Using a system of equations, it is found that £52 was originally shared.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
Variable x: Angela's share.Variable y: Michelle's share.Variable z: Daniel's share.Angela and Michelle shared some money in the ratio 4: 9, hence, considering t as the total:
[tex]x = \frac{4t}{13}[/tex].[tex]y = \frac{9t}{13}[/tex]Angela gave Daniel half her share.Michelle gave Daniel a third of her share. Daniel was given a total of £20, hence:
[tex]\frac{x}{2} + \frac{y}{3} = 20[/tex]
[tex]\frac{4t}{26} + \frac{9t}{39} = 20[/tex]
[tex]\frac{12t + 18t}{78} = 20[/tex]
30t = 20 x 78
t = 20 x 78/30
t = £52.
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(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
. . . . .
Given a decile cut point value of 10.4, where the tenth sequential value is 32 and the eleventh value is 42, what is the actual decile value
The actual decile value is 126.6
To get the actual decile value, the decile formula is used. The formula used is:
Di = I (n+1) / 10 multiplied by (n - n+1)/10
This implies that the decreased fee, which in this case is 32 + 1, is delivered to the entire multiplication of the cut point 10.4, and the difference among the more tremendous value whilst organized in the ascending fee and the newly brought decreased value.
This gives:
33 + 10.4 * (42 - 33)
= 126.6
The actual decile value is 126.6
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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]
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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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
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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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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Which expression is equal to the equation?
Answer: [tex]-11\sqrt{7}[/tex]
Step-by-step explanation:
To find the expression equal to the given, we will simplify the original.
Given:
[tex]\displaystyle 2\sqrt{28} -5\sqrt{63}[/tex]
Simplify:
[tex]-11\sqrt{7}[/tex]
Answer: [tex]-11\sqrt{7}[/tex]
Answer: [tex]-11\sqrt{7}[/tex]
Step-by-step explanation:
[tex]2\sqrt{28}-5\sqrt{63}[/tex]
= [tex]2\sqrt{4*7}-5\sqrt{7*9}[/tex]
= [tex]2*\sqrt{4}*\sqrt{7} - 5*\sqrt{7} *\sqrt{9}[/tex]
= [tex]2*2*\sqrt{7} - 5*\sqrt{7}*3[/tex]
= [tex]4\sqrt{7} - 15\sqrt{7}[/tex]
= [tex]-11\sqrt{7}[/tex]
Find the equation of the horizontal line at a height of -3.9.
y = -3.9x
x = -3.9
y = -3.9
the height must be an integer
The equation of the line will be y = -3.9, and the height after rounding off will be -4.
What is a straight line?
A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The horizontal line can be defined as:
y = a
Where a is the constant.
Here a = -3.9
y = -3.9
The height = -3.9 ≈ -4
Thus, the equation of the line will be y = -3.9, and the height after rounding off will be -4.
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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:
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
Can 10 people be divided into two groups with a ratio of 1 : 2? Explain.
No
Let the groups be x and 2x
x+2x=103x=10x=10/3Its decimal not natual so can't be divided
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:
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.
NOTE: Angles not necessarily drawn to scale.
Answer:
x = 100 degrees
Step-by-step explanation:
Angle AEG is vertical to angle BEF. Vertical angles are congruent angles. The measure of angle BEF is 100 degrees (80 + 20 = 100), so angle AEG is 100 degrees which makes the measure of x 100 degrees.
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
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]
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.
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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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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Find the value of x. Round to the
nearest tenth.
9
4
X =
Step-by-step explanation:
ATTACHED IS THE SOLUTION!Drag the sliders.
Which slider creates scale copies of the shape?
Select the correct answer from each drop-down menu. Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system? The graph represents the system of inequalities . The test point satisfies both of the inequalities in the system represented by the graph.
The system of inequality that the graph represents is E. 2x + 3y is less than or equal to 4 and 2x + 2y is less than or equal to 3
How to illustrate the graph?In the graph, when 2x + 3y = 4
3y = 4 - 2x
y = -2/3x + 4/3
When 2x + 2y = 3
2y = -2x + 3
y = -x + 3/2
On the graph, -2/3x + 4/3 is illustrated on the first line while -x + 3/2 is illustrated on the second line.
Therefore, the correct option is E.
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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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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:
Find the value of x. please helpp
Answer:
A
Step-by-step explanation:
given 2 secants drawn from an external point to the circle , then
the product of the measures of one secant's external part and that entire secant is equal to the product of the other secant's external part and that entire secant, that is
9(9 + 2 + 3x) = 10(10 + 2x + 2)
9(11 + 3x) = 10(12 + 2x) ← distribute parenthesis on both sides
99 + 27x = 120 + 20x ( subtract 20x from both sides )
99 + 7x = 120 ( subtract 99 from both sides )
7x = 21 ( divide both sides by 7 )
x = 3
Answer:
(A). 3
Step-by-step explanation:
[ 9 + ( 2 + 3x )] × 9 = [ 10 + ( 2x + 2 )] × 10
27x + 99 = 20x + 120
7x = 21
x = 3
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
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
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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