point e is located at -12 on the numbers line. Point f is located at 9 on the numbers line.

what is the distance between point E and point F on the number line?

Answer:

The number of apple bought is 3

The number of orange bought is 2  

Step-by-step explanation:

Given as :

The price of each apple = 27 p = 27 × 0.01 pound = 0.27 pound

The price of each orange = 36 p = 36 × 0.01 pound = 0.36 pound

The Total money paid for the fruits = 1.53 pounds

Let The Total number of apple bought = a

And The Total number of orange bought = o

Now, According to question

Total money paid for the fruits = Total number of apple bought × price of each apple + Total number of orange bought × price of each orange

Or, 0.27 a + 0.36 o = 1.53               ......A

Here The Total quantity of fruits bought is not given, so apply hit and trial method to calculate total number of each fruit

Let The a = 1   and  o = 1

So,  0.27 × 1 + 0.36 × 1 = 1.53    

∴   0.63 ≠ 1.53

Again

Put a = 2 , o = 2

So,  0.27 × 2 + 0.36 × 2 = 1.53    

∴   1.26 ≠ 1.53

Again

Put a = 3 , o = 3

So,  0.27 × 3 + 0.36 × 3 = 1.53    

∴   1.89 ≠ 1.53

Now, Let a = 3  , o = 2

So,  0.27 × 3 + 0.36 × 2 = 1.53    

∴   1.53 = 1.53

so, from hit and trial method , we get the number of apple = a = 3

And he number of orange = o = 2

Hence, The number of apple bought is 3

And The number of orange bought is 2 . Answer

Answer:

x = 30, y = 18

Step-by-step explanation:

Given the 2 equations

x - 2y = - 6 → (1)

x - y = 12 → (2)

Subtracting (2) from (1) term by term will eliminate the term in x

||(x - x) + (- 2y - (- y)) = (- 6 - 12), that is

- y = - 18 ( multiply both sides by - 1 )

y = 18

Substitute y = 18 into either of the 2 equations for value of x

Substituting in (2)

x - 18 = 12 ( add 18 to both sides )

x = 30

Answer: (30,18)

x - 2y = -6

x - y = 12

x - y = 12

- y = 12 - x

y = -12 + x

x - 2y = -6

x = -6 + 2*y

y = -12 + (-6+ 2*y)

y = -12 - 6 + 2*y

y - 2*y = -18

-y = -18

y = 18

y = -12 + x

18 = -12 + x

-x = -12 - 18

x = 12 + 18

x = 30

Answer:

5(4-1)

Step-by-step explanation:

5(4-1)

20-5

5x4= 20

5x1= 5

Answer:

The simplified fractional equivalent is [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

we know that

A terminating decimal is a decimal that ends. So, it's a decimal with a finite number of digits.

we have

[tex]0.25[/tex]

Let

[tex]x=0.25[/tex]

Multiply by 100 both sides

[tex]100x=25[/tex]

Divide by 100 both sides

[tex]x=\frac{25}{100}[/tex]

Simplify

Divide by 25 both numerator and denominator

[tex]x=\frac{1}{4}[/tex]

Answer:

He spend on cheese is $23.63.

Step-by-step explanation:

Given:

Chan Hee bought 3.4 pounds of cheese that  cost $6.95 per pound.

Now, to find the amount he spend on cheese.

As given the unit rate:

Cost of per pound of cheese = $6.95.

So, to get the amount Chan Hee spend on buying cheese we multiply the number of pounds of cheese to the cost of per pound of cheese.

[tex]Number\ of\ pounds\ of\ cheese\times cost\ of\ per\ pound\ of\ cheese.[/tex]

[tex]=3.4\ pounds\times \$6.95[/tex]

[tex]=\$23.63.[/tex]

Therefore, he spend on cheese is $23.63.

Answer:

Her gross pay is $118.50

Step-by-step explanation:

Firstly, find out how much she earn in each day :

Day 1 => 3.3hr × $7.50

= $24.75

Day 2 => 2.9hr × $7.50

= $21.75

Day 3 => 4.0hr × $7.50

= $30.00

Day 4 => 3.5hr × $7.50

= $26.25

Day 5 => 2.1hr × $7.50

= $15.75

Lastly, sum up altogether to calculate how much she earns in 5 days:

$24.75 + $21.75 + $30 + $26.25 + $15.75

= $118.50

Answer:

x=(-2+sqrt(11))/2, (-2-sqrt(11))/2.

