Answer:
16 Liters of the correct answer.
Emil started his lemonade stand with 12 litres of Lemonade.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-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 litres of lemonade left. Let the total lemonade he started with is x litres. Now we will form an expression from the given data to calculate the value of x.
x - (x/2) -(1/4)(x/2) - ( 1/4)(x/2)(1/3) = 4
x - ( x/2) - (x/8) - ( x/24) = 4
[ 24x -12x -3x - x][24] = 4
8x = 96
x = 12 liters
Therefore Emil started his lemonade stand with 12 liters of Lemonade.
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HELPPP PLSSS
The center of an eclipse is located at (0, 0). One focus is located at (12, 0), and one directrix is at x = 14 1/2
The equation that represent the eclipse in the image attached is option A.
What is the ellipse equation about?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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Drag each number to the correct location on the table. Not all numbers will be used.
The table gives ratios between distance and time. Complete the table to form equivalent ratios.
The table for the complete ratios between distance and time is shown below.
What is the Ratio of Distance to Time?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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Drag the sliders.
Which slider creates scale copies of the shape?
What’s the length of three pipes, when combined they equal 72m, how do I find the answer
Answer:
Each pipe is 24m
Step-by-step explanation:
Given:
three pipescombined equal 72mlet the variable x represent the length of 1 pipeAlgebraic 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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given f(x)=x^2-6x+8 and g(x)=x^2-x-12, find the y intercept of (g/f)(x)
The y-intercept of the function (g/f)(x) is [tex]\mathbf{-\dfrac{3}{2} }[/tex]
What is the y-intercept of a given function?The y-intercept of a given function f(x) is those values of y when x is equal to zero.
From the information given:
f(x) = x² - 6x + 8g(x) = x² - x - 12The 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 y-intercept of g(x) = x² - x - 12 is: (0, -12)The y-intercept of f(x) = x² - 6x + 8 is: (0, 8)The division of the y-intercept is:
[tex]\mathbf{=-\dfrac{12}{8} }[/tex]
[tex]\mathbf{=-\dfrac{3}{2} }[/tex]
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Find all the missing sides and angles of this triangle.
I know angle a, and c but not the missing sides!
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
The price of a bungalow in 1990 was $850000. If there was a 125% increase in 2000, followed by a 30% decrease in 2013, what was the price in 2013?
Answer:
1,338,750$
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
Write the slope-intercept form of the equation of the line described.
1) through: (3, 0), parallel to y=2/3 x + 1
2) through: (4, 1), parallel to y= -1/2 x + 2
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.
(03.01 MC) The length of a rectangle is 5 units and its width is 4 units. What is the approximate length of the diagonal of the rectangle? O 5 units ( 03.01 MC ) The length of a rectangle is 5 units and its width is 4 units . What is the approximate length of the diagonal of the rectangle ?
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
The line on the graph passes through the points A (0, 6) and B (3, 0).
YA
a) Calculate the gradient of line AB.
b) Find the gradient of a line perpendicular
to AB.
c) Find the equation of the line passing
through point A and perpendicular
to AB.
B
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.
What is the slope or gradient?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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1. Which of the following is a polynomial written in standard form? Explain.
x² + 3x - 1
X
5-7x+4x²
3x³ 2x² + 5x-8
2√x +3
Find y. Help me please thank u:)
The value of y is 116 degrees
How to solve for y?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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Use the Law of Cosines to find the specified missing value. Approximate your answer to the nearest tenth.
If A = 60°, b = 20 ft, c = 30 ft, find B.
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]
On a coordinate plane, A line is drawn from point Fernando to point Maria. Fountain is labeled in between the 2. Fernando is at (negative 4, negative 2) and Maria is at (4, 2).
Fernando and Maria are at opposite sides of a park. They plan to meet later at a fountain that is located somewhere between them. Maria will arrive at the fountain first, before Fernando even leaves his starting location. The ratio of Maria's starting location to the fountain to Fernando's starting place is 5:3. What is the location of the fountain? Round to the nearest tenth, if necessary.
(, )
The location of the fountain as described in the task content is; (-1, -0.5).
What is the location of the Fountain?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:
19
Select the correct answer from each drop-down menu.
Mr. Montoya instructs the students in his math class to draw a rectangle with a certain area. Catlynn draws a rectangle with a length
18 centimeters and a width of 6 centimeters.
This proportional situation represents
variation.
The constant of variation, k, is equal to
if Sergio draws a rectangle with a length of 27 centimeters, the width of the rectangle must be
centimeters.
Reset
Next
The constant of variation, k, is equal to 108. This is an inverse proportion and when L is 27 cm, W is 4 cm
What is an equation?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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Which of the following is not a real number?
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]
The following two-column proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally:
The missing statement are:
4. ∠B ≅ ∠B; Reflexive Property of Equality.
5. ΔBDE ~ ΔBAC; Side-Angle-Side (SAS) Similarity Postulate.
What are the proofs?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
In this figure AB||CD and m<1=120°
What is m<5?
Answer:
120 degrees
Step-by-step explanation:
Angle 1 is congruent to angle 5 by the corresponding angles theorem.
what is m
help ASAP pleasee!!
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
x° = 121°∠BEA and ∠CED are vertical angles. Vertical angles are congruent, meaning that they have the same angle measure.
Therefore
|∠CED| = 121°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
y° = 32°|∠EDC| = 32°Leonard has built a crate for his car. The crate measures (x+5) ft by (x+1) fr by (2x+3) ft. Write an expression that represents the volume in the crate in cubic feet
Answer:
(x+5)(x+1)(2x+3) cubic feet
Step-by-step explanation:
(2a²-a²-7a+2)÷(a-2) Answer Please
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
. . . . .
pls help - Which number is the additive inverse of –5?
– One-fifth
0
Negative one-fifth
5
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
Which of the following is parallel to the line 2x+4y=16
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
Which is equal to K−L ?
K=[1325 7 18] L=[619 10 18]
[76−30]
[−7−630]
[7847570324]
[13251018]
The result of the subtraction of the vectors is: [706 -3 0].
What is the result of a subtraction of vectors?To subtract two vectors, we subtract the corresponding elements.
In this problem, the vectors are given as follows:
K = [1325 7 18].L = [619 10 18].The subtractions of the corresponding elements are:
1325 - 619 = 706.7 - 10 = -3.18 - 18 = 0.Hence the result is:
[706 -3 0].
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What is the product of (5−6i)(2−3i)
Answer:Multiply using the FOIL method, then combine the real and imaginary parts of the expression.
−
28+3i
Step-by-step explanation:
A roulette wheel has 37 numbers (0 through 36).
Use the Multiplication Principle of Probability to
calculate the probability of getting a 27 followed
by a 15. Write your answer as a fraction.
[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]
A building produces a shadow that is 73 feet long when the elevation of the sun is 59°. What is the height of the building to the nearest foot? It may be necessary to draw a picture to work through this problem.
The height of the building to the nearest foot is 121.5 ft.
How to find height of the building?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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Name the ray that is opposite . Type the proper name for the ray in the space provided. Type only uppercase letters and do not include symbols or spaces with your answer.
The ray that is opposite FH in the image given is: FE.
What is a Ray?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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The table shows populations for 4 countries, rounded to the nearest thousand. Which country's population decreased from 1985 to 2005?
A)Iceland
B)Portugal
C)Peru
D)Hungary
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.
ComparisonsWhenever 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)
QuestionThe "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.
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y - 4 = 1/4 (x-8). What
IS the slope-intercept form of the equation for this line?
O y= 1/4x -12
O y= 1/4x-4
O y=1/4x+2
O y= 1/4x+6
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