If y is directly proportional to x and y is 12 when x = 10, what is the constant of variation?

Answers

Answer 1

Answer:
constant of variation = 1.2

Explanation:
y varies directly with x means that as x increases, y increases and vice versa.
This can be translated into the following equation:
y = kx
where k is the constant of pvariation.

We are given that:
y = 12 when x = 10.
Therefore, we will substitute with these values in the above equation and solve for k as follows:
y = kx
12 = k * 10
k = 12 / 10
k = 1.2

This means that the equation relating x and y is:
y = 1.2x
where 1.2 is the constant of variation.

Hope this helps :)

Answer 2

Answer:constant of variation = 1.2

Step-by-step explanation:

Related Questions

Match each whole number with a rational exponential expression. HELPP ME PLEEASE FASTTT

Answers

1. 343^(2/3)
3rdrt[(343(343)]
49

2. [2,197^(1/3)]^2
[3rdrt(2,197)]^2
169

3. 729^(2/3)
3rdrt[729(729)]
81

4. (1,000^2)^(1/3)
3rdrt(1,000^2)
100

5. [3rdrt(9261)]^2
441

6. [3rdrt(216^2)]
36

Hope this helps!

Answer:

1. 49

2. 169

3. 81

4. 100

5. 441

6. 36

Step-by-step explanation:

1. [tex](343)^{\frac{2}{3}}=\sqrt[3]{(343)^{2} }[/tex]

= [tex]\sqrt[3]{(343)(343)}=\sqrt[3]{(7^{3})(7)^{3}}[/tex]

= 7×7 = 49

2. [tex](2197^{\frac{1}{3}})^{2}=(\sqrt[3]{2197})^{2}[/tex]

= [tex](\sqrt[3]{13^{3}})^{2}=13^{2}[/tex]

= 169

3. [tex]729^{\frac{2}{3} }=(\sqrt[3]{729})^{2}[/tex]

= [tex](\sqrt[3]{9^{3}})^{2} = 9^{2}[/tex]

= 81

4. [tex](1000^{2})^{\frac{1}{3}}=(\sqrt[3]{1000})^{2}[/tex]

= 10²

= 100

5. [tex](\sqrt[3]{9261})^{2}=(\sqrt[3]{(21)^{3} })^{2}[/tex]

= 21²

= 441

6. [tex](\sqrt[3]{216})^{2}=(\sqrt[3]{6^{3} })^{2}[/tex]

= 6²

= 36

Find the value of the missing side of a triangle practice

Answers

There are many formulas to finding a side of a triangle.

Be sure to understand the differences between a right-angled triangle and an irregular-shaped triangle.

Right-angled triangle
Two sides must be known.
[tex] {a}^{2} = {b}^{2} + {c}^{2} [/tex]
where 'a' squared is the hypotenuse of the triangle.

To find the non-hypotenuse side, the formula can be rearranged to
[tex] {b}^{2} = {a}^{2} - {c}^{2} [/tex]
'b' can be any non-hypotenuse side.

Non-right angled triangle.
Cosine rule
Two sides and an angle must be know.
[tex]a = {b}^{2} + {c }^{2} - 2ab \cos(angle \: facing \: a) [/tex]
That is just a few of the formulas I have listed.

table Mary used Delicious (d) and Golden Delicious (g) apples to make homemade applesauce. Delicious apples are $0.75 each and Golden Delicious apples are $1.25 each. Mary spent $21.00 on 22 apples. How many Golden Delicious apples did Mary buy?

Answers

1. To solve this problem, you must make a System of equations.

2. The equations are:

d+g=22 (i)
0.75d+1.25g=21 (ii)

3. If you clear "d" from the equation (i), you have:

d+g=22
d=22-g

4. Now, you must substitute d=22-g into the equation (ii):

0.75d+1.25g=21
0.75(22-g)+1.25g=21

5. When you clear "g", you obtain its value:

16.5-0.75+1.25g=21
16.5+0.5g=21
0.5g=21-16.5
g=4.5/0.5
g=9 Golden Delicious apples

6. If you also want to know the value of "d", you can substitute g=9 into the equation (i) and clear "d":

d+g=22
d+9=22
d=22-9
d=13 Delicious apples

How many Golden Delicious apples did Mary buy?

The answer is: Mary bought 9 Golden Delicious apples.

Tldr: The answer is 9

express the perimeter of the rectangle as a polynomial. help please.

Answers

7y-9+7y-9+10y+2+10y+2=34y-14

which or the following will happen if you miss a monthly credit card payment?

A)You will be charged a late fee.
B)You loose reward points
C)Your APR will increase the next month
D)Both A & B

Answers

The answer is A you will be charged a late fee

99 POINT QUESTION!!!!!
The prime factorization of a number is 2^3*3^2*5. Which is a true statement about the factors of the number?

Answers

2^3 = 8 and 3^2 = 9

so the number = 8 * 9 * 5 = 360

15 is a factor of 360, so the answer would be the first one: Fifteen is a factor of the number because both 3 and 5 are prime factors

2³ = 8
3² = 9

8 x 9 x 5 = 360
15 is a factor of 360, so the answer would be 1. Fifteen is a factor of the number because both 3 and 5 are prime factors

what is a possible value for the missing term of the geometric sequence ?
50, blank, 450, ..

a. 1,350
b. 150
c. 3
d. 53

Answers

50 * 3 = 150 and 150 * 3 = 450

So the answer is b 150

Which polynomial is a quintic trinomial?

x³ + 2x² -8x + 16
x² + 4
3x⁵ + 7x² -9x⁴
-x⁴ -5x² +1

Answers

Answer:

3x⁵ + 7x² -9x⁴

Step-by-step explanation:

In the order given, the polynomials have degrees 3, 2, 5, 4. The one of degree 5 is "quintic." That one also happens to be a trinomial. It is ...

3x⁵ + 7x² -9x⁴

what is the slope of the line through (2,-2) and (9,3)

Answers

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 2 &,& -2~) % (c,d) &&(~ 9 &,& 3~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-(-2)}{9-2}\implies \cfrac{3+2}{9-2}\implies \cfrac{5}{7}[/tex]

The prime factorization of a number is 2^3*3^2*5. Which is a true statement about the factors of the number?
1. Fifteen is a factor of the number because both 3 and 5 are prime factors.
2. Fifteen is not a factor of the number because 15 is odd and the number is even.
3. Sixteen is a factor for the number because 2^3=8 and 16 is divisible by 8.
4. Sixteen is not a factor of the number because the exponent of 2 is not even.

Answers

2^3 = 8
3^2 = 9

8 * 9 * 5 = 360
15 is a factor of 360, so the answer would be 1. Fifteen is a factor of the number because both 3 and 5 are prime factors

Fifteen is a factor of the number because both 3 and 5 are prime factors and this can be determined by using the arithmetic operations.

Given :

Number -- [tex]2^3\times 3^2\times 5[/tex]

The following steps can be used in order to determine the correct statement:

Step 1 - Write the given number.

[tex]2^3\times 3^2\times 5[/tex]

Step 2 - Simplify the above expression.

[tex]= 8\times 9 \times 5[/tex]

Step 3 - Multiply 8 by 9 in the above expression.

[tex]= 72\times 5[/tex]

Step 4 - Multiply 72 by 5 in the above expression.

= 360

Step 5 - 15 is a factor of 360.

Therefore, the correct option is 1).

For more information, refer to the link given below:

https://brainly.com/question/10454590

PLEASE HELP
7.03

1. Write the sum using summation notation, assuming the suggested pattern continues.
1 - 3 + 9 - 27 + ...

A) summation of one times three to the power of n from n equals zero to infinity
B) summation of one times three to the power of the quantity n plus one from n equals zero to infinity
C) summation of one times negative three to the power of n from n equals zero to infinity
D) summation of one times negative three to the power of the quantity n plus one from n equals zero to infinity

