Molly and Liza are exercising. Molly does
10 push-ups at the same time
as Liza
does 15 push-ups. When Molly does
40 push-ups, how many push-ups does
Liza do?

Answer:

2b - 1

Step-by-step explanation:

To solve this problem, we will need to open the parentheses. To do this, we will put an imaginary 1 in front of both sets of parentheses to open them using the distributive property, this gives us:

1(6b + 2) - 1(4b + 3)

We will open the first set of parentheses with no problem, but in the second set, we have -1, so we need to make every positive number negative and every negative number positive, giving us:

6b + 2 - 4b - 3

Then, we group our like terms:

6b - 4b + 2 - 3

Then, we subtract, giving us:

2b - 1

So the most simplified version is 2b - 1.

Hope this helped!

Answer:

Step-by-step explanation:

You begin by distributing the negative so -4b -3

then you will multiply (6b+2) by (-4b -3)

24b^2 - 18b - 8b - 6

answer = 24b^2 - 26b - 6

An expression that represents the total cost of an order of n number of tickets: 35n + 15

Let n be the number of tickets to a concert.

Let C be the cost for the tickets

Given that the tickets to a concert are $35 each.

So, by unitary method the cost of n number of tickets would be,

n × 35

And the cost for the tickets would be,

C = 35n

In addition to the cost for the tickets ordered, there is a $15 processing charge per order.

So, the cost for the tickets would be,

C = 35n + 15

This is the required expression.

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The complete question is:

Tickets to a concert are $35 each. In addition to the cost for the tickets ordered, there is a $15 processing charge per order.

Write an expression that represents the total cost of an order of n number of tickets.​

The equation of the line perpendicular to x - 4y = 7 can be written as:

y = 4*x + b

Where b could be any real number.

Two lines are perpendicular if the product between the slopes of the lines is equal to -1.

Where a general line in the slope-intercept form is written as:

y  =a*x +b

And the given line is:

x - 4y = 7

Writing this in the slope-intercept form we will get:

-4y = -x - 7

y = (-1/4)*x + 7/4

So the slope is -1/4, then the slope of our line must be such that:

a*(-1/4) = -1

a = -4*-1 = 4

a =4

So the line perpendicular to the given one is:

y = 4*x + b

Where b can be any real number.

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Answer:

Step-by-step explanation:

ASA requires that both triangles have two angles and the included side to be congruent.

We have one side and an adjacent angle and need the second angle adjacent to the marked side to be congruent as well

It is the ∠BAC of ΔABC and ∠DPF of ΔPDF or simply ∠A and ∠P.

The total cost for Ben to buy 1 binder and P pencils is 2.25 + 0.75 P.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Cost of a binder = 2.25

Cost of a pencil = 0.75

We have to find the total cost for Ben to buy 1 binder and P pencils.

Cost of 1 binder = 2.25

Cost of P pencils = 0.75 × P = 0.75 P

Total cost of 1 binder and P pencils = 2.25 + 0.75 P

Hence the total cost for Ben to buy 1 binder and P pencils is 2.25 + 0.75 P.

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The smallest amount that Byron could have converted is £73.44.

An exchange rate is the rate at which one currency can be exchanged for another currency. It is the value of one country's currency against another country's currency. Exchange rates fluctuate based on supply and demand for a particular currency, as well as economic and political factors.

Exchange rates are typically quoted as the value of one currency in terms of another currency. For example, an exchange rate of 1.2 US dollars (USD) to 1 Euro (EUR) means that 1 EUR can be exchanged for 1.2 USD.

There are two types of exchange rates, Floating and Fixed exchange rate.

According to question :-

To determine the smallest amount that Byron could have converted, we can use the exchange rate from shop A, which is €47.20 for £40.

If we divide the amount of euros he received (€68.44) by the exchange rate (€47.20 for £40), we get:

€68.44 ÷ €47.20/£40 = £73.44

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f(7) = 14 is calculated. Each function is given a domain and a codomain, or scope.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

We note that x=7 is on 1<x< 9 so we use the second piece. Replace x with 7 and

evaluate to find f(7):

f(7)=2(7)

f(7)=14

so f( 7 ) = 14

f(7) = 14 is calculated. Each function is given a domain and a codomain, or scope.

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Answer:

T=(I/p)/r

Step-by-step explanation:

I = Prt is the same thing as: I = P*r*t

We want the answer to be as:

T = ???

The only thing you need to do is the get T to one side.

1. [tex]I = P*r*t[/tex]

2. [tex]I/p=r*t[/tex]

3. [tex](I/p)/r=t[/tex]

4. [tex]t=(I/p)/r[/tex]

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[tex]\quad \qquad \huge \bf \dag \: Answer \: \dag[/tex]

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[tex] \underline{ \large \rm Solution} : [/tex]

[tex]\rm Given : [/tex]

Two equations are -

[tex] \rm Procedure : [/tex]

Considering the equations as (i) and (ii) respectively

From equation (i) -

put this value of y in equation (ii) -

Next thing to do would be to put value of x we got in equation (i) to get y

Values asked are :

[tex] \rightarrow \rm y = - 4[/tex]

[tex] \rightarrow \rm x= - 2[/tex]

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[tex] \large \bf hope \: \: it \: \: helps \: - dabI [/tex]

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Answer:

See picture below

Step-by-step explanation:

The point at a graph where the graph cuts the x-axis is known as the x-intercept. Therefore, the x-intercept is a point.

