Find the area of quadrilateral math with vertices M(7, 6), A(3, - 2), T(- 7, 1) and H(- 1, 9)
Answers
Lets draw a picture of our quadrilateral:
In order to find the area, we can divide our parallelogram in 2 triangles:
The area of triangle AHT is given by
[tex]\text{Area }\Delta AHT=\frac{1}{2}(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))[/tex]where
[tex]\begin{gathered} (x_1,y_1)=(3,-2)=A \\ (x_2,y_2)=(-1,9)=H \\ (x_3,y_3)=(-7,1)=T \end{gathered}[/tex]By substituting these points into the given formula, we get
[tex]\text{Area }\Delta AHT=\frac{1}{2}(3_{}(9_{}-(-7))-1((-7)-(-2))-7((-2)-9))[/tex]which gives
[tex]\begin{gathered} \text{Area }\Delta AHT=\frac{1}{2}(3_{}(16)-1(-5)-7(-11)) \\ \text{Area }\Delta AHT=\frac{1}{2}(48+5+77) \\ \text{Area }\Delta AHT=\frac{130}{2} \\ \text{Area }\Delta AHT=65 \end{gathered}[/tex]Similarly, for the area of triangle AHM, we can choose
[tex]\begin{gathered} (x_1,y_1)=(3,-2)=A \\ (x_2,y_2)=(-1,9)=H \\ (x_3,y_3)=(7,6)=M \end{gathered}[/tex]By substuting in our area formula, we get
[tex]\text{Area }\Delta AHM=\frac{1}{2}(3_{}(9_{}-6)-1(6-(-2))+7((-2)-9))[/tex]which gives
[tex]\begin{gathered} \text{Area }\Delta AHM=\frac{1}{2}(3_{}(3)-1(8)+7(-11) \\ \text{Area }\Delta AHM=\frac{1}{2}(9-8-77) \\ \text{Area }\Delta AHM=\frac{76}{2} \\ \text{Area }\Delta AHM=38 \end{gathered}[/tex]Then, the total area is given by
[tex]\begin{gathered} A=\text{Area }\Delta AHT+\text{Area }\Delta\text{AHM} \\ A=65+38 \\ A=103 \end{gathered}[/tex]then, the answer is 103 units squared.
Related Questions
this temperature to Fahrenheil. 1.3 If 1 cm'- 1 ml and 1 000 cm -1 4. Determine the following: 1.3.1 How many cm' are in 875 ? 1.3.2 How many t are there in 35,853 cm'?
Answers
We will solve it as follows:
1.3.1: We transform liters to cubic centimeters:
[tex]x=\frac{875\cdot1000}{1}\Rightarrow x=875000[/tex]So, there are 875 000 cubic centimeters.
1.3.2: We transfrom cubic centimenters into liters:
[tex]x=\frac{1\cdot35853}{1000}\Rightarrow x=35.853[/tex]So, there are 35.853 liters.
A principal of S2400 is invested at 8.75% interest compounded annually How much will the investment be worth after 7 years?
Answers
Explanation
The question wants us to determine the amount $2400 will yield after 7 years if compounded annually at a rate of 8.75%
To do so, we will use the formula:
[tex]\begin{gathered} A=P(1+r)^t \\ where \\ P=\text{ \$2400} \\ r=8.75\text{ \%=}\frac{8.75}{100}=0.0875 \\ t=7 \end{gathered}[/tex]Thus, if we substitute the values above we will have
[tex]\begin{gathered} A=\text{ \$}2400(1+0.0875)^7 \\ A=\text{ }\$2400\lparen1.0875\rparen^7 \\ A=\text{ \$2400}\times1.79889 \\ A=\text{ \$4317.34} \end{gathered}[/tex]Therefore, after 7 years, the investment will be worth $4317.34
Write a similarity relating the two triangles in each diagram.
