Before Sarah does open her account, she sees her grandmother for the holidays. Grandma wants to contribute to Sarah’s ROTH and even matches her contribution, giving her an additional $500 to invest. Now that Sarah has an initial investment of $1000, how much would Sarah have at age 68 based on her predicted rate of return from historical data

The perimeter of a shape is the sum of its side lengths.

Joshua miscalculated the third length of the triangle

First, we calculate the third length (x) of the triangle.

Because the triangle is right-angled, we can make use of Pythagoras.

So we have:

[tex]x^2 = 7^2 + 7^2[/tex]

[tex]x^2 = 2(7^2)[/tex]

Take square roots of both sides

[tex]x = \sqrt{2(7^2)[/tex]

[tex]x = 7\sqrt{2[/tex]

The other shape in the figure is a square.

So, the perimeter (P) is

[tex]P = 7 + x + x + x + 7[/tex] ---- i.e. the sum of the visible lengths

So, we have:

[tex]P = 7 + 7\sqrt2 + 7\sqrt2 + 7\sqrt2+ 7[/tex]

Evaluate like terms:

[tex]P = 14 + 21\sqrt2[/tex]

Hence, Joshua's error is that:

He miscalculated the third length of the triangle

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Answer:

Given: 2PQ = PR

Prove: Q is the midpoint of line PR

Statement: 2PQ = PQ + QR

Step-by-step explanation:

If Q is the midpoint of PR then

PR = PQ + QR [by segment addition postulate]

2PQ = PR [given]

2PQ = PQ + QR

2PQ-PQ = PQ + QR-PQ [by subtracting PQ from both sides]

PQ = QR

[tex] \because[/tex] Q lies on PR and PQ = QR

[tex] \therefore[/tex] Q is the midpoint of PR

Answer:

how do u solve this?

Step-by-step explanation:

Answer: y = 2 (x+4)

Tim = alice + 4

Bob = tim x 2

Alice = x

y = 2 (x+4)

Bob (y), Alice (x), tim (x+4)

Answer:

D) -2.14< root10 <|-2.8|

Step-by-step explanation:

the value for -2.14 is as plain as you can see, the negative version of 2.14.

The square root of 10 is 3.16227766.

The lines next to -2.8 is asking for the absolute value of -2.8, or the distance between that number and zero. The distance between -2.8 and 0 is positive 2.8, because distance can't be negative.

The 3 numbers taken from the explanations are -2.14, 3.16, and 2.8. Ranking them from least to greatest would give you -2.14, 2.8, 3.16, or -2.14< root10 <|-2.8|

Answer:

so what are you trying to figure out

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

convert 35% to a decimal by moving the decimal to the left two places

.35

.35 × 40 = 14

Answer:

87 percent

Step-by-step explanation:

You just simply divide percent you got (35) by the full amount you could get (40)

35 ÷ 40

Answer: P = A/6

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

113. x = √65 cm

114. x= 7.10 cm

The maximum or minimum of a quadratic function is found evaluating the polynomial at [tex]x = -\frac{b}{2\cdot a}[/tex].

A quadratic function is an algebraic function of the form:

[tex]y = a\cdot x^{2}+b\cdot x + c[/tex], [tex]\forall \,x, y, a, b, c\,\in \mathbb{R}[/tex] (1)

Where:

The maximum/minimum of a quadratic function is represented graphically by the vertex, which is the only point that has no a "twin" point by any means of symmetry. We can get the x-coordinate of the vertex by means of the quadratic formula:

[tex]a\cdot x^{2} + b\cdot x + (c- y) = 0[/tex] (2)

[tex]x = \frac{-b\pm \sqrt{b^{2}-4\cdot a\cdot (c-y)}}{2\cdot a}[/tex], where [tex]b^{2}-4\cdot a\cdot (c-y) = 0[/tex].

Hence, the x-coordinate of the vertex is:

[tex]x = -\frac{b}{2\cdot a}[/tex] (3)

And the y-coordinate of the vertex is determined by evaluating (1) at (3):

[tex]y = f\left(-\frac{b}{2\cdot a} \right)[/tex] (4)

The maximum or minimum of a quadratic function is found evaluating the polynomial at [tex]x = -\frac{b}{2\cdot a}[/tex].

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Answer:

5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

5 - 8 ÷ 2 + 4

Step 2: Simplify

Answer:

SENCOND TO LAST

Step-by-step explanation:

Answer:

this sequence is geometrical sequence

and it's formula is

[tex]y = a {r}^{n} \\ here \: a \: is \: first \: number \: is \: equal \: 1 \\ and \: the \: ratio \: is \: r \: is \: equal \: - 3 \\ y = 1 \times {( - 3)}^{n} [/tex]

Answer:

Assuming f(x) = 3x^2 - 3x + 1, f(-2) is 16.

