Base of an isosceles triangle can be right angles

The algebraic fundamental theorem states that there are 12 zeros in the function f(x) = 15x12 + 41x9 + 13x2 10.

acc to our question-

hence,there are 12 zeros

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Answer:

No

Step-by-step explanation:

Total money = €150

1 pair of sunglasses = €70

3 pairs of shorts = €15 × 3 = €45

then, Total = €70 + €45 + x

€150 = €115 + x

x = €150 - €115

x = €35

Which means Eddie got only €35 left on him which is not enough for him to buy the trainers

Answer:

[tex]\sqrt{2}[/tex] × [tex]\sqrt{8}[/tex]   And [tex]\sqrt{2}[/tex] ×[tex]\sqrt{3}[/tex]  

Step-by-step explanation:

3x9 are both whole numbers and 0x[tex]\sqrt{5}[/tex] has only one irrational number

Answer:

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

The inequality that can be used to solve for x, the number of minutes it will take Amy to finish typing her paper is D. 38x + 1,450 > 4,000.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Since Amy types at an average speed of 38 words per minute and has already typed 1,450 words of her final paper, which will be more than 4,000 words.

Let the number of minutes be x.

This will be:

1450 + 38(x) > 400

1450 + 38x > 4000

In conclusion, the correct option is D.

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The angle-side-angle (ASA) Congruence theorem proves that

ΔABC and ΔPQR are congruent triangles.

We know that the angle-side-angle ASA Congruence theorem states that if two angles and the side between these angles of one triangle are equal to two angles and the side between then of another triangle then those two triangles are congruent.

In given triangles ABC and PQR,

∠ABC ≅ ∠PQR

BC ≅ QR

∠BCA ≅ ∠QRA

so, by ASA Congruence theorem ΔABC ≅ ΔPQR

Therefore, the angle-side-angle (ASA) Congruence theorem proves that

ΔABC and ΔPQR are congruent triangles.

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Line a and line b are parallel to each other, and c is neither parallel nor perpendicular.

Line a passes through (2, 10) and (4, 13).

Line b passes through (4, 9) and (6, 12).

Line c passes through (2, 10) and (4, 9).

If a line passes through two points, then the slope of the line is

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Line a passes through (2, 10) and (4, 13).  So, the slope of this line is

[tex]m_{a}=\frac{13-10}{4-2}=\frac{3}{2}[/tex]

Line b passes through (4, 9) and (6, 12).  So, the slope of this line is

[tex]m_{b}=\frac{12-9}{6-4}=\frac{3}{2}[/tex]

Line c passes through (2, 10) and (4,9).  So, the slope of this line is

[tex]m_{c}=\frac{9-10}{4-2}=\frac{1}{2}[/tex]

The product of slopes of perpendicular lines is -1.

and if the slope of 2 lines is equal then those lines are parallel

so, line a and line b are parallel to each other, and c is neither parallel nor perpendicular.

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The equation of the line in slope - intercept form will be -

y = (4/5)x + 5

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

At [c] = 0 -

y = mx

We have a directly proportional relation.

The general equation of a straight line is -

[y] = [m]x + [c]

At [c] = 0, y = mx

m = y/x

where [m] acts as a constant of proportionality.

So -

y = mx : represents direct proportionality between [y] and [x]. Its graph is a straight line.

Therefore, y = mx : represents direct proportionality between [y] and [x]. Its graph is a straight line.

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The Missing Lengths are AB = 10 units, OP = 10 units and f = 4 units

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

When two triangles ΔABC and ΔXYZ are similar then

                    AB/XY = BC/YZ = AC/XZ

Here we have

ΔABC and ΔOPQ which are similar and right-angled triangles

As we know in a right-angled triangle

=>  Hyp² = side² + side²  

From ΔABC,

AB² = AC² + BC²  

=> AB² = 6² + 4²

=> AB² = 100 = 10²

=> AB = 10 units

Since  ΔABC and ΔOPQ are similar

=>  AB/OP = BC/OQ = AC/PQ  

=>  10/OP = 4/ f = 6/ 6

Take 10/OP = 6/ 6  

=>  6(10) = 6(OP)

=>  OP = 10 units  

4/ f = 6/ 6  

=> f = 4 units    

Therefore,

The Missing Lengths are AB = 10 units, OP = 10 units and f = 4 units

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Answer:

Option A

Step-by-step explanation:

→ Multiply both sides by 2

2s = a + b + c

→ Minus b and c from both sides

2s - b - c = a

Step-by-step explanation:

Range = Highest number - Lowest number

= 23 - 4

= 19

The value of m is 8.

