Martin deposits $200 in a savings account that earns 5% annual interest. four years later, cary deposits $200 in an account earning the same interest. let m represent the balance in martin’s account and let c represent the amount of money in cary’s account. choose the pair of expressions that describe the accounts y years after martin opened his account. martin: 200(1.05)y cary: 200(1.05)y+4 martin: 200(1.05)y+4 cary: 200(1.05)y–4 martin: 200(0.05)y cary: 200(0.05)y–4 martin: 200(1.05)y cary: 200(1.05)y–4

Answer:

[tex]y=cos(x)+6[/tex].

Step-by-step explanation:

We are asked to write an equation for the translation of the function [tex]y=cos(x)[/tex] to 6 units upwards.

Let us recall transformation rules.

[tex]f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}[/tex]

[tex]f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}[/tex]

[tex]f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}[/tex]

[tex]f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}[/tex]

Since we need to shift our given function 6 units upwards, so we will add 6 to our given function outside the parenthesis as:

[tex]y=cos(x)+6[/tex]

Therefore, our required equation would be [tex]y=cos(x)+6[/tex].

Answer:

True

Step-by-step explanation:

Consider triangle ABC inscribed in the circle with center at point O. Point O is a point of intersection of perpendicular bisectors of sides AC, AB and BC. According to the attached diagram, points E, F and G are midpoints of sides BC, AC and AB, respectively.

Then

Since segments OE, OF and OG are perpendicular bisectors of sides BC, AC and AB, then

You get three pairs of congruent triangles:

This gives you that

[tex]OB=OC=OA.[/tex]

Each of these segments is a radius of the circumscribed circle about a triangle ABC, then the center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle.

Answer:

If there are 52 ounces of cereal in 2 boxes, how many ounces are there in 5 boxes?

Step-by-step explanation:

If we have 52 ounces in 2 boxes, in 1 box we have: 52/2 = 26 ounces.

If we have 5 boxes and 26 ounces in each, we have: 5 x 26 = 130 ounces in total.

Answer:             10 min

Step-by-step explanation:

Final answer:

The bacterial culture that triples every 2 minutes will surpass 9500 cells just after 10 minutes. Since we cannot have a fraction of a minute in this context, the answer is 11 minutes (Option C).

Explanation:

The student is asking about exponential growth, specifically in a bacterial culture that triples every 2 minutes. To find out how many minutes it will take for the initial 40 cells to grow to more than 9500, we can use the formula for exponential growth:

N = N0 × 3t/2

Where N is the final number of cells, N0 is the initial number of cells (40 in this case), and t is the time in minutes.

We want N to be greater than 9500, so we solve the inequality:

9500 < 40 × 3t/2

Dividing both sides by 40 gives:

237.5 < 3t/2

Next, we find the smallest t for which the inequality holds by applying logarithms and solving:

t > 2 × (log3(237.5))

Calculating the right side, we get:

t > 10.096

So, the culture will have more than 9500 cells just after 10 minutes. The smallest whole number of minutes greater than 10.096 is 11, hence the answer is: C) 11 min

Since the growth is exponential, therefore I believe the correct form of the equation is:

P = 100 (2)^(t / 6)

Where t / 6 is the exponent of 2

So to find for the amount of time needed to exceed the population of 50,000, all we have to do is to plug in that value in the equation and find for t. Therefore:

P = 100 (2)^(t / 6)

50000 = 100 (2)^(t / 6)

500 = 2^(t / 6)

log 500 = (t / 6) log 2

t / 6 = log 500 / log 2

t = 6 * 8.96578

t = 53.8 mins = 54 mins

Answer:

D. 54 min

If a radius of a circle is perpendicular to a chord, then it _bisects____ that chord.

What is radius of circle?

In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin radius, meaning ray but also the spoke of a chariot wheel.

What is chord?

