Teresa has $451 in a personal bank account,and then withdraws $10 per week.Andrew has $10 in a personal bank account,and then deposits $53 earned from dog grooming each week.After how many weeks will they have the same amount of money in the bank.
Given:
Teresa has $451 in a personal bank account,and then withdraws $10 per week.
Andrew has $10 in a personal bank account,and then deposits $53 each week.
To find:
After how many weeks will they have the same amount of money in the bank.
Solution:
Let x be the number of weeks after which they have the same amount.
Teresa has $451 in a personal bank account,and then withdraws $10 per week. So, the amount in Teresa's account is:
[tex]\text{Teresa's account}=451-10x[/tex]
Andrew has $10 in a personal bank account,and then deposits $53 each week. So, the amount in his account is:
[tex]\text{Andrew's account}=10+53x[/tex]
They have equal amount after x weeks. So,
[tex]451-10x=10+53x[/tex]
Isolate variable terms.
[tex]451-10=10x+53x[/tex]
[tex]441=63x[/tex]
Divide both sides by 63.
[tex]\dfrac{441}{63}=x[/tex]
[tex]7=x[/tex]
Therefore, they will have the same amount of money in the bank after 7 weeks.
Which of the following statements is false?
A. A rectangle is a parallelogram.
B. A rhombus is a parallelogram.
C. The height of a trapezoid is the distance between its bases.
D. Given quadrilateral ABCD, AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯ are adjacent
to Answer:
D is false
Step-by-step explanation:
AB and CD are not adjacent.
AB is adjacent to BC and AD but not to CD.
find the missing length for the following trapezoid
Answer:
KL = 18
Step-by-step explanation:
The midsegment TU is half the sum of the parallel bases , that is
[tex]\frac{KL+JM}{2}[/tex] = TU
[tex]\frac{KL+34}{2}[/tex] = 26 ( multiply both sides by 2 )
KL + 34 = 52 ( subtract 34 from both sides )
KL = 18
please answer correctly and i will give 10 extra points
Answer:
I believe the answer would be 48.6 milliliters
Step-by-step explanation:
54 * 0.9 = 48.6
Olympia ate lunch at a restaurant. The amount of her check was $6.89. She left $8.00 on the table, which included the amount she owed plus a tip for the waiter. Which equation shows t, the amount of her tip, in dollars?
6.89 + t = 8.00
6.89 - t = 8.00
6.89t = 8.00
6.89 = 8.00 Divided by t
Answer:
not sure if the answer is obvious but I'd say $6.89 + t = $8.00
Step-by-step explanation:
so to make it more understandable you have to first go over the question and ask your self is the tip included in the totally amount owed or is it apart
after you figure out that its apart all you have to do is plug in the numbers you could verify this by checking every equation like this
$6.89 + t = $8.00 (t) in this case is the tip which would be $1.11 all you do to arrive at that answer is subtract the amout owed from the amount given like this $8.00 - $6.89 = $1.11 which will be your tip
now continue checking your answer next is , $6.89 - t = $8.00
which would be $6.89- $1.11 = $5.78 not quite right because now she is short on the pay , on to the next its $6.89t= $8.00 which would be $6.89 x $1.11= $7.65 rounded to neartest tenth which would included the amount but not all the tip given meaning tip would be short 0.35 cents and finally $6.89= $8.00 divided by t , now this takes the amount give which is $8.00 and divides by t which is $1.11 doing this $6.89 = $8.00/$1.11 which it is trying to imply that $6.89 is equal to $7.21 which would be incorrect making the only reasonable equation $6.89 + t = $8.00 reaveling that the tip given was $1.11
hopefully that help maybe i can get brainlist?!
Answer:
6.89 + t = 8.00
Step-by-step explanation:
it's A
Edge 2021
11) Seven times a number subtracted from 29 gives 43. Find the number.
Answer:
-2
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
7x-2=-14
29-(-14)=43
hope this helps :)
help please ITS OF TRIGONOMETRY
PROVE
Answer:
The equation is true.
Step-by-step explanation:
In order to solve this problem, one must envision a right triangle. A diagram used to represent the imagined right triangle is included at the bottom of this explanation. Please note that each side is named with respect to the angle is it across from.
Right angle trigonometry is composed of a sequence of ratios that relate the sides and angles of a right triangle. These ratios are as follows,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
One is given the following equation,
[tex]\frac{sin(A)+sin(B)}{cos(A) +cos(B)}+\frac{cos(A)-cos(B)}{sin(A)-sin(B)}=0[/tex]
As per the attached reference image, one can state the following, using the right angle trigonometric ratios,
[tex]sin(A)=\frac{a}{c}\\\\sin(B)=\frac{b}{c}\\\\cos(A)=\frac{b}{c}\\\\cos(B)=\frac{a}{c}[/tex]
Substitute these values into the given equation. Then simplify the equation to prove the idenity,
[tex]\frac{sin(A)+sin(B)}{cos(A) +cos(B)}+\frac{cos(A)-cos(B)}{sin(A)-sin(B)}=0[/tex]
[tex]\frac{\frac{a}{c}+\frac{b}{c}}{\frac{b}{c}+\frac{a}{c}}+\frac{\frac{b}{c}-\frac{a}{c}}{\frac{a}{c}-\frac{b}{c}}=0[/tex]
[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{b-a}{c}}{\frac{a-b}{c}}[/tex]
Remember, any number over itself equals one, this holds true even for fractions with fractions in the numerator (value on top of the fraction bar) and denominator (value under the fraction bar).
[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{b-a}{c}}{\frac{a-b}{c}}[/tex]
[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{-(a-b)}{c}}{\frac{a-b}{c}}[/tex]
[tex]1+(-1)=0[/tex]
[tex]1-1=0[/tex]
[tex]0=0[/tex]
please answer this question!!
or which polygon is the sum of the interior angles equal to 540? A 5-sided figure. A 6-sided figure. A 6-sided figure. A 4-sided figure.
Answer:
A 5 sided figure
Step-by-step explanation:
To find the sum of interior angles we use the formula
S = (n - 2) *180
540 = 180n - 360
180n = 540 + 360
180n = 900
n = 900/180
n = 5
The number of sides of a polygon with the given sum of interior angles is 5.
Option A)5-sided figure is the correct answer.
What is a polygon?A polygon is simply a two-dimensional a plane shape enclosed by line segments called sides.
The formula for calculating the sum of interior angles of a polygon is;
S = ( n − 2 ) × 180°
Where S is the sum and n is the number of sides.
Given that the sum of the interior angles equal to 540°.
From the above expression;
S = ( n − 2 ) × 180°
540° = ( n − 2 ) × 180°
540° = 180°n − 360°
180°n = 540° + 360°
180°n = 900°
n = 900° / 180°
n = 5
The number of sides of a polygon with the given sum of interior angles is 5.
Option A)5-sided figure is the correct answer.
Learn more about polygons here: brainly.com/question/22408868
#SPJ2
Use the grouping method to factor this polynomial.
x2 + 2x2 + 12x + 24
O A. (x2 +12)(x+2)
O B. (x2 +6)(x+2)
C. (x² + 2)(x+6)
O D. (x2 + 2)(x+12)
Answer:
A. (x² + 12)·(x + 2)
Step-by-step explanation:
Question; Factor x³ + 2·x² + 12·x + 24, using the grouping method
The given polynomial is presented as follows;
x³ + 2·x² + 12·x + 24
Using the grouping method, we have;
(x³ + 2·x²)( + 12·x + 24)
Which gives;
x²·(x + 2) + 12·(x + 2)
Therefore, we get;
(x² + 12)·(x + 2)
The correct option is A. (x² + 12)·(x + 2).
What is the value of x in the equation
3x - y = 30, when y = 15?
Answer:
x = 15
Step-by-step explanation:
3x - y = 30
Given;
y = 15
To find;
value of 'x'
Putting the value of y in the given equation;
3x - 15 = 30
3x = 30 + 15
3x = 45
x = 45/3
x = 15
Answer:
x = 15Step-by-step explanation:
3x - y = 30let y = 153x - 15 = 303x = 30 + 153x = 45x = 45/3x = 15Let's check:3x - y = 303(15) - 15 = 3045 - 15 = 3030 = 30[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
whats the correct ordered pair for, x+y=12 and -x=-y-10
i'm doing this as a system, ok?
x + y = 12
- x = - y - 10
x + y = 12
-x + y = -10
2y = 2
y = 1
x + 1 = 12
x = 11
so, the ordered pair is (11, 1) -> remember that the x always comes first
hope it helps :)
Answer:yes yes culo Rotox (b
Step-by-step explanation: pro gard1bas x12x14x20¿142
If SP and CP of an article is Rs. x and Rs. y, write the formulae to find profit and loss percentage.
Answer:
profit= sp-cp
loss %= loss ×100%/cp
=(cp-sp) ×100%/cp
= (1-sp)×100%/cp
Why can't x^2+9 be factored? And is there a way to tell if a problem can be factored or not just by looking at it?
