Find the slope of the line through the points (4, 8) and (5, 10).

A. -1/2

B. 2

C. 1/2

D. -2

For the transformations of the triangle, we have that:

1. The translation of triangle ABC preserves side lengths and angles.

2. The dilation of triangle ABC preserves angles but not side lengths.

Hence the correct options are, respectively, C and B.

A translation involves shift left, shift right, shift down, or shift up, meaning that just the coordinates of the figure change, not the angles or the side lengths,

1. The translation of triangle ABC preserves side lengths and angles.

For a dilation, the coordinates of the vertices are multiplied by a constant, hence the side lengths change while the angles remain constant, thus:

2. The dilation of triangle ABC preserves angles but not side lengths.

Hence the correct options are, respectively, C and B.

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The expression that is a factor of both x² - 9 and x² + 8x + 15 is (x + 3).

Given the polynomials in the question:

x² - 9

x² + 8x + 15

To find a factor that is common to both x² - 9 and x² + 8x + 15, we can factorize the two expressions and look for any common factors.

First, factorize x² - 9:

Using the difference of sqaure formula

a² - b² = ( a + b )( a - b )

x² - 9

x² - 3² = (x - 3)(x + 3)

Next, factorize x² + 8x + 15:

Using AC method

( x + 3 )( x + 5 )

From the factorizations, we can see that both expressions have a common factor of (x + 3).

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Answer:

A.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

hope it helps you

Answer:

Step-by-step explanation:

3: ANSWER = 864

4; ANSWER = I DONT KNOW TNH YOU JUST HAVE TO MULTIPLY AMD THEN SUBRACT BOTH

Answer:

The correct answer:

(B) SAS Similarity

The values of x that satisfy the equation are x = (-4 + 2√6) / 5 and x = (-4 - 2√6) / 5

The values of x that satisfy the equation 5x² + 4x - 4 = 0 can be determined using the quadratic formula given below:

x = (-b ± √(b² - 4ac)) / (2a)

From the equation:

a = 5, b = 4, and c = -4.

Substituting these values into the quadratic formula:

x = (-(4) ± √((4)² - 4(5)(-4))) / (2(5))

Simplifying to solve for values of x

x = (-4 ± √(16 + 80)) / 10

x = (-4 ± √96) / 10

x = (-4 ± 4√6) / 10

x = (-4 ± 2√6) / 5

Hence, x = (-4 + 2√6) / 5 or x = (-4 - 2√6)

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A simplification of the given expression is 1/m¹⁶.

In Mathematics, an exponent is a mathematical operation that is commonly used in conjunction with an algebraic equation or expression, in order to raise a given quantity to the power of another.

Mathematically, an exponent can be represented or modeled by this mathematical expression;

bⁿ

Where:

By applying the division and multiplication law of exponents for powers of the same base to the given algebraic expression, we would have the following simplified expression:

[tex](m^{\frac{4}{5}} \cdot m^{\frac{4}{5}} )^{-10}\\\\(m^{\frac{4}{5} +\frac{4}{5} } } )^{-10}\\\\(m^{\frac{8}{5} } )^{-10}\\\\(m^{\frac{8 \times -10}{5} } )\\\\(m^{\frac{-80}{5} } )\\\\m^{-16}[/tex]

1/m¹⁶

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The resulting mixture contains approximately 64.5% alcohol, not 58.6% as you mentioned.

We can calculate the weighted average of the alcohol percentages based on the volumes of each component.

Let's figure out how much alcohol there is overall in the mixture:

Total alcohol is calculated as follows: (Volume of 45% alcohol) * (Property of 45% alcohol) + (Volume of 82% alcohol) * (Property of 82% alcohol) + (Volume of 92% alcohol) * (Property of 92% alcohol).

Total alcohol = (5 liters) * (45%) + (4 liters) * (82%) + (1 liter) * (92%)

Total alcohol = 2.25 liters + 3.28 liters + 0.92 liters

Total alcohol = 6.45 liters

Let's now determine the amount of alcohol included in the final mixture:

Alcohol content is calculated as (total alcohol / total mixture volume) * 100.