Step-by-step explanation:

Check answer.

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Answer:

Step-by-step explanation:

-5 is bigger because it’s closer to 0 in a number line

Answer:

-5 because it is closer to 0 and -15 is farther away from 0 .

Step-by-step explanation:

Answer:

Edit: Both are same.

Step-by-step explanation:

Volume is the total space occupied by an object.

The rule in vector notation for the translation to the right is described by the following formula:

[tex]V'(x,y) = V(x,y) + (9, -4)[/tex]

Vectorially speaking, a translation is described by the following expression:

[tex]V'(x,y) = V(x,y) + T(x,y)[/tex] (1)

Where:

By direct inspection we see that parallelogram C'D'E'F' translated to the right is moved 9 in +x direction and 4 in -y direction. Hence, the translation vector is equal to:

[tex]T(x,y) = (9, -4)[/tex]

And the rule in vector notation for the translation to the right is described by the following formula:

[tex]V'(x,y) = V(x,y) + (9, -4)[/tex]

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Answer:

20 units

Step-by-step explanation:

to solve this equation you need the pythagorean theorem: a^2 + b^2 = c^2

2^2 + 7^2 = 53; square root of 53 is 7.28010989; or about 7.3 units (line AC)

2^2 + 6^2 = 40; square root of 40 is 6.32455532; or about 6.3 units (line BC)

4^2 + 5^2 = 41; square root of 41 is 6.40312424; or about 6.4 units (line AB)

7.3 + 6.3 + 6.4 = 20

20 units

Answer:

about 110

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

[tex]\frac{-5}{k} + 1\\\frac{-5}{-1} + 1\\5+1 = 6[/tex]

Answer:

the systems of equations corresponding to the given solutions, in order

Step-by-step explanation:

Wednesday

If you use a calender, it falls on a wednasday

Step-by-step explanation:

D = b² - 4ac

D = 10² - 4 · 3 · 2

D = 100 - 24

D = 76

D = (-5)² - 4 · 1 · (-4)

D = 25 - (-16)

D = 26 + 16

D = 42

D = 7² - 4 · 1 · (-8)

D = 49 - (-32)

D = 49 + 32

D = 81

D = 0² - 4 · 1 · (-9)

D = 0 - (-36)

D = 36

D = (-6)² - 4 · 5 · 10

D = 36 - 200

D = - 164

Answer:

700=25x28

Step-by-step explanation:

The product of the two given numbers is 700.

The given expression is 25 × 28.

We need to find the product of these two numbers in different ways.

The distributive property of multiplication over addition states that multiplying the sum of two or more addends by a number gives the same result as multiplying each addend individually by the number and then adding the products together. This property of multiplication over addition is used when we need to multiply a number by a sum.

Now, direct multiplication 25 × 28=700

Using distributive property we get 25 × (20+8)

=25 × 20 + 25 × 8

=500 + 200

=700

Therefore, the product of two given numbers is 700.

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The price of one adult ticket is $15 and the price of one child ticket is $8.

Two sets of equations can be derived from this question:

14a + 14c = 322 equation 1

12a + c = 188 equation 2

These equations are known as simultaneous equations and they can be solved to determine the cost of each ticket using the elimination method.

In order to determine the cost of the adult's ticket multiply equation 2 by 14

168a + 14c = 2632 equation 3

Subtract equation 1 from 3

2310 = 154a

Divide both sides by 154

a = $15

To determine the cost of the children's ticket substitute for a in equation 1

14(15) + 14c = 322

210 + 14c = 322

322 - 210 = 14c

112 = 14c

c = $8

To learn more about simultaneous equations, please check: brainly.com/question/23589883?referrer=searchResults

Answer:

i think u are right

Step-by-step explanation:

Answer:

2143

Step-by-step explanation:

2 × 4^5 + 10 (5 × 2) -10 ÷ 2

= 2 × 4^5 + 10 × 10 (-10) ÷ 2

= 2 × 4^5 + 10 × 10 - 10 ÷ 2

= 2 × 4^5 + 10 × 10 - 5

= 2048 + 100 - 5

= 2148 - 5

= 2143

Answer:

Your answer is 2143

Step-by-step explanation:

2 × 4^5 + 10 × 10 - 10 ÷ 2

*How i got the -5 is becuase 10/2 = 5

= 2 × 4^5 + 10 × 10 - 5

* How i go the 100 is becuase 10 *10 = 100

2048 + 100 - 5

How i go 2148 is becuase 2048+100 = 2148

2148 - 5

Answer = 2143