Why is the discriminant a useful tool to use when solving quadratic equations?

We calculated length of model bird in the picture = 2 ¹⁵₁₆ inch and scale factor =1/2

It is expressed as the ratio of the dimension of a model object and dimension of an actual object.

A scale factor is a number which is multiplied by an object in order to form a proportional enlarged or reduced object.

Given, the length of an actual bird = 5⁷₈ inch = 47/8 inch

also given, 1 inch = 0.5 inch

   1 inch = 1/2 inch

we need to determine the length of model bird by multiplying the above factor.

now, length of model bird = 47/8 × 0.5 inch = 47/16 inch = 2¹⁵₁₆ inch

scale factor = length of model bird/ length of actual bird = 47/16 /47/8

scale factor = 1/2

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8.96848786347

i think this should be right i did it with my 5th grade math skills and dont wory i have an a+

Answer:

yes

Step-by-step explanation:

51 to nearest ten is 50

37 to nearest ten is 40

50 * 40 = 2000

and it's an estimate so yes

The coordinates of Point D are (2.5, 8).

What is parallelogram?

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of equal size.

Given:

Parallelogram ABCD has vertices at A (-3, 6.5), B (-1, -1.5), and C (4.5, 0).

We have to find the coordinates of Point D.

Let its fourth vertex be D(a, b).

Join AC and BD. Let AC and BD intersect at point O.

We know that the diagonals of a parallelogram bisect each other.

So, O is the midpoint of AC as well as that of BD.

Using the midpoint formula,

Midpoint = [tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

Here, ([tex](x_1, y_1) = (-3, 6.5), (x_2, y_2) = (4.5, 0)[/tex]

⇒  Midpoint of AC = [tex](\frac{-3 + 4.5}{2}, \frac{6.5 +0}{2}) = (\frac{1.5}{2}, \frac{6.5}{2}) = (0.75, 3.25)[/tex]

Now,

Midpoint of BD is = [tex](\frac{-1+a)}{2}, \frac{-1.5+b}{2})[/tex]

⇒

[tex]\frac{-1+a}{2} = 0.75, \frac{-1.5+b}{2} = 3.25 \\ -1 + a = 1.5, -1.5 + b = 6.50\\a = 2.5, b = 8[/tex]

Hence, the coordinates of Point D are (2.5, 8).

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An example of limit in polynomial will be the polynomial function f(x) = x³ + 2x² - 5. As x approaches 2, the value of the function approaches 11. So, the limit of f(x) as x approaches 2 is 11.

A polynomial simply means an expression which is composed of variables, constants and exponents, which are combined using mathematical operations such as addition, subtraction, multiplication and division

In mathematical notation, we can write it as: Here, lim x->2 (x³ + 2x² - 5)

= x³ + 2x² - 5

= 2³ + 2(2²) - 5

= 8 + 8 - 5

= 11

This means that as x gets arbitrarily close to 2, the values of the function gets arbitrarily close to 11.

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Answer: To translate the given sentence into an equation, we can start by replacing the words "five times the sum" with the mathematical expression "5(x + 9)". Then, we can replace the word "number" with the variable y, to get:

5(y + 9) = 3

Next, we can distribute the 5 to obtain:

5y + 45 = 3

Finally, we can subtract 45 from both sides to solve for y:

5y = -42

y = -42/5

y = -8.4

Therefore, the equation that represents the given sentence is y = -8.4.

Step-by-step explanation:

Linear function Is a function that can be graphed as a solid line discrete or continuous

Linear functions are simply known as functions whose graph is a straight line.

They have one dependent variable and one independent variable.

These functions have either one or two variables without exponents.

Continuous graphs are used to represent functions that are continuous along their entire or whole domain.

Whereas, discrete graphs are used to represent values at specific points along the number line from different directions.

Types of the linear function;

Hence, it is a linear function

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Answer:

----------------------------------------

Two copies of one tenth translates as:

Answer:

Two copies of 1/10 = 1/5

Step-by-step explanation:

Given statement,

→ two copies of one tenth.

