Let [tex] x,y [/tex] be the lengths of the original legs. The original area is thus
[tex] \dfrac{xy}{2} [/tex]
Now, we triple the legs, so we have [tex] (x,y)\mapsto(3x,3y) [/tex]
The new area is
[tex] \dfrac{(3x)(3y)}{2} = \dfrac{9xy}{2} = 9\dfrac{xy}{2} [/tex]
which is 9 times the original area.
So, if you triple both legs, the area will be nine times as much as the original one.
For the following figure, complete the statement for the specified points.
Point A, B, and Q are _____.
collinear
coplanar
both collinear and coplanar
neither collinear nor coplanar
The correct answer is coplanar
EXPLANATION
Coplanar means the three points A , B and Q are on the same plane.
They are not colinear, because they are not in a straight line. It is only A and Q that are on the same straight line. If B had fallen in line with them, the three points would have been collinear as well.
Answer:
the answer is coplanar
Step-by-step explanation:
Justin purchased a 20 pound pumpkin for$9.80. How much did he pay per pound
Please help asap 35 pts
I’m pretty sure the answer is B. Add 15 to 73. Divide 88 by 8 to get 11. A>11
Over the weekend koko spend a total of 16 hours working on school work she spent equal amounts of time working on 4 projects plus 2 hours working on her language arts homework how much time did she spend on each project
Vector's map has the scale missing. He knows that the distance from the lake to the youth center is 8 miles. On the map, they are 2 inches apart. What is the scale for vector's map
How many points are collinear with points C and D
Only point U.
Therefore your answer is ONE.
Answer:
B) One
Step-by-step explanation:
If the points are collinear, then they lie on the same line.
Here U is lie on the same line where C and D points lie.
Therefore, answer is B) One.
Hope this will helpful.
Thank you.
Kendall is buying a home for 119,000 she is making a 12% down payment and financing the rest with 20-year loan at 4.5% interest what is her monthly mortgage payment ?
662.46 is your answer
The required Kendall's monthly mortgage payment is $662.14.
What is interest?Simple interest is defined as the percentage of earnings on the lending for a period of time.
Here,
Kendall's down payment is 12% of $119,000, which is:
0.12 * $119,000 = $14,280
So the amount she is financing is:
$119,000 - $14,280 = $104,720
To calculate her monthly mortgage payment, we can use the formula for a fixed-payment loan:
[tex]M = P * (r / (1 - (1 + r)^{-n}))[/tex]
First, we need to calculate the monthly interest rate. The annual interest rate is 4.5%, so the monthly interest rate is:
4.5% / 12 = 0.375%
Next, we need to calculate the total number of monthly payments. Kendall has a 20-year loan, which is:
20 years * 12 months/year = 240 months
Now we can plug in the values and solve for M:
[tex]M = $104,720 * (0.00375 / (1 - (1 + 0.00375)^{-240}))[/tex]
M = $662.14
So Kendall's monthly mortgage payment is $662.14.
Learn more about interest here:
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If f(x) = 3x-2 what is the value of 5
A. 9
B. 13
C. 15
D. 33
B
Assuming you mean the value of f(5)
If so then substitute x = 5 into f(x)
f(5) = (3 × 5) - 2 = 15 - 2 = 13 → B
A dolphin is swimming with her friend. The dolphin jumps to a height of 4.54.54, point, 5 meters above the surface of the water as her friend swims 9.89.89, point, 8 meters directly below her. What is the position of the dolphin's friend relative to the surface of the water?
The dolphin's friend is 8.63 meters below the surface of the water relative to the dolphin's jumping point.
Explanation:To solve this problem, we can use the kinematic equation that relates initial velocity, final velocity, acceleration, and displacement:
vf² = vi² + 2ad
Knowns:Plug in the knowns: (-13.0 m/s)² = (0 m/s)² + 2(-9.8 m/s²)(d)Simplify and solve for d: d = (169 m²/s²) / (-19.6 m/s²)Calculating: d = -8.63 mThe positive value of d indicates that the dolphin's friend is 8.63 meters below the surface of the water relative to the dolphin's jumping point.
The dolphin's friend is 5.3 meters below the surface of the water.
Let's reassess the problem with the given constraints more carefully.
We need to find the position of the dolphin's friend relative to the surface of the water.
1. Dolphin's height above the water:
[tex]\[ 4.5 \text{ meters above the surface} \][/tex]
2. Distance between the dolphin and her friend:
[tex]\[ 9.8 \text{ meters below the dolphin} \][/tex]
Since the friend is swimming below the dolphin, we need to subtract this distance from the height of the dolphin above the surface to find the position of the friend relative to the water surface.
