there are 4 properties we can use to prove if it is a parallelogram, in which 3 of them involve seeing if the sides are parallel or congruent, however for those we must know the value for the angles or sides, the other property is to prove that the diagonals bisect each other.
To prove the diagonals bisect each other is to see if the point of crossing divides into equal parts.
in this case since the division of the points gives the same values for both diagonals we can say that ABCD because the diagonals bisect each other.
Mika opened a bank account that earns simple interest with an initial deposit of $2,200.She made no other transactions throughout the year. At the end of the year, Mika had $2,260.50 in her account. What was the simple interest rate?
Answer:
2.75%
Step-by-step explanation:
2260.5-2200=60.5 the extra
60.5/2200=0.0275*100=2.75%
Starting at the origin (0,0), what is the ordered pair of a value that is 4 units to the left and 5 units up?
(-4,5)
4 to the left on the axis is neg. 5 units up on the y axis makes it positive.
6. Find the sale prices. a. $4,200 with a 35% markdown b. $5,000 with a 44% markdown
Answer: The Correct Sales Prices:
a. $2,730
b. $2,800
Step-by-step explanation:
a. $4,200 x 35%
$4,200 x .35 = $1,470
$4,200 - $1,470 = $2,730
b. $5,000 x 44%
$5,000 x .44 = $2,200
$5,000 - $2,200 = $2,800
If -3/4 is the dividend and 2/5 is the divisor what is the quotient
[tex]-\cfrac{3}{4}\div \cfrac{2}{5}\implies -\cfrac{3}{4}\cdot \cfrac{5}{2}\implies -\cfrac{15}{8}\implies {\Large \begin{array}{llll} -1\frac{7}{8} \end{array}}[/tex]
The aquarium has 6 fewer yellow fish than green fish. 40% of the fish are yellow. How many green fish are in the aquarium? Show your work
Answer: 18 fishes
Step-by-step explanation:
y=0.40(y+g)(2)
g-6=0.40(g-6)+0.40g
=0.40g-2.4+0.40g
=3.6/0.2
g=
In 2012, the U.S. population was about
314 million. How many people over the
age of 64 were in the U.S.?
There are 38,936,000 people over the age of 64 were in the U.S.
Option 2 is true.
What is Percentage?
A relative value indicating hundredth part of any quantity is called percentage.
Given that;
In 2012, the U.S. population was about 314 million.
Now,
Total population = 314,000,000
In the pie chart, The percent of people over the age of 64 were in the U.S will be 12.4%
Hence, Solve as;
Number of people over the age of 64 = 314,000,000 × 12.4%
= 314,000,000 × 12.4 / 100
= 31,400,00 × 12.4
= 38,936,000
Thus,
There are 38,936,000 people over the age of 64 were in the U.S.
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A bank account gathers compound interest at a
rate of 5% each year.
Another bank account gathers the same amount of
money in interest by the end of each year, but
gathers compound interest each month.
If Cameron puts £4200 into the account which
gathers interest each month, how much money
would be in his account after 2 years and
7 months?
Give your answer in pounds to the nearest 1p.
Based on the amount that Cameron invests in the bank account that gathers interest each month, the amount in the account after 2 years and 7 months is £4,777.81
How to find the amount in the account?The number of periods in months is:
= 2 years and 7 months
= 31 months
The periodic interest in months is:
= 5% / 12 months
= 5/12%
The amount in the bank account after 2 years and 7 months is:
= 4,200 x (1 + 5/12%)³¹
=£4,777.81
In conclusion, the amount after 2 years and 7 months have elapsed is £4,777.81
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Write the given transformation in vector notation (please help its due in 20 mins)
Answer:
-1, 1
Step-by-step explanation:
The translation is 1 unit left and 1 unit up.
Mr. Burke wants to invest part of his lottery winnings in a safe fund that earns 2.5% annual interest and the rest in a
risky fund that expects to yield 8% annual interest. The amount of money invested in the safe fund, x, is to be exactly
four times the amount invested in the risky fund, y. Use the system of equations to determine the amount to be
invested in each fund if a total of $1080 is to be earned at the end of one year.
