Answer:
93 square units (the figure is not a rhombus)
Step-by-step explanation:
You want the area of the figure whose vertex coordinates are A(0,-5), B(9,2), C(12,13), and D(2,7).
Area from coordinatesThe formula for the area of a polygon based on its coordinates might be written ...
[tex]\displaystyle A=\frac{1}{2}\left|\sum_{k=1}^n{x_k(y_{k+1}-y_{k-1})}\right|[/tex]
where coordinate indices wrap around from the end to the beginning.
Using this formula, we find the area to be ...
A = 1/2|0(2-7) +9(13-(-5)) +12(7-2) +2(-5-13)|
A = (1/2)|0 +162 +60 -36| = 1/2(186) = 93
The area of the figure is 93 square units.
DiagonalsThe area of a rhombus could be calculated as half the product of the lengths of the diagonals. This is only true because the diagonals of a rhombus cross at right angles.
Here, the differences between diagonally opposite coordinates are ...
AC = (12, 18) . . . . slope = 18/12 = 3/2
BD = (-7, 5) . . . . slope = 5/-7 = -5/7
If the diagonals are perpendicular, their slopes have a product of -1. Here, the product is ...
(3/2)(-5/7) = (-15/14) ≠ -1
The given figure is not a rhombus.
If we assume the diagonals are perpendicular, then the area would be ...
A = 1/2√(12²+18²)√((-5)²+7²) = 1/2√34632 ≈ 93.048
Rounded to the nearest tenth, this area would be 93.0 square units.
The diagonals actually cross at an angle of about 88.152°, so the area is actually ...
93.048·sin(88.152°) = 93 square units (exactly)
(Development of this formula is beyond the scope of this answer.)
What is the slope of the line that passes through the points (9, 1) and (10,−1)? Write your answer in simplest form.
Slope of the point is 11/8.
here we use the slope equation so -1-10 would be -11, Then 1-9 is -8 and then -11 divided by -8 is a positive 11/8.
given;
x1=9
x2=1
y1=10
y2=-1
slope=y2-y1/x2-x1
=-1-10/1-9
= 11/8
therefore, the slope of the line that passes through the points ; 11/8.
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run"
there are 4 types of slope,
negative, positive, zero, and undefined. as x increases
Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b)..
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PLEASE ANSWERING THIS QUESTION!!!
Solve the quadratic equation by completing the square: [tex]\sf{z^2+8z-44=20}[/tex]
Give the equation after completing the square, but before taking the square root. Your answer should look like: [tex]\sf{(z-a)^2=b}[/tex]
The equation is: (blank)
List all solutions to the equation in simplest radical form, separated by commas. The solutions are:
z= (blank)
Rules answering these questions:
Explain your answer!
Do not spam answers!
Show your work!
Nonsense answers will be reported and delete your answers.
Thanks!
The equation after completing the square is (z + 4)² = 80
The solutions to the given equation in the simplest radical form are z = -4 + 4√5 and z = -4 - 4√5
Completing the squareFrom the question, we are to solve the given quadratic equation by completing the square
The given equation is
z² +8z - 44 =20
First, add 44 to both sides of the equation
z² +8z - 44 + 44 = 20 + 44
z² +8z = 64
Now, divide the coefficient of z by 2, square the value and add to both sides
The coefficient of z is 8
Dividing
8/2 = 4
Squaring
4²
Now, add this to both sides
That is,
z² +8z +4² = 64 + 4²
(z + 4)² = 64 + 16
(z + 4)² = 80
The equation after completing the square is
(z + 4)² = 80
Continuation
(z + 4)² = 80
Take the square root of both sides
√(z + 4)² = ±√80
z + 4 = ±√80
z = -4 ± √80
z = -4 ± 4√5
z = -4 + 4√5 and z = -4 - 4√5
Hence,
The equation after completing the square is (z + 4)² = 80
The solutions to the given equation in the simplest radical form are z = -4 + 4√5 and z = -4 - 4√5
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Solve the following system of equations using either Gaussian elimination or a
matrix. Write your answer as a point and explain how you would check your work:
2x-y + 4z = 33
x + 2y-3z = -26
-5x - 3y + 5z = 23
Using Gaussian elimination, the solution to the given system of equations is given as follows:
x = 5, y = -11, z = 3.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.
For this problem, the variables are x, y and z, and the system is given as follows:
2x - y + 4z = 33.x + 2y - 3z = -26.-5x - 3y + 5z = 23.There are multiple ways in which a system can be solved, and for this one, Gaussian elimination will be used.
The first step is writing the augmented matrix of the system, as follows:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\1&2&-3&-26\\-5&-3&5&23\end{array}\right][/tex]
Then, the first column, which is equivalent to be coefficient of y, has to be of zero on the second and on the third row, hence:
R2 -> 2R2 - R1.R3 -> 5R1 + 2R3.The updated matrix will be given by:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&-11&30&211\end{array}\right][/tex]
Then, the second column, equivalent to the coefficient of y, on the third row has to be zero, hence:
R3 -> 11R2 + 5R3.
Then the matrix is:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&0&40&120\end{array}\right][/tex]
From each row of the system, from bottom up, we find the variables, as follows:
40z = 120
z = 120/40
z = 3.
5y - 10z = -85
5y - 30 = -85
5y = -55
y = -11.
2x - y + 4z = 33
2x + 11 + 12 = 33
2x = 10
x = 5.
Hence the solution for the system is:
x = 5, y = -11, z = 3.
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Find a linear equation whose graph is the straight line with the given properties.
through (1, 4) with slope 6
Answer:
y = 6x - 2
Step-by-step explanation:
We will use the slope-intercept form of a line to help us. We know the slope, we need to determine the y-intercept. To find this, we need an x and y on the line and the slope. Fortunately, they have given us all of the information. An ordered pair is in the form (x,y) So we will use x = 1 and y = 4 from the point they have given us (1,4) They have also given us the slope of 6. We will plug this all into our equation and solve for b the y-intercept.
y = mx + b
4 = 6(1) + b
4 = 6 + b Subtract 6 from both sides of the equation.
-2 = b
Now, write the equation
y = mx + b
y = 6x -2
Translate this sentence into an equation.
54 is the sum of 12 and Rhonda's height.
Use the variable r to represent Rhonda's height.
Answer:
54=12+r
Step-by-step explanation:
'Sum' means to add.
54 = 12 + rhonda's height
54 = 12 + r
HELP ASAP Question 4(Multiple Choice Worth 2 points) (Scientific Notation in the Real World MC) A TV show had 3.6 x 104 viewers in the first week and 4.1 x 104 viewers in the second week. Determine the average number of viewers over the two weeks and write the final answer in scientific notation. 3.85 x 104 7.7 x 104 3.85 x 108 7.7 x 108
The average number of viewers over the two weeks will be 3.85 × 10⁴.
How to calculate the value?It should be noted that based on the information, the TV show had 3.6 x 10⁴ viewers in the first week and 4.1 x 10⁴ viewers in the second week.
Therefore, the average number of viewers over the two weeks will be:
= [(3.6 × 10⁴) + (4.1 × 10⁴)] / 2
= 3.85 × 10⁴
Therefore, the average number of viewers over the two weeks will be 3.85 × 10⁴.
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Is (0, 3) a solution to the equation y=x+3? (1 point)
O yes
Ono
Answer: Yes, it is.
Step-by-step explanation:
given: x is 0 and y is 3. Plug in the equation and solve
y=x+3
3=0+3
3=3
Yes, it is a solution
3y+z=am-4y look for y
The value of y is am-z/7
How to calculate the value of y ?The expression is given as follows
3y +z= am-4y
The first step is to collect the like terms in both sides, this way the numbers that both have y as their coefficient will be on the same side
3y + 4y= am-z
y(3+4)= am -z
7y= am-z
Divide both sides by the coefficient of y which is 7
7y/7= am-z/7
y= am-z/7
Hence the value of y in the expression is am-z/7
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Which is the graph of f(x)=√4x ?
Answer:
These are the type of graphs that equation would equal too.
Hope this helps! <3
- 8/32 in simplistic form
What is the slope of the line represented by the equation y = -x +?
0-1/2
HELP
in the equation y= -x-1/2
the slope is -1/1 which can also be shown as -1.
2. Josh went shopping for records and tapes on Monday and Tuesday.
He paid $95 for 4 records and 3 tapes on Monday and paid $70 for 2
records and 2 tapes on Tuesday. Write a system of equations that
could be used to determine the amount of each item and solve.
Answer:
it is very tough questions
Given that p=3i+j+2kand q=i-2j-4k are the position vectors
of points P and Q respectively, use the information to answer
Questions 2 and 3.
2.
Find an equation for the plane passing through Qand
perpendicular to liné PQ.
The equation for the plane passing through Q and perpendicular to line PQ is r (2 i + 3 j + 6 k) + 28 = 0.
Let position vector of point P be:
p = 3 i + j + 2 k
Let position vector of point Q be:
q = i - 2 j - 4 k
So, PQ = Q - P
PQ = n = i - 2 j - 4 k - (3 i + j + 2 k)
n = i - 2 j - 4 k - 3 i - j - 2 k
n = - 2 i - 3 j - 6 k
The Equation of plane passing through point Q and perpendicular to PQ will be:
(r - q).n = 0
r n = q n
q n = (i - 2 j - 4 k) . (- 2 i - 3 j - 6 k)
q n = - 2 + 6 + 24
q n = 28
r n = 28
r (- 2 i - 3 j - 6 k) = 28
r (2 i + 3 j + 6 k) + 28 = 0
Therefore the equation for the plane passing through Q and perpendicular to line PQ is r (2 i + 3 j + 6 k) + 28 = 0.
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Tony buys CDs at a music store. You get 20% off the price of a CD. You still have to add 5% sales tax. But you find the sales tax after the discount. So you save money on taxes, too." How much money does Tony save by getting the discount before adding the sales tax? Explain by using expressions.
Answer:
Lets say a CD costs a 100 dollars (which it obviosly doesn't)
No matter whether we do the discount before or after tax, it'll end up costing 84 dollars to by the CD.
80% of 100 = 80
80 * 1.05 = 84
80% of 105 = 84
The order in which he does the discount and the tax doesn't matter.
Hope this helps.
What is 4,788 divided by 54?
Answer:
88.7 rounded and 88.66 not rounded
......................................
Set B = {a,b,c,d} and Set C = { b,d,f,g}. Find B u C.
Answer:
do ur best
Step-by-step explanation: somebody else might can help u
ALGEBRA 1 HW!! PLEASE HELP I WILL GIVE BRAINLYEST also pls explain what the heck an explicit formula is..
Answer:y=10n+15
Step-by-step explanation:
replace the stars with digits. how many solutions does each problem have. ***-**=1
Answer: We have two solutions:
1000-998=2
or
1001 - 999 = 2
Have this done correctly for brainliest!
Answer:
expression
Step-by-step explanation:
It's an expression. The expression happens to be a quadratic polynomial.
An equation must have an equal sign.
An equation is a statement that a number or expression equals a number or expression.
Here, there is no equal sign. There is only an expression.
Answer:
This is an expression
8x2+7x-15
A phone company has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 410410 minutes, the monthly cost will be \$71.50$71.50. If the customer uses 720720 minutes, the monthly cost will be \$118.00$118.00. Use your equation to find the total monthly cost if 687687 minutes are used.
The required cost is $ 101.22.
This problem can be solved by unitary method.
Given that monthly cost of customer if he uses 410 minutes is $71.
So, cost per minute = [tex]\frac{71}{410}[/tex]
=$ 0.17
And if the customer uses 720 minutes then the cost is $118.
So, cost per minute is = [tex]\frac{118}{720}[/tex]
=0.16
Now if he uses 687 minutes then for 410 minutes cost incurred will be
= 410 × 0.17
= $ 69.7
And for next 197 minutes cost incurred will be = 197 × 0.16
= $ 31.52
Total cost for 687 minutes = $(69.7 + 31.52)
= $ 101.22
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what is the formula to find time from distance
The formula to find time from distance is time = distance/speed
How to determine the formula of time?As a general rule, the formula of speed is
Speed = Distance/Time
Multiply both sides by Time
Time * Speed = Distance
Divide both sides by Speed
he formula to find time from distance
Hence, the formula to find time from distance is time = distance/speed
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HELPP
You want to enclose a rectangular region with an area of
1200 square feet and a length of 40 feet, 50 feet, or 60 feet.
Find the perimeter for each possible region. Explain why
you might rewrite the area formula to find the solutions.
The possible perimeters are 140 feet, 148 feet and 160 feet.
In order to determine the width that would be used to determine the possible perimeters, the formula for the area would have to be rewritten.
What are the possible perimeters?A rectangle is a 2-dimensional quadrilateral with four right angles and two diagonals that bisect each other at right angles.
Area of a rectangle = length x width
Width = area / length
1200 / 40 = 30 feet
1200 / 50 = 24 feet
1200 / 60 = 20 feet
Perimeter of a rectangle = 2 x (length + width)
Perimeter when width is 30 feet : 2(40 + 30) = 140 feet
Perimeter when width is 24 feet : 2(24 + 50) = 148 feet
Perimeter when width is 20 feet : 2 (20 + 60) = 160 feet
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mathematics [tex]what is the product of 17 and 41?[/tex]
Answer: 697
Step-by-step explanation:
17 * 41=
17 * (40+1)=
17 * 40 + 17 * 1=
17 * 10 * 4 + 17=
170 * 4 + 17=
680+17=697
If EF = 5x, FG = 10, and EG = 10x, what is EF?
geometry
If points E,F,G are collinear, then,
EF+FG = EG
5x+10 = 10x
10 = 10x-5x
10 = 5x
5x = 10
x = 10/5
x = 2
So,
EF = 5x = 5*2 = 10EG = 10x = 10*2 = 20As a check, EF+FG = 10+10 = 20 = EG to help confirm the answer
Final Answer: EF = 10Answer:
EF = 10
Step-by-step explanation:
EF = 5x
FG = 10
EG = 10x
Geometry study guide help? I will give brainliest.
What is the volume of a right rectangular prism that is packed with 300 1/5-foot cubes?
The volume of the right rectangular prism = 2.4 ft³
How to Find the Volume of a Cube?A cube is a three dimensional shape that has equal edges and sides. The volume of a cube is calculated as:
Volume = a³, where a is the side length of the cube.
Given:
Side length of one cube (a) = 1/5 ft
Volume of one cube = (1/5)³ = 1/125 ft³
The right rectangular prism has 300 of these cube. Therefore:
Volume of the right rectangular prism = 300 × 1/125
Volume of the right rectangular prism = 300/125
Volume of the right rectangular prism = 2.4 ft³
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Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2700 grams and a standard deviation of 900 grams while babies born after a gestation period of 40 weeks have a mean weight of 3000 grams and a standard deviation of 430 grams. If a 32-week gestation period baby weighs 2900 grams and a 41-week gestation period baby weighs 3200 grams, find the corresponding z-scores. Which baby weighs more relative to the gestation period?
Find the corresponding z-scores. Which baby weighs relatively more? Select the correct choice below and fill in the answer boxes to complete your choice.
(Round to two decimal places as needed.)
A. The baby born in week 41 weighs relatively more since its z-score, enter your response here, is larger than the z-score of enter your response here for the baby born in week 32.
B. The baby born in week 41 weighs relatively more since its z-score, enter your response here, is smaller than the z-score of enter your response here for the baby born in week 32.
C. The baby born in week 32 weighs relatively more since its z-score, enter your response here, is larger than the z-score of enter your response here for the baby born in week 41.
D. The baby born in week 32 weighs relatively more since its z-score, enter your response here, is smaller than the z-score of enter your response here for the baby born in week 41.
Answer:
The 32 week gestation's period baby weighs 0.31 standard deviations below the mean.
The 41 week gestation's period baby weighs 0.65 standard deviations below the mean.
The 41 week gestation's period baby weighs relatively less.
Step-by-step explanation:
Normal model problems can be solved by the zscore formula.
On a normaly distributed set with mean and standard deviation , the z-score of a value X is given by:
The zscore represents how many standard deviations the value of X is above or below the mean .
Find the corresponding z-scores.
Babies born after a gestation period of 32 to 35 weeks have a mean weight of 2700 grams and a standard deviation of 800 grams. A 32-week gestation period baby weighs 2450.
Here, we have .
So
A negative z-score indicates that the value is below the mean.
So, the 32 week gestation's period baby weighs 0.31 standard deviations below the mean.
Babies born after a gestations period of 40 weeks have a mean weight of 2900 grams and a standard deviation of 385 grams. A 41 week gestation period baby weights 2650 grams.
Here, we have
So, the 41 week gestation's period baby weighs 0.65 standard deviations below the mean.
Which baby weighs relatively less?
The 41 week gestation's period baby has a lesser z-score, so this means that he weighs relatively less.
the question is on the screenshot
Answer:
I believe it's option 3, because you multiply 3 by 4, and get 12
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
Why do banks charge a fee when clients transact on their accounts?
Answer:
Banks charge fees to help make a profit.
Step-by-step explanation:
Bank fees allow financial institutions to recoup operating expenses. Banks also make money on loans, via interest and other fees.