The amount of times a number has been multiplied by itself is shown by its exponent. The result of multiplying 8 by itself n times is represented as follows:

8 x 8 x 8 x 8 x …..n times = [tex]8^n[/tex]

Given:

[tex]$(m-4)^4 = \left(\frac 1{16}\right)^{-1}$.[/tex]

Now, solving for m

[tex](m-4)^4[/tex] = 16

[tex](m-4)^4[/tex] = [tex]4^4[/tex]

Taking the quad root we have

m -4 = 4

m = 4+ 4

m = 8

Hence, the value of m is 8.

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Answer: C. (2, 1)

Step-by-step explanation:

The numbers labeled are

(-5, -8)

(-2, 1)

(4, 0)

(2, 9)

Find coordinates by looking at each line. (x, y)

The x-axis is the horizontal line in the middle.

The y-axis is the vertical line going across.

The x-axis always goes first when plotting down coordinates, and y goes second.

So, the one NOT labeled is C (2, 1)

The 27.4 m² of carpet is needed for three bedrooms.

Firstly we will calculate the area of each room.

Area of bedroom a = 3.1 × 3.1

Area of bedroom a = 9.61 m²

Area of bedroom b = 2.9 × 3.2

Performing multiplication on Right Hand Side of the equation

Area of bedroom b = 9.29 m²

Area of bedroom c = 2.5 × 3.4

Area of bedroom c = 8.5 m²

Total area of all the rooms = 9.61 + 9.29 + 8.5

Performing addition on Right Hand Side of the equation

Total area of all the rooms = 27.4 m²

Hence, 27.4 m² carpet is required for three bedrooms.

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The area of the of the rectangle is 5.25square inch and the area of the square is 6.25square inch. Therefore the square has larger area.

The area of a shape is the “space enclosed within the perimeter or the boundary” of the given shape. We calculate the area for different shapes using formulas.

Area formula in rectangle is L× W and in square is L^2. This happened in square becos square has all it's sides equal. Where L and W are length and Width respectively

The area of rectangle with dimension 7inches by 3/4 inch is 7×3/4= 5.25 square inches

The area of the square with dimension 2 1/2 inches is( 5/2)^2= 25/4= 6.25m

Therefore the square has larger area

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Answer:

x < 1 and x > -4 (more down below)

Step-by-step explanation:

First we have to solve the algebra
|-2x - 3| + 2 < 7
|-2x - 3| < 5
1. -2x - 3 < -5                    2.  -2x -3 < 5
-2x < -2                           -2x < 8                        

x < 1                                x > -4 (switch the expression)
Now... The two answers are x < 1 and x > -4

The interval notation is a number line with circles on the two points (answers)
Sorry I can't exactly explain what that is you might have to search it up, but you need a number line like this, and you need to draw another line above the -5 and 1 with an open circle on -5 and 1

    O-----------------------O

<---5, -4, -3, -2, -1, 0, 1, 2-->

For graphing, make a graph with 5 points on each side with 4 quadrants or whatever reasonable size, and draw a vertical line that extends all the way above and below your graph above 1 on line x and a vertical line all the way above and below your graph above above -5 on x, then shade everything in between those two lines.

This helps you to know what value you plug in for X makes the inequality true (shaded region)

Answer:

domain: [tex](-\infty, \infty)[/tex]

range: [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

You can put any real number into [tex]x[/tex] and get any real number out oft the function [tex]f(x)[/tex]

The graph of (y = 4x), which depicts the relationship between the quantity of tickets sold (x) and the sum of the proceeds from the sales (y), can be drawn by first formulating the linear equation and then using the transformation.

Which is the function's graph?

We have a piecewise function right here:

If x > 6, f(x) = 0.5*x - 2.

If x > 6, f(x) = -x - 1

Given:

Each ticket for the school play is $4.

There have been 'x' tickets sold in total.

The tickets generated 'y' in total revenue.

The graph showing the relationship between the quantity of tickets sold (x) and the sum of the ticket sales (y) can be drawn using the procedures below:

Form the linear equation in two variables as a first step.

y = 4x

The total revenue from the tickets is shown in the equation above.

Draw the graph of (y = x) in step two.

Step 3: In the graph of (y = x), multiply the x-axis by 4 units. The graph that is produced is (y = 4x).

You may find the graph for (y = 4x) below.

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Considering the figure of a right angle triangle, the given length is the hypotenuse,. The unknown side x is calculated to be 6.86 cm

information given in the question

hypotenuse = 9.7 cm

opposite = x

adjacent =  x

The problem is solved using the Pythagoras theorem is applicable to right angle triangle.  the formula of the theorem is

hypotenuse² = opposite² + adjacent²

opposite = adjacent

plugging the values as in the problem

let x be the required distance

9.7² = x² + x²

94.09 = 2x²

47.045 = x²

x² = 47.045

x = √47.045

x = 6.8589

x = 6.86 to 3 significant figures

side x is 6.86 cm

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Answer:

The ratio of acid to water is 2 to 3 in the mixture of the two solutions

This can be thought of as a chemistry problem or a math problem, but both use practically the same process to find the final answer.

So, let's say 2 liters of 50% acid and 1 liter of 20% acid is mixed.
In total, there is 2*(50%) + 1*(20%) of acid, so there is 1 liter of pure acid in 2 liters of 50% acid, and 0.2 liters of pure acid in 1 liter of 20% acid. This in total is 1.2 liters of acid. The total volume is 2 + 1 liters, which is 3 liters. the percentage can be found by dividing the amount of pure acid by the total volume, so 1.2/3, which equals 0.4, or 40%. The ratio would be 40% to 100-40%, or 40% to 60%, or 2 to 3

The students that will like exactly one of the two sports out of football and baseball is 200.

These are the fundamental set of set theory formulas. When there are two sets P and Q, the number of elements in one of the sets P or Q is denoted by n(P U Q). The number of elements in both sets P and Q is represented by the expression n(P ⋂Q). n(P U Q) is equal to n(P) + n(Q) - n (P Q).

Here,

F=140

B=144

F∩B=42

F-B=n(F)-n(F∩B)

=140-42

F-B=98

B-F=n(B)-n(F∩B)

=144-42

=102

So, the students that will like exactly one of the two sports,

=102+98

=200

There are 200 students who will only enjoy one of the two sports—football or baseball.

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The value of 9 and a half will be 9 1/2.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this case, addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

Here, we want to find the value of 9 and half. This will be:

= 9 + 1/2

= 9 1/2

The value is 9 1/2.

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Answer:

24

Step-by-step explanation:

lets set up the equation

x=25-(0.05x20) this is

x=25-1

x=24

The measure of ∠MCJ is 130° because ∠MCJ and ∠CMB are alternate interior opposite angles.

According to the question,

We have the following information:

We have a figure where angle MCJ is 130°.

Now, we can extend the two given lines as imaginary lines. After extending the lines, we will find that these lines are parallel and the lines are being cut by another line.

We know that in this case the alternate interior opposite angles are equal and the sum of consecutive alternate interior angles is 180°.

Now, ∠MCJ and ∠CMB are alternate interior opposite angles and thus they are equal.

Hence, the measure of ∠MCJ is 130° because ∠MCJ and ∠CMB are alternate interior opposite angles.

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The probability that Roger Federer wins at least 2 Grand Slam titles is 60.82%

Given data:

To calculate the probability that Roger wins at least 2 Grand Slam titles out of the 20 competitions during the 5-year period, we can use the binomial distribution.

The binomial distribution calculates the probability of obtaining a certain number of successes (in this case, Roger winning a Grand Slam) in a fixed number of independent trials (the 20 competitions), given the probability of success in a single trial (0.1).

We need to calculate the probability of Roger winning 2, 3, 4, ..., up to 20 Grand Slam titles and then sum those probabilities to find the overall probability of winning at least 2 titles.

Using a binomial probability formula, the probability of getting exactly k successes in n trials is given by:

[tex]P(X = k) = C(n, k) * p^k * (1 - p)^{(n - k)}[/tex]

Where:

C(n, k) is the binomial coefficient (n choose k)

p is the probability of success in a single trial (0.1)

n is the number of trials (20)

To find the probability of winning at least 2 Grand Slam titles, we calculate the probabilities for k = 2, 3, 4, ..., 20, and sum them up:

P(X ≥  2) = P(X = 2) + P(X = 3) + ... + P(X = 20)

P(X ≥  2) = Σ(P(X = k)) from k = 2 to 20

Calculating each individual probability P(X = k) and summing them up can be tedious. However, use complementary probability to simplify the calculation:

P(X ≥  2) = 1 - P(X = 0) - P(X = 1)

[tex]P(X = 0) = C(20, 0) * 0.1^0 * (1 - 0.1)^{(20 - 0) }[/tex]

[tex]=(1 - 0.1)^{20}[/tex]

= 0.12157

[tex]P(X = 1) = C(20, 1) * 0.1^1 * (1 - 0.1)^{(20 - 1) }[/tex]

[tex]= 20 * 0.1 * (1 - 0.1)^{19 }[/tex]

= 0.27017

P(X ≥  2) = 1 - 0.1074 - 0.2684

P(X ≥ 2 ) = 0.60826 (approximately)

Hence, the probability that Roger Federer wins at least 2 Grand Slam titles out of the 20 competitions is approximately 0.60826, or 60.82%.

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Answer:

equation: y= -2x-1

Step-by-step explanation:

y= -2x+b

-3= -2(1)+b

-3= -2+b

b= -1

equation: y= -2x-1

The solution for the system of equations -

x+3y+z=-8      

2x+y-6z=20    

x-2y+z=-13    

is x = 5.875, y = 1, z = 16.875

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line in point slope form can be also written as-

[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]

We have the following set of equations -

x+3y+z=-8       ..[1]

2x+y-6z=20     ..[2]

x-2y+z=-13        ..[3]

We can write eq [3] as -

z = - 13 - x + 2y

So, eq [1] and [2], will become -

x + 3y + (-13 - x + 2y) = -8

x + 3y - 13 - x + 2y = -8

5y = - 8 + 13

5y = 5

y = 1       ..Eq[4]

AND

2x + y - 6z = 20

2x + y - 6(- 13 - x + 2y) = 20

2x + y + 78 + 6x - 12y = 20

2x + 1 + 78 + 6x - 12 = 20

8x = 47

x = 5.875      ..Eq[5]

Now -

x - 2y + z = -13

5.875 - 2 + z = - 13

z = 16.875

Therefore, the solution for the system of equations -

x+3y+z=-8      

2x+y-6z=20    

x-2y+z=-13    

is x = 5.875, y = 1, z = 16.875.

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The largest area of the rectangle is 6502.5 square feet.

Given that,

Using fence parallel to one of the rectangle's sides, a cattle rancher wants to surround a rectangular area and divide it into four pens (see the figure below). To finish the task, 510 feet of fencing are available.

We have to find what could the four pens' combined total area be.

We know that,

The rectangular shape's length is l and its width is b.

Total fencing= 2l + 5b=510 feet

2l +5b =510 feet

We can write as,

l=1/2(510-5b)

Total area of the rectangle is length into breath

A(b) = l × b

A(b) = 1/2(510-5b)×b

A(b)= 1/2(510b -5b²)

For maximum area

A'(b)=0

1/2(510b -5(2b))=0

b=51

We get l as

l = 1/2(510-5b)

l = 1/2(510-5(51))

l = 127.5

Total area of the rectangle is 127.5 × 51

Total area of the rectangle is 6502.5 square feet.

Therefore, The largest area of the rectangle is 6502.5 square feet.

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There are 10 students in a class: 6 boys and 4 girls. If the teachers chooses 3 at random, then the probability that everyone in the group is a girl is 1/30

It is given that,

Total number of students = 10

Number of boys = 6

Number of girls = 4

Total number of ways to select 3 students from 10 students.

10C3= 10!/ 3!7!= 120

Total number of ways to select 3 students from 4 girls

4C3 = 4!/ 3!=4

The probability that everyone in the group is a girls is

P = 4/120

  = 1/30

Hence ,  the probability that everyone in the group is a girl is 1/30

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