Answer:
eywgw6 the car is in the car is in the car is in
Step-by-step explanation:
Wu and I will be in the car is in the car is in the car is in the car is here and we can 4
Answer:
Safe fund = $24,000
Risky fund = $6,000
Step-by-step explanation:
Definition of variables:
Let x = the amount of money invested in the safe fund.Let y = the amount of money invested in the risky fund.Given information:
Safe fund = 2.5% annual interest.Risky fund = 8% annual interest. Total interest earned at the end of one year = $1080.The amount of money invested in the safe fund, x, is to be exactly four times the amount invested in the risky fund, y.Convert the percentages into decimal form:
[tex]\implies 2.5\%=\dfrac{2.5}{100}=0.025[/tex]
[tex]\implies 8\%=\dfrac{8}{100}=0.08[/tex]
Create a system of equations from the given information and defined variables:
[tex]\begin{cases}0.025x+0.08y=1080\\x=4y\end{cases}[/tex]
Substitute the second equation into the first equation and solve for y:
[tex]\implies 0.025(4y)+0.08y=1080[/tex]
[tex]\implies 0.1y+0.08y=1080[/tex]
[tex]\implies 0.18y=1080[/tex]
[tex]\implies \dfrac{0.18y}{0.18}=\dfrac{1080}{0.18}[/tex]
[tex]\implies y=6000[/tex]
Substitute the found value of y into the second equation and solve for x:
[tex]\implies x=4(6000)[/tex]
[tex]\implies x=24000[/tex]
Therefore, the amount invested in each fund was:
Safe fund = $24,000Risky fund = $6,000Three consecutive integers have a sum of 81. Find the integers
Answer:
26, 27, 28
Step-by-step explanation:
Let the 3 integers be: x, x+1, x+2
x+x+1+x+2 = 81
3x+3 = 81
3x = 78
x = 26
x+1 = 27
x+2 = 28
write a quadratic function in standard form containing the point (5,-6) and x-intercepts -7 and 3
WILL GIVE BRAINLIEST
Answer:
[tex]y=-\dfrac{1}{4}x^2-x+\dfrac{21}{4}[/tex]
Step-by-step explanation:
Intercept form of a quadratic equation
[tex]y=a(x-p)(x-q)[/tex]
where:
p and q are the x-intercepts.a is some constant.Given:
x-intercepts: -7 and 3Point on the curve: (5, -6)Substitute the given values into the formula and solve for a:
[tex]\begin{aligned} y&=a(x-p)(x-q)\\\\\implies-6&=a(5-(-7))(5-3)\\-6&=a(12)(2)\\-6&=24a\\a&=\dfrac{-6}{24}\\\implies a&=-\dfrac{1}{4}\end{aligned}[/tex]
Substitute the given x-intercepts and the found value of a into the formula:
[tex]\implies y=-\dfrac{1}{4}(x+7)(x-3)[/tex]
Expand to standard form:
[tex]\implies y=-\dfrac{1}{4}(x^2-3x+7x-21)[/tex]
[tex]\implies y=-\dfrac{1}{4}(x^2+4x-21)[/tex]
[tex]\implies y=-\dfrac{1}{4}x^2-x+\dfrac{21}{4}[/tex]
Demarcus and Lauren each take out a $90,000 loan for a new condo. Each has to repay the loan in 10 years. Demarcus will pay an interest rate of 2.8% per year. His monthly payments will be $771. Because Lauren has a lower credit score, she will have to pay an interest rate of 3.7% per year. Her monthly payments will be $840. How much more will a $90,000 loan cost Lauren than Demarcus?
The amount that a $90,000 loan cost Lauren than Demarcus will be $8280.
How to calculate the value?From the information, Demarcus and Lauren each take out a $90,000 loan for a new condo and each has to repay the loan in 10 years. It should be noted that 10 years in months will be:
= 10 × 12 = 120 months
The difference in the amount paid as a result of the credit score will be:
= ($840 × 120) - ($771 × 120)
= $100800 - $92520
= $8280
Therefore, the amount is $8280.
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3.4-2.8d+2.8d-1.3Combine like terms to create an equivalent expression.
The given expression is
3.4 - 2.8d + 2.8d - 1.3
By collecting like terms, we have
- 2.8d + 2.8d + 3.4 - 1.3
= 0 + 2.1
= 2.1
Find the function f whose zeros are 6 and 3
Please hurry due today I will give you brainlest
Which numbers are solutions of x² + 20 = 9x + 2? choose
Answer:
x = 6 or x = 3
Step-by-step explanation:
Solve for x over the real numbers:
x^2 + 20 = 9 x + 2
Subtract 9 x + 2 from both sides:
x^2 - 9 x + 18 = 0
The left-hand side factors into a product with two terms:
(x - 6) (x - 3) = 0
Split into two equations:
x - 6 = 0 or x - 3 = 0
Add 6 to both sides:
x = 6 or x - 3 = 0
Add 3 to both sides:
Answer: x = 6 or x = 3
Is it right?????????
Check the picture below.
let's bear in mind that the standard deviation measures deviation in a dataset, so is a measure of how much the data fluctuates, so a dataset of 3 , 1000, will have a much higher deviation value than a same total of 450 , 553.
Help me answer this please!!!
Answer:2 choice
Step-by-step explanation:you use the rise over run technique with 2 points, it should give you rise 1 run 4 since the line is decreasing its a negative. For the y-int its the point where the line crosses Y int which is (0,-2) answer is -2
On a given planet the weight of an object varies directly with the mass of the object. Suppose that an object whose mass is 80 KG weighs 80 n calculate the mass of another object that weighs 70 n
We are told that the weight of an object varies directly with the mass of the object. This basically means that if w is the weight and M is the mass then these two magnitudes are related by the following expression:
[tex]w=k\cdot M[/tex]Where k is a constant.
We know that an object with a mass of 80kg weights 80 newtons. Then for this object we have w=80kg and M=80n so we get:
[tex]80n=k\cdot80kg[/tex]We divide both sides of this equation by 80:
[tex]\begin{gathered} \frac{80n}{80}=\frac{k\cdot80kg}{80} \\ 1n=k\cdot1kg \end{gathered}[/tex]Here it's important to remember that 1 newton (i.e. 1n) is equal to:
[tex]n=\frac{kg\cdot m}{s^2}[/tex]Then we get:
[tex]1\frac{kg\cdot m}{s^2}=k\cdot1kg[/tex]We divide both sides by 1 kg:
[tex]\begin{gathered} \frac{1\frac{kg\cdot m}{s^2}}{1kg}=\frac{k\cdot1kg}{1kg} \\ 1\frac{kg\cdot m}{kg\cdot s^2}=k\cdot\frac{1kg}{1kg} \\ k=1\frac{m}{s^2} \end{gathered}[/tex]So now that we found k we have the following expression for the weight of an object as a function of its mass:
[tex]w=M\cdot1\frac{m}{s^2}[/tex]For an object that weights 70n we get:
[tex]\begin{gathered} 70n=M\cdot1\frac{m}{s^2} \\ 70\frac{kg\cdot m}{s^2}=M\cdot\frac{m}{s^2} \end{gathered}[/tex]We divide both sides by 1 m/s²:
[tex]\begin{gathered} \frac{70\frac{kg\cdot m}{s^2}}{1\frac{m}{s^2}}=\frac{M\cdot\frac{m}{s^2}}{1\frac{m}{s^2}} \\ 70\frac{kg\cdot m\cdot s^2}{m\cdot s^2}=M\cdot\frac{m\cdot s^2}{s^2\cdot m} \\ 70kg=M \end{gathered}[/tex]AnswerSo the mass of an object that weights 70n is 70kg.
Use the diagram find the image of c under the translation described by the translation rule
(X,y) (x+11,y-8)
○ B
○ A
○ D
○ E
14. In baseball, a player's batting average is calculated by using the formula. A=h/b,
where A is the batting average, h is the number of hits, and b is the number of at
bats.
a. Solve the equation for h. What is the equation to solve h
Answer: h = b/A
Explanation: If i hit 5 out of 10 balls thrown, my batting average is 2.
.5 = 5/10.
If my batting average is .5, and 10 balls were thrown, I only hit half or 5 of them. 5 = 10/.5
HELP ASP YOULL GET 20 POINTS AND BRAINLIEST!!!
Answer:
7 Games
Step-by-step explanation:
1. take the information and put it into a equation (being y=3.25x+3 or f(x)=3.25+3)
2. replace the x with a whole number because you can't bowl half a game.
Ex: f(3)=12.75 or f(6)=22.50
3. The highest you can go without going over your money is 7 games ($25.75) leaving you with a total of 2.25.
Hello, I’m struggling with my geometry homework
Answer
Explanation
Given:
m
To determine the mAs we can see, CD form a straight line, so the angle of it must be 180°. Now, we can get the m[tex]\begin{gathered} m\angle APE+m\angle APD=180 \\ 67+m\angle APD=180 \\ Simplify\text{ and rearrange} \\ m\angle APD=180-67 \\ m\angle APD=113\degree \end{gathered}[/tex]Since the line ED is at the center of the circle:
[tex]m\angle APD=m\hat{AD}[/tex]Therefore,
[tex]m\hat{AD}=113\degree[/tex]given a number line C=11 and D=13 CD=?can u help me solve this problem?
The diagram of the number line is shown below
Thus, the distance CD which is the distance between point D and point C is
13 - 11 = 2
CD = 2
please solve the inequality in the picture shown below i will give brainliest
[tex]\frac{3}{4} -\frac{1}{2} p > \frac{5}{4} \\\frac{3}{4}(4)-\frac{1}{2} p(4) > \frac{5}{4} (4)\\3-2p > 5\\-2p > 5-3\\-2p > 2\\\frac{-2p}{-2} > \frac{2}{-2} \\p < -1[/tex]
when you divide or multiply by a negative number the signs <> change directions.
The depth of a local lake averages 26 ft, which is represented as |−26|. In February, it measured 5 ft deep, or |−5|, and in July, it was 18 ft deep, or |−18|. What is the difference between the depths in February and July?
21 feet
23 feet
8 feet
13 feet
The difference between the depths in February and July is D. 13 feet.
How to illustrate the information?From the information illustrated, it was stated that the depth of a local lake average 26 ft is represented as |−26|. In February, it measured 5 ft deep, or |−5|, and in July, it was 18 ft deep, or |−18|.
Therefore, it should be noted that the depth in July is -18.
Therefore, the difference between the depths in February and July will be:
= -5 - (-18)
= -5 + 18
= 13
Therefore, the difference is 13 feet.
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A right rectangular prism is packed with cubes of side length 1/8 inch. if the prism is packed with 16 cubes along the length, 8 cubes along the width, and 6 cubes along the height, what is the volume of the prism?A. 1 1/2 cubic inchesB. 1 3/4 cubic inchesC. 2 1/2 cubic inchesD. 2 3/4 cubic inches
Answer:
A. 1 1/2 cubic inches
Explanation:
We are told that the side length of the cube is 1/8 of an inch. Furthermore, we are also told that the rectangular prism fits 16 cubes along the length, 8 cubes along the width, and 6 cubes along the height. This means the measures of the dimensions of the prism are
[tex]\begin{gathered} \frac{1}{8}\times16\: in=2\: in \\ \end{gathered}[/tex][tex]\frac{1}{8}\times6\: in=0.75\: in[/tex][tex]\frac{1}{8}\times8\: in=1\: in[/tex]Therefore, the volume of the prism is
[tex]2\: in\times0.75\: in\times1\: in=1\frac{1}{2}\: in^3[/tex]Hence, the volume of the prism is 1 1/2 cubic inches
P
TU =
UV =
32°
-
5.5 cm
3.1 cm
VW-
Tech Support
151°
S
cm
cm
Q
Look carefully at quadrilateral PQRS.
Consider the transformation Rz (PQRS) that produces its image, quadrilateral
TUVW.
Find all the following:
cm
147°
3.8 cm
6.0 cm
30°
R
N
Answer:
Step-by-step explanation:
You get paid an annual salary of $67,100/year. You get paid bi-
weekly. Calculate the gross pay.
The product of 3 and the difference of a number and 1
Where”a number” is the letter x
Which conversion factors can be used to multiply to 4 km/min to get meters per hour?Select each correct answer. 1 km1000 m1 h60min60min1 h1000 m1 km
Step 1: Concept
To convert km to meters you will multiply with 1000.
To convert minute to hour you will divide by 60
Step 2: Convert
[tex]\begin{gathered} 4\operatorname{km}\text{ to meters = 4 }\times\text{ }\frac{1000m}{1\operatorname{km}}\text{ } \\ 1\text{ min to hour = 1}\min \times\frac{1\text{hour}}{60\text{ min}} \end{gathered}[/tex]Step 3: Final answer
[tex]\frac{1000m}{1\operatorname{km}}\text{ and }\frac{1hour}{60\min }[/tex]Option B and D