Answers
We know by the figure that angles
Suzy was reading Aniya's math notebook. Aniya wrote forty-six thousand three hundredfifteen > 46, 350. Suzy replied, "I think there is an errorExplain why Suzy said this using numbers, words, or another method to representyour thinking
Answers
it is an error because the number is
[tex]46,315[/tex]b. expanded form
[tex]\begin{gathered} 40,000+ \\ 6,000 \\ 300 \\ 50 \\ 0 \\ ------ \\ 46,350 \end{gathered}[/tex]c. 46,350 to the nearest thousand
[tex]46,350\longrightarrow46,000[/tex]Find the center and the radius of the circle whose equation is x^2+y^2+8x-10y-23=0
Answers
Finding the equation of the standard form:
[tex]\begin{gathered} x^2+y^2+8x-10y-23=0 \\ x^2+y^2+8x-10y=23 \\ x^2+8x+16+y^2-10y+25=23+16+25 \\ \\ \\ (x+4)^2+(y-5)^2=64 \end{gathered}[/tex]
Based on the image, h = -4, k = 5 and r = 8, then...
Answer:
Center: ( -4, 5)
Radius: 8
Answer:the center would be (-4 -5)
Hope this helps
In the coordinate plane the vertices of angle RST are R(6,-1) S(1,-4) and T(-5,6). Prove that angle RST is a right triangle. State the coordinates of point P such that quadrilateral RSTP is a rectangle. Prove that your quadrilateral RSTP is a rectangle.
Answers
We are given coordinates of three points RST and are asked to prove that it forms a Right Triangle.
We kn
Compare the ratios in Table 1 and Table 2. Table 1 5 6 10 9 15 12 20 Table 2 7 10 20 21 30 28 40 Which statements about the ratios are true? Check all that apply. The ratio 3:5 is less than the ratio 7:10. Save and Exit Nexd Mark this and return
Answers
Table 1
3:5 , 6 : 10 , 9 :15 , 12 : 20
Table 2
7 : 10 , 14 : 20 , 21 : 30 , 28 : 40
Notice that all ratios in each table are equal. Additionally, since:
[tex]\frac{3}{5}=\frac{6}{10}[/tex]And 6<7, then the ratio 3:5 is less than the ratio 7:10.
Therefore, all ratios in table 1 are less than all ratios in table 2.
Some specific comparisons between ratios may apply as well. For example:
The ratio 14:20 (table 2) is greater than the ratio 9:15 (table 1).
A random sample of n= 100 observations is selected from a population with u = 30 and 6 = 21. Approximate the probabilities shown below.a. P(x228) b. P(22.1sxs 26.8)c. P(xs 28.2) d. P(x 2 27.0)Click the icon to view the table of normal curve areas.a. P(x228)(Round to three decimal places as needed.)
Answers
Problem Statement
We have been given random sample of 100 observations and we have been asked to find the probabilities of getting certain observed values given the population mean of 30 and a standard deviation of 21.
Method
To solve this question, we need to:
1. Find the z-score of the observations. The formula for calculating the z-score is:
[tex]\begin{gathered} z=\frac{X-\mu}{\sigma} \\ \text{where,} \\ X=\text{ The observed value} \\ \mu=\text{population mean} \\ \sigma=\text{ standard deviation} \end{gathered}[/tex]2. Convert the z-score to probability using the z-score table.
Implementation
Question A
1. Find the z-score of the observations.:
[tex]\begin{gathered} X\ge28 \\ \mu=30,\sigma=21 \\ z\ge\frac{28-30}{21} \\ z\ge-\frac{2}{21} \\ \\ \therefore z\ge-0.0952 \end{gathered}[/tex]2. Convert the z-score to probability using the z-score table.:
Using a z-score calculator, we have the probability to be:
[tex]P(z\ge-0.0952)=0.037938[/tex]This probability is depicted in the drawing below:
If the mean is represented by 0 and the right-hand side of 0 has a probability of 0.5, then the probability of getting greater than or equal to 28, is the addition of the probability 0.037938 gotten above with the 0.5 on the right-hand side of zero.
Thus, the answer to Question A is:
[tex]\begin{gathered} P(X\ge28)=0.037938+0.5=0.537938 \\ \\ \therefore P(X\ge28)\approx0.538\text{ (To 3 decimal places)} \end{gathered}[/tex]
Question B:
[tex]undefined[/tex]A line has a slope of 2/3 and contains point A(-6,-4) and point B (a, 2) what is the value of a?
Answers
From the point-slope formula, we have:
[tex]y-y_0=m(x-x_0)[/tex]where m is the slope, (x_0,y_0) are known points.
In this case, we have the slope and two points, we can substitute in the formula to get:
[tex]\begin{gathered} \text{if:} \\ (x,y)=(-6,-4) \\ \text{and} \\ (x_0,y_0)=(a,2) \\ \Rightarrow-4-2=\frac{2}{3}(-6-a) \\ \Rightarrow-6=-\frac{2\cdot6}{3}-\frac{2}{3}a \\ \Rightarrow-6=-4-\frac{2}{3}a \\ \Rightarrow-6+4=-\frac{2}{3}a \\ \Rightarrow-2=-\frac{2}{3}a\Rightarrow a=-\frac{2}{-\frac{2}{3}}=\frac{3\cdot2}{2}=\frac{6}{2}=3 \\ a=3 \end{gathered}[/tex]therefore, a=3
Note: you can also find a if you use the slope formula.
1 pointQuestion 5: Which one is NOT a correct description of these angles? *119BThey create a right angle.They are adjacent angles.UΟ Ο Ο ΟO They are complementary angles.O They are supplementary angles.
Answers
SOLUTION:
The one that is not a correct description of these anles is tption D. (They are supplementary angles)
EXPLANATION:
Two angles are said to be supplementary if they add up to be 180 and considering the sum of these angles which is 90 (right angle)
which of the following is equivalent to the expression i^41?
Answers
The Solution:
Given:
[tex]i^{41}[/tex]Required:
Find the equivalent of the given expression.
[tex]i^{41}=i^{40}\times i^1=i[/tex]Answer:
[option A]
A worker is getting a 3% raise. His current salary is $35,868. How much will his raise be?
Answers
Hello there. To solve this question, we'll simply have to multiply the percent and the salary to find how much will the raise of the worker.
Given his salary: $35,868 and knowing he'll get a 3% raise, we make:
3/100 * 35,868
107,604/100 = 1,07604
Rounding up the answer to the nearest tenth, we have that his raise will be $1,1.
Directions: Solve the problems below on a separate sheet of paper. You will use a variety of strategies (drawingpictures, building multiple towers, area models, algorithms, and partial products method for division) to solvethe problems. Please submit your answer by writing a complete sentence that expresses the final answer.1. Books are on sale for $8. Peter has $25 in his wallet. How many books can he buy?
Answers
books are on sale for $8
Peter has $25 dollar in his wallet
let the numbers of book be x
so,
if a book cost $8
x number of books cost $25
lets put it into mathematical statement
1 = $8
x = $25
lets cross multiply
1 X 25 = 8 X x
25 = 8x
8x = 25
divide both sides by 8
8x/8 = 25/8
x = 25/8
x = 3.125
x = 3 (approximately)
recall, we say x is the numer of books
so,
the number of books peter can by with is $25 in his wallet is 3atement
1
2(x+4)=150+ (-2) can u solve
Answers
Given equation:
[tex]2(x+4)\text{ = 150 + (-2) }[/tex]Open the bracket:
[tex]\begin{gathered} 2x\text{ + 8 = 150 - 2} \\ 2x\text{ + 8 = 148} \end{gathered}[/tex]Collect like terms:
[tex]\begin{gathered} 2x\text{ = 148 - 8} \\ 2x\text{ = 140} \end{gathered}[/tex]Divide both sides by 2:
[tex]\begin{gathered} \frac{2x}{2}\text{ = }\frac{140}{2} \\ x\text{ = 70} \end{gathered}[/tex]Answer:
x = 70
how to solve 7.-4y=48
Answers
solve for y
[tex]\begin{gathered} 7-4y-7=48-7 \\ -4y=41 \\ -\frac{4y}{-4}=\frac{41}{-4} \\ y=-\frac{41}{4} \end{gathered}[/tex]Answer:
y = -41/4 or 10.25
Step-by-step explanation:
7 - 4y = 48
Move 7 across the equals sign to make y stand alone
-4y = 48 - 7
= 41
Divide both sides by the coefficient of y, which is -4
-4y/4 = 41/4
y = -41/4 or 10.25
Can you please help me out with a question
Answers
We have the following diagram
We are told that the arc NOL has an angle measure of 300°. Recall that the angle measure of the whole circle is 360°. Since the whole circle is the sum of the measures of arcs LMN and NOL we have that the measure of the arc LMN is
[tex]\text{LMN+NOL=360}[/tex][tex]\text{LMN}+300=360[/tex]By subtracting 300 on both sides, we get
[tex]\text{LMN=360-300=60}[/tex]so arc LMN has a measure of 60°. However, note that measure of the arc LMN is the sum of the measures of arcs LM and MN. So
[tex]LM+MN=\text{LMN}=60[/tex]Now, note since lines MX and LM are perpendicular, we can do the following drawing
We can take a look at triangles LDX and NDX. Since the angles NDX and XDL are perpendicular, we can think of line MX as an axis of symmetry. That is, the left side of the circle with respect line MX is an exact copy of what is on the right. This means that the measure of the arc LM is the same as the measure of the arc MN. So we have that
[tex]LM\text{ + MN = MN+MN=2MN=60}[/tex]So, dividing both sides by 2, we get
[tex]MN\text{ =}\frac{60}{2}=30[/tex]So the measure of the arc MN is 30°.
Jamie is cutting for a craft project.she has a ribbon that is 2 1/4 inches long. How many pieces of ribbon can she cut that are 3/8inches long
Answers
Total Lenght = 2 1/4
Lenght of each piece = 3/8
Divide the total lenght by the lenght of each piece:
Total lenght = 2 1/4 = (2*4+1)/4 = 9/4
Total lenght / lenght of each piece = (9/4 ) / (3/8)
To divide 2 fractions we can multiply by the inverse of the second fraction:
[tex]\frac{9}{4}\times\frac{8}{3}=\frac{72}{12}[/tex]Simplify by 12:
6
Answer: 6 pieces
how to solve this problem
Answers
Let
x -----> number of students that preferred vanilla cupcakes
y ----> number of students that preferred chocolate
we know that
x+y=750 -----> equation A
and
2/5=x/y
x=(2/5)y ------> equation B
substitute equation B in equation A
(2/5)y+y=750
solve for y
(7/5)y=750
y=750*5/7
y=536
find the value of x
x=(2/5)(736)
x=214
therefore
the answer is 214 students preferred vanilla cupcakesUse a calculator to find θ to the nearest tenth of a degree, if 0° < θ < 360° and sin θ = -0.9945
Answers
Solution:
Given:
[tex]\sin \theta=-0.9945[/tex]Using the inverse trigonometric function,
[tex]\begin{gathered} \theta=\sin ^{-1}(-0.9945) \\ \theta=-83.988 \\ \theta\approx-84.0^0\text{ to the nearest tenth} \end{gathered}[/tex]However, since the sine of the angle is negative, it shows that the angle is in the third or fourth quadrant.
Hence, the possible values of the angle are,
[tex]\begin{gathered} \theta=-84+360=276.0^0 \\ \theta=180-(-84)=264.0^0 \end{gathered}[/tex]Therefore, the value of the angle to the nearest tenth of a degree is 264.0 degrees or 276.0 degrees.
simplified (-4+2i)(3-9i)
Answers
6 + 42i
Expanding the expression, by using FOIL acronym
(-4+2i)(3-9i)
-12+36i+6i-18i²
-12 +42i -18i² Remember i²= -1
-12 + 42i -18(-1)
-12 + 42i +18
6 + 42i
2) Now we have that complex number in the form a +bi
-
Simple Interest Practice P5(A)-2135-7-MATH / Simple Interest 2. What was the original amount deposited on an account with a total amount of $80 in the account after 8 years with a 2% interest rate?
Answers
The formula to use for solving simple interest rate problems is:
[tex]i=\text{Prt}[/tex]Where
i is interest accumulated
P is the initial, or principal, amount
r is the rate of interest [in decimal]
t is the time
Given,
Total amount in account is 80 [principal plus interest]
rate is 2%
time is 8 years
Let's write:
[tex]\begin{gathered} 80=P+\text{Prt} \\ 80=P(1+rt) \\ 80=P(1+(0.02)(8)) \\ 80=P(1+0.16) \\ 80=P(1.16) \\ P=\frac{80}{1.16} \\ P=68.9655 \end{gathered}[/tex]The amount in the account was around $68.97
I need to find the composite function with these two equations. I also need to find the domain.
