Question Progress
Rectangles ABCD and DEFG are congruent.
AB = 7cm
AD = 17cm
Work out the length of CE.
Optional working

Answer:

172 cm

Step-by-step explanation:

a=Adult height. n=9 year-old height

a*3/4=n

a*3/4=129

a*3/4 / 3/4 = 129 / 3/4

a = 129 * 4/3   ==> dividing by a number is equal to multiply by its reciprocal

a = 516/3

a = 172 cm

A graphical method that can be used to show both the rank order and shape of a data set simultaneously is a stem-and-leaf display. The Option C is correct.

This is a device used for presenting quantitative data in a graphical format to assist in visualizing the shape of a distribution. They evolved in the early 1900s and are very useful in exploratory data analysis.

Also known as stem-and-leaf plot, was invented by John Tukey (but the idea can be traced back to the work of Arthur Bowley in the early 1900s.) in his work titled “Some Graphic and Semigraphic Displays” in 1972.

Missing options "a. relative frequency distribution b. pie chart c. stem-and-leaf display d. pivot table

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Answer:

B

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

The [tex]n[/tex]term is [tex]2n+1[/tex].

[tex]S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)[/tex]

The number of terms that needed to make the sum to 99 is 9

The first term of the arithmetic progression = 3

The common difference = 2

The sum of n term is = (n/2) [2a+(n-1)d]

Where a is the initial term

d is the common difference

Substitute the values in the equation

(n/2) [2(3)+(n-1)2] = 99

(n/2) [6 + 2n - 2] = 99

(n/2)[4+2n] = 99

n(2 + n) = 99

2n + [tex]n^2[/tex] = 99

[tex]n^2[/tex] + 2n - 99 = 0

Split the terms

[tex]n^2[/tex] - 9n +11n - 99 =0

n(n -9) + 11(n - 9) = 0

(n + 11)(n - 9) = 0

n = -11 or 9

Since n cannot be a negative number, therefore n = 9

Hence, the number of terms that needed to make the sum to 99 is 9

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The scatter plot is given by the image at the end of the answer, and the exponential function of best fit is given by:

y = 10000(1.0513)^x.

The scatter plot is built inserting all the points of the data-set in a graph, which are in the following input-output format:

(time in years, balance in dollars).

Hence the points for this problem are given as follows:

(5, 12840), (10, 16487), (15, 21170), (20, 27183), (25, 34903), (30, 44817).

From the graph given at the end of the answer, we can see that the function is exponential.

The exponential function of best fit is found inserting the points into a calculator, and is given as follows:

y = 10000(1.0513)^x.

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It will take 2.76 seconds an object to fall to the top.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

We are given that The height of a building is 1957 feet.

S = the distance

Given d = 16t²  is the function for the height as a function of time.  It will hit the ground when h=0 so:

16t² - 1957 =0

16t² - 1957 =0

16t² =1957

t²  =1957 /16

t=√(1957 /16) seconds

t≈ 2.76 seconds  (to nearest hundredth of a second)

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Answer:

y=-28 and x=6

Step-by-step explanation:

y=-6x+8...... eqn(1)

7x+2y=-14.......eqn(2)

Two times equation (1)

2y=-12x+16..... eqn(3)

2y=-14-7x........ eqn (2)

eqn(3) - eqn(2)

0=-5x+30

5x=30

x=6

from eqn (1) where x=6

y=-6(6)+8

y= -36+8

y=-28

Answer:

Step-by-step explanation:

u got this! try ur best

Answer:

B and G

Step-by-step explanation:

f(x) = a|x-h|+k

The number inside the absolute value argument "h" represents the x-value of the vertex. For -1, the number inside has to be +1.

k represents the y-value of the vertex, in this case 3.

The only two expressions that have an h value of 1 and k value of 3 are B and G.

Answer:

4

Step-by-step explanation:

[tex]p^{2}[/tex][tex]p^{0}[/tex][tex]p^{3}[/tex][tex]p^{x}[/tex] = [tex]p^{9}[/tex]

When you multiply powers with the same bases, you add the exponents.

9 - 2 - 0 - 3 = 4

Answer:

below

Step-by-step explanation:

x = one angle and the other = 2x

solve this to find 'x'   and  '2x'

x + 2x + 66  = 180         because all of the angles of a triangle = 180

The probability that a random sample of 34 smoke detectors will have a mean lifetime between 58 and 63 months, using the normal distribution, is of:

0.9135 = 91.35%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters in the context of this problem are given as follows:

[tex]\mu = 60, \sigma = 8, n = 34, s = \frac{8}{\sqrt{34}} = 1.37[/tex]

The probability that a random sample of 34 smoke detectors will have a mean lifetime between 58 and 63 months is the p-value of Z when X = 63 subtracted by the p-value of Z when X = 58, hence:

X = 63:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (63 - 60)/1.37

Z = 2.19

Z = 2.19 has a p-value of 0.9857.

X = 58:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (58 - 60)/1.37

Z = -1.46

Z = -1.46 has a p-value of 0.0722.

