Two boats, originally 35 km apart, sail toward each other. The
first goes at a speed of 8.5 kph. The second goes at a speed of
5.5 kph. How long until they meet? Hint: your answer will be a
decimal.

Answer:

a = 9

Step-by-step explanation:

Step 1: Add 3 to both sides

2a – 3 = 15

2a – 3 + 3 = 15 + 3

Step 2: Simplify

add the numbers ( 2a = 18 )

Step 3: Divide both sides by the same factor

2a = 18

2a 18

––– = –––

2 2

Step 4: Simplify

l

Cancel the terms that are in both the numerator and the denominator

l

l

Divide the numbers

l

a = 9

Answer: a = 9

The total walking distance of the week is 12.1 km.

So, let the total walking distance be 'x'.

Then,

Therefore, the total distance of walking in the week is 12.1 km.

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Answer:

-4

Step-by-step explanation:

-12+3(-8+(-4)^2-6)+2

first the -4^2

-12+3(-8+16-6)+22

now everything in the parenthesis

-12+3x2+2

now the multiplying.

-12+6+2

now calculate this all together.

-4

Triangle ABC with coordinates A (2, 4),

B (3, 6), and C (5, 1) is translated

4 units horizontally is (6,4), (7,6) ,( 1,9)

A triangle is a basic polygon with three sides and three internal angles. It is one of the fundamental shapes in geometry in which the three vertices are connected together, and it is represented by the symbol. Triangles are categorized into many sorts based on their sides and angles. All geometrical shapes have unique qualities relating to sides and angles that aid in their identification. The following are some of the most important qualities of a triangle.

There are three sides, three vertices, and three internal angles in a triangle.

The angle sum property of a triangle asserts that the sum of a triangle's three internal angles is always 180°. Consider the triangle PQR shown above .

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The expression is equivalent to quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power is  [tex]z^{-18}.y^{18}[/tex] .

The given expression is [tex](\frac{y^{-3}.z^5}{z^{-4.y^6}} )^{-2}[/tex]

Let us take the numerator terms to denominator.

When shifting numerator terms to denominator the sign of the power will be changed.

[tex](\frac{1}{z^{-4.y^6.y^{3}.z^{-5}}} )^{-2}[/tex]

Combine like terms in denominator:

[tex](\frac{1}{z^{-9}.y^9} )^{-2}[/tex]

[tex](z^9.y^{-9})^{-2}[/tex]

[tex]z^{-18}.y^{18}[/tex]

Hence, [tex]z^{-18}.y^{18}[/tex]  is equivalent to quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power.

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Answer:

The two smaller angles equal 24 and together they equal 48

Step-by-step explanation:

The bisector tells us that the smaller angles equal each other

3x + 6 = 7x - 18  Subtract 3x from both sides

6 = 4x - 18  Add 18 to both sides

24 = 4x  Divide both sides by 4

6 = x

Now, plug 6 back into each equation.

3x + 6

3(6) + 6

18 + 6

24

7x - 18

7(6) - 18

42 - 18

24

Answer:

B store is cheaper since 790.56<823

B price<A price

Step-by-step explanation:

A:

549(0.5)=274

264+549=823

Josh need to pay the refrigerator for $823 in this store without tax.

B:

549(0.6)= 329.4

329.4+549=878.4

878.4(09)=790.56

Josh need to pay $790.56 in this store without the tax.

C:

B, department store is cheaper so he could pay less

The inverse of the fuction y=2x³+10 is y = [tex]\sqrt[3]{\frac{x-10}{2} }[/tex].

So,

All we have to do to find the inverse of an equation is switch the variables x and y.

Now, solve for y as follows:

Therefore,  the inverse of the fuction y=2x³+10 is y = [tex]\sqrt[3]{\frac{x-10}{2} }[/tex].

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After dividing and simplifying the expression 4√162 x⁴ / 4√2 y⁸, we get the result as 9 x ² / y⁴.

We are given the expression

4√162 x⁴ / 4√2 y⁸

We need to divide the expression and simplify it.

First, cancelling the terms that are same in the numerator and the denominator:

√162 x⁴ / √2 y⁸

Now , using the properties of the exponents, we get that:

= √81 x² / y⁴

= 9 x ² / y⁴

Therefore, after dividing and simplifying the expression 4√162 x⁴ / 4√2 y⁸, we get the result as 9 x ² / y⁴.

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The missing step 7 in the two column proof is; Consecutive ∠s in a ▱ are supplementary

We are told that WXYZ is a parallelogram in which  we have to prove that: WXYZ is a rectangle. The two column proof is as follows;

           Statement                                              Reason

1. WXYZ is a parallelogram,                 1. Given

    ZX ≅WY

2.  ZY ≅ WX                                           2. Opposite sides of parallelogram

                                                                 are congruent.

