What is the value for y?



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y =

312miles/6hours=52mph

52mph

To make the 312-mile road trip in 6 hours, Rosie would need to drive at a constant rate of 52 miles per hour.

To find the constant rate at which Rosie needs to drive, we can divide the total distance by the total time. In this case, Rosie needs to drive 312 miles in 6 hours. So the rate would be 312 miles ÷ 6 hours = 52 miles per hour.

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The possible rational roots of the polynomial 9x³ + 14x² - x + 18 = 0, according to the Rational Root Theorem, are ±1, ±2, ±3, ±6, ±1/3, ±2/3, ±1/9, and ±2/9.

To find the possible rational roots of the polynomial 9x³ + 14x² - x + 18 = 0 according to the Rational Root Theorem, we look at the factors of the constant term (the last term, 18) and the leading coefficient (the coefficient of the term with the highest power of x, which is 9).

The factors of 18 (±1, ±2, ±3, ±6, ±9, ±18) are divided by the factors of 9 (±1, ±3, ±9), which gives a list of possible rational roots:

±1

±2/3

±3

±1/3

±2

±6

±1/9

±2/9

±6/9

±18/9

However, not all these values are in simplified form. After simplification, we get a list of unique possible rational roots for the given polynomial equation:

±1

±2

±2/3

±1/3

±3

±6

±1/9

±2/9

Let the first number be = x

Then other number according to question is

4 less than 5 times the number i.e. 5x-4

Also ,sum of numbers is 32

x+5x-4=32

6x-4=32

Add 4 to both sides

6x-4+4=32+4

6x=36

Divide both sides by 6

x=36/6

x=6

First number =x =6

Other number =5(6)-4 = 30-4 =26

Answer: 26 and 6

Step-by-step explanation: Let's use two variables to represent our two numbers in this problem. Since a variable is a letter that represents any number, we can pick any letters we want to but I will use with x and y.

So if the sum of two numbers is 32, that means x + y = 32.

To solve for two separate variables, we will need two separate equations. So for the second equation, let's read through the second sentence in the problem.

"One of the numbers" that's x, "is" means equals, "4 less than 5 times the other" is not 4 - 3y, it means 5y - 4. The word "less than" switches the order around. So we now have x = 5y - 4.

So to solve this system of equations, let's use substitution. Since x = 5y - 4, we can substitute a 5y - 4 in for x in the first equation to get (5y - 4) + y = 32. Solving from here we get 6y - 4 = 32 by combining like terms. Now we can get rid of that -4 by adding 4 to both sides of the equation to get 6y = 36. Now, we will divide both sides of the equation by 6 in order to isolate y and we end up with y = 6.

To find x, plug 6 back in for y in the second equation to get x = 5 (6) -4 which we can simplify to x = 30 - 4 which simplifies to x = 26.

Therefore, our two numbers in this problem are 26 and 6.

Final answer:

To find dy/dx for y=log(tan(2x)), we can use the chain rule: dy/dx = (2sec²(2x))/tan(2x).

Explanation:

To find dy/dx for y = log(tan(2x)), we can use the chain rule. Let's break it down step by step:

First, we identify the inner function, which is u = tan(2x).

Next, we find the derivative of the inner function with respect to x: du/dx = 2sec²(2x).

Then, we identify the outer function, which is y = log(u).

Finally, we find the derivative of the outer function with respect to u and multiply it by the derivative of the inner function with respect to x: dy/dx = (1/u) * (du/dx) = (2sec²(2x))/tan(2x).

(a) What are you being asked to find?

the number of pounds of soil Emmanuel purchased last week

(b) Write an equation to model the problem.

Let x = amount of potting soil Emmanuel bought last week.

2x + 5 = 27

(c) How many pounds of potting soil did Emmanuel buy last week? Show the calculations

2x + 5 = 27

Subtract 5 from both sides.

2x = 22

Divide both sides by 2.

x = 11

Answer: Emmanuel bought 11 lb of potting soil last week.

Answer:

1. Not congruent

2. Not congruent

3. Congruent

4. Congruent

5. Not congruent

6. Not congruent

???

Step-by-step explanation:

Answer:

its not even 20 pts

Step-by-step explanation:

so first lets make the denominators the same so that we can divide

1/3 = 2/6

5/6

if you divide johny can make 2 cups of serving and  R 1/5

V = s*s*s where s is the side length

V = s^3

Answer:

1st blank: Multiply

2nd blank: 4 quarts per cup

3rd blank: 16 cups

4th blank: Multiply

5th blank: 16 cups per gallon  

6th blank: 48 cups.

