18. Recall that 0°C = 32°F and 100°C = 212°F.
a. Using x for degrees Celsius and y for degrees Fahrenheit, find
an equation of the line passing through (0, 32) and (100, 212).
b. What is the slope of the line? Explain what the slope means in
terms of degrees Celsius and degrees Fahrenheit.
c. What is the y-intercept of the line? Explain what the y-intercept
means in terms of degrees Celsius and degrees Fahrenheit.​

Final answer:

The scale factor from Solid A to Solid B is found by taking the cube root of the ratio of their volumes, resulting in approximately 0.6996.

Explanation:

The question involves finding the scale factor between two similar solids based on their volumes. Since the volumes of similar solids are related by the cube of the scale factor, we can find the scale factor by taking the cube root of the ratio of their volumes. Solid A has a volume of 171.5 m³, and Solid B has a volume of 500 m³. To find the scale factor from Solid A to Solid B, we calculate the cube root of (171.5/500), which will give us the linear scale factor.

The formula we use is:

Scale Factor (k) = ∛(Volume of Solid A / Volume of Solid B)

k = ∛(171.5 m³ / 500 m³)

k ≈ ∛(0.343) ≈ 0.6996

Therefore, the scale factor of Solid A to Solid B is approximately 0.6996.

Answer:-(3x+5)^2

Step-by-step explanation:

The polynomial is factored to give (-3x -5)(3x + 5)

From the information given, we have that the polynomial is given as;

-9x - 30x-25

Now,  multiply the constant value by the coefficient of x squared in the expression, we have;

-9(-25)

225

Now, find the pair factors of 225 that adds up to -30

Then, substitute the values, we get;

-9x² - 15x - 15x - 25

Group in pairs, we get;

(-9x² - 15x ) - (15x - 25)

Factorize the expressions

-3x(3x + 5) - 5(3x + 5)

Then, we have;

(-3x -5)(3x + 5)

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Answer:

Terms = x

Coefficients = 3

Constants = 10

Hope this helped! :)

In the expression 3x+10, there are two terms: 3x and 10. The coefficient is 3, which multiplies the variable x, and the constant is 10, which is the term without a variable.

In the expression 3x+10, the terms are 3x and 10. A term is a single mathematical expression. The coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression, so here the coefficient is 3, which is the number multiplying the variable x. The constant is a term without a variable, and in this case, it is 10.

Answer:

-1154

Step-by-step explanation:

(-554) - 600 = -1154

Answer:

1. books | the first place to look when researching a speech-by-step explanation

2. encyclopedia | source of current information

3. almanac | provides statistical information on a variety of subjects

4. atlas | provides geographical data

5. periodical | most commonly used reference work

6. newspaper | source of current international, national, and local news

7. bibliography | list of related sources

8. mind map | collection of related ideas

9. thesis statement | a one-sentence summary of the speech

10. statement of purpose | identifies the expected reaction or response of the audience

Explanation:

1. Books are written texts which contain mostly all the detailed information, hence its the first place to look when researching for a speech

5. Periodicals are mainly journals, articles or magazines so we often use it as reference

8. Mind map is usually collection of all many ideas, major ideas.

9. Thesis statement is used at the first paragraph of an essay or speech which usually summarizes the entire speech in one sentence.

Answer:

1. books - the first place to look when researching a speech. 

2. encyclopedia - collection of related ideas. 

3. almanac - provides statistical information on a variety of subjects. 

4. atlas - provides geographical data.

5. periodical - source of current information.

6. newspaper - source of current international, national, and local news list of related sources.

7. bibliography - most commonly used reference work.

8. mind map - list of related sources 

9. thesis - statement a one-sentence summary of the speech 

10. statement of purpose - identifies the expected reaction or response of the audience.

Answer:

the first one is the answer

Step-by-step explanation:

Answer:

the data is discrete, so the points are connected with a line

Step-by-step explanation:

ANSWER

5

EXPLANATION

The equation that expresses the approximate height h, in meters, of a ball t seconds after it is launched vertically upward from the ground is

[tex]h(t) = - 4.9 {t}^{2} + 25t[/tex]

To find the time when the ball hit the ground,we equate the function to zero.

[tex] - 4.9 {t}^{2} + 25t = 0[/tex]

Factor to obtain;

[tex]t( - 4.9t + 25) = 0[/tex]

Apply the zero product property to obtain,

[tex]t = 0 \: or \: \: - 4.9t + 25 = 0[/tex]

[tex]t = 0 \: \: or \: \: t = \frac{ - 25}{ - 4.9} [/tex]

t=0 or t=5.1 to the nearest tenth.

Therefore the ball hits the ground after approximately 5 seconds.

Answer:

The ball will hit the ground after 5 seconds ⇒ first answer

Step-by-step explanation:

* Lets study the information in the problem

- The ball is lunched vertically upward from the ground with an initial

  velocity 25 meters per second

- The ball will reach the maximum height when its velocity becomes 0

- The ball will fall down to reach the ground again

- The equation of the height (h), in meters of the ball t seconds after

  it is lunched from the ground is h = -4.9t² + 25t

- When the ball hit the ground again the height of it is equal 0

∵ h = 0

∴ 0 = -4.9t² + 25t ⇒ Multiply the two sides by -1 and reverse them

∴ 4.9t²  - 25t = 0 ⇒ factorize it by taking t as a common factor

∴ t(4.9t - 25) = 0 ⇒ equate each factor by 0

∵ t = 0 ⇒ the initial time when the ball is lunched

∵ 4.9t - 25 = 0 ⇒ add 25 to both sides

∴ 4.9t = 25 ⇒ divide each side by 4.9

∴ t = 5.102 ≅ 5 seconds

* The ball will hit the ground after 5 seconds

Answer:

  A.  3√(7/5) +√(-9/5)

Step-by-step explanation:

The square root of a negative number is imaginary. Only answer choice A contains any imaginary numbers, so only answer choice A is complex.

Answer:

[tex]x=n\pi[/tex] or [tex]x= \frac{(2n\pm1)\pi}{2}[/tex], where [tex]n\ge0[/tex]

Step-by-step explanation:

The given trigonometric equation is:

[tex](\sin x)(\cos x)=0[/tex]

By the zero product principle;

Either [tex]\sin x=0[/tex] or [tex]\cos x=0[/tex]

When  [tex]\sin x=0[/tex],  then [tex]x=n\pi[/tex]

When [tex]\cos x=0[/tex], then [tex]x=2n\pi \pm \cos^{-1}(0)[/tex]

This implies that: [tex]x=2n\pi \pm \frac{\pi}{2}[/tex]

Therefore the general solution is  [tex]x=n\pi[/tex] or [tex]x= \frac{(2n\pm1)\pi}{2}[/tex], where [tex]n\ge0[/tex]

Answer:

B. pi divided by two plus n pi comma n pi such that n equals zero, plus or minus one, plus or minus two to infinity

Step-by-step explanation:

Given equation,

[tex](sin x)(cosx)=0[/tex]

[tex]\implies sinx=0\text{ or }cosx=0[/tex]

[tex]x=sin^{-1}(0)\text{ or }x=cos^{-1}(0)][/tex]

[tex]x=\pi, 2\pi, 3\pi,......\text{ or }x=\frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{2}....[/tex]

[tex]\implies x = n\pi\text{ or }x=\frac{\pi+2n\pi}{2}[/tex]

Or

[tex]x=n\pi\text{ or }x= \frac{\pi}{2}+n\pi[/tex]

Where, n = 0, 1, -1, -2, ........∞

Hence, option 'B' is correct.

d. x=-3

hope this helps!

Answer:

It's D

Step-by-step explanation:

Because the X axis is -3

Answer:

(√2)/2

Step-by-step explanation:

A right triangle with one acute angle equal to 45° will also have the other acute angle equal to 45°. The angles being equal means the legs will be equal. If we assign each leg the length 1, then the Pythagorean theorem tells us the hypotenuse is length ...

√(1^2 +1^2) = √2

The cosine of the acute angle is the ratio of the nearest leg length (1) to the hypotenuse length (√2), so the exact value of the cosine is ...

cos(45°) = 1/√2 = (√2)/2

____

(√2)/2 is the fraction with the denominator "rationalized". Sometimes, that is the preferred presentation of this number.

Hello There!

This would certainly be true.

The horizontal axis on a coordinate graph is called the X axis

And the vertical line is called the y axis.

Answer:true

Step-by-step explanation:

Horizontal axis on a graph is labeled the x-axis while the vertical axis is labeled the y-axis. Where they intersect is called the origin

Answer:

D

Step-by-step explanation:

If you drew a line of best fit to encompass all the data points it would be a line that has a negative slope. The correlation coefficient would be negative.

The option (D) the data shows a negative linear relationship because the slope of the line is negative.

It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.

[tex]\rm r = \dfrac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{{[n\sum x^2- (\sum x)^2]}}\sqrt{[n\sum y^2- (\sum y)^2]}}[/tex]

As we can see in the picture, the dots pattern are going up to down if we draw a line of best fit.

