Use the distributive property to simplify the following expression: 3(−5+2x)

The approximate annual cost of raising a child born in 2013 at age 17 is 15230.

Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.

a) Plot (2, 12,940), (5, 12,970), (8, 12,800), (11, 13,600) 1nd (14, 14420) on graph.

b) (8, 12800) and (14, 14420)

Here, slope m=(14420-12800)/(14-8)

= 1,620/6

= 270

Substitute m=270 and (x, y)=(8, 12800) in y=mx+c, we get

12800=270(8)+c

12800=2160+c

c=10640

Substitute m=270 and c=10640 in y=mx+c, we get

y=270x+10640

c) Now, substitute x=17 in y=270x+10640, we get

y=270×17+10640

y=15230

Therefore, the approximate annual cost of raising a child born in 2013 at age 17 is 15230.

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Answer:

0.67 or 67%

Step-by-step explanation:

The probability that a single part will pass inspection is 0.93, so the probability that all 5 parts will pass inspection is (0.93)^5 = 0.67 or 67%.

The solution is 0.67 or 67%,  is the probability that the next 5 part examined will all pass inspection.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

given that,

Understand Only 93% of the airplane parts being examined pass inspection.

now, we have to find that the probability that the next 5 part examined will all pass inspection.

now, we have,

The probability that a single part will pass inspection is 0.93,

so the probability that all 5 parts will pass inspection is :

(0.93)^5

= 0.67

= 67%.

Hence, The solution is 0.67 or 67%,  is the probability that the next 5 part examined will all pass inspection.

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The pair of triangles are congruent. using the angle side angle (ASA) congruency theorem

Two triangles are said to be congruent if all the three sides are equal to each other and all the three angles are equal to each other.

The angle side angle (ASA) congruency theorem states that two triangles are congruent if two angles and an included side of one triangle is equal to two angles and an included side of another triangle.

From the diagram, for both triangles, two angles and an included side is equal to that of the other triangle.

The pair of triangles are congruent.

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The equation used to determine the regular price is :

5(p - 1.50) = 48.75

Regular price of a hat and glove set = $11.25

The correct option is (B).

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side.

Given,

No. of hat and glove sets Mrs. James bought = 5

Discount with each coupon = $1.50

Total cost after using coupons = $48.75

Regular price of Hat and glove set = p

Cost of hat and glove set = p - $1.50

Cost of 5 sets of hat and glove = 5(p - 1.50)

By the question,

5(p - 1.50) = 48.75

p - 1.50 = 9.75

p = 9.75 + 1.50

p = 11.25

Regular price of a hat and glove set = $11.25

Hence, $11.25 is regular price of a hat and glove set,

5(p - 1.50) = 48.75

is the equation used to determine the regular price.

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Answer:

-4d - 6

Step-by-step explanation:

-1/3(12d+18)

-4d - 6

That is the simplest we can simple the function

So, the answer is -4d - 6

The required graph has been attached below which represents the inequality x ≥ 11 on a number line.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The inequality is given in the question, as follows:

x ≥ 11

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout.

A number line is typically shown horizontally and can be extended indefinitely in any direction.

Thus, the graph has been attached below which represents the inequality on a number line.

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The subtraction of the expression (5x + 1/3) - (3x - 1/6) is given by 2x + 1/2

Subtraction refers to one of the mathematical operations which involves finding the difference between expressions or values.

(5x + 1/3) - (3x - 1/6)

Open parenthesis

= 5x + 1/3 - 3x + 1/6

Collect like terms

= 5x - 3x + 1/3 + 1/6

= 2x + (2+1) / 6

= 2x + 3/6

= 2x + 1/2

In conclusion, 2x + 1/2 is the result of the given expression (5x + 1/3) - (3x - 1/6)

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Answer:

2x + (1/2)

Step-by-step explanation:

Given expression,

→ (5x + (1/3)) - (3x - (1/6))

Let's simplify the expression,

→ (5x + (1/3)) - (3x - (1/6))

→ 5x + (1/3) - 3x + (1/6)

→ (5x - 3x) + ((1/3) + (1/6))

→ (2x) + ((2 + 1)/6)

→ 2x + (3/6)

→ 2x + (1/2)

Hence, answer is 2x + (1/2).

