The area A of polygon ABCDEFG with the given vertices is 10 square units
How to find the area A of polygon ABCDEFG with the given vertices?The vertices are given as
A(0,5), B(2,5), C(2,3), D(3,2), E(1,2), F(0,3), G(−4,3)
The area of the polygon is calculated using
Area = 1/2 * |(x1y2 -x2y1) +(x2y3 -x3y2) + ..... + (xny -xyn)|
So, we have
Area = 1/2 * |(0 * 5 - 5 * 2) + (2 * 3 - 5 * 2) + (2 * 2 - 3 * 3) + (3 * 2 - 2 * 1) + (1 * 3 - 2 * 0) + (0 * 3 - 3 * -4) +(-4 * 5 - 3 * 0)|
Evaluate the sum of products
So, we have
Area = 1/2 * |-20|
Remove the absolute bracket
So, we have
Area = 1/2 * 20
Evaluate the products
So, we have
Area = 10
Hence, the area A of polygon ABCDEFG with the given vertices is 10 square units
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please help (due in 8 minutes!! have a blessed day/night)
Answer:
13
Step-by-step explanation:
[tex]--› \: \: \:3x + \frac{1}{4} {y}^{2} [/tex]
Insert values
[tex]--› \: 3(3) + \frac{1}{4} {4}^{2} [/tex]
multiply 3 by 3
[tex]--› \: 9 + \frac{1}{4} {4}^{2} [/tex]
follow PEDMAS of operation
Calculate exponents 4[tex]{}^{2}[/tex]
[tex]--› \:9 + \frac{1}{4} \times 16[/tex]
divide 16 by 4
[tex]--› \: 9 + 4[/tex]
add 9 to 4
[tex]--› \: 13[/tex]
Malcolm has $638.54 in his checking account. He must maintain a $500 balance to avoid a fee. He wrote a check for $159.50 today. Write and solve an inequality to solve for the least amount of money he needs to deposit to avoid a fee. (2 points)
638.54 + 159.50 − x ≥ 500; x ≥ $298.04
638.54 + 159.50 − x ≤ 500; x ≤ $298.04
638.54 − 159.50 + x ≥ 500; x ≥ $20.96
638.54 − 159.50 + x ≤ 500; x ≤ $20.96
Answer:
638.54 − 159.50 + x ≥ 500; x ≥ $20.96
Can y’all please help me I really need a lot of help
please mark me the brainlist
Find the equation of the line shown
Answer:
Y = 1/2x + 1/2
Step-by-step explanation:
I'm not sure, but I think this is correct
Answer:
Slope intercept form;
y = mx + b
Where y is the independent variable and x is the dependent variable. 'm' represents the slope, and 'b' represents the y - intercept.
If we look at this graph:-
We can see that the line that intersects the y - axis is half of 1 which is 0.5, so that'll be our y-intercept.
It also rises one and goes over two so that'll be our slope.
To double check, we select two fixed points (1,1) and (3,2), we then divide the y-coordinates by the x-coordinates in the following order: (rise/run)
y2(second y-coordinate) - y1(first y-coordinate)
_____________________________________
x2(second x-coordinate) - x1(first x-coordinate)
2 - 1 1
_____ = ______, the slope is 1/2.
3 - 1 2
Now we format it in slope-intercept form:-
y = mx + b
y = 1/2x + 0.5
Where 1/2 is the slope, and 0.5 is the y-intercept
The radius of a circle is 11 feet. What is the circle's area? Use 3.14 for
Answer:
Formula for area of a circle;
A = πr^2
where pi is 3.14 in this case, and r is the radius squared
Plug in the actual values;
A = 3.14 x 11^2
A = 3.14 x 121
A = 379.94 square feet
A quadrilateral can be partitioned into two triangles. What is the sum of the angles of a quadrilateral?
Answer:
360°
Step-by-step explanation:
Each of the two triangles have 3 angles that add up to 180°.
So,
180° + 180° = 360°
The sum of the angles of a quadrilateral is 360°
Consider the system of equations.
2.+y=0
- 3x + 4y= 22
How do you solve the system of equations with Cramer's rule?
