A person invests 7000 dollars in a bank. The bank pays 7% interest compounded
quarterly. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 12400 dollars?

The equation that represents the amount saved by Alyssa after tt weeks is AA = 100 + $7tt

The equation that represents the amount saved by Colton after tt weeks is CC = $55 + $10tt

The amount they would have when they have same amount of money is $205.

The total amount saved: inital amount + (amount saved per week x total number of weeks

AA = 100 + $7tt

CC = $55 + $10tt

$55 + $10tt = 100 + $7tt

Combine similar terms and solve for tt

100 - 55 = 10tt - 7tt

45 = 3tt

tt = 15 weeks

100 + $7(15) = $205

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Answer:

x= -1/3

x = -7

Step-by-step explanation:

9x^2 +66x+21 = 0​

a=9 b=66 c=21

quadratic formula

x=(-b +/- square root of (b^2 – 4ac))/(2a)

x = (-66 +/- square root of (66^2 -4*9*21))/(2*9)

x = (-66 +/- square root of (4356 -756))/(18)

x = (-66 +/- square root of (3600))/(18)

x = (-66 +/- 60)/18

split the fraction

(-66 +/- 60)/18 = -6/18 and -126/18 because of the +/-

x = -6/18  x = -126/18

x = -1/3   x = -7

[tex]~~~~~~9x^2+66x+21 = 0\\\\\implies 3(3x^2+22x+7)=0\\\\\implies 3x^2+22x+7=0\\\\\implies 3x^2 +21x +x +7=0\\\\\implies 3x(x+7) +(x+7)=0\\\\\implies (x+7)(3x+1)=0\\\\\implies x = -7~~ \text{or}~~ x =-\dfrac 13[/tex]

The equation of the line that is perpendicular to y = 4x + 5, in slope-intercept form is: y = -1/4x - 2.

Lines that are perpendicular to each other have slope that are negative reciprocal to each other.

Slope of y = 4x + 5 is 4.

Negative reciprocal of 4 is -1/4.

Substitute m = -1/4 and (a, b) = (8, -4) into y - b = m(x - a):

y - (-4) = -1/4(x - 8)

y + 4 = -1/4x + 2

y = -1/4x + 2 - 4

y = -1/4x - 2

Equation of the perpendicular line is: y = -1/4x - 2.

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Answer:

Therefore, the GCF of 15 and 50 is 5.

Step-by-step explanation:

Solution:

The greatest number that divides 15 and 50 exactly is their greatest common factor, i.e. GCF of 15 and 50.

⇒ Factors of 15 and 50:

Factors of 15 = 1, 3, 5, 15

Factors of 50 = 1, 2, 5, 10, 25, 50

Therefore, the GCF of 15 and 50 is 5.

After solving the equation (work shown in image) your answer would be x > -2. I drew an image of how the number line should look at least similar to, using the solution.

*whenever you divide or multiply with a negative number reverse/flip the sign

< or > signs will always have an open circle

≥ or ≤ signs will have a closed/filled in circle

TIP: To know which way the arrow should point, look at the sign and think of it as an arrow.

< would have the arrow on the number point

this way: <-

or > which would have the arrow on the number line point this way: ->

The expression indicated that the values of a will be between 4.01 and 4.99 and b will be between 2.01 and 3.99.

From the first expression, 4 < a < 5. This means that 4 is less than a and a is less than 5. This means the values of a will be between 4.01 and 4.99.

Also, 2 < b < 4. This means that 2 is less than b and b is less than 4. Therefore, the values of b will be between 2.01 and 3.99.

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Answer:

The answer to a is 4.5, and the answer to b is 3.

Step-by-step explanation:

The averages are found as shown:

4+5=9

9/2=4.5

2+4=6

6/2=3

To find averages, first add all of the certain amount of numbers shown, then divide it all by the same amount of numbers there are.

Example:

5+7+9=21

21/3=7

Answer:

I think one is 5 and another is 6 because 5+6=11

Answer:

a=5

a=6

add the exponents and keep the base the same

Answer:

16

Step-by-step explanation:

2 pounds = 32 ounces

32 ounces / 2 ounces = 16 ounces

Answer:

angle fde = 37 degree

Step-by-step explanation:

we have,

angle bdc = angle fde

for angle bdc

adf = 90, adb = 53

let the value be x

=>             90+53+x = 180

=>             143+x = 180

=>             x = 180 - 143

=>             x = 37

bdc = 37

so, fde = 37

[tex]3x^2y+6xy-9xy^2\\\\=3xy(x+2-3y)[/tex]

[tex]5 {}^{ \frac{1}{8} } \times 5 {}^{ \frac{3}{8} } [/tex]

[tex] = 5 {}^{ \frac{1 + 3}{8} } = 5 {}^{ \frac{4}{8} } = 5 {}^{ \frac{1}{2} } = \sqrt{5} [/tex]

Answer:

B

Step-by-step explanation:

-10 and -2

Answer:

-10 and -2

Step-by-step explanation:

Answer:

4 1/4 cups were served

Step-by-step explanation:

Just multiply 5 2/3 cups by 3/4:  

17      3

---- * ---- = 4 1/4 cups were served.

 3      4

An equation shows the amount of juice that Jose served is x= 3/4 × 17/3.

The product of two fractions is the product of the numerators and the product of the denominators.

Product of two fractions = Product of their numerators / Product of their denominators.

Given that, Jose made [tex]5\frac{2}{3}[/tex] cups of juice. He served 3/4 of it at dinner.

Here, [tex]5\frac{2}{3}[/tex] cups can be written as 17/3

Let the amount of juice that Jose served be x

Now, x= 3/4 × 17/3

x= 17/4

x= [tex]4\frac{1}{4}[/tex] cups

Therefore, an equation shows the amount of juice that Jose served is x= 3/4 × 17/3.

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Answer:

well jus subtract

Step-by-step explanation\

think about it

Answer:

The total amount of students in the primary school is 1,980.

Step-by-step explanation:

130, 210, 290, ......

210 - 130 = 80

The difference between each grade is 80 students.

(g = grade)

g1 = 130, g2 = 210, g3 = 290, g4 = 370, g5 = 450, g6 = 530

130+210+290+370+450+530 = 1980

Answer:

x = -4

Step-by-step explanation:

4 = 2/3x - 5/3x

4 = -3/3x

4 = -x

-4 = x

Answers:

Mode = 6

Range = 7

====================================================

Explanation:

The mode is the most frequent value. Based on that, we simply go for the tallest stack of 'x's which in this case is 6.

Therefore, 6 is the mode. It shows up four times which is the most of any other value.

-------

The range is the difference of the min and max

range = max - min = 8 - 1 = 7

Answer:

C. 11

Step-by-step explanation:

Calculating range is subtracting the highest data value(11) from the lowest data value(0)

11 - 0 = 11

Answer:

1 year and a half or 18 months

Step-by-step explanation:

Answer:

$240

Step-by-step explanation:

200% x 80 = 160

80 + 160 = $240

Using proportions, it is found that the correct option regarding how much faster she is in the first 5 minutes compared to the last 5 is given by:

B. 0.3 mile/minute faster

A proportion is a fraction of a total amount

Researching the problem on the internet, it is found that on the first 5 minutes, she bikes 2 miles, hence the ratio is:

r1 = 2/5 = 0.4 miles/minute.

On the last 5 minutes, she bikes 0.5 miles, hence:

r2 = 0.5/5 = 0.1 miles/minute.

The difference is given by:

D = 0.4 - 0.1 = 0.3 miles/minute.

Which means that option B is correct.

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Answer:

39.36cm

Step-by-step explanation:

Since each bead has a radius of 1.64cm and there are 12 beads, all we have to do is multiply amount of beads by their length. Since it is the radius, we have to multiply the length by 2.

So [tex]3.28[/tex] × [tex]12 = 39.36[/tex]cm.

Answer:

$2.33

Step-by-step explanation:

6.99/3 = 2.33

Divide cost of 3 boxes by 3:

6.99/3 = 2.33

1 box cost $2.33

Answer: D

Step-by-step explanation:

Using the two point slope form with points (0, 0) and (4, -3):

[tex]\frac{y-0}{x-0}=\frac{4-0}{-3-(0)}[/tex]

[tex]\begin{aligned}&\frac{y}{x}=\frac{4}{-3} \\&y=-\frac{3}{4} x\end{aligned}[/tex]

Therefore, D is the correct answer

Answer:

D. y=-3/4x

Step-by-step explanation:

because when doing slope, you have to remember that it goes y/x and the fact that this is a negative slope meaning that you count from point (0,0) to (4,-3), and the lines on the graph count by 2's, so you would be counting down 3 (because point (4,-3) is inbetween -2 and -4) and to the right 4. making the answer -3/4, and it is negative because it is a downward facing slope. oh, and the x is there because it is an ever changing variable (ever continuing)

Answer:

Step-by-step explanation:

Domain is x-values the graph can have

  x = [-3,22]

range is the y values the graph includes

   range-=  [-3,+2]

Answer:

b pizza hut

Step-by-step explanation:

sorry im wrong

The equivalent expression of 3 to the power of 4. is 9 to the power of 2.

The expression is given as:

3 to the power of 4.

Mathematically the expression is

[tex]3^4[/tex]

Express 4 as 2 * 2

[tex]3^{2*2}[/tex]

Evaluate 3^2

[tex]9^2[/tex]

This means that:

9 to the power of 2.

Hence, the equivalent expression of 3 to the power of 4. is 9 to the power of 2.

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Answer:

97 1/3 or 97.3333

Step-by-step explanation:

multiply 2 2/3 by 36 1/2

:)

16x²+ 4y² = 16 is an equation of ellipse, domain of the equation is all real numbers and the range is -2 ≤ y ≤ 2.

A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane.

The given equation is 16x²+ 4y² = 16.

Divide both sides by 16.

x²/1 + y²/4 = 1

This is the equation of an ellipse.

It is an ellipse centered at the origin, with semi-major axis length of 2 and semi-minor axis length of 1.

Since the x² term is not negative, the domain is all real numbers.

The range of the ellipse is the range of y-values that make the equation true.

Since the y² term is not negative, the range is all real numbers as well. However, since the ellipse is centered at the origin, the range is bounded by -2 and 2, which are the y-coordinates of the endpoints of the major axis. Therefore, the range is -2 ≤ y ≤ 2.

Hence, 16x²+ 4y² = 16 is an equation of ellipse, domain of the equation is all real numbers and the range is -2 ≤ y ≤ 2.

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Answer:

ellipse; Domain: {-1≤y≤1}; Range: {-2≤y≤2}

Step-by-step explanation:

Graph the equation. An ellipse has two lines of symmetry, the x-axis, and the y-axis. The domain is the set of all real numbers with x, written as -a ≤ x ≤ a. The range is the set of all real numbers with y, written as -b ≤ y ≤ b.