3. Calculate the position of the dolphin's friend:
[tex]\[ \text{Position of friend} = 4.5 \text{ meters} - 9.8 \text{ meters} \][/tex]
[tex]\[ \text{Position of friend} = -5.3 \text{ meters} \][/tex]
This means the dolphin's friend is 5.3 meters below the surface of the water.
HELP PLZ SOMEONE I AM DESPERATE. PLX ANSWER MY OTHER MATH QUESTION TOO PLZ
There 2 which are correct
13/3 - 4/6
= 13/3 - 2/3
= 11/3
and
3/2 - 1/6
= 9/6 - 1/6
= 8/6
= 4/3
Tim is buying packages of paper plates & cups. He wants to have equal amounts of each, but plates come in 24 per pack and cups come in 16 per pack. What is the least amount of plates & cups Tim will buy to get the same number of each ? A. 8 B. 16 C. 24 D. 48
30 points! How do I factor 6x^2+x-15
Using the Grid Box Method?
Thank you! Thanks for helping - that was all of my factoring problems! :D ^.^ Most educational sites explain the factoring methods well, but in a very confusing way! :'3 Thank you so much again; have an awesome day! :)
Now for this you would have to think what two numbers multiplied to get 6x^2. Let's say for example 3x and 2x=6x^2
And now what two numbers multiplied together make -15, For example it can be 5 and -3
Now your ANSWER: (3x+5)(2x-3)
You work 1.15 hours on your English Homework and 1.75 hours in your math homework. Your science homework takes 1.05 hours less than your math homework. How many more hours do you work on your homework? The answer is 4 but it's saying it's wrong
Answer:
Total time taken for doing home work = 3.6 hours.
Explanation:
Time taken for English home work = 1.15 hours.
Time taken for Mathematics home work = 1.75 hours.
Time taken for Science home work = Time taken for Mathematics home work - 1.05 hours = 1.75 - 1.05 = 0.7 hours
Total time taken for doing home work = 1.15 + 1.75 + 0.7 = 3.6 hours.
So the answer is not 4 hours, it is 3.6 hours, that is why it is showing it as wrong.
a card is chosen from a standard deck of cards. what is the probability that the card is a queen, given that the card is a club?
Answer:
Probability that card is queen given that card is club is [tex]\frac{4}{13}[/tex]
Step-by-step explanation:
Given : A card is chosen from a standard deck of cards.
To find : What is the probability that the card is a queen, given that the card is a club?
Solution : It is the conditional probability
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
Let A is probability that card is queen.
Let B is the probability that card is a club.
Probability that card is queen given card is club [tex]P(A\cap B)=\frac{4}{52}=\frac{1}{13}[/tex]
Probability that card is club from deck of 52 cards [tex]P(B)=\frac{13}{52}=\frac{1}{4}[/tex]
To find probability that card is queen given that card is club [tex]P(A|B)[/tex]
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
[tex]P(A|B)=\frac{\frac{1}{13}}{\frac{1}{4}}[/tex]
[tex]P(A|B)=\frac{1\times4}{13\times 1}=\frac{4}{13}[/tex]
Therefore, Option A is correct.
Probability that card is queen given that card is club is [tex]\frac{4}{13}[/tex]
Answer:
the correct answer was 1/13
Step-by-step explanation:
i took my test and put 4/13 which was wrong and said that 1/13 is the right answer
The graph of g(x) is obtained by reflecting the graph of f(x)=4|x| over the x-axis.
Which equation describes g(x)?
A) g(x)=|x−4|
B) g(x)=|x+4|
C) g(x)=−4|x|
D) g(x)=|x|−4
That would be choice C.
The graph of 4|x| is shaped like a V whose vertex is at the origin.
Every y value will be positive for y = 4|x| as |x| is always positive and a reflection in the x axis will make every y value negative.
Through moving up c units, the graphs of g can be determined from the graph of f. If we subtract c from f(x), the graph shifts downward. Let [tex]\bold{ h(x) = f(x) - c}[/tex]. Shifting downward c units yields this graph of h from the graph of f.
Given:
[tex]\bold{f(x)=4|x|}[/tex]
Calculation:
It is stated that its graph of [tex]g(x)[/tex] is obtained by reflecting a graph of [tex]f(x)=4|x|[/tex] over the x-axis.When a figure is reflected across the x-axis, the rule for reflection is [tex]\bold{(x,y) \to (x,-y)}[/tex].To use the preceding logic, if the given function is reflected from across the x-axis, then [tex]g(x)=-f (x)[/tex].[tex]\bold{g(x)=-(4|x|)}\\\\\bold{g(x)=-4|x|}\\\\[/tex]
So, the equation [tex]g(x)=-4|x|[/tex] describes [tex]g(x)[/tex].
Therefore, the final choice is "Option C".
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Olivia divided a fraction by 3/4. The quotient was a whole number. Was the the dividend less than 3/4? Explain
Let's assume
Let's assume that fraction as 'x'
and whole number as 'n'
Olivia divided a fraction by 3/4
so, we get
[tex]\frac{x}{\frac{3}{4} }[/tex]
The quotient was a whole number
so, we get
[tex]\frac{x}{\frac{3}{4} }=n[/tex]
now, we can solve for x
[tex]\frac{3}{4}\times \frac{x}{\frac{3}{4} }=\frac{3}{4}\times n[/tex]
[tex]x=\frac{3n}{4}[/tex]
where n is whole numbers
At n=0:
[tex]x=\frac{3*0}{4}[/tex]
[tex]x=0[/tex]
here , x is not fraction
so, n=0 is not possible
At n=1:
[tex]x=\frac{3*1}{4}[/tex]
[tex]x=\frac{3}{4}[/tex]
At n=2:
[tex]x=\frac{3*2}{4}[/tex]
[tex]x=\frac{3}{2}[/tex]
we know that x is dividend
and x can be equal to 3/4
and greater than 3/4
But it can not be less than 3/4..............Answer
Answer:
Let's assume
Let's assume that fraction as 'x'
and whole number as 'n'
Olivia divided a fraction by 3/4
so, we get
The quotient was a whole number
so, we get
now, we can solve for x
where n is whole numbers
At n=0:
here , x is not fraction
so, n=0 is not possible
At n=1:
At n=2:
we know that x is dividend
and x can be equal to 3/4
and greater than 3/4
But it can not be less than 3/4..............Answer
Step-by-step explanation:
If eight trash bags last for thirty days then how many trash bags do you need for 180 days
Set up the proportion. Then cross multiply and isolate the variable to solve.
[tex]\frac{8(trash bags)}{30 (days)} = \frac{x (trash bags)}{180 (days)}[/tex]
8(180)= 30(x)
[tex]\frac{8(180)}{30} = \frac{30x}{30}[/tex]
8(6) = x
48 = x
Answer: 48 trash bags
Amy wants to carpet a room that is 12 feet by 8 feet.How many square yards of carpet will she need to complete the room?
96 square yards would complete the room
Use the graph of the parent function f(x)=√x, to describe the transformation for the graph of g(x)=√x-5
Answer : C
[tex]f(x)= \sqrt{x}[/tex]
[tex]g(x)= \sqrt{x-5}[/tex]
Parent function is f(x). In g(x) 5 is subtracted from x
If any number is added or subtracted from x, then we move left or right
When a number 'a' is added with x then we shift 'a' units to the left
When a number 'a' is subtracted from x then we shift 'a' units to the right
f(x) is our parent function. Here 5 is subtracted from x to get g(x)
For -5, the graph of g(x) is the graph of f(x) shifted right 5 units
the first answer would be C
the next 3 questions are ACB
Define a variable and write and inequality for the statement: In order to earn credit for your Algebra 1A course, you must earn at least 70%.
We are given statement: "In order to earn credit for your Algebra 1A course, you must earn at least 70%."
We need to define a variable and write an inequality for the given situation.
Let us assume variable for now for earn credit = c.
Now, we can repharse the given statement as " earn credit c must be atleast 70%".
Therefore, we can write the inequality for above rephared statement as :
c ≥ 70 : Read as c is greater than 70.
what else would need to be congruent to show that abc def by aas
The answer is A=D apex
Answer:
It's the first one, I just literally got done taking the test it was my last question anyways.
im terrible with graphs help me out...but explain it cuz im a math inclined typa person sooo.......idek just help i guess?
Answer:
14. The correct option is 2.
13. The correct option is 4.
Step-by-step explanation:
14.
The given function is
[tex]f(x)=4|x|[/tex]
The function is non-negative for all values of x. So, the function opens in upward direction.
The function uis in the form of
[tex]f(x)=k|x|[/tex]
Where, a is vertical stretch factor or compress factor.
If k>1, then it represent vertical stretch and if 0<k<1, then it represent vertical compression.
Since the value of k is 4, therefore it represents vertical stretch and option 2 is correct.
13.
The given function is
[tex]y=x^3[/tex]
The traslate form of given function is
[tex]y=(x+a)^3+b[/tex]
Where, a represents the horizontal shift and b represents the vertical shift.
If a>0, then the graph shifts left side by a units and if a<0, then the graph shifts right side by a units.
If b>0, then the graph shifts upward by b units and if b<0, then the graph shifts downward by b units.
Since the graph shifts vertically 5 units down and horizontally 4 units left, therefore the value of a is 4 and value of b is -5. The required equation is
[tex]y=(x+4)^3-5[/tex]
Therefore option 4 is correct.