Drag a value or determinant expression into each box to correctly
solve the system using Cramer's rule.
I've arranged the tiles into the correct positions, and wrote in the final result for each x and y.
The basic idea is to divide determinants as the vertical bars indicate (they aren't absolute value bars).
In each denominator is the determinant of the matrix [tex]\begin{bmatrix}2 & 1\\-3 & 4\end{bmatrix}[/tex] which are the coefficients of the left hand side of each original equation given to you.
-------------
The numerators are a slight variation of this matrix. The x determinant will have you replace the first column with 0 & 22 getting [tex]\begin{bmatrix}0 & 1\\22 & 4\end{bmatrix}[/tex] which helps figure out the x solution. The y solution is similar as well, but we replace the y column instead of the x column. So that explains the [tex]\begin{bmatrix}2 & 0\\-3 & 22\end{bmatrix}[/tex]
After you have the proper determinants set up, you just evaluate each determinant using the formula
[tex]\begin{vmatrix}a & b\\ c & d\end{vmatrix} = a*d - b*c[/tex]
and then simplify the results.
what is 12/8 in the simplest form
Answer:
3/2
Step-by-step explanation:
Answer: 3/2
Step-by-step explanation: 12 and 8 can be reduced by dividing them by 4, so 12/8 can be simplified to 3/2.
PLEASE HELP ME!!! SOLVE FOR X!!! THANKS!!!!! (look at pic)
Answer:
x = 698.771
step-by-step explanation:
[tex]\sf \rightarrow \log _{2x}\left(5^{\dfrac{3}{2}}\right)=\dfrac{1}{3}[/tex]
apply ln rules
[tex]\sf \rightarrow \dfrac{\ln \left(5^{\dfrac{3}{2}}\right)}{\ln \left(2x\right)}=\dfrac{1}{3}[/tex]
cross multiply
[tex]\sf \rightarrow \ln \left(5^{\dfrac{3}{2}}\right)\cdot \:3=\ln \left(2x\right)\cdot \:1[/tex]
simplify using calculator
[tex]\sf \rightarrow 7.24247 = ln(2x)[/tex]
shift sides
[tex]\sf \rightarrow e^{7.24247 }= 2x[/tex]
divide both sides by 2
[tex]\sf \rightarrow 698.771= x[/tex]
Answer:
[tex]x=698.771[/tex]
Step-by-step explanation:
[tex]log_{2x} (5\frac{3}{2})=\frac{1}{3}[/tex]
[tex](5\frac{3}{2})*3=In(2x)*1[/tex]
[tex]7.24247=In(2x)[/tex]
[tex]e^{7.24247}=2x[/tex]
÷ [tex]2[/tex] ÷ [tex]2[/tex]
[tex]698.771=x[/tex]
Which number line shows the correct placement of 10%, 1/4, and 3/4?
Answer:
<-----10%-----1/4------3/4----->
The top left most answer (or A)
Step-by-step explanation:
Let's get all of these terms into the same representation. Meaning let's convert all of the numbers into either fraction or a decimal or percentage.
I find that fraction would be hard and so would percentage, lets try decimal.
1/4 = 0.25 as a decimal. (1/4 = 25/100 = 0.25) 3/4 = 0.75 (same manner as 1/4) Now for 10%. 10% in technical speaking is equal to 10/100 again which means it would be 0.10.
Okay so now they're all decimals let's put them in ascending order!
0.10, 0.25, 0.75. Yay! Now we can see on a number line the order would be
<-----10%-----1/4------3/4----->
I hope this helps!
Question 12 of 12 Use the volume formula to find the volume of the prism. A. 18 cubic units B. 4 1/2 cubic units C. 9 cubic units D. 7 cubic units
Answer:
C. 9 cubic units
Step-by-step explanation:
The formula for the volume of a prism is V=Bh, where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 4 and the width is 3/2 (1 1/2 = 3/2). The area A of a rectangle with length l and width w is A=lw
so the area of the base is 4 x 3/2 which is 6
then we multiply that by the height (3/2) to get 9.
i hope this helped :)
Alma was making soup, her recipe called for 24 potatoes, 15 carrots, and 4 stalks of celery.How many onions should she add, if it needs to be the same amount as the average of the potatoes and carrots?
