Find the value of x
2x + 6
18

By using the vertex and the given point of the parabola, we conclude that the equation is:

y = -1*(x - 2)^2 + 2

For a parabola with a leading coefficient a and a vertex (h, k), the vertex form is:

y = a*(x - h)^2 + k

In this case, we can see that the vertex is (2, 2), replacing that we get:

y = a*(x - 2)^2 + 2

We also can see that the parabola passes through (0, -2) replacing that in the above equation we get:

-2 = a*(0 - 2)^2 + 2

-2 = a*4 + 2

-2 - 2= a*4

-4 = a*4

-4/4 = a

-1 = a

Then the equation for the parabola is:

y = -1*(x - 2)^2 + 2

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Answer:

B)

Step-by-step explanation:

4+5*(3^2-9)/3^2=4+5*0/9=4

The missing reasons in the proof that shows that both lines are parallel are:

1. Given

2. Alternate interior angles theorem

3. Transitive property of congruency

4. Converse of corresponding <s theorem

If two corresponding angles are congruent to each other and lie on each line that is cut across by a transversal, both lines are said to be parallel to each other based on the converse of corresponding angles theorem.

Also, if two lines are parallel, alternate interior angles are proven to be congruent to each other based on the alternate interior angles theorem.

The transitive property of congruency states that if two angles are each both congruent to a third angle, then all three angles are congruent to each other.

The reasons for each statement in the proof would therefore be as shown below:

Statements                                       Reasons                                          

1. a║b, <2 is congruent to <3    1. Given

2. <1 is congruent to <3             2. Alternate interior angles theorem

3. <1 is congruent to <2             3. Transitive property of congruency

4. c║d                                          4. Converse of corresponding <s theorem

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A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

The denominator is the value written at the bottom of a fraction.

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Numerator:

It is the value written at the top.

Denominator:

It is the value written at the bottom when we write a fraction.

Example:

Fraction:

1/2, 3/4, and 5/6.

1, 3, and 5 are the numerator.

2, 4, and 6 are the denominator.

Thus,

The denominator is the value written at the bottom of a fraction.

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The equivalent expression to 6y - 12 is given by:

3y + 3y - 12.

In this problem, we are given four expressions, which are the four options to the problem. The expression that is equivalent to 6y - 12 is the expression that after it is simplified, it has a result of 6y - 12.

To simplify the expressions, we combine the like terms, adding the constants and the terms with y.

Hence, the simplified expressions are given as follows:

The problems asks for which of these expressions is equivalent to 6y - 12.

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The percentage who decided to not sell their products as required in the task content is; 58.33%.

It follows from the task content that the percentage of schools who decided to not sell their products be determined.

Since the number of schools given is; 300 schools and only 125 were convinced by the representative, it follows that;

The number of schools that didn't sell their product is simply; the difference between the total number of schools and the number of schools that sold their products ;

Hence, the number of schools that didn't sell their products is;

300 - 125 = 175.

Hence, when expressed as a percentage of the whole, we have;

= (175/300) × 100%

= 0.5833 × 100%

= 58.33%.

The required percentage of schools who decided to not sell their products is; 58.33%.

PS: A percentage, put simply refers to an ratio expressed as a fraction of 100. Conventionally, it is denoted by the sign; %.

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Answer:

Step-by-step explanation:

QUESTION 1

The sum means addition. The one-fourth means ( 1 / 4 ).

Define

let x;

let y = ( 1 / 4 )x;

x + y = 125;

Substitute and Isolate

x + ( 1 / 4 )x = 125;

( 5 / 4 )x = 125;

Divide Both Sides

( 1 / 4 )x = 25;

Multiply Both Sides

x = 100;

y = ( 1 / 4 )( 100 );

y = 25;

100 and 25

QUESTION 2

No need to write the odd number as 2n + 1 for this question. The next odd number is always spaced out by 2 because there is an even number in between them.

( x - 2 ) + x + ( x + 2 ) = 135;

x + x + x - 2 + 2 = 135;

3x = 135;

x = 45;

x - 2 = 43;

x + 2 = 47;

The 3 odd numbers are 43, 45, and 47.

QUESTION 3

The double means multiply by 2.

2x + 12 = 32;

Subtract 12 from both sides.

2x = 20;

Divide both sides by 2.

x = 10;

Easy there we go!

In elementary arithmetic and elementary algebra, one can cross-multiply to solve an equation involving two fractions or rational expressions or to discover the value of a variable. If the formula be t = r/r-3 then r = 3t / (t -1).

In mathematics, specifically in elementary arithmetic and elementary algebra, one can cross-multiply to solve an equation involving two fractions or rational expressions or to discover the value of a variable.

In cross-multiplication, we multiply the first fraction's numerator by the second fraction's denominator, and the second fraction's numerator by the first fraction.

Only use cross multiplication to check whether one fraction is greater than another or to locate a denominator or numerator that is absent in similar fractions.

Let the formula be t = r/r-3

Cross multiply,

t(r - 3) = r

simplifying the above equation, we get

tr - 3t = r

tr = r + 3t

tr - r = 3t

r(t -1) = 3t

r = 3t / (t -1)

Therefore, the value of r = 3t / (t -1).

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Answer:

They found the slope of the same line. This is because 2/6 is equal to 1/3.

Answer:

x = 7

Step-by-step explanation:

It will be written as 80 = 12x - 4

80=12x−4

Step 1: Flip the equation.

12x−4=80

Step 2: Add 4 to both sides.

12x−4+4=80+4

12x=84

Step 3: Divide both sides by 12.

12x/12 = 84/12

x=7

Answer:

x = 7

Step-by-step explanation:

Answer: 1:2 = 2:4

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

2 ÷ 4 = 2

1 x 2 = 2

so 2 is your answer

The lowest average he could get on his subsequent two tests and still have an average of 90 overall in the six tests is 93.

An average is a middle value that indicates the mean.

The average is computed by dividing the sum of the data set by the number of values in the data set.

The number of tests = 6

The points for each test = 100

The total points for the 6 tests = 600 (6 x 100)

The average for the first four tests was 88.5.

The total score for the first four tests equaled 354 (88.5 x 4).

For Wilbur to get an overall average of 90, he needs to score a total of 540 out of 600.

The remaining scores in the two tests should be = 186 (540 - 354).

The average of the two remaining tests should be = 93 (186/2).

Thus, Wilbur needs to score 93 on average for the remaining two math tests.

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Answer:

12

Step-by-step explanation:

16x16 = 256

20x20 = 400

400-256 = 144

square root 144 = 12

The value of x or maximum height is equal to 5ft

The maximum height that can be achieved by the see-saw can first be solve if we find the angle between the height and the adjacent side.

We have to proceed with trigonometric ratio which is SOHCAHTOA

To do this, we can take the first triangle and then find the value of the angle

Using Tangent of the angle;

[tex]tan\theta = \frac{opposite}{adjacent} \\tan\theta =\frac{2.5}{4}\\\theta = 32^0[/tex]

Using this value of theta, can find the maximum height attained by the see-saw.

Using Tangent of the angle again;

[tex]tan\theta = \frac{opposite}{adjacent}\\ tan 32 = \frac{x}{4 + 4} \\tan 32 = \frac{x}{8} \\x = 4.9998 = 5ft[/tex]

The maximum height attained by the seesaw is approximately equal to 5 ft

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The dimension of the base is measured the Length, L be 3 1/2 yd and

Width, W be 1 3/4 yd. The area covered by the containers is 55.125 yd².

Given: Base dimension of container = 3 1/2yds by 1 3/4yds

Array: 3 × 3 containers without space

It'll be assumed that the container has a rectangular base.

The dimension of the base is measured out as follows:

Length, L = 3 1/2 yd

Width, W = 1 3/4 yd

To calculate the area of 1 container..

Area = 3 1/2 yd × 1 3/4 yd

Convert mixed numbers to improper fractions:

[tex]$3 \frac{1}{2}=\frac{7}{2}$[/tex]

[tex]$=\frac{7}{2} \cdot 1 \frac{3}{4}$$[/tex]

Convert b to improper fractions,

[tex]$=\frac{7}{2} \cdot \frac{7}{4}$$[/tex]

Apply the fraction rule,

[tex]$=\frac{7 \cdot 7}{2 \cdot 4}$$[/tex]

[tex]$=\frac{49}{2 \cdot 4}$$[/tex]

Multiply the numbers:

[tex]$=\frac{49}{8}$$[/tex]

Convert improper fractions to mixed numbers:

[tex]$\frac{49}{8}=6 \frac{1}{8}$[/tex]

Area = 6.125 yd²

Next, is to calculate the area of the 3 by 3 containers.

Given that the container formed a 3 by 3 array;

This means that there 3 × 3 containers

3 × 3 = 9 containers.

Area of the 9 containers = 9 × Area of 1 container.

Area = 9 × 6.125 yd²

Area = 55.125 yd²

Therefore, the area covered by the containers is 55.125 yd².

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The given statement can be translated into an algebraic expression as: s - 6.

Algebraic expression can be defined as a mathematical statement that expresses a given statement or word problem using numbers, variables, and operation signs.

To translate a given statement into algebraic expression, the unknown number is usually represented by a letter or alphabet.

In the given statement, "the difference of a number s and 6", s is the unknown number. "Difference" means subtraction. Subtraction would then be represented by the operation sign, "-".

The statement would therefore be translated into an algebraic expression as: s - 6.

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If [(80 * a) = (7200 * b) = 51840000], then solving this equation, we get the values of the variables "a" as 648000, and "b" as 7200.

As per the question statement, we are provided with an equation containing two variables, "a" and "b" which is

[(80 * a) = (7200 * b) = 51840000].

We are required to calculate the values of "a" and "b" from the above mentioned equation.

Let us consider the part [(80 * a) = 51840000] of our concerned equation, solving which, we get,

[(80 * a) = 51840000]

Or, [a = (51840000/80)]

Or, (a = 648000)

Similarly considering the part [(7200 * b) = 51840000] of our concerned equation, solving which, we get,

[(7200 * b) = 51840000]

Or, [b = (51840000/7200)]

Or, (b = 7200)

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Answer:

a= -np+2s/n

Step-by-step explanation:

The missing statements and reasons are;

Statement 4; m∠ABC = m∠BED

Reason 4: Corresponding Angles Theorem

We are given the two column proof table of the angles as;

Statement 1; BC is parallel to ED

Reason 1; Given

Statement 2; m∠ABC = 70°

Reason 2: Given

Statement 3; m∠CED = 30°

Reason 3: Given

Statement 4; m∠ABC = m∠BED

Reason 4: Corresponding Angles Theorem

Statement 5; m∠BEC + m∠CED = m∠BED

Reason 5: Angle Addition Postulate

Statement 6; m∠BEC + 30° = 70°

Reason 6: Substitution Property of Equality

Statement 7; m∠BEC = 40°

Reason 7: Subtraction Property of Equality

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Answer:

1) D) 16

2) B) 5

Step-by-step explanation:

1) 16 is a perfect square = 4*4

Factors of 16 = 2, 4, 8

2) Absolute value of a positive integer or a negative integer is always positive integer.

If the hair has length 15 cm and diameter 0.1mm then , the volume of hair in m³ is   11.78×10⁻¹⁰m³.

In the question

it is given that ,

length of hair = 15 cm = 0.15m

diameter of hair = 0.1 mm

radius of hair = 0.05 mm = 0.00005 m

we know that , the shape of hair is cylindrical form,

the volume of cylinder is given by the formula = πr²h

Substituting the values , we get

Volume = π*(0.00005)²*(0.15)

= 0.4712*(0.00005)²

= 4712*25×10⁻¹⁴

= 117800×10⁻¹⁴

= 1178×10⁻¹²

= 11.78×10⁻¹⁰

Therefore , if the hair has length 15 cm and diameter 0.1mm then , the volume of hair in m³ is 11.78×10⁻¹⁰m³.

The given question is incomplete , the complete question is

A hair has a length of 15 cm and a diameter of 0.1 mm. What is its volume in m³ ?

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Given:

an expression is given as below

Find:

we have to combine like terms.

Explanation:

we will combine like terms as follows

Therefore, the answer is

SRQ and SARAH ttttsttetits get t for the candy and I need to do a red ♥️

The null hypothesis is based on the idea that there is no relationship between the variables.

What is null hypothesis?

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable. The null hypothesis can be evaluated to determine whether or not there is a relationship between two measured phenomena, which makes it valuable. It can let the user know if the outcomes are the product of random chance or deliberate manipulation of a phenomenon.

The null hypothesis states that there is no relationship between two population parameters, i.e., an independent variable and a dependent variable. Therefore, the null hypothesis is based on the idea that there is no relationship between the variables.

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Fourth relation is not a function, fifth relation is a function with Domain {1,2,3,4} and Range {4} and sixth relation is also a function with Domain {0,2,4} and Range {6,3}.

What is relation and function?

A function is a relation that states that there should only be one output for each input. Alternatively, we could say that a function is a special sort of relation (a collection of ordered pairs) that adheres to the rule that every X-value should only be connected with one y-value.

The Cartesian product is a subset of a relation. Or just a lot of points (ordered pairs). In other words, the ordered pair collection, where the ordered pair is made up of an object from each set, is used to define the relationship between the two sets.

The most important condition for a relation to be a function is that all its input value should have one and only one out put value.

So, in fourth question we can see that both the input have two output values, that's why this relation is not a function.

In fifth all the input values have only one out put value that's why it is a function with Domain {1,2,3,4} and Range {4}

Similarly, in sixth all the input values have only one out put value that's why it is a function with Domain {0,2,4} and Range {6,3}

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Using mathematical operations, we know that Nina saves 60% of his allowance which is $30.

So, the percentage of the amount Nina saves:

She spends $5 per week which is:

She saves:

Now, the percentage of savings:

Therefore, using mathematical operations, we know that Nina saves 60% of his allowance which is $30.

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