The formula Q=MCT where Q=heat flow M=mass, C specfic heat, and T change of temperature is used to calculate heat flow Solve this formula for t

Answer:

2/3

Step-by-step explanation:

2 • 9 = 18

3 • 9 = 27

2/3 is equal to 18/27. All you have to do is multiply 9 to the numerator and the denominator for proof.

Hope this helps :)

Answer:

The coefficient is 9

Step-by-step explanation:

(a)(b)(c)+(a)(2c)(2a)+(2b)(b)(c)+(2b)(2c)(2a)

abc+4ca^2+2cb^2+8abc

9abc+4ca^2+2cb^2

To find speed, divide total distance by total time:

Speed = 19.2 / 3 = 6.4 kilometers per hour

102°

Opposite angles of an inscribed quadrilateral are supplementary.

∠Q = 180° -∠A = 180° -78°

∠Q = 102°

Answer:

The sum is rational.

Step-by-step explanation:

-3/8 is a rational number  (the ratio of 2 integers)

3/5 is a rational number  (the ratio of 2 integers)

When you add 2 rational numbers, you get a rational number.

The correct equation for the multiplication of means and extremes in the proportion 13/78 = 9/54 is C, which states 13 * 54 equals 78 * 9.

The equation that correctly shows the multiplication of the means and extremes in the proportion 13/78 = 9/54 is option C. This can be demonstrated by cross-multiplying the terms of the two ratios, where the product of the means (the two middle terms) is equal to the product of the extremes (the two outer terms). Therefore, the correct equation is 13 * 54 = 78 * 9.

To check, we can multiply the numbers:

Both products are equal, confirming that option C is the correct answer.

The first step is correct, because you changed the order of two terms in an addition, and the property [tex] a+b=b+a [/tex] is indeed called commutative property of addition.

In the second step, you do the same, but with multiplication: you use [tex] (6x)\cdot y = y \cdot (6x) [/tex]. This means that you're using the commutative property again, except for multiplication. So, the answer should be "commutative property of multiplication.

Finally, the third step is correct, because you're distributing the multiplication by 3 to both terms in the parenthesis, and this is called distributive property: it states that

[tex] a(b+c)=ab+ac [/tex]

tan(Q) = RS/RQ

The mnemonic SOH CAH TOA reminds you that ...

... Tan = Opposite/Adjacent

The side opposite angle Q is RS. The side adjacent is RQ. (QS is the hypotenuse, which does not come into play in the tangent function.)

Then ...

... tan(Q) = Opposite/Adjacent = RS/RQ

In right triangle QRS, with angle R being 90 degrees, tan Q is represented by the length of the side opposite to angle Q divided by the length of the side adjacent to Q which tan Q = SR/ QR.

In right triangle QRS, with angle R being 90 degrees, the ratio that represents tan Q is the length of the opposite side to angle Q divided by the length of the adjacent side.

In trigonometry, the tangent (tan) of an angle in a right triangle is a ratio of the length of the side opposite to the angle to the length of the side adjacent to the angle.

Therefore, if we label the sides opposite and adjacent to angle Q as opposite and adjacent respectively, the formula for tan Q would be:

tan Q = opposite/adjacent

         = SR/QR

For example, if a right triangle has sides of lengths 3, 4, and 5, with the side lengths of 3 and 4 being adjacent to and opposite angle Q respectively, the tan Q would be calculated as 4/3.

Final answer:

Two circles that have the same center but different radii are similar because they share the same shape but differ in size. The answer, therefore, is D. They are similar because they are of the same shape but different sizes.

Explanation:

The question involves two circles that share the same center but have different radii. According to geometric principles, similar figures have the same shape but not necessarily the same size, while congruent figures have both the same shape and the same size. Since the two circles share the same center (co-centric circles) and therefore the same shape (both are circular) yet differ in size, due to their different radii, the correct answer is that they are similar. Hence, the correct option is:

D. They are similar because they are of the same shape but different sizes.

This addresses the concept that similarity in geometry is about shape, rather than size. If the circles were both identical in size and shape, they would be congruent; however, because their sizes vary, they cannot be congruent.

