Answer:
please give my answer first
Answer:
408 is correct
0.8 x 510 = 408
Step-by-step explanation:
When we get a sale value or reduced value to find
This is a short cut of workings in bold to find correct value.
10% of 510 = 51
20% of 510 = 102
510-102 =408
17 x 30 = 510 Not correct as calculated before taxes.
100-80/ 100 = 0.8
0.8 x 510 = 408
408/510 = 0.8 Is correct
0(17) (30) = 510 Not correct as calculated before tax
510 - 2(17)(30) = 510 i Not correct as calculated before tax.
A line passes though two points A(-2, 2). B(-1, 2). What is the slope:
Answer:
The slope is 0
Step-by-step explanation:
Slope = (y2 - y1) / (x2 - x1)
Where the values of x and y are from the known points
Here the points are (-2,2) and (-1,2)
So we have (x1,y1) = (-2,2) and (x2,y2) = (-1,2)
This means, x1 = -2 , x2 = -1 , y1 = 2 and y2 = 2
We now plug these values into the slope formula
Recall slope = (y2 - y1) / (x2 - x1)
==> plug in x1 = -2 , x2 = -2 , y1 = 2, y2 = 2
Slope = (2 - 2) / (-1 - (-2)
==> remove parenthesis
Slope = (2-2) / (-1 + 2)
==> simplify addition and subtraction
Slope = 0 / 1 = 0
What is -60a^2+642a-420
Answer:
The answer is −6(10a−7)(a−10)
Step-by-step explanation:
1) Factor out the common term 6.
\( - 6( {10a}^{2} - 107a + 70)\)
2) Split the second term in 10a² - 107a + 70 into two terms.
\( - 6( {10a}^{2} - 7a - 100a + 70)\)
3) Factor out common terms in the first two terms, then in the last two terms.
\( - 6(a(10a - 7) - 10(10a - 7))\)
4) Factor out the common term 10a - 7.
\( - 6( 10a - 7)(a - 10\)
Therefor, the answer is -6 ( 10a - 7) (a - 10).
According to Wikipedia, the following are the lengths of terms of the US Presidents that preceded Joe Biden. There is a total of 44. You may have expected to see a total of 45, as Biden is the 46th us President, but Grover Cleveland was considered the 22nd and the 24th President, but is only counted once in this list The 2922 is the length of two full terms and the 1461 is the length of one full term FDR, the 4422 in the table, had actually started his FOURTH term before dying in office The 31 is William Henry Harrison who became ill shortly after his inauguration. His death may have been due to pneumonia Number of US Presidents 12 1 1 Term in Days 4422 2922 2865 2.840 2.728 2.041 2.027 1.886 1,654 1.503 1,461 1.460 1.430 1.419 1 1 12 1 1 1.419 1.262 1,036 969 895 881 492 199 31 TOTAL: 1 1 1 1 1 1 1 1 1 44 Determine the mean, median and mode for this set of data Give each to the nearest whole day Mean = Median = Mode = and With one of the modes being a high value as well as the term of FDR being much higher than all others, was pulled up to a higher value than another of hte measures of central tendency the
The mean of the given data is 1744 days, median of the given data is 1460.5 days, mode of the given data is 1461 days & 4422 days.
To find the mean, median, and mode of the lengths of terms of the US Presidents that preceded Joe Biden:
Mean:
To find the mean, we add up all of the term lengths and divide by the total number of terms:
Mean = (4422 + 2922 + 2865 + 2840 + 2728 + 2041 + 2027 + 1886 + 1654 + 1503 + 1461 + 1460 + 1430 + 1419 + 1262 + 1036 + 969 + 895 + 881 + 492 + 199 + 31) / 44
Mean = 1743.77 days
Median:
To find the median, we need to arrange the term lengths in order from smallest to largest, and then find the middle term. In this case, since we have an even number of terms, we will take the average of the two middle terms:
31 199 492 881 895 969 1036 1262 1419 1430 1460 1461 1503 1654 1886 2027 2041 2728 2840 2865 2922 4422
Median = (1460 + 1461) / 2
Median = 1460.5 days
Mode:
The mode is the most frequently occurring term length. In this case, there are two modes: 1,461 days and 4,422 days.
