what is this expression in simplified form?

Answer: he drives 273 miles for 7 hours

Step-by-step explanation:

The angle of depression is 35 degree in the right angle triangle if the angle BAC is 55 degree.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have shown a right-angle triangle in the picture.

In the right angle triangle, ABC

The angle BAC = 55 degree

Angle BAA' = 90 degree

In the figure, the angle of depression = CAA'

= BAA' - BAC

= 90 - 55

= 35 degree

Thus, the angle of depression is 35 degree in the right angle triangle if the angle BAC is 55 degree.

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The solution of the given radical expression√20 using factorization is [tex]2 \sqrt{5}[/tex]. Therefore, the correct option for the  radical expression√20 is option A, i.e  [tex]2 \sqrt{5}[/tex].

A collection of constants, variables or numbers connected using one or more arithmetic operator is called an expression.

Example = 4y, 3x+4.

An expression containing the values in the form of square root, cube root is called a radical expression.

The breaking of a number into its own factors, so that they multiply to give the same number again, is called factorization.

Given expression, √20

The solution of the expression can be obtained by the factors of 20.

[tex]\sqrt{20} = \sqrt{2\times2\times5}[/tex]

[tex]\sqrt{20}[/tex] = [tex]2 \sqrt{5}[/tex]

Here, 2 and 5 are factors of 20.

Thus, the value of the radical expression [tex]\sqrt{20}[/tex]  is [tex]2 \sqrt{5}[/tex].

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Answer:

y=5+14=19

Step-by-step explanation:

Y=5+14=19 this is the right answers

Based on the definition of sequence and the characteristics of the given sequence, the complete sequence is: 4, 543, 65432, 7654321, 876543210.

Sequences are sets whose elements observes at least a condition. In this question we have a sequence formed by numbers formed by decimal digits ordered in descent way. Where the consecutive element has more digits than the previous one.

Then, we conclude that the complete sequence is: 4, 543, 65432, 7654321, 876543210.

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In trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).

" Trapezoid is defined as the quadrilateral whose one pair of opposite side is parallel."

According to the question,

Given

Length of AE=5.2

Length of  AC=11.7

Length of  CD=10.5

As shown in figure

In trapezoid ABCD,

AB is parallel to CD, AC is the transversal.

AC and BD intersect at point E.

In ΔABE and ΔCDE,

∠BAE ≅∠ECD

∠ABE ≅∠EDC

By AA theorem,

ΔABE ~ ΔCDE

Therefore,

[tex]\frac{AE}{EC}=\frac{AB}{CD}[/tex]

  AE + EC = AC

⇒ 5.2 + EC = 11.7

⇒ EC = 11.7 - 5.2

⇒ EC = 6.5units

Substitute the value in the given proportion we get,

   [tex]\frac{5.2}{6.5}=\frac{AB}{10.5}[/tex]

⇒ [tex]AB = \frac{(10.5)(5.2)}{6.5}[/tex]

⇒[tex]AB = 8.4[/tex] units

Hence, in trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).

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Answer:

40[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

V = L × W × H

V = 1.5 × 6 × 4.5

V = 40.5 or 40[tex]\frac{1}{2}[/tex]

Answer:

40 1/2ft

Step-by-step explanation:

H(4 1/2 )x W(1 1/2) = 6.75

HW(6.75)x L(6) = 40.5

Answer:

Step-by-step explanation:

Answer: [tex]h=\frac{23}{10} =2.300[/tex]

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

[tex]h+\frac{4}{-2} -((\frac{3}{10} ))=0[/tex]

[tex]Simplify~ \frac{3}{10}[/tex]

[tex](h+\frac{4}{-2} )-\frac{3}{10} =0[/tex]

Subtracting a fraction from a whole

Rewrite the whole as a fraction using  10  as the denominator :

[tex]h-2=\frac{h-2}{1} =\frac{h-2x10}{10}[/tex]

Equivalent fraction: The fraction thus generated looks different but has the same value as the whole

Common denominator: The equivalent fraction and the other fraction involved in the calculation share the same denominator

  Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to the lowest terms if possible:

[tex]\frac{(h-2)x10-(3)}{10} =\frac{10h-23}{10}[/tex]

[tex]\frac{10h-23}{10} =0[/tex]

When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, CalderonJ multiplys both sides of the equation by the denominator.