Forming the expression,

→ 2 × (1/10)

Let's simplify the expression,

→ 2 × (1/10)

→ (2 × 1)/10

→ 2/10

→ 1/5

Hence, the answer is 1/5.

Answer:

Let y be the expression for the minutes you do both activities.then

y=m+30 is the required expression

The equation to represent the cost of shoes is 0.08s=10 and the cost of shoes is $125.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, your brother gave you $10 to help with a shoe purchase. This covered 8% of the cost.

Let s represent the cost of the shoes.

Now, equation is

8% of s=10

8/100 ×s=10

0.08s=10

s=10/0.08

s=$125

Therefore, the equation to represent the cost of shoes is 0.08s=10 and the cost of shoes is $125.

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Plug in values of x to find corresponding values of y.

For example, replace x with 0 to find that...

y = -5x-3

y = -5*0 - 3

y = 0 - 3

y = -3

We have x = 0 lead to y = -3.

Therefore, the point (0, -3) is on this line. This is the y intercept.

Now try something like x = 1

y = -5x-3

y = -5*1 - 3

y = -5 - 3

y = -8

It shows the point (1,-8) is also on the line.

The straight line goes through (0,-3) and (1,-8)

We can repeat this process infinitely many times since there are infinitely many numbers to pick for x.

See the graph below. I used GeoGebra to make it, but you can use something like Desmos or similar.

By using the definition of vertical angles, we will see that the correct option is B, the measure of the other angle is 95°.

We define by vertical angles as angles that share a vertex and are in opposite sides of the two intersecting lines that form that vertex.

Vertical angles always have the same measure, in this particular case, we know that one of the vertical angles has a measure of 95 degrees, then the other vertical angle (whose measure we want to find) will also be 95 degrees, just by definition of vertical angles.

In that way, we conclude that the correct option is B: 95°

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The graphs as per the transformations are given below.

What are transformation of graphs?

There are four transformations that happens in a graph -

When a figure is translated, it is moved in any direction.

Flipping a figure over a line is called reflection.

Rotation is the process of turning a figure a specific amount around a point.

When we dilate a figure, we increase or decrease its size.

The triangle CHV have points C(-4,5), H(-3,3) and V(-3,5). When it is reflected across x=-3. The image gets mirrored in the negative y-axis with the points C(-4,-2), H(-3,0) and V(-3,-2).

The parallelogram CJWY have points C(-3,-1), J(-2,-1), W(-2,-4), Y(-1,-4). It needs to be translated by (x,y)->(x+2,y+0)

C=(-3+2,-1+0)=(-1,-1)

J=(-2+2,-1+0)=(0,-1)

W=(-2+2,-4+0)=(0,-4)

Y=(-1+2,-4+0)=(1,-4)

The parallelogram TSCH have points T(-1,3), S(1,4), C(1,-1), H(3,0). It needs to be translated by (x,y)->(x+0,y-1)

T=(-1+0,3-1)=(-1,2)

S=(1+0,4-1)=(1,3)

C=(1+0,-1-1)=(1,0)

H=(3+0,0-1)=(3,-1)

The triangle RDP have points R(0,0), D(-2,-2) and P(3,-3). On rotation of 180 degrees graph (x,y) becomes (-x,-y).

R=(0,0)

D=[-(-2),-(-2)]=(2,2)

P=[-(3).-(-3)]=(-3,3)

Therefore, the transformations are made.

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Answer:

70

Step-by-step explanation:

for every 5 $20 notes is $100 70 notes is $1400 and the other 20 is $2000 which makes 3400

If we use 2 liters of OJ, you will need to change the recipe and use:

We know that a recipe calls for 6 liters of OJ, 3 liters of grape juice and 9.5 liters of ice cream.