Use the two points (4,92) and (1,82) from the scatterplot and the slope formula to find the slope of a linear model (regression line), rounded to three decimal places. Show your work. (5 points)
Using the slope and a point from question (a) to write the equation of the linear model in point-slope form? (5 points)
Simplify the equation you wrote in problem (b) into slope-intercept form. Show your work. (5 points)
Answer:
a) The slope is : 3.333
b) [tex](y-92)=3.333(x-4)[/tex]
c) [tex]y=3.333x+78.66[/tex]
Step-by-step explanation:
a) - The formula to calculate the slope is:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
- Use the given points to calculate the slope:
[tex]y_{2}=82\\y_{1}=92\\x_{2}=1\\x_{1}=4[/tex]
[tex]m=\frac{82-92}{1-4}\\m=\frac{10}{3}\\m=3.333[/tex]
b) - The equation of the linear model in point-slope form is:
[tex](y-y_{1})=m(x-x_{1})[/tex]
Where [tex]m[/tex] is the slope and [tex]x_{1},y_{1}[/tex] are the coordinates of a point.
- Substitute values:
[tex](y-92)=3.333(x-4)[/tex]
c) - The equation of the linear model in slope-intercept form is:
[tex]y=mx+b[/tex]
Where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
- Let's find [tex]b[/tex]. Use one of the points given in the problem to solve for [tex]b[/tex]:
[tex]92=3.333(4)+b\\b=92-13.332\\b=78.66[/tex]
- Therefore, the equation is:
[tex]y=3.333x+78.66[/tex]
Find all points on the x-axis that are 14 units from the point (3,-7).
Answer:
(3±√147, 0) ≈ (-9.124, 0) and (15.124, 0)
Step-by-step explanation:
The points (x, 0) satisfy the distance formula:
d = 14 = √((x -3)² +(0+7)²)
196 = (x -3)² +49 . . . . . square both sides
147 = (x -3)² . . . . . . . . . subtract 49
3 ±√147 = x . . . . . . . . . take the square root and add 3
The points at distance 14 from (3, -7) on the x-axis are (3±√147, 0).
Find two consecutive positive odd no. Such tht the sum of thier squares is equal to 130
7 squared is 49, and 9 squared is 81. 49+81=130 7,9 are your answers
Please help, I would appreciate it!!
Two Angles are Supplementary when they add up to 180°.
m∠2 + m∠1 = 180° (*)
If ∠1 ≅ ∠3, then m∠1 = m∠3.
Substitute to the (*)
m∠2 + m∠3 = 180°
Therefore ∠2 and ∠3 are supplementary.
Which pair is the gcf of 1, 30 and 70, 24 and 44, 12 and 30, and 16 and 21
The GCF is 1.
Explanation:
1 has: 1 (LOL)
12 has: 1,2,3,4,6,12
16 has: 1,2,4,8,16
21 has: 1,3,7,21
24 has: 1, 2, 3, 4, 6, 8, 12, 24
30 has: 1, 2, 3, 5, 6, 10, 15, 30
44 has: 1, 2, 4, 11, 22, 44
70 has: 1, 2, 5, 7, 10, 14, 35, 70
So therefore, The GCF is 1
Hope this helps!
-Queenb369
P.S Could you possible give me the brainlist if i get it right.
Question 1 of 10 Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12
Hey there!!
The question states that a sum is invested which is $3000 and hence, this would be counted as the principle amount or the principle sum.
The term given is 3 years, which gives us the idea that this interest is being counted or being active for 3 years.
She ( Diana ) earned the sum $450 at the end of three years. This means, the simple interest is $450.
Never get confused with the principle amount, principle sum and interest.
Principle amount = Principle sum + The interest.
Formula given :
I = prt
'p' is denoted as the principle sum, r is the rate and the t is the term or the number of years.
Now, plugging in all the values :
... 450 = 3000×r×3
... 450 = 9000×r
... r = 450 / 9000
... r = 0.05
... r = 5%
As we need the answer in the decimal form, the answer would be 0.05
Hope my answer helps!!
Write the equation of the line, given the y and x-intercepts. x-intercept = –6, y-intercept = –8
The slope-intercept form of a line: y = mx + b
m - slope, b - y-intercept
We have:
y-intercept = -8. Substitute:
y = mx - 8
x-intercept = -6 for y = 0. Substitute:
0 = m(-6) - 8
0 = -6m - 8 |+6m
6m = -8 |:6
m = - 8/6
m = - 4/3
Answer; y = - 4/3 x - 8
Find the equation of a line given two points P1(?4, 8), P2(?4, ?7)
Using the distance formula, it equals sqrt(1)