3.  YX≅YX                                            3. Reflexive property of congruence

4. ΔZYX ≅ Δ WXY                             4.  SSS congruence postulate

5.  ∠ZYX ≅ ∠WXY                                 5. CPCTC

6. m∠ZYX ≅ m∠WXY                            6. definition of congruence.

7.m∠ZYX + m∠WXY = 180°                   7. Consecutive ∠s in a ▱ are

                                                                   supplementary

8.m∠ZYX + m∠ZYX = 180°                    8. By substitution

9. 2(m∠ZYX) = 180°                                9. By simplification

10.m∠ZYX = 90°                                     10. Division property of equality

11. WXYZ is a rectangle                       11. Rectangle angle theorem.

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Answer:

A) y =  2.91x + 64.61 with x hours after 6:00 am

B) at 2:00pm, temperature is 87.89°

Step-by-step explanation:

(>>Regression Equation y = bx + a )With b- Sum of products/Sum of Square = sq/SSx. a = My- bMx,)

set 6.00 am is an original time, when x = 0

use the unit: hour to get a new table

X time 0, 0.75, 1.5, 2.5, 3, 3.75, 4.5, 5

Y temp 65°, 67", 68° ,72° ,74", 75° ,77° ,78°

a). with temperature y and x hour after 6:00 am,

can get Sum of x = 21 Mx = 2.63

Sum of - 578 My = 72.25

SSx = Sum of (X-Mx)² = 22.25

= sum of (X-Mx)(}-My)= 64.75

So b= sq/SSx =64.75/22.25 = 2.91

a= My- bMx = 72.25 - 291 x 2.63 = 64.61

So regressing equation Y= 2.91x + 64.61

b). at 02:00 pm , means 8 hours after 6:00 am

meaning X-8, )= 2.91×8 + 64.61 = 87.8)

The required equation of regression is y = 2.91x + 64.6 and at 2.00 pm temperature is 87.8°

Given that,
The table shows the recorded temperature on a certain day starting at 6:00 am.

The equation is the relationship between variables and is represented as y =ax +b is an example of a polynomial equation.

Here,
The standard form of the regression equation,
y = bx + a,
where b = sum of product/sum of squares a = My - bMx
Since
b = 2.91 , My = 72.25, Mx = 2.63
a = 72.25 - 2.91 * 2.63
a = 64.6
The required regression equation is,
y = 2.91x + 64.6

B)
For 2.00 PM, x = 8
Now,
y = 2.91 * 8 + 64.6
y = 87.8°

Thus, the required equation of regression is y = 2.91x + 64.6 and at 2.00 pm temperature is 87.8°

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Answer:

∠ GRS = 74°

Step-by-step explanation:

∠ GRS + ∠ QRG = ∠ QRS , that is

∠ GRS + 105° = 179° ( subtract 105° from both sides )

∠ GRS = 74°

Answer:

75°

Step-by-step explanation:

While it may appear that QRS is a straight line, it is not so since m∠QRS = 179° and if it was a straight line, it would be 180°

The figure actually represents three rays with endpoint at R

The three rays are RQ, RS and RG

Draw another ray RT with endpoint at R and opposite to ray RG. Opposite rays have angles that add up to 180°

Therefore m∠GRT = 180°

m∠SRT = m∠QRG since they are opposite angles

Since m∠QRG = 105°, therefore m∠SRT = 105°

m∠GRS + m∠SRT=180° since these angles are formed by two opposite rays

Substituting we get
m∠GRS + 105 = 180

m∠GRS = 180-105 = 75°

Answer:

2/375

Step-by-step explanation:

We can multiply 8/15 by 1/100 to get

[tex]\frac{8}{15} *\frac{1}{100}=\frac{8}{1500}[/tex]

Now we simplify this fraction into simplest form.

2/375

Answer:

1 1/2+4/5 and the vertical would be graphed?

Answer:

The graph of g(x) = -|x| - 8.

Answer:

212.

Step-by-step explanation:

Given: 3m^2 + 2p^2 - 15

When m = 3 and p = 10

Substituting the values

= 3(3)^2 + 2(10)^2 - 15

By further calculation

= 3(9) + 2(100) - 15

So we get

= 27 + 200 - 15

= 212

Therefore, the value of the expression is 212.

The value of x for the equation log₈2=x is 0.333

Logarithmic function properties. You have encountered several characteristics during your study of algebra, including the commutative, associative, and distributive properties. These characteristics make it easier to simplify a complex statement or equation. With logarithms, the same holds true.

Given,

log₈2=x

It can be expressed in the form -

2 = 8ˣ

2 =  2³ˣ

As base is same -

1 = 3x

x = 1/3

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The equation which models the number of calculators packed by the machine in certain minutes is x = 2.5y

No. of calculators packed after 10 minutes = 25 calculators

No. of calculators packed after 30 minutes = 75 calculators

Using the unitary method for finding calculators packed in a minute,

10 minutes = 25 calculators

1 min = 25/10 = 2.5 calculators

Let x be the number of minutes the machine is running

Let y be the number of calculators packed

Formulation of the equation we get:

x = 2.5y

Hence, the equation which gives the number of calculators packed after certain minutes is given by: x = 2.5y

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The number that should fill in the blank is 10. Therefore, the complete equation is 0.05 × x = 0.5.

Given that, 0.05 × ----- = 0.5.

To multiply decimals, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.

Let the number should fill in the blank be x.

So, 0.05 × x = 0.5

⇒ x = 0.5/0.05

⇒ x = 10

The number that should fill in the blank is 10. Therefore, the complete equation is 0.05 × x = 0.5.

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The factoring of the expression 4 x²=-8 x+5 is (2x-1) (2x+5)

By ordering the values, we get:

4 x² + 8 x - 5

To solve this exercise, we have to follow the rules of factoring:

1. Factor 8 from 8x:

4 x² + 8 x - 5

4 x² + (-2 + 10) x - 5

2. Apply the distributive property:

4 x² - 2x + 10x - 5

3. Groups the first two terms and the last two terms:

(4 x² - 2x) + 10x - 5

4. Factorize the greatest common denominator (GCM) of each group:

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

5. Factor the polynomial by factoring the greatest common denominator, (2x-1):

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

Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.

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Answer:

10000

Step-by-step explanation:

Answer:

[tex]x = 17[/tex].

Step-by-step explanation:

Simplify the given equation:

[tex]2\, (x - 1)^{3/4} = 16[/tex].

[tex](x - 1)^{3/4} = 8[/tex].

[tex]((x - 1)^{1/4})^{3} = 8[/tex].

Take the cubic root of both sides to eliminate the numerator of the exponent. Only roots of even degree could introduce alternative solutions. Since the degree of this root is an odd number, this step would not create extraneous solutions.

[tex]\sqrt[3]{((x - 1)^{1/4})^{3}} = \sqrt[3]{8}[/tex].

[tex](x - 1)^{1/4} = 2[/tex].

Raise both sides to the fourth power to eliminate the denominator of the exponent:

[tex](x - 1) = 2^{4}[/tex].

[tex]x - 1 = 16[/tex].

[tex]x = 17[/tex].

Substitute the solution [tex]x = 17[/tex] into the equation:

[tex]\begin{aligned}& 2\, (17 - 1)^{3/4} \\ =\; & 2\times (16^{1/4})^{3} \\ =\; & 2 \times 2^{3} \\ =\; & 16\end{aligned}[/tex].

Thus, [tex]x = 17[/tex] isn't an extraneous solution since setting [tex]x[/tex] to [tex]17[/tex] satisfies the original equation.

Answer:

arccos(51/100)

Step-by-step explanation:

By the Law of Cosines,

[tex]a^2 = b^2 + c^2 - 2bc \cos A \\ \\ a^2 - b^2 - c^2=-2bc \cos A \\ \\ \cos A=\frac{b^2 + c^2 - a^2}{2bc} \\ \\ m\angle A=\arccos \left(\frac{b^2 + c^2 - a^2}{2bc} \right) \\ \\ =\arccos \left(\frac{10^2 + 5^2 - 8^2}{2(5)(10)} \right) \\ \\ =\arccos(51/100)[/tex]

Danladi says that it cannot be rewritten as either of these expressions. He is correct.

It should be noted that 2³ × 42 will be:

= 2³ × 42

= 8 × 42

= 336

Therefore, Zoe says that 2³.42 can be rewritten as 86 and Juana says that it can be rewritten as.85. They're both wrong.

In the other hand, Danladi says that it cannot be rewritten as either of these expressions. Therefore, he is correct.

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Answer: electronics worth $1,650

1500 (1+5%)^2 = $1653.75

3.75 dollars will be left over.

Step-by-step explanation:

We get that, for the equation 2 x + 2 y = 8, when we solve for y, we get the result as y = 4 - x.

We are given an equation:

2 x + 2 y = 8

Divide both the sides by 2, we get that:

2 x / 2 + 2 y / 2 = 8 / 2

x + y = 4

Now, we will subtract x from both the sides, so, we get that:

x + y - x = 4 - x

y = 4 - x

Therefore, we get that, for the equation 2 x + 2 y = 8, when we solve for y, we get the result as y = 4 - x.

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Answer:

17x and 3x

Step-by-step explanation:

like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power.

Answer:

9ft by 9ft

Step-by-step explanation: