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The factored expression of the expression given as (a + b)^2 = 4 is (a + b + 2)(a + b - 2) = 0

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

(a + b)^2 = 4

Express 4 as 2^2

So, we have

(a + b)^2 = 2^2

Rewrite as

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

Apply the difference of two squares

So, we have

(a + b + 2)(a + b - 2) = 0

Hence, the equivalent expression of the expression given as (a + b)^2 = 4 when it is factored is (a + b + 2)(a + b - 2) = 0

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Answer:

Step-by-step explanation:

C

Check the picture below.

The distance between the two men is 7.2 ft. That is, they are 7.2 ft apart

From the question, we are to determine the distance between the two men

Let the distance between the men be x

From the given information,

The man of the diving board is 6 ft tall

and

The angle of elevation from the man in the water to the man on the diving board is 40°

Considering the triangle formed, we can write that

Opposite = 6 ft

Adjacent = x

Angle = 40°

From SOH CAH TOA, we have that

tan (angle) = opposite / adjacent

∴ tan 40° = 6 / x

x = 6 / tan 40°

x ≈ 7.2 ft

Thus,

The men are 7.2 ft apart

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Answer:

Cost per egg = 8.4/12 = 0.7

Cost per hundred egg =Rs70

Let selecting price per hundred be Rs.y

⇒ 70/y-70 ×100 = 15

⇒ 10y−700 = 105

The mass of ingredient is given by 66g, 45g, 100g, 150g.

What is mass?

Mass is a parameter of measurement that calculates how much matter is contained in a body.

Mass is a physical quantity. Mass is measured in terms of the weight of a body. Gram, kilogram, and pounds are some standard mass units to measure it. The SI unit of mass is the kilogram; however, smaller objects are measured in grams.

Given, the ratio of the ingredients by mass as 2:2:1.

Let x be the mass of the ingredients.

A) total mass is given by 330g

therefore, 2x+2x+1x = 330

5x = 330

x = 330/5

x = 66

Hence the mass of oat = 2(66) = 132g

mass of cereal = 2(66) = 132 g

mass of nuts = 66g

B) 2x+2x+1x = 210

5x = 210

x = 210/5

x = 42g

Hence,  the mass of oat = 2(42) = 84g

mass of cereal = 2(42) = 84 g

mass of nuts = 84

C) 2x+2x+1 = 500

5x = 500

x = 100

hence,  the mass of oat = 2(100) = 200g

mass of cereal = 2(100) = 200 g

mass of nuts = 100g

D) 2x+2x+1 = 750g

5x = 750

x = 750/5

x = 150

Hence, the mass of oat = 2(150) = 300g

mass of cereal = 2(150) = 300 g

mass of nuts = 150g

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By taking some products between fractions and mixed numbers, we will see that your trip along the bank has a length of (2 and 9/24) miles.

Here we know that the total distance of the travel is (14 + 1/4) miles.

In this case, we know that 1/3 of that distance is traveled in the woods, so the total distance traveled in the woods is given by the product:

D = (1/3)* (14 + 1/4) mi = (14/3 + 1/12) mi

Now we know that 1/2 of the distance traveled in the woods is traveled along the bank of a strem, then the distance that we are looking for is given by the product:

D' = (1/2)*(14/3 + 1/12) mi = (7/3 + 1/24)mi

Now we can simplify that mixed number as:

(7/3 + 1/24)mi = (6/3 + 1/3 + 1/24) mi = (2 + 8/24 + 1/24)mi = (2 + 9/24) mi

Your trip along the bank of the stream has a length of (2 + 9/24) miles.

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The expression after applying the distributive property is: (-3.6)(-2) + (-3.6)(-7).

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

The distributive property states that when the sum of two (2) or more addends are multiplied by a specific number, the same output would be produced as when each addend is multiplied respectively by the number, and the products are added together.

Mathematically, the distributive property of multiplication is given by this expression:

x(y + z) = xy + xz.

By applying the distributive property of multiplication to the given expression, we have the following expression:

-3.6(-2 + (-7)) = (-3.6)(-2) + (-3.6)(-7).

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Missing side length of the given measures of the triangle is equal to           x = 1/2 units (approximately).

