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.
Find the equation of the tangent to the circle, whose equation is given below, at the point (-4,2).
(x+2)^2+(y−3)^2=5
The equation of the tangent is y = –2x – 6
The step by step process is in the pic attached.
The top part was cropped out, it says the centre point is (–2,3)
Find the surface area of the rectangular prism. 7 m 4 m 5m
Answer:
A = 2 (wl+hl+hw)=2·(4.7+5·7+5·4)=166
Answer: A=2(wl+hl+hw)=2·(4·7+5·7+5·4)=166
Step-by-step explanation:
A. In a complete sentence, describe the angle relationship in the diagram. B. Find the value of x
Answer:
x = 30
Step-by-step explanation:
a) The sum of the angles along the line is 180°. That means ...
2x° +90° +x° = 180°
__
b) Subtracting 90° and dividing by 3° gives ...
3x° = 90°
x = 30
Answer:
a) supplamentary angles b) X= 30
Step-by-step explanation:
A) Equal to 180 b) 90 divided by 3 gives you 30
CAN SOMEBODY PLEASE HELP ME
Answer:
x and y are both equal to 57.5°
Step-by-step explanation:
180° - 65° = 115°
115 ÷ 2 = 57.5
Scale: 2inches = 1 ft
1.)Jenna's father is going to use the blueprint above to make a playhouse for her. The length of the entire first floor is 12 inches. What is the actual length?
2.)The width of the entire first floor it is 8 inches. What is the actual width?
3.)What scale factor did Jenna's father use to go from the drawing to the actual house?
4.)What is the perimeter of the first that floor Jenna's that father built?
5.) What is the area of the first floor that Jenna's that father built?
The actual lenght will be 6 fee
The actual width will be 4 feet
The scale factor that Jenna's father used to go from the drawing to the actual house is 1.5
The perimeter of the floor is 20 feet
The area of the first floor that Jenna's that father built is 24ft²
Given the conversion factor 2inches = 1feet
1) If Jenna's father is going to use the blueprint above to make a playhouse for her and the length of the entire first floor is 12 inches, the actual length in feet is expressed as:
12 inches = x
2inches = 1feet
_____________________________
2x = 12
x = 6 feet
Hence the actual lenght will be 6 feet
2) If the width of the entire first floor is 8 inches, the actual width is expressed as;
8 inches = x
2inches = 1feet
_____________________________
2x = 8
x = 4 feet
Hence the actual width will be 4 feet
3) Thee scale factor will be the ratio of the length to the width as shown:
Ratio = length/width
Ratio = 6/4
Ratio = 3/2
Hence the scale factor that Jenna's father used to go from the drawing to the actual house is 1.5
4) The perimeter of the floor = 2(L + W)
Perimeter = 2(6 + 4)
Perimeter = 2(10)
Perimeter of the floor is 20 feet
5) Area of the floor = length * width
Area of the floor = 6ft * 4ft
Area of the floow = 24ft²
Hence the area of the first floor that Jenna's that father built is 24ft²
Learn more on area and perimeter of rectangle here:https://brainly.com/question/19819849
angle A and angle B are complementary angles. If m angle A = (4x – 28)° And angle B = (4x - 8)°, then find the measure of A.
Complementary angles have a submission of 90 degrees thus :
[tex]angle \: \: A + angle \: \: B = 90°[/tex]
[tex](4x - 28)° + (4x - 8)° = 90°[/tex]
[tex]4x + 4x - 28 - 8 = 90[/tex]
Collect like terms
[tex]8x - 36 = 90[/tex]
Add both sides 36
[tex]8x - 36 + 36 = 90 + 36[/tex]
[tex]8x = 126[/tex]
Divide both sides by 8
[tex] \frac{8x}{8} = \frac{126}{8} \\ [/tex]
[tex]x = 15.75[/tex]
_____________________________________________
Now let's find the measure of A :
[tex]A = 4x - 28[/tex]
[tex]A = 4 \times (15.75) - 28[/tex]
[tex]A = 63 - 28[/tex]
[tex]A = 35°[/tex]
And we're done...
Don't have a good day , Have a great day ♡
please helppp !
whats the measure of angle 1
Answer:
1 = 70
Step-by-step explanation:
The triangle is an isosceles.
Subtract the angle 40 from 180 (all angles in a triangle add up to 180
The bottom two angles are the same, so dividing the number given by 180 - 40 by 2
180 - 40 = 140
140 / 2 = 70
simplify the expressions 4y+2x-y+8
Hey there!
4y + 2x - y + 8
= 4y + 2x - 1y + 8
COMBINE the LIKE TERMS
= (4y - 1y + (2x) + (8)
= (4y - y) + (2x) + (8)
= (2x) + (4y - y) + 8
= 2x + 3y + 8
Therefore, your answer is: 2x + 3y + 8
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Answer:
3y+2x+8
Step-by-step explanation:
All you really do is combine the like terms, which in this case is the 3y and the -y. think of the y more as -1y and that is why it's subtrcated.
Daniel purchased a 1 year CD, c, from a bank. He bought it at an annual interest rate of 6%. After 1 year, Daniel cashes in the CD. What is the total amount it it worth?
Step-by-step explanation:
if I understand correctly, then he bought a CD with a balance of c and an annual interest rate of 6%.
now, after this one year the CD is worth (the account balance is) c + 6% = 100% + 6% = 106% = 1.06×c
This is my question pls help!!!
Answer:
[tex]20 {e}^{9} {f}^{11} [/tex]
Show Work:
[tex]5 \times {e}^{3} \times {f}^{3} \times 4 \times {f}^{8} \times {e}^{6} \times {e}^{0} [/tex]
[tex]5 \times {e}^{3} \times {f}^{3} \times 4 \times {f}^{8} \times {e}^{6} \times 1[/tex]
[tex]5 {e}^{3} {f}^{3} \times 4 {f}^{8} {e}^{6} [/tex]
[tex]20 {e}^{9} {f}^{11} [/tex]
[tex]5 \times {e}^{3} \times {f}^{3} \times 4 \times \times {f}^{8} \times {e}^{6} \times {e}^{0} \\ = 5 \times 4 \times {e}^{3 + 6 + 0} \times {f}^{3 + 8} \\ = 20 {e}^{9} {f}^{11} [/tex]
Answer:
[tex]20 {e}^{9} {f}^{11} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
1) For which pair of triangles could ONLY the Side Angle Side postulate (SAS) be used to prove the triangles congruent?
A) Pair A
B) Pair B
9 Pair
D) Pair D
2) For which pair of triangles could either the Side Angle Side postulate (SAS) or Side Side Side postulate (SSS) be used
to prove the triangles congruent?
A) Pair A
B) Pair B
C) Pair C
D) Pair D
Answer:
1) A
2) D
Step-by-step explanation:
1) You can see that both sides are equal and they have only one angle in common
2) This one is a bit more quirky. You have to complete the angles. First, you name the two that are in front of each other because of the vertice. In that way, you can see that they have one side in common (S), then the angle which we just explained (A), and finally another side (S)
Hope this was helpful.
Write 90 as a product of primes. Use index notation when giving your answer.
Answer:
90 =3 × 3 × 5 × 2.
Step-by-step explanation:
............
are 3x + 2 and 3 (x + 2 ) equal
Answer:
No
Step-by-step explanation:
Parenthesis means to multiply. So, to simplify the expression 3(x + 2), we need to distribute 3. In other words, we need to multiply 3 to x and to 2. Thus 3(x + 2) = 3x + 6.
HELLLLLLLLLLLLLPPPPPPPPPP
The first option. 100% correct.
[tex]a_n = 3\cdot a_{n-1}\\\\a_1 = 7\\\\a_2 = 3 a_{2-1} =3a_1 = 3(7) =21\\\\a_3 = 3 a_{3-1} =3a_2 = 3(21) = 63 \\\\a_4 = 3 a_{4-1} = 3 a_3 = 3 (63)=189\\\\7,21,63,189,......[/tex]
ricks bikes 24 miles in 3/4 of an hour what is the speed in the miles per hour.
Answer:
=32
Step-by-step explanation:
the speed = distance / time = 24 / (3/4) = 24*4 / 3 = 96 / 3 = 32 (mile/hour)
Find the volume of the box
Use the formula V = lwh
3x - 2, 2x + 1, x + 1
A. 6x^3 + x - 2
B. 6x^3 + 5x^2 - 3x - 2
C. 6x^3 - 2
D. 6x^3 - 13x^2 - 3x - 2
answer is B. detrjrajaetkterjaejq
an equilateral triangle with the perimeter of 90cm, what is the length of its side?