So on solving the provided question we can say  that coefficient of expression 5xyz2 is 5  and 3zy is 3

It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression) A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)It is possible to compare expressions and phrases.

Mathematicians can multiply, divide, add, or subtract. An expression is structured as follows: Number/variable, mathematical operator, and expression Numbers, variables, and functions make constitute a mathematical expression (such as addition, subtraction, multiplication or division etc.) It is possible to contrast phrases and expressions.

here,

coefficient of 5xyz2 is 5

and 3zy is 3

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To find the mirror image of a point with respect to a line in 3D, you can use the projection of the point on the line, multiply it with the normal vector of the line, and then subtract the obtained vector from the position vector of the point twice.

To find the mirror image of a point with respect to a line in 3D, you can use the following method:

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Answer: A polynomial is a mathematical expression that is composed of a sum of powers in one or more variables (indeterminates) with non-negative integer exponents, and coefficients that are real numbers.

Out of the options given, option "b" is not a polynomial.

Option "a" √3x^2-2√3x+3 is a polynomial, it consists of terms with non-negative integer exponents (x^2, x^1) and the coefficients are real numbers (√3, -2√3, 3)

Option "c" x+1/x is not a polynomial , it's called a rational function, it consists of one polynomial divided by another polynomial, it's not a polynomial because of the fraction 1/x

Option "d" 5x^2-3x+ √2 is a polynomial, it consists of terms with non-negative integer exponents (x^2, x^1) and the coefficients are real numbers (5, -3, √2)

So, option "b" 3x^3/2-5x^2-1/√2x-1 is not a polynomial, because of the fraction and the non-integer exponent (3/2)

Step-by-step explanation:

The coordinates of the image of point Y following these modifications are thus -2.

After these adjustments, the image of point Y has coordinates that are -2.

The coordinates of the image of point Y following these modifications are thus -2.

The complete question is,
The figure below is translated up 2 units and then rotated 180° counterclockwise. What are the coordinates of the image of point Y after these transformations?

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Answer:

Step-by-step explanation:

1.7108 is the answer

The base of a exponential function is not allowed to equal 1 because it would create a graph that would violate the properties of the exponential functions.

An exponential function cannot produce an increasing graph when base is taken as 1. This would lead to violation of its properties. However, an exponential function can have any positive number as its base, however some bases are more advantageous than others. The base 2 is useful, for instance, in computer science applications. The number represented by the letter e, however, is the most significant base. A function of the form is an exponential function, when:

f(x) = b^x

where x is any real value and b is a positive constant. B is frequently referred to as the base. Typically, the particular case b=1 is not considered because it would only produce the constant function f(x) = 1.

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Therefore , the solution of the given problem of equation comes out to be a.60 , b.20 and c.21.

An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.

Here,

9(x - y) = 30,

or (x-y) =30/9

To find :  

a) 18(x - y) = ?

=> 2(9(x - y))

=> 2(30)

=> 60

b)6x - 6y = ?

=> 6(x-y) = 6(30/9)

=> 2*30/3

=> 20

c) 9(x-y)-9

=> 30 -9

=>21

Therefore , the solution of the given problem of  equation comes out to be a.60 , b.20 and c.21.

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On solving the provided question, we can say that the inequality provided is  -s < 6  he values that stratifies will be = 0-6

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

the inequality provided is

-s < 6

the values that stratifies will be = 0-6

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Along with the second order backward differentiation formula (BDF2) for dissipative PDEs, the method (1.3), an implicit second-order.

The maximum number of rotations that a geometry may accommodate is the order of rotational symmetry. The degree of rotational symmetry is denoted as 360°A°, where A° is the lowest angle that may be used to rotate a figure from its rotated shape back to its original shape. (170 degrees) How many times a perfect circle may be rotated while still preserving its appearance is a measure of a shape's rotational symmetry. The appearance of a full 360° revolution will be the same only when a triangle is placed back in its initial starting position.

given

Along with the second order backward differentiation formula (BDF2) for dissipative PDEs, the method (1.3), an implicit second-order.

A-stable time-stepping approach, is the recommended method for solving evolutive conservative systems of PDEs.