Answer:
10
Step-by-step explanation:
Answer:
19.5
Step-by-step explanation:
First, we have to find the average of the pottoes and carrots. To do this we divide the sum of the potatoes and carrots by 2.
24+15=39
39/2=19.5
Alma will need 19.5 onions.
Find the missing side length of the similar shapes.
Answer:
15
Step-by-step explanation:
because the sides 15, 25 are corresponding, sides 18, 30 are corresponding, 9 and x (unknown side) are corresponding. here we discover that the ratio is 3:5 (15:25) and (18:30). so if the ratio of 9 to x is 3:5, the unknown side is 15.
An equilateral triangle has a height of 7 square root 3 cm. Find the perimeter of the triangle.
Answer:
42
Step-by-step explanation:
Explanation in image
A countertop is 16 feet long and 3 feet wide Tile costs $28 per square meter how much will it cost to cover the countertop with new tile
Answer:The total cost is about $124.86
Step-by-step explanation:
The area of the counter top is 16 ft by 3 ft so 16 x 3= 48. The area of the counter top is 48 ft squared.Then you have to convert it to meters squared, 48 x 0.092903 = 4.459244. Then multiply that by 28 to get your answer.4.459244 x 28 = 124.861632. The total cost is about $124.86
RN means registered nurse. LP means licensed practical
nurse. What is the hourly pay for the LP? How much
more is the RN paid for a 40-hour work week than
the LPN?
Answer:
Answer: B. The law says you must write a new living will each time you re admitted to the hospital.
Explanation:
The law does not require that you make a new will whenever you are admitted to the hospital. Any existing will that has fulfilled the provisions of the law are biding unless the person decides to change the will of their own volition.
There is therefore no need to make a new will every time if there is already one in existence and the person is satisfied with it. The Registered Nurse should therefore correct this statement by the Licensed Practical Nurse.
Rob deposits $1,000 in a savings account at New York State Bank that pays 1.4% interest, compounded monthly.
How much is in his account at the end of one year?
What is the APY for this account to the nearest hundredth of a percent?
Answer:
14
Step-by-step explanation:
p=$1000
rate percent=1.4%
time=one year
then
1.4/100*100=14
The amount of money in his account at the end of one year will be $1014.90. Then the APY for this account to the nearest hundredth of a percent will be 1.41%.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
[tex]\rm A = P \left (1 + \dfrac{r}{n} \right )^{t \times n}[/tex]
Where A is the amount, P is the initial amount, r is the rate of interest, and t is the number of years.
Rob deposits $1,000 in a savings account at New York State Bank that pays 1.4% interest, compounded monthly.
The amount of money in his account at the end of one year will be
A = 1000 × [1 + 0.014 / 12]¹²
A = 1000 × 1.01409
A = $1014.09
The APY for this account to the nearest hundredth of a percent will be
APY = [(1 + r/n)ⁿ - 1] x 100
APY = [(1 + 0.014 / 12)¹² - 1] x 100
APY = 1.41%
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Round answer to the nearest cent
70% of $50
Answer:
$35
Step-by-step explanation:
You could just multiply
70 × .5
35
Marco made $50 for every 2 hours he works, how much will he make in 10 hours?
Answer:
$500
Step-by-step explanation:
if Marco gets $50 for every 2 hours and it say how much he'll have every 10 hours what your gonna do is multiply 10 by 50 so 10×50= 500 so Marco will make $500 every 10 hours
$250 will he make in 10 hours for the work that Marco has done.
What is multiplication?When you take a single number and multiply it by several, you are multiplying. There are a number of distinct indications of amplification that people utilize. The "x" sign represents the most typical, however, other symbols like the "*" sign are also occasionally used.
The information that is provided is:
Marco made $50 for the two hours he is working for.
For one hour of the work that he is doing the amount that he will be paid is
= 50 / 2
$25
For working 10 hours Marco will earn
= 10*25
$250
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Hazel deposited $1,000 in her savings account. She earned 6.5% annual simple interest on the first $700 of her deposit and 3.5% simple interest on the remainder, How much interest did Hazel earn
after one year? (1 point)
O $45.00
O $51.00
O $56.00
O $65.00
Answer:
The answer is C. $56.00
Hazel earned $56.00 in interest after one year.
Step-by-step explanation:
700 x 6.5% =
700 x 0.065 = 45.5
300 x 3.5% =
300 x 0.035 = 10.5
45.5 + 10.5 = 56.00
Help please I need it asap
Answer:
<2 ~= < 4 - Vertical Angles Theorem
<2 ~= <8 - Alternate Exterior Angles
<4 ~= <8 - Corresponding Angles Theorem
line I || line m - Transitive Property
Please help me ........
Answer:
How are we supposed to do this do we just write out every answer? :D
Step-by-step explanation:
What is the area, in square inches, of the rectangle? Show your work!!
Answer:
[tex]\huge\boxed{\sf 7 \frac{13}{20} \ in. ^2}[/tex]
Step-by-step explanation:
Length of the rectangle = [tex]\displaystyle 2 \frac{1}{4} = \frac{9}{4} \ in.[/tex]
Width of the rectangle = [tex]\displaystyle 3 \frac{2}{5} = \frac{17}{5} \ in.[/tex]
Area of the rectangle:
= Length × Width
[tex]\displaystyle = \frac{9}{4} \times \frac{17}{5} \\\\= \frac{9 \times 17}{4 \times 5} \\\\= \frac{153}{20} \\\\= 7 \frac{13}{20} \ in.^2\\\\\rule[225]{225}{2}[/tex]
Answer:
Above is the solution to the question
list angles B,E,C, and D.
Step-by-step explanation:
Angles A and B form a linear pair, and are thus supplementary. Therefore, the measure of angle B is 180-105=75 degrees.
Angles E and F are a linear pair, and by the same logic, the measure of angle E is 70 degrees.
Since the sum of the measures of the angles in a triangle is 180 degrees, the measure of angle C is 180-75-70=35 degrees.
Since angles C and D are supplementary, the measure of angle D is 145 degrees.
An art teacher has 2 gallons of paint to pour into containers. If each container holds 1/3 gallon, how many containers can they fill?
Answer:
Six containers.
[tex]2 \div \frac{1}{3} = 6[/tex]
Multiply and verify the result when x=1,y=2
(Xy+xy^2 -1) (2x+3y)
check which of the following is a solution to the equation x-2y=4.
Answer:
solve for y y= -2+x/2
solve for x x=4+2y
Step-by-step explanation:
x-2y=4
+x =4+x
-2y = 4 + x divide both sides by -2
2 -2
y=-2 + x/2
x-2y=4
+2y=4+2y
x = 4+2y
is f(x) = -3x + 4 and g(x) =2 solve for the value of x for which f(x) = g(x) is true
Answer:f(x)=-3+4
g(x)=2
that means:f(x) is -3 AND
g(x) is 2.
Step-by-step explanation:
What is the range of this data set?
27,5,11,13,10,8,14,18,7
Help! Will mark brainliest! Promisw
Answer:
22
Step-by-step explanation:
Range is the highest value - the lowest value so in this case it's:
27-5 = 22
in an arithmetic sequence, the 5th term is equal to 75 and the 7th term is equal to 111 write an expression for the nth term of the sequence
Answer:
[tex]\bold{\underline{a_n=18n-15}}[/tex]
Step-by-step explanation:
[tex]a_n=a_1+d(n-1)\\\\a_5=a_1+d\cdot4\\\\a_7=a_1+d\cdot6\\\\a_7-a_5=a_1+6d-(a_1+4d)=2d\\\\111-75=2d\\\\2d=36\\\\d=18\\\\\\a_1+18\cdot4=75\\\\a_1=75-72=3\\\\\\a_n=3+18(n-1)=3+18n-18\\\\\underline{a_n=18n-15}[/tex]