Since the term length of FDR is much higher than all the other term lengths, it has pulled up the mean to a higher value than the other measures of central tendency. Additionally, the mode being a high value is likely due to the fact that FDR served for more than three terms, which is an outlier in the data set.
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John has a 100 cm cubed pencil holder. If John wants to hide a pencil in the pencil holder (so the pencil holder) what is the longest length of pencil he can hide
Therefore, the longest length of pencil that John can hide in the pencil holder is approximately 127.32 cm (rounded to two decimal places).
Given that John has a 100 cm³ pencil holder, the longest length of pencil he can hide in the pencil holder can be found by using the formula for the volume of a cylinder which is given by: V = πr²h where r is the radius of the cylinder and h is the height of the cylinder.The volume of a cylinder can also be expressed as V = lwh where l is the length of the cylinder, w is the width of the cylinder and h is the height of the cylinder.
If we assume that the pencil is cylindrical in shape, then its volume can be given by V = πr²l where r is the radius of the pencil and l is the length of the pencil.Since the volume of the pencil holder is given to be 100 cm³, then we have:100 = πr²h (Equation 1)
Now, we need to find the value of l that can fit inside the pencil holder. We can use the formula for the volume of the pencil to do this as follows:
V = πr²lLet V = 100 cm³ and
r = 0.5 cm
(since the pencil holder is cylindrical in shape, we can assume that it has a radius of 0.5 cm)Then, we have:100 = π(0.5)²lSolving for l, we get:
l = 100 / (π(0.5)²)
l = 100 / (0.7854)l ≈ 127.32 cm
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Simplify the expression:
3x+b+p^2
Answer:
\(3x+b+p^2\) is already simplified
Step-by-step explanation:
\(3x+b+p^2\) is already simplified
Answer:
The equation is already simplified
Step-by-step explanation:
Nothing fuurther can be done to this equation
3x+4
12. Simplify +
x+2
x²+2x
2x+4
Answer:
\(\dfrac{x^2+8x+8}{2x+4}\\\\\)
Step-by-step explanation:
Simplify:
\(\dfrac{3x + 4}{x +2}+\dfrac{x^2+2x}{2x+ 4}\)
Multiply the denominator and the numerator of the first term by 2,
\(=\dfrac{2*(3x +4)}{2*(x+ 2)}+\dfrac{x^2+2x}{2x+4}\\\\\\=\dfrac{2*3x+2*8}{2*x +2*2}+\dfrac{x^2+2x}{2x+4}\\\\\\=\dfrac{6x+8}{2x+4}+\dfrac{x^2+2x}{2x+4}\)
\(\sf = \dfrac{6x+8+x^2+2x}{2x+4}\\\\\text{\bf Combine like terms,}\\\\=\dfrac{x^2+8x+8}{2x+4}\\\\\)
Please please look at the picture and answer the question thank you for your help
Answer:
20 for both
Step-by-step explanation:
hope this helps
HELP PLEASE I NEED HELPPPP!!!!!!!!!!
two triangles is equal to 12 ft squared
the area of rectangles is equal to 8 ft x 6 ft which will give you 48 feet squared
you add them together to get the total area and you will get 84 feet sqaured
Which of the following is the graph of f(x)=║x║translated 2 units right, 2 units up, and dilated by a factor of 1/3?
Answer:
c on edge2021
Step-by-step explanation:
Peter set off from Town A at 10 am, driving at an average speed of 84 km/h. He reached
Town B at 2 pm. If William set off 1 hour 25 minutes earlier than Peter and took the
same route at an average speed of 70 km/h, at what time would William reach Town B?
Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.
Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter
Time taken by Peter = 2PM - 10AM
= 4 hrs
Speed of Peter = 84 km/h
Distance travelled by Peter = speed × time
= 84 × 4
= 336 km
So, the distance between Town A and Town B = distance travelled by Peter = 336 km.
Now, we will calculate time taken by William.