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Answer:

X=3+1/8

Step-by-step explanation:

X * 40/6 = 125/6

(Multiply each side by 6 to get rid of the denominator)
X *40=125
Divide each side by 40
X = 125/40
X= 25/8
X=3+1/8

a) The amount of money that Tony invested is; £1350

b) The rate of compound interest is; 4%

c) The graph that represents the growth in Toni's account is; Graph C

The formula for the total value of her investment  after t years is given by the formula; v = 1350 * 1.04^t

The general formula used to calculate the interest rate is given by,

a = p * (1 + r)^t

where;

a is amount

p is principal

r is rate of interest

t is time period

Comparing the given equation with standard equation, we have;

a = v  

p = 1350

t = t    

Now, 1 + r = 1.04

1 + r = 1 + 0.04

Thus;

r = 0.04  = 4%

Therefore, the money invested by tony P = £1350

The rate of compound interest is 4%

The graph that represents Toni's account is an exponential equation and since the initial amount is not zero, then the correct graph is graph C

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Answer:

A) 2^4 x 2^7 = 2^(4 + 7) = 2^11

Exponent Law(s): Product Law

B) (-3)^9 divided (-3)^5 = (-3)^(9 - 5) = (-3)^4

Exponent Law(s): Quotient Law

C) (5^2)^-3 x 5^0 = 5^(-6) × 1 = 5^(-6)

Exponent Law(s): Power of a power rule; zero exponent rule

Answer:

3w(3w²+5)(3w²-5)

There is not sufficient data provided to answer the question. So it cannot be answered.

To find the length of the part of the ramp that is on the ground, we need to know the angle of the ramp and the height of the ramp. If the height of the ramp is 6 inches, and we know the angle of the ramp, we can use the Pythagorean theorem to find the length of the ramp.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the ramp in this case) is equal to the sum of the squares of the other two sides. If we call the length of the ramp "x", and the height of the ramp "h", we can write the equation as:

x^2 = h^2 + (6 inches)^2

We don't have the angle of the ramp, so we can't use the Pythagorean theorem. Therefore, we can't find the length of the part of the ramp that is on the ground with the information given. To find the length, we would need additional information, such as the angle of the ramp or the length of the ramp.

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The length of each square Kumar cuts is 10cm and 13cm, and altogether he cuts 130 squares.

Given that,

Length of paper = 65 cm

Breadth of paper = 50 cm

The length of each square,

The greatest common factor of 65 and 50 is 5.

So,

50/5 = 10

65/5 = 13

Therefore the length of each square is 10cm and 13cm.

To find the number of squares cut altogether ,

10 x 13 = 130 squares.

Therefore altogether Kumar cuts 130 squares.

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The is 1 four-digit integers that is a perfect squares and perfect cube and it is 4096

A perfect cube is the cube of a whole number, found by multiplying a whole number by itself three times. For example, the number 8 is a perfect cube because 2 × 2 × 2 = 8 .

A perfect square is a number that can be expressed as the product of an integer by itself or as the second exponent of an integer. For example, 25 is a perfect square because it is the product of integer 5 by itself, 5 × 5 = 25.

The only four-digit integers that is a perfect square and a perfect cube is 4096

i.e 64² = 4096

16³ = 4096

Therefore the number of four-digit number that is a perfect square and a perfect cube is 1

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The graph of the Equation and Inequalities is attached below.

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.

Usually, data that varies over time is represented with a line graph.

Given:

1. 2y – 4x < 8

The region is shaded by red region.

and, the inequality intersect y axis at 4 and x axis at -2.

2.  -4y > -x + 12

The region is shaded by red region.

and, the inequality intersect y axis at -3 and x axis at 12.

3. | x + 3 |= y

The vertex of the equation is (-3, 0)

4. |2x – 6| + 2 = y

The vertex of the equation is (3, 2)

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If the angle ∠S and ∠Y are complementary angles. Then the measure of the angle ∠Y will be 40°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.

Suppose you know that ∠S and ∠Y are complementary and that ∠S = 5(∠Y) − 150°.

Then the other equation is given as,

∠S + ∠Y = 90°

5(∠Y) − 150° + ∠Y = 90°

6 (∠Y) = 240°

∠Y = 40°

If the angle ∠S and ∠Y are complementary angles. Then the measure of the angle ∠Y will be 40°.