Step-by-step explanation:

Apply the quadratic formula with a=4, b=8 and c=-7.

Answer:

The equation that shows the temperature over time is t(x) =  -7 + 3x

Step-by-step explanation:

Given:

Temperature at every morning =    -7°F

Rise in Temperature per hour = 3 degrees

To Find:

Equation that shows the temperature over time

Solution:

Let x be  the time (hours)

Now the temperature at time x (hours)  is

=> [tex]-7 + (\text{Number of hours} \times \text {Increase in temperature per hour)}}[/tex]

=>-7 + 3x

Hence at time x hours the temperature will be

t(x) =  -7 + 3x

Answer:

  (x, y) = (-1.8, -1.4)

Step-by-step explanation:

Modern graphing calculators make it trivially simple to solve many problems by graphing. It has become my favorite method.

The graph shows the solution to be (x, y) = (-1.8, -1.4).

___

If you're graphing by hand, it is usually convenient to start with the y-intercepts, then draw the lines with the required slopes. These equations are written in slope-intercept form, making that approach relatively simple.

The first equation has a y-intercept of (0, 4) and a slope of 3. So, another point on the graph will be left 1 and down 3 (as opposed to right 1 and up 3). That point is (-1, 1).

The second equation has a y-intercept of (0, -5) and a slope of -2. So, another point on the graph of that will be left 1 and up 2, to (-1, -3)

Answer:

B. 70

Step-by-step explanation:

[tex]7 \div 12 = \frac{7}{12} \\ 120 \times \frac{7}{12} = 70[/tex]

Answer:

B

Step-by-step explanation:

Given that for every 12 seeds, 7 grew into plants

Then for 120 seeds, that is 120 ÷ 12 = 10 times as many seeds, thus

number growing into plants = 10 × 7 = 70 → B

Answer:

B

Step-by-step explanation:

Quotient means divide. I just used a calculator to divide it.

Answer: e) 2(n+1)

Step-by-step explanation:

De las opcionas dadas, e) 2(n+1) es la correcta.

Empecemos por explicar la siguiente regla:

(número par)(número par)=número par

(número par)(número impar)=número par

(número impar)(número impar)=número impar

Ahora bien, en la expresión  2(n+1) el resultado de lo que se encuentra dentro del paréntesis va a ser multiplicado por 2, el cual es un número par, por lo tanto el resultado final va a ser un número par independientemente de si lo que está en el paréntesis es par o impar.

Por ejemplo, si elegimos 1 que es impar:

2(1+1)=2(2)=4

El resultado es par.

Si probamos con las otras opciones, los resultados serán impares:

a) 2n +1

2(1)+1=2+1=3 impar

b) n(n+2)

1(1+2)=1(3)=3 impar

c) n+(n-1)

1+(1-1)=1+0=1 impar

Answer:

76

Step-by-step explanation:

if w=45, you'd get 2(45-7) by replacing the variable (w) with its value (45)

so first you'd distribute 2 to the 45 and the 7

now it'd be:

90-14=76

so the answer would be 76! :)

Answer:

The answer is 76

Step-by-step explanation:

First you swap in the number like so: 2(45-7)

Then you figure out what's is the parentheses first going with PEMDAS like so : 2(38)

Finally you multiply the number getting your final answer which is :76

Answer:

58.50/6= $9.75 unit cost for each pizza

Answer:

y=-2x

Step-by-step explanation:

Answer:

y+2x=8

Step-by-step explanation:

when you put this in slope intercept form it will equal y=-2x+8 . Parallel lines need to have the same slope

Answer:

D

Step-by-step explanation:

We require to calculate the volume (V) of the cone and sphere.