The mixture's total volume is  = 5 liters + 4 liters + 1 liter = 10 liters

Alcohol content: (6.45 liters / 10 liters) x 100 = 64.5%

Therefore, the resulting mixture contains approximately 64.5% alcohol, not 58.6% as you mentioned.

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Answer:

38 yards

Step-by-step explanation:

First, subtract to find out how much money was spent.

30 - 25.06

= 4.94

Then divide to find out how many groups of $0.13 are in $4.94.

4.94 ÷ .13

= 38

Ashley bought 38 yards of ribbon.

38 × .13 = 4.94

4.94 + 25.06 = 30

This answer does not consider tax at all. Because it wasn't mentioned in the question and it complicates the problem. So probably don't worry about tax. Unless your teacher /book/program said to consider it. I can edit the answer.

Also, if they said to write an equation:

Let x = yards of ribbon

30 - .13x = 25.06

subtract 30

-.13x = -4.94

divide by -.13

x = 38

The statement "x + 3 is a factor of p(x) = [tex]x^3 - 7x^2 + 15x - 9[/tex]" is false.

To determine whether x + 3 is a factor of p(x) = [tex]x^3 - 7x^2 + 15x - 9[/tex], we can use the factor theorem.

According to the factor theorem, if a polynomial p(x) has a factor (x - a), then p(a) = 0.

In this case, we have x + 3 as a possible factor. To check if it is indeed a factor, we substitute -3 for x in the polynomial p(x):

[tex]p(-3) = (-3)^3 - 7(-3)^2 + 15(-3) - 9[/tex]

= -27 - 63 - 45 - 9

= -144

Since p(-3) is not equal to zero, we conclude that x + 3 is not a factor of p(x).

Therefore, the statement "x + 3 is a factor of [tex]p(x) = x^3 - 7x^2 + 15x - 9[/tex]" is false.

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Answer:

78

Step-by-step explanation:

Let the number of hamburgers sold = x.

Then, the number of cheeseburgers sold = 2x.

Total number of sales: x + 2x = 3x

Total number of sales: 234

3x = 234

x = 78

Answer: 78

The total distance she cover after running is 9600 meters

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

Number of times = 12 times

Dimensions of the playground = 240 m by 160 m

The perimeter of the playground is calculated as

Perimeter = 2 * sum of dimensions

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

Perimeter = 2 * (240 + 160)

The total distance she cover is calculated as

total distance = 12 * 2 * (240 + 160)

Evaluate

total distance = 9600 meters

Hence, the total distance she cover is 9600 meters

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The height of domino #7 is approximately 6.89 cm tall.

The formula for the nth term of a geometric progression is:

[tex]a_n = a * r^(^n^-^1^)[/tex]

where:

a is the first term (the height of the smallest domino, 4.00 cm),

r is the common ratio (the growth rate, 1.12), and

n is the term number (for domino #7, n = 7 + 1 = 8, because the sequence starts with domino #0).

Let's plug these values into the formula:

[tex]a_8 = 4.00 cm * (1.12)^7[/tex]

(Note that we're using 7, not 8, because the first domino is #0, not #1.)

Now, compute the value:

[tex]a_8 = 4.00 cm * (1.12)^7[/tex]

=  6.89 cm

So, domino #7 is approximately 6.89 cm tall.

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The value of x in the equation 15(2x - 10) + 4x = -3(15x + 4) is 1.7

An equation is an expression that shows the relationship between numbers and variables using mathematical operators.

Given the equation:

15(2x - 10) + 4x = -3(15x + 4)

Solving the parenthesis:

30x - 150 + 4x = -45x - 12

Collect like terms:

30x + 4x + 45x = -12 + 150

79x = 138

Dividing both sides by 79:

x = 1.7

The value of x is 1.7

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The binomials represents the length of each of it sides = a + 5.

The given expression is;

a² + 10a + 25

It represents the area of square.

Since area of square = (side)²

Therefore,

(side)² = a² + 10a + 25

           =  a² + 5a + 5a + 25

           =  a(a+5) + 5(a+5)

           =   (a+5)(a+5)

           =   (a+5)²

⇒(side)² = (a+5)²

Taking square root both sides

Hence

side of square = a + 5

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The algebraic expression for the sentence "5 subtracted from 3 times p" is given as follows:

A. 5 - 3p.

The sentence in the context of this problem is defined as follows:

"5 subtracted from 3 times p"

The expression that represents 3 times p is given as follows:

3p.

(that is, 3 and p are multiplied).

Then 5 subtracted from 3 times p means that the number 5 subtracts the above expression, hence the expression is given as follows:

5 - 3p.

Meaning that option A gives the correct answer in the context of this problem.

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The resultant of the force that acts in opposite directions is 7 N.

We have,

We know that the resultant force is the force that has the same effect in magnitude and direction as two or more forces that is acting together. We have to note that the force that is actinmg on an object is a vector quantity. The implication of this is that the magnitude and the direction of the forces that are acting on the body is very important.

By the use of the law of vectors we can be able to write in the case of the question that we have here, we can see that the forces are acting in the opposite directions. The implication of this is that we would have to subtract the forces so as obtain the resultant force.

We have to note that when we have opposite forces, one is said to be positive and the other negative and the resultant force can be found by subtraction. As such the resultant force can be obtained from;

Let the +B force be 12 N

Let the -B force be 5N

12 N - 5 N = 7 N

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Answer:

57 kilograms. .........................................................................kg

Answer:

y=3.5x

Step-by-step explanation:

to find the the feet mary walks per second, divide 14 by 4

14/4=3.5 feet/second

the total distance mary walks can be represented by multiplying the number of feet she walks per second by the number of seconds she walks

y= 3.5x

in this model, x is seconds

The amount of liabilities at December 31, 2019, is $900,000.

To determine the amount of liabilities at December 31, 2019, we can use the accounting equation:

Assets = Liabilities + Stockholders' Equity

Given that the company reported assets of $1,500,000 and liabilities of $700,000 on January 1, 2019, we can set up the equation as follows:

$1,500,000 = $700,000 + Stockholders' Equity

During 2019, assets decreased by $100,000, so the new value of assets at December 31, 2019, would be $1,500,000 - $100,000 = $1,400,000.

Stockholders' equity decreased by $200,000, so the new value of stockholders' equity at December 31, 2019, would be $700,000 - $200,000 = $500,000.

Now we can substitute these values into the accounting equation to solve for liabilities:

$1,400,000 = Liabilities + $500,000

Rearranging the equation, we find:

Liabilities = $1,400,000 - $500,000

Liabilities = $900,000

Therefore, the amount of liabilities at December 31, 2019, is $900,000.

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Mrs. Horwitz needs 670 square inches of wrapping paper to wrap the present.

We have,

To figure out how much wrapping paper Mrs. Horwitz needs, she should find the surface area of the rectangular prism box.

The surface area of a rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Given dimensions:

Length (l) = 13 in

Width (w) = 8 in

Height (h) = 11 in

Plugging these values into the formula, we get:

Surface Area = 2(13)(8) + 2(13)(11) + 2(8)(11)

Surface Area = 208 + 286 + 176

Surface Area = 670 in²

Therefore,

Mrs. Horwitz needs 670 square inches of wrapping paper to wrap the present.

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The odds against a direct hit is 3 to 1.

Given that the probability of a hurricane hitting at a coast is 1/4 = 0.25.

Therefore, the probability of not hitting = 1-0.25

= 0.75

we know that,

Odds against direct hit = [P(no direct hit)]/P[(direct hit)] = 0.75/0.25 = 3/1

= 3:1

Hence the odds against a direct hit is 3 to 1.

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The classroom coin box required less than 11.11 Square feet of cardboard (100 square feet divided by 9), then 100 square feet would be sufficient

The 100 square feet of cardboard is enough to build the new coin box with a scale factor of 3 times the classroom coin box, we need to consider the relationship between the areas of the two boxes.

The area of the original classroom coin box is unknown, as it is not given in the problem. However, since we know that the new coin box has a scale factor of 3 times the original, we can infer that its area will be 3^2 = 9 times greater than the original.

Let's assume that the area of the classroom coin box is A square feet. In that case, the area of the new coin box would be 9A square feet.

Now, we are given that 100 square feet of cardboard is available. To determine if it's sufficient, we need to compare this value to the area of the new coin box, which is 9A.

If 100 square feet is greater than or equal to 9A, then it would be enough to build the new coin box. Conversely, if 100 square feet is less than 9A, it would not be enough.

Since we do not have a specific value for A, we cannot determine the exact answer. However, we can provide the argument to defend our solution.the classroom coin box required less than 11.11 square feet of cardboard (100 square feet divided by 9), then 100 square feet would be sufficient.

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Note the question be like :

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If two marbles are drawn from the bag without replacement, what is the probability that both marbles are red?

Answer:

(a) 5 ft^2

Step-by-step explanation:

The formula for area of a triangle is given by the formula,

A = 1/2bh, where

Thus, we can plug in 5 for b and 2 for h in the formula to find the area of the triangle in square feet:

A = 1/2(5)(2)

A = (5/2)(2)

A = 10/2

A = 5

Thus, the area of a triangle whose base is 5 ft and whose height is 2 ft is 5 ft^2

Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 4 ← is in slope- intercept form

with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex] , then

y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute (- 1, 5 ) into the partial equation

5 = - [tex]\frac{1}{3}[/tex] + c ( add [tex]\frac{1}{3}[/tex] to both sides )

5 [tex]\frac{1}{3}[/tex] = c ⇒ c = [tex]\frac{16}{3}[/tex]

y = [tex]\frac{1}{3}[/tex] x + [tex]\frac{16}{3}[/tex] ( multiply through by 3 to clear the fractions )

3y = x + 16

The required reference angle of 13π/8 is 3π/8.

The reference angle of an angle in standard position is the positive acute angle formed between the terminal side of the angle and the x-axis.

Given an angle of 13π/8, we can determine its reference angle as follows:

Angle: 13π/8

Since the angle is in the fourth quadrant, we subtract it from 2π (one full revolution) to find the reference angle:

Reference angle: 2π - 13π/8 = 3π/8

Therefore, the reference angle of 13π/8 is 3π/8.

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According to the angles between intersecting secant and tangent, the value of

angle DF is 52 degrees

angle PQR = 49 degrees

The value of angle DF is solved using the angles of intersecting secant out side the circle

The theorem give the formula in the form

44 = 1/2 (140 - DF)

88 = 140 - DF

DF = 140 - 88

DF = 52 degrees

Using intersection of tangents, for the second figure

exterior angle = 1/2 (major arc - minor arc)

major arc = 360 - 131 = 229

PQR = 1/2 (229 - 131)

PQR = 49 degrees

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Answer:

x = 24.5

Step-by-step explanation:

27/(x + 7) = (27 - 6)/x

27x = (x + 7)(21)

27x = 21x + 147

6x = 147

x = 24.5

Answer:

x = 31.5

Step-by-step explanation:

given a line parallel to a side of a triangle and it intersects the other two sides then it divides those sides proportionally , that is

[tex]\frac{6}{27-6}[/tex] = [tex]\frac{7}{x}[/tex]

[tex]\frac{6}{21}[/tex] = [tex]\frac{7}{x}[/tex] ( cross- multiply )

6x = 21 × 7 = 147 ( divide both sides by 6 )

x = 24.5

The value of x is 9.

Given,

Trapezoid with two bases and median.

base 1 = 44

base 2 = 2x + 10

median = 36

Now,

In trapezoid two bases will be parallel to each other.

Median = 1/2(sum of two bases)

From the formula of median the value of x will be,

Median = 1/2( base 1 + base 2 )

Substitute the values,

36 = 1/2( 44 + 2x + 10 )

72 = 54 + 2x

x = 9

Hence both the bases of trapezoid are obtained.

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The number of possible outcomes that Event E has is 33.

The 36 possible conclusions when rolling two dice is given in the image.

Now, we need to find the event where the sum of two rolled dice is greater than 3

Then, from the outcomes given above we can write those pair whose sum is greater than 3 as

1 + 3=4

1 + 4= 5

1+ 5 = 6

1 + 6 = 7

2+ 2 = 4

2 + 3 = 5

2 + 4 =6

2 + 5 = 7

2 + 6 = 8

3 +3=6

3 + 4 = 7

3 + 5 =8

3 + 6 =9

4 + 3 =7

4 + 4=8

4 + 5 = 9

5+ 5 = 10

5 + 6= 11

6 + 6 = 12

So, there are 33 outcomes whose sum is greater than 3.

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