Answer:

8763

Step-by-step explanation:

Let x represent the number of students the college had last year. Then this year's enrollment is ...

... x - 3%·x = 8500

... x(1 - 0.03) = 8500 . . . . . collect terms

... x = 8500/0.97 ≈ 8762.89 . . . . divide by the coefficient of x

Enrollment last year was about 8763.

_____

Of course, you know 3% = 3/100 = 0.03.

Answer:

see attached plot for  y ≥ |x - 1|

Step-by-step explanation:

Answer:

Graph below. x=1.

Step-by-step explanation:

1) Check the graph below. Take a closer look at the green area. This great Triangle intercepts the y-axis at the point (0,1) since it's an absolute value.

2) Algebraically, turning this function into an equation, since modulus

|x|=0, x=0.

[tex]y\geq |x-1|\\ |x-1|\geq 0\\ x-1\geq 0\\ x-1+1\geq 0+1\\ x\geq 1[/tex]

Answer:

A is the answer or (6 1/2, 8 1/2)  or (13/2, 17/2) or (6.5,8.5)

Step-by-step explanation:

Given : A line segment AB with

[tex]A= (x_1,y_1)=(4,8)[/tex] and [tex]B= (x_2,y_2)=(14,10)[/tex]

let C partitioned the line AB by 1:3  let m:n = 1:3

shown in the figure attached

Formula used:

[tex]C= (\frac{n x_1 + m x_2 }{m+n},\frac{n y_1+ m y_2 }{m+n})[/tex]

putting value in formula we get,

[tex]C= (\frac{(4) (3)+ (14)(1) }{1+3},\frac{(8)(3)+ (10)(1)}{1+3})[/tex]

[tex]C= (\frac{(13 }{2},\frac{17}{2})[/tex]

[tex]C= (6.5 ,8.5)[/tex]

[tex]C= ( 6 1/2,8 1/2)[/tex]

therefore, A is the answer

Answer:

Step-by-step explanation:

The midsegment of a triangle is half the length of the side it is parallel to.

1. For a distance of 6.08 m between wall plates, the colar tie will be half that, or 3.04 m.

2. The perimeter of ΔXYZ is ...

... 10 + 12 + 14 = 36

The sides of ΔABC are half the length of the sides of ΔXYZ, so the perimeter of ΔABC is half the perimeter of ΔXYZ.

... perimeter of ΔABC = 36/2 = 18

The location of the number k is -1.4 and the sum of 1.4 and k is 0

How to determine the positions of the numbers

From the question, we have the following parameters that can be used in our computation:

The number k and 1.4 are additive inverses.

This means that

k + 1.4 = 0

Evaluate the like terms

So, we have

k = -1.4

So, the location of the number k is -1.4 and the sum of 1.4 and k is 0

Answer:

[tex]CD=3\sqrt{3}\ cm,\\ \\A_{ABC}=18\sqrt{3}\ cm^2[/tex]

Step-by-step explanation:

Triangle ABC is right triangle. Since  m∠ACB = 90°  and m∠ACD = 60°, you get m∠BCD = 90°-60°=30°.

Triangle BCD is rigth triangle, then the leg that is opposite to the angle of 30° is half of the hypotenuse. Thus,

[tex]BD=\dfrac{1}{2}BC=\dfrac{1}{2}\cdot 6=6\ cm.[/tex]

By the Pythagorean theorem,

[tex]CD^2=BC^2-BD^2=6^2-3^2=36-9=27,\\ \\CD=3\sqrt{3}\ cm.[/tex]

Then

[tex]CD^2=AD\cdot BD,\\ \\27=3\cdot AD,\\ \\AD=9\cm.[/tex]

Hypotenuse AB of the triangle ABC is equal to

[tex]AB=AD+BD=9+3=12\ cm.[/tex]

The area of the triangle ABC is

[tex]A_{ABC}=\dfrac{1}{2}\cdot AB\cdot CD=\dfrac{1}{2}\cdot 12\cdot 3\sqrt{3}=18\sqrt{3}\ cm^2.[/tex]

CD is √3 cm, and the area of right-angled triangle ABC, with ∠ACB = 90° and ∠ACD = 60°, is 9 cm², obtained by applying the Pythagorean Theorem and area formula.