Here's how:

[tex]\frac{10h-23}{10} *10=0*10[/tex]

Now, on the left hand side, the  10  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  10h-23  = 0

Add  23  to both sides of the equation :

                     10h = 23

Divide both sides of the equation by 10:

                    h = 23/10 = 2.300

Final Answer: 2.3(decimal form) aka 23/10 (fraction)

Answer:

See below ~

Step-by-step explanation:

Applying section formula :

⇒ x = 1(14) + 2(2) / 1 + 2 = 18/3 = 6

⇒ y = 1(14) + 2(2) / 1 + 2 = 18/3 = 6

We understand after substituting the values of the endpoints in the section formula that the Point X divides the line in the ratio 1 : 2.

The conclusion that can be drawn from this graph on the long-run frequency of 100 rolls is The long-run frequency of rolling a 3 appears to be about 0.17.

At the 0.17 probability, the proportion of 3s calculated levels off from around the 40th roll to the 100th roll.

This means that the long-run frequency of rolling a 3 is around 0.17 because this was the probability seen for most of the rolls over time.

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Answer:

Step-by-step explanation:

The matrix of coefficients has one row corresponding to each equation. The constants in that row are the coefficients of the variables in the equation. Coefficients are listed in the same order on each row. A missing term is represented by a coefficient of 0.

The first attachment shows the coefficient matrix and its determinant.

__

The solution to the system of equations can be found by left-multiplying the constant vector by the inverse of the coefficient matrix.

  [tex]\textbf{A$\cdot$X}=\textbf{B}\\\\\textbf{X}=\textbf{A}^{-1}\cdot\textbf{B}[/tex]

This multiplication is shown in the second attachment. It tells us ...

  [tex]\textbf{X}=\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}3\\4\\1\end{array}\right][/tex]

Answer:

0.1

Step-by-step explanation:

You are adding on 0.1 for each line and since G is the first line after 0, it is 0.1.

Step-by-step explanation:

0.75x + 0.8(x + 10) = 101

0.75x + 0.8x + 8 = 101

1.55x = 101 - 8

1.55x = 93

x = 93 ÷ 1.55

x = 60

The equation that has infinitely many solutions is A. 4x + 5(2x + 6) = 14x + 30

An equation with infinitely many solutions is represented as:

ax + b = ax + b

This means that both sides of the equation must be the same.

Next, we test the options:

4x + 5(2x + 6) = 14x + 30

Open the bracket

4x + 10x + 30 = 14x + 30

Evaluate the like terms

14x + 30 = 14x + 30

Both sides of the equation must be the same.

Hence, the equation that has infinitely many solutions is A. 4x + 5(2x + 6) = 14x + 30

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Answer:

Step-by-step explanation:

Comment

It is not possible to figure out what choices are are given for the first blank. I will say that the probable choice has the word product in it.

The second blank is the actual number of choices. It is 3 page count times color or 3*4 = 12 different choices.

Answer

product

12

Answer:

Angles of the isosceles triangle are 36°, 72° , 72°

Step-by-step explanation:

Vertex angle : Base angle = 1 : 2

Vertex angle = x

Base angle = 2x

Sum of all angles of a triangle = 180°

          x + 2x + 2x = 180°

                      5x = 180

                        x = 180 ÷ 5

                        x = 36°

2x = 2 *36 = 72°

Angles of the isosceles triangle are 36°, 72° , 72°

Answer:

2/8, 3/12 and 4/16

Step-by-step explaination:

All these fractions are equivalent to 1/4 as the numerator is a multiple of 1, the denominator is a multiple of 4, and the numerators are all a quarter of their respective denominators.

Answer:

[tex]2x+16y[/tex]

Add  [tex]12y[/tex] and [tex]4y[/tex].

[tex]2x+16y[/tex]

Answer:

2x + 16y

Step-by-step explanation:

The y terms can be added together. 12y + 4y is 16y. The 2x has to just stay the way it is because it could only be added to another x term and there aren't any. So you are left with 2x + 16y

Answer:

7

Step-by-step explanation:

The answers to the options are:

This inequality is known tp imply that the normal body temperature is taken (subtracted) from the minimum and maximum body temperature.

Note that in case A, the The inequality that represent the temperatures  is less than sign.

In case b, it is an open interval because it means that in -40°F to -140°F , it is not equal to as that is the reason that  the gas cannot stay liquid.

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Answer:

n+3-(5n+6)=0

n+3-5n-6=0

5n-n=6-3

4n=3

4n/4=3/4

n=3/4

The angle the longer chain makes with the ceiling is 38.5°

The two chains and ceiling form a triangle and with two sides and an angle, we use the sine rule to find the other angle

The sine rule states in any triangle with sides a, b, c and angles A, B and C, repsectively, we have that

a/sinA = b/sinB = c/sinC

Since one chain is 46cm long and forms an angle of 60° with the ceiling. the other chain 64cm long. So, we find the other angle.