A graph is made up of four quadrants in which two are positive and two are negative quadrant.

There are two types of axis which are x-axis and y-axis two negative and two positive.

The y-intercept is the point where the graph cuts the y-axis .Graph Theory is the study of graphs which comes under discrete mathematics.

It is defined as a mathematical structure that connects a group of points to express a specific function.

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Yes, the lengths of the two sides of an isosceles triangle are equal.

An isosceles triangle is a type of triangle that has two sides that are equal in length. The other side of the triangle can be either longer or shorter than the two equal sides. The two equal sides are called the legs, and the other side is called the base. The angles opposite the two equal sides are also equal in measure. Because of this, the two equal sides create an angle bisector that divides the base into two equal parts. This angle bisector forms two angles of equal measure as well. Thus, the two equal sides of an isosceles triangle are a defining feature of the shape.

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x+5 is the way we can write 5 more than a number.

In a formula or equation involving mathematical operations, the representation of numbers by alphabet is referred to as algebra.

Using the knowledge provided above, we must translate the mathematical statement provided in the question into an algebraic expression. Let's say that number is "x". The result of adding 5 to the provided number is a number that is 5 greater than this number. Thus, a number that is 5 more than x is equal to x+5. As a result, "5 more than a number" is represented by the algebraic expression "x+5".

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Answer:

It's neither:

x =√ 9.000 = 3.00000 or :

x =√ 9.000 = -3.00000 or :

x =√ 8.000 = 2.82843 or :

x =√ 8.000 = -2.82843

Four solutions

Answer:

x^4 - 17x^2 + 72 = (x^2 - 9)(x^2 - 8)

Step-by-step explanation:

First, we need to find two numbers that multiply to give us 72 and whose sum is -17. We can see that 8 and 9 multiply to give us 72, and their sum is 8 + 9 = 17. Since we want the sum to be negative, we need to change one of the signs. So we write -(8 + 9) = -17.

Next, we write the expression as the product of two binomials. We factor out the common factor x^2 from the first two terms: x^4 - 17x^2 + 72 = x^2(x^2 - 17) + 72

Now, we complete the square in the first binomial. To do this, we need to add and subtract (17/2)^2 = (8.5)^2 = 72.25 inside the bracket:

x^2(x^2 - 17) + 72 = x^2(x^2 - 17 + 72.25 - 72.25) + 72 = x^2(x^2 - 17 + 72.25) - 72.25 + 72

Now we can rewrite the square of a binomial :

x^2(x^2 - 17 + 72.25) = x^2((x-8.5)^2)

Finally, we can combine the two binomials

x^2((x-8.5)^2) + 72 = (x^2(x-8.5)^2) + 8(9)

So the expression x^4 - 17x^2 + 72 factors completely as (x^2 - 9)(x^2 - 8)

Hope this helps!

Answer:

According to arithmetic progression, natural numbers can be written down as 1, 2, 3, 4, 5, 6, 7, and 8 to 100. Basically, the sum of the first 100 natural numbers is equal to 5050.

Step-by-step explanation:

to find the equation of any line we have to first find the slope. the slope formula is:

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

our slope here would be 8/13

now we input the points in the equation

y = mx + b

then we find b to be -3(7/13)

so the final equation would be:

[tex]y = \frac{8x}{13} - 3( \frac{7}{13} )[/tex]

If Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1) then the scale factor used is 1/3

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller.

Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1).

A(−3, −3)---->A(−3/3, −3/3)---->A′(−1, −1)

B(3, 3)---->B(3/3, 3/3)---->B′(1, 1)

C(0, 1)---->C(0/3, 1/3)---->B′(0, 1/3)

Hence, the scale factor used is 1/3.

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Check the picture below.

Answer:

There are 5 choices for the first digit, 5 choices for the second digit, 4 choices for the third digit, 3 choices for the fourth digit, and 2 choices for the fifth digit.

The point(s) on the surface at which the tangent plane is horizontal are (0, 0, 1).

To find the point(s) on the surface at which the tangent plane is horizontal, we need to find the points at which the partial derivatives of z with respect to x and y are both equal to 0. This means we need to solve the system of equations:

Solving this system of equations yields x = 0, y = 0, and z = 1. Therefore, the point(s) on the surface at which the tangent plane is horizontal is (0, 0, 1).

To understand why solving the system of equations yields the points for which the tangent plane is horizontal, it is important to understand what the partial derivatives represent. The partial derivative of z with respect to x is the rate of change of z with respect to x, and similarly for y.

When the partial derivatives are both equal to 0, it means that the rate of change of z with respect to x and y is 0, which implies that the tangent plane is horizontal.

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The values of x and y, given the angles in the diagram, can be found to be :

The angles given above are called vertical angles and they are such that the two corresponding angles are equal to each other.

This means that ( 8 x + 7 ) ° is equal to ( 9 x - 4 )° and 5 y° is equal to  ( 7y - 34 )°.

The value of x is :

8 x + 7 = 9 x - 4

9x - 8x = 7 + 4

x = 11

The value of y is :

5 y = 7y - 34

7y - 5y = 34

2 y = 34

y = 34 / 2

y = 17

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Answer:

Below

Step-by-step explanation:

3% = .03 in decimal      4 (yearly) periods

The effective interest and deposit amount after  3 years compounded yearly will be

3300 (1 +.03)^4   =  £ 3714.18  

The color of the 15th figure is green.

The shape of the 40th figure star.

The shape of the 22nd figure triangle.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

We have,

The pattern of shapes we get is:

circle - Triangle - Square - Star

The pattern of color we get is:

Purple - Red - Green

Now,

The color of the 15th figure.

= 15 is a multiple of 3

= 5 x 3

So,

Green will be the color of the 15th figure

Now,

The shape of the 40th figure.

= 40 is a multiple of 4

= 10 x 4

So,

Star will be the shape of the 40th figure.

Now,

The shape of the 22nd figure.

= 22 ÷ 4

We get 2 as the remainder.

So,

Triangle will be the shape of the 22nd figure.

Thus,

The 15th figure color is green.

The 40th figure is a star.

The 22nd figure is a triangle.

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The simplified form of the given radical expression is rational.

Exponent can be defined as the method of expressing large numbers in terms of powers. Exponent refers to how many times a number multiplied by itself. For example, 6 is multiplied by itself 4 times, i.e. 6 × 6 × 6 × 6.

We are asked to determine whether the simplified form of  2√3.√12

To solve our given problem we will use exponent property for radicals

           √m.√n = a√m.n

          2√3.√12=2√3.12

            2√3.√12=2√36

             2√3.√12=2×6

              2√√3.√12=12

The simplified form of the given radical expression is rational.

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Since our given radical expression simplifies to a rational, therefore, our answer is yes

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Answer:

D. 8

Step-by-step explanation:

8*3=24

8*5=40

8*4=32

Fencing that Luke and Seth did each buy is 72 feet

Using the information given, you can set up and solve the system of equations. Let x be the length of Seth's garden.

Seth's garden is square, so it has four times the perimeter.

The perimeter of Luke's garden is a rectangle of length x + 3 feet and width x/2 feet, so 2(x + 3) + 2(x/2).

We also know that Luke and Seth should buy the same amount of fences. So:

4x = 2(x + 3) + 2(x/2)

Solving this equation for x gives x = 6 feet.

So Seth's yardage is 6 feet and Luke's yardage is 9 feet.

So the fence required for Seth's garden is 46 = 24 feet

and the fence required for Luke's garden is 2(9) + 2(9/2) = 29 + 2*4.5 = 36 + 9 = 45 It's feet.

So the total fencing required is 24 + 45 = 72 feet.

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The angles of triangle ABC are 60 degrees when altitude BH and bisector AL intersect at point M.

What is equilateral triangle?

An equilateral triangle in geometry is a triangle with equal-length sides on all three sides.

Given that:

[tex]\angle HML = 100 \\\\\angle MLC = 110[/tex]

Since, BH is the altitude [tex]\angle MHC= 90[/tex].

The total angle of a quadrilateral is 360, hence:

100 + 110 + 90 + C = 360

C = 60 degrees.

Now consider triangle BHC:

The sum of angle of a triangle is 180, hence:

90 + 60 + B = 180

B = 30

Since the half angle B = 30, the entire [tex]\angle ABC = 60[/tex].

Consider triangle ABC:

Using sum of triangles, we have:

[tex]\angle A + \angle B + \angle C = 180\\\\\angle A + 60 + 60 = 180 \\\\\angle A = 60[/tex]

Hence the measure of angles of triangle ABC is 60 degrees.

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The equation of the line in fully simplified intersect is y = mx + b

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Using multiplication as a mathematical operator, Kareem will 864 more cards and Nicole will get 24 more cards

Multiplication is a mathematical operation that involves multiplying two or more numbers together. It is one of the four basic operations in mathematics, along with addition, subtraction, and division.

In this problem, we may require the use of some mathematical operators to find the solution to the problem.

1.

He currently has 216 cards, but he needs 15 sets of cards.

1 set of card = 72 cards

Let's calculate the number of sets he currently has.

1 set of card = 72 cards

x set = 216 cards

cross multiply both sides and solve for x.

x * 72 = 216 * 1

x = 216 / 72

x = 3 sets

He currently has 3 sets of cards.

Since he wants 15 sets of cards, we will need 12 more set of cards.

The number of cards can be calculated by multiplying 12 by 72

Number of cards = 12 * 72 = 864

He needs 864 more cards.

2.

1 set of card = $27

1 set = 72 cards

But she's bringing $9 to join, we can calculate the ratio of cards she will get.

1 / 27 = x / 9

x = 9 / 27

x = 1/3

She will get 1/3 of the cards bought which will be

72 * 1/3 = 24 cards

She will get 24 cards

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