The given triangle is right-angled at C (as per the given condition m∠ACB = 90°), and ∠ACD is 60°.

Thus, we know that ΔACD is a 30-60-90 triangle because the remaining angle of the triangle (∠ADC) would have to be 30° (since all angles in any triangle sum up to 180°).

In a 30-60-90 triangle, the ratio of the sides opposite to these angles respectively is 1 : √3 : 2. This tells us AC is 2 times the length of CD and AC is √3 times the length of AD.

We don't have the lengths of AC, AD, or CD yet, but we can solve for CD using the Pythagorean Theorem in triangle ABC. Since it's a right triangle, the square of the hypotenuse (AC in our case) is equal to the sum of the squares of the other two sides. We can express this as:

AC² = BC² - CD²

Substituting AC = 2CD into this equation, we get:

(2CD)² = 6² - CD²

Solving this equation yields CD = BC / (2 √3) = 6 / (2 √3) = √3 cm

So the length of CD is √3 cm.

Now let's find the area of triangle ΔABC. The area is typically given by the formula 0.5 * base * height.

In this case, BC is the base of triangle ABC, and CD is the height due to its perpendicular nature to side AB by the given condition (CD ⊥ AB). So, the calculation would go as follows:

Area = 0.5 * BC * CD = 0.5 * 6 cm * √3 cm = 3 √3 cm².

But by rationalizing the denominator, which is a common practice especially when having square roots in the denominator, we get Area = 3√3 * √3 * √3 cm² = 3 * 3 cm² = 9 cm².

Therefore, CD = √3 cm and the area of ΔABC is 9 cm².

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Answer:

I have different options

Step-by-step explanation:

Im not sure because I dont have (l)(w)(h)

Answer:

x=56

Step-by-step explanation:

There are 3 angles in the triangle

x, 60 and the unknown angle we will call y

y  and 2x+4 make a straight line, so that adds to 180

y + 2x+4 = 180

Solve for y

y = 180 - (2x+4)

y = 180 -2x-4

y = 176 -2x

The three angles in a triangle add to 180

x + 60 + y = 180

Substitute in for y

x + 60 + 176 -2x = 180

Combine like terms

-x +236 = 180

Subtract 236 from each side

-x+236-236 = 180-236

-x = -56

Multiply by -1

x = 56

Answer:

z-score for 900 points = -4

Step-by-step explanation:

To find the z scores

z=(x-mean)/standard deviation

so

z=(900-1500)/150

z= -600/150

Answer:

This may help you I think so

We can let the variables A and B stand for the length in inches of fish A and fish B, respectively.

If we assume each person bought fish having a total length of 1 inch per gallon of aquarium, then we can write equations ...

... 3A +2B = 33 . . . . . total length of Marta's fish

... 3A +4B = 45 . . . . . total length of Hank's fish

Subtracting the first equation from the second, we get ...

... 2B = 12

... B = 6 . . . . . divide by 2

Using this value in the first equation, we have ...

... 3A + 2·6 = 33

... 3A = 21 . . . . . . . . subtract 12

... A = 7 . . . . . . . . . . divide by 3

Fish A is 7 inches long; fish B is 6 inches long.

To determine the lengths of fish A and fish B, two simultaneous equations were formed using the information provided. Solving these equations resulted in finding that fish A is 7 inches long and fish B is 6 inches long.

The problem revolves around figuring out the length of fish A and fish B given the rule that each inch of fish requires 1 gallon of water.

Marta's aquarium holds 33 gallons and she bought 3 of fish A and 2 of fish B. Hank's aquarium holds 45 gallons and he bought 3 of fish A and 4 of fish B. Let's denote the length of fish A as 'a' inches and fish B as 'b' inches.

