Given: DC =6x, and DA =4x+18 EB =4y-12, and ED =y+17 Y Find y. Then find ED, DB and EB.

Answer:

Step-by-step explanation:

since it is 100% and the pie chart circle is 360°, then for each % it will be 3.6°

applying this into drawing, just times 3.6° to the percentage and then get the final angle for the data.

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if you don't need to be so concise, just see as you fit

Step-by-step explanation:

Because the ratio of length:width is..

15:10 for b

and

30:15 for c.

Now we will divide..

3:2 for b

and

2:1 for c.

Those are NOT the same things!

Answer:  0.753.

Step-by-step explanation:

The value of the correlation coefficient is denoted by 'r'. It is used to describe the strength and direction of the relationship between two variables.

Given: The relationship between the number of hours a person practices a task and the time it takes them to complete the task is calculated to have R-sq = 56.7%.

= 0.567

Then, [tex]r=\sqrt{R^2}[/tex]

[tex]=\sqrt{0.567}\approx0.753[/tex]

Hence, the value of the correlation coefficient is 0.753.

Answer: (0.8115, 0.8645)

Step-by-step explanation:

Let p be the proportion of people who leave one space after a period.

Given:  Sample size : n= 525

Number of people responded that they leave one space. =440

i.e. sample proportion: [tex]\hat{p}=\dfrac{440}{525}\approx0.838[/tex]

z-score for 90% confidence level : 1.645

Formula to find the confidence interval :

[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]0.838\pm (1.645)\sqrt{\dfrac{0.838(1-0.838)}{525}}\\\\=0.838\pm (1.645)\sqrt{0.00025858285}\\\\=0.838\pm (1.645)(0.01608)\\\\= 0.838\pm0.0265\\\\=(0.838-0.0265,\ 0.838+0.0265)\\\\=(0.8115,\ 0.8645)[/tex]

Hence, a 90% confidence interval for the proportion of people who leave one space after a period: (0.8115, 0.8645)

The rule we use here is [tex]\frac{a^b}{a^c} = a^{b-c}[/tex]

If the font size is too small, then it says (a^b)/(a^c) = a^(b-c)

We subtract the exponents when dividing exponentials like this. The bases must be the same.

So this means the exponents 13 and 3 subtract to get 13-3 = 10

We either have an exponent of "13-3" or an exponent of "10" as an equivalent expression. The base stays at 2 the entire time.

Answer:

x=35°

Step-by-step explanation:

So first, recall that the interior angles of a triangle must total 180°.

The sum of the angles for the given triangle can be described by:

[tex]110+x+x\\=2x+110[/tex]

Since the total must equal 180°, set the expression equal to 180°.

[tex]2x+110=180[/tex]

To find the value of x, we just need to solve for x.

To start, subtract 110 from both sides. The 110s on the left cancels:

[tex](2x+110)-110=(180)-110\\2x=70[/tex]

Now, divide both sides by 2. The 2s on the left cancel.

[tex]\frac{(2x)}{2}=\frac{(70)}{2}\\ x=35 \textdegree[/tex]

Therefore, the value of x is 35°.

Step-by-step explanation:

[tex]180 - 110 = 60 - 2 = 30 \\ so \: x = 30[/tex]

Answer:

x = 1

y = 5

Step-by-step explanation:

5x - 2y = -5

5x + 6y = 35

=> 5x + 6y = 35

=> 5x - 5x + 6y = 35 - 5x

=> 6y = 35 - 5x

=> 6y/6 = 35/6 - 5/6x

=> y = 35/6 - 5/6x

=> 5x - 2 (35/6 - 5/6x) = -5

=> 5x - 35/3 + 5/3x = -5

=> 15/3x -35/3 + 5/3 = -15/3

=> 20/3x -35/3 = -15/3

=> 20/3x -35/3 + 35/3 = -15/3 + 35/3

=> 20/3x = 20/3

=> 20/3x * 3 = 20/3 * 3

=> 20x = 20

=> 20x/20 = 20/20

=> x = 1

=> 5x + 6y = 35

=> 5(1) + 6y = 35

=> 5 + 6y = 35

=> 5 -5 + 6y = 35 -5

=> 6y = 30

=> 6y/6 = 30/6

=> y = 5

So, x = 1

     y = 5

Answer:

There are 10 perfect squares between 1 and 100;

A perfect square is basically an integer that is a square of an integer. Or simply the product of an integer with itself.

Explanation:

The perfect squares between 1 and 100 are:

1*1 = 1

2*2 = 4

3*3 = 9

4*4 = 16

5*5 = 25

6*6 = 36

7*7 = 49

8*8 = 64

9*9 = 81

and

10*10 = 100

☆ The relation between x and y is y = a cos x° +b

Taking 1st condition from the table .

→ x = 0 and y = 9

→ y = a + cos 0° + b

→ 9 = a + cos 0° + b

☆ We know that cos 0° = 1

→ 9 = a(1) + b

Now taking other condition

→ x = 90° and y = 1

→ y = a cos 90° + b

→ 1 = a cos 90° + b

☆ We know that cos 90° is 0

→ 1 = a(0) + b

Putting the value of b in equation 1st .

→ 9 = a + 1

→ a = 8 .

Now taking the value of x according to the question .

☆ x = 45 °

→ y = 8 ( cos 45°) + 1

☆ We know that cos 45° is 1/√2

→ y = 8(1/√2) + 1

→ 8 = 4×√2×√2

So the answer is 4√2+1

Answer:  see proof below

Step-by-step explanation:

Proof LHS → RHS

[tex]\dfrac{1}{3-2\sqrt2}-\dfrac{1}{2\sqrt2-7}+\dfrac{1}{\sqrt7-\sqrt6}-\dfrac{1}{\sqrt6-\sqrt5}+\dfrac{1}{\sqrt5-2}\\\\\\\text{Rationalize the denominator (multiply by same numbers but opposite sign)}\\\dfrac{3+2\sqrt2}{1}-\dfrac{2\sqrt2+7}{1}+\dfrac{\sqrt7+\sqrt6}{1}+\dfrac{\sqrt6+\sqrt5}{1}+\dfrac{\sqrt5+2}{1}\\\\\\\text{Group like terms:}\\3+(2\sqrt2-2\sqrt2)+(-\sqrt7+\sqrt7)+(\sqrt6-\sqrt6)+(-\sqrt5+\sqrt5)+2\\\\\\\text{Simplify:}\\3 + 0+0+0+0+2 \\= 5[/tex]

LHS = RHS:  5 = 5  [tex]\checkmark[/tex]

Answer:

x=8

Step-by-step explanation:

3x -5 =2.5x + 3 - (x-4)

3x - 5 = 2.5x + 3 -x+4

3x - 5 = 1.5x +7

1.5x = 12

x =8

The solution to the linear equation 3x - 5 = 2.5x + 3 - (x-4) is x = 8.

The given expression is,

x-5=2.5x+3-(x-4)

Simplify the equation by combining like terms.

Start with the terms on the right-hand side of the equation:

2.5x+3-(x-4)

= 2.5x + 3 - x + 4 (distributing the negative sign)

= 1.5x + 7

Now let's combine the terms on the left-hand side of the equation:

3x - 5

Now the reduced equation be,

3x - 5 = 1.5x + 7

Isolate the variable (x) on one side of the equation.

Subtracting 1.5x from both sides:

3x - 1.5x - 5 = 1.5x - 1.5x + 7

1.5x - 5 = 7

Add 5 to both sides:

1.5x - 5 + 5 = 7 + 5

1.5x = 12

Solve for x by dividing both sides by 1.5:

1.5x/1.5 = 12/1.5

x = 8

So the solution to the linear equation 3x - 5 = 2.5x + 3 - (x-4) is x = 8.