Answers
Recall that:
[tex](f\circ f)(x)=f(f(x)).[/tex]Therefore:
[tex](f\circ f)(x)=f(\sqrt[]{x+2})=\sqrt[]{\sqrt[]{x+2}+2}.[/tex]Now, the above function is well defined as long as x+2 remains positive, therefore, it is well defined as long as x is greater or equal to -2.
Answer: The domain is:
[tex]\lbrack-2,\infty).[/tex]The composition is:
[tex](f\circ f)(x)=f(\sqrt[]{x+2})=\sqrt[]{\sqrt[]{x+2}+2}.[/tex]What is 6 x 1/4 in the simplest form
Answers
Answer:
[tex]6\cdot\frac{1}{4}=\frac{3}{2}[/tex]Step-by-step explanation:
Divide 6 by 4:
[tex]6\cdot\frac{1}{4}=\frac{6}{4}=\frac{3}{2}[/tex]Galina runs a bakery, where she sells packages of 4 dozen cookies for $24.96 per package. The amount of money she makes by selling x packages is represented by the function f(x)=24.96x, and her cost for making each package is g(x)=0.04x2+4x+71.If profit is equal to sales minus cost, which function represents her profit, p?
Answers
Answer:
p(x) = f(x) - g(x) = -0.04x² + 20.96x - 71
Explanation:
The sales are given by f(x) = 24.96x and the cost are represented by g(x) = 0.04x² + 4x + 71.
Then, the profit is equal to
p(x) = f(x) - g(x)
p(x) = 24.96x - (0.04x² + 4x + 71)
p(x) = 24.96x - 0.04x² - 4x - 71
p(x) = -0.04x² + 20.96x - 71
Therefore, the answer is
p(x) = f(x) - g(x) = -0.04x² + 20.96x - 71
(3,-4); m=6 write an equation in slope intercept form for the line through the given point with the given slope
Answers
y= 6x-22
Explanation
Step 1
Let
slope=6
Point (3,-4)
to find the equation in slope intercept form use
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ \text{where} \\ (x_0,y_0)\text{ are the coordinates of the known point} \end{gathered}[/tex]Step 2
Replace,
[tex]\begin{gathered} \text{the know point = (3,-4) so} \\ y-y_0=m\left(x-x_0\right) \\ y-(-4)=6(x-3) \\ y+4=6x-18 \\ \text{substract 4 in both sides} \\ y+4-4=6x-18-4 \\ y=6x-22 \end{gathered}[/tex]I hope this helps you
please help! I don't need a huge explanation I was just wondering if my answer is right
Answers
In the expression, there are 3 terms so polynomial is trinomial.
In trinomial the highest degree of term
[tex]10y^5[/tex]is 5. So degree of the polynomial is 5.
Anwer:
Trinomial
Degree is 5.
Student Beyonce You decide to buy a Super Size Hamburger Combo at the Burger Princess for 5.95. much change would you receive from 10.00. division Subtraction multiplication addition
Answers
Answer: 4.05
Just subtract 10.00 by 5.95 to get 4.05
hope this helps :)
Which one of the following simplifications is incorrect?
Group of answer choices
sqrt(48x^4)*root(4)(16x^10)=8x^4root(4)(3x^2)
sqrt(4x)*sqrt(12x^8)=4x^4sqrt(3x)
sqrt(x^3)*sqrt(xy^4)= x^2y^2
root(3)(64)*sqrt(18)=12sqrt(2)
Answers
After simplification, the option 2, [tex]\sqrt{4x}\times \sqrt{12x^8}=4x^4\sqrt{3x}[/tex] is correct option.
In the given question,
We have to find which simplifications is incorrect.
Option 1: [tex]\sqrt{48x^4}\times\sqrt[4]{16x^{10}}=8x^4\sqrt[4]{3x^2}[/tex]
To check whether the given expression is true or not simplifying the left hand side expression.
