Given: Line A // line B, ∠2≅∠4 Prove: ∠1≅∠3 line 2 and 3 have the same reason

The total amount of money that farmer will make to sell the tomatoes for $2 per tomato will be $14720.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

Multiplication = to multiply any two or more numbers or variables called multiplication.

The number of red tomato = 128 × 32

The number of yellow tomato = 102 × 32

The total cost will be,

2(128 × 32) + 2(102 × 32)

⇒ 2(4096) + 2(3264)

⇒8192 + 6528

⇒$14720

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In a triangle ABC the value of side a is 13.12 cm.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know in a ΔABC, a/sinA = b/sinB = c/sinC.

GIven, In a ΔABC A = 29°, B = 36°, b = 15.8 cm.

∴ a/sinA = b/sinB.

a/sin(29°) = 15.8/sin(36°).

a/0.49 = 15.8/0.59.

a = (15.8×0.49)/0.59

a = 7.742/0.59.

a = 13.12.

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The decimal that Juanita can use to update her report is 1.6.

A decimal is a number with a whole and a fractional part. Decimal numbers are between integers and represent numerical value for whole plus some fraction of a whole.

The decimal numeral system is the most widely used system for representing both integer and non-integer numbers. It is the Hindu-Arabic numeral system's extension to non-integer numbers. Decimal notation refers to the method of representing numbers in the decimal system.

In this case, the the pitcher threw a total of 384 pitches and used a fastball 240 times. The decimal will be:

= Number of throws / Fastball

= 384 / 240

= 1.6

The decimal is 1.6.

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Answer:

Step-by-step explanation:

It A (x,y) (0.4x,0.4y)

Answer:

3n³ + 2n + 3

Step-by-step explanation:

(3+6n³ + 3n) - (3n+3n³-2n¹)

3 + 6n³ + 3n - 3n - 3n³ + 2n

3n³ + 2n + 3

The asymptote tells us the number of mice will approach zero as cats increased y-intercept shows the number of mice with zero cats and the asymptote is y = 0 thus option (A),(B), and (E) is correct.

The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.

For example plot of y = x³ ,y = sinx.

The given graph of the number of mice in the number of weeks the cat adopted.

The asymptote of the graph is y = 0.

The asymptote tells that the number of the mouse will become zero when the number of cats becomes infinite.

Hence "The asymptote tells us the number of mice will approach zero as cats increased y-intercept shows the number of mice with zero cats and the asymptote is y = 0".

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Answer:

Step-by-step explanation:

3060

Answer:

0

Step-by-step explanation:

153 isn't between 1-100 making the probability 0

The expression that represents a 20% discount off the price of an item that originally cost d dollars include:

0.8d

d - 0.2d

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this case, the cost of the item is d. Since there's a 20% discount, the new cost will be:

= d - (20% × d)

= d - 0.2d

= 0.8d

The cost is 0.8d.

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Answer:C. (1,-3)

E. (2,5)

Step-by-step explanation:

So, for this question, there are two answers possible that you could put in.

-25 < 4y + 3 < 19 in inequality form: -7<y<4

-25 < 4y + 3 < 19 in interval notation form: (-7,4)

The graph that goes alongside it should be attached to this answer as well.

Hope this helps! :)

The transformation f(x)—>f(1/3x) due to the graph of f(x), will be dilation horizontally and vertically.

What is Transformation of Function?

Transformation of functions refers to the graph's curve moving to the left, right, up, or down, expanding, contracting, or reflecting. Just dilation, out of these three transformations, alters the size of the original shape; the other two only adjust the position.

A translation happens when each point on a graph (which represents a function) travels in the same direction and by the same amount. There are two kinds of function translations.

Stretching or compressing is a dilation. The x-values on a graph are all scaled up by the same amount when a dilation that is parallel to the x-axis occurs. The y-values are all increased by the same scale factor if it is dilated parallel to the y-axis.

f(x) to become f(1/3x), Then it will go dilation "vertically and horizontally".

Referring to the graph mentioned below we can conclude the same.

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The value of f(10) = 107 and f(-3) = 16.