Speed of William = 70 km / hr
Distance travelled by William = distance between Town A and town B = 336 km
Time taken by William = distance / speed
= 336 / 70 hr
= 4.8 hr
This can b converted into hrs and minutes
4.8 hr = 4 hr + 0.8 × 60
= 4 hr 48 mins
Time William took off = 10 AM - 1hr 25 mins
= 8:35 AM
Now, we will calculate the time William would reach town B.
Time = 8:35 + 4hr 48 mins
= 1:23 PM
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How many different sums of money can be made from 4coins of different denomination
Answer:
15 different sums----------------------
There are various combinations of coins.
1 coin:4 options2 coins:4C2 = 4!/(2!2!) = 6 options3 coins:4C3 = 4!/(3!1!) = 4 options4 coins: 1 optionIn total there are:
4 + 6 + 4 + 1 = 15 different sumsHeeeelp please, Can be zero or not?
with all steps and explanay.
The value of integral is 3.
Let's evaluate the integral over the positive half of the interval:
∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx
Let u = 4 + 3sin(x), then du = 3cos(x) dx.
Substituting these expressions into the integral, we have:
∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du
Using the power rule of integration, the integral becomes:
∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]
Evaluating the definite integral at the limits of integration:
(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))
(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0
So, the value of integral is
= 3-0
= 3
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Answer:
\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)
Step-by-step explanation:
First, compute the indefinite integral:
\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)
To evaluate the indefinite integral, use the method of substitution.
\(\textsf{Let} \;\;u = 4 + 3 \sin x\)
Find du/dx and rewrite it so that dx is on its own:
\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)
Rewrite the original integral in terms of u and du, and evaluate:
\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)
Substitute back u = 4 + 3 sin x:
\(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)
Therefore:
\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)
To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.
Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.
\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)
Therefore, the curve of the function is:
Below the x-axis between -π and -π/2.Above the x-axis between -π/2 and π/2.Below the x-axis between π/2 and π.So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.
Integrate the function between -π and -π/2.
As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:
\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)
Integrate the function between -π/2 and π/2:
\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)
Integrate the function between π/2 and π.
As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:
\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)
To evaluate the definite integral, sum A₁, A₂ and A₃:
\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)
Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:
\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)
Therefore, the given expression cannot be zero.
23 1/5 +45 7/8 fast plz
Answer:
69.075 or 69 3/40
Step-by-step explanation:
(^-^)
Answer:
68 43/40
Step-by-step explanation:
Suppose A={0,12,−3,7,18}, B={−1,5,7,18}, and C={−3,5,9}. What is A∩(B∪C)?
Answer: {-3, 7, 18}
Step-by-step explanation:
B ∪ C = {-3, -1, 5, 7, 9, 18}
A ∩ (B∪C) = {-3, 7, 18}
please give me a brainliest answer
Answer:
A∩(B∪C)={-3, 7, 18}Step-by-step explanation:
First we look at PEMDAS.
In A∩(B∪C), parentheses come first.
So, we do B∪C.
The ∪ symbolizes union, which means you have to combine the elements of the two sets.
If B={−1,5,7,18}, and C={−3,5,9}, then both of them together is {-3,−1,5,7,9,18}. I used underlining and italics to show where the numbers came from. There is a 5 in both sets, but you only have to put it once.
B∪C={-3,−1,5,7,9,18}.
Now that we have B∪C, we can solve for A∩(B∪C).
∩ means intersection, so you find the elements in both sets. Basically, just look for numbers that appear in both A and B∪C.
B∪C={-3,−1,5,7,9,18}
A={0,12,-3,7,18}
Therefore, A∩(B∪C)={-3, 7, 18}
Hope this helped! <3
An investor earns 12.49 percent before tax and is subject to a 32 percent tax on such earnings. Calculate the investor's after-tax rate of return.
Answer:
How do you calculate after tax rate of return?
After-tax return on investment is the net return to the investor after ordinary income and capital gains taxes are subtracted. This is calculated as: After-tax return on investment = ((P1 - Po) (1 - Tc) / Po) + C1(1 - To) / Po.
How do you calculate before tax return?
The pre-tax rate of return is calculated as the after-tax rate of return divided by one, minus the tax rate. For example, suppose a person obtains a 4.25% reporting rate for ABC shares and is subject to a 15% income tax. Therefore, the pre-tax rate of return is 5% or 4.25%/(1 - 15%).