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Answer:

B)1-x≤-1 OR 1-x≥1

[tex]S=\{x\in\mathbb{R}| x\le 0\quad \text{or}\quad x\ge 2 \}[/tex]

Step-by-step explanation:

[tex]2|1-x|+1\geq 3[/tex]

[tex]2|1-x|\geq 2[/tex]

[tex]|1-x|\geq 1[/tex]

Once we have an absolute value inequality, remember that:

For a > 0

[tex]\boxed{\text{If } |x|\leq a \Longleftrightarrow -a\leq x \leq a}[/tex]

[tex]\boxed{\text{If } |x|\geq a \Longleftrightarrow x\leq -a \text{ or } x\geq a }[/tex]

Therefore,

[tex]1-x\le -1\quad \text{or}\quad 1-x\ge 1[/tex]

Solving

[tex]1-x\le -1 \Longleftrightarrow x\geq 2[/tex]

[tex]1-x\ge 1 \Longleftrightarrow x\leq 0[/tex]

We have

[tex]x\geq 2 \quad \cup \quad x \leq 0[/tex]

[tex](-\infty, 0] \cup [2, \infty)[/tex]

[tex]S=\{x\in\mathbb{R}| x\le 0\quad \text{or}\quad x\ge 2 \}[/tex]

Answer:

ABC  = 27

DBC  = 56

Step-by-step explanation:

ABC + CBD = ABD

x+10 + 4x-12 = 83

Combine like terms

5x -2 = 83

Add 2 to each side

5x-2+2 = 83+2

5x = 85

Divide each side by 5

5x/5 = 85/5

x =17

ABC = x+10 = 17+10 = 27

DBC = 4x-12 = 4*17 -12 = 68-12 = 56

Answer:

Angle ABC = 27°

Angle DBC = 56°

Step-by-step explanation:

So we have to set an equation first.

x + 10 + 4x - 12 = 83

This simplified = 5x - 2 = 83

--> 5x = 85

so x = 17

Plug it in to the formula for ABC and DBC

ABC = x + 10

17 + 10 = 27

ABC = 27

DBC = 4x - 12

68 - 12

DBC = 56

Thus, we have our 2 answers.

Hope this helps!

Answer:

F: 48

Step-by-step explanation:

Let x be the length of the side of the cube. RQ can be expressed as a triangle consisting of a diagonal of a face of the cube and the side length x. By the pythagorean theorem, we know that a^2+b^2=c^2. So, we can express the diagonal as x^2+x^2=c^2, giving us the value of c to be [tex]x\sqrt{2}[/tex]. Now, we can once again use the pythagorean theorem to find RQ^2=2x^2+x^2=3x^2, so RQ=[tex]x\sqrt{3}[/tex]=12, so x=[tex]4\sqrt{3}[/tex]. To find the area of the shaded part, we multiply the length times width which gives us [tex](4\sqrt{3})^2=48[/tex]. So, the area of the shaded face of the cube is F: 48.

Answer:

(x + 5)(x + 1)

Step-by-step explanation:

First, notice that because this is a trinomial (has three terms separated by some operation), we will use a basic factoring technique.

The parent function for a quadratic is ax²+bx+c=0.

Therefore, the factoring technique is to see what factors of C add up to give you B.

Factors of 5 are 5 and 1, and 5 + 1 = 6.

So, therefore, your factors are (x + 5) (x + 1).

Performing the FOIL function on this gives you x² + 1x + 5x + 5. Simplify by adding like terms and your final answer is x² + 6x + 5.

Answer:The graph f(x)   is shifted 2 units to left and shifted down by 6 units to form the graph r(x) .

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

1+4x=7+x

↦4x-x=7-1

↦3x=6

↦x=6/3

↦x=2

.°. x=2

Hope you understand it

Answer:

x = 2

Step-by-step explanation:

For this equation, we simply need to solve for x.

1 + 4x = 7 + x

1 + -1 + 4x = 7 + -1 + x

4x = 6 + x

4x + -x = 6 + x + -x

3x = 6

3x * (1/3) = 6 * (1/3)

x = 2

So the solution to this equation is x = 2.

Cheers.

Answer:

160

Step-by-step explanation:

Divide 24 by 15 percent (.15)

24/.15

=160

Answer:

160

Step-by-step explanation:

from the question, we know that 24 balloons are 15% of total.

make equation:

[tex]\frac{15}{100} =\frac{24}{x}[/tex]

calculate:

100*24/15=160 balloons

Answer:

y=kx

20=10k

k=20/10

k=2

Answer: $1.8

Step-by-step explanation:

From the question, we are informed that the price for 2 kilograms of ham is $36.00. We should remember that 1000 gram = 1 kilogram; therefore, 2 kilograms = 2000 grams.

The cost of a gram of ham will then be:

= $36.00/2000

= $0.018

The unit price of ham per 100 grams will be:

= 100 × 0.018

= $1.8

Answer:

x+4

x+1-2=x-1

Step-by-step explanation:

x+4/x-1=11/16 x should be different than 1 cz 1-1=0

16(x+4)=11(x-1)

16x+64=11x-11

16x-11x=-11-64

5x=-75

x=-15

Answer:

4/6 and 8/12 and 16/24

Step-by-step explanation:

well because it is math and math works like this basically all of theese are equal to 2/3

Answer:

2x + 22

Explanation

2(4x + 7) -2(3x -4)

Factor 2 out of  the Expression

2(4x + 7 -(3x -4)

- × - is +

2(4x + 7 - 3x +4)

Collect like terms

2(x+7+4)

2(x+11)

2x + 22

==================================================

Explanation:

Using your calculator, you should find that

Each approximate result has its decimal digits go on forever without any pattern. So we cannot write those values as a fraction of two integers. The decimal expansion must have some kind of pattern that repeats forever, so we could consider it rational.

Only choice B results in a whole number. The value 14 is the same as 14/1, showing it can be written as a fraction of two integers. Therefore choice B is rational.

Answer:

28

Step-by-step explanation:

[tex]5x -7\\x =7[/tex]

Substitute 7 for x in the given equation

[tex]5x -7\\\\= 5(7) -7\\\\= 35-7\\\\= 28[/tex]

Answer:

28 is the answer

Step-by-step explanation:

5(7)= 35

35-7=28

Answer:

A

Step-by-step explanation:

125 is the amount of discount, so for example if p was 500 and discounted by 125 (p-125), you'd get 375(example of reduced price).

Answer:

D is correct.

Step-by-step explanation:

2x ≤ 14

x  ≤ 7

Answer:

D) x ≤ 7

Step-by-step explanation:

2x + 1 ≤ 15

2x ≤ 15 - 1

2x ≤ 14

x ≤ 14 : 2

x ≤ 7

Answer:

Domain= possible x values

Range= possible y values.

Domain= all real numbers

Range= all numbers greater than -2.

Let me know if this helps :)

Domain = all real numbers and Range = ( -2 , ∞) of the given exponential graph

" Domain of exponential function y = aˣ is all the values of x and range is the all calculated values of 'y' after substituting value of x."

General exponential function

y = aˣ

According to the graph,

Given exponential function,

y = 3ˣ - 2

x represents the domain of the function.

y represents the range of the function

compare with exponential equation

a= 3 >1

As the value of 'x' increases value of 'y' moves to infinity.

Therefore, value of y defined for all the values of 'x'.

Therefore,

Domain is set of all real numbers.

Function y is transformed by -2.

Substitute x=0 in y = 3ˣ-2 we get,

y = -2

Therefore,

Range = (-2 , ∞)

Hence, Domain = all real numbers and Range = ( -2 , ∞) of the given exponential graph.

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Greetings from Brasil....

From Pythagoras we have

AB² = AC² + BC²

13² = 12² + X²

Answer:

5 cm

Step-by-step explanation:

Pythagoras theorem gives us:

[tex]hypotenuse^{2} = side^{2} + side^{2}[/tex]

We know the hypotenuse is 13 cm.

We know one side is 12 cm.

[tex]13^{2} = 12^{2} + side^{2}[/tex]

[tex]169= 144 + side^{2}[/tex]

Subtracting 144 from both sides:

[tex]25 = side^{2}[/tex]

Reversing the sides:

[tex]side^{2}=25[/tex]

[tex]\sqrt{side^{2}}= \±\sqrt{25}[/tex]

[tex]side = \±\sqrt{25}[/tex]

[tex]side = \±5[/tex]

Since a distance can't be negative:

[tex]side=5[/tex]

The third side is 5 cm.