Solve the equation t − 3 = 17 for t.

Answer:

y = [tex]\frac{x+1}{2}[/tex]

Step-by-step explanation:

y = 2x - 1

switch the x and y variables

x = 2y - 1

solve for y

x + 1 = 2y

[tex]\frac{x+1}{2}[/tex] = y

The total interest earned at the end of first year is $250 and the percentage of interest for his total investment is 6.25%.

Given, Chau invested his money by purchasing the following:

a certificate of deposit for $1000 at the rate of 2% per year, and

corporate bonds for $3000 at the rate of 7% per year.

we know that simple interest is calculated by multiplying the amount invested P by the interest rate r times the number of years invested t.

therefore, I = P × r × t

a. The first investment has a principal of P = $1,000, r = 2% = 0.02, t = 1 yr

I₁ = 2000 × 0.04 × 1

I₁ = 40

The second investment has a principal P = $3,000, interest rate r = 7% = 0.07 and time t = 1yr

I₂ = 3000 × 0.07 × 1

I₂ = 210

Therefore, total interest  = I₁ ₊ I₂

= 40 ₊ 210

= $250

b. The overall rate of interest can be found by dividing:

Total interest/Total amount invested × 100

= 250/(1000 ₊ 3000) × 100

= 250/4000 × 100

= 25/4

= 6.25%

Hence we get the total interest earned at the end of first year as $250 and its overall rate of interest as 6.25%

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Your question was incomplete. Please find the missing content here.

Last year, Chau invested his money in two purchases. He purchased a certificate of deposit for $1000 that paid 2% interest per year and purchased $3000 in corporate bonds paying 7% interest per year.

(a) What was the total investment earned at the end of 1 year?

(b) What was the percentage interest for her total investment?

Darcy requires 24.14 gallons of paint to cover an area of 2716 feet².

Length of the house = 35 feet

width of the house = 28 feet

Height of the house = 6 feet

Total surface area = 2 l b + 2 b h + 2 h l

A = 2 (35) (28) + 2 (28) (6) + 2 (6) (35)

A = 1960 + 336 + 420

A = 2716 feet²

If he uses 2 coats of stain, the area he need to cover = 2 (2716) = 5432 feet²

Gallon of paint required = 5432 / 225 = 24.14 gallons.

Therefore, Darcy requires 24.14 gallons of paint to cover an area of 2716 feet².

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Answer:

Hey there!

Step-by-step explanation:

This is ur answer....

Hope it helps!

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Answer:

E would be 6 spaces or the middle of points C and D.

Step-by-step explanation:

Please see picture.

Answer:

0.012÷2=12 thousandths ÷ 2

Answer:

30 yards

Step-by-step explanation:

9+9+6+6=30yards

Answer:

923.08

Step-by-step explanation:

48000/52 weeks

Answer:

923.08

Step-by-step explanation:

There are 52.1429 weeks in a year, so divide.

Answer:

10

Step-by-step explanation:

If the decimal is .5 or above, round up to the next whole number. If the decimal is below .5, round down to the last whole number. Because .7 is greater than .5, we round up to 10.

Answer:

10

Step-by-step explanation:

In rounding, we look at the digit one place to the right of what we are rounding to.  If that digit that is one place to the right is 5 or greater, we increase our digit by one.  If that digit that is one place to the right is 4 or less, we leave our digit as it is.

Answer:

42°, 101°

Step-by-step explanation:

These answers come from the angle subtraction postulate.

The experimental method has one advantage over the correlational method in that it "determines cause and effect," whereas the correlational study does not.

Quantitative methods are used in both experimental and correlational research to investigate interactions between variables. However, there are significant differences with how data is gathered as well as the conclusions that can be drawn.

Experimental research is scientific research that employs two sets of variables. The first set serves as a constant against which the differences in the second set are measured. Experimentation is used in quantitative research, for example.

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Answer:

13 1/3

____

         [tex]1\:2/3 = 5/3\\1/8 = 1/8\\\\5/3 \div 1/8\\=\frac{5\cdot8}{3\cdot1}\\= \frac{40}{3}\\= 13\:1/3[/tex]

When working with mixed numbers that are being divided, you know where to start. Start by converting mixed numbers to fractions, then multiply the fractions together to divide them. Simplify your improper fraction by counting how many times it surpasses the denominator.

Answer:

x = -2

TU = 4

UB = 2

Step-by-step explanation:

you can add x^2 with 4x+10 and equate it to 6:

x^2 + 4x + 10 = 6

x^2 + 4x + 4

then u can use the roots formula : x = (-b ± √ (b2 - 4ac) )/2a

so it'll be   x = {-4±[√16 - 4(4)]}/2

x= -2

then u can substitute it and find TU and UB

TU= (-2)^2 = 4

UB= 4(-2)+10 = 2

Answer:

Coordinates of D are (-1, 4)

Step-by-step explanation:

I have assumed that what you wrote as 1n is actually 1/n otherwise the question does not make sense

1/n with n = 5 ==> that D is 1/5th of the distance from C on the CD line segment

Point D is 1/5th of the way from C to D

I will represent the (x, y) coordinates of points C, D and E as
[tex](x_C, y_C), (x_D, y_D) , (x_E, y_E)[/tex] respectively

Then the x-distance from C to E = [tex]x_E - x_C[/tex] and the y-distance from C to E will be [tex]y_E - y_C[/tex]

[tex]\text{1/5th of }[/tex] [tex]x_E - x_C = \dfrac{x_E - x_C}{5}[/tex] but this is relative to the location of [tex]x_C[/tex].
So we have to add this to [tex]x_C[/tex] to get the absolute x-coordinate of D

So
[tex]\displaystyle \large x_{D}=x_{C}+\dfrac{x_{E}-x_{C}}{5}[/tex]

and similarly

[tex]{\displaystyle y_{D}=y_{C}+\dfrac{y_{E}-y_{C}}{5}}[/tex]

Putting in the values for these coordinates we get

[tex]x_{D}=-2.5+\dfrac{5-(-2.5)}{5} \\\\= -2.5 + \dfrac{5 + 2.5}{5}\\\\\= -2.5 + \dfrac{7.5}{5}\\\\= - 2.5 + 1.5\\\\= -1.0[/tex]

[tex]y_{D}=1.25+\dfrac{15-1.25)}{5} \\\\= 1.25+ \dfrac{15 - 1.25}{5}\\\\\ = 1.25+ \dfrac{13.75}{5}\\\\= 1.25+ 2.75\\\\= 4.0[/tex]

So the coordinates of D are:

[tex]\boxed{D(-1, 4)}[/tex]

The graph shows the point D is indeed 1/5th of the distance from C to D

Answer:

S' (- 3, 9 ) , V' (- 4, 3 )

Step-by-step explanation:

consider the coordinates of R and R'

R (2, 1 ) , R' (- 4, 8 )

2 → - 4 in the x- direction is - 6

1 → 8 in the y- direction is + 7

then the translation rule is

(x, y ) → (x - 6, y + 7 )

S (3, 2 ) → S' (3 - 6, 2 + 7 ) → S' (- 3, 9 )

V )2, 6 ) → V' (2 - 6, 6 + 7 ) → V' (- 4, 13 )

The surface area and the volume of the triangular prism are 26.88 square cm and 7.68 cubic cm.

When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.

It is given that:

The triangular prism is given in the picture:

The surface area = 4x2 + 2x2.4 + 3.2x2 + 2(1/2)3.2x2.4

The surface area = 8 + 4.8 + 6.4 + 7.68

The surface area = 26.88 square cm

The volume = (1/2)x3.2x2x2.4

The volume 7.68 cubic cm

Thus, the surface area and the volume of the triangular prism are 26.88 square cm and 7.68 cubic cm.

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Equation of line p:

[tex]{\sf{2x - 3y = 4}}[/tex]

[tex]{\sf{y = \frac{2x}{3} - \frac{4}{3}}}[/tex]

Slope of line p (m):

[tex]{\sf{\frac{2}{3}}} [/tex]

Since, l is perpendicular to line p, the product of slopes of line l & p should be -1. We assume slope of line l be m2

Hence,

[tex]{\sf{m \times m2 = - 1}}[/tex]

[tex]{\sf{ \frac{2}{3} \times m2 = - 1}}[/tex]

[tex]{\sf{m2 = \frac{ - 3}{2}}}[/tex]

Since, line l passes through points (6, 0).

We apply,

[tex]{\sf{(y - y1) = m2(x - x1)}}[/tex]

[tex]{\sf{y - 0 = \frac{ - 3}{2}(x - 6)}} [/tex]

[tex]{\sf{2y - 0 = - 3x + 18}}[/tex]

[tex]{\sf{3x + 2y - 18 = 0}}[/tex]

The equation of line l:

[tex]{\sf{\red{\boxed{\sf{3x+2y-18=0}}}}}[/tex]

Answer: x=3

Step-by-step explanation:

-2(7-x) + 4= -4

-14 + 2x + 4= -4

2x - 10= -4

2x = 6

x=3

Let's change the equation,

→ 6x - y = 2

→ y = 6x - 2

Then the value of x will be,

→ -4x + 3y = 1

→ -4x + 3(6x - 2) = 1

→ -4x + 18x - 6 = 1

→ 14x = 1 + 6

→ x = 7/14

→ [ x = 1/2 ]

Hence, the value of x is 1/2 (or) 0.5.

Now the value of y will be,

→ y = 6x - 2

→ y = 6(1/2) - 2

→ y = 3 - 2

→ [ y = 1 ]

Hence, the value of y is 1.

Answer:

3.4, 1/4, 12%, -0.01, -26.1

Step-by-step explanation:

The simplest way to do these type of problems is to convert all of the numbers into either a fraction, decimal, or a percentage. In my opinion, it is easier to use a percentage here.

12% is already a percentage

-0.01 = -1%

1/4 = 25%

3.4 = 340%

-26.1 = -2610%

Now that the rational numbers are all in the same unit, it is easier to sort them. In the end, we get this list (from greatest to least):

3.4, 1/4, 12%, -0.01, -26.1

FINAL ANSWER: 3.4, 1/4, 12%, -0.01, -26.1

Raíz cuadrada de 864

Para resolver este problema debemos tomar en cuenta los datos que nos dan y la ecuación de una hipérbola. Comencemos con los datos:

The general equation of ellipse is given as, x2a2+y2b2=1 x 2 a 2 + y 2 b 2 = 1 , where, a is length of semi-major axis and b is length of semi-minor axis.

centro: (0,0)

focus : (0, -√28) , (0, √28)

eje conjugado = 2√3

por los focos podemos ver que la hipérbola se dirige hacia el eje y, por lo que debemos tomar la siguiente forma de la ecuación de la parábola:

de los focos podemos obtener que: √28

y del eje conjugado podemos saber que al dividir la longitud del eje conjugado dentro de 2 obtenemos b, así que:

b = √3

podemos utilizar la siguiente fórmula para obtener a:

si despejamos a en la ecuación obtenemos lo siguiente:

ahora podemos sustituir los valores:

a=5

así que media vez conozcamos a, podemos sustituir los datos en la ecuación de la hipérbola así que obtenemos lo siguiente:

si graficamos la hipérbola, queda como en el documento adjunto.

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Answer: 7, and 31

Step-by-step explanation:

7 + 12 = 19 or 19 - 12 = 7

19 + 12 = 31

The other number will be - 7.

Yes, There is only one answer.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The difference of two numbers is 12.

And, one of the numbers is 19.

Now,

Let two numbers are x and y.

So, We get;

x + y = 12

Here, one of the numbers is 19.

So, x = 19

We get;

x + y = 12

19 + y = 12

y = 12 - 19

y = - 7

Thus, The other number will be - 7.

Yes, There is only one answer.

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Annually The amount after 10 years = $ 7247.295

quarterly compound after 10 years = $7393.5

Continuously interest =$7,419

Given:

P = the principal amount

r = rate of interest

t = time in years

n = number of times the amount is compounding.

Principal =  $4500

time= 10 year

Rate = 5%

To find: The amount after 10 years.

The principal amount is, P = $4500

The rate of interest is, r = 5% =5/100 = 0.05.

The time in years is, t = 10.

Using the quarterly compound interest formula:

A = P (1 + r / 4)4 t

A= 4500(1+.05/4)40

A= 4500(4.05/4)40

A= 4500(1.643)

Answer: The amount after 10 years = $7393.5

Using the Annually  compound interest formula:

A = P (1 + r / 100) t

A= 4500(1+5/100)10

A= 4500(105/100)10

Answer: The amount after 10 years = $ 7247.295

Using the Continuously  compound interest formula:

e stands for Napier’s number, which is approximately 2.7183

[tex]A=Pex^{rt} \\A=4500(e)^{.5} \\A= 4500(2.71)^{.5}[/tex]

A= $2,919

Answer: The amount after 10 years = $4500+$2,919=$7,419

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Using exponent power property, ³√x²y³ = x^r y^s, where x and y are non-negative real numbers.

r, the exponent of x, is: 2/3

s, the exponent of y, is: 1

According to the Power of a Power Property, you can multiply the exponents if one exponent is increased to a higher exponent. This characteristic may be used to resolve the equation (3 x 2) 3.

³√x²y³ = x^r y^s

Cubing on both sides,

x²y³ = x^3r y^3s

As base is same, equating the powers

⇒ 2 = 3r; r = 2/3

⇒ 3 = 3s; s = 1

The expression

³√x²y³ = x^ry^s

where x and y are non-negative real numbers.

r, the exponent of X, is:

s, the exponent of y, is:

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Answer: 13512

100332

Step-by-step explanation:

The shortest time for her run is approximately 36 minutes and the longest time is approximately 67 minutes.

To represent Kenzie's situation, we can use an absolute value equation. Let x represent the length of her run in miles.

The equation would then be |x - 6| ≤ 1, which means the distance between x and 6 is less than or equal to 1.

To find the shortest or longest amount of time for Kenzie's run, we need to consider the speed.

The time can be found by dividing the distance by the speed, so the minimum time would be (6 - 1)/6.25 hours,

which is approximately 0.6 hours or 36 minutes.

The maximum time would be (6 + 1)/6.25 hours,

which is approximately 1.12 hours or 67 minutes.

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The amount Jasmin was paid altogether was $210

From the question, we are to determine how much Jasmin was paid altogether

From the given information,

The Smith family pay her $10 an hour.

and

She babysat for the Smith family for 12 hours

Thus,

The amount she was paid by the Smith family is 12 × $10 = $120

Also,

The Johnson family pay her $15 an hour

and

She babysat for the Johnson family for 6 hours

Thus,

The amount she was paid by the Johnson family is 6 × $15 = $90

Therefore,

The amount she was paid altogether = $120 + $90

The amount she was paid altogether = $210

Hence, the amount Jasmin was paid altogether was $210

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The consecutive even integers are 8, 10 and 12.

Let the integers be x, x + 2, and x + 4.

Therefore, the equation will be:

6(x) = x + 2 + x + 4 + 26

6x = 2x + 32

Collect like term

6x - 2x = 32

4x = 32

Divide

x = 32/4.

x = 8

The numbers are 8, 10 and 12.

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The value of the longest of the four side length is 29 inches, if the lengths of the four sides of a quadrilateral (in inches) are consecutive integers.

According to the given question.

The lengths of the four sides of a quadrilateral (in inches) are consecutive integers.

So, let the length of the quadrilateral be x, (x + 1), (x + 2), and (x + 3).

Also, it is given that the perimeter of the quadrilateral is 110 inches.

⇒ x + x+1 + x + 2 + x + 3 = 110

⇒ 4x + 6= 110

⇒ 4x = 110 -6

⇒ 4x = 104

⇒ x = 104/4

⇒ x = 26 inches

Thereofore, the length of the sides of the quadrilaterals is given by

x = 26 inches

x + 1 = 26 + 1 = 27 inches

x + 2 = 26 + 2 = 28 inches

x + 3 = 26 + 3 = 29 inches

Hence, the value of the longest of the four side length is 29 inches, if the lengths of the four sides of a quadrilateral (in inches) are consecutive integers.

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Option 1, {x | x = –4, –1, 3, 5, 6} is the domain of the given function.

For any function, domain is the set of all input values that are accepted by the given function. For example, if there is a function, say f(x) = x + 2, then all the values of x will make up the domain of f(x).

Here, we are given a function {(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)}

In this case, all the input values = all the x values

and all the output values = all the y values

Thus, the domain of the given function will be a set containing the following x values-

3, 6, -1, 5, -4

Arranging these values in the ascending order we get,

-4, -1, 3, 5, 6

Therefore, the domain of the function can be represented as {x | x = –4, –1, 3, 5, 6}.

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