) What is the measure of ∠x in the diagram below?

Answer:

Step-by-step explanation:

To find the possible length and breadth of the rectangle, we need to factor the given expression:

x^2 - 6x + 8 = (x - 4)(x - 2)

Therefore, the length and breadth of the rectangle can be any combination of (x-4) and (x-2).

For example, if we choose (x-4) as the length and (x-2) as the breadth, we have:

Length = x - 4

Breadth = x - 2

Conversely, if we choose (x-2) as the length and (x-4) as the breadth, we have:

Length = x - 2

Breadth = x - 4

So, the possible length and breadth of the rectangle are (x-4) and (x-2), and vice versa.

Answer:(x-4) and (x-2)

Step-by-step explanation:

Answer:

28 is the ans of 252÷9here we go

252 divided by 9 equals 28.

To divide 252 by 9, you can use long division, which involves dividing the number in steps until there is no remainder left.

Here's the step-by-step process:

Write down the dividend (252) and the divisor (9), and set up the long division format:

9 | 252

Look at the leftmost digit of the dividend (2) and see if it's divisible by the divisor (9). Since 2 is less than 9, we bring down the next digit (5) to the right of 2, making it 25.

9 | 252

2

Divide the new number (25) by the divisor (9). The result is 2, which is the first digit of the quotient. Multiply this result by the divisor (2 x 9 = 18) and write it below the 25, then subtract it from 25:

9 | 252

25

18

--

7

Bring down the next digit (2) from the dividend to the right of the remainder (7), making it 72. Now, divide 72 by 9, which gives you 8. Multiply this result by the divisor (8 x 9 = 72) and write it below the 72, then subtract it from 72:

9 | 252

25

18

--

72

72

---

0

There is no remainder left, and the dividend has been completely divided. The quotient is the result of the division, which is 28.

Therefore, 252 divided by 9 equals 28.

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10/73 is the value of x in inequality.

What does the word "inequality" mean?

In mathematics, inequalities describe the connection between two values that are not equal. Equal does not imply inequality. The "not equal symbol ()" is typically used to indicate that two values are not equal.

                    However different inequalities are used to compare the values to determine if they are less than or higher than. The term "inequality" refers to a relationship between two expressions or values that is not equal to one another. Inequality originates from an imbalance, thus.

the inequality  12≥ 73x + 2

                    = 12 - 2  ≥  73x

                     = 10 ≥ 73x

                   = 10/73 ≥ x

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The matrix of predicted rankings UVT is [[48,24,12],[0,0,0],[24,12,6]].

The matrix of predicted rankings UVT can be calculated using the formula UVT = UV.The provided initial values for U() and V(0) are as follows:U() = [[2,1],[1,0],[3,-1]]V(0) = [[24,12,6],[0,0,0],[12,6,3]]Using the above values, the matrix of predicted rankings UVT can be computed as follows:UVT = UVU = [[2,1],[1,0],[3,-1]]V = [[24,12,6],[0,0,0],[12,6,3]]UVT = [[2,1],[1,0],[3,-1]] x [[24,12,6],[0,0,0],[12,6,3]]= [[48,24,12],[0,0,0],[24,12,6]]Therefore, the matrix of predicted rankings UVT is [[48,24,12],[0,0,0],[24,12,6]].

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Answer:

x=1

Step-by-step explanation:

2.5+x=3.5

3.5-2.5=x

1=x

x=1

Answer:

Step-by-step explanation:

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Answer:

s= 6

Step-by-step explanation:

The speed s (in miles per hour) of a car can be given by s = √(30fg), where fis the

coefficient of friction and d is the stopping distance (in feet). The table shows the

coefficient of friction for different surfaces. You are driving 35 miles per hour on an

icy road when a deer jumps in front of your car. How far away must you begin to

brake to avoid hitting the deer? Round your answer to the nearest whole integer. NO

UNITS NEEDED

Length of the median of the triangle is b. 18

How to find the length of the median of a triangle?
Given that the centroid of a triangle is located 12 units from one of the vertices of a triangle. We need to find the length of the median of the triangle drawn from that same vertex.

Let ABC be a triangle.

Let AD be median of the triangle.

Let E be centroid of ΔABC

Length of the median of triangle = AD

AD = Length of AE + Length of ED

But,

AE = 12

ED = x

So,

AD = 12 + x

Since, centroid divides median in 2:1 ratio.

Then,

[tex]12 : x = 2 : 1\\12/x = 2/1\\\\12= 2x\\[/tex]

Divide by 2 each side

[tex]x = 6[/tex]

So,  AD = 12 + x = 12 + 6 = 18

Thus, Length of the median of triangle is 18.

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Therefore, the 95% confidence interval for the population proportion of disks that are defective is (0.8357, 0.9475). This means that there is a 95% probability that the true population proportion of disks that are defective is between 0.8357 and 0.9475.

The quality-conscious disk manufacturer can use a 95% confidence interval to estimate the fraction of defective disks made by the company. The 95% confidence interval is calculated using the sample data to construct an interval estimate of the population proportion.
Using the given data, the sample proportion of disks that are not defective is 904/1015 = 0.8915.
The 95% confidence interval for the population proportion of disks that are defective is then given by:
Lower limit = 0.8915 – (1.96 x √(0.8915 x (1- 0.8915)/1015))
= 0.8915 – (1.96 x 0.0285)
= 0.8915 – 0.0558
= 0.8357
Upper limit = 0.8915 + (1.96 x √(0.8915 x (1- 0.8915)/1015))
= 0.8915 + (1.96 x 0.0285)
= 0.8915 + 0.0558
= 0.9475
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Answer:

U=8

Step-by-step explanation:

48<5U+8

-5U<8-48

-5U<-40

-5U/-5<-40/+5

U>8

Answer:

C is your answer

Step-by-step explanation:

in my opinion, i think it would be the mode.

The scale factor of the following pair of similar polygons after the dilation is 0.7

Given

The pair of similar polygons

From the pair of similar polygons, we have the following corresponding side lengths

Pre-image of the polygon = 30

Image of the polygon = 21

The scale factor of the similar polygons is then calculated as

Scale factor = 21/30

Evaluate the quotient

Scale factor = 0.7

Hence, the scale factor is 0.7

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As a result, y has a mean of 203 and a variance of 85 as let x1 and x2 be two independent random variables both with mean 10 and variance 5.

A variable is a symbol or letter that is used to indicate a variable quantity in mathematics. The context or issue under consideration can alter the value of a variable. In order to express relationships between quantities, variables are frequently utilized in equations, formulae, and functions. For instance, x and y are variables in the equation y = mx + b, which depicts the linear relationship between x and y. Variables in statistics can reflect various traits or features of a population or sample, such as age, body mass index, or income.

given

To get the mean and variance of y, we can apply the characteristics of expected value and variance:

We can start by determining the expected value of y:

E[y] = 2E[x1] = E[2x1x2 + 3x1 + 2]

By the linearity of expectation, E[x2] + 3E[x1] + 2 is 2(10)(10) + 3(10) + 2 = 203.

Next, we may determine y's variance:

Var(y) = Var(3x1 + 2 + 2 + 3x1 ) = 4

Var(x1)

Var(x2) + 9

Var(x1) + Var(constant) = 4(5)(5) + 9(5) + 0 = 85 since x1 and x2 are independent.

As a result, y has a mean of 203 and a variance of 85 as let x1 and x2 be two independent random variables both with mean 10 and variance 5.

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Answer:

Step-by-step explanation:

Given f(x) = 2x³ +x² +ax +b has a factor (x -2) and a remainder of 18 when divided by (x -1), you want to know a, b, and the factored form of f(x).

If (x -2) is a factor, then the value of f(2) is zero:

  f(2) = 2·2³ +2² +2a +b = 0

  2a +b = -20 . . . . . . . subtract 20

If the remainder from division by (x +1) is 18, then f(-1) is 18:

  f(-1) = 2·(-1)³ +(-1)² +a·(-1) +b = 18

  -a +b = 19 . . . . . . . . . . add 1

Subtracting the second equation from the first gives ...

  (2a +b) -(-a +b) = (-20) -(19)

  3a = -39

  a = -13

  b = 19 +a = 6

The values of 'a' and 'b' are -13 and 6, respectively.

We can find the quadratic factor using synthetic division, given one root is x=2. The tableau for that is ...

  [tex]\begin{array}{c|cccc}2&2&1&-13&6\\&&4&10&-6\\\cline{1-5}&2&5&-3&0\end{array}[/tex]

The remainder is 0, as expected, and the quadratic factor of f(x) is 2x² +5x -3. Now, we know f(x) = (x -2)(2x² +5x -3).

To factor the quadratic, we need to find factors of (2)(-3) = -6 that have a sum of 5. Those would be 6 and -1. This lets us factor the quadratic as ...

  2x² +5x -3 = (2x +6)(2x -1)/2 = (x +3)(2x -1)

The factored form of f(x) is ...

  f(x) = (2x -1)(x -2)(x +3)

Thus, the total area of composite figure (circle on a rectangle) is found as  29.91 m².

Area of sector of the circle = (Ф/360°) *π*r²

r is the radius = 5.5 m

π = 3.14

Area =  (30/360°) *3.14 * 5.5²

Area = 7.91 m²

Area of rectangle = width × length

Area = 4 × 5.5 = 22 m²

Total area of composite figure = area of the circle's sector + area of the rectangle

Total area of composite figure =  7.91 m² + 22 m² = 29.91 m²

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Answer:

3 packages

Step-by-step explanation:

61 - 20 * 2 (small grain sandpaper) = $21 remain. The largest grain costs $7, so 21/7 = 3 packages of the largest grain sandpaper was bought.

Hope this helped!

The solution to the logarithmic equation [tex]2log12(-8x) = 6[/tex] is [tex]x = -9/32[/tex] .

What are logarithmic properties ?

Logarithmic properties are the rules that govern the behavior of logarithmic functions. These properties are important in simplifying logarithmic expressions and solving logarithmic equations. Some of the commonly used logarithmic properties include:

Product property: [tex]logb(xy) = logb(x) + logb(y)[/tex]

This property allows us to simplify the logarithm of a product of two numbers into the sum of logarithms of the individual numbers.

Quotient property: [tex]logb(x/y) = logb(x) - logb(y)[/tex]

This property allows us to simplify the logarithm of a quotient of two numbers into the difference of logarithms of the individual numbers.

Power property:[tex]logb(x^y) = ylogb(x)[/tex]

This property allows us to simplify the logarithm of a power of a number by bringing the exponent outside of the logarithm and multiplying it with the logarithm of the base.

Change of base formula: [tex]logb(x) = logc(x) / logc(b)[/tex]

This property allows us to change the base of a logarithm by dividing the logarithm of the number by the logarithm of the base in a different base.

Solving the given logarithmic equation :

The equation can be solved by using logarithmic properties and basic algebraic manipulation.

We can begin by using the property that states [tex]loga(b^n) = nloga(b)[/tex] for any base a and any positive real number b. Applying this property, we can rewrite the left side of the equation as:

[tex]log12((-8x)^2) = log12(64x^2)[/tex]

Next, we can use the property that states [tex]loga(b) = c[/tex] is equivalent to [tex]a^c = b[/tex]. Applying this property, we can rewrite the equation as:

[tex]12^{2log12(64x^2)} = 12^6[/tex]

Simplifying the left side, we get:

[tex]64x^2 = 12^6 / 12^2[/tex]

[tex]64x^2 = 144[/tex]

Dividing both sides by 64, we get:

[tex]x^2 = 144/64[/tex]

[tex]x^2 = 9/4[/tex]

Taking the square root of both sides, we get:

[tex]x=\pm 3/2[/tex]

However, we need to check the solutions for extraneous roots since the original equation has a logarithm with a negative argument. We can see that the solution x = 3/2 is extraneous since it results in a negative argument for the logarithm. Therefore, the only valid solution is x = -9/32.

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We have that, using Euclid's algorithm, we find the inverse of 200 modules 1001 is -5 (or 1001+5).

To find the inverse of a module m using Euclid's algorithm, the steps are as follows:

1. Calculate the greatest common divisor (GCD) of a and m using the Euclidean algorithm.

2. Let a = GCD * s + m*t, where s is the inverse of a module m.

3. The GCD in terms of a and my is written as 1 = m-s*a.

4. Find s = -a, so the inverse of a module m is -a (or m+s).

For example, a = 2, m=17, so GCD = 1 = 17-8*2 and the inverse of 2 modulo 17 is -8 (or 17+8). Similarly, for a = 34, m= 89, the GCD = 1 = 89-34*2 and the inverse of 34 modulo 89 is -34 (or 89+34). Finally, for a = 200, m= 1001, the GCD = 1 = 1001-5*200 and the inverse of 200 modulo 1001 is -5 (or 1001+5).

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Answer:

30 minutes

Step-by-step explanation:

Use ratios. This is an inverse function, as speeding up makes the time traveling go down. So, when dividing the speed by 3 (done so 15 can get to 5), we multiply the time traveled by 3.

10 minutes * 3 = 30 minutes

Answer:

-12 is the y intercept while your slope is -4

Step-by-step explanation:

Answer: It should be 470 cm^2

Step-by-step explanation:

The null hypothesis is rejected whenever "there is a low probability that the obtained results could be due to random error." The correct answer is Option B.

The null hypothesis is a statistical hypothesis used to test the difference between two sample data groups. The null hypothesis is the hypothesis that the sample statistics are not significantly different. Any significant differences between the sample data are seen as supporting the alternative hypothesis.

A null hypothesis is often expressed as "no difference," "no correlation," or "no significant effect." For example, the null hypothesis for an experiment comparing two groups of people could be "there is no difference between the two groups." When the null hypothesis is rejected, it means that the results of the experiment are statistically significant, and the alternative hypothesis is supported.

Therefore, the null hypothesis is rejected whenever there is a low probability that the obtained results could be due to random error.

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Answer:

D. The electrician charges $23 per hour.

Step-by-step explanation:

C(h)= 23h+30 is in the form y=mx +b

$30 is the initial fee (b)

$23 is the amount charged per hour (h)

In the fractions prompts given, the correct output are:

A fraction represents a part of a whole. It consists of a numerator and a denominator, with the numerator indicating the number of parts and the denominator indicating the total number of parts.

The calculations are given as follows;

1 )

= (1/2) x (1/4) [dividing by a number is the same as multiplying by its reciprocal]

= 1/8

2) (1/5) ÷ 2

= (1/5) x (1/2)

= 1/10

3)

(1/3) ÷ 5

= (1/3) x (1/5)

= 1/15

4) (1/4) ÷ 4

= (1/4) x (1/4)

= 1/16

5) One day, Amy baked a cake and wanted to divide it equally among 3 of her friends. She realized she only had half a cake left, so she decided to divide it into equal parts. Each friend received 1/6 of a cake. To check her calculation, she multiplied 1/6 by 3 and got 1/2. Thus, (1/2) ÷ 3 = 1/6, since dividing by 3 is the same as multiplying by 1/3.

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In conclusion  the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc.  The equation showing that Elena saves exactly $20 is:

5 + (1.5)p = 20

Why it is?

The expression for how much money Elena saves after selling p pens is:

Total money saved = 5 + (1.5)p

The equation showing that Elena saves exactly $20 is:

5 + (1.5)p = 20

Solving the equation:

5 + (1.5)p = 20

(1.5)p = 15

p = 10

We notice that the value of p is a whole number, which makes sense since Elena cannot sell a fractional number of pens.

If Elena wants to have some money left over, we can write the inequality:

5 + (1.5)p > 20

Some values for p where Elena would have money left over are p = 11, p = 12, p = 13, etc.

To describe the values of p where Elena would be able to buy the t-shirt and still have money left over, we can write the inequality:

5 + (1.5)p > 20

(1.5)p > 15

p > 10

Therefore, the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc.

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The volume of lemon juice in the glass is 0.38 cubic inches.