We simplifying the left hand side by writing it as
[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=\sqrt{16\times3\times (x^2)^2}\times\sqrt[4]{(2)^4\times x^{8}\times x^2}[/tex]
[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=\sqrt{(4)^2\times3\times (x^2)^2}\times\sqrt[4]{(2)^4\times (x^{2})^4\times x^2}[/tex]
Now simplifying the roots
[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=4\times x^2\times\sqrt{3}\times2\times x^2\times\sqrt[4]{ x^2}[/tex]
Now writing it in a simplified form
[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=8\times x^{2+2}\times\sqrt{3}\sqrt[4]{ x^2}[/tex]
[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=8x^{4}\sqrt{3}\sqrt[4]{ x^2}[/tex]
Hence, the simplified form of [tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}[/tex] is [tex]8x^{4}\sqrt{3}\sqrt[4]{ x^2}[/tex].
So the given statement is wrong.
Option 2. [tex]\sqrt{4x}\times \sqrt{12x^8}=4x^4\sqrt{3x}[/tex]
To check whether the given expression is true or not simplifying the left hand side expression.
We simplifying the left hand side by writing it as
[tex]\sqrt{4x}\times \sqrt{12x^8}=\sqrt{(2)^2\times x}\times \sqrt{3\times4\times (x^4)^2}[/tex]
[tex]\sqrt{4x}\times \sqrt{12x^8}=\sqrt{(2)^2\times x}\times \sqrt{3\times(2)^2\times ({x^4})^2}[/tex]
Now simplifying the roots
[tex]\sqrt{4x}\times \sqrt{12x^8}=2\sqrt{x}\times 2\times x^4\times\sqrt{3}[/tex]
[tex]\sqrt{4x}\times \sqrt{12x^8}=4x^4\sqrt{3x}[/tex]
Hence, the simplified form of [tex]\sqrt{4x}\times \sqrt{12x^8}[/tex] is [tex]4x^4\sqrt{3x}[/tex].
Hence, the option 2 is correct.
Since we get the write answer so we haven't solve the next option.
The next 2 options also can be solved in the way that we use in previous option to solve.
So the option 2 [tex]\sqrt{4x}\times \sqrt{12x^8}=4x^4\sqrt{3x}[/tex] is correct option.
To learn more about the simplification of expression link is here
https://brainly.com/question/14575743
#SPJ1
ZABC is a right angle.А2197032°Bс
Answers
Given that angle ABC is a right angle, then:
21° + x° + 32° = 90°
x = 90° - 21° - 32°
x = 37°
This corresponds to the option: subtract 21° and 32° from 90°, x = 37°.
Weights of 2-year-old girls are normally distributed with a mean of 253 lbs, and a standarddeviation of 1.12 lbs. According to this information, what weight would be the 33rd percentile? You must
Answers
We have here a case of a normally distributed variable. We can solve this kind of problem using the standard normal distribution, and the cumulative standard normal table (available in any Statistic Book, or on the internet).
We have that we can find z-scores to normalized the situation, and then, using the cumulative standard normal table, we can find the percentile. Then, we have:
[tex]z=\frac{x-\mu}{\sigma}[/tex]In this case, we need to find the raw value, x. We need to find a z-score that represents that before it there are 33% of the cases for this distribution: in this case, the value for z is approximately equal to z = -0.44.
Now, we have the mean (253 lbs), and the standard deviation (1.12 lbs):
[tex]-0.44=\frac{x-253}{1.12}[/tex]And now, we can determine the value, x, which is, approximately, the 33% percentile of this normal distribution:
1. Multiply by 1.12 to both sides of the equation:
[tex]1.12\cdot(-0.44)=\frac{1.12}{1.12}\cdot(x-253)\Rightarrow-0.4928=x-253[/tex]2. Add 253 to both sides of the equation:
[tex]-0.4928+253=x-253+253\Rightarrow252.5072=x\Rightarrow x=252.5072[/tex]Therefore, the weight that would be the 33rd percentile, is, approximately, x= 252.5072 or 252.51lbs (rounding to the nearest hundredth).