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. The infinite line extension of a chord is a secant line, or just secant. More generally, a chord is a line segment joining two points on any curve, for instance, an ellipse.

According to question, we have to fill in the blank.

The property of the circle is that if a radius of a circle is perpendicular to a chord, then it  bisects that chord.

Hence we can conclude that Option(B) is correct.

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Final answer:

A radius of a circle that is perpendicular to a chord bisects the chord, dividing it into two equal segments.(Option b)

Explanation:

If a radius of a circle is perpendicular to a chord, then it bisects that chord. This statement is supported by a theorem in geometry which states that, in a circle, the radius bisecting an angle at the centre is perpendicular to the chord which subtends the angle and also bisects this chord. Therefore, by drawing a radius from the center of a circle to the midpoint of a chord, you create two equal segments, effectively bisecting the chord.

Thus, a perpendicular radius drawn from the center of a circle to a chord's midpoint ensures that the chord is bisected into two equal segments. This geometric principle facilitates chord division and enhances the understanding of circle properties.

For this case, the first thing we should do is define a variable.

We have then:

x: unknown number

Then, we write the algebraic expression that models the following problem:

the difference of 54 and a number.

We have then:

[tex]54-x[/tex]

Answer:

An algebraic expression that represents "the difference of 54 and a number" is:

[tex]54-x[/tex]

Answer:

A

Step-by-step explanation:

1/4 = 0.25

s0 3 1/4 = 3.25

62x3.25 = 201.50 miles = 201 1/2 if you need it in fraction form

Answer:  three over two

Step-by-step explanation:

We know that the rate of change of a function [tex]y=f(x)[/tex] is given by :-

[tex]k=\dfrac{\text{change in y}}{\text{change in x}}[/tex]

From the consecutive values in the table, the change in x = [tex]3-1=2[/tex]

Change in y = [tex]5-2=3[/tex]

Now, the rate of change of the linear relationship modeled in the table will be ;-

[tex]k=\dfrac{3}{\text{2}}[/tex]

Answer:

1. 10

2. 12

3. Sqrt 130

4. Sqrt 45

Step-by-step explanation:

To find the missing side of a right triangle, use the Pythagorean Theorem. The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex] where a and b are the legs with a being the smallest and c is the hypotenuse.

1. a=6, b=8, c=?

[tex]6^2+8^2=c^2\\36+64=c^2\\100=c^2\\10=c[/tex]

2. a=5, b=?, c=13

[tex]5^2+b^2=13^2\\25+b^2=169\\169-25=b^2\\144=b^2\\12=b[/tex]

3. a=7, b=9, c=?

[tex]7^2+9^2=c^2\\49+81=c^2\\130=c^2\\\sqrt{130}=c[/tex]

4. a=2, b=?, c=7

[tex]2^2+b^2=7^2\\4+b^2=49\\49-4=b^2\\45=b^2\\\sqrt{45}=b[/tex]

Answer:    (quartered spinner)     (4)     (1/256)

Answer:

The answer is 92%.

Step-by-step explanation:

5 of the 60 students reported that they like school. This means that the other 55 don't like school. You then divide 55/60 and you get 92%. So, therefore, your answer is 52%.

subtract 75 from 120

120-75 =45 more campsites

The both numbers are = 17 and 16

The sum of two numbers = 33

Let the two numbers be X and y.

therefore X + y = 33 ----> equation 1

Twice the first number minus the second number= 18.

That is,

2x - y = 18 -----> equation 2

From equation 1 make X the subject of formula;

X = 33 – y

substitute X into equation 2,

2(33 – y) - y = 18

66 – 2y – y = 18

66 – 3y = 18

66 – 18 = 3y

48 = 3y

y = 48/3

y = 16

Substitute y = 16 into equation 1

Therefore, X +16 = 33

X = 33 –16

X = 17

Therefore, he both numbers are = 17 and 16

Learn more about summation here:

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Answer: it’s 1:1

Step-by-step explanation: