compare 6.51326 and the square root of 39. (show work)

Final answer:

The statement is B. sometimes true. Two polygons are similar if their corresponding angles are equal and their corresponding sides are in proportion. However, it is possible for two polygons to have equal angles and not be similar if their sides are not in proportion.

Explanation:

The statement that if two angles of one polygon are equal to two angles of a second polygon then the two polygons are similar is sometimes true.

Two polygons are similar if their corresponding angles are equal and their corresponding sides are in proportion. Therefore, if two angles of one polygon are equal to two angles of a second polygon, it is possible that the polygons are similar, but it is not always the case.

For example, consider two rectangles. Both rectangles have two pairs of equal angles, but they may not be similar if their sides are not in proportion.

Answer:

a

Step-by-step explanation:

The algebraic expression for the word phrase 40% of x is 0.40x.

The algebraic expression for the word phrase 40% of x is 0.40x. To find 40% of x, you multiply x by 0.40. This means that 40% of x is equal to 0.40 times x.

Final answer:

To write an algebraic expression for the phrase '40% of x', multiply x by 0.40, resulting in the expression 0.40x.

Explanation:

The student is asking to write an algebraic expression for the phrase 40% of x. To convert this phrase into an algebraic expression, we take into account that "of" typically means multiplication in mathematics, and we know that 40% can be written as 0.40. Therefore, the algebraic expression for 40% of x is 0.40 * x or 0.40x.

Answer: The value of c must be 36 to make it perfect square trinomial.

Explanation:

A standard perfect square trinomial is [tex]x^2+2ax+a^2=(x+a)^2[/tex] where [tex]a^2[/tex] is the constant term.

Given trinomial [tex]x^2-12x+c=x^2+2(-6)a+c[/tex]

On comparing with standard perfect square trinomial we get a=-6

Therefore the constant term c=[tex]a^2=(-6)^2=36[/tex]

Such that the trinomial becomes [tex]x^2-12x+36=x^2+2(-6)x+(-6)^2=(x-6)^2[/tex] a perfect square trinomial.

Hence the value of c for the given trinomial must be 36 to make it perfect square trinomial.

The equation in vertex form is given as:

y = a (x - h) ² + k where a, h, and k are constant.

The equation y = 3x² - 12x + 11 in vertex form is  y = 3(x - 2)² + 7.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The equation in vertex form is given as:

y = a (x - h) ² + k where a, h, and k are constant.

We have,

y = 3x² - 12x + 11

3x² - 12x can be written as:

Taking out common value.

3(x² - 4x).

Now,

y = 3(x² - 4x)  + 11 _____(A)

x² - 4x can be written as:

Squaring we get,

= x² - 2.2x + 2² - 2²

= (x² - 2.2x + 4) - 4

[ (a - b)² = a² - 2ab + b ]

= (x - 2)² - 4 ________(B)

Now,

From (A) and (B) we get,

y = 3 (x - 2)² - 4 + 11

y = 3(x - 2)² + 7

Thus,

The equation y = 3x² - 12x + 11 in vertex form is  y = 3(x - 2)² + 7.

Learn more about equations here:

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Answer:

Option B. $170.10

Step-by-step explanation:

Gail bought groceries worth = $165.00

She gets rebate of taxes on the amount = $80.00

She has to pay tax on = 165 - 80 = $85.00

In her state sales tax are = 6%

So her tax on groceries  = 6% of 85 = 0.06 × 85 = $5.10

Now she paid total amount = 165 + 5.10 = $170.10

Gail paid $170.10 for the groceries, including sale tax

Option B. $170.10

12 days

12X24= 288 HRS

288X60=17280 MINS

17280X60=1036800 SECONDS

690-6 = 684

690+6 = 696

 the answer is A

Answer:

[tex]x=4[/tex]

Step-by-step explanation:

We have been given an image of two right triangles and we asked to find the value of x.

First of all , we will find the length of segment RT using sine.

[tex]\text{Sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

Upon substituting our given values in above formula we will get,

[tex]\text{Sin}(60^{\circ})=\frac{2\sqrt{3}}{RT}[/tex]

[tex]RT=\frac{2\sqrt{3}}{\text{Sin}(60^{\circ})}[/tex]

[tex]RT=\frac{2\sqrt{3}}{\frac{\sqrt{3}}{2}}[/tex]

[tex]RT=\frac{2\sqrt{3}}{\sqrt{3}}\times 2[/tex]

[tex]RT=2\times 2[/tex]

[tex]RT=4[/tex]

Now we know that length of segment RT and angle QRT of triangle QRT, so we will use tangent to find the length of segment QR (x) as:

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

[tex]\text{tan}(45^{\circ})=\frac{x}{4}[/tex]

Multiplying both sides of our equation by 4 we will get,

[tex]\text{tan}(45^{\circ})*4=\frac{x}{4}*4[/tex]

[tex]\text{tan}(45^{\circ})*4=x[/tex]

Substituting [tex]\text{tan}(45^{\circ})=1[/tex] we will get,

[tex]1*4=x[/tex]

[tex]4=x[/tex]

Therefore, the value of x is 4 units.

Final answer:

To find the value of 10 times the big number minus 6 times the small number, we need to solve a system of equations. The solution to the system is x = 2 and y = 11, so the value of 10y - 6x is 98.

Explanation:

To find the value of 10 times the big number minus 6 times the small number, we need to solve the system of equations:

4x + 3y = 41 (equation 1)

2x + y = 15 (equation 2)

We can first solve equation 2 for y by subtracting 2x from both sides: y = 15 - 2x. Now we can substitute this value of y into equation 1:

4x + 3(15 - 2x) = 41

Simplifying, we get: 4x + 45 - 6x = 41

Combining like terms, we have: -2x + 45 = 41

Subtracting 45 from both sides, we get: -2x = -4

Dividing both sides by -2, we get: x = 2

Now we can substitute this value of x back into equation 2 to solve for y:

2(2) + y = 15

Simplifying, we get: 4 + y = 15

Subtracting 4 from both sides, we get: y = 11

Finally, we can calculate 10 times the big number minus 6 times the small number:

10y - 6x = 10(11) - 6(2) = 110 - 12 = 98