Answer:
The length of its side is 30 cm
Step-by-step explanation:
Given:An equilateral triangle with the perimeter of 90cm.
In a Equilateral Triangle all sides are equal
i.e., all 3 sides are equal
Now,
90/3 = 30 cm
Thus, The length of its side is 30 cm
-TheUnknownScientist 72
an equilateral triangle with the perimeter of 90cm, what is the length of its side?
Answer:-30cm
Explanation:-Given,
Perimeter of the equilateral triangle = 90cm
We know that,
All three sides of an equilateral triangle are equal.
So,
90/3 = 30cm
The length of the side is 30cm.
What percent is equivalent to 24/50?
24%
48%
50%
52%
Answer:
48%
Step-by-step explanation:
24 is almost 25 which is half of 50 you it would be 48%, hope this helps!:)
what is 25% off $27
Answer:
6.75 $
Step-by-step explanation:
25%
= 25 / 100
= 1 / 4
25% of $ 27
= ( 1 / 4 ) x ( 27 )
= ( 1 x 27 ) / 4
= 27 / 4
= 6.75 $
Answer:
$20.25
Step-by-step explanation:
x*y=xy+2y find 4*[1*-5]
Answer:
- 90
Step-by-step explanation:
Evaluate 1*- 5 then the outer one
1*- 5 ( with x = 1 and y = - 5 )
= 1(- 5) + 2(- 5)
= - 5 - 10
= - 15
Then
4*- 15 ( with x = 4 and y = - 15 )
= 4(- 15) + 2(- 15)
= - 60 - 30
= - 90
A basketball player makes 75% of her free throws. If she made 84 free throws this season, how many has she attempted?
A. 112
B. 105
C. 63
D. 168
Answer:
A
Step-by-step explanation:
84 / 0.75 = 112
112 x 0.75 = 84
Answer:
Its A
Step-by-step explanation:
solve for x -22=-7+3/5x
|-13| = I do not get how I solve this equation could you please help me
Answer:
13
Step-by-step explanation:
whenever you take the absolute value of something it changes from negative to positive
make r the subject of the formula
Answer:
r=[tex]\frac{3t}{t-1}[/tex]
Step-by-step explanation:
t(r-3)=r
tr-3t=r
tr-r=3t
r(t-1)=3t
r=[tex]\frac{3t}{t-1}[/tex]
Need help with this thank u
Answer:
Add 1 multiply by two
Step-by-step explanation:
As you see when 0 goes to 1, 9 goes to 18 so it is add 1 multiply by two.
Answer:
y=9x+9
Step-by-step explanation:
y=mx+c
You can use any of the 2 points
pnt1. (1;18)
pnt2. (3;36)
find the gradient
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]m = \frac{36 - 18}{3 - 1} [/tex]
[tex]m = \frac{18}{2} [/tex]
[tex]m = 9[/tex]
substitute one point and gradient to find c
y=mx+c
18=9(1)+c
18=9+c
c=18-9
c=9
therefore the equation is y=9x+9
Find the surface area of a sphere with a diameter of 10 centimeters.
a. 1,256.6 cm3
b. 104.7 cm3
c. 314.2 cm3
d. 209 cm3
The sum of a number and negative three, multiplied by the number?
Answer:
x² - 3
This expression is not linear
Step-by-step explanation:
Let x = unknown number
The sum of a number and negative 3
Sum = addition
We are adding the unknown number "x" and -3
So we have x + (-3) or just x - 3
The sum of that is multiplied by the unknown number
So we get ( x - 3 ) x
We can then simplify this expression to get x² - 3x
Any expression with an exponent is not linear. Refer to the attached image for more validation. A linear expression would create a straight line. The expression x² - 3x creates a curved line
(sin^2(0)) I really need help with this asap
Answer:
Asapa
[tex] (sin2(0) [/tex]
Is this sample of the coins likely to be representative?
Answer: yes
Step-by-step explanation:
Which statement is not used to prove that triangle ABC is similar to triangle ADC?
Answer:
what are the statements we pick from?
Step-by-step explanation:
most likely look out for angles and lengths that go against the established ratio