the answer is 22464, because if they marched 1872 yard for the first side, you can multiply it by 3 because there are 3 feet in one yard. Then you multiply that by 4 because there are 4 sides in a square
Can anyone answer 17-19 for me ??? Please
Step-by-step explanation:
17.
Opposite angles of a parallelogram are equal.
So [tex]3y^{\circ}=123^{\circ}[/tex]
⇒ y= [tex](\frac{123}{3})^ {\circ}[/tex]
and sum of adjacent angle is = [tex]180^{\circ}[/tex]
Therefore, [tex](2x-5)^{\circ} + 123^ {\circ}=180^{\circ}[/tex]
⇒[tex](2x-5)^{\circ} =180^{\circ}-123^ {\circ}[/tex]
⇒[tex]2x^\circ=57^\circ+5^\circ[/tex]
⇒x=[tex]31^\circ[/tex]
Therefore x=[tex]31^\circ[/tex] and y= [tex](\frac{123}{3})^ {\circ}[/tex]
18.
The diagonals of rectangle bisect each other.
so, 2x=x+9
⇔2x- x=9
⇔x = 9 units
Again opposite sides are congruent.
So,3y -9 =y+12
⇔3y - y =12+9
⇔y [tex]=\frac{21}{2}[/tex] units =10.5 units
Therefore x = 9 units and y = 10.5 units
19.
[tex]3x^\circ=45^\circ[/tex] [∵ they are transversal angles]
⇔[tex]x=15^\circ[/tex]
And opposite sides are equal
7y = 4y + 21
⇔7y - 4y = 21
⇔3y = 21
⇔y = 7 units
Therefore [tex]x=15^\circ[/tex] and y = 7 units
You can also write an equation for equivalent ratios. The equation at the right can be used to find the actual length x of the sculpture room in the museum. Complete the equation and explain what each part represents
The equation relates the scale drawing of the sculpture room to its actual dimensions using equivalent ratios. By setting the actual length corresponding to 6 cm on the drawing to 30 m, we can solve for the unknown actual length, which is 6 meters. So, the actual length of the sculpture room in the museum is 6 meters.
Completing the equation:
The equation in the image is missing a part: it should be:
1 cm : 5 m = x cm : 30 m
Explanation of the equation:
1 cm: This represents the length of the sculpture room on the scale drawing, as indicated by the scale 1 cm : 5 m.
5 m: This represents the actual length corresponding to every 1 cm on the scale drawing.
x cm: This is the unknown variable we're trying to solve for. It represents the actual length of the sculpture room in the museum.
30 m: This is a constant value, chosen because we want to find the length corresponding to 6 cm on the scale drawing (since the sculpture room in the drawing is 6 cm long).
What each part represents:
The colon (:) separates the two equivalent ratios.
The first ratio (1 cm : 5 m) represents the scale factor, which is the conversion factor between the scale drawing and the actual museum dimensions. It tells us that every 1 cm on the drawing corresponds to an actual length of 5 m.
The second ratio (x cm : 30 m) represents the unknown ratio we want to solve for. It relates the unknown actual length (x cm) to the desired actual length of 30 m (corresponding to 6 cm on the drawing).
Solving for x:
To solve for x, we can cross-multiply the two ratios:
(1 cm) * (30 m) = (5 m) * (x cm)
Simplifying the equation, we get:
30 m = 5x cm
Finally, dividing both sides by 5, we get:
x = 6 m
Therefore, the actual length of the sculpture room in the museum is 6 meters.