The volume of a cone is calculated as

V = [tex]\frac{1}{3}[/tex]πr²h ( r is the radius and h the height )

Here diameter = 5, hence r = 5 ÷ 2 = 2.5, thus

V = [tex]\frac{1}{3}[/tex]π × 2.5² × 8 ≈ 52.36 cm³

The volume of a sphere is calculated as

V = [tex]\frac{4}{3}[/tex]πr³ ( r is the radius )

Here diameter = 5, hence r = 5 ÷ 2 = 2.5, thus

V= [tex]\frac{4}{3}[/tex]π × 2.5³ ≈ 65.45 cm³

Since volume of the sphere is greater than the volume of the cone

Thus when the ice cream melts it will overflow → D

Answer:

∠A ≈ 19.47°

Step-by-step explanation:

As you know , the angle that tangent makes with the radius at the point of tangency is 90°.

∴∠OKA = 90°

As  AO = 15 and OK = 5 ,

[tex]sin(A) = \frac{OK}{AO}[/tex]

[tex]sin(A) = \frac{5}{15} [/tex]

[tex]sin(A) = \frac{1}{3} [/tex]

∠A = [tex]sin^{-1} (\frac{1}{3} )[/tex]

∠A ≈ 19.47°

Answer:

[tex]\mathbf{m\angle A = sin^{-1}(\frac{1}{3}) \approx 19.47^{\circ}}[/tex]

Step-by-step explanation:

This question involves some basic knowledge of trigonometric function. The following formula only works for right angled triangles.

[tex]\mathbf{sin(x) = \frac{perpendicular}{hypotenuse}}[/tex]

In ΔAKO,

m∠AKO = 90°

Therefore ΔAKO is a right angled triangle. If we take ∠A into consideration then base will be AK, perpendicular will be OK and hypotenuse will be AO.

AO = 15

OK = 5

[tex]\therefore \mathrm{sin(\angle A) = \frac{OK}{AO} = \frac{5}{15} = \frac{1}{3}}[/tex]

[tex]\mathrm{sin(\angle A)=\frac{1}{3}}[/tex]

[tex]\mathrm{\angle A=sin^{-1}(\frac{1}{3})}[/tex]

To calculate [tex]\mathrm{sin^{-1}(\frac{1}{3})}[/tex] use scientific calculator

value of [tex]\mathrm{sin^{-1}(\frac{1}{3})}[/tex] is approximately equal to 19.47°

Therefore [tex]\mathbf{m\angle A \approx 19.47}[/tex]

(NOTE : When a line passing through center of a circle, is drawn to a tangent at the point of tangency then the angle made between then is 90°

Therefore m∠AKO = 90°)

Answer:

[tex]x \approx -0.208[/tex]

Step-by-step explanation:

By applying logarithms to each side of the equation and some algebraic handling:

[tex]x+2 = \log_{4} 12[/tex]

[tex]x + 2 = \frac{\log_{10} 12}{\log_{10} 4}[/tex]

[tex]x = \frac{\log_{10}12}{\log_{10}4} - 2[/tex]

[tex]x \approx -0.208[/tex]

Final answer:

To solve the equation

for x, you can use the change of base formula log base b of y equals log y over log b. By following the steps, you should find the solution to be x ≈ -0.086.

Explanation:

To solve the equation

for x, we can use the change of base formula log base b of y equals log y over log b. Let's solve it step by step:

Therefore, the solution to the equation

is approximately x = -0.086.

Answer:

If each youth saves $10 daily, their weekly savings would be $1400. So they donated $1400 to the church.

Step-by-step explanation:

Let the daily pay plan for each youth be $y

Daily pay plan for 20 youth = $20y

Weekly pay plan = 7×20y = $140y

Assuming each youth saves $10 daily

Daily savings for 20 youth = 20×$10= $200

Weekly savings for 20 youth = 7×$200= $1400

If they used the early pay plan ($140y) to go swimming, they saved $1400 which they donated to the church.

Answer:

$375 saved or roughly 33%.

Step-by-step explanation:

With daily plan;

(15)4.00 = 60.00  

(25)60.00 = $1,500.00

If the youth group saved up enough for each of them to swim 15 times and 25 students are attending, they originally had $1,500.00 saved for the trip.  

With early pay;

(25)45.00 = $1,125.00

1,500.00 - 1,125.00 = $375 saved or roughly 33%.

Hope this helps! And please, do not copy-paste this answer. Write it in your own words, thanks <33

Answer:

S = 2 - 0.25W

Step-by-step explanation:

A lake near the Arctic Circle is covered by a  2 meters thick sheet of ice during the cold winter months.

At the warm air of spring gradually melts the ice thickness gradually.

Therefore, the equation that models the situation is S = 2 - bW ....... (1), where S is the remaining thickness of the ice sheet and W is the number of weeks passed and b is the rate of decrease of ice sheet thickness with respect to the number of weeks.

Now, putting W = 3 weeks and S = 1.25 meters in the equation (1) we get,

1.25 = 2 - 3b

⇒ 3b = 0.75

⇒ b = 0.25 meters per week.

Therefore, the equation (1) becomes S = 2 - 0.25W (Answer)

Answer:

  Max is correct

  If one reflects a figure across the x-axis, the points of the image can be found using the pattern (x, y) ⇒ (x, –y).

  If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) ⇒ (–x, y).

  Taking the result from the first reflection (x, –y) and applying the second mapping rule will result in (–x, –y), not (y, x), which reflecting across the line should give.

Step-by-step explanation:

The answer above pretty well explains it.

The net result of the two reflections will be that any figure will retain its orientation (CW or CCW order of vertices). It is equivalent to a rotation by 180°. The single reflection across the line y=x will reverse the orientation (CW ⇔ CCW). They cannot be equivalent.

Max is correct in stating that two reflections, one across the x-axis and another across the y-axis, will not result in a reflection across the line y = x for a pre-image in quadrant II. Josiah's conjecture is incorrect. Statements that will help Max prove his conjecture include reflecting a figure across the x-axis and the y-axis, and how the coordinates of the image points change in each reflection.

Max is correct. When a figure is reflected across the x-axis, the y-coordinate of each point is negated, resulting in an image in a different quadrant. Therefore, reflecting a figure across the x-axis from quadrant II will place the image in quadrant III. Similarly, when a figure is reflected across the y-axis, the x-coordinate of each point is negated, resulting in an image in a different quadrant. Reflecting a figure across the y-axis from quadrant III will place the image in quadrant IV.

A figure that is reflected from quadrant II to quadrant IV will be reflected across the line y = x. However, reflecting a figure across the x-axis followed by a reflection across the y-axis will result in an image that is reflected across the line y = -x, not y = x. Therefore, Josiah's conjecture is incorrect.

The following statements will help Max prove his conjecture:

Therefore, Max's statements are correct and Josiah's conjecture is incorrect.

the answer is 5.8 x 10-7m

your welcome

The required wavelength of the yellow light is [tex]5.8\times10^{-7}[/tex] m

The correct option is (A).

Wavelength:

The wavelength can be calculated when frequency and speed of the wave are given as

wavelength [tex]\lambda[/tex] = [tex]\frac{v}{f}[/tex]

where v is the velocity of the wave and f be the frequency of the wave.

Here we have given that

The frequency f = [tex]5.2 \times10^{14}[/tex] Hz

The speed v = [tex]3 \times10^{8}[/tex] m/s

Therefore substitute into above formula

Wavelength [tex]\lambda[/tex]= [tex]\frac{3\times10^{8}}{5.2\times10^{14}}}[/tex]

Wavelength [tex]\lambda[/tex] = [tex]\frac{3}{5.2}\times10^{8-14}[/tex]

Wavelength [tex]\lambda[/tex] = [tex]0.5769\times10^{-6}[/tex]

Wavelength [tex]\lambda[/tex] = [tex]0.5769\times10^{-6}[/tex]

Wavelength [tex]\lambda[/tex] = [tex]5.769\times10^{-7}[/tex]

Wavelength [tex]\lambda[/tex]= [tex]5.8\times10^{-7}}[/tex] m

Therefore the correct option is (A).

This is the conclusion to the answer

Learn more about wavelength here-

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Answer:

y = 5/2x + 5

Step-by-step explanation:

Your b value is the place where the line crosses the y-axis. So, we can tell right away the b value in the equation is 5.

I'll use negative 2 as the point to find the slope. You go down 5, so we have -5, and go left 2, so -2. 2 negatives make a positive, so the slope is 5/2.

Final equation -

y = 5/2x + 5

Answer: [tex]2z^{2} + 14 z +6[/tex] and [tex]2(z^{2} + 7 z +3)[/tex]

Step-by-step explanation:

We have the following expression:

[tex]z+(z+6)z+(z+6)z+(z+6)[/tex]

Let's solve it:

[tex]z+z^{2}+6z+z^{2}+6z+z+6[/tex]

We have this result:

[tex]2z^{2} + 14 z +6[/tex]

However if we apply coomon factor 2, we will have a simplified result:

[tex]2(z^{2} + 7 z +3)[/tex]

Answer:

The average rate of change on [1,3] is [tex]\frac{1}{2}[/tex] the average rate of change on [2,4]. The average rate of change on [1,3] is [tex]\frac{2}{5}[/tex] the average rate of change on [1,5]. So the function can not be linear.

Step-by-step explanation:

See the table attached.

The average rate of change on [1,3] is = [tex]\frac{32 - 8}{3 - 1} = 12[/tex]

The average rate of change on [2,4] is = [tex]\frac{64 - 16}{4 - 2} = 24[/tex]

Again, the average rate of change on [1,5] is = [tex]\frac{128 - 8}{5 - 1} = 30[/tex]

Therefore, the average rate of change on [1,3] is [tex]\frac{1}{2}[/tex] the average rate of change on [2,4]. The average rate of change on [1,3] is [tex]\frac{2}{5}[/tex] the average rate of change on [1,5]. So the function can not be linear. (Answer)

Answer:

Profit is positive and bill is negative I believe. I hope this helped!

Answer:

Both ( if I had to choose one I would choose negative)

Step-by-step explanation:

The reason for my answer is because it could teach responsibility and time management. But it can also leave people without a home if not payed on time as well as hungry families.

Answer:

y-6=-1/4(x+2)

Step-by-step explanation:

y-3=4(x+2)

y=4x+8+3

y=4x+11

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

Perpendicular means negative reciprocal of the slope.

y-6=-1/4(x-(-2))

y-6=-1/4(x+2)

Answer:

hi there!

the correct answer to this question is: 78 ft^3

Step-by-step explanation:

you use the volume formula: V= Base * height

base: 1 * 13

height: 6

so multiply 13 by 6 and you get 78

Answer:

True false true

Step-by-step explanation:

TRUE, the student lunch price was generally increasing between 2000 and 2015 as the equation [tex]y=0.057x+1.150[/tex]  is a linearly increasing function.

TRUE, the student lunch price was changed by approximately [tex]5.7\rm cents[/tex]  a year.

FALSE, the student price in 2015 was approximately $1.15.

The best-fit line for the data has the equation  [tex]y=0.057x+1.150[/tex] , where [tex]x[/tex] is the number of years since 2000 and [tex]y[/tex]  is the student lunch price, in dollars.

So, it can be seen here from the best-fit line equation that it is a linearly increasing function so, the student lunch price was generally increasing between 2000 and 2015.

Now, differentiating the given best-fit line for the data has the equation  [tex]y=0.057x+1.150[/tex] with respect to [tex]x[/tex] to determine the approximated change of the lunch price per year

[tex]\dfrac{dy}{dx}=\dfrac{d}{dx}(0.057x+1.150)\\\dfrac{dy}{dx}=\$0.057\\\dfrac{dy}{dx}=5.7\rm cents[/tex]

And, [tex]2015[/tex] is [tex]15[/tex] years from the year [tex]2000[/tex] so, substitute the value of the parameter [tex]x=15[/tex] in the best-fit line equation, we get

[tex]y=0.057\times 15 +1.150\\y=0.855+1.150\\y=2.005[/tex]

So, the lunch price in 2015 was approximately [tex]\$2.005[/tex].

Hence, the first two statements are TRUE while the last statement is FALSE.

Learn more about the best-fit line equation here:

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Step-by-step explanation:

3×+3(x+y) is equal to 6x+3y