Marta's equation: 3a + 2b = 33 (1)

Hank's equation: 3a + 4b = 45 (2)

To find the length of fish A and B, we solve these simultaneous equations:

Fish A is 7 inches long, and fish B is 6 inches long.

Answer:

g + h =  -4

g - h =  -10

h -g = 10

gh =  -21

g+ h^2 =  2

g^2 -h =  46

Step-by-step explanation:

We know g = -7 and h = 3

g + h = -7 +3 = -4

g - h = -7 - 3 = -10

h -g = 3 --7 = 3+7 = 10

gh = (-7) * 3 = -21

g+ h^2 = -7 + (3)^2 = -7+9 = 2

g^2 -h = (-7)^2 -3 = 49 -3 = 46

Answer:

Correct choice is D

Step-by-step explanation:

Consider the exponential function [tex]R=10.5\cdot (0.535)^t.[/tex]

The exponential function of exponential decay can be written as

[tex]y=a\cdot (1-r)^x,[/tex]

where r is the decay rate.

Note that 1-0.535=0.465. The decimal 0.465 is 46.5% and this percent represents the rate of exponential decay.

Answer:

dont try B its wrong on edge :(

Step-by-step explanation:

i just took the text

Answer:

16.0

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you ...

... Tan = Opposite/Adjacent

... tan(32°) = 10/AC

Multiplying by AC and dividing by the tangent gives you ...

... 10/tan(32°) = AC = 16.0

Answer:  The required length of AC is 16.1 units.

Step-by-step explanation:  We are given to find the length of side AC of triangle ABC.

From the figure, we note that

the triangle ABC is a right-angled triangle, where

m∠C = 90°, m∠A = 32° and BC = 10 units.

For the acute angle A, side AC is the base and side BC is the perpendicular.

So, from trigonometric ratios, we have

[tex]\tan m\angle A=\dfrac{perpendicular}{base}\\\\\\\Rightarrow \tan32^\circ=\dfrac{BC}{AC}\\\\\\\Rightarrow \tan32^\circ=\dfrac{10}{AC}\\\\\\\Rightarrow 0.62=\dfrac{10}{AC}\\\\\\\Rightarrow AC=\dfrac{10}{0.62}\\\\\Rightarrow AC=16.13.[/tex]

Rounding to nearest tenth, we get

AC = 16.1 units.

Thus, the required length of AC is 16.1 units.

Answer:

The maximal number of smothies that Carol can make with the yogurt is 4.

Step-by-step explanation:

Divide the number of cups Carol has by the number of cups needed to make one smoothie.

[tex]1\dfrac{5}{8}:\dfrac{1}{3}=\dfrac{13}{8}\cdot \dfrac{3}{1}=\dfrac{39}{8}=4\dfrac{7}{8}.[/tex]

The maximal number of smothies that Carol can make with the yogurt is 4.

Answer:4

Step-by-step explanation:

1 5/8 multiply then add,you will get 13 Over 8.Keep,Change,recipical,And turn 1/3 To 3/1.Multiply,then divide because it will become an improper fraction.So divide then you will get 4 7/8.4 is a closer Number

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

If a polynomial function P(x) with rational coefficients has a root z. the so is the complex conjugate of z is a root. (In order to see that, take the complex conjugates of the equation P(x)=0, and note that complex conjugates of rational numbers equal to itself.)

Therefore the complex conjugates of the given roots i and 7+8i , are -i and 7-8i is the required answer.

Answer:

D U E = { 6,8,9,10,11}

Step-by-step explanation:

U stands for union, which is join the sets together

D U E = { 6,8,9,10,11}

Answer:

C) -4

Step-by-step explanation:

This is easy:)

54 - 4 = 50

50 - 4 = 46

46 - 4 = 42

42 - 4 = 38

Hope this helped u!!!

Good luck:))

The common difference for this arithmetic sequence is -4.

An arithmetic sequence is defined in two ways. It is a "sequence where the differences between every two successive terms.