Answer:
There are no like terms
Step-by-step explanation:
×^2+9
=ײ+9
Suppose f(x) = x^2. what is the graph of g(x)
Answer: g(x) = (1/16)*x^2
========================================================
Explanation:
Plug x = 4 into f(x) to find that f(4) = 16.
The output y = 16 drops to y = 1. We've multiplied by 1/16 to get this to happen.
In other words,
g(x) = (1/16)*f(x)
g(4) = (1/16)*f(4)
g(4) = (1/16)*16
g(4) = 1
So we can say that,
g(x) = (1/16)*f(x)
g(x) = (1/16)*x^2
and furthermore, we can say f(x) has been vertically compressed by a factor of 16.
Determine the perimeter of the following figure
pls help! ill mark brainliest
Answer:
Step-by-step explanation:
Use Pythagorus to find the length of the unmarked length
c^2 = a^2 + b^2
a = 5
b = 17 -10 = 7
c = ?
c^2 = 5^2 + 7^2
c^2 = 25 + 49
c = sqrt(74)
c =8.602
P = 5 + 10 + 17 + 8.602
P = 40.602
Help plz and thanks
if 2x + 3x.find the value of x
if 2x + 3x = ? the question is incomplete or is it about traingle
Can someone please help me with these work rate questions!
Answer:
1/8 rooms per hour
Step-by-step explanation:
We are given that Beatrice can wallpaper 1 room in 8 hours. The work rate is how many rooms Beatrice can wallpaper in one unit of time (in this case, one hour).
Another way of saying 1 room in 8 hours is 1 room/8 hours. We want to find the rate over one hour, so we want to make the denominator ( in hours) equal to 0.
With fractions, we can divide/multiply both the numerator and denominator by the same amount, and still keep the fraction. Therefore, we want to make 8 hours 1 hour by multiplication or division. Since anything divided by itself is equal to 1, we can say that 8/8 is equal to 1. Therefore, we can divide both the numerator and denominator by 8 to get
(1 room/8) = (8 hours / 8)
= (1/8 rooms) / 1 hour
Therefore, the work rate is 1/8 rooms per hour
Someone please help me. Asap ?
Answer:
Graph A
Step-by-step explanation:
A directly proportional relationship must create a straight line that goes through the origin (0,0) ( note that the slope can be negative or positive in a proportional relationship. )
All graphs show a straight line going through the origin except Graph A.
Graph A shows a straight line however that line does not go through the origin therefore it is not a proportional relationship
Draw a rough sketch of a quadrilateral KLMN. State, (a) two pairs of opposite sides, (b) two pairs of opposite angles, (c) two pairs of adjacent sides, (d) two pairs of adjacent angles. please draw the answer
Answer:
Please find attached the drawing of quadrilateral KLMN created with MS Whiteboard using the Ink to Shape command
(a) Two pairs of opposite sides are [tex]\overline {KN}[/tex], [tex]\overline {LM}[/tex] and [tex]\overline {KL}[/tex], [tex]\overline {NM}[/tex]
(b) Two pairs of opposite angles are ∠LKN, ∠LMN, and ∠KLM and ∠KNM
(c) Two pairs of adjacent sides are [tex]\overline {KN}[/tex], [tex]\overline {NM}[/tex] and [tex]\overline {KL}[/tex], [tex]\overline {LM}[/tex]
(d) Two pairs of adjacent angles are ∠LKN, ∠KLM and ∠LMN, ∠KNM
Step-by-step explanation:
If f(x) = 3x2 - 7x, what is the ordered pair for x = 1 ?
A (1.4)
B (1,-4)
C (1,7)
D(1,10)
Answer:
b option is the weight answer I think.
WILL MARK BRAINLIEST!! Multiply. −1/2⋅3/4 a)−2/3 b) −3/8 c) 3/8 d)2/3
Explanation:
When multiplying fractions, we multiply the numerators together, and the denominators are handled separately.
The numerators in this case are -1 and 3. They multiply to -3
The denominators multiply to 2*4 = 8
So that's how we end up with -3/8 as the final answer
This fraction cannot be reduced any further, because 3 and have 8 no factors (other than 1) in common.
(1)
A piece of wire is bent to form a square of area 121 cm?
Calculate:
a)
The length of each side of the square
b)
The perimeter of the square
Step-by-step explanation:
that is really a problem ?
come on !
you know, the area of a square is side length × side length = length²
that is basically all of us learn as the very first thing when we are learning about squaring and multiplication.
how do we get the regular side length out of length² ?
we pull the square root. you have a calculator (at least on your computer, cell phone,...).
sqrt(121) = .... .... .... 11 ! tada !
and the perimeter of a square ... you really have to ask ?
it is the way all around the whole square. you need to go along every one of the 4 sides.
so, it is side length × 4 = 11×4 = 44 cm
again - you really needed help with THAT ?
log 55 is the power to which ---- must be raised in order to produce a value of 55
Answer:
10
Step-by-step explanation:
just took the quiz
BRAINLEST IF CORRECT
Answer:
422.39
Step-by-step explanation:
[tex]A = \pi r^2\\A = 144\pi \\\\144\pi -30 = 422.39[/tex]
use a calculator for the above and round
WILL GIVE BRAINLIEST TO THE CORRECT ANSWER!!
Suppose you obtain a five-year lease for a Porsche and negotiate a selling price of $146,000. The annual interest rate is 8.4%, the residual value is $75,000, and you make a down payment of $3000. Find each of the following.
A.) The net capitalized cost.
B.) The money factor. (Rounded to four decimal places)
C.) The average monthly finance charge. (Rounded to the nearest cent).
D.) The average monthly depreciation. (Rounded to the nearest cent.)
E.) The monthly lease payment. (Rounded to the nearest cent.)
Answer:
Look down below
Step-by-step explanation:
A.)Net capitalized cost=146,000-3000= $143,000
Net capitalized cost = 143,000
B.)Money factor=8.4/100 over 24=0.084/24=0.0035
Money Factor= 0.0035
C.)Average monthly finance charge= (143,000+75,000)x 0.0035= 218,000 x 0.0035=$763
Average Monthly Finance Charge= $763
D.)Average monthly depreciation= 143,000-75000/5 x 12=68000/60=$1133.33
Average monthly deprecation= $1133.33
E.)monthly lease payment=1133.33/5= $226.66
Monthly lease payment= $226.66
In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from $1$ to $10$, and one SuperBall is drawn (at random) from ten red balls numbered from $11$ to $20$. When you buy a ticket, you choose three numbers from $1$ to $10,$ and one number from $11$ to $20$.
If the numbers on your ticket match the three white balls and the red SuperBall, then you win the jackpot. (You don't need to match the white balls in order). What is the probability that you win the jackpot?
This question is solved using probability concepts.
A probability is given by the number of desired outcomes divided by the number of total outcomes.The order in which the balls are chosen don't matter, which means that the combinations formula is used to find the number of outcomes.Doing this, we get that:
[tex]\frac{1}{1200}[/tex] probability that you win the jackpot.
------------------------------------------
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
----------------------------------------------------
Total outcomes:
3 white from a set of 10(numbered from $1 to $10).1 red from a set of 10(numbered from $11 to $20).Thus:
[tex]T = C_{10,3}C_{10,1} = \frac{10!}{7!3!} \times \frac{10!}{1!9!} = 120 \times 10 = 1200[/tex]
Desired outcomes:
The correct balls, order does not matter, so only one outcome, that is, [tex]D = 1[/tex]
What is the probability that you win the jackpot?
[tex]p = \frac{D}{T} = \frac{1}{1200}[/tex]
[tex]\frac{1}{1200}[/tex] probability that you win the jackpot.
A similar question is given at https://brainly.com/question/23966554
Answer:
6/7200=1/1200
Step-by-step explanation:
[3! ways to arrange the three white balls] over [10x9x8 ways to pick three white balls and 10 ways to pick a red] =3x2x1/10x9x8x10=6/72x100=6/7200=1/1200
<(-_-)>__ConNelL__>(-_-)<
What is the resulting ordered pair if the value of the independent variable is 2?
f(x) = -5x + 4
Answer:
y= -6
x = 2
(2,-6)
Step-by-step explanation:
Indepedent variable = x = 2
Plug 2 in for x
f(2) = -5(2) + 4
-10 + 4 = -6
y = -6
Find the value of x in the triangle shown below.
This is a isoceles triangle so base angles will be equal.
Therefore
ATQ
55 + 55 + x = 180
110 + x = 180 (Angle Sum Property)
x = 180 - 110
x = 70
Therefore x° = 70°
Answered by Gauthmath must click thanks and mark brainliest
Answer:x°=70°
Step-by-step explanation:
This is an isoceles triagle because the values on the sides of the figure are the same. Therefore the base angles will be equal.
55+55+x=180
110+x=180
Next, you will subtract 110 from both sides.
110+x=180
-110 -110
x°=70°
