

a = -2b + 8

f(2) = 2 means that when x = 2, y = 2, hence:

2 = 2a/(2b - 4)

2a = 4b - 8

a = 2b - 4.

Equaling the two equations, the value of b is obtained as follows:

-2b + 8 = 2b - 4

4b = 12

b = 3.

Hence the value of a is ob:

a = 2b - 4

a = 2(3) - 4

a = 2.

Hence the sum is of:

a + b = 2 + 3

a + b = 5.

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Answer:

16.2m^2

16.2*20=324

324 rupees

Step-by-step explanation:

Based on the information of area of rhombus and length of diagonal, the other diagonal of rhombus is 10.5 cm in length.

The diagonal and area of rhombus are related to each other by the formula -

Area = diagonal1 × diagonal2/2

Keep the values in formula to find the diagonal.

360 = 40 × diagonal 2/2

Rewriting the formula -

Diagonal 2 = (360 × 2)/40

Performing multiplication on Right Hand Side of the equation

Diagonal 2 = 420/40

Performing division on Right Hand Side of the equation

Diagonal 2 = 10.5 cm

The other diagonal is 10.5 cm.

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Since the length of the string is not specified, we cannot find the Y value (fret position) exactly.

Given in this word problem:

Length of the string: Not specified

Number of notes higher than the root note: 3 (G note is 3 notes higher than the E string's root note)

Scale: Not specified

The equation for the fret position can be represented as follows:

fret position = length of string * 2^(-12 * n)

where n is the number of notes higher than the root note.

To find the X value, we need to know the length of the string, which is not specified in the problem.

To find the Y value, we need to calculate the fret position using the equation:

fret position = length of string * 2^(-12 * n)

fret position = length of string * 2^(-12 * 3)

fret position = length of string * 2^-36

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Answer:

The statements that are true about the ordered pair (1, 2) and the system of equations are:

When (1, 2) is substituted into the first equation, the equation is true.
The ordered pair (1, 2) is a solution to the system of linear equations.

So, the correct options are:

When (1, 2) is substituted into the first equation, the equation is true.
The ordered pair (1, 2) is a solution to the system of linear equations.

Step-by-step explanation:

Answer: £3136

Step-by-step explanation:

First you want to find 28% of 800 to find out how much it increases by every year.

So 800*0.28= 224

And then you want to multiply 224 to 14 years to see how much he has to pay in 14 years

224*14=3136

Your answer: £3136

Option D and E are equivalent to the given expression.

First we find the x and y values of the equation -2y+3/2x+7/4.

For example x= 0, substitute:

-2y+3/2x+7/4=0

-2y=-7/4

y=7/8

For example y=0, substitute:

-2y+3/2x+7/4=0

3/2x=-7/4

x=-7/6

Then we look for choices A, B, C, D and E, which one produces x=-7/6 and y=7/8 if for example x=0 and y=0.

And those that have the same value are equations D and E.

Equivalent equations are systems of equations that have the same solutions. Identifying and solving equivalent equations is a valuable skill, not only in algebra class, but also in everyday life.

The simplest example of an equivalent equation doesn't have any variables.

For example, these three equations are equivalent to each other:

3 + 2 = 5

4 + 1 = 5 5 + 0 = 5

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The process of converting individual raw scores in a distribution to a set of scores for which we know the percentiles is known as "normalizing the data" or "standardizing the data."

The steps for standardizing the data are as follows:

Order the raw scores in the distribution from smallest to largest.

Assign each score a percentile rank. This is the percentage of scores in the distribution that are equal to or lower than the score. For example, if a score has a percentile rank of 75, it means that 75% of the scores in the distribution are equal to or lower than that score.

Convert the raw scores to standardized scores (also known as z-scores). This is done by subtracting the mean of the distribution from each score and then dividing by the standard deviation of the distribution. The resulting standardized score represents the number of standard deviations above or below the mean that the raw score falls.

The process of standardizing the data helps to put the raw scores into a common context, which makes it easier to compare scores from different distributions and to draw meaningful conclusions about the data. Additionally, standardized scores can be used to determine the probability of a score falling within a particular range.

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Answer:

23.50y+1

Step-by-step explanation:

2(4.25y-7.5+7.5y+8)

2(4.25y+7.5y-7.5+8)

2(11.75y+0.5)

2(11.75y) + 2(0.5)

23.50y + 1

Probability that Erin selects a bulb for a yellow flower or a dahlia is 52.8%.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Given, by the table

Total number of flowers = 5+4+3+3+1+2+2+5+6+0+1+4 = 36

Number of yellow flowers = 4 + 1 + 5 + 1 = 11

Number of Dahlia flowers = 5 + 4 + 3 = 12

Number of yellow Dahlia = 4

Probability of selecting bulb for a yellow flower P(y)= 11/36

Probability of selecting bulb for dahlia P(d) = 12/36

Probability of selecting bulb for yellow Dahlia P(y and d) = 4/36

Probability of selecting bulb for yellow flower or dahlia

= P(y) + P(d) - P(y and d)

= 11/36 + 12/36 - 4/36

= (11 + 12 - 4)/36

= 19/36

= 0.528

= 52.8%

Hence, 52.8% is probability that she selects a bulb for a yellow flower or a dahlia.

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Answer: A

Step-by-step explanation:

Convert the equation into quadratic form (y=ax^2+bx+c)

y=-3(x-4)(x+6)   =  y=-3x^2-6x+72

Calculate -b/2a

which is 6/-6=-1

then put the value -1 into the equation for x.  

-3+6+72=75

The answer is therefore A.

Answer:

240in^3

Step-by-step explanation:

V = whl

= (12in)(8in)(2.5in)

= 240 in ^3

The value of a and b are -179/171 and -20/171 respectively.

Rationalising surds is where we convert the denominator of a fraction from an irrational number to a rational number. In more complex cases, it is useful to multiply the denominator by its conjugate to cancel out the surds in the denominator.

(2+5√7)/(2-5√7)

by rationalization

(2+5√7)/(2-5√7) × (2+5√7)/(2+5√7)

=( 4+10√7 + 10√7 + 175)/4+10√7 - 10√7- 175

= (20√7+179)/-171

= -20/171 √7 -179/171

therefore the value of a = -179/171 and b = -20/171

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