So, a/sinA = b/sinB  where

Making A subject of the formula, we have

A = sin⁻¹(asinB/b)

So, substituting the values of the variables into the equation, we have

A = sin⁻¹(asinB/b)

A = sin⁻¹(46 cm × sin60/64 cm)

A = sin⁻¹(46 cm × 0.8660/64 cm)

A = sin⁻¹(39.84 cm/64 cm)

A = sin⁻¹(0.6225)

A = 38.49°

A ≅ 38.5°

So, the angle the longer chain makes with the ceiling is 38.5°

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Answer:

1814400

Step-by-step explanation:

Answer:

[tex]\dfrac{\sqrt[12]{55296} }{2}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies \dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}=\dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}}[/tex]

Multiply the numerator and denominator by [tex]2^{\frac{2}{3}}[/tex] :

[tex]\implies \dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}} \times \dfrac{2^{\frac{2}{3}}}{2^{\frac{2}{3}}}[/tex]

[tex]\textsf{Apply exponent rule to the denominator} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies \dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}} \times \dfrac{2^{\frac{2}{3}}}{2^{\frac{2}{3}}}=\dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2^{\frac{1}{3}+\frac{2}{3}}}=\dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2}[/tex]

Rewrite 1/4 as 3/12 and 2/3 as 8/12 :

[tex]\implies \dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2}=\dfrac{6^{\frac{3}{12}} \cdot 2^{\frac{8}{12}}}{2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^c \cdot b^c=(a \cdot b)^c:[/tex]

[tex]\implies \dfrac{6^{\frac{3}{12}} \cdot 2^{\frac{8}{12}}}{2}=\dfrac{(6^3 \cdot 2^{8})^\frac{1}{12}}{2}[/tex]

Simplify the operation in the parentheses:

[tex]\implies \dfrac{(6^3 \cdot 2^{8})^\frac{1}{12}}{2}=\dfrac{(216\cdot 256)^\frac{1}{12}}{2}=\dfrac{(55296)^\frac{1}{12}}{2}[/tex]

[tex]\textsf{Finally, apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]

[tex]\implies \dfrac{(55296)^\frac{1}{12}}{2}=\dfrac{\sqrt[12]{55296} }{2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6^{\dfrac{1}{4}}}{2^{\dfrac{1}{3}}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2^{\dfrac{1}{4}}3^{\dfrac{1}{4}}}{2^{\dfrac{1}{3}}}[/tex]

[tex]\\ \rm\Rrightarrow 2^{\dfrac{1}{4}-\dfrac{1}{3}}3^{\dfrac{1}{4}}[/tex]

[tex]\\ \rm\Rrightarrow 2^{\dfrac{-1}{12}}3^{\dfrac{1}{4}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{3^{\dfrac{1}{4}}}{2^{\dfrac{1}{12}}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{3^{\dfrac{3}{12}}}{2^{\dfrac{1}{12}}}[/tex]

[tex]\\ \rm\Rrightarrow \left(\dfrac{3^3}{2}\right)^{\dfrac{1}{12}}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt[12]{\dfrac{3^3}{2}}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt[12]{\dfrac{3^3\times 2^82^3}{22^82^3}}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt[12]{\dfrac{27(256)(8)}{2^12}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{\sqrt[12]{6912(8)}}{2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{\sqrt[12]{55296}}{2}[/tex]

Answer:

The choice A.

[tex]y > \frac{3}{2} x + 2[/tex]

The formula for calculating the height is h = 3V/πr²

The formula given is the formula for calculating the volume of a cone

V = 1/3πr²h

where

h is the height

r is the radius

Make h the subject of the formula

Cross multiply

3V = πr²h

Divide both sides by πr²

3V/πr² = πr²h/πr²

h = 3V/πr²

Hence the formula for calculating the height is h = 3V/πr²

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The system of linear equations that best represents the situation are:

z+y=18

3z +2y=44

In order to determine the values of the two types of cheese, two set of linear equations can be formed from the question. The equations have to be solved together using either the elimination , substitution or graphical methods.

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Answer:

a-x=y+25

b-35 minutes

c-nort possible

Step-by-step explanation:

can't explain due to the fact it will take 30m to type up

The attached image represents the interval 2 < x ≤ 9 on the number line

The interval is given as:

2 < x ≤ 9

The above interval means that:

In inequality, the < symbol uses an open circle, while the ≤ uses a closed circle

Next, we highlight the interval using the above rules (see attachment)

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