The function is defined as in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). An example of this would be y=x2. You only get one output for y if you enter anything for x. Considering that x is the input value.

Given that f(x)=x² + 7

We do determine the values of F (10) and F(-3)

Now f(10)

= (10)2 +7

= 100 +7

= 107

Now f(-3)

= (-3)2 +7

= 9 +7

= 16

Therefore the value of f(10) = 107 and f(-3) = 16

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The ratio table's missing values are 6: 3, 24:12, and 18:9.A ratio shows how many of one number there are of another. Two numbers are expressed as x: y, which is equivalent to x/y, to represent their ratio.

A ratio shows how many of one number there are of another. Two numbers are expressed as x: y, which is equivalent to x/y, to represent their ratio.

where each of the two variables, x and y, is a separate quantity.

Additionally, the combined total is given as x + y.

Therefore, Peoples = 6, 18 and Benches = 3, 12

Now,

These ratios are equivalent: 6: 3, x: 12, and 18: y.

Ascertain the values of x and y.

Given that all ratios are equal.

so we obtain;

⇒ 6 : 3 = x : 12

⇒ 6 / 3 = x / 12

⇒ 6 × 12 / 3 = x

⇒ x = 24

And, ⇒ 6 : 3 = 18 : y

⇒ 6 × y = 18 × 3\s⇒ y = 18 × 3 / 6\s⇒ y = 9

Therefore, the ratio table's missing values are 6: 3, 24:12, and 18:9.

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The fraction 3/5 fits into 2 1/5 more than once. The quotient is more than one.

We are given two fractions. The first fraction is 3/5, which is a simple fraction. The second fraction is 2 1/5, which is a mixed fraction. We will first convert the mixed fraction into a simple fraction.

F = 2 1/5

F = (2*5 + 1)/5

F = 11/5

We need to find out if the quotient is more or less than one. So we will divide the second fraction by the first fraction. Let the quotient be represented by the variable "Q".

Q = (11/5)÷(3/5)

Q = (11/5)×(5/3)

Q = 11/3

Q = 3.667

We can see that the quotient is more than one. Hence, the fraction 3/5 fits into 2 1/5 more than once.

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Answer:

the fraction 3/5 fits into 2 1/5 more than 1 time. That means the quotient is greater than.

Step-by-step explanation:

Answer:

y= 12

Step-by-step explanation:

Just change the y-value (b in y=mx+b)

Bobby spent $20 out of $75 of his monthly allowance on paintbrushes.

What is monthly allowance?

Giving someone money on a regular basis to help them pay for the things they need is known as giving them an allowance.

Main Body:

total monthly allowance = $75

Now Bobby spent 40% on his art supplies,

which means we need to calculate 40% of 75.

⇒(40/100)*75

⇒30

so Bobby spent $30 on art supplies.

now according to question,

Bobby spent 2/3 on paintbrushes

⇒2/3 of art supplies

⇒(2/3 )*30

⇒$20

Hence Bobby spent $20 on his paintbrushes.

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Answer:

ok ask your teacher

Step-by-step explanation:

Using the properties of similar triangle and parallel lines we calculate the length of GF as √65 units.

It is given that GH is parallel to DE or GH || DE in the trapezium GHDE .

Therefore in the triangles ΔFDH and ΔFDE , we can say that

ΔFDH is similar to ΔFDE by angle angle angle axiom of similarity.

Now using the properties of similar triangles we can say that :

FG / DF = GH / DE

Now let us consider the length of GF be x.

Therefore DE = x

Now using the properties of similar triangles and substituting the values we get:

x / 13 = 5 / x

or, x² = 65

or, x = √65

Therefore the length of DE and GF is equal to √65.

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0.1367 percent of randomly chosen cookies will weigh less than 14 grams.

Given data;

Is it possible to calculate the likelihood that a randomly selected cookie weighs less than 14g using the information provided above?

Let,

X = Average cookie weight in a pack of 30

E (X) = μ = 15

Var (X) = σ²/n

           = 1²/30 =  0.0333

⇒ Standard Deviation (X) = √0.0333 = 0.1826

P(X ≤ 14.8) = (X-15 / 0.1826 < 14.815/0.1826)

= P(14.815 - 0.1826)

= P(Z-1.1)

= 0.1367

Hence, the probability that a randomly selected cookie has a weight less than 14g is 0.1367

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The coefficient would be 3.6

Since more than 4 vans will be required in total, at least 4 vans should be reserved.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another. In mathematics, inequalities specify the relationship between two non-equal values. Equal does not imply inequality. The "not equal symbol ()" is typically used to indicate that two values are not equal. The expression 5x 4 > 2x + 3 resembles an equation, but the equals sign has been replaced by an arrowhead. It is an illustration of inequality. This shows that the left part, 5x 4, is bigger than the right part, 2x + 3.

Here,

Since the total number of people is at least 28, then the total number of people must be 28 or more, so

7v≥28

v≥4

The total number of vans needed will be more than 4 that is at least 4 vans should be booked.

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Answer: P and Q could both be equal to -1

The features for each of the exponential functions are listed as follows:

1.

2.

3. The key features are listed as follows:

The features to the graphs of the exponential functions are listed as follows:

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The expression for the perimeter of the square with and without brackets is 4(t + 5) and 4t + 20, respectively.

We are given a shape. The shape is a square. The side length of the square is equal to (t + 5). We have to find the expression for the perimeter of the square. A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. Let the perimeter of the square be denoted by the variable "P".

The expression for the perimeter of the square in brackets is given below:

P = 4(t + 5)

The expression for the perimeter of the square without brackets is given below:

P = 4t + 20

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By applying the exterior angle property, the measure of the exterior angle to ∠G in triangle EFG is 120.7°

In Mathematics, the exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle.

To determine the value of ∠G in triangle EFG (ΔEFG), we would have to apply exterior angle property.

Then, the exterior angle property can be used to model triangle EFG (ΔEFG)  is given by:

∠G = m∠E +m∠F

Now Substituting the given parameters into the formula, we have

∠G = 84.3° + 36.4°.

∠G = 120.7°.

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Answer:

He is using the commutative property of multiplication.

Error = (10-9)°C & Error percentage = 10%.

Given that temperature today in Chicago is 50°F

Standard conversion formula

°C = [tex]\frac{5}{9} *(T^{0}F-32)[/tex]   - 1

Given T = 50°F

Put the value in equation 1

[tex]^{0}C = \frac{5}{9} *(50-32) \\\\= \frac{5}{9}*18\\ \\= \frac{90}{9}[/tex]

= 10°C

Tommasa's grandmothers rule is to subtract 32 from the value in °F and multiply the result by 0.5

i.e. [tex]^{0}C = 0.5(T^{0} F-32)[/tex]   - 2

Given temperature is T = 50°F

Put the value of T in equation 2

[tex]^{0}C = 0.5*(50-32)[/tex]

= 0.5 * 18

= 1/2 * 18

= 9°C

Temperature obtained by standard conversion Formula is 10°C and the temperature obtained by Tammaso's grandmother rule is 9°C.

So error = (10-9)°C

= 1°C

Error percentage = [tex]\frac{1}{10}*100[/tex]

= 10%

Hence the answer is Error = (10-9)°C & Error percentage = 10%.

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The smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.

What is the intermediate value theorem?

Intermediate value theorem is theorem about all possible y-value in between two known y-value.

x-intercepts

-x^2 + x + 2 = 0

x^2 - x - 2 = 0

(x + 1)(x - 2) = 0

x = -1, x = 2

y intercepts

f(0) = -x^2 + x + 2

f(0) = -0^2 + 0 + 2

f(0) = 2

(Graph attached)

From the graph we know the smallest positive integer value that the intermediate value theorem guarantees a zero exists between 0 and a is 3

For proof, the zero exists when x = 2 and f(3) = -4 < 0 and f(0) = 2 > 0.

Your question is not complete, but most probably your full questions was

Given the polynomial f(x)=− x 2 +x+2 , what is the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a ?

Thus, the smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.

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