pls explain with working out

The total amount of money in the savings account after 11 weeks is  $1010.

The from of the equation that can be used to determine the total amount of money in the savings account is a linear equation. A linear equation is an equation that has one variable that is raised to the power of one. When a linear equation is drawn on a coordinate graph, it is usually a straight line.

The form of the linear equation is:

Total amount = amount she starts with + (number of weeks x amount of money she adds each week)

S = $350 + ($60 x W)

S = $350 + $60W

Amount she would have in 11 weeks :  $350 + ( 11 x $60)

$350 + 660 = $1010

Here is the complete question:

Lisa is putting money into a savings account. She starts with $350 in the savings account, and each week she adds $60. Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Jenny has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 11 weeks.

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Answer:

32, 52

Step-by-step explanation:

84=x+y

x=2y-12

Solving the system of equations

Plug second equation into first

84=(2y-12)+y

84=3y-12

y=32

Plug y into first equation

84=x+32

x=52

1) Considering e =2.72

Then let's plug it in the inequality, and calculate the natural logarithm.

2) Then option 5 is the answer

X≥ 1.52

We can use the sine rule to find the hole angle, and then find the golfer angle:

Now we can find the golfer angle:

Answer: 25.6 degrees.

Complex number z has a power of 5 represented by (-16√3 + 16) + 4(-√3 + 3)i

Given that,

z = 1 + StartRoot 3 EndRooti, what is z5? 16 + 16StartRoot 3 EndRoot i –16 + 16StartRoot 3 EndRoot i –16 – 16StartRoot 3 EndRoot i 16 – 16StartRoot 3 EndRoot i

What is a complex number?

It is characterized as a number that can be expressed as x+iy, where x is a real number or the real portion of the complex number, y is the imaginary portion of the complex number, and I is the iota, which is just the square root of -1.

We have:

z = 1 + √3i

We have to find: z⁵

z⁵ = (1 + √3i)(1 + √3i)(1 + √3i)(1 + √3i)(1 + √3i)

z⁵ = (-2 + 2√3)(1 + √3i)(1 + √3i)(1 + √3i)

z⁵ = (-16√3 + 16) + 4(-√3 + 3)i

Therefore, the complex number z's power of 5 is -16√3 + 16) + 4(-√3 + 3)i

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1) To understand how that works, let me draw a number line:

If we only add positive numbers like 2 +3 = 5, 6+8 =14, etc. we'll only get a positive result (right to the zero) on the number line, we are moving to the right

2) If we add positive and negative numbers, for example:

2 +(-3) =2 -3=-1

0+(-1)= -1

6+(-2)= 4

On the number line, we are starting from one point and moving to the left.

In this session we will focus on calculating the composition of f and f.

given the function f, the composition f composition f is obtained by taking the definiton of f and replace the varaible x with the function f itself. So we are given that

So

So we have that f composition f is the function x.

Answer:

A. (1/2) bucket

Step-by-step explanation:

    6           11

4 ------ - 3 ------- = ?

    14          12

14 × 4 = 56

56 + 6 = 62

12 × -3 = -36

-36 - 11 = -47

 62       47

------- - -------

  14        12

 62(12)        47(14)

-------    -     -------

  14(12)         12(14)

744     658       86

------- - ------- = --------

 168     168       168

 86 ÷ 2

-------

168 ÷ 2

43

----- = 0.511

84

0.511 ≈ (1/2)

I hope this helps!

Answer:

1/2 bucket

Step-by-step explanation:

Congruent angles simply means angles that are equal. A triangle has three angles . Since one of the angle is given as 98 degree, the other 2 angles which are congruents are therefore equal. The total angle of a triangle is equals to 180 degree. Therefore,

x = 41 degree

Remember that

In a unit circle, the radius of the circle is 1

see the figure below to better understand the problem

we have that

and we know that

so

and we know that

so

therefore

the coordinates (x,y) are

the point which will fall in the line is (14, 7)

Explanation:

The coordinates o f S = (2, 1)

When we draw a line from the origin (0, 0) touching the point S, we will see the next point will be (4, 2). Followed by (6, 3).

So when we look at the trend, we see that the x axis is the double of the y axis:

(2y, y) = (x, y)

(2,1 ) , (4, 2), (6, 3)

From the above, we can say the point which will fall in the line will follow that trend:

When we check the options, the only point with that trend is (14, 7).

This because (2(7), 7) = (2y, y)

Hence, the point which will fall in the line is (14, 7)

Step-by-step explanation:

Write 98 as the product of prime factors. Write the prime factors in ascending order.​

2 × 7 × 7

2 × 7 × 7 = 98

Answer: 2×7×7

Step-by-step explanation: 98= 2×7×7

Lets first know about what is prime factor :- A factor which is a Prime number and not a composite number.

prime factor in ascending order = 2,7

hence the required product of prime factor is 2×7×7 or 2×[tex]7^{2}[/tex]

Answer:

I gotchu

Step-by-step explanation:

1= 155

2= 222

3= 44

4= 132

5= 163

Answer:

The only image with edges at the given coordinates is;

Given the figure in the attached image.

we want to identify the image after a translation;

Using one of the edges of the figure;

Applying the above translation we have;

The edge of the image would be at;

Therefore, the only image with edges at the given coordinates is;

You have the following vertices of a triangle:

A(1,1)

B(4,1)

C(4,5)

For the translation four untis to the right, consider this kind of translation means that it is necessary to sum 4 units to the x-coordinate:

A(1,1) => A'(1+4,1) = A'(5,1)

B(4,1) => B'(8,1)

C(4,5) => C'(8,5)

Next, a translation three units up is done by adding 3 units to the y-coordinate of points A', B' and C':

A'(5,1) => A''(5,1+3) = A''(5,4)

B'(8,1) => B''(8,4)

C'(8,5) => C''(8,8)

Next, a reflection around y=-1 consists in subtracting to the y-coordinate units equivalent to the vertical distance to the line y =-1, just as follow:

for the point A''(5,4) you can notice that the vertical distance of the y-coordinate, which is 4, to the line y=-1 is 5 units, then, it is necessary to subtract 5 units to such line:

A''(5,4) => A'''(5,-1-5)=A'''(5,-6)

for the point B''(8,4), the distance is again 5 units, then, you have:

B''(8,4) => B'''(8,-1-5) = B'''(8,-6)

for the point C''(8,8) the distance from y-coordinate y=8 to the line y=-1 is 9 units, then, yu subtract 9 units to -1:

C''(8,8) => C'''(8,-1-9) = C'''(8,-10)

Hence, the final points are:

A'''(5,6)

B'''(8,-6)

C'''(8,-10)

The value of sin 2x=0.8304 ,cos 2x=0.557,tan 2x=1.498 when the value of tan x is 8/15 and using the trigonometry identities as tan x as the formula in sin 2x, cos 2x, tan 2x.

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations (csc).

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.

sin 2x=2 tan x/(1+(tan x)²)

cos 2x=(1-(tan x)²)/(1+(tan x)²)

tan 2x=sin 2x/cos 2x=2 tan x/(1-(tan x)²)

Here,

tan x=8/15

sin 2x=2 tan x/(1+(tan x)²)

= 2*8/15/(1+(8/15)²)

=(16/15)/(289/225)

=(16*15)/(289)

≈0.8304

cos 2x=(1-(tan x)²)/(1+(tan x)²)

=(1-(8/15)²)/(1+(8/15)²)

=(225-64)/(225+64)

≈0.557

tan 2x=sin 2x/cos 2x

tan 2x= 0.8304/0.557

=1.498

≈1.5

When the value of tan x is 8/15, the values of sin 2x=0.8304, cos 2x=0.557, and tan 2x=1.498 using the trigonometry identities as tan x as the formula in sin 2x, cos 2x, tan 2x.

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Answer:

a) 95%

b) 2%

c) 16%

d) 98%

Explanation:

We have the following:

This is a normal distribution

Mean = 69

Standard Deviation = 6

a) Between 57 and 81%

The probability that a score is between 57 & 81 is given by the Area between (z = -2) & (z = 2):

b) Above 81%

The probability that a score is above 81% is given by the area of the graph greater than (z = 2):

c) Below 63%

The probability that a score is below 63% is given by the area of the graph lesser than (z = -1):

d) Between 51 and 81

The probability that a score is between 51 & 81 is given by the Area between (z = -3 & (z = 2):

The most appropriate choice for area of rectangle will be given by-

a) Area of the wall =  [tex]26508[/tex] [tex]in^2[/tex]

b) Area of wall left uncovered = [tex]25347[/tex] [tex]in^2[/tex]

What is area of rectangle?

Area of rectangle is the total space taken by the rectangle. If l is the length of the rectangle and b is the breadth of the rectangle, then area of the rectangle is given by

Area = [tex]l \times b[/tex]

Here,

Width of the wall = [tex]15\frac {2}{3}[/tex] feet = [tex]\frac{47}{3}[/tex] feet

Height of the wall = [tex]\frac{3}{4} \times \frac{47}{3}[/tex] feet

                               = [tex]\frac{47}{4}[/tex] feet

a) Area of the wall = [tex]\frac{47}{3} \times \frac{47}{4}[/tex] [tex]ft^2[/tex]

                               =[tex]\frac{2209}{12} \times 12 \times 12[/tex] [tex]in^2[/tex]

                               = [tex]26508[/tex] [tex]in^2[/tex]

b) Length of painting = [tex]40 \frac{1}{2}[/tex]  in = [tex]\frac{81}{2}[/tex] in

Breadth of painting = [tex]28\frac{2}{3}[/tex] in = [tex]\frac{86}{3}[/tex] in

Area of painting = [tex]\frac{81}{2} \times \frac{86}{3}[/tex] [tex]in^2[/tex]

                           = [tex]1161[/tex] [tex]in^2[/tex]

Area of wall left uncovered = (26508 - 1161) [tex]in^2[/tex]

                                             = 25347 [tex]in^2[/tex]

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The correct option for the fraction with polynomials is y=6.

Expressions of more than two algebraic terms that contain different powers of the same variable is a polynomial.

The polynomial fraction is an expression of polynomial divided by another polynomial.

We can solve the fraction to get the value of y as follows;

[-8/(2y-8)]= [5/(y+4)]-[(7y+8)/(y²-16)]

[-8/(2y-8)]= [5/(y+4)]-[(7y+8)/(y+4)(y-4)]

[-8/(2y-8)]= [5(y+4)-(7y+8)]/(y+4)(y-4)] (L.C.M) of the fraction

[-8/(2y-8)]= (5y-20-7y-8)/(y+4)(y-4)

[-8/(2y-8)]= (-2y-28)/(y+4)(y-4)

[-8/2(y-4)]= (-2y-28)/(y+4)(y-4)

[-8/2(y-4)]= [-2(y-14)]/(y+4)(y-4)

[-4/(y-4)]= [-2(y-14)]/(y+4)(y-4)

Multiply both sides of the equation by -(y-4)

4= 2(y-14)/(y+4)

Cross multiply

4(y+4)=2(y+14)

Divide through by 2

2(y+4)=y+14

2y+8=y+14

collect like terms

2y-y=14-8

y=6.

Hence, we can state that the value of y for the polynomial with fraction is 6.

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Answer:

1 knife cost £6.6

Step-by-step explanation:

Simultaneous equation is;

4x = y ----------(equation 1)

12y + 16x = 105.64 ----------- (equation 2)

Rewrite equations:

4x=y;16x+12y=105.64

Step: Solve4x=yfor y:

4x=y

4x+−y=y+−y(Add -y to both sides)

4x−y=0

4x−y+−4x=0+−4x(Add -4x to both sides)

−y=−4x

−y/−1 = −4x/−1

(Divide both sides by -1)

y=4x

Step: Substitute 4x for y in 16x+12y=105.64:

16x+12y=105.64

16x+124x=105.64

64x=105.64(Simplify both sides of the equation)

64x/64 = 105.64/64

(Divide both sides by 64)

x=1.650625

Step: Substitute 1.650625 for x in y=4x:

y=4x

y=(4)(1.650625)

y=6.6025(Simplify both sides of the equation)

1 knife cost = 4x = 4(1.65) = 6.6

∴ 1 knife cost £6.6

12/35 fraction of the total number is unused from two different cards.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Assuming the total first kind of card form is 1 and the total second kind of card form is also one.

Given, a company buys equal numbers of two different card forms. it utilizes 4/5 of one kind and 6/7 of the other.

∴ The total unused card form is,

= (1 + 1) - (4/5 + 6/7).

= 2 - (28 + 30)/35.

= 2 - 58/35.

= (70 - 58)/35.

= 12/35.

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Answer:

2(x + 9)

Explanation:

Let x represent the unknown value.

Double a quantity increased 9 means;

*We'll multiply the quantity by 2

*Increased by signifies addition

*Quantity means we'll put the expression after it in brackets

Let's go ahead and write the required algebraic expression;

Answer:

Step-by-step explanation:

x

=

−

2

x

=

−

5

Explanation:

x

2

+

7

x

+

10

=

0

We could right the equation in another form using brackets.

(

x

+

2

)

(

x

+

5

)

=

0

In order to get two numbers to multiply and give 0, at least one number has to be 0.

a stands for the first bracket and b for the second.

a x b = 0

a=0 or b=0 to make this equation valid.

Therefore x= -2 or x= -5 because -2+2=0 and -5+5=0 according to both brackets.

Answer:

203.5

Step-by-step explanation:

just divide 814 by 4

Answer:

203.5 miles per day

Step-by-step explanation:

divide 814 by 4= 203.5

Answer:

32 shirts

Step-by-step explanation:

419÷13

=32.230

Answer:

32

Step-by-step explanation:

419 divided by 13

= 32.230

△PQR is congruent to △STU (△PQR ≅ △STU) under ASA condition using options (B) and (D).

So, to prove that △PQR ≅ △STU:

So, with these three conditions, △PQR ≅ △STU is under ASA condition.

Therefore, △PQR is congruent to △STU (△PQR ≅ △STU) under ASA condition using options (B) and (D).

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For part A. One way to know if there is a correlation between the data is to graph the data set, like this

Then, as can you see the data presents a positive linear correlation.

For part B. You can take the coordinates of two points and find the slope of the line using the formula

If you take

Now, using the slope formula, you can find the equation of the line in its slope-intercept form

Therefore, the function that best fits the data is

For part C. The slope of the plot is 10 and indicates that for every hour students spend time studying, they get 10 more points on the science test.

The y-intercept of the plot is 57 and indicates that if students study 0 hours for the science test, they will obtain 57 points as a grade.

Answer: Midpoint = 0

Explanation:

The midpoint of segment ED can be calculated as:

Where E and D are the coordinates of E and D respectively.

So, replacing E by 2 and D by -2, we get:

Therefore the midpoint of segment ED is equal to 0.