In the diagram, triangle SOP~ triangle GNQ, fine the value of x and explain

Step-by-step explanation:

[tex]( {x - 2)}^{2} + 2 = 38 \\ {x }^{2} + 4 - 2 {x}^{2} + 2 = 38 \\ x = 38 - 2 - 4 \\ x = 32[/tex]

[tex]\left( \dfrac 49 \right) \div \left( \dfrac{18} 3 \right)\\\\\\=\dfrac 49 \div6\\\\\\=\dfrac 49 \times \dfrac 16\\\\\\=\dfrac{2}{9\times 3}\\\\\\=\dfrac{2}{27}[/tex]

Answer:

YES

Step-by-step explanation:

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers

- 23 and 100 are both integers

- 23 / 100 = 0.23 which is not a continious decimal

Answer:

Yes,it is.

Step-by-step explanation:

Rational numbers are usually expressed in fractions with both the numerator and denominator greater than zero

Answer:

[tex]\textsf{D.} \quad x=4 \pm \sqrt{17}[/tex]

Step-by-step explanation:

Rearrange the equation so it equals zero:

[tex]\begin{aligned} x^2+4 & =8x+5 \\ \implies x^2+4-8x-5 & = 0\\x^2-8x-1&=0\end{aligned}[/tex]

Now use the quadratic formula to solve for x:

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

[tex]a=1, \quad b=-8, \quad c=-1[/tex]

[tex]\implies x=\dfrac{-(-8) \pm \sqrt{(-8)^2-4(1)(-1)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{8 \pm \sqrt{68}}{2}[/tex]

[tex]\implies x=\dfrac{8 \pm \sqrt{4\cdot 17}}{2}[/tex]

[tex]\implies x=\dfrac{8 \pm \sqrt{4}\sqrt{17}}{2}[/tex]

[tex]\implies x=\dfrac{8 \pm 2\sqrt{17}}{2}[/tex]

[tex]\implies x=4 \pm \sqrt{17}[/tex]

Answer:

113.1 inches

Step-by-step explanation:

The area of a circle can be calculated using the formula [tex]\pi r^{2}[/tex], with r being the radius of the circle.

On this circle, the radius is 12 inches, making the area of the entire circle [tex]\pi 12^{2} =\pi 144[/tex], which is about 452.39.

The shaded area of the circle is 1/4 of the circle, so we use the equation [tex]\frac{452.39}{4}[/tex] to get an area of 113.1 inches.

Hope this helps! :)

The employee that has the larger pay increase is Jane. Her income is larger by £65.

Percentage is the fraction out of an amount that is usually expressed as a number out of hundred.

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Answer:

0

Step-by-step explanation:

simplfy: 4.5(6.2) = 0

Multiply 4.5 * 6.2

27.9 = 0

and solve

27.9 = 0

I  hope this helps ^^

Answer:

= -27.9

If you mean multiplication,  [tex]4.5\times(-6.2)=-27.9[/tex].

The product is negative because the (-)6.2 is negative.

Step-by-step explanation:

Answer:

15, 2

Step-by-step explanation:

Number one: 15

Number two: 2

Well 15 is 13 more than two meaning this is correct.

By eliminating numbers, I was able to find a range of possible numbers which eliminated all the others. Then using that range I found out the number.

The first number is 2 and the second number will be 15.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

There are two numbers that add up to 17.

If one number is 13 more than the other.

Then the two numbers will be

Let the first number be x. Then the second number will be x + 13

x + x + 13 = 17

  2x + 13 = 17

         2x = 4

           x = 2

The first number is 2 and the second number will be 15.

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It is TRUE, so shade on the SAME side as (0,0)

For 1st row

For 3 Rd row

For last row

Answer:

The only complete ordered pair in the given table is:

5 months → $60 saved

Therefore, to determine the relationship between the variables, divide the amount saved by the number of months:

[tex]\implies \sf \dfrac{Amount\:saved}{Number\:of\:months}=\dfrac{\$60}{5}=\$12[/tex]

So we can assume that $12 is saved each month.

To complete the table:

⇒ 3 × $12 = $36

⇒ $72 ÷ $12 = 6

⇒ 10 × $12 = $120

Completed table:

[tex]\large\begin{array}{| c | c |}\cline{1-2} \sf Times\:(month) & \sf Amount\:Saved\: (\$) \\\cline{1-2} 3 & 36 \\\cline{1-2} 5 & 60 \\\cline{1-2} 6 & 72 \\\cline{1-2} 10 & 120 \\\cline{1-2} \end{array}[/tex]

Answer:

(0,6), (0,4), (0,-10)

Step-by-step explanation:

#x

#y

#z

Answer:

C

Step-by-step explanation:

M is less than n because it comes before it in the number line

Step-by-step explanation:

please mark me as brainlest

Answer:

[tex]x < - 5[/tex]

Step-by-step explanation:

[tex] - 2x - 6 > x + 9[/tex]

[tex] - 2x - x > 9 + 6[/tex]

[tex] - 3x > 15[/tex]

[tex] \frac{ - 3x}{ - 3} > \frac{15}{ - 3} [/tex]

[tex]x < - 5[/tex]

Answer:

28

Step-by-step explanation:

▪︎ ADE and ABC are similar triangles (AAA)

▪︎ DA = DB + BA = 30 + 12 = 42

▪︎ k = DA / BA = 42 / 12 = 3.5

▪︎ DE = BC * k = 8 * 3.5 = 28

Step-by-step explanation:

I hope this will help you

Answer:

198

Step-by-step explanation:

The expression with a single rational exponent as follows

Exponents are often known as powers or indices. In simple terms, power can be defined as an expression that represents repeated multiplication of the same number whereas exponent is the quantity that represents the power to which the number is raised.

1) The expression ⁴√x³ can be expressed as;

[tex]x^{\frac{3}{4} }[/tex]

2)The expression ¹/x⁻¹.

This is expressed as a single rational exponent as x

3) The given expression as a single rational exponent.

The expression is; ¹⁰√(x⁵ · x⁴ · x²)

¹⁰√(x¹¹) = [tex]x^{(11/10)}[/tex]

4) [tex]x^{(1/3)} * x^{(1/3)} * x^{(1/3)}[/tex]

x¹ = x

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Answer:

The expression with a single rational exponent as follows

What is exponents and powers?

Exponents are often known as powers or indices. In simple terms, power can be defined as an expression that represents repeated multiplication of the same number whereas exponent is the quantity that represents the power to which the number is raised.

1) The expression ⁴√x³ can be expressed as;

x^{\frac{3}{4} }x

4

3

2)The expression ¹/x⁻¹.

This is expressed as a single rational exponent as x

3) The given expression as a single rational exponent.

The expression is; ¹⁰√(x⁵ · x⁴ · x²)

¹⁰√(x¹¹) = x^{(11/10)}x

(11/10)

4) x^{(1/3)} * x^{(1/3)} * x^{(1/3)}x

(1/3)

∗x

(1/3)

∗x

(1/3)

x¹ =11

Step-by-step explanation:

Here in the given figure b and 30° are alternate to each other so it can be name as alternative angle....

b = 30°

Now...

a + 30° = 180° ( being supplementary angle )

a = 180° - 30°

a = 150°

Now the value of c will be 150° being corresponding

angle with a

c = 150°

z = 60° ( being alternative angle )

Now let's find the value of x.....

here ,

60° + 50° + x = 180° ( the sum of interior angle of triangle is 180°

x = 180° - 110°

x = 70°

Now...

y = 70° ( alternative angle )

[tex]....[/tex]

Using proportions, considering the amount she received from each person, it is found that Annie had 30 sweets originally.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, we have that:

The final amount was of 63, hence:

1.4 x 1.5 x n = 63

n = 63/(1.4 x 1.5)

n = 30.

Annie had 30 sweets originally.

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Answer:

1. Center: (-4,3) Radius: 4

2. C

3. C (x^2 + (y+4)^2 = 16)

4. 50 miles

Step-by-step explanation:

1. Look up how to read equations of circles

2.Soh Cah Toa

3. equations of circles again

4. Pythagorean Theorem

The correct option is option B.

The common difference between given data is -3/4.

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Here, given points;

                            x₁ = 1 , x₂ = 2 and y₁ = -3.75 , y₂ = -4.5

Now,

    d = (y₂ - y₁)/(x₂-x₁)

    d = (-4.5 - (-3.75))/(2 - 1)

     d = -0.75 / 1

     d = - 75/100

      d = -3/4

Thus, The correct option is option B.  The common difference between given data is -3/4.

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Answer:

12:11

Step-by-step explanation

Answer:

I think it would be 12:11

Step-by-step explanation:

This is because you can't down size the 11

Answer:

(x+3)^2 + (y-12)^2 =root 5

Step-by-step explanation:

Assumming you meant equation of the circle with center ()

Answer:

Area = 63ft

Step-by-step explanation:

7*9=63

multiply the base and height

157.5 square feet is the area of the roof.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that the roof of a clock tower is a pentagonal pyramid.

a pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point

Each side of the base is 7 ft long.

The slant height is 9 ft.

We need to find the  area of the roof.

Area=1/2×7×9×5

=315/2

=157.5

Hence, 157.5 square feet is the area of the roof.

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Answer:

Radius = 3

Circumference = 18.84

Step-by-step explanation:

A = πr²

28.26 = 3.14r²

√9 = √r²

3 = r

C = 2πr

C = (2)(3.14)(3)

C = 18.84

The expression is rewritten in standard form and they are not the same due to the negative.

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

Both (x−3)(x+3) and (3−x)(3+x) contain a sum and a difference and have only 3 and x in each factor.

Let see the equation formed by the factor;

(x−3)(x+3)

= x^2 + 3x - 3x - 9

= x^2 - 9

(3−x)(3+x)

= 9 + 3x - 3x - x^2

= 9 - x^2

The expression is rewritten in standard form and they are not the same due to the negative.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

here,

principal (p)=£6000

Rate (R)=. 3.4%

time (t)=3 yrs

now,

total investment is compound amount i.e CA

here,

[tex]CA = p(1 + \frac{r}{100} ) ^{t} [/tex]

=£6000(1+3.4/100)^3

=£6633.044

here he will get his total investment as £6633.044 in compound interest of 3.4%