James wants to set aside money each month to save for a down payment on a new home. How much will James need to save each month if he wants to have $30,000 in three years and can earn a 6% interest rate that compounds monthly

To solve for the two numbers that sum to -102, with one number being 62 less than the other, we use algebraic methods to find the numbers as -20 and -82.

To find the two numbers that sum to -102 and where one number is 62 less than the other, we can set up the following system of equations based on the given information:

Substitute y from the second equation into the first equation:

Now that we have x, we can find y by substituting x back into the equation y = x - 62:

Therefore, the two numbers are -20 and -82.

Answer:

C(-4,-2), D(3,-7)

[tex]Ar=35unit^{2}[/tex]

Step-by-step explanation:

we procced to identify points:

A(-4,-7), B(3,-2)

for being the sides of a rectangle parallel to the axes, we find the other two vertices (VIEW GRAPH)

C(-4,-2), D(3,-7);  Area of the rectangle Ar=b*h, where

[tex]b=(X_{D}-X_{A}); h=(Y_{B}-Y_{D})[/tex]

So Ar=(3-(-4))*(-2-(-7)) = (3+4)*(-2+7)=7*5=[tex]35unit^{2}[/tex]

Final answer:

The other two vertices of the rectangle are (3, -7) and (-4, -2), and the area of the rectangle is 35 square units.

Explanation:

To find the coordinates of the other two vertices of a rectangle given two vertices on the coordinate plane, use the fact that the sides of the rectangle are parallel to the axes.

The two given vertices are (3, -2) and (-4, -7). A rectangle has opposite sides of equal length, so the x-coordinates of the opposite vertices must be the same for one pair, and the y-coordinates must be the same for the other pair. Therefore, the other two vertices will have coordinates (3, -7) and (-4, -2).

To find the area of the rectangle, calculate the difference in the x-coordinates (length) and the difference in the y-coordinates (width), then multiply these together.

The length is |3 - (-4)| = 7 and the width is |-2 - (-7)| = 5,

so the area is 7 × 5 = 35 square units.

Answer:

The answer would be 5.03x10^-3   ^-^

Step-by-step explanation:

Answer:

-3.

Step-by-step explanation:

Counting the digits after the point until we get to the 5:

The count is 3.

The power is -3:

5.03 * 10^-3.

Answer: The answer is x = 12

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

1. Get all x varibles to one side.

-7x - 11 = 25 - 10x

+ 10x            +10x

2. Get all constants to one side.  

3x - 11 = 25

+ 11         +11

3. Divide on both sides to get x alone.

3x = 36

÷3    ÷3

x = 12

Answer:

x = 4

Step-by-step explanation:

Using "number sense"

2x=8​

Double a number is 8.

What is half of 8? 4.

Double of 4 is 8.

Therefore the number, x, is 4.

Check:

2x = 8

x = 8/2

x = 4

2x = 8

2(4) = 8

8 = 8

Answer:The value of f is;

Step-by-step explanation:

f=1/t

Answer:

0.2 Newtons

Step-by-step explanation:

Newton's Second Law of Motion states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

Newton's Second Law formula:

F = m * a

Where:

F: the magnitude of the net force, in N

m: the mass of the object, in Kilogram

a: the acceleration of the object, in m/s2

Answer:

Step-by-step explanation:

Givens

[tex]m=100 gr[/tex]

[tex]a= 2m/s^{2}[/tex]

First, we need to transform the mass to kilograms, we know that 1 kilogram equals 1000 grams.

[tex]100gr\frac{1kg}{1000gr} =0.1 kg[/tex]

Then, by Newton's Second Law, we have

[tex]F=ma[/tex]

Replacing each variable

[tex]F=0.1kg(2m/s^{2} )\\F=0.2 N[/tex]

Therefore, the force on this wagon is 0.2 Netwons.

Answer:

294 square feet

Step-by-step explanation:

If the volume is one  side  at the 3rd power, then  If we know the volume, we calculate   the cubic root of 343  that is 7

So 1 side =7

The cube has 6 faces

1 face of the cube is 7*7=49

Six faces =

49*6= 294

Answer:

- y + 8(0) = -2              -y + 8(1)=-2                 -y + 8(2) = -2

-y + 0 =-2                    -y + 8 - 8 = -2 -8         -y +16 - 16 = -2 -16

-y= -2                           -y = -10                        -y = -18

Step-by-step explanation:

- y + 8(0) = -2              -y + 8(1)=-2                 -y + 8(2) = -2

-y + 0 =-2                    -y + 8 - 8 = -2 -8         -y +16 - 16 = -2 -16

-y= -2                           -y = -10                        -y = -18

for x = 0, 1, 2

The corresponding y values for the given x values (0, 1, 2) into the linear equation y + 8x = -2 is equal to -2, -10, and -18, respectively, it illustrates how the y value changes with different x values in a linear equation.

The linear equation y + 8x = -2 for given values of x (0, 1, 2).

Let's solve it step-by-step for each x value:

For x = 0: Substitute x with 0 in the equation, y + 8(0) = -2, which simplifies to y = -2.

For x = 1: Substitute x with 1 in the equation, y + 8(1) = -2, resulting in y = -10.

For x = 2: Substitute x with 2 in the equation, y + 8(2) = -2, simplifying to y = -18.

This exercise demonstrates how changing the value of x affects the corresponding value of y in a linear equation.

It highlights the importance of substitution in solving equations and understanding linear relationships.

Answer: 4 and 5/18

Step-by-step explanation: In this problem, we have 7/6 divided by 3/11. Dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division sign to multiplication and flip the second fraction.

So here, 7/6 ÷ 3/11 can be rewritten as 7/6 × 11/3.

Now we are simply multiplying fractions so we multiply across the numerators and multiply across the denominators.

So we have 7 × 11 which is 77 and 6 × 3 which is 18.

Now we have the fraction 77/18.

We can write 77/18 as a mixed number by dividing the denominator of the fraction into the numerator.

18 divides into 77 4 times with a remainder of 5.

So we can write 77/18 as 4 and 5/18.

Notice that the 18 stays which is the denominator of our original answer.

This means that 7/6 ÷ 3/11 = 4 and 5/18.

The point located 3/5 of the way from point A(4, 5) to point B(-6, 0) on line segment BA is at (0, 3). This is found using the formula for division of a line segment at given ratio.

The subject of this question is Geometry, specifically finding the coordinates of a point along a line segment. Line segment BA has coordinates B(-6, 0) and A(4, 5). To find the point located 3/5 of the way from point A to point B, we will need to use the formula for the division of a line segment which is: X = x1 + r(x2 - x1) and Y = y1 + r(y2 – y1), where r is the ratio, in this case 3/5.

Using the formula, the x coordinate of the point can be calculated as: X = (-6) + 3/5 [(4) - (-6)] = -6 + 3/5 * 10 = -6+6 = 0. The y coordinate of the point can be calculated as: Y = 0 + 3/5 [(5) - 0] = 0 + 3 = 3. Therefore, the point is at (0,3) which is located 3/5 of the way from point A to point B on the line segment.

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Final answer:

The coordinates of the point located 3/5 of the way from point A to point B are (0, 3), calculated by finding the weighted average of the x and y coordinates of the endpoints.

Explanation:

To find the coordinates of the point located 3/5 of the way from point A to point B, we need to calculate the weighted average of the endpoints. The coordinates of point B are (-6, 0) and the coordinates of point A are (4, 5).

The x-coordinate of the point is calculated as follows:
(-6) + ((4 - (-6)) × (3/5)) = (-6) + (10 × (3/5)) = (-6) + 6 = 0.

The y-coordinate of the point is calculated as follows:
0 + ((5 - 0) × (3/5)) = 0 + (5 × (3/5)) = 3.

Therefore, the coordinates of the point located 3/5 of the way from point A to point B are (0, 3).

Expanded form of 3( 6 + 7) is [tex]3 \times 10+9 \times 1[/tex]

Need to use distributive property to write the expanded form of 3(6 + 7)

Let’s understand what is distributive property.

The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products together.

According to distributive property, for numbers a , b and c

[tex]a(b+c)=a \times b+b \times c[/tex]  ----- eqn 1

3(6 + 7) can be rewritten as 3 ( 6 + 4 + 3 ) = 3 ( 10 + 3 )

Now in our case a = 3 , b = 10 and  c = 3  

On substituting the values of a , b and c in equation 1 we get

[tex]3(10+3)=3 \times 10+3 \times 3=3 \times 10+9 \times 1[/tex]

So expanded form of 3( 6 + 7) is [tex]3 \times 10+9 \times 1[/tex]

Answer:

Teo is 5 and Richard is 12

Step-by-step explanation:

r+t=17

2t+2=r

2t+2+t=17

3t+2=17

3t=15

t=5

r+5=17

r=12

None of the given expressions (0.375 x 0.5, 0.625 x 0.5, 0.5 x 0.5, 4/5 x 1/2, 3/8 x 1/2) have the same product as 3 x 0.5, which equals 1.5.

To find out which expressions have the same product as 3 x 0.5, we first need to determine the product of 3 x 0.5. This is easy to do: 3 x 0.5 equals 1.5.

Now, let's check the given expressions:

As we can see, none of these expressions equals 1.5. Thus, none of them have the same product as 3 x 0.5.

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The factorization of the expression 2b + 8 is 2 ( b + 4 ).

Given data:

The expression is represented as 2b + 8.

To factor out the coefficient of the variable in the expression 2b + 8, determine the greatest common factor (GCF) of the terms.

The GCF of 2b and 8 is 2.

So, divide each term by 2 to factor out the coefficient:

2b + 8 = 2(b) + 2(4)

Now, rewrite the expression factored out:

2b + 8 = 2(b + 4)

Hence, the expression 2b + 8 factored is 2(b + 4).

To learn more about factorization, refer:

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Answer:

r(x) = -7

Step-by-step explanation:

r(x) = -x - 7

+ 7 + 7

7 = -x

÷ -x ÷ -x

7/-1 = x

-7 = x

Answer:

then he would made an 85 bc he wouldve got 5 points added on to his quiz

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &5 \end{cases} \\\\\\ A=4000\left(1+\frac{0.03}{2}\right)^{2\cdot 5}\implies A=4000(1.015)^{10}\implies A\approx 4642.16[/tex]

Answer:

n= Total number of packages on trucks= 6096

n = T x P (Model Equation)

Step-by-step explanation:

No. Of delivery trucks = T = 127

Package on each truck = P = 48

Total number of packages on trucks =n= ?

Each truck contains 48 packages and total trucks were 127, to find total number of packages on trucks , we just need to multiply the number of trucks with the number of package on each truck.

Total number of packages on trucks =n= (No. Of delivery trucks) x (Package on each truck)

n = T x P (Model Equation)

n= 127 x 48

n= 6096 (Total number of packages on trucks)

Answer:

(8, -4)

Step-by-step explanation:

Answer:

12.45 pm

7.30 pm

00 00

20 15

Answer:

The second method gives the greater heart rate.

Step-by-step explanation:

In the second method, the age and heart rate(bpm) are in a linear relationship.

Therefore, the maximum heart rate for a 90-year-old person in the second method is = 194 - (194 - 187)7 = 145 bpm.

{Since, the maximum heart rate in the second method decreases in an A.P. having value at the age of 20 is 194 and it decreases by 7 bpm per 10 years}

Now, in the first method, the maximum heart rate for 90-year-old person is y = 220 - 90 = 130 bpm.

Therefore, the second method gives a greater heart rate. (Answer)

Answer:

Step-by-step explanation:

The given expression is

[tex]y=220-x[/tex]

Where [tex]x[/tex] is age.

Now, for [tex]x=90[/tex], we have

[tex]y=220-90=130[/tex]

The equation gives 130 bpm for a 90-year-old patient.

Now, if we observe the given table, we would find a pattern there. The heart rate decreases by 7 while ages decreases by 10, so

For 60 y/o we have 166 bpm.

For 70 y/o we have 159 bpm.

For 80 y/o we have 152 bpm.

For 90 y/o we have 145 bpm.

If we compare, the second method (table) gives the greater heart rate.

Answer:

i believe it would be 36

Answer:36

Step-by-step explanation:

Answer:

x = -1

Step-by-step explanation:

Let's solve your equation step-by-step.

7x + 12 = 2(1 − x) − x

Step 1: Simplify both sides of the equation.

7x + 12 = 2(1 − x) − x

7x + 12 = (2) (1) + (2) (− x) + − x (Distribute)

7x + 12 = 2 + − 2x + − x

7x + 12 = (− 2x + − x) + (2) (Combine Like Terms)

7x + 12 = − 3x + 2

7x + 12 = − 3x + 2

Step 2: Add 3x to both sides.

7x + 12 + 3x = − 3x + 2 + 3x

10x + 12 = 2

Step 3: Subtract 12 from both sides.

10x + 12 − 12 = 2 − 12

10x = − 10

Step 4: Divide both sides by 10.

10x/10 = - 10/10

x = - 1

Hope this helps! Sorry if it is confusing!

Answer:

- 2 < x < 4

Step-by-step explanation:

We have to write in interval notation of the following interval.

The interval is given by (-2,4) which means the values of the variable, say x, vary from -2 (but not including -2) to 4 (but not including 4).

So, in interval notation this can be written as - 2 < x < 4 (Answer)

Therefore, the values -2 and 4 are the limiting end values of the variable x.

Answer:

1/0.04 = 25

Step-by-step explanation:

Answer:

Step-by-step explanation:

well 1/4% wouldnt be 25% because they are 25% = 0.25 = 1/4

the percentage sign changes everything

since it is 1/4% rather than 1/4 by itself

1/4% = 0.25%

if you want to know the percent as a decimal you move the "." to the left twice

(or divide by 100)

so that means that the decimal of 0.25% would be 0.0025

Answer:

The value of x is 25.

Step-by-step explanation:

Given:

side AB = [tex]3x-5[/tex]

side BC = [tex]2x+20[/tex]

side AC = [tex]4x-30[/tex]

In Δ ABC is an equilateral triangle.

In equilateral triangle all three angles are same and also the sides are same.

Hence side AB = side BC

Substituting the values for side AB and side BC we get,

[tex]3x-5=2x+20\\3x-2x=20+5\\x=25[/tex]

Hence the value of x = 25.

Answer:

The value of x for the given figure is 95 And 1.67

Step-by-step explanation:

From Given figure :

Sin angle = [tex]\dfrac{\textrm perpendicular}{\textrm Hypotenuse}[/tex]

or ,  Sin C =  [tex]\dfrac{\textrm 3x - 5}{\textrm 4 x - 30}[/tex]

Cos angle =  [tex]\dfrac{\textrm Base}{\textrm Hypotenuse}[/tex]

or ,  Cos C =  [tex]\dfrac{\textrm 2x + 20}{\textrm 4 x - 30}[/tex]

Or, Cos c = [tex]\sqrt{1 - sin^{2}C }[/tex]

Or, [tex]\dfrac{\textrm 2x + 20}{\textrm 4 x - 30}[/tex] = [tex]\sqrt{1-(\frac{3x - 5}{4 x + 20} })^{2}[/tex]

or, [tex](\frac{2x+20}{4x-30}) ^{2}[/tex] = 1 - [tex](\frac{3x-5}{4x-30} )^{2}[/tex]

[tex]\frac{4x^{2}+400+80x}{16x^{2}+900-240x}[/tex]= 1- ( [tex]\frac{9x^{2}+25-30x}{16x^{2}+900-240x}[/tex] )

Or, 4x²+400+80x = [tex]16x^{2}+900-240x[/tex] - 9x² -25 +30x

or, 4x²+400+80x = 7 x² + 875 -210x

or, 3 x² + 475 -290 x = 0

Or, Solving the equation

3 x² - 285 x - 5 x + 475 = 0

or, 3 x ( x - 95 ) - 5 ( x - 95 ) = 0

or, ( x - 95 ) ( 3 x - 5 ) = 0

∴ x = 95  and x = 1.67

Hence The value of x for the given figure is 95 And 1.67  Answer

Answer:

96/5

Hope this helps!

To have $18,000 in 2 years with a 20% annual interest rate compounded continuously, you need to invest approximately $12,065.76.

To determine the amount of money you need to invest to have $18,000 in 2 years with a 20% annual interest rate compounded continuously, we can use the formula:

A = P * e^(rt)

Where:

Substituting the values into the formula:

18,000 = P * e^(0.20*2)

Simplifying:

18,000 = P * e^(0.40)

P = 18,000 / e^(0.40)

Using a calculator to evaluate the exponential term:

P ≈ 12,065.76

Therefore, you need to invest approximately $12,065.76 to have $18,000 in 2 years.