If instead we use 2 liters of OJ, then the ratio of the recipe that we use is given by the quotient below:

2L/6L = 1/3

So we will just use 1/3 of each of the amounts that the recipe calls, we will se:

(1/3)*3 liters of grape juice = 1 liter of grape juice.

(1/3)*9.5 liters of water = 3.2 liters of water.

These are the amounts that you need to use.

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Answer:

144

Step-by-step explanation:

9+2+4+6+123=

11+10+123
21+123
144

The expression A' represents the statement for all of the elements which are not in set A.

A set is a collection of well defined objects.

Given that A students wants to write an expression for all of the elements which are not in set A.

The elements within set A are denoted by A.

We have to find  all of the elements which are not in set A.

U represents the universal set and A is the given set.

A'=U-A

Hence, the expression A' represents the statement for all of the elements which are not in set A.

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Dana's estimated length was 66.67% far off the actual length and her estimated width was 25% far off the actual width.

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.

Percent Error Formula

The formula for percent error is:

PE = (|Estimated value-Actual value|/ Actual value) × 100

Given,

Actual length of the book = 24 cm

Actual width of the book = 16 cm

Dana's estimated length of the book = 40 cm

Dana's estimated width of the book = 20 cm

Error in measurement of length of the book =

(Measured Length - Actual Length/Actual length) × 100

= (40 - 24/24) ×100 = 66.67%

Error in measurement of width of the book =

(Measured width - Actual width/Actual width) × 100

= (20 - 16 / 16) × 100 = 25%

Hence, Dana's estimated length and breadth was 66.67% and 25% far off the actual length and width of the book respectively.

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The binomials which correctly represent the factors of the given trinomial; x² + x - 30 as required in the task content are; ( x - 5 ) and ( x + 6 ).

As evident in the task content; the given trinomial whose binomial factors are to be determined is; x² + x - 30.

By factorisation; the given trinomial expression can be written as;

x² + 6x - 5x - 30

x ( x + 6 ) -5 ( x + 6 )

( x - 5 ) ( x + 6 )

On this note, the required binomials which are factors of the given trinomial expression are; ( x - 5 ) and ( x + 6 ).

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Answer:

1.05

Step-by-step explanation:

it is 105 divided by 1000

Answer:

0.105 metres

Step-by-step explanation:

105 divided by 1000

The value of x is 10 yards. The given shape is a trapezoid.

What are trigonometry ratios?

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Draw a line parallel to the base.

Name the corner point of the shape.

Assume that ∠ADG = θ.

Consider △BDF:

BD = 6 + x

DF = 8 + 4.8 = 12.8 yrds.

The cosine of an angle is the ratio of the base to the hypotenuse of the right-angle triangle.

cos θ = DF/BD

cos θ = 12.8 /(6+x)  .....(i)

Consider △CDE:

cos θ = DE/CD

cos θ = 8/x  .....(ii)

Now equate equations (i) and (ii):

12.8 /(6+x) = 8/x

Cross multiply:

12.8 × x = 8(6+x)

12.8x = 48 + 8x

12.8x - 8x = 48

4.8x = 48

Divide both sides by 4.8:

x = 48/4.8

x = 10

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The value of x is 10 yards. The given shape is a trapezoid.

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Draw a line parallel to the base.

Name the corner point of the shape.

Assume that ∠ADG = θ.

Consider △BDF:

BD = 6 + x

DF = 8 + 4.8 = 12.8 yrds.

The cosine of an angle is the ratio of the base to the hypotenuse of the right-angle triangle.

cos θ = DF/BD

cos θ = 12.8 /(6+x)  .....(i)

Consider △CDE:

cos θ = DE/CD

cos θ = 8/x  .....(ii)

Now equate equations (i) and (ii):

12.8 /(6+x) = 8/x

Cross multiply:

12.8 × x = 8(6+x)

12.8x = 48 + 8x

12.8x - 8x = 48

4.8x = 48

Divide both sides by 4.8:

x = 48/4.8

x = 10

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Answer: 24 units.