The given arithmetic sequence is;

54, 50, 46, 42, 38

The difference first term and second term is;

[tex]\rm a_2-a_1= 50-54=-4[/tex]

The difference second term and third term is;

[tex]\rm a_3-a_2= 46-50=-4[/tex]

The difference third term and fourth term is;

[tex]\rm a_4-a_3=42-46=-4[/tex]

The difference fourth term and last term is;

[tex]\rm a_5-a_4=38-42=-4[/tex]

Hence, the common difference for this arithmetic sequence is -4.

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Answer:

C, D, F are correct.

Step-by-step explanation:

If we look at the equation:

[tex]P(t)=16.8(0.94)^t[/tex]

Is molded after this equation:

[tex]Population_{final}=Population_{initial}(1+r)^t[/tex]

Where 1 represents 100%, r is the rate in decimals and t is time.

So this means that the initial population is 16.8 thousand or in other words 16,800 people.  The rate is 1-r, so the rate that the population is decreasing is 0.06 i.e. 6% (because 1-0.06=0.94).

It's a quadratic function.

[tex]f(x)=ax^2+bx+c[/tex]

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

[tex]f(x)=3x^2-8[/tex]

a = 3, b = 0, c = -8

a = 3 > 0, therefore the parabola open up.

The range of this function is [k, ∞).

k - second coordinate of the vertex (h, k)

[tex]h=\dfrac{-b}{2a},\ k=f(h)[/tex]

Substitute:

[tex]h=\dfrac{-0}{2(3)}=0\\\\k=f(0)=3(0^2)-8=0-8=-8[/tex]

Answer: The range is [tex][8,\ \infty)[/tex]

To find the range of the function ƒ(x) = 3x^2 - 8, we need to determine the set of all possible output values. The range of the function is all real numbers greater than or equal to the y-coordinate of the vertex, which is -8. Therefore, the range of the function ƒ(x) = 3x^2 - 8 is y ≤ -8.

To find the range of the function ƒ(x) = 3x2 − 8, we need to determine the set of all possible output values. Since the function is a quadratic function, its graph is a parabola. The range can be found by considering the vertex of the parabola and the direction it opens.

The vertex of the parabola is given by the formula x = -b/(2a), where a and b are the coefficients of the quadratic function. In this case, a = 3 and b = 0. So, the x-coordinate of the vertex is x = -0/(2*3) = 0.

Since the parabola opens upward (the coefficient of x2 is positive), the vertex represents the minimum value of the function. Therefore, the range of the function is all real numbers greater than or equal to the y-coordinate of the vertex. Plugging the x-coordinate (0) into the function gives us ƒ(0) = 3*(0)2 − 8 = -8. So, the range of the function ƒ(x) = 3x2 − 8 is y ≤ -8.

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The actual value of sin(π/3) is (√3)/2 ≈ 0.86602540.

If the sine function is approximated by y=x (no error at x = 0), then the error at x=π/3 is ...

... x -sin(x) @ x=π/3

... π/3 -(√3)/2 ≈ 0.18117215 ≈ 0.1812

You know right away this is a bad approximation, because the approximate value is π/3 ≈ 1.04719755, a value greater than 1. The range of the sine function is [-1, 1] so there will be no values greater than 1.

___

If the sine function is approximated by y=(x+1-π/4)/√2 (no error at x=π/4), then the error at x=π/3 is ...

... (x+1-π/4)/√2 -sin(x) @ x=π/3

... (π/12 +1)/√2 -(√3)/2 ≈ 0.026201500 ≈ 0.02620

Therefore, the error due to linear interpolation to estimate the value of [tex]\( \sin\left(\frac{\pi}{3}\right) \)[/tex] is approximately [tex]\( 29.59 \% \).[/tex]

To estimate the error due to linear interpolation for [tex]\( \sin(x) \)[/tex] at [tex]\( x = \frac{\pi}{3} \)[/tex], we need to compare the actual value of [tex]\( \sin\left(\frac{\pi}{3}\right) \)[/tex] with the value obtained through linear interpolation.

The actual value of [tex]\( \sin\left(\frac{\pi}{3}\right) \)[/tex] is [tex]\( \frac{\sqrt{3}}{2} \)[/tex], which is approximately [tex]\( 0.8660 \)[/tex] .

For linear interpolation, we typically use two nearby points to estimate the value of a function at an intermediate point. Let's consider the points [tex]\( (\frac{\pi}{4}, \sin(\frac{\pi}{4})) \) and \( (\frac{\pi}{2}, \sin(\frac{\pi}{2})) \)[/tex], which are [tex]\( \left(\frac{\pi}{4}, \frac{\sqrt{2}}{2}\right) \) and \( \left(\frac{\pi}{2}, 1\right) \)[/tex], respectively.

Now, we'll use linear interpolation to estimate [tex]\( \sin\left(\frac{\pi}{3}\right) \):[/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx \sin\left(\frac{\pi}{4}\right) + \left(\frac{\pi}{3} - \frac{\pi}{4}\right) \cdot \frac{\sin\left(\frac{\pi}{2}\right) - \sin\left(\frac{\pi}{4}\right)}{\frac{\pi}{2} - \frac{\pi}{4}} \][/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx \frac{\sqrt{2}}{2} + \left(\frac{\pi}{3} - \frac{\pi}{4}\right) \cdot \frac{1 - \frac{\sqrt{2}}{2}}{\frac{\pi}{2} - \frac{\pi}{4}} \][/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx \frac{\sqrt{2}}{2} + \left(\frac{\pi}{3} - \frac{\pi}{4}\right) \cdot \frac{1 - \frac{\sqrt{2}}{2}}{\frac{\pi}{4}} \][/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx \frac{\sqrt{2}}{2} + \left(\frac{\pi}{3} - \frac{\pi}{4}\right) \cdot \frac{1 - \frac{\sqrt{2}}{2}}{\frac{\pi}{4}} \][/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx \frac{\sqrt{2}}{2} + \left(\frac{\pi}{3} - \frac{\pi}{4}\right) \cdot \frac{1 - \frac{\sqrt{2}}{2}}{\frac{\pi}{4}} \][/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx 0.7071 + \left(\frac{\pi}{3} - 0.7854\right) \cdot \frac{1 - 0.7071}{0.7854} \][/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx 0.7071 + (0.5236 - 0.7854) \cdot \frac{0.2929}{0.7854} \][/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx 0.7071 + (-0.2618) \cdot 0.3732 \][/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx 0.7071 - 0.0977 \][/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx 0.6094 \][/tex]

Now, we can find the error:

[tex]\[ \text{Error} = \left| \frac{\text{Actual value} - \text{Interpolated value}}{\text{Actual value}} \right| \times 100 \% \][/tex]

[tex]\[ \text{Error} = \left| \frac{0.8660 - 0.6094}{0.8660} \right| \times 100 \% \][/tex]

[tex]\[ \text{Error} = \left| \frac{0.2566}{0.8660} \right| \times 100 \% \][/tex]

[tex]\[ \text{Error} = 0.2959 \times 100 \% \][/tex]

[tex]\[ \text{Error} = 29.59 \% \][/tex]

C. AB ║ DC

The congruence of the two triangles means ∠ABD≅∠CDB. These, then, are alternate interior angles on either side of transversal BD between lines AB and DC. If alternate interior angles are congruent, the lines are parallel:

... AB ║ DC

_____

Congruence of the triangles does not require ∠B to be bisected or that it be 90°.

All the three sides of the given triangles are equal to the sides of another triangle then, [tex]\rm \overline{AB}=\overline{DC}[/tex]. Therefore the correct option is C).

Given :

Triangle ABD is congruent to the triangle CBD.

A triangle has three sides and the sum of all the interior angles are equal to [tex]180^\circ[/tex].

If the triangle ABD is congruent to the triangle CBD then:

AB = DC

AD = BC

BD = BD

If all the three sides of the given triangles are equal to the sides of another triangle then, [tex]\rm \overline{AB}=\overline{DC}[/tex]. Therefore the correct option is C).

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