The slope of the line will be negative.

We can say the relationship between car's value and car's age is negative correlated.

Thus, the option (D) the data shows a negative linear relationship because the slope of the line is negative.

Learn more about the correlation here:

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Answer:

Yes. Hexagon is 10 cm

Step-by-step explanation:

Answer:

18.85

Step-by-step explanation:

you divide 37.7 by 2

Hello There!

The answer to adding 3/14 and 1/7 together give you a sum of 5/14

STEP #1 The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

STEP #2 Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

Answer:

C

Step-by-step explanation:

Because harder problems do require equations you cannot solve E=MC square without an equation. OH wait it is an equation E represents units of energy, m represents units of mass, and c2 is the speed of light squared, or multiplied by itself.

Answer:

C

Step-by-step explanation:

If you ask me none of these are reasons to not use a table but for the sake of the question it is probably C. Both A and D are reasons to use a table, and option B is simply false, you very much can find patterns when using tables. As for why C is the most viable answer? Well thats the only one that (truthfully) describes a flaw of using a table, the rest are either untrue or they are describing the pros of using a table.

Answer:

The mean of the worker's salary would be $26,667

The standard deviation is $2915.43

Step-by-step explanation:

Add the salaries together and divide by the number of workers for the mean

Use the formula for standard deviation s=√∑(x¹-x⁻)²/n-1

Answer:

The expression is [tex](4)*(3)+(1)*(1)[/tex]

Step-by-step explanation:

we know that

The algebraic expression of the phrase " the sum of the products of 4 and 3 and 1 and 1" is equal to

[tex](4)*(3)+(1)*(1)[/tex]

[tex]=(12)+(1)[/tex]

[tex]=13[/tex]

Answer:

The teacher can hand out pizza to 8 students.

Step-by-step explanation:

To find how many slices of pizza the teacher can hand out , you can divide 7 by 7/8 and round down the nearest whole number.

7 ÷ 7/8 = 8

8 is already a whole number. No need to round down.

The teacher can hand out pizza to 8 students.

Answer is 8 students

N= 7/(7/8)

N= (7*8)/7

N= 56/7

N= 8

We can rewrite the equation of the circle as

[tex](x-0)^2+(y-0)^2=10^2[/tex]

so that we can be in the form

[tex](x-h)^2+(y-k)^2=r^2[/tex]

When you write the equation of a circle in this form, then the center is [tex](h,k)[/tex] and the radius is [tex]r[/tex].

So, in our case, the radius of the circle is 10.

To find the length of the bridge, we find the two points where the bridge crosses the lake (i.e. we solve the system between the equations of the line and the circle), and compute the distance between those points:

[tex]\begin{cases}y=x+2\\x^2+y^2=100\end{cases}\implies\begin{cases}y=x+2\\x^2+(x+2)^2=100\end{cases}[/tex]

Solving the second equation for x, we have

[tex]x^2+(x+2)^2=100 \iff x^2+x^2+4x+4=100\iff\\2x^2+4x-96=0 \iff x^2+2x-48=0\\\iff x=-8\ \lor\ x=6[/tex]

We use the first equation to compute the correspondent values of y:

[tex]x=-8\implies y=x+2=-6 \implies P_1 = (-8,-6)[/tex]

[tex]x=6\implies y=x+2=8 \implies P_1 = (6,8)[/tex]

Now, the distance between these two points is given by the pythagorean's theorem:

[tex]d = \sqrt{(-8+6)^2+(-6+8)^2} = \sqrt{4+4}=2\sqrt{2}[/tex]

The radius of the lake is 10 units. The length of the bridge is 14√2 units. We found this by solving the equations of the circle and the line representing the bridge.

The equation of the circular lake is given as  [tex]x^2 + y^2 = 100[/tex] . This equation is of the form  [tex](x -b)^2 + (y - c)^2 = r^2,[/tex] where the center of circle is at (b, c) and the radius is r. In this case, the center is at (0, 0), and the radius squared is 100. Therefore, the radius (r) is:

r = √100 = 10

So, the radius of the lake is 10 units.

The bridge is represented by the function y - x = 2, which can be rewritten as y = x + 2.

To find the points of intersection between this line and the circle, substitute y = x + 2 into the circle's equation  

[tex]x^2 +[/tex][tex]y^2 = 100:[/tex]

[tex]x^2 + (x + 2)^2 = 100[/tex]

Simplify this to:

[tex]x^2 + x^2 + 4x + 4 = 100[/tex]

[tex]2x^2 + 4x + 4 = 100[/tex]

[tex]2x^2 + 4x - 96 = 0[/tex]

Divide everything by 2:

[tex]x^2 + 2x - 48 = 0[/tex]

To solve this quadratic equation, use the quadratic formula x = (-b ± √([tex]b^2[/tex] - 4ac))/(2a), where a = 1, b = 2, and c = -48:

x = (-2 ± √([tex]2^2[/tex] - 4*1*(-48)))/(2*1)

x = (-2 ± √(4 + 192))/2

x = (-2 ± √196)/2

x = (-2 ± 14)/2

This results in two solutions:

x = (12)/2 = 6

x = (-16)/2 = -8

Thus, the points of intersection are (6, 8) and (-8, -6).

Finally, to find the length of the bridge, calculate the distance between these two points using the distance formula: d = [tex]\sqrt{ ((x2 - x1)^2 + (y2 - y1)^2)[/tex]

[tex]d = \sqrt{((6 - (-8))^2 + (8 - (-6))^2)[/tex]

[tex]d = \sqrt{((6 + 8)^2 + (8 + 6)^2)[/tex]

d = [tex]\sqrt{(14^2 + 14^2)[/tex]

d = [tex]\sqrt{(196 + 196)[/tex]

[tex]d = 14\sqrt{2}[/tex]

Therefore, the length of the bridge is [tex]14\sqrt{2}[/tex] units.

Answer:

The hypotenuse is  [tex]\sqrt{2}[/tex] times as long as either leg

Step-by-step explanation:

a true statement about a 45-45-90 triangle

The common ratio of 45-45-90 degree triangle is

x:x:[tex]\sqrt{2}x[/tex]

Suppose the value of x is 1  then the ratio becomes

1:1:[tex]\sqrt{2}[/tex]

1 is the side length of the triangle and [tex]\sqrt{2}[/tex] is the hypotenuse

The hypotenuse is  [tex]\sqrt{2}[/tex] times as long as either leg

Answer:

D

Step-by-step explanation:

Answer:

y = 3x - 14

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 4 is in this form with slope m = 3

• Parallel lines have equal slopes, hence

y = 3x + c ← is the partial equation of the parallel line

To find c substitute (4, - 2) into the partial equation

- 2 = 12 + c ⇒ c = - 2 - 12 = - 14

y = 3x - 14 ← equation of parallel line

The line that is parallel to y=3x-4 and passes through the point (4,-2) has the equation y=3x - 14. This is determined by knowing that parallel lines have the same slope and using the point-slope form of a line equation.

In Mathematics, two lines are parallel if they have the same slope. The line provided in this case is y=3x-4. The slope is 3, which we identify by taking the coefficient of x. Thus, any line parallel to this one will also have a slope of 3.

We also know the line we're seeking passes through the point (4,-2). We will use the point-slope form of a line equation, which is y - y1 = m(x - x1), where m is the slope, and (x1,y1) is a point on the line. Substituting the known values, we get: y - (-2) = 3(x - 4).

Simplifying this equation gives us the equation of the line that is parallel to y = 3x - 4 and passes through the point (4,-2) as: y = 3x -14.

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Answer:

35 square units

Step-by-step explanation:

multiply the base by the hight

Answer:

35 square units

Step-by-step explanation:

rectangle with vertices  (2,3), (7,3), (7,10), and (2,10)

Area of a rectangle = length times width

Apply distance formula to find the distance between the sides

[tex]D= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

points (2,3) and  (7,3)

[tex]D= \sqrt{(7-2)^2+(3-3)^2}=5[/tex]

points (7,3) and (7,10)

[tex]D= \sqrt{(7-7)^2+(10-3)^2}=7[/tex]

Area of the rectangle = length times width = 5 times 7 = 35

Answer:

Step-by-step explanation:

[tex]2.\\(a-b)^2=a^2-2ab+b^2\\\\x^2-16x=-8\\\\x^2-2(x)(8)=-8\\\\\text{We have}\ 2ab=2(x)(8).\ \text{Therefore}\ b=8.\\\\x^2-2(x)(8)=-8\qquad\text{add}\ 8^2=64\ \text{to both sides}\\\\x^2-2(x)(8)+8^2=-8+64\\\\(x-8)^2=56[/tex]

