Is a triangle 90 or 180?.

For the given set of information, the inequality 25 - 1 ≤' temperature ≤' 25 + 1

Linear inequalities in two variables are statements containing symbols such as "'<'(less than), '>' (greater than), '≤''(less than or equal to), '≥' (greater than or equal to) and two separate variables.

Linear inequalities are defined as an inequality (expressed by inequality symbols) that holds a linear function.

A linear function is any function with a straight line as its graph.

The inequality representing the situation is:

25 - 1 <= temperature <= 25 + 1

So the temperature must be greater than or equal to 24°C and less than or equal to 26°C.

The highest possible temperature is 26°C.

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Answer:

80 students received a flu vaccine

Step-by-step explanation:

1. graph the equation.

2. Go to 65 on the y-axis.

3. Go to 80 on the x-axis.

4. If the line stops at the point (80,65) then for the 65 cases of the flu at school, 80 students received the vaccine.

Answer:

-13, -22, -31, -40

Step-by-step explanation:

substitute n for each term

The sum of the polynomials (-x² + 9) + (-3x² - 11x + 4) is -4x² - 11x - 5.

A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).

In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.

Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.

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Complete Question:

What is the sum of the polynomials (-x² + 9) + (-3x² - 11x + 4)?

The base angle for the isosceles triangle is 53°.

Any triangle with two sides that have the same length is said to be an isosceles triangle. If the two sides of a triangle are congruent, then the angle across from them must likewise be, according to the theorem that explains the isosceles triangle. As a result, the two angles of an isosceles triangle that are on opposite sides with equal numbers are equal in size.

Given base length = 6 and leg length = 5

draw a perpendicular to the base that divides the base into equal parts,

as shown in the image attached

let the base angle be Ф,

and using a cosine formula for the base angle

cosФ = base/hypotenuse

from construction  base = 3 and hypotenuse = 5

cosФ = 3/5

Ф = cos⁻¹(3/5)

Ф = 53.13°

Ф = 53° (approx)

Hence the base angle is 53°

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The remaining amount of antibiotic in the cow's body after 6 hours will be 2,431 milligrams * [tex]0.5^5[/tex]= 305.39 milligrams.

Every hour, the cow's body will break down 50% of the initial amount of 9,724 milligrams of the antibiotic. So in the first hour, 50% * 9,724 milligrams = 4,862 milligrams will break down.

The remaining amount of antibiotic in the cow's body after the first hour will be 9,724 milligrams - 4,862 milligrams = 4,862 milligrams.

In the next hour, 50% * 4,862 milligrams = 2,431 milligrams will break down. So the remaining amount will be 4,862 milligrams - 2,431 milligrams = 2,431 milligrams.

This process will repeat for 6 hours, the remaining amount of antibiotic in the cow's body after 6 hours will be 2,431 milligrams * [tex]0.5^5[/tex]= 305.39 milligrams.

The concept used here to solve this is called the half-life, which is the amount of time required for half of the amount of a substance to decay or be used up. In this case, the antibiotic has a half-life of 1 hour, meaning that every hour, half of the initial amount of 9,724 milligrams will be broken down in the cow's body.

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The answer is option (D) : Find the midpoint of segment NP.

What is Midpoint?

The midpoint of a line segment is a point that lies exactly halfway between two points. It is the same distance from each endpoint of the straight line segment. Midpoint formula is a mathematical equation that is used to locate the halfway point between two data points. The midpoint formula is applied when one is required to find the exact center point between two defined points.

As Shown in below diagram given below,

suppose need to park at point M (i.e. midpoint of NP)

distance = NM + MP

so, when M is the midpoint of NP and has the minimum distance.

Therefore, the answer is option (D) : Find the midpoint of segment NP.

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There is a points of multiply a 3 digit number :

Now, According to the question:

To multiply means to add equal groups. When we multiply, the number of things in the group increases. The two factors and the product are parts of a multiplication problem. In the multiplication problem, 6 × 9 = 54, the numbers 6 and 9 are the factors, while the number 54 is the product.

If we need to multiply 123 × 3, we place them as shown below where 123 is the multiplicand and 3 is the multiplier. After multiplying these numbers we get the product as 269

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If overtime was compensated at time and a half, Mr. Riley would receive 15 hours of base pay.

By first figuring out the value of a single unit and then multiplying that value to get the requisite value, a problem can be solved using the unitary technique. For multiplication and dividing by fractions, the unitary strategy is frequently beneficial because it makes sense immediately and can be executed mentally if the numbers add up. Since written methods for fractions are frequently employed, notably division by a fraction, it is useful to explain or defend these algorithms. The unitary method's formula is to get the value of one unit, multiply it by the number of units, and then divide the result by the desired value.

given

The standard workweek is 40 hours.