0.9857 - 0.0722 = 0.9135 = 91.35%.

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Answer:

amplitude = 6

midline = -4.5

Period =5

Step-by-step explanation:

The graph represents a function is graph a

A function is a relationship between two sets or groups that maps each one of the elements contained in the first set to exactly one of the elements of the second set.

The graph a is a linear function, in which when we take any x value or y value, it gives the x and y value.

Hence, The graph that is a function is graph a.

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Answer:

25% were knives

Step-by-step explanation:

Answer:

f(- 2) = 0

Step-by-step explanation:

to evaluate f(- 2), substitute x = - 2 into f(x)

f(- 2) = [tex]\frac{2(-2)+4}{6}[/tex] = [tex]\frac{-4+4}{6}[/tex] = [tex]\frac{0}{6}[/tex] = 0

Answer: 13200 yards

Step-by-step explanation: 1 mile is equivalent to 1760 yards. If you multiply 1760 by 7.5, you get 13200 yards.

method 2: algebra

1. if you set the problem up as an equation, it's y/7.5=1760. Then you cross multiply, so y=13200. (Both methods are different but will get you to the same answer)

The equation of each line that satisfies the given conditions are:

1. y - 2 = 5/2(x - 3)

2. y - 4 = m(x + 3)

3. y = -3x + 5

1. Given the points, (3, 2) and (5, 7), find the slope (m):

Slope (m) = change in y / change in x = (7 - 2)/(5 - 3)

m = 5/2

Write the equation in point-slope form by substituting m = 5/2 and (a, b) = (3, 2) into y - b = m(x - a):

y - 2 = 5/2(x - 3)

2. Given:

A point = (-3, 4)

Slope (m) = 2

Substitute (a, b) (-3, 4), and m = 2 into y - b = m(x - a):

y - 4 = m(x + 3) [equation of the line]

3. Given:

Slope (m) = -3

Y-intercept (b) = 5

Substitute m = -3 and b = 5 into the equation y = mx + b:

y = -3x + 5

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Answer:

[tex]y-2=3(x-4)[/tex]

Step-by-step explanation:

We are given a line contains the point (4, 2).

We also know that the line is parallel to y= 3x - 7.

We want to write the equation of this line.

Parallel lines have the same slopes.

First, let's find the slope of y = 3x - 7.

3 is in the place of where m (the slope) is, so that means it is the slope of that line.

It is also the slope of the line whose equation we want to write.

The equation of the line can be written in three ways:

All of these ways are valid, but for this problem, let's write the equation in point-slope form, as it is the easiest.

Substitute 3 as m in [tex]y-y_1=m(x-x_1)[/tex].

[tex]y-y_1=3(x-x_1)[/tex]

Now, substitute 4 as [tex]x_1[/tex] and 2 as [tex]y_1[/tex].

[tex]y-2=3(x-4)[/tex]

Topic: parallel and perpendicular lines

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The named terms in the sequence are a₂₂ = -66, a₃₇ = -1050 and a₂₃ = 32

Sequence 1

From the question, we have the following sequence that can be used in our computation:

18,14,10,6,

In the above sequence, we can see that the 4 is subtracted from the previous term to get the current term

Using the above as a guide,

So, we have the following representation

a₁ = 18

d = -4

The nth term can be represented as

aₙ = a₁ + (n - 1)d

For the 22nd term, we have

a₂₂ = 18 + (22 - 1) * -4

Evaluate

a₂₂ = -66

Sequence 2

Here, we have

30,0,-30,-60,

In the above sequence, we can see that the 30 is subtracted from the previous term to get the current term

Using the above as a guide,

So, we have the following representation

a₁ = 30

d = -30

The nth term can be represented as

aₙ = a₁ + (n - 1)d

For the 37th term, we have

a₃₇ = 30 + (37 - 1) * -30

Evaluate

a₃₇ = -1050

Sequence 3

Here, we have

-34,-31,-28,-25,

In the above sequence, we can see that the 3 is added from the previous term to get the current term

Using the above as a guide,

So, we have the following representation

a₁ = -34

d = 3

The nth term can be represented as

aₙ = a₁ + (n - 1)d

For the 23rd term, we have

a₂₃ = -34 + (23 - 1) * 3

Evaluate

a₂₃ = 32

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Answer:

60

Step-by-step explanation:

First set up your equation

All triangles have angles that add up to 180, this means that you can make an equation where all your sides = 180

here is the equation: 7x-3+9x-1+40= 180 (i just wrote all the sides we can see)

Then you'll want to solve for x

7x-3+9x-1+40= 180

first combine like terms. We have a 7x and a 9x, so add them together

This will give you 16x-3-1+40=180

Now since your plain numbers (no variable) are on the same side of the = sign, you can just deal with them now. You can do -3-1+40 which is 36.

Now you have 16x+36=180

Now you'll want to take 36 from both sides. 36 is positive right now so you should do the opposite and subtract it from both 180, and itself.

This leaves you with: 16x=144

You have 16x which is the same as 16 times x. You want to do the opposite again. The opposite of multiplying is dividing so divide 144 by 16. This gives you 9 which is your x value.

Now one last thing. to get A on the triangle you can plug your X value (9) into the equation it gave you (7x-3)

this looks like 7(9)-3. 7 times 9 is 63. 63 -3 is 60.

(you can check your answer by plugging 9 into the other equation and adding everything up. it will equal 180)

Answer:

238

Step-by-step explanation:

child: $5.10

adult: $8.30

4 times as many adult as children

total: $9119.20

Let c = number of child tickets.

Let a = number of adult tickets.

5.1c + 8.30a = 9119.2

a = 4c

5.1c + 8.3(4c) = 9119.2

38.3c = 9119.2

c = 238.099

There must be a mistake with the numbers because the number of child tickets must be a whole number.

The cost of the first lesson based on the information is E. $80.

From the information, the cost of the first lesson is twice the cost of each additional lesson. Let the others lesson b represented by x.

The first lesson will be: = 2 × x = 2x

Since there are 8 lessons, this will be:

First lesson + Other lesson = Cost

2x + (7 × x) = 360

2x + 7x = 360

9x = 360

Divide

x = 360/9

x = 40

Therefore, first lesson will be:

= 2x

= 2 × 40

= 80

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a) The amount of the required down payment is $42,750.

b) The mortgage amount after the down payment is $242,250.

c) The monthly payment for both principal and interest is $1,416.17.

The down payment refers to the upfront cash payment made to reduce the cost of the home.

After deducting the down payment from the home price the result is the loan amount.

Monthly payments pay part of the loan amount the computed interest.

The monthly payments and the down payment can be determined with an online finance calculator.

Home Price = $285,000

Down Payment = 15%

Loan Term = 25 years

Interest Rate = 5%

Monthly Pay:   $1,416.17

Loan Amount $242,250 ($285,000 - $42,750)

Down Payment = $42,750 ($285,000 x 15%)

Total of 300 Mortgage Payments = $424,851 ($1,416.17 x 300)

Total Interest = $182,601

Thus, after making a down payment of $42,750 cash, Anna will be making monthly payments of $1,416.17 for 300 months.

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Answer: [tex]\frac{1}{40}[/tex] or 0.025

Step-by-step explanation:

[tex]\frac{5}{32}[/tex] ÷ [tex]\frac{25}{4}[/tex] = [tex]\frac{5}{32}*\frac{4}{25} =\frac{5}{4(8)} *\frac{4}{5(5)} =\frac{1}{40}[/tex]

The horizontal distance from the base of the skyscraper is 984 feet.

A study on the uses of trigonometry is called Heights and Distances. It can be used in many real-world situations to measure things like an object's height, depth, or the separation between two heavenly objects, among other things.

Given that,

Height of deck h = 984 feet,

Angle of depression θ= 45°

Let horizontal distance is x,

To find horizontal distance of base, use height and distance formula,

tanθ = h/x

Substitute, the values of h and θ,

tan45 = 984/x

∵tan45 = 1

1 = 984/x

⇒x = 984 feet

The horizontal distance from the base of the skyscraper is 984 feet.

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Answer: The answer is 984

Step-by-step explanation:

The total path length covered in 5 second will be 69.45 meter.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a train going at 70 km/h must reduce its speed to 30 km/h when passing over a bridge. It performs the operation in five seconds.

Using the first equation of motion -

v = u + at

(30 x 5/18) = (70 x 5/18) + 5a

(30 x 5/18) - (70 x 5/18)  = 5a

- (5/18) x 40 = 5a

- (200/18) = 5a

a = - (40/18)

a = - 2.22 m/s²

S = 19.44 x 5 + 0.5 x (- 2.22) x 25

S = 97.2 - 27.75

S = 69.45 meter

Therefore, the total path length covered in 5 second will be 69.45 meter.

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[Question translation in english -

A train going at 70 km/h must reduce its speed to 30 km/h when passing over a bridge if it performs the operation in five seconds what total path has been traveled in that time.]

I'm not sure but I'd say 31

The monthly payment, car cost in total, and the interest to be paid, based on the loan amount and the number of years are:

First, find the loan amount:

= Cost of car x ( 1 - down payment percent)

= 14, 800 x ( 1 - 12%)

= $13, 024

Then find the monthly rate and the number of periods:

Monthly rate:

= Yearly rate / 12 months per year

= 4.5% / 12

= 0.375%

Number of periods:

= Number of years x Months per year

= 6 years x 12

= 72 months

Using these, the monthly payment can be found by the formula:

= Loan amount / Present value interest factor of annuity, 72 periods , 0.375%

= 13, 024 / 62.995976235992

= $206.74

Total cost paid on loan for car:

= Monthly payment x Number of months

= 206. 74 x 72

= $14, 885. 52

This means that the total interest paid was:

= Total amount paid on cost of car - Loan amount

= 14, 885.52 - 13, 024

= $1, 861.52

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