Question 7 of 10
The value of -16 is not-4 because
OA. 4² -16
OB. (-4)²-16
OC. 162-4
OD. (-16)2-4
SUBMIT

Answer:

no solution

Step-by-step explanation:

Since you are using substitution, you will plug in one of the variables using one of the equations.

y=x+4

x-y=8

put the y from above into the y below

x-(x+4)=8

Now, solve the equation

x-x-4=8

Put x's together

-4=8

-4 does not equal 8, so this system of equations has no solution

The graph of an absolue value function is V shaped, symmetric about y-axis or any line parallel to y-axis.

We know that an absolute value of any number describes the distance from zero of that a number is on the number line, without considering its sign (negative / positive number).

Consider an absolute value function f(x)

f(x) = |x|

This means, |x| = x              .......(if x ≥ 0)

            and |x| = -x              .......(if x < 0)

We know that the graph of the absolute value function is V shaped and symmetric about the y -axis or any line parallel to y-axis.

The graph makes a right angle at the origin.

The graph of absolute value consists of two pieces: one with a negative slope and the one with a positive slope.

Also, in the graph of absolute value function a vertex is the point at which the graph of the function changes its direction.

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The value of the variable 'a' by solving the given equation 3a²- 21 = 27 is given by :

option B. a = plus or minus 4.

As given in the question,

Given equation is equal to :

3a²- 21 = 27

Express the given equation in the given form of ax² =c which is equal to :

3a²- 21 = 27

Add 21 on both the side of the equation we get,

⇒3a² -21 + 21 = 27 + 21

⇒ 3a² = 48

Now divide both the side by 3 we get,

⇒ 3a² / 3 = 48 / 3

⇒ a² = 16

Take square root both the side we have,

⇒ a = √ 16

⇒ a = ± 4

Therefore , the solution of the given equation 3a²- 21 = 27  is  given by :

option B. a = ±4.

The above question is incomplete, the complete question is:

Solve the following equation by first writing the equation in the form

ax² =c

3a²- 21 = 27

A. a = 4

B. a = plus-or-minus 4

C. a = plus-or-minus 16

D. a = 16

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The answer of 10 more than 24 is 34.

The answer of 10 more than 24 is 34 which can be derived using simple mathematical calculations.

To find 10 more than 24, you can add 10 to the original number 24.

10+ 24 = 34

It's a simple arithmetic operation where you add a specific number, in this case 10, to the original number.

An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.

Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.

Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.

Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.

Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.

Therefore, The answer of 10 more than 24 is 34.

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Answer: The vertex of the parabola is (2, -6)

The total amount with Siobhan is given by the equation S = $ 8.33

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount with Siobhan be represented as S

Let the amount with Priya be represented as P

Let the amount with James be J = $ 7.00

And , Priya makes 40% more than James

So , P = ( 40 / 100 ) x P + P

Substituting the values in the equation , we get

The amount with P = ( 0.40 ) ( 7 ) + 7

The amount with Priya P = 2.8 + 7

The amount with Priya P = $ 9.80

Now ,

Siobhan makes 15% less than Priya

So , the amount with Siobhan S = P - ( 15/100 )P

Substituting the values in the equation , we get

The amount with Siobhan S = 9.80 - ( 0.15 )( 9.80 )

On simplifying the equation , we get

The amount with Siobhan S = 9.80 - 1.47

The amount with Siobhan S = $ 8.33

Hence , the amount with Siobhan is $ 8.33

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Answer:

The maximum height = 14 ft, and the time caught at 5 ft high = 1.5 seconds

Step-by-step explanation:

Used desmos.

Acute angles can be measured with the help of a protractor.

Find the measure of x, y, and z?

The angles 2x x+2 =180°

2x+x+2=180°

3x+2=180°

3x=180-2

3x=178

x=178/2

X=88

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The relationship between consecutive angles a and b is a° + b° = 180°

A quadrilateral is a polygon that has four sides and four angles. Types of quadrilaterals are square, rectangle, parallelogram, kite etc.

A parallelogram is a quadrilateral in which opposite sites are equal and parallel to each other. All the angles sum up to 360 degrees and the diagonals bisect each other.

The opposite angles of a parallelogram are equal to each other while the consecutive angles are supplementary. Also, the perimeter is gotten by adding all the individual sides

a° + b° = 180° (consecutive angles)

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They are both quadrilaterals and they both have equal and parallel opposite sides.

Rectangles and parallelograms both have four sides, and thus are quadrilaterals.

Quadrilaterals

The definition of a quadrilateral is a 2-D shape with 4 sides and 4 angles. Rectangles and parallelograms both fall under this category. So, they both have all the attributes listed in the definition.

This means 3 shared attributes of rectangles and parallelograms are:

Opposite Sides

Rectangles and parallelograms also have unique relationships between opposite sides. Remember that opposite sides are directly across from each other and not adjacent. In both shapes, opposite sides are parallel. This means that if the sides were to continue forever, they would never intersect. Also, opposite sides are equal. By this, I mean that the lengths of opposite sides are equal. Another way to say this is that opposite sides are congruent.

In Mike's study, the sample is the group of 50 randomly selected professors from colleges or universities in Michigan that he is obtaining salary information from.

The sample is a smaller representative group of the larger population, which in this case is all the professors who work for colleges or universities in Michigan. The population is the group of individuals or objects that the researcher is interested in studying. In this case, the population is the group of all professors in Michigan and their salaries. The goal of the study is to make inferences about the population based on the sample data.

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2 and 3 has a multiplicative inverse of -3 and 2, which is 2. A number that, when multiplied by the inputted number, produces the result 1 is said to be the multiplicative inverse of that number.

When a number is multiplied by another, the result is 1, this is known as the multiplicative inverse of the original number . It is the reciprocal of a number per multiplicative inverse definition. A-1 or is used to denote the multiplicative inverse of a number "a".

According to the multiplicative inverse property, a multiplies with its reciprocal, 1/a, to get 1, for any number a. It follows that 1/a is a number's multiplicative inverse. The multiplicative inverse of 5, when applied to the integer 5, is 1/5, according to this characteristic. Dividing 1 by a real number yields the multiplicative inverse of that number. One fifth (1/5, or 0.2) and one-quarter (0.25, or 1 divided by 0.25, respectively) are examples of reciprocals.

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The steps to factor an equation with 5 terms is explained below.

In math the definition of equation is written as a mathematical statement that shows that two mathematical expressions are equal

Basically the equation with five terms in polynomial is known as Monomial.

The steps to factorize the monomial is explained below.

Here the very first steps is to factor By Grouping With 5 Terms

Then we have to take the common terms out of it, then factor out the GCF of the entire expression.

Then split the terms and it must be in the form of quadratic expression, and then use the quadratic formula to factor out the terms.

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The equation of the line that passes through the points (36,-30) and (-12,34) is  y = - 4 / 3 x + 18.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, let's find the equation of the line  that passes through the points (36, -30) and (-12, 34).

Hence, the slope can be found as follow:

slope = y₂ - y₁ / x₂ - x₁

slope = 34 + 30 / -12 - 36

slope = 64 / -48

slope = - 8 / 6 = - 4 / 3

Therefore, let's find the y-intercept of the line using (-12, 34)

y = - 4 / 3 x + b

34 = - 4 / 3 (-12) + b

34 = 16 + b

b = 34 - 16

b = 18

Therefore, the equation is y = - 4 / 3 x + 18.

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The hypotenuse is 17 units.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

The hypotenuse of a right triangle can be found using the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (legs).

So the hypotenuse of a right triangle with legs 8 units and 15 units can be found by:

c = √(a² + b²)

Where c is the hypotenuse and a and b are the legs of the triangle.

c = √(8² + 15²) = √(64 + 225) = √289 = 17

So the hypotenuse of a right triangle with legs 8 units and 15 units is 17 units.

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The solution is k = -257.57

What is simplification?

Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.

Here, we have

Given: k/6.3 + 99.8 = 55.9

We have to find the solution to k.

By applying simplification in the given equation we get the solution to k

k/6.3 + 99.8 = 55.9

k + 99.8 × 6.3 =  55.9 × 6.3

k + 628.74 = 352.17

k = 352.17 - 628.74

k = 276.57

Hence, the solution is k = 276.57.

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Step-by-step explanation:

Using a proportion:

5.5 liters * 1,000 milliliters/liter = 5,500 milliliters

Conversion method:

1 liter = 1,000 milliliters

So, 5.5 liters = 5.5 liters * 1,000 milliliters/liter = 5,500 milliliters

Answer:

Step-by-step explanation:

What you can do in this case is the following rule of three to find the result:

1 light year ---> 5.88 * 10 ^ 12 miles

3.2 * 10 ^ 2 light year ---> x

Clearing x we have:

x = ((3.2 * 10 ^ 2) / (1)) * (5.88 * 10 ^ 12)

x = 1.88 * 10 ^ 15 miles

answer:

In scientific notation, approximately it is 1.88 * 10 ^ 15 miles

a. The fraction of the cup of juice that remained in the jug is 0

b. the total amount of juice in the 3 glasses is 1 cup of juice

c. The total amount of juice in the four glasses is 2 cups of juice

d. no juice was left in the jug after the 4 glasses have been poured

The total amount of juice is deduced from the problem to be 2 cups of juice

Total amount of juice poured out

= 1 cup was shared among three glasses + 1cup of juice in the fourth glass

= 1 cup + 1cup

= 2 cups of juice hence nothing is left in the jug

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The finance charge is. s= 80/3 m.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The price of a stove is s dollars.

Pedro makes 10% down payment for a two year installment purchase.

The monthly payment is m dollars.

Also, 2 years= 24 month

Then, the finance charge is

s x(1- 10%) / 24 = m

m= s ( 1- 0.10) / 24

24m = 0.9s

s= 24m/ 0.9

s= 80/3 m

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Answer: In a parallelogram, opposite angles are congruent, which means they have the same measure. So, if angle g has a measure of (4x - 16)°, then angle h also has a measure of (4x - 16)°. Therefore, the measure of angle h is (4x - 16)°.

So, the answer is 88°.

Step-by-step explanation:

The six trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.

sine: Sine of an angle is defined as the ratio of the side opposite(perpendicular side) to that angle to the hypotenuse.

cosine: Cosine of an angle is defined as the ratio of the side adjacent to that angle to the hypotenuse.

tangent: Tangent of an angle is defined as the ratio of the side opposite to that angle to the side adjacent to that angle.

cosecant: Cosecant is a multiplicative inverse of sine.

secant: Secant is a multiplicative inverse of cosine.

cotangent: Cotangent is the multiplicative inverse of the tangent.

Thus, The six trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

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A triangle's perimeter is determined by the sum of its three sides. The perimeter of triangle is 16

Sum of the three sides determines a triangle's perimeter.Additionally, the units used to measure the lengths of a triangle's sides and perimeter are the same.If the sides of it have lengths that are measured in various units, convert them to that unit first.

The lengths of all four side edges must be added up in order to determine the rectangle's perimeter.Since there are two of each side length, it is easy to accomplish this by simply multiplying the sum of the length and width by two.

(Length + Width)2 is the perimeter calculation formula.

The perimeter is the sum of the lengths of all sides.

Using the distance formula, determine the lengths of the sides:

d  = √ ( x2 - x1 ) ² + ( y2 - y1 )²

A = ( -3 ,0 ) , B= (0,4) C= (3,0)

AB = √ (0 - (-3)² + ( 4 - 0) ² = √ 25 =5\sAC = √ ( 3 (-3)²+ (0 -0)²  = √6² = 6

BC √ (3-0)² +(0 - 4) ² =  √ 25 =5

P = ( AB) + (AC)+ (BC) = 5+ 6+5

= 16

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Answer: the perimeter is 16

When we write a number in fraction with denominator 1, then we evaluate an expression with fractions like evaluating an expression with whole numbers.

But when we write a fraction with denominator other that 0 and 1, then we evaluate an expression with fractions is different from evaluating an expression with whole numbers.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Here, We know that;

To evaluating an expression with fractions like evaluating an expression with whole numbers is possible only when we write a number in fraction with denominator 1.

And, To evaluating an expression with fractions is different from evaluating an expression with whole numbers is possible only when we write a number in fraction with denominator other that 0 and 1.

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Adrian need to invest $2041.88,  to the nearest hundred dollars for the value of the account to reach $3900 in 14 years.

Let principal amount is x

And interest is y

Then, according to question

X + y = 3900    --------------eq(1)

and formula of interest

I = (P*t*R)/ 100

Y = (x * 14 * 6.5) / 100   ----------------------eq(2)

3900 – x = (x * 14 * 6.5) / 100  from eq(1) and eq(2)

390000 – 100x = 91x

191x = 390000

X = 2041.88

So, therefore principal amount = $2041.88

and interest = $1858.12

You can earn interest on interest by using compound interest. Compound interest is interest that is earned on both the initial principal and interest that builds up over time in a savings account.

You get interest based on the amount you deposit when you add money to a savings account or other account of a similar nature. For instance, if you deposit $1,000 in an account that offers 1% yearly interest, after a year you would have received $10 in interest.

There may be a difference in the timing of when interest is paid out and compounded. For instance, interest on a savings account may be paid monthly but compounded daily. The account balance plus any interest that has accrued but has not yet been paid out are used by the bank to determine your daily interest earnings.

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The figure has an image of right triangle and the dimensions are solved to get

The right triangle's sides are solved using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

From the question it can be deduced that

opposite = 12 ft

adjacent = b

hypotenuse = c

Using tan, TOA the adjacent is solved

tan 30 = Opposite / Adjacent

tan 30 = b / 12 ft

b = 12 / tan 30

b = AC = 20.784 ft

The hypotenuse is calculated using cos, CAH

cos 30 = Adjacent / hypotenuse

cos 30 = 20.784 / c

c = 20.784 / cos 30

c = AB = 24 ft

< A + < B + < C = 180 (angles in a triangle)

30 + < B + 90 = 180

< B = 60

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Answer:

Step-by-step explanation:

(0.7}

Answer:

[tex]y=-\frac{4}{3} + 2[/tex]

Step-by-step explanation:

[tex]y=mx+b\\(-8)=-(\frac{4}{3} )(3)+b\\-8=-4 +b\\2=b\\y=-\frac{4}{3} + 2[/tex]

They will be at same altitude is 171 minutes when their altitude will be 24300 feet.

It should be noted that an equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Based on the information, to calculate the period when the airplane will be at same altitude will be:

51300 - 3000m = 2700m

Collect the like terms

-3000m - 2700m = -51300

-5700m = -51300

Divide

m = 51300 / 5700

m = 9

The number of minutes will be 9 minutes

The altitude will be:

= 2700m

= 2700 × 9

= 24300 feet

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