Gross wages totaled $490.15.

Pay for overtime: $156.75

Total compensation based on a basic week = Total Gross salaries minus overtime pay

Total wages calculated based on a standard week are $490.15 - $156.75 = $334.

Let the basic hourly salary be $8.36 ($x = x).

Let y hours equal the number of overtime hours.

Due to the fact that overtime pay is time-and-a-quarter.

According to the calculation: Equals 15 hours

If overtime was compensated at time and a half, Mr. Riley would receive 15 hours of base pay.

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Answer:

c

Step-by-step explanation:

V=a2h

3=14.22·3.9

3=262.132cm³

By applying the future values, the amount of money the parents should deposit to have $8,250 for a child’s education in 10 years is $2,529.09

A current asset's future value, abbreviated as FV, is the value that asset is expected to have at some point in the future, based on a projected rate of growth. The future value is essential for investors and financial planners because they use it to estimate how much money an investment made now will be worth in the future.

To find the future values, we can use this following formula:

FV = I x (1 + R)^T

Where:

I = investment amount

R = interest rate

T = number of years

In this case, we are given that:

Future values (FV) = $8,250

The periodic rate = 12% : 4 = 0.03 (compounded quarterly)

Number of period = 10 years x 4 = 40

Hence, the amount of money the parents should deposit to have $8,250 for a child’s education in 10 years is:

8,250 = I x (1 + 0.03)⁴⁰

I = 8,250: ((1 + 0.03)⁴⁰)

I = $2,529.09

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Answer: y=2x²+3x-5

Step-by-step explanation:

Solve 4x²+6x-2y=10

1. subtract 4x² and 6x from both sides

(you do this to leave y by itself)

-2y=10-4x²-6x

2. divide -2 on both sides

y= -5+2x²+3x

This is technically the right answer but you still need to put the numbers and variables in the right order.

y=2x²+3x-5

(variables w/ exponents go first, then the variable, then the number)

Hope this helps! Good luck!

To change the log base 2 to log base 10, we can use the change of base formula for logarithms.

We know that the change of base formula for logarithms.

The formula to change the base of a logarithm from base 'a' to base 'b' is:

[tex]log_a(m)=\frac{log_b(m)}{log_b(a)}[/tex]

Here, we need to change log base 2 to base 10

By using this change of base formula, we can change the log base 2 to log base 10.

We know that log base 10 is called the common logarithm.

We denote [tex]log_{10} (x)[/tex] as log(x).

Let us assume that we want to change a number log of x to the base 2 to log of x to the base 10

From above formula of change of base we get,

[tex]log_2(x)\\\\=\frac{log_{10}(x)}{log_{10}(2)}\\\\=\frac{log(x)}{log(2)}[/tex]

Thus, we can use the change of base formula for logarithms  to change the log base 2 to log base 10,

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The entire range of values visible on a graph, from left to right, constitutes the graph's domain. All of the graph's values, from lower to higher, are included in the range.

How do you tell the difference between domain and range on a graph?

A function's range is all of its y values, which are its outputs, and all of its x values, which are its inputs. The entire range of values visible on a graph, from left to right, constitutes the graph's domain. All of the graph's values, from lower to higher, are included in the range.

Every potential value of y is included in a function's range. A function's range can be determined using the formula y = f. (x). Only if every x value in a relation has a unique y value can it be considered a function.

The various output values are displayed on the y-axis and make up the range. Remember that the domain and range may be larger than the observable values if the graph extends beyond the area that we can view.

Without evaluating or graphing the functions, it is not possible to determine the exact ranges of g(x) and h(x). However, we can see that both functions are linear and have the same slope (2), so their ranges will be in the same direction.

Since the y-intercept of g(x) is 1 and the y-intercept of h(x) is 2, it can be inferred that the range of h(x) will be greater than the range of g(x) for all values of x in the given domain (0 < x < 5).

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The height of the cylinder is given by the equation h = 12 cm

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

Surface area of cylinder = 2πr ( r + h )

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Let the cylinder be represented as A

Now , the radius of the cylinder be r = 6 cm

Let the height of the cylinder be h

Let the volume of the cylinder be V = 432π cm³

Volume of Cylinder = πr²h

Substituting the values in the equation , we get

432π = π ( 6 )² x h

On simplifying the equation , we get

432 = 36h

Divide by 36 on both sides of the equation , we get

h = 12 cm

Hence , the height of the cylinder is 12 cm

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A polynomial or a rational function in simplest form is (f. g)(x) is 4x² + 25x + 6.

The exponents of all the variables of an algebraic statement known as a polynomial must all be whole numbers. In any polynomial, the exponents of the variables must be non-negative integers.By identifying which phrases only contain the processes of adding, subtract, multiplying, and non-negative integer exponents, the polynomials can be located. Expressions with additional processing are considered as non expressions.

Given,  f(x) = 4x + 1

          g(x) = x + 6

Now, (f. g)(x) = f(x).g(x)

                   = (4x + 1)(x + 6)

                   = 4x² + 24x + x + 6

                   = 4x² + 25x + 6

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The value of P(F or G) using the general addition rule be 8/12.

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is stated. To forecast the likelihood of events, probability has been introduced in mathematics.

We have that

F∪G = {5, 6, 7, 8, 9, 10, 11, 12}

P(FG) = 0.667

P(F or G) = 5/12 + 4/12 - (1/12)

P(F or G) = 5/12 + 1/4

From the question we are told

S = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14},

F = [5, 6, 7, 8, 9]

G = {9, 10, 11, 12}

Generally

The P(F or G) by counting the number of outcomes in F or G exists

[tex]$F \& G=\{5,6,7,8,9,10,11,12\}$$[/tex]

P(F or G) using the general addition rule

[tex]$& P(F G)=\frac{N_f}{N_g} \\[/tex]

substitute the values in the above equation, we get

[tex]$& P(F G)=\frac{8}{12} \\[/tex]

simplifying the equation, we get

P(F G) = 0.667

Using addition Rue to attain P(F or G) we get

P(F or G) = PF + PG - P(F + G)

substitute the values in the above equation, we get

[tex]$& P(\text { For } G)=5 / 12+4 / 12-(1 / 12) \\[/tex]

simplifying the equation, we get

[tex]$ P({For} G)=5 / 12+1 / 4 \\[/tex]

[tex]$& P(\text { For } G)=\frac{8}{12}[/tex]

Therefore, the value of P(F or G) using the general addition rule be 8/12.

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x² + y = 55 ---1

y=6---2

subs 2 in 1

x²+ 6 = 55

x² = 55-6

x² = 49

x =√49

x = 7

Answer: d=0.5

Step-by-step explanation: 4.8d=2.4

Divide 4.8 form both sides to isolate d.

[tex]\frac{4.8d}{4.8} =\frac{2.4}{4.8}[/tex]

Then, just do 2.4 divided by 4.8 to get d=0.5.

The sum of the two polynomials 6s^2t^2 + 2st^2 + 4s^2t + 3st^2 is

6s^2t^2 + 2st^2 + 4s^2t + 3st^2 = (6+4)s^2t^2 + (2+3)st^2 = 10s^2t^2 + 5st^2

The polynomials are being added term by term, and the coefficient of each term is being added.

The coefficient of s^2t^2 in the sum is 10, which is the sum of the coefficients of s^2t^2 in the original polynomials (6 and 4).

The coefficient of st^2 in the sum is 5, which is the sum of the coefficients of st^2 in the original polynomials (2 and 3).

So the sum of the polynomials is 10s^2t^2 + 5st^2, this is the final result.

It's important to note that the polynomials have to be in the same order of terms (same exponent) to obtain the correct result when adding them.

The algebraic identities are

(x + y)² = x² + y² + 2xy,

(x – y)² = x² + y² – 2xy,

x² – y² = (x + y) (x – y),

(x + a) (x + b) = x² + (a + b)x + ab,

(x + y)³ = x³ + y³ + 3xy(x + y),

(x – y)³ = x³ – y³ – 3xy(x – y),

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx,

x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx) .

These algebraic identities basically carry variable equations in such a way, that the Left-hand side (L.H.S) of the equation is equal to its Right-hand side(R.H.S).

What is the use of algebraic identities?

Algebraic Identities help in simplification. Algebraic Identities play a major role in solving quadratic equations and higher power equations.

The algebraic identities are also used to calculate products of numbers and other things.

Let us consider x, y and z are variables.

Algebraic Identities for Two Variables x and y :

(x + y)² = x² + y² + 2xy

(x – y)² = x² + y² – 2xy

x² – y² = (x + y) (x – y)

(x + a) (x + b) = x² + (a + b)x + ab ; a and b are two constant values

(x + y)³ = x³ + y³ + 3xy(x + y)

(x – y)³ = x³ – y³ – 3xy(x – y)

Algebraic Identities for Three Variables x, y and z :

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx

x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx)

So, the algebraic identities are

(x + y)² = x² + y² + 2xy,

(x – y)² = x² + y² – 2xy,

x² – y² = (x + y) (x – y),

(x + a) (x + b) = x² + (a + b)x + ab,

(x + y)³ = x³ + y³ + 3xy(x + y),

(x – y)³ = x³ – y³ – 3xy(x – y),

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx,

x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx) .