PLEASE ANSWER THIS ASAP
Write an equation in slope intercept form for the line that passes through (4,-1) and is perpendicular to the graph of y=7/2x-3/2
Answer:
The equation of line passes through [tex](4,-1)[/tex] and perpendicular to the graph [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex] is [tex]y=\frac{-2x}{7}+\frac{1}{7}[/tex]
Step-by-step explanation:
Given point is [tex](4,-1)[/tex] and equation of line is [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex]
Let the slope of line that passes through point [tex](4,-1)[/tex] is [tex]m_1[/tex]
And slope of line [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex] is [tex]m_2=\frac{7}{2}[/tex] . As it is in the form of [tex]y=mx+c[/tex]
We know the relation between slope of perpendicular line are given by
[tex]m_1\times m_2=-1\\And\ m_1=\frac{-1}{m_2}[/tex]
So, the slope [tex]m_1=\frac{-1}{\frac{7}{2}}=\frac{-2}{7}[/tex]
Now, we can write the equation of line having point [tex](4,-1)[/tex] and slope [tex]\frac{-2}{7}[/tex]
[tex](y-y_1)=m(x-x_1)\\\\(y-(-1))=\frac{-2}{7}(x-4)\\\\y+1=\frac{-2x}{7}-(\frac{2\times -4}{7})\\ \\y+1=\frac{-2x}{7}+\frac{8}{7}\\\\y=\frac{-2x}{7}+\frac{8}{7}-1\\\\y=\frac{-2x}{7}+\frac{8-7}{7}\\\\y=\frac{-2x}{7}+\frac{1}{7}[/tex]
So, the equation of line passes through [tex](4,-1)[/tex] and perpendicular to the graph [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex] is [tex]y=\frac{-2x}{7}+\frac{1}{7}[/tex]
The sum of three consecutive even numbers is 84. What is the smallest of the three numbers?
Answer: 26
Step-by-step explanation: In this problem we have 3 consecutive even numbers whose sum is 84 and it asks us to find the smallest number.
Consecutive even numbers can be represented as x, x + 2, and x + 4.
Since the sum of these is 84, our equation reads
x + (x + 2) + (x + 4) = 84.
Simplifying on the left we get 3x + 6 = 84.
Subtract 6 from both sides and we have 3x = 78.
Divide both sides by 3 and x = 26.
So our smallest number is 26.
To find the smallest of three consecutive even numbers that sum up to 84, we set up an equation and solve for 'x', where 'x', 'x+2', and 'x+4' represent the numbers. Solving this gives us the smallest number, which is 26.
Explanation:Finding the Smallest of Three Consecutive Even NumbersIf the sum of three consecutive even numbers is 84, we can find the smallest number by setting up an equation. Let's denote the smallest even number as 'x'. The next consecutive even number would be 'x + 2', and the one after that would be 'x + 4'. The sum of these three numbers should equal 84:
x + (x + 2) + (x + 4) = 84
Simplifying this equation, we get:
3x + 6 = 84
Subtracting 6 from both sides, we have:
3x = 78
Now, dividing both sides by 3 gives us:
x = 26
Therefore, the smallest of the three consecutive even numbers is 26.
Is 16.275 greater then 16.28
Answer:
no
Step-by-step explanation:
16.28 can also be written 16.280 (you could add as many zeros to the end as you want its still the same number)
280 is bigger than 275
A line contains points F, G, H, I, J. The space between F G is 2. The space between H and I is 1. The space between F and I is 7.
If FG = 2 units, FI = 7 units, and HI = 1 unit, what is GH?
3 units
4 units
5 units
6 units
Answer:
4 units
Step-by-step explanation:
if f to g is 2 units and h to i is one unit you just add thoes together because that is what the outside of the f to i is. And 7-3 is 4
hope this helps luvs
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The distance between the points G and H on the line that contains points F, G, H, I, and J is 4 units.
What is a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.
Given that a line contains points F, G, H, I, J. The space between F and G is 2. The space between H and I is 1. The space between F and I is 7. Therefore, the distance between the two points G and H on the given line can be written as,
GH = FI - FG - Hi
= 7 units - 2 units - 1 unit
= 4 units
Hence, the distance between the points G and H on the line that contains points F, G, H, I, and J is 4 units.
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5+7
can you cell me answer fasr
Answer:
12
Step-by-step explanation:
This is an example of Addition property between two positive integers (i.e. whole value numbers), which means the result will be positive and larger than the two numbers.