How do you calculate real rate of return after tax and inflation?
To calculate the real rate of return after tax, divide 1 plus the after-tax return by 1 plus the inflation rate. Dividing by inflation reflects the fact a dollar in hand today is worth more than a dollar in hand tomorrow. In other words, future dollars have less purchasing power than today's dollars.
Hope this help's :)
The circumference of a circle 69.1 yard. what is the diameter?
Answer:
D = 22 yards
Step-by-step explanation:
D = C ÷ π
D = 69.1 ÷ 3.14
D = 22.006
D = 22 yards
hi guys please help me to solve the following question
Answer:
D!
Step-by-step explanation:
To find the area, we multiply the length times the width to find the number of squares in each box.
A) 1 square down times 7 squares across is 1 x 7, which is 7.
B) 2 squares down times 6 squares across is 2 x 6= 12.
C) 3 squares down times 5 squares across is 3 x 5 = 15.
D) 4 squares down times 4 squares across = 4 x 4 =16.
16 is the biggest number here, so that is the greatest area!
If you enjoyed my answer, please give it a rating and a Thanks! If you think this answer was pretty brainly, please give it a Brainliest!
Have a great day!
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
C
Step-by-step explanation:
Step-by-step explanation:
Hi tag brainliest ❣️
Thanks
Since the shaded area equal 4
our answer is A
that is the number of shaded area ÷ the total number of points
-
A hiker is at an elevation of 238 feet above sea level. He climbs downward until his elevation has decreased by 144 ft. Which expression can be used to determine his current elevation above sea level?
Answer:
Based on the given conditions, formulate:
238
−
144
Calculate the sum or difference:
94
get the result:
94
Answer: Step-by-step explanation:
Given a = 4, b = -2 and c = 8, evaluate a + b + c.
14
10
6
Answer:
i think its 10
Step-by-step explanation:
please I need help with this
A. The following are sets A and B:
A = {2, 3, 5, 7, 11}
B = {1, 2, 3, 4, 6, 12}
C. Elements not in A or A' = ∅
B. The Venn diagram is attached
How to solve sets?A universal set is a set which consists of all elements related to the given sets. It is denoted by U.
A. Set A:
A = {2, 3, 5, 7, 11}
Set B:
B = {1, 2, 3, 4, 6, 12}
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A' = {1, 4, 6, 8, 9, 10, 12}
C. Elements not in A or A' = ∅
Complement of set A is refers to a set that contains the elements present in the universal set but not in set A.
Hence, the Venn diagram of sets A, B and U has been attached.
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Which ones right ????
Marcus was interested in whether the frequency that students check emails impacts their grades in the class. He categorized students into three groups. Those who checked email daily, those who checked email at least 2x a week (but not every day), and those who checked email less than 2x a week. Below are the GPAs for the students he studied. Conduct the steps of hypothesis testing on these data.
Table of data: GPAs for students separated by how often they check their email
Daily 2x a week Less than 2x a week
3.6 3.5 2.9
3.5 3.4 3.0
3.7 3.2 3.2
4.0 3.2 2.7
The steps to conduct the steps of hypothesis testing on these data are:
State the null hypothesis (H0) as well as the alternative hypothesis (H1):Select the significance level (alpha): Select the right test statistic:Formulate the decision rule:Compute the test statistic as well as the p-value:Decide on a decision.What is the hypothesis?The hypothesis will be:
H0: Email frequency does not affect grades.H1: Email frequency affects grades.Since we are comparing (GPAs) of three groups (students who check e-mail day by day, students who check mail at least 2x a week, and students who check mail less than 2x a week), one can be able to make use of one-way analysis of variance (ANOVA) as the fitting test measurement.
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PLEASE HELP ! The height of a triangle is 4 feet greater than the base. The area of the triangle is 142.5 square feet. Find the length of the base and the height of the triangle
Answer:
Base: \(15\), Height: \(19\)
Step-by-step explanation:
Let the base be \(b\). Then the height is \(b+4\).
By the area of a triangle theorem, we have that \(bh/2=b(b+4)/2=142.5\).
