Use the method of completing the square to solve x2-8x+7=0

4 3/8 because 1 2/3 and 2 5/8 multiplied together is that.

change each to an improper fraction

1 2/3 = (3*1+2)/3 = 5/3

2 5/8 = (8*2+5)/8 = 21/8

5/3 * 21/8  = 105/24

divide by 3

35/8

4*8 = 32  35-32 = 3

4 3/8

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

V = s^3

Answer:

[tex]\dfrac{4x+1}{x+2}+\dfrac{x-1}{3x}=\dfrac{13x^2+4x-2}{3x^2+6x}[/tex]

Step-by-step explanation:

[tex]Domain:\\x+2\neq0\ \wedge\ 3x\neq0\\\\x\neq-2\ \wedge\ x\neq0[/tex]

[tex]\dfrac{4x+1}{x+2}+\dfrac{x-1}{3x}=\dfrac{(4x+1)(3x)}{(x+2)(3x)}+\dfrac{(x-1)(x+2)}{(3x)(x+2)}\\\\=\dfrac{(4x)(3x)+(1)(3x)+(x)(x)+(x)(2)+(-1)(x)+(-1)(2)}{(3x)(x+2)}\\\\=\dfrac{12x^2+3x+x^2+2x-x-2}{(3x)(x)+(3x)(2)}\\\\=\dfrac{13x^2+4x-2}{3x^2+6x}[/tex]

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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To find the total mass of the four cars, first convert the mass given in kilograms to tonnes, and then sum all the masses. The total mass of the cars on the car transporter is 10.3 tonnes.

The total mass of the four cars loaded on a car transporter can be calculated by first ensuring all the masses are in the same unit. The masses are given as 2.1 tonnes, 3.7 tonnes, 2.8 tonnes, and 1700 kg. We must convert the mass given in kilograms to tonnes before we add them together, as there are 1000 kg in a tonne.

To convert 1700 kg to tonnes:

Now that all masses are in tonnes, we sum them up:

Total mass in tonnes = 2.1 + 3.7 + 2.8 + 1.7 = 10.3 tonnes.

Therefore, the total mass of the four cars on the car transporter is 10.3 tonnes.

No it is not a real number

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

Answer:

Option C

Step-by-step explanation:

Given

Total length of ribbon lucy has=4 inches

She wants to divide it into 6 equal sized pieces so  

Length of each piece=4/6

This can also be written as:

Length of each piece=4*(1/6 )

Now we will look at the options one by one:

For A, Each piece has 6/4 inches of ribbon.. This statement is not true as we have to divide 4 inches into 6 pieces so 4 is supposed to be in the numerator.

For B, breaking down 4/6 gives us 4*(1/6), so the statement is not true.

For C , as we can see that the expression is 4*(1/6), each piece will have 1/6 of inches of ribbon.

So option C is the correct answer..

Answer:

c

Step-by-step explanation:

−2^6 − 6^2 =

-64 - 36 =

-100

[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]

So, first we have to find the width.

Area of a rectangle = length * width

54 = 9 * width

width = 6cm

Now we can plug this into the perimeter formula.

2w + 2l = P

P = 2(6) + 2(9)

P = 12 + 18

P = 40

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

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

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!

C is the correct answer. It is the third graph.

Answer:

c is the correct answer

Step-by-step explanation:

The fraction of the wall that is concrete is obtained by dividing the width of concrete (12 inches) by the total wall width (26 inches). This gives a fraction of 12/26, which simplifies to 6/13. Therefore, 6/13 of the wall is made of concrete.

To solve this problem, we can express the width of the concrete part of the wall as a fraction of the total wall width. First, we will identify the total width of the wall, which includes the different sections of concrete, brick, and limestone. In this case, that is 26 inches (12 inches of concrete + 9 inches of brick + 5 inches of limestone = 26 inches).

Next, we need to determine the width of the concrete section, which is 12 inches.

To express the width of the concrete wall as a fraction of the total wall width, we divide the width of the concrete part by the total wall width. So, we have: 12 inches / 26 inches. Therefore, the fraction of the wall that is concrete is 12/26, which simplifies to 6/13. Out of every 13 parts of the wall, 6 parts are made up of concrete.

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

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

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]

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

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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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.

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:

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:

Answer:

C) Graph B

Step-by-step explanation:

All of these equations have the line y = -2x - 2 graphed.

In the inequality, we have the symbol greater than or equal to.  This tells us the line drawn must be solid, not dashed.  This means the correct graph is either B or D.

Since it is greater than or equal to, the shaded area must be above the line.  This is graph B.

We need to therefore plot the graph passing through the coordinate point (0, -2) and (-1, 0). Option B is correct

Inequality are expression not separated y an equal sign. For an inequality, the upper graph is shaded for greater than and the lower part shaded for less than sign.

Since the sign is greater than and equal to, hence the line will be a solid line as shown in the graph.

Given the inequality y≥ -2x -2. Find the intercepts

If x = 0

y = -2(0) - 2

y = -2

The y-intercept is at (0,-2

If y = 0

0 = -2x - 2

2x = -2

x = -1

The x-intercept is at (-1,0)

We need to therefore plot the graph passing through the coordinate point (0, -2) and (-1, 0) as shown

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Your answer is true.

[tex]y=mx+b[/tex]

The equation is used to find the equation of a line in slope-intercept form.

m is used to represent the slope.

x is used to represent the x-axis.

y is used to represent the y-axis.

b is used to represent the y-intercept.

If you have any questions, feel free to ask! :)