Question 1-7
Similar triangles MRC and WYC are shown where MR = 14, CR=28, WY = 6, and MW = 17.88.

What is the length of YC?

Distributive property make it easier to multiply a 2 digit number t0 a 1 digit number because by using distributive property we can multiply the number place of the two digit number by one digit number and inlast we can add it , which makes the whole process easier.

According to Distributive property it helps to solve the complex problems easily either they are of 2 digit or many more . Distributive property multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

In other words, according to the distributive property, an expression of the form A (B+C) can be solved as A (B+ C) = AB + AC.

This property applies to subtraction as well.

A (B –C) = AB – AC

For example :- 19 X 6

= 10 X 6 + 9 X 6

= 60 + 54

= 114

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Answer:

$220

Step-by-step explanation:

Because, from 1 to 20 there are 10 odd numbers (1, 3, 5, 7, 9, 11, 13, 15, 17, 19) so it is said that for one odd number you win $22, as for 10 odd numbers, that is $22 x 10 which is $220

The graph that correctly represents the function f(x) = [√(x + 3)] - 2 is; Graph D

We are given the function;

f(x) = [√(x + 3)] - 2

Remember that the argument of a square root must be zero or larger, then the minimum of the domain is the value of x such that:

x + 2 = 0

x = -2

Then the function starts at:

f(-2) = [√(-2 + 3)] - 2

f(-2) = 3

Then the graph should start at (-3, 2).

We can also identify another point by evaluating in x = 2.

f(2) = [√(2 + 3)] - 2

f(2) = -1

So the function also passes through (2, - 1).

Notice that the only graph that contains these two points is the last graph with x-intercept at 7.

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In the given expression  14 - 0.6t, variable t represents the number of gallons of fuel used by the car each day.

For teh stated question-

In the given expression  14 - 0.6t, t represents the number of gallons of fuel used by the car each day.

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An inequality that represents the number of both kinds of DVD players that can be sold to reach or beat the sales target  is 30p+60r≥250.

An inequality in mathematics is a comparison between two numbers or other mathematical expressions that is done in an unfair manner. On the number line, it is most typically used to compare the sizes of two numbers.

A and b are not equal in either situation. These interactions are recognized as robust inequalities.

Given,

Profit gained by selling portable DVD player=$30

Profit gained by selling portable DVD recorder=$60

Let,

The number of portable DVD player=p

The number of DVD recorders=r

And also given that,

The profit must be at least $250.

Therefore, 30p+60r≥250

Hence, an inequality that represents the number of both kinds of DVD players that can be sold to reach or beat the sales target  is 30p+60r≥250.

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Answer:

50% increase

Step-by-step explanation:

If we call the number of people x;

On the first afternoon, everyone plants 8x (Average 8 per person)

In the future, the plan to plant 12x trees (Average 12 per person)

From 12x to 8x is a 50% increase, (12/8 = 1.5)

Hope this helps,

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Answer: y=13\3 or 4 1\3

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

900 divided by 15 is 60

What is the alternate exterior angle of ∠11?

[tex]\angle 1 \cong \angle 7 \text { and } \angle 4 \cong \angle 6[/tex]

The number of sides in the given polygon is, n=11 . The sum of all exterior angles is 360o .

An exterior angle of a triangle is created by extending one side of the triangle. The angle between the extended side and the side next to it is called an exterior angle.

What is a alternate exterior?

Alternate Exterior Angles: The pair of angles on the outside of the two parallel lines but on the other side of the transversal are known as alternate exterior angles.

Look at the area above and below the crossed lines to find outside angles. Look at that outside area for each crossed line on different sides of the transversal to locate alternative outside angles. We assume you stated that the external angles are 1, 2, 7, and 8.

When a transversal connects two coplanar lines, alternate interior angles are created. They are located on the transverse sides of the parallel lines, but on the inner side of the parallel lines. At two different locations, the transversal passes through the two lines that are coplanar.

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Answer: 60%

Step-by-step explanation:

Take 42 divided by 70, then times 100% = 60%

Yoko has ridden 60% so far!

Answer:

(x+3, y-3)

Step-by-step explanation:

Using system of linear equation the number of popcorn and drinks bought are 5 and  3 respectively

In solving a system of linear equation, we have two unknown variables which we are to find. However, we can use either substitution, elimination or graphical method to solve them.

In this case, to solve this problem, we have to write out two equations and solve for the unknown variable;

let;

x + y = 8 ...eq(i)

6x + 4y = 42 ...eq(ii)

From eq(i)

x + y = 8

x = 8 - y ...eq(iii)

Put eq(iii) into (ii)

6(8 - y) + 4y = 42

y = 3

put y = 3 into eq(i)

x + 3 = 8

x = 5

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Answer: You did wrong at Y=11/8! It should be -11/8, not positive 11/8

Step-by-step explanation:

You solved it all right; just the y is wrong! The reason why y is -11/8 is that a negative and a negative will make a positive, and add an x positive, and you will get a positive answer. If y is negative, the answer would be negative!

The probability for the experiment of drawing two marbles (without replacement) from a bag containing three green, three yellow, and four red marbles =  0.0111

In this question we need to find the probability for the experiment of drawing two marbles (without replacement) from a bag containing three green, three yellow, and four red marbles.

Total marbles in tha bag

= 3 green marbles + 3 yellow marbles + 4 red marbles

= 10 marbles

the probability of drawing one marble from a bag,

P1 = 1/10

Now there are 9 marbles in the bag.

So, the probability of drawing second marble would be,

P2 = 1/9

So, the required probability of drawing two marbles (without replacement) from a bag would be,

P = P1 * P2

P = 1/10 * 1/9

P = 1/90

P = 0.0111

Therefore, the probability of drawing two marbles (without replacement) from a bag = 0.0111

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The area of rhombus is 100m²

What is rhombus ?

A rhombus is a quadrilateral with four equal-length sides in planar Euclidean geometry. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.

A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is also referred to as a diamond or rhombus.

A quadrilateral with four equal sides that has the shape of a diamond is called a rhombus. In everyday life, rhombus-shaped objects can be seen. In the illustration below, two instances of rhombuses in nature are shown: a diamond and a kite.

The area of rhombus is

A = pq / 2

The  value of p is 10 and q is 20

A = (10 * 20) / 2

  = 100m²

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Two ordered pairs 45 is x^2 + y^2, 12 is x - y.An ordered pair is made up of the x (abscissa) and y (ordinate) coordinates, with two values stated in a certain order inside parenthesis.

Explanation:

45 = x^2 + y^2,

12 = x - y.

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Answer:

x = 5

Step-by-step explanation:

Find the scale factor from figure B to A

let x = the scale factor

5x = 2  Divide both sides by 5

x = [tex]\frac{2}{5}[/tex] or .4

12.5 x .4 = 5

18 first-year teachers were in the meeting.

In this question, we have been given that a school staff meeting had 60 teachers in attendance, 30% of whom were the first-year teachers.

We need to find the number of first-year teachers present in the meeting.

Let x be the number of first-year teachers present in the meeting.

As 30 percent of school staff are the first-year teachers, we need to find the 30 percent of 60.

Using the formula of percentage,

x = 60 * (30/100)

x = 18

Therefore, the number of first-year teachers present in the meeting = 18

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As a new cell phone plan charges a flat monthly fee of $24 and allows for an unlimited number of text messages, but charges $0.15 per minute (m) used for phone calls, the equation that will represent the problem is C=24+0.15m.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here,

Let m be the minutes talked on phone,

C=24+0.15m

The problem is represented by the equation C=24+0.15m since the new cell phone plan charges a fixed monthly fee of $24 and permits unlimited text messages, but each minute (m) utilized for phone calls costs $0. 15.

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Answer:

Step-by-step explanation:

$80.75 Your welcome

Answer:

$80.75 dollars

Step-by-step explanation:

15% of 95 is 14.25

95 - 14.25 = 80.75

Answer:

Step-by-step explanation:

set the height function = 0 and solve for t-16t2+6400=0t2 = -6400/(-16)=

The equation of the line is y = -1/2x + 7 which passes through the point (2, 6) and has a slope of -1/2.

What is the equation of a line?

The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. Key Point. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.

The equation of a line that passes through the point (2, 6) and has a slope of -1/2 can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.

To find the equation of the line, we can use the point-slope form of a line, which is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

Substituting the values for the point and the slope into this equation, we get:

y - 6 = (-1/2)(x - 2)

y - 6 = -1/2x + 1

y = -1/2x + 7

Hence, The equation of the line is y = -1/2x + 7 which passes through the point (2, 6) and has a slope of -1/2.

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Given :  55.7796

To Find : rounded off to 3 decimal places

Solution:

55.7796

To round off to   3 decimal places need to check digit at

4th decimal place

if  digit is 5 or greater than 5 then digit at 3rd decimal place has to be increased by  1  and all decimal places after that to be removed

if  digit is  less than 5 then digit at 3rd decimal place remains same and all decimal places after that  to be removed

55.7796

Digit at 4th decimal place is 6 which is greater than 5

Hence digit at 3rd decimal place has to be increased by 1

9 + 1 = 10  Hence 1 to be carried forward to digit at 2nd decimal place

7 + 1 = 8

Hence  number rounded off to 3 decimal places  is

55.780

55.7796 rounded off to 3 decimal places is  55.780

The orthogonal basis produced using the Gram-Schmidt process for W is[tex]y_1=\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right], y_2=\left[\begin{array}{c}5 \\1 \\-6 \\-1\end{array}\right][/tex]

What is orthogonal ?

The concept of orthogonality in mathematics is an extension of perpendicularity in geometry. By extension, the term "orthogonality" is also used to describe the division of particular system properties. The phrase also has specific applications in other disciplines, such as chemistry and painting.

[tex]$$x_1=\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right] \quad \text { and } \quad x_2=\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]$$[/tex]

Using Gram-Schmidt process to produce an orthogonal basis for W

[tex]$$y_1=x_1=\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right]$$[/tex]

Now we know [tex]$X_1, X_2$[/tex] and [tex]$Y_1$[/tex]

Lets solve for [tex]$Y_2$[/tex]

[tex]y_2=x_2-\frac{x_2+y_1}{y_1+y_1} y_1$$[/tex]

[tex]y_2=\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]-\frac{\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right]}{\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right]\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right]}\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right][/tex]

[tex]\begin{aligned}y_2 & =\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]-\frac{7+28-0+1}{1+16+0+1}\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right] \\& =\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]-\frac{36}{18}\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right]\end{aligned}[/tex]

[tex]\begin{aligned}& =\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]-2\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right] \\& =\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]-\left[\begin{array}{c}2 \\-8 \\0 \\2\end{array}\right] \\y_2 & =\left[\begin{array}{c}5 \\1 \\-6 \\-1\end{array}\right]\end{aligned}[/tex]

Complete question: The set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W. Assume the vectors are in the order bold x1 and bold x2

1 7

-4 -7

0 -6

1 1

The orthogonal basis produced using the Gram-Schmidt process for W is:__________. (Use a comma to separate vectors as needed.)

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Answer:

Step-by-step explanation:

No x intercept means it can't touch the x axis y=x^{2}+1 does the trick since it moves the whole thing up one unit

Answer: [tex]\frac{2\sqrt{2}-1 }{2}[/tex]

Step-by-step explanation:

1. multiply both the numerator and denominator by [tex]2\sqrt{2}[/tex]

2. distribute on the top to get [tex]8\sqrt{2} - 4[/tex] ([tex]\sqrt{2} *\sqrt{2}[/tex] equals 2)

3. multiply the bottom to get 8

4. after getting [tex]\frac{8\sqrt{2}-4 }{8}[/tex], factor out a 4 from each term to get [tex]\frac{4(2\sqrt{2}-1)}{4(2)}[/tex]

5. the fours will cancel and the answer will be [tex]\frac{2\sqrt{2}-1 }{2}[/tex]

Answer: A

Step-by-step explanation: Divide your miles by hour hours:

12.25/2.5 = 4.9

Her average speed was 4.9 miles per hour

The value of 'a'  in the system of equations will be;

⇒ a = - 4

What is an expression?

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

Given that;

The system of equation are;

⇒ ax + 12y = - 6

⇒ 2x - 6y = 4

Now,

By the condition of No solution for the system, we get;

⇒ a / 2 = 12 / - 6

⇒ a / 2 = - 2

⇒ a = - 4

Thus, The value of 'a'  in the system of equations will be;

⇒ a = - 4

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