Explanation:

Given,

Let the volume of the lemonade in the glass be V cubic inches

Therefore, the volume of lemon juice in the lemonade is [tex]$\frac{1}{12}$[/tex] V cubic inches

Volume of water in the lemonade is [tex]$\frac{11}{12}$[/tex] V cubic inches

The volume of the cylindrical glass is given by:

[tex]$V_{\text{cylindrical glass}} = \pi r^2h$[/tex]

Here,

Radius r = 1 inch

Height h = 6 inches

[tex]$V_{\text{cylindrical glass}} = \pi r^2h = \pi (1)^2(6) = 6 \pi$[/tex]

Since the glass is half full of lemonade, the volume of lemonade in the glass is:

[tex]$V_{\text{lemonade}} = \frac{1}{2}V_{\text{cylindrical glass}} = \frac{1}{2} 6 \pi = 3\pi$[/tex]

The volume of lemon juice in the lemonade is given by:

[tex]$V_{\text{lemon juice}} = \frac{1}{12}V$[/tex]

Therefore

[tex]$V_{\text{lemon juice}} = \frac{1}{12}3\pi = \frac{1}{4}\pi = 0.7854$[/tex] cubic inches

Hence, the volume of lemon juice in the glass is 0.38 cubic inches (rounded to the nearest hundredth).

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Step-by-step explanation:

40 Years is the right answer

Answer:

son is 10 , father is 40

Step-by-step explanation:

let x be the sons age then father is x + 30

in 5 years

son is x + 5 and father is x + 30 + 5 = x + 35

at this time the father is three times as old as his son , then

x + 35 = 3(x + 5)

x + 35 = 3x + 15 ( subtract x from both sides )

35 = x + 15 ( subtract 15 from both sides )

20 = x

then sons age = x = 10 and fathers age = x + 30 = 10 + 30 = 40

ANSWER

Jules paid $0.70 for one pencil

STEPS

Cost of One Pencil.

Let's assume the cost of one notebook be x and one pencil be y.

According to the given information,

Shanika bought 1 notebook and 5 pencils at a cost of $10.00. Therefore,

1x + 5y = 10 --- equation 1

Jules paid $14.90 for 1 Notebook and 12 pencils. Therefore,

1x + 12y = 14.9 --- equation 2

We need to find the cost of one pencil, i.e., y.

We can solve the above equations simultaneously to find the value of y.

Multiplying equation 1 by 12 and equation 2 by 5, we get:

12x + 60y = 120 --- equation 3

5x + 60y = 74.5 --- equation 4

Subtracting equation 4 from equation 3, we get:

7x = 45.5

x = 6.5

Substituting the value of x in equation 1, we get:

1(6.5) + 5y = 10

5y = 3.5

y = 0.7

Therefore, Jules paid $0.70 for one pencil.

ChatGPT

Answer:

Jules pay:

$0.7

Step-by-step explanation:

1n + 5p = 10                  Eq. 1

1n + 12p = 14.9              Eq. 2

n = cost of one notebook

p = cost of one pencil

From Eq. 1

n = 10 - 5p               Eq. 3

From Eq. 2

n = 14.9 - 12p            Eq. 4

Equalizing Eq. 3 and Eq. 4:

10 - 5p = 14.9 - 12p

12p - 5p = 14.9 - 10

7p = 4.9

p = 4.9 / 7

p = 0.7

From Eq. 3:

n = 10 - 5p

n = 10 - 5*0.7

n = 10 - 3.5

n = 6.5

Check:

From Eq. 2:

n + 12p = 14.9

6.5 + 12*0.7 = 14.9

6.5 + 8.4 = 14.9

Then:

1 pencil = $0.7

Answer:

25 computers per hour

Step-by-step explanation:

look ate the point 2 hours corresponding to 50 computers

50/2 = 25/1 or 25 computers per hour

The value of x is equal to; A. 5.

In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

By applying the basic proportionality theorem to the given triangle, we have the following:

x/(x + 5) = (x - 2)/(x + 1)

By cross-multiplying, we have the following:

x(x + 1) = (x - 2)(x + 5)

x² + x = x² + 5x - 2x - 10

By rearranging and collecting like-terms, the value of x is given by:

2x - 10 = 0

2x = 10

x = 10/2

x = 5.

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