As given,

Given measures of the triangle ABC are

Angle A=(18 +18)°

             =36°

Consider side opposite to ∠A=a ,∠B=b ,∠C=c

Given side length

AC=b

     =20

AB=c

    =12

BC=c

    =x+12

Using cosine law

cos A= (b²+c²-a²)/2bc

⇒cos36°= [20²+12²-(x+12)²]/2(20)(12)

⇒(1+√5)/4=(544-x²-24x-144)/480

⇒x²+24x-280+120√5=0

⇒x²+24x-11.7=0

Now, x = [-24±√24²-4(1)(-11.7)]/2(1)

           = (-24±24.955)/2

           ≈ (-24 ±25)/2

Hence, x = (-24+25) /2

               = 1/2

or x = -24.5 side length cannot be negative.

Therefore, Missing side length of the given measures of the triangle is equal to x = 1/2 units (approximately).

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Answer:

[tex]7 * x^2[/tex]

That indicates that in order to make a solution that is 60% acid, you will need to add a total of 300 milliliters of pure acid into the mixture.

This is further explained below.

In general, pure acid refers to an acid concentration of 100%. It is feasible to formulate the following equation if you assume that X represents the volume addition of the pure acid:

[tex]Va=100 \%X + 600 * 40 \%[/tex]

[tex]Va= (600+X)60 \% (M_1V_1=M_1 V_2)[/tex]

100X + 24000 = 36000 + 60x

X = 300.

In conclusion, That implies in order to generate a solution that is 60% acid, you will need to add 300 milliliters of pure acid.

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By means of vector sum and Pythagorean theorem, the line segment BC has a length of 5 units.

We find a line segment whose endpoints are known and set on Cartesian plane, the length of the line segment must be found by means of vector sum and Pythagorean theorem. First, determine the vector associated to the line segment:

[tex]\overrightarrow {BC}[/tex] = C(x, y) - B(x, y) = (0, 2) - (- 3, - 2) = (3, 4)

Second, determine the magnitude of the vector derived in the previous step:

BC = √(3² + 4²)

BC = 5

The length of the line segment BC is equal to 5 units.

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Answer: You would pay $7.97 for the bagels.

Step-by-step explanation:

(Price per Dozen * Amount) - Coupon = Price of Bagels

(5.98 * 1.5) - 1 = Price of Bagels

8.97 - 1 = Price of Bagels

Price of Bagels = $7.97

Answer:

4:8:12

Step-by-step explanation:

To find the ratio of 24 in 1:2:3,

first add the ratios = 6 then divide each ratio as a fraction of the total

Therefore, 24 in ratio 1:2:3 is 4:8:12

The required absolute value linear inequality is 15 ≤ t ≤ 20.

What is absolute value linear inequality?

A variable enclosed by the absolute value sign of an inequality is known as an absolute value inequality.

Given highest temperature as 20°C and lowest temperature as 15°C

Given variable is t.

From the first condition we get t ≤ 20  ...........(1)

From  the second condition we get 15 ≤ t  .....(2)

From the inequalities (1) and (2), we get

15 ≤ t ≤ 20

Therefore, the required absolute value linear inequality is 15 ≤ t ≤ 20.

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Answer:

(5,7)

Step-by-step explanation:

Answer:

(5,7)

Step-by-step explanation:

Abscissa of D will be the abscissa of A. A(5,9)

Abscissa of D = 5

Ordinate of D will the ordinate of C. C(8,7).

Ordinate of D = 7

So, D(5,7)

In this Triangle, ΔUVW, UW is extended through point w to point x

∠ WUV = (3x - 4)°

∠ VWX = (6x + 6)°

∠ UVW = (x + 20)°,  

the value of x is 5

According to the question, given that

∠ WUV = (3x - 4)°

∠ VWX = (6x + 6)°

∠ UVW = (x + 20)°

because ∠ VWX = ∠ WUV + ∠ UVW

             ⇒  (6x + 6) = (3x - 4) + (x + 20)

             ⇒  (6x + 6) = 4x + 16

             ⇒ 2x = 10

             ⇒ x = 5

{The sum of triangle's interior angles is 100°}

{The sum of supplementary angles is 180°}

Therefore, In ΔUVW, UW is extended through point w to point x, then the value of x is 5.

The interior angles of a triangle always add up to 180° while the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it. By deducting the angle of the target vertex from 180°, one can also determine a triangle's exterior angle.

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The length of the segment indicated to the nearest tenth are as follows:

The length of the segment can be found as follows:

Therefore, the segment indicated in question 5 is the radius of the circle.

The radius of a circle is the distance from the centre of the circle to any point on it's circumference.

The radius is half of diameter.

The radius from the second to one end of the circumference is given as 7. Therefore, the radius from the centre to another end of the circumference will be as follows:

The second circle, the line from the centre bisect the chord into equal halves. Since the other half is 8, that means the second half will be as follows:

Therefore, the length of the segment indicated are 7 and 8 respectively.

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Owing 175 dollars is more than owing 150 dollars.

Thereby, the correct answer is A) -175 dollars

Answer: 0.93

There are 9 tenths

Step-by-step explanation:

The first graph from the right as shown in the reference image attached hereby alongside the question statement, represents a function.

As per the question statement, we are provided with 4 distinct graphs attached hereby alongside.

We are required to determine, which of the above-mentioned graphs represent a function.

To solve this question, we need to know about the characteristics of a function, which we can match against our provided graphs and identify our required function.

A function is an operator, and hence, there will be a fixed pattern or sequence among it's outputs, which we can only find in the first graph from the right as shown in the reference image, since it is a straight line parallel to the Y-axis at (x = 1).

Therefore, the first graph from the right as shown in the reference image attached hereby alongside the question statement, represents a function.

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Answer:

2/3

Step-by-step explanation:

The amount of honey each jar holds is 2/3 cups.

Fraction

The fraction is termed as a portion or section of any quantity. It is denoted by using ‘/’ symbol, such as a/b. For example, in 5/8 is a fraction where the upper part denotes the numerator and the lower part is the denominator.

Given that:-

Number of equal sized jars filled by Isabelle = 24 jars

Total amount of honey brought by Isabelle to the sell at the farmer's market = 16 cups

We have to find the amount of honey each jar holds.

From the data given in the question, we can write,

24 jars = 16 cups

Hence, using the equation, we can write the fraction,

1 jar = (16/24) cups

1 jar = 2/3 cups

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Answer: A

Step-by-step explanation:

A. True by the definition of a bisector.

B. False, this is an assumption based on appearances.

C. False, this is an assumption based on B.

D. False, this is an assumption that LN and JK are perpendicular.

E. False, assumption based on appeareances

F. False, assumption based on D.

The  statements that would prove the lines are parallel are;

∠GHI ≅ ∠KJH

∠MJH + ∠NHJ = 180°

∠KJH + ∠IHJ = 180°

In congruency of angles formed in this type of scenario, we will make use of the following rules;

Using the above congruency rules and applying them to our question, we can say that for lines HN and KM to be parallel to each other, then;

∠GHI ≅ ∠KJH because they are corresponding angles

∠MJH + ∠NHJ = 180° because they are supplementary angles

∠KJH + ∠IHJ = 180° because they are supplementary angles

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Check the picture below.

[tex]\stackrel{\measuredangle U}{(3x-4)}~~ + ~~\stackrel{\measuredangle V}{(x+20)}~~ + ~~\stackrel{\measuredangle W}{(6x+6)}~~ = ~~180 \\\\\\ 10x+22=180\implies 10x=158\implies x=\cfrac{158}{10}\implies {\Large \begin{array}{llll} x=\cfrac{79}{5} \end{array}}[/tex]

Answer:

Step-by-step explanation:

Area = L times w ( length times width.)

Your lengthyot Length is 4 units and width is 4. so what is 4 times 4?

your right, its 16. Answer A is correct.

Answer:

B

Step-by-step explanation:

To find the number of extra flowers ordered, we can start by forming an equation based on the total amount paid by the customer.

Let the number of extra flowers be n.

Total paid

= cost of standard arrangement +(number of extra flowers)(cost per additional flower)

= $25 +n($1.25)

Given that the customer paid $45,

25 +1.25n= 45

Now that we have formed the equation, let's solve for n.

Subtract both sides by 25:

1.25n= 45 -25

1.25n= 20

Divide both sides by 1.25:

n= 20 ÷1.25

n= 16

The domain and range of the function f(x) = 4x - 6 in order from least to greatest include the following:

A range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range refers to the set of all possible output numerical values, which are shown on the y-axis of a graph.

A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.

In order from least to greatest, the range and domain of the given function f(x) = 4x - 6 are as follows:

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Answer: This is the graph