2. Write the sum using summation notation, assuming the suggested pattern continues.
-4 + 5 + 14 + 23 + ... + 131

A) summation of the quantity negative four plus nine n from n equals zero to fifteen
B) summation of negative thirty six times n from n equals zero to fifteen
C) summation of the quantity negative four plus nine n from n equals zero to infinity
D) summation of negative thirty six times n from n equals zero to infinity

3. Write the sum using summation notation, assuming the suggested pattern continues.
25 + 36 + 49 + 64 + ... + n2 + ...

A) summation of n squared from n equals five to infinity
B) summation of n minus one squared from n equals five to infinity
C) summation of n squared from n equals six to infinity
D) summation of n plus one squared from n equals five to infinity

4. Find the sum of the arithmetic sequence.
-1, 2, 5, 8, 11, 14, 17

A) 56
B) 63
C) -7
D) 20

5. Find the sum of the geometric sequence.
1, one divided by four, one divided by sixteen, one divided by sixty four, one divided by two hundred and fifty six

A) 341
B) one divided by one hundred and ninety two
C) one divided by seven hundred and sixty eight
D) three hundred and fourty one divided by two hundred and fifty six

6. Find the sum of the first 8 terms of the sequence. Show all work for full credit.
1, -3, -7, -11, ...

Answers

6.
1, -3, -7, -11, -15, -19, -23, -27...

sum:
8/2 (1 + -27)
8/2 (-26)
-104

This are 6 question and 6 answers

Problem 1. Write the sum using summation notation, assuming the suggested pattern continues.
1 - 3 + 9 - 27 + ...

Answer: option C) summation of one times negative three to the power of n from n equals zero to infinity

Explanation:

1) Sequence: 1 - 3 + 9 - 27: given

2) ratio of two consecutive terms:

- 3 / 1 = - 3

9 / (-3) = - 3

-27 / (9) = - 3

=> ratio = - 3 means that every term is the previous one multiplied by - 3

3) terms

First term: 1 * (-3)^0 = 1

Second term: 1* (-3)^1 = - 3

Third term: 1 * (-3)^2 = 9

Fourth term: 1 * (-3)^3 = - 27

So, the summation is:

∞
∑ 1 * (-3)^n ,
n=0

which is read summation of one times negative three to the power of n from n equals zero to infinity => option C.

Problem 2. Write the sum using summation notation, assuming the suggested pattern continues.

- 4 + 5 + 14 + 23 + ... + 131

Answer: option A) summation of the quantity negative four plus nine n from n equals zero to fifteen

Probe the statement A):

15
∑ (- 4 + 9n)
n=0

Now develop that summation: - 4 +9(0) - 4+ 9(1) - 4 + 9(2) - 4 + 9(3) +....+ - 4 + 9(15) = - 4 + 5 + 14 + 23 + 131

Which is the very same sequence given.Therefore, the first statement if right.

Problem 3. Write the sum using summation notation, assuming the suggested pattern continues.
25 + 36 + 49 + 64 + ... + n^2 + ...

Answer: option A) summation of n squared from n equals five to infinity

Explanation

First term: 25 = 5^2
Second term: 36 = 6^2
Third term: 49 = 7^2
Fourth term: 64 = 8^2

nth term n^2

last term: the sequence is infinite

So, you can see that the sequence is the sum of the square of the integers from n = 5 to infinity =
∞
∑ (n^2)
n = 5

which is what summation of n squared from n equals five to infinity means.

Problem 4. Find the sum of the arithmetic sequence.
-1, 2, 5, 8, 11, 14, 17

Answer: option A) 56

Explanation:

You just have to sum all the terms (since they are few numbers that is the best way): - 1 + 2 + 5 + 8 + 11 + 14 + 17 = 56

Answer: 56

Problem 5. Find the sum of the geometric sequence.
1, one divided by four, one divided by sixteen, one divided by sixty four, one divided by two hundred and fifty six

Answer: option D) 341 / 256

Explanation:
Write in form of fractions: 1 + 1/4 + 1/16 + 1/64 + 1/256

You'd better use the formula for the summation of a geometric sequence

k
∑ A * (r^n) = A * (1 - r^k) / (1 - r)
n=1

In this case: r = 1/4 (the ratio)
k = 5 (the number of terms)
A = 1 (the first term)

=> The sum = 1 * [1 - (1/4)^5 ] / [ 1 - 1/4], which when you simplify turns into 341 / 256 which is the option D.

Problem 6. Find the sum of the first 8 terms of the sequence. Show all work for full credit.
1, -3, -7, -11, ...

Answer: - 104

Explanation:

You can either sum the 8 terms or use the formula for the sum of an aritmetic sequence.

I will sum the 8 terms.

Note the the constant distance to sum is - 4, so the sum of the first eight terms is:

1 - 3 - 7 - 11 - 15 - 19 - 23 - 27 = - 104

Ryanne is 14. her brother's age is three more than half her age. how old is her brother?

Answers

Ryanne = 14
half her age : 14 ÷ 2 = 7
three more : 7 + 3 = 10
Her brother is 10 years old.

Answer:

10 years old

Step-by-step explanation:

I will use the letter r to denote Ryanne's age:

r = 14

And according to the problem, her brother's age is THREE MORE THAN HALF HER AGE

so, we start by finding how much is half of Ryanne's age:

r/2 = 14/2 = 7

and next, we find that three more than half her age is:

7 + 3 = 10

Her brother is 10 years old

An investment of $750 will be worth $1500 after 12 years of continuous compounding at a fixed interest rate. What percent is the interest rate?

Answers

Final answer:

The interest rate is 100%, or 1 as a decimal, for continuously compounded interest.

Explanation:

To find the interest rate, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount ($1500)P is the principal amount ($750)r is the interest rate (unknown)n is the number of times interest is compounded per year (continuously compounded)t is the time in years (12)

Using the given information, we can plug in the values and solve for r:

$1500 = $750(1 + r/1)^(1*12)$2 = 1 + rr = $2 - 1 = $1

The interest rate is 100%, or 1 as a decimal, for continuously compounded interest.

The interest rate, for continuous compounding, is approximately 5.775%.

To find the interest rate for continuous compounding, we can use the formula for compound interest:

[tex]\[ A = P \times e^{rt} \][/tex]

Where:

- [tex]$ A $[/tex] is the final amount of money,

- [tex]$ P $[/tex] is the principal amount (initial investment),

- [tex]$ r $[/tex] is the interest rate (annual rate in decimal),

- [tex]$ t $[/tex] is the time the money is invested for (in years),

- [tex]$ e $[/tex] is the base of the natural logarithm, approximately equal to 2.71828.

Given:

- [tex]$ P = $750 $[/tex],

- [tex]$ A = $1500 $[/tex],

- [tex]$ t = 12 $[/tex] years.

We need to solve for [tex]$ r $[/tex], the interest rate.

Step 1 :

**Substitute the Given Values into the Formulaa :

[tex]\[ 1500 = 750 \times e^{12r} \][/tex]

Step 2 :

**Divide Both Sides by 750**:

[tex]\[ \frac{1500}{750} = e^{12r} \][/tex]

[tex]\[ 2 = e^{12r} \][/tex]

Step 3 :

**Take the Natural Logarithm of Both Sides**:

[tex]\[ \ln(2) = \ln(e^{12r}) \][/tex]

[tex]\[ \ln(2) = 12r \ln(e) \][/tex]

[tex]\[ \ln(2) = 12r \][/tex]

Step 4 :

**Solve for [tex]$ r $[/tex]**:

[tex]\[ r = \frac{\ln(2)}{12} \][/tex]

[tex]\[ r = \frac{0.693}{12} \][/tex]

[tex]\[ r = 0.05775 \][/tex]

Step 5 :

**Convert the Interest Rate to a Percentage**:

[tex]\[ r_{\text{percentage}} = 0.05775 \times 100\% \][/tex]

[tex]\[ r_{\text{percentage}} = 5.775\% \][/tex]

So, the interest rate is approximately 5.775%.

A field project superintendent earns an annual salary of $72,800, and she contributes $7900 per year to her 401(k) plan. If she has a required deduction for income taxes (federal, state, and local combined) of 28% of pretax income, how much does she have withheld in income taxes per year?

Answers

Contributions to one's 401K plan are taken out without paying tax on them (they are pre-tax contributions). In the end, when you retire you will pay taxes on the money but it is deferred for now.

What this means in terms of the question is that we should deduct the $7,900 first and then take 28% of what is left for taxes.

This person's salary is $72,800 a year and they set aside $7,900 for their retirement account (401K) so that leaves $72800-$7900 = $64,900

She now pays taxes of 28% on this amount ($64,900). Percent means "out of 100" so 28% means [tex] \frac{28}{100}=.28 [/tex] and to find 28% of 64900 we multiply (64900)(.28) = $18172.

That is she has $18,172 withheld in taxes each year.

3/4 of what number is 8?

Answers

I got 10.6666 but I am not sure if it’s right ( ◠‿◠ )

Twenty-seven minus of a number (x) is not more than 36. What is the number? x > 42 x ≥ -6 x < 3 x ≤ -6

Answers

27 - 1.5x ≤ 36
54 - 3x ≤ 72
-3x ≤ 72 - 54
-3x ≤ 18
x ≥ 18/(-3)
x ≥ -6
..........................................................

The profits of mr cash’s company is represented by the equation p(t)=-3t^2+18t-4, where p(t) is the amount of profit in hundreds of thousands of dollars and t is the number of years of operation. he realizes his company is on the down turn and wishes to sell before he ends up in debt. in what year of operation does mr cash’s business show the maximum profit?

Answers

Answer: 3rd year of operation

Explanation:

Note that p(t) is a quadratic function and so its graph is a parabola. Since the coefficient of t² in p(t) is negative, the maximum point in p(t) exist at its vertex. Moreover, the maximum value of p(t) is the y-coordinate of its vertex.

Note that p(t) can be expressed as:

[tex]p(t) = a(t-h)^2 + k [/tex] (1)

Where (h, k) are the coordinates of the vertex of p(t).

To manipulate p(t) in the form expressed in equation (1), we factor out the coefficient of t² in p(t) so that

[tex]p(t) = -3t^2+18t-4 \\ \boxed{p(t) = -3 \left( t^2 - 6t + \frac{4}{3} \right)}[/tex]

Then, we let

[tex]q(t) = t^2 - 6t + \frac{4}{3}[/tex]

So that

[tex]p(t) = -3q(t)[/tex] (2)

We need q(t) to be expressed as the sum of a perfect square trinomial and a constant. To form the perfect square trinomial in q(t), we can find a constant k such that [tex]t^2 - 6t + k [/tex] is a perfect square.

To find the value of k, we divide the coefficient of t by 2 and get the square of the result. Since the coefficient of t in q(t) is -6,

[tex]k = \left( \frac{-6}{2} \right)^2 = 9[/tex]

To avoid changing the value of q(t), if we add the constant k = 9, we need to subtract it by the same number. Since k = 9,

[tex]q(t) = t^2 - 6t + \frac{4}{3} + k - k \\ = t^2 - 6t + \frac{4}{3} + 9 - 9 \\ = (t^2 - 6t + 9) + \frac{4}{3} - 9 \\ \boxed{q(t) = (t - 3)^2 - \frac{23}{3}} [/tex]

From equation (2),

[tex]p(t) = -3q(t) \\ p(t) = -3\left( (t - 3)^2 - \frac{23}{3} \right) \\ \boxed{p(t) = -3 (t - 3)^2 + 23}[/tex]

Hence the vertex of p(t) is (3, 23) and maximum value is attained at t = 3. Therefore, the Mr. Cash's business has maximum profit at the 3rd year of operation.

How many pieces of pie will you have if 4 banana caramel cream pies are sliced into 1 8 servings? A) 12 B) 18 C) 24 D) 32

Answers

Final answer:

When 4 banana caramel cream pies are sliced into 1/8 servings, the number of pieces of pie obtained is 32.

Explanation:

To determine the number of pieces of pie obtained when 4 banana caramel cream pies are sliced into 1/8 servings, we need to find the total number of pie servings. Each pie is sliced into 1/8 servings, so if we have 4 pies, we can calculate the total number of servings by multiplying 4 by 1/8.

4 x 1/8 = 4/8 = 1/2

Therefore, we will have 1/2 pie when 4 banana caramel cream pies are sliced into 1/8 servings. Since 1/2 pie is equivalent to 4/8 pie, the answer is D) 32 pieces.

What is the area of a sector with a central angle of π3 radians and a radius of 12.4 m? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box.

Answers

Answer: [tex]80.47\ m^2 [/tex]

Step-by-step explanation:

The area of a sector is given by :-

[tex]\text{Area of sector}=\frac{\theta}{2}\times( r^2), \text{where }\theta\text{ is measure of central angle in radians.}[/tex]

Given :Central angle = [tex]\theta=\frac{\pi}{3}[/tex]

radius = 12.4 m

Then,

[tex]\text{Area of sector}=\frac{\frac{\pi}{3}}{2}\times( (12.4)^2)\\\\\Rightarrow\ \text{Area of sector}=\frac{\pi}{6}\times153.76\\\\\Rightarrow\ \text{Area of sector}=\frac{3.14}{6}\times153.76\\\\\Rightarrow\ \text{Area of sector}=80.4677333333\approx80.47\ m^2 [/tex]

What is the approximate area of the circle shown below 60cm

Answers

It is A 2827cm
This is the answer your welcome

Answer:

[tex]\text{Hence, the approx. area of circle }2827 cm^2[/tex]

Step-by-step explanation:

Given the diameter of circle 60 cm

we have to find the area of circle

Diameter=60 cm

Radius=30 cm

[tex]\text{Area of circle=}\pi r^2[/tex]

[tex]=\frac{22}{7}\times (30)^2=2828.57143\sim 2827(approx)[/tex]

[tex]\text{Hence, the approx. area of circle }2827 cm^2[/tex]

Option A is correct

Could someone explain this to me?

Answers

This is a simple differentiation problem. Let's start by taking the derivative of both sides (with respect to x):
[tex]5y^4\frac{dy}{dx}+6y^2x+6x^2y\frac{dy}{dx}+20x^3 = 0[/tex]

Simplify:
[tex] \frac{dy}{dx} (5y^4+6x^2y) + 6y^2x+20x^3 = 0[/tex]

Solve for dy/dx:
[tex] \frac{dy}{dx} = \frac{-6y^2x-20x^3}{5y^4+6x^2y} [/tex]

Now, plug in the given points:
[tex]\frac{dy}{dx} = \frac{-6(2)^2(-1)-20(-1)^3}{5(2)^4+6(-1)^2(2)} = \frac{24+20}{80+12}[/tex]

Further simplification gives:
[tex]\frac{dy}{dx}|_{(2,-1)} =\frac{44}{92} = \frac{11}{23} [/tex]

So, your answer is 11/23 or B.

WILL GIVE A BRAINLEST!!!!!!

Solve and check : c-4/c-2=c-2/c+2 - 1/2-c

The solution is c =

How many extraneous solutions are there?

Answers

we have that
(c-4)/(c-2)=(c-2)/(c+2) - 1/(2-c)
- 1/(2-c)=-1/-(c-2)=1/(c-2)

(c-4)/(c-2)=(c-2)/(c+2)+ 1/(c-2)------- > (c-4)/(c-2)-1/(c-2)=(c-2)/(c+2)
(c-4-1)/(c-2)=(c-2)/(c+2)---------------- > (c-5)/(c-2)=(c-2)/(c+2)

(c-5)/(c-2)=(c-2)/(c+2)------------- > remember (before simplifying) for the solution that c can not be 2 or -2
(c-5)*(c+2)=(c-2)*(c-2)------------------ > c²+2c-5c-10=c²-4c+4
-3c-10=-4c+4----------------------------- > -3c+4c=4+10----------- > c=14

the solution is c=14

the domain of the function is (-∞,-2) U (-2,2) U (2,∞) or
all real numbers except c=-2 and c=2

The solution is c = 14

How many extraneous solutions are there? zero

Can someone help me please I would appreciate it.
I well mark brainliest if u explain
Please.

Answers

The answer is c to my calculations.

WILL GIVE BRAINLIEST

WILL GIVE BRAINLIEST AND 50 points

out of a port departed a steam boat with a speed of 36.8km/h. In 1.75 hours out of the same port and going the Sam direction departed a speed boat. In 1.8 hours after the the department of the speed boat, the distance between the speed boat and the steam boat was 86.9km. What was the speed boats speed in km/h?

Answers

To solve this, you need to use the equation that gives the relationship between time(t), speed(s), and distance(d):

s=d/t
d=st

For the steam boat, the velocity was 36.8, and the time was 1.75 hours before the speedboat left plus the 1.8 hours after the speedboat left. Substitute this information into the equation to find the distance it travels:

d=36.8*(1.75+1.8)
d=130.64 km

According to the question, we know that the distance the speedboat travels is 86.9 km behind the steam boat. So d for the speedboat is 130.64-86.9, or
43.74 km. It is also given that the speedboat travels for 1.8 hours, so t=1.8. Substitute this information into the equation to find the speed.

s=43.74/1.8
s=24.3 km/h

So the speed of the boat is 24.3 km/h

Hi there!

My name is Chris and I'll be helping you today!

So your question states that a boat departed the port at 36.8 km/h.

After 1.75 hours, a second boat emerges from the port.

After 1.8 hours, the second boat is 86.9 km away from the first boat.

Also, remember that speed equals distance over time.

Therefore, your answer will be: The speed boat's speed in km/h was 24.3 km/h. Forgive me if I am incorrect.

Enjoy your day!

The perimeter of a rectangle is 42 inches. If the length of the rectangle is 14 inches, which equation could be used to find the width, x? A. 2(x + 14) = 42 B. x + 2(14) = 42 C. 14(x + 2) = 42 D. x + 14 = 42

Answers

A. 2(x+14) = 42

(2x = 14
x = 7

2(7) + 2(14) = 14 + 28 = 42)

Answer:

Option A is correct

equation [tex]2(x+14)=42[/tex] could be used.

Step-by-step explanation:

Given: The length of a rectangle [tex](l)[/tex] is 14 inches and perimeter of rectangle is 42 inches.

Perimeter(P)of a rectangle in inches is given by:

[tex]P= (2l+w)[/tex] ; where [tex]l[/tex] is the length of the rectangle and w is the width of the rectangle.

Substitute the value of P=42 inches , w =x inches and [tex]l = 14[/tex] inches in the above formula we get;

[tex]42 = 2 \cdot (14+x)[/tex]

Divide by 2 on both sides we get;

[tex]21 = 14+x[/tex]

On simplify, we get;

x = 21-14 = 7 inches

therefore, the width of the rectangle is, x = 7 inches

Check :

Substitute the value of x =7 in option A.

[tex]2(x+14) =42[/tex]

[tex]2(7+14)=42[/tex]

[tex]2\cdot 21 =42[/tex]

42 = 42

Hence, the only equation that could be used to find the width, x is, [tex]2(x + 14) = 42[/tex]

30 POINTS + BRAINLIEST!

Answers

We have to find the value of 'x' in [tex] \sin (x+22)^{\circ}=\cos (2x-7)^{\circ} [/tex]

By using the complementary angle formula which states:

[tex] \cos (90-\Theta )=\sin \Theta [/tex]

Now,

[tex] \cos (90^{\circ}-(x+22)^{\circ})=\cos (2x-7)^{\circ} [/tex]

Therefore, we get

[tex] 90-(x+22)= (2x-7) [/tex]

[tex] 90-x-22= (2x-7) [/tex]

[tex] 68=3x -7 [/tex]

[tex] 75=3x [/tex]

[tex] x=25^{\circ} [/tex]

Answer:

Lets go by a step-by-step process.

Step-by-step explanation:

\cos (90-\Theta )=\sin \Theta

Now,

\cos (90^{\circ}-(x+22)^{\circ})=\cos (2x-7)^{\circ}

Now we have...

90-(x+22)= (2x-7)

90-x-22= (2x-7)

68=3x -7

75=3x

x=25^{\circ}

A FIELD HOCKEY TEAM IS A RECTANGLE 60YARDS BY 100YARDS .WHAT IS THE LENGTH OF THE DIAGONAL FROM ONE CORNER TO THE FIELD TO THE OPPOSITE CORNER ROUND YOUR ANSWER TO THE NEAREST HUNDRETH

Answers

60^2 + 100^2 = X^2
3600 + 10000 = X^2
13600 = x^2
X = Sqrt(13600)
X = 116.619

Diagonal = 116.62 yards

60^2 + 100^2 = c^2
3600 + 10000 = c^2
13600 = c^2
c = 116.62 yd

Answers anybody???????

Answers

The area of the 150° sector is
.. As = (1/2)*r^2*(5π/6)

The area of the white triangle in that sector is
.. At = (1/2)*r^2*sin(5π/6)

The orange shaded area is the difference between these.
.. A = As -At = (1/2)*r^2*(5π/6 -sin(5π/6))
.. = (1/2)*(27.8 in)^2*(5π/6 -1/2)

.. A ≈ 818.4 in^2

Kim solved the equation below by graphing a system of equations. log2(3x-1)= log4(x+8) What is the approximate solution to the equation?

Answers

The approximate solution of the equation log₂(3·x - 1) = log₄(x + 8), obtained algebraically is about x = 1.353. The solution cain be verified using the attached graph created with MS Excel

The steps used to find the solution of the logarithm equation can be presented as follows;

The logarithm equation is; [tex]\log_2(3\cdot x - 1) = \log_4(x + 8)[/tex]

Converting the logarithm to the same base, we get;

[tex]\log_4(x + 8) = \frac{\log_2(x + 8)}{\log_2 4}[/tex]

[tex]\log_4(x + 8) = \frac{\log_2(x + 8)}{2}[/tex]

[tex]\log_2(3\cdot x - 1) = \frac{\log_2(x + 8)}{2}[/tex]

2 × log₂(3·x - 1) = log₂(x + 8)

log₂(3·x - 1)² = log₂(x + 8)

(3·x - 1)² = (x + 8)

(3·x - 1)² - (x + 8) = 0
9·x² - 7·x - 7 = 0

Solving using technology, we get; x ≈ 1.353 and x ≈ -0.575

Plugging in the value of x = 1.353, we get;

log₂(3 × 1.353 - 1) ≈ 1.613

log₄(1.353 + 8) ≈ 1.613

The value of the logarithm are much different when x ≈ -0.575, the expression log₂(3·x - 1) have no solution. The solution is therefore; x ≈ 1.353

Please find the attached the graph of the equation log₂(3·x - 1) = log₄(x + 8), showing the solution as x ≈ 1.353

Final answer:

To solve the equation log2(3x-1) = log4(x+8), we can rewrite the equation and simplify it to calculate the approximate solution as x = 4.5.

Explanation:

To solve the equation log2(3x-1) = log4(x+8), we can start by using the property of logarithms that states log(a) = log(b) if and only if a = b. Based on this property, we can rewrite the equation as 3x - 1 = x + 8. Simplifying this equation, we get 2x = 9. Finally, by dividing both sides by 2, we find that x = 4.5. Therefore, the approximate solution to the equation is x = 4.5.

the width of an architects desk is represented by four times x squared and the length is represented by the expression 2x cubed. what represents the area of the tabletop

Answers

You will use the formula A=lw to find the area. Substitute 2x^3 in for the length and 4x^2 for the width. You would multiply both of these. 2×4 = 8, and x cubed times x squared equals X to the fifth power. You will add the exponents together because the exponent tells you how many times to multiply that value. If there are three x multiplied together (in x cubes) and two x multiplied together(in x squared) that makes five x multiplied together. The answer is represented as A=8x^5. ^ means to the power of.

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