Emil is running a lemonade stand. He sells half of his lemonade in the morning, a quarter of what was left at lunchtime, and a third of what was left in the afternoon. When he closes for the day, he has 4 liters of lemonade left. How many liters of lemonade did he start the day with?

Answer:

120 degrees

Step-by-step explanation:

Angle 1 is congruent to angle 5 by the corresponding angles theorem.

Answer:

5

Step-by-step explanation:

a number and its additive inverse sum to zero , then

the additive inverse is the opposite of the number

the opposite of - 5 is + 5

and - 5 + 5 = 0

Answer:

y = (1/4)x + 2

Step-by-step explanation:

y - 4 = 1/4 (x-8)

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

y = (1/4)x + 2

The height of the building to the nearest foot is 121.5 ft.

The height of the building can be found using trigonometric ratios.

Therefore,

tan 59° = opposite / adjacent

tan 59°= h / 73

cross multiply

h = 73 tan 59°

h = 73 × 1.66427948235

h = 121.492402212

h = 121.5 ft

Therefore, the height of the building to the nearest foot is 121.5 ft.

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Answer:

(x+5)(x+1)(2x+3) cubic feet

Step-by-step explanation:

Answer:

[tex]\sqrt{-3}[/tex]

Step-by-step explanation:

Since each of these answers contain a radical, you want to find the one that has a negative value, because technically sqrt(some negative number) isn't defined, or rather it has no real solution. This is because you can rewrite a radical as [tex]\sqrt{a * b} = \sqrt{a} * \sqrt{b}[/tex]. And since [tex]i = \sqrt{-1}[/tex] you can rewrite [tex]\sqrt{-3}[/tex] as [tex]\sqrt{-1} * \sqrt{3}[/tex] which becomes [tex]i\sqrt{3}[/tex]

[tex]\large\boxed{\frac{1}{1369}}[/tex]

We'll assume that there is an equal probability of any position on the wheel, so a [tex]\frac{1}{37}[/tex] chance for any given number.

We must take the probability of getting a 27, then the probability of getting a 15, and multiply them together to find the chances that they both happen in a row.

[tex]\frac{1}{37}\cdot\frac{1}{37}=\boxed{\frac{1}{1369}}[/tex]

Answer:

  D)  Hungary

Step-by-step explanation:

You are being asked to compare 4 pairs of numbers. The population will have decreased if the number in the 2005 column is less than the number in the 1985 column.

Whenever you compare numbers, you start with the most-significant digit. If the most-significant digit has a higher place value, the number is larger. If the digits have the same place value, the number with the larger digit is larger. If no determination can be made by these comparisons, then the digits to the immediate right are compared.

  27,... > 19,...  2 > 1 in the 10-millions place

  10,... > 9,...  1 has a greater place value

  29... > 24...  comparison shifts to the 10-thousands place: 9 > 4

  10,058,... < 10,649,... . . . . the population decreased (0 < 6)

The "population decreased" result is found on the last line of the table, identified by the Country name "Hungary."

Hungary's population decreased from 1985 to 2005.

Answer:

√41, or about 6.4 units

Step-by-step explanation:

[tex] \sqrt{ {5}^{2} + {4}^{2} } = \sqrt{25 + 16} = \sqrt{41} [/tex]

√41 is about 6.4 units

Answer:

24 and 25

Step-by-step explanation:

Angle a will be 20° because angle a+angle b=90°

angle c is 90°(right angle)

now to find the sides we will have to do a Pythagoras theorem for this indirectly therefore:

7²=49/2 sides

=24.5

therefore one side will be 24 the other side will be 25

if I am right mark as brainliest

Answer:Multiply using the FOIL method, then combine the real and imaginary parts of the expression.

−

28+3i

Step-by-step explanation:

The result of the subtraction of the vectors is: [706 -3 0].

To subtract two vectors, we subtract the corresponding elements.

In this problem, the vectors are given as follows:

The subtractions of the corresponding elements are:

Hence the result is:

[706 -3 0].

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Answer:

Option C: y=-1/2x + 8

Step-by-step explanation:

So we have the options:

A) y=2x+5

B) y=-1/2x+4

C)y=-1/2x+8

D)y=-2x+5

But first let's define what parallel even is. When two lines are parallel it means that there slope is the same value and the same sign, while there y-intercepts are different, because if they were the same, then they wouldn't be parallel, they would just be the same exact line.

So we're given the equation in standard form. To find the slope we can change it so it's in the form of y=mx+b. This can be done by simply isolating y. The reason we want it in the slope-intercept form is because m represents the slope and b represents the y-intercept. m is the slope because as x increases by 1 the y-value will increase by m. So the "rise" will be m and the "run" will be 1, thus the slope will be m/1 or in other words m because the slope is defined as rise/run. So let's start the steps to isolating y

Original equation

2x+4y=16

Subtract 2x from both sides

4y=-2x+16

Divide both sides by 4

y = -1/2x + 4

Here we have it in slope-intercept form. In this case the slope, or m, is -1/2 and the y-intercept or b is 4. So now let's look at the other equations.

Option A: This equation has a slope of 2, which is not the same as -1/2 so it is not parallel

Option B: This equation has a slope of -1/2 which is the same as -1/2 so it might be parallel. But look at the y-intercept it's 4, that's the same y-intercept as the original equation. This means the two equations are equal and not parallel

Option C: This equation has a slope of -1/2 which is the same as -1/2 so it might be parallel. It has a y-intercept of 8 which is not the same as 4, so the two lines are parallel and not equal! This is the answer

Answer:

Each pipe is 24m

Step-by-step explanation:

Given:

Algebraic Expression:

3 pipes times length equals 72m (the total length)

3x = 72, we want x to be alone so divided both sides by 3

3x / 3 = 72 / 3

x = 24

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The table for the complete ratios between distance and time is shown below.

The ratio of distance to time, given that 280 miles will be covered in 4 hours is: 280/4 = 70 miles per hour.

Thus, for 2 hours: 2(70) = 140 miles distance.

For 350 miles, we would have: 350/70 = 5 hours time.

For 6 hours: 6(70) = 420 miles distance.

For 8 hours: 8(70) = 560 miles distance.

For 700 miles, we would have: 700/70 = 7 hours time.

The complete table is shown in the image below.

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Answer:

1) y = 2/3x - 2

2) y = -1/2x + 3

Step-by-step explanation:

1) Parallel lines have the same slopes. Write it in standard form (y = mx + c), then substitute the values of the coordinates into the equation.

y = 2/3x + c

0 = 2/3(3) + c

0 = 2 + c

0 - 2 = c

- 2 = c

Therefore, the slope-intercept form for the first part is y = 2/3x - 2.

2) Parallel lines have the same slopes. Write it in standard form (y = mx + c), then substitute the values of the coordinates into the equation.

y = -1/2x + c

1 = -1/2(4) + c

1 = -2 + c

1 + 2 = c

3 = c

Therefore, the slope-intercept form for the second part is y = -1/2x + 3.

The missing statement are:

4.  ∠B ≅ ∠B; Reflexive Property of Equality.

5.   ΔBDE ~ ΔBAC; Side-Angle-Side (SAS) Similarity Postulate.

The missing statement are number 4 and 5.

If we say that  4. ∠B ≅ ∠B; Reflexive Property of Equality then:

∠B ≅ ∠B,

Note that  there are two triangles, which are ΔABC and ΔDBE and we also have ∠BDE ≅∠BAC and ∠B ≅ ∠B,

∠BDE + ∠B + ∠BED = 180°

∠BAC + ∠B +  ∠BCA = 180°

Hence, ∠BED = ∠BCA Substitution property of equality

That  birth ΔABC ~ ΔDBE,which is Angle Angle Similarity Postulate

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Answer: 4.∠B ≅ ∠B; Reflexive Property of Equality

5. ΔBDE ∼ ΔBAC; Angle-Angle (AA) Similarity Postulate

Step-by-step explanation:

I just took the test; this exact order should be correct. :D

The y-intercept of the function (g/f)(x) is [tex]\mathbf{-\dfrac{3}{2} }[/tex]

The y-intercept of a given function f(x) is those values of y when x is equal to zero.

From the information given:

The division of the function (g/f)(x) can be computed as:

[tex]\mathbf{y= \dfrac{x^{12}-x -12}{x^2-6x+8}}[/tex]

The division of the y-intercept is:

[tex]\mathbf{=-\dfrac{12}{8} }[/tex]

[tex]\mathbf{=-\dfrac{3}{2} }[/tex]

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The sum of angles of a triangle equals 180°.

Therefore:

|∠EAB| + |∠ABE| + |∠BEA| = 180°

Susbtitute

|∠EAB| = 14°

|∠ABE| = 45°

|∠BEA| = x°

14° + 45° + x° = 180°

59° + x° = 180°    |subtract 59° from both sides

∠BEA and ∠CED are vertical angles. Vertical angles are congruent, meaning that they have the same angle measure.

Therefore

In ΔCDE:

|∠CED| + |∠DCE| + |∠EDC| = 180°

Substitute:

|∠CED| =121°

|∠DCE| = 27°

|∠EDC| = y°

121° + 27° + y° = 180°

148° + y° = 180°    |subtract 148° from both sides

Answer:

2a^2 + 3a - 1 ,

Step-by-step explanation:

I am assuming you mean

2a^3-a^2-7a+2

By long division:

a - 2 ) 2a^3 -   a^2 - 7a +  2 ( 2a^2 + 3a - 1 <------- Quotient

          2a^3 - 4a^2

                     3a^2 - 7a

                     3a^2 - 6a

                                -a + 2

                                -a + 2

                                 . . . . .

The value of y is 116 degrees

To solve for y, we make use of the following angle theorem.

The angle at the center is twice the angle at the circumference.

So, we have:

y = 2 * 58

Evaluate the product

y = 116

Hence, the value of y is 116 degrees

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The equation for the line passing through point A and perpendicular to AB will be y-0.5x=6, the gradient of line AB is -2, and the gradient of a line perpendicular to AB is 0.5.

A numerical assessment of a line's angle relative to the ground is known as the slope.

Given data;

m₁ is the slope of line AB

m₂ is the slope of a line perpendicular to AB

The coordinate points are,

A,(x₁,y₁)= (0, 6)

B,(x₂,y₂)=(3, 0).

The gradient of line AB;

[tex]\rm m_{{1} }= \frac{y_2-y_1}{x_2-x_1} \\\\ \rm m_{{1} }= \frac{0-6}{3-0} \\\\ m_{{1} }=-2[/tex]

The slope of the lines has a perpendicular relation is -1;

m₁ × m₂ = -1

(-2) × m₂ = -1

m₂ = 1/2

m₂ = 0.5

The equation of the line passing through point A and perpendicular to AB;

(y - y₁) = m₂(x-x₁)

(y-6)=0.5(x-0)

y-6 = 0.5 x

y-0.5x=6

Hence, the gradient of line AB, the gradient of a line perpendicular to AB, and the equation of the line passing through point A and perpendicular to AB will be -2,0.5 and y-0.5x=6.

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The ray that is opposite FH in the image given is: FE.

A ray is a straight line that starts from one end and extends infinitely towards the opposite end.

We are asked to find the ray that is opposite to FH. This means the ray opposite to FH will definitely start from point B and extends to the opposite direction.

Ray FE is opposite FH.

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Answer:

40.9

Step-by-step explanation:

Law Of Cosines:

   [tex]cos(A)=\frac{b^2+c^2-a^2}{2bc}[/tex]

   This can generally be understand as the cosine(angle) = the sum of squares of the two other sides - the opposite side squares divided by 2 times the other two sides

   If this is to confusing to understand I'll just provide the formula for the other two angles which is essentially the same thing just different variables

   [tex]cos(B)=\frac{a^2+c^2-b^2}{2ac}\\\\cos(C)=\frac{a^2+b^2-c^2}{2ab}[/tex]

Anyways for the law of cosines we need all three sides, but since we're given the two other sides, we can also rearrange the equation to solve for the other missing side.

Original Equation

[tex]cos(A)=\frac{b^2+c^2-a^2}{2bc}\\[/tex]

Multiply both sides by 2bc

[tex]cos(A)*2bc=b^2+c^2-a^2[/tex]

Add a^2 to both sides

[tex]cos(A)*2bc+a^2=b^2+c^2[/tex]

Subtract 2bc * cosA from both sides

[tex]a^2=b^2+c^2-2bc*cos(A)[/tex]

So this can be applied for any side, and it can be generally seen as: side ^2 = sum of squares of other two sides - 2 times the other two sides * cos(opposite angle of the original side). If that's to confusing you can also just look at the other formulas which are essentially the same just different variables

[tex]b^2=a^2+c^2-2ac * cos(B)\\c^2=a^2+b^2-2ab*cos(C)[/tex]

anyways, applying this formula we get the equation:

[tex]a^2=20^2+30^2-2(20)(30)*cos(60)[/tex]

Square and multiply values you get

[tex]a^2=400+900-1200*cos(60)[/tex]

Now add the values and you can calculator cos(60) using a calculator or using the unit circle, both should give the same value

[tex]a^2=1300-1200(0.5)[/tex]

Multiply

[tex]a^2=1300-600[/tex]

Simplify

[tex]a^2=700[/tex]

Take the square root of both sides

[tex]a\approx 26.4575[/tex]

So now use this to solve for B using the original law of cosines equation. Plugging in all the sides you get the equation:

[tex]cos(B)=\frac{26.4575^2+30^2-20^2}{2(26.4575)(30)}[/tex]

Square values and simplify denominator

[tex]cos(B)=\frac{700+900-400}{1,587.451}[/tex]

Simplify numerator

[tex]cos(B)=\frac{1200}{1,587.451}[/tex]

Convert to decimal

[tex]cos(B)\approx 0.755[/tex]

Take the inverse cosine of both sides

[tex]B \approx cos^{-1}(0.755)[/tex]

Approximate this using a calculator

[tex]B\approx 40.8934[/tex]

Round to the nearest tenth

[tex]B\approx40.9[/tex]

The location of the fountain as described in the task content is; (-1, -0.5).

According to the task content, the locations of Fernando and Maria are given as; (-4, -2) and (4,2) respectively and the ratio of division is expected to be; 5: 3.

Hence, the coordinates of the fountain can be evaluated as;

x = (4) - (4-(-4)) × (5/8) = -1.

y = 2 - (2-(-2)) × (5/8) = -0.5

Hence, it follows that the coordinates of the fountain location is; (-1, -0.5) since the fountain is closer to Fernando than Maria.

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Answer:

-1 AND -0.5

Step-by-step explanation:

Answer:

1,338,750$

Step-by-step explanation:

1990 price was 850,000

in 2000

850,000 + 125% = 1,062,500

850,000 + 1,062,500 = 1,912,500

in 2013

1,912,500 - 30% = 573,750

1,912,500 - 573,750 = 1,338,750

The constant of variation, k, is equal to 108. This is an inverse proportion and when L is 27 cm, W is 4 cm

An equation is an expression that shows the relationship between two or more numbers and variables.

The length (L) is inversely proportional to the width (W), hence:

L = k/W

18 = k/6

k = 108

When L = 27:

27 = 108/W

W = 4

The constant of variation, k, is equal to 108. This is an inverse proportion and when L is 27 cm, W is 4 cm

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The equation that represent the eclipse in the image attached is option A.

We were given:

The center of an ellipse  (0, 0).

One focus is located at (12, 0),

One directrix is at x = 14 1/12.

To Find the equation of the ellipse will be:

The standard equation of an ellipse is :  [tex]\frac{(x- h )^ 2}{a^2} + \frac{(y - k)^2}{b^2}[/tex]

Note that c = 12

One need to compare the equation of directrix with the above equation:

a^2/c = 14[tex]\frac{1}{12}[/tex]

a^2/c = 169/12

Then Substitute the value c=12 and solve for a.

a^2/12 = 169/12

a² = 169

a = 13

Use the equation of  c² = a² - b² to find b.

= (12)² = (13/12)² - b²

b²= 169-144

b²= 25

b = 5

Then substitute the value of a and b into the standard equation of the ellipse.

[tex]\frac{(a- h )^ 2}{a^2} + \frac{(y - k)^2}{b^2}[/tex]

[tex]\frac{(x- 0 )^ 2}{13^2} + \frac{(y - 0)^2}{5^2}[/tex]

Therefore: [tex]\frac{(x)^ 2}{13^2} + \frac{(y)^2}{5^2}[/tex]

Hence, The equation that represent the eclipse in the image attached is option A.

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