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Answer:

1a) x+11=x+11 becomes 0=0. What this means is that at all x values the y values are the same, in other words, they are the same line.

Please split up your questions as it is difficult to answer.

The rule for the transformation, which is a dilation, is given as follows:

(x,y) -> (3x/4, 3y/4).

Hence the coordinates of B' are given as follows:

B'(3, -12).

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The general rule is:

(x,y) -> (kx, ky).

In which k is the scale factor.

The scale factor for this problem is given as follows:

k = 3/4.

Hence the rule is:

(x,y) -> (3x/4, 3y/4).

The coordinates of B' are obtained multiplying each of the coordinates of B by the scale factor k = 3/4.

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The solution to the quadratic equations are

a) The number of seconds for the ball to reach the ground is t = 5 seconds

b) The number of seconds to reach the maximum height T = 2 seconds

c) The maximum height of the ball is h ( 2 ) = 144 feet

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as h ( t )

Now , the equation will be

h ( t ) = -16t² + 64t + 80   be equation (1)

a)

The number of seconds for the baseball to reach the ground be t

The height when the ball reaches the ground will be h = 0

Substituting the value of h ( t ) = 0 , we get

0 = -16t² + 64t + 80

On simplifying the equation , we get

16t² - 64t - 80 = 0

Divide by 16 on both sides of the equation , we get

t² - 4t - 5 = 0

On factorizing the equation , we get

t² + t -5t - 5 = 0

t ( t + 1 ) - 5 ( t + 1 ) = 0

( t - 5 ) ( t + 1 ) = 0

The value of t is time and it is not negative

So , when ( t - 5 ) = 0

Adding 5 on both sides of the equation , we get

t = 5 seconds

b)

The number of seconds the baseball to reach the maximum height be T

And graph of the function is a parabola open down because the leading coefficient is negative. Therefore, to get the maximum height we just have to find the vertex of this parabola

T = ( -b / 2a )

On simplifying the equation , we get

T = ( -64 / ( 2 ( 16 )

T = -64 / 32

T = 2 seconds

c)

The maximum height of the baseball is when T = 2

Substituting the value of t = 2 in the equation , we get

h ( t ) = -16t² + 64t + 80

h ( 2 ) = -16 ( 2 )² + 64 ( 2 ) + 80

On simplifying the equation , we get

h ( 2 ) = -64 + 128 + 80

h ( 2 ) = 64 + 80

h ( 2 ) = 144 feet

Hence , the equation is solved

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Answer: 9.8 feet!

Step-by-step explanation:

The time it would take the space craft to reach earth from Mars would be: 1440 hours

the distance from Mars to Earth = 57.6 million km

= 57, 600,000 km

The time it takes the space craft to travel per km = 40000

We would use the formula t = d / v

where t is the unknown time we want to find

d is the distance =  57, 600,000 km

v is the velocity or speed = 40000

Hence we have

t = 57,600,000 / 40000

= 1,440 hours

It would take the space craft 1440 hours to reach mars from earth

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Answer: Proportional and nonproportional linear relationships can be used to solve problems by creating equations and using them to find unknown values. A proportional linear relationship is a relationship in which the ratio of the dependent variable to the independent variable is constant. For example, y = kx is a proportional linear relationship, where k is the constant of proportionality. Nonproportional linear relationships, on the other hand, have a variable ratio between the dependent and independent variables. For example, y = mx + b is a nonproportional linear relationship, where m is the slope and b is the y-intercept.

To solve a system of equations is to find the values that make all the equations in the system true simultaneously. This can be done by using methods such as substitution, elimination, or graphing.

A system of equations is a set of two or more equations with the same variables, and solving such a system is finding the values of the variables that satisfy all the equations in the system.

For example, if we have a system of two equations,

y = 2x+1

y = -x+5

we can solve it by finding the values of x and y that make both equations true at the same time.

In summary, proportional and nonproportional linear relationships can be used to solve problems by creating equations and using them to find unknown values. Solving a system of equations is finding the values of the variables that satisfy all the equations in the system.

Step-by-step explanation: