Which expression has the same value as
-4 - (-5)

F. -4 + (-5)
G. -4 +5
H. -5 + (-4)
J. -5-(-4)

The distance between points A and B is: A. 4√5 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given parameters into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(4 - (-4))² + (-2 - 2)²]

Distance = √[(8)² + (-4)²]

Distance = √(64 + 16)

Distance = √80

Distance = √16 × √5

Distance = 4√5 units.

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Answer:

none of them are right it is 4 to the 10

Step-by-step explanation:

Using linear equations, Tiffany was charged $10.77 for 8 minutes at the self-serve car wash.

Solving a linear equation involves determining the answer to a linear equation with one, two, three, or more variables. The answer to a linear equation is the value or values of the variable(s) that are part of the equation. In the elimination procedure, any coefficient is first made equal, then deleted. After elimination, the equations are solved to provide the other equation.

Given that, the car wash charges $5.25 to use its facilities, plus an additional $0.69 for each minute.

C = 5.25 + 0.69x

For 8 minutes:

C = 5.25 + 0.69(8)

C = $10.77

Hence, Tiffany was charged $10.77 for 8 minutes at the self-serve car wash.

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Answer:

The volume V of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height, respectively.

In this case, we have l = 2, w = 7/3, and h = 2. Therefore, the volume is:

V = (2)(7/3)(2)

V = 28/3

V = 9.33 (rounded to two decimal places)

So the volume of the rectangular prism is approximately 9.33 cubic units.

So, the simplified form of the given expression is cosxsinx(3cosx - sinx).

A statement, at least two parameters or integers, and one or more calculations make up a mathematical expression. It is possible to multiply, divide, add, or subtract quantities using this mathematical operation. The following is the expression's structure: An expression is (total count, numerical operator, number, or variable).

We can simplify the given expression using the product-to-sum identities:

sin2x × cosx + cos2x × sinx

= 2sinx × cosx × cosx + (cos²x - sin² x) × sinx [using the identity sin2x

= 2sinx × cosx and cos²x = cos² x - sin² x]

= 2sinx × cos² x + cos²x × sinx - sin² x × sinx [expanding the brackets]

= cosx × sinx(2cosx + cosx - sinx)

= cosx × sinx(3cosx - sinx)

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Answer:

The flag pole is 12 feet tall

Option C.

Step-by-step explanation:

We can use the Pythagorean theorem to evaluate the height of the flagpole.

The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of each of the legs squared and can be written as

[tex]a^2+b^2=c^2[/tex]

Numerical Evaluation

In this example we are given the value of the hypotenuse and the value of one of the legs.

[tex]b=16\\c=20[/tex]

Substituting our values into the equation yields

[tex]a^2+16^2=20^2[/tex]

Lets solve for [tex]a[/tex].

Evaluate [tex]16^2[/tex].

[tex]a^2+256=20^2[/tex]

Evaluate [tex]20^2[/tex].

[tex]a^2+256=400[/tex]

Subtract [tex]256[/tex] form both sides of the equation.

[tex]a^2=144[/tex]

Take the square root of both sides to eliminate the exponent.

[tex]a=\sqrt{144}[/tex]

Evaluate [tex]\sqrt{144}[/tex].

[tex]a=12[/tex]

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According to given conditions, I will earn $913,441.60.

What is interest ?

Interest is the cost of borrowing money, usually expressed as a percentage of the amount borrowed. It is also the amount earned on an investment, usually expressed as a percentage of the amount invested. The rate of interest is determined by factors such as the level of risk involved, the term of the loan or investment, and prevailing market conditions.

To calculate the monthly deposit required, we can use the formula for the future value of an annuity:

FV = P * (((1 + r/n)[tex]^{(n*t)}[/tex]- 1) / (r/n))

where FV is the future value, P is the monthly deposit, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, we want to solve for P, so we can rearrange the formula:

P = FV * (r/n) / (((1 + r/n)[tex]^{(n*t)}[/tex]- 1))

Substituting the given values, we get:

P = 600000 * 0.04/12 / (((1 + 0.04/12)[tex]^{(12*25)}[/tex]- 1))

Simplifying and solving for P, we get:

P ≈ $1,518.14 per month

To calculate the interest earned, we can use the formula:

I = FV - P * t

where I is the interest earned, FV is the future value, P is the monthly deposit, and t is the number of years.

Substituting the given values, we get:

I = 600000 - 1518.14 * 12 * 25

Simplifying, we get:

I ≈ $913,441.60

Therefore, according to given conditions, I will earn $913,441.60.

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Answer:

We can simplify the given expression using the rules of exponents and radicals:

4xy³√ 27x^2y^5

= 4xy * ³√(27x^2y^5) (since y and ³√(27) cannot be simplified further)

= 4xy * ³√(3^3 * x^2 * y^3 * y^2)

= 4xy * 3xy * ³√y^2

= 12x^2y^2 * ³√y^2

Therefore, the expression 4xy³√ 27x^2y^5 simplifies to 12x^2y^2 * ³√y^2.

Step-by-step explanation:

It will take {log(1 - r/n)/n} years to exactly double your investment.

The formula for compound interest is -

[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]

Given is that an investment of $2800 made at an APR of 5% compounded monthly.

The formula for compound interest is -

[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]

For A = 2P, we can write -

Substituting 2P = A, we get -

2P = P(1 + r/n)^nt

2 = (1 + r/n)^nt

log 2 = log {(1 + r/n)^nt}

log 2 = (nt) log(1 + r/n)

(log 2)/log(1 + r/n) = nt

{t} = log{2 - 1 - r/n}/n

{t} = log{1 - r/n}/n

Therefore, it will take {log(1 - r/n)/n} years to exactly double your investment.

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The equations of the relationship are

A: y = 1/4x

B: y = 2/5x

From the question, we have the following parameters that can be used in our computation:

The graph

We can see that the lines pass through the origin

This means that the equations can be represented as

y = mx

Where

m = slope

From the graph. we have

A = (8, 2)

B = (5, 2)

When these points are substituted, we have

A: 8m = 2

B: 5m = 2

When solved, we have

A: m = 1/4

B: m = 2/5

So, the equations are

A: y = 1/4x

B: y = 2/5x

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Answer:

Step-by-step explanation:

We can use the Pythagorean theorem to find the distance from second base to home plate, which is the diagonal of a right triangle with legs of 60 feet each:

d = sqrt(60^2 + 60^2) = sqrt(7200) ≈ 84.85 feet

So the total distance that you ran is:

60 + 60 + 84.85 ≈ 204.9 feet

Rounded to the nearest tenth, the answer is:

204.9 feet ≈ 204.9 feet

The area of the sector is 37.7 ft.

A sector is a region of a circle that is bounded by two radii and the arc of the circle that lies between the endpoints of those radii.

The formula for the area of a sector is given by

Where θ is the central angle in degrees, and r is the radius of the circle

Here we have

A circle has a radius of 4 ft.  

The central angle of sector formed = 270°

Using the formula, Area of sector = (θ/360°) × π r²

Area of the given sector = [ 270/360] × 3.14 × (4)²

= [0.75 ] × [50.24]

= 37.68 ft

= 37.7 ft

Therefore,

The area of the sector is 37.7 ft.

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The monthly payment for a 30-year mortgage in this scenario is $1,713.78.

What are Percentages?

Percentages are a way of expressing a proportion or ratio in terms of a fraction of 100.

To solve this problem, we can use the formula for calculating the monthly payment for a mortgage:

[tex]M = P[r(1+r)^n/((1+r)^n)-1][/tex]

where M is the monthly payment, P is the principal (the amount borrowed), r is the monthly interest rate, and n is the number of monthly payments (the term of the loan in months).

First, we need to calculate the down payment, which is 10% of the purchase price:

Down payment = 0.1 x $340,000 = $34,000

The principal is the purchase price minus the down payment:

Principal = $340,000 - $34,000 = $306,000

Next, we need to calculate the monthly interest rate. The annual interest rate is 5.3%, so the monthly interest rate is:

r = 0.053/12 = 0.00441667

Finally, we need to calculate the number of monthly payments. A 30-year mortgage has 360 monthly payments (30 years x 12 months per year).

n = 360

Now we can plug in these values into the formula and solve for M:

[tex]M = \$306,000[0.00441667(1+0.00441667)^360/((1+0.00441667)^360)-1][/tex]

M = $1,713.78

Therefore, the monthly payment for a 30-year mortgage in this scenario is $1,713.78.

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The volume of the figure is 93π

From the question, we have the following parameters that can be used in our computation:

The composite figure

The volume is calculated as

Volume = Cone + Cylinder

Using the above as a guide, we have the following:

Volume = 1/3πr²(H - h) + πr²h

Substitute the known values in the above equation, so, we have the following representation

Volume = 1/3π * 3² * (15 - 8) + π * 3² * 8

Evaluate

Volume = 93π

Hence, the volume is 93π

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It will take apprοximately 23.29 years fοr the accοunt tο reach $15,000, assuming the given initial investment and interest rate.

A lοgarithm is an inverse οperatiοn tο expοnentiatiοn. It is a mathematical functiοn that helps tο sοlve equatiοns where the variable is in the expοnent. The lοgarithm οf a number tο a certain base is the expοnent tο which the base must be raised tο get that number.

Accοrding tο given infοrmatiοn :

In the given expressiοn, 1,000 • e0.034t, the variable "t" represents the time in years, and "e" is a mathematical cοnstant called Euler's number (apprοximately 2.71828).

The entire expressiοn represents the amοunt οf mοney in an accοunt after "t" years, assuming an initial investment οf $1,000 and a cοntinuοus interest rate οf 3.4% per year (0.034 in decimal fοrm).

Tο find the number οf years it will take fοr the accοunt tο reach $15,000, we can set the expressiοn equal tο 15,000 and sοlve fοr "t".

1,000 • e0.034t = 15,000

Dividing bοth sides by 1,000 gives:

e0.034t = 15

Tο sοlve fοr "t", we can take the natural lοgarithm (ln) οf bοth sides:

ln(e0.034t) = ln(15)

0.034t • ln(e) = ln(15)

Since ln(e) = 1, we can simplify tο:

0.034t = ln(15)

Dividing bοth sides by 0.034 gives:

t = ln(15) / 0.034

Using a calculatοr, we get:

t ≈ 23.29

Therefοre, it will take apprοximately 23.29 years fοr the accοunt tο reach $15,000, assuming the given initial investment and interest rate.

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The missing values in the ratio tables are  

For table 1, 150, 250, and 500

For table 2, 200, 400, and 600

A ratio is a mathematical comparison of two quantities or values. It is expressed as the quotient or fraction of one value to another value.

Ratios are often written in the form of a:b or a/b, where a and b are the two quantities being compared.

To complete the following table determine the ratio of the table using the values in the table and calculate the remaining values

Here we have

The ratio table -1

Pages   50                        

Hours    1      3      5      10

Here, the ratio of page/ hours = 50/1 = 50

Let the x, y, and z be the values

According to ratio

=> x/3 = y/5 = z/10 = 50

=> x/3 = 50 => x = 150

=> y/5 = 50 => y = 250

=> z/10 = 50 => z = 500

The ratio table - 2

Feet    100

Hours   1       2     4     6  

The ratio of feet/ second = 100/1 = 100

Let a, b, and c be the values

=> a/2 = b/4 = c/6 = 100

=> a/2 = 100 => a = 200

=> b/4 = 100 => b = 400

=> c/6 = 100 => c = 600

Therefore,

The missing values in the ratio tables are  

For table 1, 150, 250, and 500

For table 2, 200, 400, and 600

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We can see that there are 9 possible outcomes for spinning the spinner two times.

By pairing each potential result for the first spin with each potential result for the second spin, we can list all the outcomes and establish the sample space for spinning the spinner twice. Since there are three possible results for each spin, spinning the spinner twice has a total of 3 x 3 = 9 outcomes.

Making a table that displays every scenario is one technique to list the sample space:

Spin 1 Spin 2

Blue  Blue

Blue Orange

Blue  Red

Red          Blue

Red   Orange

Red          Red

Orange  Blue

Orange  Orange

Orange   Red

Listing all the potential pairs of outcomes is another way to list the sample space:

Blue, Blue, Blue, Orange, Blue, Red, Red, Blue, Orange, Red, and Orange, Red; Blue, Blue, Blue, Orange, Blue, Red; and Orange, Blue, Orange, Orange, Red

In either case, we can see that spinning the spinner twice can result in 9 different results.

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Answer:

Kara has 67 in total

Tyrone has 82 in total

and together they have 149

im not to sure what your asking but heres what i got...

Answer:

32 : 1

Step-by-step explanation:

dimensions of the parts of the ratio must be in the same units

convert 9 feet to inches

1 foot = 12 inches

then

9 feet = 9 × 12 = 108 inches

then ratio

9 feet : 3 [tex]\frac{3}{8}[/tex] inches

= 108 inches : 3 [tex]\frac{3}{8}[/tex] inches ( change mixed number to improper fraction )

= 108 : [tex]\frac{27}{8}[/tex] ( multiply both parts by 8 to clear the fraction )

= 864 : 27 ( divide both parts by 27 )

= 32 : 1

Answer: .654 not rounded

Step-by-step explanation:

5.232 divided by 8 is 0.654

Answer:

4.5%

Step-to-Step Explanation:

[tex]y=8700*1.045^{x}[/tex]

[tex]y=a(1+r)^{x}[/tex]

1 + r = 1.045

r = 1 - 1.045

r = 0.045

Multiply 0.045 by 100 to ger 4.5%

r = 4.5%

The zeros ( roots ) of the function y = (x + 2)^2 - 25 are x = 3 and x = -7.

Given the function in the question;

y = ( x + 2 )² - 25

To find the zeros of the function, simply means find the values of  x in the function y = ( x + 2 )² - 25, when y equals zero.

Equat the function to 0

(x + 2)^2 - 25 = 0

Adding 25 to both sides, we get:

(x + 2)^2 - 25 + 25  = 0 + 25

(x + 2)^2  = 25

Taking the square root of both sides, we get:

x + 2 = ±√25

x + 2 = +5

Solving for x, we get:

x = -2 + 5 = 3

or x = -2 - 5 = -7

Therefore, the zeros of the function are 3 and -7.

Option 4) -7 and 3 is the correct answer.

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Answer:

x=3

x=-7

Step-by-step explanation:

Answer:

it should be DCE

Step-by-step explanation:

Since both ABE and DCE are similar because because they are both corresponding angels that are congruent.  I'm sorry i couldn't think of another triangle but I'm hoping that at least helped a  bit

Answer:

Part 1:

Range = 98 - 23 = 75

Part 2:

First, find the sample mean:

Mean = (23 + 53 + 67 + 61 + 66 + 91 + 27 + 85 + 98 + 44 + 73)/11 = 61.9

Then, find the sum of the squared differences between each jersey number and the mean:

(23-61.9)^2 + (53-61.9)^2 + (67-61.9)^2 + (61-61.9)^2 + (66-61.9)^2 + (91-61.9)^2 + (27-61.9)^2 + (85-61.9)^2 + (98-61.9)^2 + (44-61.9)^2 + (73-61.9)^2 = 12388.4

Sample variance = 12388.4/10 = 1238.84

Sample standard deviation = √1238.84 = 35.17

Part 3:

Sample variance = 1238.84

Part 4:

The results tell us that there is a relatively large range in jersey numbers, with a difference of 75 between the highest and lowest numbers. The sample variance and standard deviation also indicate that there is a considerable amount of variability in the data, with jersey numbers varying significantly from the mean. This suggests that there is no pattern or structure to the jersey numbers on the football team, and that they are assigned somewhat randomly.

Step-by-step explanation:

In response to the query, we have that The Pythagorean identity for theta = 30° is therefore confirmed since sin(30°) + cos(30°) = 1.

The fundamental Euclidean geometry relationship between the three sides of a right triangle is the Pythagorean Theorem, sometimes referred to as the Pythagorean Theorem. This rule states that the areas of squares with the other two sides added together equal the area of the square with the hypotenuse side. According to the Pythagorean Theorem, the square that spans the hypotenuse (the side that is opposite the right angle) of a right triangle equals the sum of the squares that span its sides. It may also be expressed using the standard algebraic notation, a2 + b2 = c2.

This trigonometric identity is valid for all theta values. Because it is connected to the geometry-related Pythagorean theorem, it is known as the Pythagorean identity.

According to Pythagorean theory,

[tex]Cos(theta)^2 + Sin(theta^)2 = 1[/tex]

So, you can easily include that value into the equation and simplify it if you need to assess sin(theta) + cos(theta) for a certain value of theta:

[tex]Cos(theta)2 + Sin(theta)2 = 1\\Sin(2) + Cos(30)\\If theta = 30, then 2(30) = 1.\\(1/2)\\c^2 + (√3/2)\\c^2 = 1 \s1/4 + 3/4 = 1 \s1 = 1[/tex]

The Pythagorean identity for theta = 30° is therefore confirmed since sin(30°) + cos(30°) = 1.

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Answer:

eeeeejjbbvvv g gyuuu u grrtyyu

The cardinality of (B ⋃ C) will be n(B ⋃ C)=3.

In mathematics, cardinality refers to the size or number of elements in a set. It is a concept used to compare the sizes of sets, regardless of their specific elements. For instance, the cardinality of the set {1, 2, 3} is 3, while the cardinality of the set {2, 4, 6, 8, 10} is 5. Cardinality is typically denoted using vertical bars, such that |S| represents the cardinality of set S.

Now,

The symbol "n(S)" represents the cardinality

To find the cardinality of the sets:

We have to see how many elements are there in (B ⋃ C) and

As we can see from Venn diagram there are 23 elements in (B ⋃ C) i.e.

5+3+1+2+4+8

Hence,

           The cardinality of n(B ⋃ C) will be 23.

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9. The discriminant is 33. And the roots are real and distinct.

10. The discriminant is 4. And the roots are real and distinct.

11. The discriminant is -23. And the roots are imaginary roots.

12. The discriminant is -4. And the roots are imaginary roots.

What is the discriminant?

The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,

D = b² - 4ac

9. 2x² + 3x - 3 = 0, the discriminant is given as,

D = 3² - 4 × 2 × (-3)

D = 33

Roots are real and distinct.

10. 4x² - 6x + 2 = y, the discriminant is given as,

D = (-6)² - 4 × 4 × (2)

D = 4

Roots are real and distinct.

11. 0 = x² - 3x + 8, the discriminant is given as,

D = (-3)² - 4 × 1 × (8)

D = - 23

Roots are imaginary.

12. y = 5x² + 4x + 1​, the discriminant is given as,

D = (4)² - 4 × 5 × (1)

D = -4

Roots are imaginary.

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