Multiplying by \(2\) and expanding gives \(b^2+4b=285\), so \(b^2+4b-285=0\). We see that this quadratic factors into \((b-15)(b+19)=0\). Because the base is a side length and must be positive, we have that the base is \(15\).
The height is then \(15+4=19\).
Station 2: Unit 3 and Unit Linear Functions given the table x 9,3,-3,-9 y 2,-2,-6,-10 ,
Find equation slope form answer the following questions.
Answer:
y = (2/3)x - 4
Step-by-step explanation:
To find the equation of the line in slope-intercept form given a table of values, you will need to calculate the slope of the line and the y-intercept. The slope of a line is a measure of its steepness, and it is calculated as the rise (change in y-values) divided by the run (change in x-values) between two points on the line. The y-intercept is the point at which the line crosses the y-axis.
Given the table x: 9, 3, -3, -9 and y: 2, -2, -6, -10, you can use any two points to calculate the slope. For example, you could use the points (9, 2) and (3, -2) to calculate the slope:
slope = (y2 - y1) / (x2 - x1) = (-2 - 2) / (3 - 9) = -4 / -6 = 2/3
To find the y-intercept, you can use the slope and one of the points from the table to substitute into the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Using the slope and the point (9, 2), you can solve for b:
y = mx + b
2 = (2/3) * 9 + b
2 = 6 + b
b = -4
Therefore, the equation of the line in slope-intercept form is y = (2/3)x - 4.
To answer the other questions, you can use this equation to determine the y-value for a given x-value or the x-value for a given y-value. You can also use the equation to graph the line on the coordinate plane.
Determine which of the following equations are linear equations in x
Determine if true. select all that apply
Name:
Chapter 5 Section 1
More Practice Finding the Coordinates of the point of Concurrency
1. The vertices of AABC are A(1,6), B(5,4), C(5,-2). Find the coordinates of the circumcenter.
a) Graph and label the triangle
b) Find the midpoint of each side of the triangle
Midpoint AB = 5, 1)
Midpointbc =
し32)
Midpointac = [1, 2]
c) Find the slope of each side of the triangle
MAB =
MBC =
MAC =
d) Find the slope of each perpendicular bisector
IMAB =
IMBc =
IMAC =
e) Use the midpoint and the perpendicular slope to accurately draw each perpendicu
bisector on the triangle.
Answer:
see the attachments for the graph, and a spreadsheet with midpoints and slopes
Step-by-step explanation:
We are given the coordinates of the vertices of a triangle, and asked to find the parameters of the perpendicular bisectors of the sides of the triangle. The perpendicular bisectors are to be plotted on the graph.
Given:Coordinates A(1, 6), B(5, 4), C(5, -2)
__
Find:a) Graph and label the triangle
b) Find the midpoint of each side of the triangle
c) Find the slope of each side of the triangle
d) Find the slope of each perpendicular bisector
e) Use the midpoint and the perpendicular slope to accurately draw each perpendicular bisector on the triangle
__
Solution:a)See the attached graph for shaded triangle ABC.
__
b)The midpoint (M) of a segment AB will be ...
M = (A+B)/2
For example, the midpoint of segment AB is ...
D = ((1, 6) +(5, 4))/2 = (1+5, 6+4)/2 = (6, 10)/2 = (3, 5)
This repetitive arithmetic is carried out in the spreadsheet shown in the second attachment. The midpoints are ...
D(3, 5) is midpoint of AB
E(5, 1) is midpoint of BC
F(3, 2) is midpoint of CA
__
c)The slope of a segment is found using the slope formula (or by counting grid squares). That formula is ...
m = (y2 -y1)/(x2 -x1)
For segment AB, this is ...
mAB = (4 -6)/(5 -1) = -2/4 = -1/2
The other slopes are calculated similarly in the spreadsheet. When the denominator is zero (a vertical line), the slope is "undefined."
mBC = undefined
mCA = -2
__
d)The slope of the perpendicular line is the opposite reciprocal of the slope of the segment.
m⟂AB = -1/(-1/2) = 2
m⟂BC = 0 . . . . . a horizontal line has 0 slope
m⟂CA = -1/-2 = 1/2
__
e)The perpendicular bisectors of each of the sides of the triangle are shown in the first attachment. As the lesson title indicates, their point of concurrency is G(1, 1), the circumcenter of the triangle.
An interior designer is redecorating a room that is 26 feet long by 18 feet wide by 9 feet high. At one end of the room is a door that is 6 feet 6 inches high and 4 feet wide. One of the walls contains 2 windows, each of which is 2 feet wide by 2 feet 6 inches high.
A: How much will it cost to carpet the floor if the carpet sells for $18.00 a square yard? $
B: How much will it cost to wallpaper all four walls if wallpaper costs $0.75 per square foot? $
C: How much will it cost to paint the ceiling using paint that sells for $25 per gallon if a quart of paint will cover 88 square feet? $
D: What will be the cost of the entire project? $
Answer: A: It will cost $936.00 to carpet the floor.
B: It will cost $297.00 to wallpaper all four walls.
C: It will cost $33.25 to paint the ceiling.
D: The cost of the entire project will be $1266.25.
Step-by-step explanation:
To calculate the costs for carpeting, wallpapering, painting, and the overall cost of the project, we need to determine the areas that need to be covered and the corresponding prices for each material.
Given dimensions:
Room length: 26 feet
Room width: 18 feet
Room height: 9 feet
Door dimensions:
Height: 6 feet 6 inches
Width: 4 feet
Window dimensions (each):
Width: 2 feet
Height: 2 feet 6 inches
A: Carpeting the floor:
To find the area of the floor, we multiply the length and width of the room:
Floor area = Length × Width = 26 feet × 18 feet = 468 square feet.
To convert to square yards (since the carpet is sold per square yard), we divide by 9:
Floor area in square yards = 468 square feet / 9 = 52 square yards.
Cost to carpet the floor = Floor area in square yards × Cost per square yard = 52 square yards × $18.00 = $936.00.
B: Wallpapering the walls:
To find the area of the walls, we calculate the perimeter of the room (2 × (Length + Width)) and multiply it by the height of the room:
Wall area = Perimeter × Height = 2 × (26 feet + 18 feet) × 9 feet = 396 square feet.
Cost to wallpaper the walls = Wall area × Cost per square foot = 396 square feet × $0.75 = $297.00.
C: Painting the ceiling:
To find the area of the ceiling, we multiply the length and width of the room:
Ceiling area = Length × Width = 26 feet × 18 feet = 468 square feet.
Since a quart of paint covers 88 square feet, we need to determine the number of quarts required:
Number of quarts = Ceiling area / Coverage per quart = 468 square feet / 88 square feet = 5.32 quarts.
Since a gallon contains 4 quarts, the number of gallons required is 5.32 quarts / 4 quarts = 1.33 gallons.
Cost to paint the ceiling = Number of gallons × Cost per gallon = 1.33 gallons × $25.00 = $33.25.
D: Cost of the entire project:
Total cost = Cost to carpet the floor + Cost to wallpaper the walls + Cost to paint the ceiling
= $936.00 + $297.00 + $33.25 = $1266.25.
Therefore:
A: It will cost $936.00 to carpet the floor.
B: It will cost $297.00 to wallpaper all four walls.
C: It will cost $33.25 to paint the ceiling.
D: The cost of the entire project will be $1266.25.
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Fernando also learns in math class that the rule Add 1 to the side length of a pentagon with equal sides length results the rule Add 5 to the perimeter. Write four ordered pairs that relate the side length of a pentagon to the perimeter of the pentagon.
All the four ordered pairs that relate the side length of a pentagon to the perimeter of the pentagon are,
⇒ (1, 5) (2, 10) (3, 15) (4, 20)
Given that;
Fernando also learns in math class that the rule Add 1 to the side length of a pentagon with equal sides length results the rule Add 5 to the perimeter.
Now,
Here are four ordered pairs that relate the side length of a pentagon to the perimeter of the pentagon:
⇒ (1, 5) (2, 10) (3, 15) (4, 20)
Hence, In each pair, the first number represents the side length of the pentagon, and the second number represents the perimeter of the pentagon.
And, If you add 1 to the side length in each pair, you'll see that the perimeter increases by 5, just as Fernando learned in math class.
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