[tex]5.\\2x^2+x-1=2\qquad\text{subtract 2 from both sides}\\\\2x^2+x-3=0\\\\2x^2+3x-2x-3=0\\\\x(2x+3)-1(2x+3)=0\\\\(2x+3)(x-1)=0\iff 2x+3=0\ \vee\ x-1=0\\\\2x+3=0\qquad\text{subtract 3 from both sides}\\2x=-3\qquad\text{divide both sides by 2}\\\boxed{x=-\dfrac{3}{2}}\\\\x-1=0\qquad\text{add 1 to both sides}\\\boxed{x=1}[/tex]

[tex]6.\\2x^2-4x=0\qquad\text{divide both sides by 2}\\\\x^2-2x=0\\\\x(x-2)=0\iff x=0\ \vee\ x-2=0\\\\\boxed{x=0}\\\\x-2=0\qquad\text{add 2 to both sides}\\\boxed{x=2}[/tex]

Answer:

2/9

Step-by-step explanation:

Prob(consonant on first spin)

= 1/3

Prob(vowel on 2nd spin)

= 2/3

prob(event as stated)

= (1/3)(2/3)

= 2/9

Answer:

Option B) add 5 to both sides of the equation

Step-by-step explanation:

we have

[tex]x^{2}+18x+76=0[/tex]

step 1

Add 5 to both sides of the equation

[tex]x^{2}+18x+76+5=0+5[/tex]

[tex]x^{2}+18x+81=5[/tex]

step 2

Rewrite as perfect squares

[tex](x+9)^{2}=5[/tex]

Answer:

B) Add five to both sides of the equation

Step-by-step explanation:

I did this test on FLVS

To find the probability of a randomly chosen person playing baseball in a country, you need to use the given probabilities and conditional probability formula.

To find the probability that a randomly chosen person from this country plays baseball, denoted as B:

The probability that a randomly chosen person from the country plays baseball is 0.068.

To find the probability that a randomly chosen person from a particular country plays baseball, we will use the given information and apply Bayes' theorem.

We are given:

We are asked to find the probability that a randomly chosen person is a baseball player (P(B)).

Using Bayes' theorem, we can express P(B) as P(L and B) / P(L | B). Plugging in the known values:

P(B) = P(L and B) / P(L | B) = 0.017 / 0.250 = 0.068

Therefore, the probability that a randomly chosen person plays baseball is 0.068, precise to three decimal places.

Answer:

[tex]BC=11\ cm[/tex]

Step-by-step explanation:

step 1

Find the measure of the arc DC

we know that

The inscribed angle measures half of the arc comprising

[tex]m\angle DBC=\frac{1}{2}[arc\ DC][/tex]

substitute the values

[tex]60\°=\frac{1}{2}[arc\ DC][/tex]

[tex]120\°=arc\ DC[/tex]

[tex]arc\ DC=120\°[/tex]

step 2

Find the measure of arc BC

we know that

[tex]arc\ DC+arc\ BC=180\°[/tex] ----> because the diameter BD divide the circle into two equal parts

[tex]120\°+arc\ BC=180\°[/tex]

[tex]arc\ BC=180\°-120\°=60\°[/tex]

step 3

Find the measure of angle BDC

we know that

The inscribed angle measures half of the arc comprising

[tex]m\angle BDC=\frac{1}{2}[arc\ BC][/tex]

substitute the values

[tex]m\angle BDC=\frac{1}{2}[60\°][/tex]

[tex]m\angle BDC=30\°[/tex]

therefore

The triangle DBC is a right triangle ---> 60°-30°-90°

step 4

Find the measure of BC

we know that

In the right triangle DBC

[tex]sin(\angle BDC)=BC/BD[/tex]

[tex]BC=(BD)sin(\angle BDC)[/tex]

substitute the values

[tex]BC=(22)sin(30\°)=11\ cm[/tex]

Answer:

4153

Step-by-step explanation:

Let the original number be  [tex]\overline{abc3}[/tex]  [a is the number of thousands, b - the number of hundreds, c - the number of tens, 3 - the number of ones]

If you put the number 3 in the first position, the number will be [tex]\overline{3abc}[/tex]

New number is 738 less than old number.

When you subtract from 3 some number c and get 8, then you have to lend one ten and subtract this number c from 13. So, 13-5=8. Thus, c=5. Remember about lending! Now when you subtrat from 4 (not 5 because of lending) some number b and get 3, then b=1. Now when you subtract from 1 some number a and get 7, then you have to lend 1 from the number of thousands and subtract a from 11 to get 7, thus 11-4=7 and a=4.

We get initial number 4153 and  rewritten number 3415. Check the difference:

4153-3415=738

Answer:

4153

Step-by-step explanation: