Can a pair of numbers have more than one common factor?
Explain Why

Given : -2(5x+1) > 48

To solve for x  we need to get x alone

Lets start with removing parenthesis from left hand side

-10x -2 > 48

Now add 2 on both sides

-10x > 50

Divide by -10 from both sides. When we divide by negative number then flip the inequality sign, so > becomes <

x < -5

Answer is x< -5

Final answer:

The solution to the inequality -2(5x+1)>48 is found by distributing the -2, adding 2 to both sides, and then dividing by -10, remembering to reverse the inequality sign, resulting in x < 5.

Explanation:

To solve the inequality -2(5x+1)>48, we start by distributing the -2 across the parenthesis:

-2 * 5x - 2 * 1 > 48

-10x - 2 > 48

Now, we add 2 to both sides of the inequality to isolate the term with the variable x:

-10x > 48 + 2

-10x > 50

Next, we divide both sides by -10 to solve for x. Remember that dividing by a negative number reverses the inequality sign:

x < -50 / -10

x < 5

So, the solution to the inequality is x < 5.

Hello there!

The answer should be the second option B. 250

[tex]2*(5^8/5^5)[/tex]

Explanation:

↓↓↓↓↓↓↓↓↓↓↓↓

[tex]2*(5^8/5^5)[/tex]

First you had to remove parenthesis.

[tex]2*\frac{5^8}{5^5}[/tex]

[tex]\frac{5^8}{5^5}=5^3[/tex]

[tex]5^3*2[/tex]

[tex]5^3=125[/tex]

[tex]2*125[/tex]

Then multiply by the numbers and it should be the correct answer.

[tex]2*125=250[/tex]

[tex]=250[/tex]

Answer⇒⇒⇒⇒⇒=250

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

The correct  answer is b) 250.

Evaluate the exponent in the denominator:

[tex]\frac{5^8}{5^5}=5^{8-5}=5^3[/tex]

The subtraction of exponents arises from the rule that when you divide two terms with the same base, you subtract the exponents.

Substitute the result back into the original expression:

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

Calculate the final result:

[tex]2 \cdot 5^3=2 \cdot(5 \cdot 5 \cdot 5)=2 \cdot 125=250[/tex]

So, [tex]2 \cdot \frac{5^8}{5^5}[/tex]  simplifies to 250. The key step is understanding how to handle the exponents when you divide terms with the same base. In this case, it simplifies to [tex]5^{3}[/tex] , and then you can evaluate the expression further to get the final result of 250.

Question:

Evaluate: [tex]2 \cdot \frac{5^8}{5^5}[/tex]

a) 350

b) 250

c) 225

d) 125

Answer:

v= p/l

Step-by-step explanation:

divide by l on both sides to get v by itself, and you have your answer.

3 + 4x - 3x = 4      Given

3 + (4x - 3x) = 4

3 + x = 4      Combine like terms

3 - 3 + x = 4 - 3

x = 1       Subtraction Property of Equality

Answer and explanation:

Given : Equation [tex]3+4x-3x=4[/tex]

To find : What is the reason for each step in the solution of the equation?

Solution :

Step 1 - Write the given equation,

[tex]3+(4x-3x)=4[/tex]

Step 2 - Combine like terms,

[tex]3+x=4[/tex]

Step 3 - Subtraction Property of Equality,

[tex]3+x-3=4-3[/tex] (Subtract both side by 3)

[tex]x=1[/tex]

So, Above three steps are the required result.

He has 7 dollars left so...

We can add 7+9+12+4 to get the amount in the beginning

32$ to start with

Final answer:

To determine how much money Darryl had at the beginning of the day, we add the amounts he spent on a book, compact disc, and magazine to the money he has left, which totals $32.

Explanation:

The question involves solving a simple arithmetic problem regarding the total amount of money Darryl had at the beginning of the day, based on his expenditures throughout the day. To find out how much money Darryl had initially, we need to add up the amounts he spent on various items and then add the money he has left.

Darryl spent:

and he has $7 left.

To find the total amount Darryl had at the beginning of the day, we add up all the expenditures and the remaining amount:

$9 (book) + $12 (compact disc) + $4 (magazine) + $7 (remaining) = $32

So, Darryl had $32 at the beginning of the day.

The answer is 2, Hope this helps

Final answer:

The line that is parallel to 4x+3y=7 and passes through (-5,2) has the equation y=(-4/3)x-14/3.

Explanation:

The line that is parallel to the line with the equation 4x+3y=7 and passes through the point (-5,2) will have the same slope as the given line. To find the slope, we need to rearrange the equation into slope-intercept form (y=mx+b), where m is the slope. In this case, we get 3y=-4x+7, which can be simplified to y=-(4/3)x+7/3. So the slope is -4/3.

Now that we know the slope, we can use the point-slope formula y-y1=m(x-x1) to find the equation of the line that passes through (-5,2).

Using y-2=(-4/3)(x-(-5)), we can simplify to y-2=(-4/3)(x+5). Expanding and rearranging, we get y=(-4/3)x-14/3.

The equation of the parallel line is: [tex]\[\boxed{4x + 3y = -14}\][/tex]

To find the equation of a line parallel to the given line 4x + 3y = 7 and passing through the point (-5, 2), follow these steps:

1. Determine the slope of the given line:

The given line's equation is in standard form: Ax + By = C. To find its slope, we can rewrite it in slope-intercept form y = mx + b, where m is the slope.

Starting with the given equation:

4x + 3y = 7

Solve for y:

[tex]\[3y = -4x + 7\]\[y = -\frac{4}{3}x + \frac{7}{3}\][/tex]

The slope m of the given line is [tex]\(-\frac{4}{3}\).[/tex]

2. Use the slope of the parallel line:

Since parallel lines have the same slope, the line we are looking for also has a slope of [tex]\(-\frac{4}{3}\).[/tex]

3. Use the point-slope form to find the equation of the new line:

The point-slope form of a line's equation is given by:

[tex]\[y - y_1 = m(x - x_1)\][/tex]

where [tex]\((x_1, y_1)\)[/tex] is a point on the line, and m is the slope.

Here, the point (-5, 2) and slope [tex]\(m = -\frac{4}{3}\):[/tex]

[tex]\(-\frac{4}{3}\).[/tex]

[tex]\[y - 2 = -\frac{4}{3}(x + 5)\][/tex]

Simplify the equation:

[tex]\[y - 2 = -\frac{4}{3}x - \frac{4}{3} \cdot 5\]\[y - 2 = -\frac{4}{3}x - \frac{20}{3}\][/tex]

Add 2 (or [tex]\(\frac{6}{3}\))[/tex] to both sides:

[tex]\[y = -\frac{4}{3}x - \frac{20}{3} + \frac{6}{3}\]\[y = -\frac{4}{3}x - \frac{14}{3}\][/tex]

The equation of the line parallel to 4x + 3y = 7 and passing through (-5, 2) is:

[tex]\[y = -\frac{4}{3}x - \frac{14}{3}\][/tex]

Converting back to standard form for consistency:

[tex]\[3y = -4x - 14\]\[4x + 3y = -14\][/tex]

Therefore, the equation of the parallel line is:

[tex]\[\boxed{4x + 3y = -14}\][/tex]

Answer:

K(-4,8) is the ortho center.

Step-by-step explanation:

In a right angled triangle, The vertex of the right angle is the ortho center.

Here we are given

J(-4,-1), K(-4,8) & L(2,8)

Using distance formula we get

[tex]JK^{2}= (-4+4)^{2}+ (8+1)^{2}=0+81=81[/tex]

[tex]KL^{2}= (-4-2)^{2}+ (8+-8)^{2}=36+0=36[/tex]

[tex]JL^{2}= (-4-2)^{2}+ (8+1)^{2}=36+81=117[/tex]

So we can say that

[tex]JK^2 + KL^2=JL^2[/tex]

By converse of pythagorean theorem we get

[tex]<K = 90°[/tex]

Hence the Vertex of the right angle is K(-4,8)

K(-4,8) is the ortho center.

Since 0.25 is the same as 25/100, find the GCF, which is 25 and divide it on the top and the bottom. 25 divided by 25 is 1, and 100 divided by 25 is 4. So in simplest form, your answer is 1/4

The decimal number, 0.25, can be simplified or written as a fraction in simplest form as: 1/4.

To turn 0.25 into a fraction in simplest form, follow these steps:

Step 1: Write the decimal as a fraction with the decimal value as the numerator and the place value as the denominator.

0.25 = 25/100

Step 2: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

GCD(25, 100) = 25

Divide both the numerator and denominator by 25:

25/100 ÷ 25/25 = 1/4

So, 0.25 as a fraction in simplest form is 1/4.

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The expression to represent the perimeter of the rug is [tex]\rm Perimeter = \dfrac{10x+28}{5}[/tex].

A hand weaved rectangular rug measures x ft long and 2 4/5 ft wide.

An expression to represent the perimeter of the rug.

The perimeter of the rug is given by two times of length and width.

[tex]\rm Perimeter = 2( Length + Width)[/tex]

The length of the rug is x feet.

And the width of the rug is 2 4/5 feet.

Therefore,

The expression to represent the perimeter of the rug is,

[tex]\rm Perimeter = 2( Length + Width)\\\\\rm Perimeter = 2( x+ 2\dfrac{4}{5})\\\\Perimeter = 2 (x + \dfrac{2 \times 5+4}{5})\\\\Perimeter = 2(x+\dfrac{10+4}{5})\\\\Perimeter = 2(x+\dfrac{14}{5})\\\\Perimeter= 2(\dfrac{5x+14}{5})\\\\Perimeter = \dfrac{10x+28}{5}[/tex]

Hence, the expression to represent the perimeter of the rug is [tex]\rm Perimeter = \dfrac{10x+28}{5}[/tex].

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Answer: [tex]\frac{-1}{3}[/tex] < n < [tex]\frac{5}{3}[/tex]

Step-by-step explanation:

| 3n - 2 | - 2 < 1

              +2 +2

| 3n - 2 |       < 3

3n - 2 < 3     and     3n - 2 > -3

     +2 +2                     +2   +2

3n       < 5      and     3n      > -1

       n <  [tex]\frac{5}{3}[/tex]       and         n > [tex]\frac{-1}{3}[/tex]

[tex]\frac{-1}{3}[/tex] < n < [tex]\frac{5}{3}[/tex]

Interval Notation:  [tex](\frac{-1}{3},[/tex][tex]\frac{5}{3})[/tex]

Graph:  [tex]\frac{-1}{3}[/tex] o--------------------o [tex]\frac{5}{3}[/tex]

[tex]|3n-2|-2<1\\\\|3n-2|<3\\\\3n-2<3 \wedge 3n-2>-3\\\\3n<5 \wedge 3n>-1\\\\n<\dfrac{5}{3} \wedge n>-\dfrac{1}{3}\\\\n\in \left(-\dfrac{1}{3},\dfrac{5}{3}\right)[/tex]

You should draw approximately 0.825 cc of fluid from the U40 insulin vial into the syringe to administer 33 units of insulin to the patient.

To calculate the amount of fluid that should be drawn into the syringe from a U40 vial in order to obtain 33 units of insulin, you can use a simple proportion based on the concentration of insulin in the vial.

The concentration of the U40 vial is 40 units of insulin per cubic centimeter (cc) of fluid.

Let "x" be the amount of fluid (in cc) to be drawn from the vial to obtain 33 units of insulin.

You can set up the proportion as follows:

(40 units insulin) / (1 cc fluid) = (33 units insulin) / (x cc fluid)

Now you can cross-multiply and solve for "x":

40 x = 33 × 1

40x = 33

x = 33 / 40

x = 0.825 cc

So, you should draw 0.825 cc of fluid from the U40 vial to obtain 33 units of insulin.

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The patient would need to draw approximately 0.825 cubic centimeters (cc) of fluid from the U40 insulin vial to obtain 33 units of insulin since the vial has 40 units per cc.

To calculate the amount of fluid that should be drawn into the syringe from a U40 insulin vial for a patient who needs 33 units of insulin, you can use the direct relationship between the units of insulin and the volume of fluid in the vial. Since the vial is labeled U40, it means it has 40 units of insulin per cubic centimeter (cc) of fluid.

Setting up a simple proportion, where the unknown volume in cubic centimeters is represented by 'V', the equation should look like this:

40 units of insulin / 1 cc = 33 units of insulin / V cc

By cross-multiplying, we have:

40 units * V cc = 33 units * 1 cc

Therefore, V = 33 units / 40 units/cc

After performing the division, V comes out to be just slightly under 1 cubic centimeter:

V ≈ 0.825 cc

So, the patient would need to draw approximately 0.82 cc or 0.825 cc (to be more precise) of fluid into the syringe from the U40 vial to obtain 33 units of insulin.

[tex]5b+4+10=2 \\\\5b=-12\\\\b=-\dfrac{12}{5}[/tex]

Hello!

[tex]5b+4+10=2[/tex]

Add the numbers with 10+4=14.

[tex]5b+14=2[/tex]

Then subtract by 14 from both sides.

[tex]5b+14-14=2-14[/tex]

Simplify

[tex]5b=-12[/tex]

You can also divide by 5 from both sides.

[tex]\frac{5b}{5}=\frac{-12}{5}[/tex]

Answer

[tex]b=-\frac{12}{5}[/tex]

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

Answer:

1.45kg of Sugar is left.

Step-by-step explanation:

First we have to make sure that both the values are represented in same units.

Lets convert 2.2kg to grams.

1 kilo gram is 1000 grams, So

2.2 kilo grams is, [tex]2.2*1000[/tex] grams. Which is equal to 2,200g.

So Bernard had 2,200g of sugar and he used 750g of it.

To find the remaining amount of sugar we need to deduct 750g from 2,200g.

[tex]2200-750=1450[/tex]

Therefore,

1450g of Sugar is left.

But the Answer should be given in kilo grams as the question requires you to do so.

So, convert grams to kilo grams you have to divide by 1000.

[tex]\frac{1450}{1000} =1.45[/tex] kilo grams.

1.45kg of Sugar is left.

Let's solve your inequality step-by-step.

[tex]\frac{4}{3}[/tex]s−3≥5−4

Step 1: Simplify both sides of the inequality.

[tex]\frac{4}{3}[/tex]s−3≥1

Step 2: Add 3 to both sides.

[tex]\frac{4}{3}[/tex]s−3+3≥1+3

[tex]\frac{4}{3}[/tex]s≥4

Step 3: Multiply both sides by 3/4.

([tex]\frac{3}{4}[/tex])*([tex]\frac{4}{3}[/tex]s)≥([tex]\frac{3}{4}[/tex])*(4)

Answer: s≥3

The Oak Island treasure is 54 feet farther below ground than the Federal Reserve gold vault.

The gold vault is located at a depth of -80 feet below ground, while the Oak Island treasure is believed to be at a depth of -134 feet below ground. This means that the Oak Island treasure is 54 feet farther below ground than the gold vault.

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Answer:

5ºF per hour decrease

Step-by-step explanation:

Given that the temperature in Fairbanks, Alaska, fell 10 degrees in 2 hours

For finding average we normally divide the total by number of units

Here change in temperature for 2 days is given as -10 degrees (negative sign is used to denote decrease)

For 2 days change in temperature = -10 degrees F

Hence average change in temperature = change for one day

= -10/2 = -5 degrees F

So answer is 5ºF per hourº decrease

Hey, CadenClough! For this, it's best to use algebra. We know that rectangles have two of each measure: two lengths and two widths. This means the formula to find the complete perimeter of the rectangle is 2l + 2w = p.

Now let's look at the problem. For length, we have x + 3 and for width we have 2x - 6. First off, fill in the values for length and width in the perimeter equation like this:

[tex]2(x + 3) + 2(2x - 6) = 26[/tex]

Now distribute the 2:

[tex]--> 2x + 6 + 4x - 12 = 26[/tex]

Combine like terms:

[tex]2x + 4x + 6 - 12 = 26[/tex]

Simplify:

[tex]6x - 6 = 26[/tex]

Isolate x:

[tex]6x = 26 + 6[/tex]

--> [tex]x = \frac{32}{6}[/tex]

Now plug in the value of x:

[tex]2(\frac{32}{6} + 3) + 2(2 * \frac{32}{6} - 6)[/tex]

= 64/3 - 12 + 32/3 + 6

= 26

So x = [tex]\frac{32}{6}[/tex] or 16/3.

The answer is B because you take 6160 divided by 1760 to get 3.5 miles total.

Answer:

x = 10

Step-by-step explanation:

If you look at the opposite side of the "x", you see the same shape, with the same values.

You can see a congruent shape on the left side of the figure.

x = 10

5.83  every second, and 840000 a year.

Lawyer makes 9.72 cents per second, $840000 per year.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

For example conversion of a kilometer to a meter is to multiply by 1000 but meter and kilometer both unit is for distance only.

Another example could be kilo gram to gram.

Given that,

Rate of lawyer bills = $350/hour

Now,

Amount of money per second ⇒

$350/hour = 350/(60×60)

$0.097/seconds = 9.7 cents per second.

Amount of money per year ⇒ $350/hour = $(350 × 50 × 48)/ year

$350/hour =$840000 per year.

Hence "Lawyer makes 9.72 cents per second, $840000 per year".

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ANSWER

[tex]5N^2=3^{2} \times 5^{5} \times x^{6}[/tex]

EXPLANATION

[tex]N=3\times5^2 \times x^3[/tex].

[tex]5N^2=5(3\times5^2 \times x^3)^2[/tex]

Recall this property of exponents;

[tex](a^m)^2=a^{m} \times a^m[/tex]

So our product becomes;

[tex]5N^2=5(3\times5^2 \times x^3) \times (3\times5^2 \times x^3)[/tex]

[tex]5N^2=5\times 3\times 3 \times 5^2 \times 5^2 \times x^3 \times x^3[/tex]

[tex]5N^2=3\times 3\times 5 \times 5^2 \times 5^2 \times x^3 \times x^3[/tex]

Recall this law of exponents:

[tex]a^m \times a^n =a ^{m+n}[/tex]

[tex]5N^2=3^{1+1} \times 5^{1+2+2} \times x^{3+3}[/tex]

[tex]5N^2=3^{2} \times 5^{5} \times x^{6}[/tex]

Hey there!

When you write an equation in function notation, one side of the equation is, "f(x)".

You can replace x with another variable such as n if you are using a different one.

f(x) takes the place of y in an equation.

For example, the equation y = 3x + 2 in function notation is f(x) = 3x + 2.

Hope this helps!

(d) [tex]\frac{75}{2}[/tex], [tex]\frac{75}{4}[/tex], [tex]\frac{75}{8}[/tex]

(e) 68, 82, 96

(d) note that the terms have a common ratio ( r )

r = [tex]\frac{300}{600}[/tex] = [tex]\frac{150}{300}[/tex] = [tex]\frac{1}{2}[/tex]

to obtain any term in the sequence, multiply the previous term by [tex]\frac{1}{2}[/tex]

75 × [tex]\frac{1}{2}[/tex] = [tex]\frac{75}{2}[/tex]

[tex]\frac{75}{2}[/tex]× [tex]\frac{1}{2}[/tex] = [tex]\frac{75}{4}[/tex]

[tex]\frac{75}{4}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{75}{8}[/tex]

(e) note that the terms have a common difference (d )

d = 26 - 12 = 40 - 26 = 54 - 40 = 14

to obtain any term in the sequence, add 14 to the previous term

54 + 14 = 68

68 + 14 = 82

82 + 14 = 96

Answer:

Step-by-step explanation:

one- one- one direction

If you need it to be simplified then it is 4/5

There are ten spots where you can put a white flag. 10  

There are nine spots where you can put a second white flag. 9  

There are eight spots where you can put a green flag. 8  

Likewise --- 7  

Likewise --- 6  

There is only one way to fill the remaining spots with red flags.  

Total: 10 x 9 x 8 x 7 x 6 = 30,240

Answer:

1

Step-by-step explanation:

6+5+4 is 15

15/1 = 15

Note that the slope-intercept form is: y = mx + b

First, set the equation as such

2x (-2x) + 3y = (- 2x) + 15

3y = -2x + 15

Isolate the y. Divide 3 from both sides

(3y)/3 = (-2x + 15)/3

y = (-2/3)x + 5

-2/3 is your slope

hope this helps

quintic means degree of 5.

a negative quintic would be: f(x) = -x⁵ +              

an example with one real zero could be: -x⁵ + x³ + x + 3   (see attachment)

Well let's start with y = -x^5 and y = - x^5 +1

The graph looks like the one on the right for these two.  The red one is y = - x^5 and the blue one is y = - x^5 + 1

See below on the right

You can tell that these two are correct because there is only 1 x axis intercept for each of them.  That means there is only 1 real solution which is what you are calling for.

Another one could be something like

y = -(x - 5)(x^2 + 2)(x^2 + 3)

The graph of that is on the left.