Step-by-step explanation:

We have been given that Elyse needs 3 gallons of water to mix a fruit drink, but she has a 1-cup measuring cup. She knows that there are 4 cups in 1 quart, and 4 quarts in 1 gallon.

Elyse can use the unit rate. First she can multiply 4 cups in a quart by 4 quarts per gallon to find that there are 16 cups in 1 gallon. She can then multiply 3 gallons by 16 cups per gallon to determine that she will need 48 cups of water to mix the fruit drink.

[tex]\frac{\text{4 cups}}{\text{Quart}}\times\frac{\text{4 quarts}}{\text{gallon}}=\frac{\text{16 cups}}{\text{gallon}}[/tex]

Step 2:

[tex]3\text{ gallons}\times\frac{\text{16 cups}}{\text{gallon}}=3\times \text{16 cups}=\text{48 cups}[/tex]

No it is not a real number

Yes, it is a number. It equals 1,000,000,000,000.

−2^6 − 6^2 =

-64 - 36 =

-100

the correct inequality is: m ≥ 8 + 4

The given information states that Demarcus has at least $8 more than his older sister, who has $4.

To find how much money Demarcus has, we denote m as the amount of money Demarcus has.

Since Demarcus has at least $8 more than his older sister, we can express this relationship as:

m ≥ 8 + 4

This inequality states that Demarcus's money m is greater than or equal to the sum of $8 (more than his sister) and $4 (his sister's money).

So, the correct inequality is: m ≥ 8 + 4

Therefore, the option is: m ≥ 8 + 4

The probable question maybe:

Demarcus has at least $8 more than his older sister. His older sister has $4.

Which of the following inequalities could be used to find how much money, m. Demarcus has?

Om> 8+4

8 - m < 4

8m > 4

The horizontal distance from Emma's house to tree house is 7 units and the vertical distance is 3 units.

Draw the horizontal and vertical lines to form a right triangle.

Label the vertices as A, B and C.

By Pythagorean theorem, [tex]AC^{2} =AB^{2}+ BC^{2}[/tex]

= [tex]3^{2} +7^{2}[/tex]

= 9 + 49

= 58

So, [tex]AC = \sqrt{58}[/tex]

Hence, distance from Emma's house to tree house is [tex]\sqrt{58}[/tex] units.

Answer: A. [tex]\frac{1}{343}[/tex]

Step-by-step explanation:

First, apply exponent rule.

[tex]=\frac{1}{7^3}[/tex]

[tex]7^3=7*7*7=343[/tex]

[tex]=\frac{1}{343}[/tex]

Hope this helps!

Thank you for posting your question.

-Charlie

[tex]\sqrt{2.4^2+0.7^2}=\sqrt{5.76+0.49}=\sqrt{6.25}=2.5\\\\because\ 2.5^2=6.25[/tex]

No.

The value of 2.29 is greater than, not less than, the value 2.129.

2 and 1 are in the same location in each number: the tenths position. 2 is larger than 1 is, and thus 2.29 is larger.

im not 100% sure but im pretty sure it is B

To cover one cake, we need approximately 1.33 times the amount of frosting that covers 1/8 of the container.

To find out how much frosting is needed to cover one cake, we need to find the ratio between the amount of frosting and the amount of cake that is covered. We are given that 1/8 of the frosting container covers 1/6 of the cake. To simplify this ratio, we can find a common denominator, which is 24. So, 1/8 of the frosting container is equivalent to 3/24 and 1/6 of the cake is equivalent to 4/24.

Since the ratio is now 3/24 frosting to 4/24 cake, we can say that for every 3 parts of frosting, we need 4 parts of cake. So, if we want to cover one cake, we would need 4/3 times the amount of frosting, which is approximately 1.33 times the amount of frosting needed to cover 1/8 of the container.

Therefore, to cover one cake, we need approximately 1.33 times the amount of frosting that covers 1/8 of the container.

I'm not sure if you were supposed to add two numbers together to get five? If that's the case the answer would be 5/3. If it's not i'm sorry, I tried.

Taking Rhs

1/2 [sin(x+y)+ sin (x-y)]

using sinA + sin B = 2 cos (A+B)/2 cos( A - B)/2

1/2 [ 2 Cos ( x+y+x-y)/2 . Cos (x+y-x+y)/2]

=Cos 2x/2. Cos 2y/2 = Cos x . Cos y

Hence true

Counterexample: 4-5=-1

they are both positive but the sum is a negative

-Hope it helps!

A counterexample that makes the conclusion false is when the two positive numbers have a difference of zero.

A counterexample that makes the conclusion false is when the two positive numbers have a difference of zero. For example, if we take the numbers 5 and 5, their difference is 0, which is not positive. So this counterexample shows that the conclusion 'the difference of two positive numbers is always positive' is false. The counterexample to the conclusion that "the difference of two positive numbers is always positive" is:

1 - 3 = -2

In this case, you have two positive numbers (1 and 3), but their difference (-2) is negative, not positive. This counterexample demonstrates that the statement is not always true, as there are situations where the difference of two positive numbers can be negative.

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B.  First and Second St appear to be parallel

Question

15 is the same as the product of 3 and a number. Which equation models this sentence?

15=3x

15=x-3

15=3+x

15=x divided by 3

Answer:

Step-by-step explanation:

15 = 3x

x = 15 : 3

x = 5

.........................

check

15 = 3 * 5

15 = 15

the answer is good

Answer:

15=3x

Hope this helps!

'a' and 'b' are placeholders for some numbers. In this case, a = 3 and b = 5. So we'll replace every copy of 'a' with 3 and every copy of 'b' with 5. Afterwards, we use PEMDAS to simplify

4(a+2b) = 4*(3+2*5) = 4*(3+10) = 4*(13) = 52

Answer: 52

Nina receives one third of Lily's fifteen dolls, which is calculated as 15 multiplied by 1/3. Thus, Nina will have five dolls.

The question asks how many dolls Lily's sister, Nina, will have if Lily gives one third of her fifteen china dolls to Nina. Mathematically, one third of fifteen is calculated by multiplying fifteen by the fraction 1/3. Working this out gives you five. So, if Lily gives one third of her fifteen dolls to Nina, Nina will receive five dolls.

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Solution: The function [tex]f(x)=x^4+2x^3-5x^2-6x[/tex] is decreasing on [tex](-\infty ,-2.303]\cup [-0.5,1.303][/tex].

Explanation:

The given function is  [tex]f(x)=x^4+2x^3-5x^2-6x[/tex].

differentiate with respect to x.

[tex]f'(x)=4x^3+6x^2-10x-6[/tex]

To find the extreme points put [tex]f'(x)=0[/tex] and find the value of x.

[tex]f'(x)=4x^3+6x^2-10x-6=0[/tex]

[tex]2(2x^3+3x^2-5x-3)=0[/tex]

By hidden trial [tex]\frac{-1}{2}[/tex] is the root of the equation and [tex](x+\frac{1}{2} )[/tex] is factor of the equation.

[tex]2(x+\frac{1}{2} )(2x^2+2x-6)=0\\4(x+\frac{1}{2} )(x^2+x-3)=0\\4(x+\frac{1}{2} )(x+2.303)(x-1.303)=0[/tex]

The extreme points of graph [tex]x=-0.5, -2.303, 1.303[/tex]

The intervals are [tex](-\infty ,-2.303]\cup[-2.303,-0.5]\cup [-0.5,1.303]\cup [1.303,\infty )[/tex].

Put any value from each interval in [tex]f'(x)=4x^3+6x^2-10x-6[/tex].

If the value of [tex]f'(x)>0[/tex], then the function increase on that interval.

If the value of [tex]f'(x)<0[/tex], then the function decrease on that interval.

Since the value [tex]f'(x)<0[/tex] on [tex](-\infty ,-2.303][/tex]. and [tex][-0.5,1.303][/tex], therefore function [tex]f(x)=x^4+2x^3-5x^2-6x[/tex] is decreasing on [tex](-\infty ,-2.303]\cup [-0.5,1.303][/tex].

We know that

Domain:

It is all possible values of x for which any function is defined

we are given function

[tex]f(x)=-(x+3)(x-1)[/tex]

we can see that our function goes from left to right side

so, domain will be all real numbers

Range:

Range is all possible values of y

we can see that

largest y-value is 4

smallest y-value is -inf ...because it keeps going downward

so, range is

[tex](-\infty , 4][/tex]

so, option-C...........Answer