Step-by-step explanation: To find the perimeter of a triangle, you need to add the length, width, and hypotenuse. The length and width are provided, but we need to find the hypotenuse of the triangle. To do this, we need to use the Pythagorean Theorem.

The Pythagorean Theorem is basically a^2 + b^2 = c^2 where a and b are the legs of the triangle and c is the hypotenuse (also known as the triangle's longest side). However, whatever answer you get needs to be square-rooted, which is your complete answer. Let's say that the side that's 6 units is leg a and the side that's 8 units is leg b.

6^2 + 8^2 = c^2

36 + 64 = 100

√100 = 10.

Now that we know the hypotenuse, we can add it to our other two sides.

6 + 8 + 10 = 24.

Therefore, 24 is your answer.

Let me know if this is right! :)

Answer: solve the same variables

Step-by-step explanation:

1. 3y + 4.1

2. 4x +

3. 5x + 22½

4. 4y²

5. + 25

6. 0

Answer:7 7/8. pounds.

Step-by-step explanation:

Dirk will make 70 pars or better.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that During the first several rounds of a golfing league, Dirk made par or better on 42 out of 90 holes.

Out of 90 holes, Dirk made par or better on 42 holes.

At this rate, Out of 1 hole, Dirk made par or better on (42/90) holes.

Then, Out of 150 holes, Dirk will make par or better on -

(42/90 x 150) holes

(42/90 x 150)

70

Therefore, Dirk will make 70 pars or better.

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Total of 44 weeks does one bag last.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator

Total amount of cat food = 33 lbs in one bag

Amount of food cat eats each week = 3/4 lb = 0.75 lb

Number of weeks one bag of cat food last = 33 / 0.75

                                                                       = 44

Hence one bag of cat food will last for 44 weeks.

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Answer:

The answer is 6.25%

Step-by-step explanation:

So,

(61 ÷ 976) × 100%

0.0625 × 100% = 6.25%

Thus, 6.25% of potatoes are rotten.

Step-by-step explanation:

% of potatoes rotten = 61/976 × 100

=> 6100/976

=> 6.25%

The next decimal number should be changed to hexadecimal. Your final response may contain up to six fractional digits. In decimal 386210, subscript 10 to F16.

F16 is 001000011000.1111. 218. F716 is 001000011000.111101112. 710 = (h0)16 = 716 is how the hexadecimal number is represented. It is necessary to add a 1 to the left and modify the number for both to 0. In base-2, the numeral 15 is represented as 1111, and the number 16 is represented as 10000. The greatest value in base-16 is the letter F, in a similar vein. such that 10 is the new value.

Binary 10 equals 1010, thus. Dividing 10 by 2 successively until the quotient equals 0 will yield the decimal to binary equivalent. By writing the remainder in each division step from bottom to top, it is possible to determine the binary equivalent.Base-16 is the definition given to hexadecimal. There are many powers of 16 in each place value in the number. The hexadecimal numbers are: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. 10 through 15 are represented, accordingly, by the letters A through F.

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Answer:

2000 workers

Step-by-step explanation:
All the workers: 100%
Women: 60%
Others: 40% = 800 workers
=> 1% of the workers: 800/40 = 20 workers
=> 100% = 20 x 100 = 2000 workers
(I can't think of another one)

A percentage of his commute that would be shorter than 32 minutes, to the nearest 10th is equal to 50%.

Mathematically, the z-score of a given sample size or data set can be calculated by using this formula:

Z-score, z = (x - μ)/σ

Where:

Substituting the parameters into the z-score formula, we have;

Z-score, z = (32 - 32)/3

Z-score, z = 0/3

Z-score, z = 0

Since a commute of 32 minutes on a test corresponds to a z-score of 0, the percentage of the commute will be shorter than 32 minutes is given by:

P(x > 32) = P(z > 0)

P(z > 0) = 0.5

P(z > 0) = 50%.

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