The result of the addition would be:
[tex]5 + 7 = 12[/tex]
Another way to do it if you are struggling a bit you can write the value of [tex]7[/tex] as [tex]7 = 5 +2[/tex] so then you can say:
[tex]5 + (5 + 2) = 5 + 5 + 2 = 10 + 2 = 12[/tex]
(8,10), (-7,14) what is the slope
Answer: 4 / -15
Step-by-step explanation:
For the graphs below, for which probability distribution is the value of the median greater than the value of the mean?
Theoretical Probability Distributions
Negativity skewed
Normal (no skew)
Positively skewed
Frequency
Negativity Direction
Perfectly Symmetrical
Distribution
Positive Direction
Negatively skewed
Normal, symmetrical distribution
Positively skewed distribution
None of the above
Answer:
The probability distribution for which the value of the median is greater than the value of the mean is - negatively skewed probability distribution.
Step-by-step explanation:
The probability distribution for which the value of the median is greater than the value of the mean is - negatively skewed probability distribution.
Answer:
negative skewed distribution
Step-by-step explanation:
As can be seen in the figure attached,
in the negative skewed distribution the median is greater than the meanin the normal (no skew or symmetrical) distribution the median is equal than the meanin the positive skewed distribution the median is lower than the meanUse the number line to show a number which rounds to 170 when it is rounded to the nearest ten.
Answer:
170
Step-by-step explanation:
A number which rounds to 170 when it is rounded to the nearest ten is 168.
What is the number line ?
A number line is a picture of a graduated straight line that serves as visual representation of the real number.
Since we are trying to round of a number, which rounds to 170 when it is rounded to the nearest ten. Therefore, it should be in the range of 166 to 174 (both included).
Let take example of 168, as it can be seen that it is closest to 170, therefore, when it is rounded it will be closest to 170.
Hence, 168 is a number which rounds to 170 when it is rounded to the nearest ten.
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write the expression in the standard form a+bi (showing all work)
(2-i)^3
[tex]2-11i \text{ is the standard form of given expression }[/tex]
Solution:
The standard form of complex number is: a + bi
where a is the real part and bi is the imaginary part
Given expression is:
[tex](2-i)^3[/tex]
Expand the above expression using algebraic identity
[tex](a-b)^3=a^3-b^3-3ab(a-b)[/tex]
[tex]\text{For } (2-i)^3 \text{ we get, a = 2 and b = i}[/tex]
Thus on expanding using the above algebraic identity we get,
[tex](2-i)^3=(2)^3-(i)^3-3(2)(i)(2-i)[/tex]
Simplify the above expression
[tex](2-i)^3=8 -i^3-6i(2-i)\\\\(2-i)^3=8 -i^3-12i+6i^2[/tex]
We know that,
[tex]i^2 = -1\\\\i^3 = -i[/tex]
Substituting in above simplified expression, we get,
[tex](2-i)^3=8-(-i)-12i+6(-1)\\\\(2-i)^3=8 + i -12i -6\\\\\text{Combine the like terms }\\\\(2-i)^3=8 - 6 + i -12i\\\\(2-i)^3=2-11i[/tex]
Thus the given expression is expressed in standard form
Solange was thinking of a number between 40 and 50 which is a multiple of 3 and 4. Of what number was she thinking?
A) 45
B) 41
C) 49
D) 48
Answer:
D
Step-by-step explanation:
3×16=48
4×12=48
evaluate the variable expression when a=-4, b=2, c=-3, and d =4. b-3a/bc^2-d
Answer:
Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is
[tex]\dfrac{b-3a}{bc^{2}-d}=1[/tex]
Step-by-step explanation:
Evaluate:
[tex]\dfrac{b-3a}{bc^{2}-d}[/tex]
When a=-4, b=2, c=-3, and d =4
Solution:
Substitute, a=-4, b=2, c=-3, and d =4 in above expression we get
[tex]\dfrac{b-3a}{bc^{2}-d}=\dfrac{2-3(-4)}{2(-3)^{2}-4}\\\\=\dfrac{2+12}{18-4}\\\\[/tex]
[tex]\dfrac{b-3a}{bc^{2}-d}=\dfrac{14}{14}=1[/tex]
Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is
[tex]\dfrac{b-3a}{bc^{2}-d}=1[/tex]
3x – 2y = 24
x + 2y = 48
x=??
y=??
Final answer:
By using the elimination method to solve the given system of linear equations, we find that x = 18 and y = 15.
Explanation:
We are looking to solve the system of linear equations:
3x – 2y = 24
x + 2y = 48
To find the values of x and y, we can use substitution or elimination methods. In this case, the elimination method is very straightforward since the y coefficients in the two equations are additive inverses. If we add both equations together, the y terms will cancel out:
3x + x = 24 + 48
4x = 72
Dividing both sides by 4 gives us the value of x:
x = 18
To find y, we can substitute x back into either of the original equations. Let's use the second equation:
18 + 2y = 48
Subtracting 18 from both sides:
2y = 30
Dividing by 2:
y = 15
Thus, the solution to the system of equations is x = 18 and y = 15.
Given: y = 3x - 4.
What is the x-intercept?
O (0, 1)
(0, -4)
O 1-4,0)
• (1, 0)
Answer:
(0,-4)
Step-by-step explanation:
see the image for explanation.
Answer:
( [tex]\frac{4}{3}[/tex], 0 )
Step-by-step explanation:
The x- intercept is where the graph crosses the x- axis. At this point the y- coordinate is zero.
Substitute y = 0 into the equation and solve for x, that is
3x - 4 = 0 ( add 4 to both sides )
3x = 4 ( divide both sides by 3 )
x = [tex]\frac{4}{3}[/tex] ← x- intercept
Predict the number of tickets that will be sold if the price is $12 per ticket
Answer:
350
Step-by-step explanation:
We have two points on the demand curve as (10, 450) and (15, 200). Using the two-point form of the equation for the line between them, we can find the "y" value for "x" = 12 as ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (200 -450)/(15 -10)(12 -10) +450
= (-250/5)(2) +450
= -100 +450 = 350
We predict the number of tickets sold at $12 will be 350.
_____
Check
The drop in sales of 50 tickets for each $1 increase in price is consistent with other table values.
What is the complete factorization of 64x2 - 48x + 9?
O A. (8x - 3)(8x+3)
B. (8x - 3)2
OC. 4(4x - 3)2
D. 4(4x - 3)(4x+3)
Please helppp
Answer:
B) (8x-3)²
Step-by-step explanation:
64x2 - 48x + 9= (8x)² - 2*8x*3 + 3²
Compare with a² - 2ab +b² = (a-b)²; a = 8x and b =3
=(8x-3)²
At Al's Athletic Club, the monthly membership fee for a student is $25 and the monthly
membership fee for an adult is $40. If Al's Athletic Club receives $12,250 in membership fees
for the month of January, which of the following represents the relationship between the
number of student memberships, 2, and the number of adult memberships, y, at Al's Athletic
Club for that month?
Answer:
The relationship ⇒ 25x + 40y = 12,250
Step-by-step explanation:
The number of student memberships = x
The number of adult memberships = y
The monthly membership fee for a student = $25
The monthly membership fee for an adult = $40
The total fee = 25x + 40y
Al's Athletic Club receives $12,250 in membership fees for the month of January.
So, the relationship between x and y is:
25x + 40y = 12,250
For every 2 student memberships (2x$25=$50), there were 305 adult memberships.
To represent the relationship between the number of student memberships (2) and the number of adult memberships (y) at Al's Athletic Club for the month of January, we can use an equation based on the given information. Let's assume that there were 2 student memberships and y adult memberships in January. The monthly membership fees for students and adults are $25 and $40, respectively. The total membership fees collected for the month were $12,250.
The total fees can be represented as:
Total Fees = (Number of Student Memberships * Monthly Fee for Student) + (Number of Adult Memberships * Monthly Fee for Adult)
Using the given information, we can write the equation:
$12,250 = (2 * $25) + (y * $40)
Now, we can simplify this equation:
$12,250 = $50 + $40y
To isolate the variable y, we can subtract $50 from both sides of the equation:
$12,250 - $50 = $40y
$12,200 = $40y
Now, divide both sides by $40 to find the relationship:
y = $12,200 / $40
y = 305
So, the relationship between the number of student memberships (2) and the number of adult memberships (y) for the month of January is represented by the equation y = 305. This means there were 305 adult memberships in January for every 2 student memberships.
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DO THE PROBLEM DOWN BELOW I WILL MARK BRAINLIEST AND GIVE 100 POINTS:Unit 1: Ratios and Rates Answer the questions below. Total score: ____ of 15 points (Score for Question 1: ___ of 4 points) 1. Mrs. Jolley is thinking of buying solar panels to put on the roof of her new house. The Sunny Solar Company told her that for every 2 panels, she will save $60 on her electric bill. (a) Draw a model or make a visual representation for the ratio of the panels to the money that she will save on her electric bill. (b) Write the ratio of panels to money saved as a reduced fraction. Show your work (Score for Question 2: ___ of 5 points) 2. Mrs. Jolley likes that she can save money on her electric bill by going solar, but she needs to know how much it is going to cost to set up her new system. She figures that it should take about 9 panels to start. They sent her the following prices of solar panels: # panels Price ($) 2 3,000 3 4,500 5 7,500 9 ? (a) What is the price per of each panel? Show your work—make sure to show at least two different calculations to show they both have the same answer. (b) How much will 9 panels cost her? Show your work. (Score for Question 3: ___ of 6 points) 3. Mrs. Jolley has determined that she does want to go ahead and get those solar panels installed. Now she has to find an installer. Her friends have also had solar installed and here are the companies that they used, how many hours they took to install their panels and their total price: Company # of hours Total price (in dollars) ABC Co. 5 128 Solar R’ Us 6 181 Light in the Sky 8 195 (a) What is the price per hour for each company? Show your work and remember your rounding rules. (b) Which company is the best deal? Explain
Answer:
1. Basically, a ratio is a relation between two values, such that the change of one value will result in the same proportional change in the other (if one value increases 6 times, or decreases 4 times, for example, the same will happen with the other value too.
Since Mrs. Jollie will save $60 for every two panels, then the ratio is:
2 panels: $60
Every ratio can be written in a form of fraction, by simply dividing these values:
2/60
or, as a reduced fraction:
1/30
2. Now we are given several ratios, which we need to use to find price for 9 panels.
First way:
we can set a proportion because we already said that if we change one value, others will change proportionally as well. So, we take any of these ratios and make a proportion:
2 : $3,000 = 9 : $ x
Solving for x, we get:
x = $3,000 • 9 / 2
x = $13,500
Second way:
From the ratio, we can find the price for a single panel. Then, we simply multiply that with 9 and find the price for nine panels:
one panel costs $3,000 / 2 = $1,500
nine panels cost $1,500 • 9 = $13,500
3. Now, we are again given several ratios and we need to find the price per hour for each company. We can do this by simply dividing:
- ABC Co. 5h : $128
so, price per hour is $128/5 = $25.6
- Solar R' Us 6h : $181
so, price per hour is $181/6 = $30.17
- Light in the Sky 8h: $195
so, price per hour is $195/8 = $24.4
So, the best deal means that the price per hour is the lowest, so the best deal is the Light in the Sky company.
1200/180 =
(can someone please help me I'm desperate)
Using a calculator, 1200/180 = 6.67 approximately
If you use long division, then you'll get what you see in the diagram below
The 6's go on forever after the decimal point, but if you round to two decimal places, then you'll get that approximate value of 6.67
---------------
If you want a remainder, then 1200/180 = 6 remainder 120
You can think of it like you having 1200 cookies and 180 friends. Each friend will get 6 whole cookies and there will be 120 left over as the remainder.
What is the solution to the system of equations?
(3x+2y = 39
(5x-y=13
O (4,7)
O (7,4)
O (12,5)
(5, 12)
Answer:
X = 5
Y= 12
Step-by-step explanation:
3x + 2y = 39 —> (1)
5x - y = 13 —> (2)
Multiply (2) with 2
10x - 2y = 26 —> (b)
(1) + (b)
This will eliminate the y factor, leaving:
13x = 65
Therefore, x = 65/14
X= 5. Put this value of 5 in equation 1, which gives;
15 + 2y = 39
2y = 39-25
2y = 24
Y = 12
Answer:
x=5
y = 12
Step-by-step explanation:
3x + 2y = 39
2y = 39 - 3x
y = (39 - 3x) / 2
5x - y = 13
5x - ((39 - 3x) / 2) = 13
5x - 39/2 + 3/2x = 13
5x + 3/2x = 13 + 39/2
13/2x = 65/2
x = 65/2 * 2/13
x = 65/13
x = 5
y = (39 - 3x) / 2
y = (39 - 3*5) / 2
y = (39 - 15) / 2
y = 24/2
y = 12
How dose 4x+7=19. Work
Answer:
3
Step-by-step explanation:
4x+7=19
4x=19-7
4x=12
x=12/4
x=3
Suppose M varies directly with S. If M is 900 when S is 500, which equation relates M to S
Answer: M = ⁹/₅S
Step-by-step explanation:
M ∞ S -------------------------------- 1
M = KS ------------------------------ 2
K is a constant and need to be calculated
substitute for M and S in 2 to find K
900 = K500
K = ⁹⁰⁰/₅₀₀
= ⁹/₅
Therefore , the equation that connect / relates M to S will be
M = KS
M = ⁹/₅S
Final answer:
The equation that relates M to S is M = kS, where k is the constant of proportionality.
If M is 900 when S is 500, the equation becomes M = 1.8S.
Explanation:
The equation that relates M to S is M = kS, where k is the constant of proportionality.
To find the value of k, we can use the given values of M and S.
If M = 900 when S = 500, we can substitute these values into the equation to get 900 = k(500).
Solving for k, we divide both sides of the equation by 500, getting k = 1.8.
Therefore, the equation that relates M to S is M = 1.8S.
During his 2001 MVP season for the Seattle Mariners, Japanese baseball
sensation Ichiro Suzuki hit 192 singles, 34 doubles, 8 triples, and 8 home runs
in a total of 692 at bats. The following table arranges these data in terms of
the number of bases for a hit, counting O bases for the times when he did not
get a hit and 4 bases for home runs.
To the nearest thousandth, what was E(X), the expected number of bases for
Ichiro Suzuki in a typical at bat in 2001?
A. 0.538
B. 0.457
C. 0.350
D. 0.441
Answer:
0.457 for all the apex students
Step-by-step explanation:
b
The expected number of bases for Ichiro Suzuki in a typical at-bat in 2001 is approximately 0.448, which rounds to 0.441 (Option D) to the nearest thousandth. Thus , the correct option is D.
To calculate the expected number of bases for Ichiro Suzuki in a typical at-bat in 2001, we can use the following formula:
E(X) = (0 ×P(Out)) + (1 × P(Single)) + (2 × P(Double)) + (3 × P(Triple)) + (4 ×P(Home Run))
First, we need to calculate the probabilities for each outcome:
P(Out) = (692 - 192 - 34 - 8 - 8) / 692 = 450 / 692 ≈ 0.651
P(Single) = 192 / 692 ≈ 0.278
P(Double) = 34 / 692 ≈ 0.049
P(Triple) = 8 / 692 ≈ 0.012
P(Home Run) = 8 / 692 ≈ 0.012
Now, plug these probabilities into the formula:
E(X) = (0 × 0.651) + (1 ×0.278) + (2 × 0.049) + (3 × 0.012) + (4 × 0.012)
E(X) ≈ 0.278 + 0.098 + 0.036 + 0.036 ≈ 0.448
Rounding to the nearest thousandth, E(X) is approximately 0.448.
So, the answer to the question is D. 0.441, which is the closest option provided.
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Mia has 12 marbles, alex has 9 marbles, and micheal has 51 marbles. use the gcf and the distributive property to find the total number of marbles mia, alex and micheal have
Answer: 5508
Step-by-step explanation:
all the numbers together equal 72 marbles in total.
(6x2)x (3x3)x (3x17)=
12 9 51 first multiply the easy numbers 12x9 =108 then
108x51= 5508
- 2.12
What is is that as a fraction or mixed number
Answer:
[tex] - \frac{53}{25} [/tex]
Step-by-step explanation:
Convert to a mixed number by placing the numbers to the right of the decimal over
100
. Reduce the fraction. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number and adding the numerator to get the new numerator. Place this new numerator over the original denominator.
How do you solve -2(x+5)=4
Answer:x = -7
Step-by-step explanation:
-2x-10=4
-2x=14
-x=7
X=-7
Answer:
x = -7Step-by-step explanation:
[tex]-2(x+5)=4\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2\!\!\!\!\diagup(x+5)}{-2\!\!\!\!\diagup}=\dfrac{4\!\!\!\!\diagup^2}{-2\!\!\!\!\diagup_1}\\\\x+5=-2\qquad\text{subtract 5 from both sides}\\\\x+5-5=-2-5\\\\x=-7[/tex]
- 2a = - 20
What is the most simplest answer?
- 2a = - 20 | x (-)
2a = 20
a = 20 : 2
a = 10
Answer:
a=10
Step-by-step explanation:
-2a=-20
Divide -2 on each side. You should get a=10
At present, a man is 5 times older than his daughter. In 7 years, the man is 3 times as old as his daughter. What are their present ages?
The present age of father is 35 and daughter is 7.
Step-by-step explanation:
Let,
Age of father = x
Age of daughter = y
According to given statement;
A man is 5 times older than his daughter.
x = 5y Eqn 1
In 7 years, the man is 3 times as old as his daughter.
x+7 = 3(y+7)
[tex]x+7=3y+21\\x=3y+21-7\\x=3y+14\ \ \ Eqn\ 2[/tex]
Putting value of x from Eqn 2 in Eqn 1
[tex]3y+14=5y\\14=5y-3y\\14=2y\\2y=14[/tex]
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{14}{2}\\y=7[/tex]
Putting y=7 in Eqn 1
[tex]x=5(7)\\x=35[/tex]
The present age of father is 35 and daughter is 7.
Keywords: linear equation, substitution method
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Final answer:
The present ages of the man and his daughter are 35 years and 7 years, respectively.
Explanation:
The question asks us to find the current ages of a man and his daughter, given that the man is currently five times older than his daughter and that after 7 years, he will be three times as old as her. To solve this, we can set up two equations based on the information provided:
Let D be the daughter's current age, the man's current age is 5D (since he is five times older).In 7 years, the daughter's age will be D+7 and the man's age will be 5D+7. At that time, the man will be three times as old as his daughter, so we have 5D+7 = 3(D+7).Now, we solve the equation from step 2 to find the daughter's age:
5D + 7 = 3(D + 7)5D + 7 = 3D + 215D - 3D = 21 - 72D = 14D = 7So, the daughter is currently 7 years old. To find the man's age, we multiply the daughter's age by 5:
Man's age = 5 x 7 = 35 years old
Therefore, the man is currently 35 years old and the daughter is 7 years old.
20-4 x(-6)= steps to solve
Answer:
20 - 4×(−6) = 20 + 4×6 = 20 + 24 = 44