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The coordinates of the vertices of the image are:

A' = (-1, 5)

B' = (-4, 0)

C' = (-2, -2)

Option A is the correct answer.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Counterclockwise means the coordinates will interchange and the sign will be depending on the quadrants.

The coordinates of the triangle ABC.

A = (5, -1)

This is in the 4th quadrant.

If rotated 90 degrees counterclockwise A will be in the 1st quadrant.

A' = (-1, 5)

B = (0, 4)

This is in the first quadrant.

If rotated 90 degrees counterclockwise B will be in the 2nd quadrant.

B = (-4, 0)

C = (-2, 2)

This is in the 2nd quadrant.

If rotated 90 degrees counterclockwise C will be in the 3rd quadrant.

C = (-2, -2)

Thus,

The coordinates of the image are:

A' = (-1, 5)

B' = (-4, 0)

C' = (-2, -2)

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Yes, it is possible to draw a triangle.

This will be done by the property: the sum of two sides of a triangle should be more than the third side.

(4.5cm + 5.8cm) =10.2cm

10.3cm = 10.2cm

LHS>RHS

A triangle is possible.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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First, you need to find the slope between the two points:

      [tex]\begin{aligned}\dfrac{8-2}{-1-1} & = \dfrac{6}{-2}\\[0.5em]&=-3\endaligned}[/tex]

Now, you use one of the points to find the equation.

You can use point-slope form:

     y - 1 = -3 (x-2)

Or you can use slope-intercept form:

    y = -3x + 5

Note:

You can find the slope-intercept form by taking y = mx + b and substituting in the slope and a point and solving for b:

    2 = -3 (1) + b

The greater than sign is '>'. If one value is greater than the other, use greater than. Therefore, we can write more than 50 as x > 50.

Greater Than:

In mathematics, the greater than sign is placed between two values ​​where the first number is greater than the second number.

Example: 60 > 50, where 60 is greater than 50.

In inequalities, the greater-than sign always refers to the greater value, and the sign consists of two equal length dashes joined at an acute angle on the right increase (>).

The greater than sign is used in linear inequalities when the value of a variable is not known to be greater than to a certain value. This symbol is a greater-than symbol (>) with a sleep line below it.

Here are some more examples.

x > 100 means the value of x is greater than to 100.

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There are various methods by which you can solve a quadratic equation such as:

In algebra, a quadratic equation is any equation that can be rearranged in standard shape wherein x represents an unknown cost, and a, b, and c represent acknowledged numbers, in which a ≠ 0. Quadratic equations are in detail related to issues about squares and quadrangles (every other name for rectangles). In reality, the word quadratic is derived from the Latin word quadratus for square.

The general shape of the quadratic equation is ax² + bx + c = 0. for instance, x² + 2x +1 is a quadratic or quadratic equation. A quadratic feature is a characteristic of the form f(x) = ax² +bx+c, in which a, b, and c are constants and a = 0. The term ax² is called the quadratic time period (therefore the call given to the feature), the term box is known as the linear term, and the time period c is known as the steady term.

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A front-end loader to load trucks with granular material that has a swell factor of 15%. If the loader has a heaped capacity of 10 cu. Yd.  the total cycle time for the loader, if it can move 55 cu, is 16.2 hours(  55 cu. Yd. / 10 cu. Yd. (heaped capacity) * 15% (swell factor) * 48 min. /hr)

The total cycle time for a front-end loader to load trucks with granular material with a swell factor of 15% can be calculated by taking the total amount of in-bank material to be loaded and dividing it by the heaped capacity of the loader. This will give us the total number of cycles the loader must complete. Once we have this number, we must multiply it by the swell factor. This gives us the total number of heaped cycles the loader will have to complete.

Finally, we must multiply the total number of heaped cycles by the efficiency of the loader. Efficiency is the amount of time it takes for the loader to complete one heaped cycle. In this case, the total cycle time for the loader to load is 55 cu. Yd. Of in-bank material with a swell factor of 15% and a heaped capacity of 10 cu. Yd. Is 16.2 hours, assuming the loader has an efficiency of 48 min. /hr.

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The value of x from the given figure is 12 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the given figure,

Consider ΔPQR and ΔPQS,

∠P=∠P (Reflex property)

PQ=PQ (Reflex property)

∠PQR=∠PSQ=90°

By AA similarity, ΔPQR ~ ΔPQS

So, PQ/PR = PS/PQ

x/45 = 25/x

x²=45×25

x=15√5 units

Therefore, the value of x from the given figure is 15√5 units.

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