The sum of three consecutive integers is 45. What are the integers

Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 5x - 6 is in this form with slope m = 5

• Parallel lines have equal slopes

y = 5x - 2 is the only line with a slope of 5 → B

Parallel lines have the same slope. As the slope of the original line is 5, the line y = 5x - 2 represents a line parallel to the original line y = 5x - 6.

When two lines are parallel, their slopes are equal. Using this fact, we can identify which equation represents a line parallel to the line y = 5x - 6 by comparing their slopes. The slope of the given line is 5, as it's the coefficient before x in the equation y = mx + b, where m is the slope.

Looking at the provided options:

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The answer is:

The fourth option,

{s | s <90}

Solving inequalities involves almost the same process of solving equalities for variable isolation.

We are given the inequality:

[tex]\frac{1}{3}s-6<24[/tex]

So, solving we have:

[tex]\frac{1}{3}s-6<24\\\\\frac{1}{3}s-6+6<24+6\\\\\frac{1}{3}s<30\\\\\frac{1}{3}s*3<30*3\\\\s<90[/tex]

Hence, we have that the correct option is the fourth option:

{s | s <90}

Have a nice day!

Answer:

{s | s < 90}   D is the correct answer

Step-by-step explanation:

It is.

Answer:

3619.11 cubic inches

Step-by-step explanation:

volume of a cylinder is [tex]V=\pi r^2h[/tex]

diameter is 16 in, so radius (r) is 8 in

plug in values: [tex]V=\pi 8^2(18) = 3619.11[/tex] cubic inches

The volume of a cylinder with a diameter of 16 inches and a height of 18 inches is calculated using the formula V = πr²h, which results in approximately 3617.3 cubic inches when rounded to the nearest tenths place.

To calculate the volume of a cylinder, we use the formula V = πr²h. Given that the diameter of the cylinder is 16 inches, which means its radius (r) is half of that, 8 inches. The height (h) of the cylinder is given as 18 inches. To find the volume, first square the radius, then multiply by π (approximated as 3.14 for this purpose), and then by the height.

So, the calculation looks like this:

Therefore, the volume of the cylinder, rounded to the nearest tenth place, is 3617.3 cubic inches.

Answer:

$4,535.05

Step-by-step explanation:

Final answer:

The correct option is $4,535.05. To find the value of Mike's investment after 10 years with compound interest, use the formula A = P(1 + r/n)^(nt) with the given values. The final value of Mike's investment is $4,535.05.

Explanation:

Mike invested $2,500 in an account with 6% annual interest compounded quarterly. We can use the compound interest formula: A = P(1 + r/n)^(nt) to calculate the value after 10 years.

Here's the calculation: A = $2,500(1 + 0.06/4)^(4*10) = $4,535.05. Therefore, the value of Mike's investment after 10 years is $4,535.05.

Answer:

D

Step-by-step explanation:

In a 30-60-90 triangle, if the short leg is x, then the long leg is x√3, and the hypotenuse is 2x.

Here, the hypotenuse is 10.  So the short leg is:

10 = 2x

x = 5

If the short leg is 5, then the long leg is 5√3.

Answer:

[tex]\large\boxed{width=4.5\ in}[/tex]

Step-by-step explanation:

[tex]V=lwh\qquad\text{divide both sides by}\ lh\\\\\dfrac{V}{lh}=\dfrac{wlh}{lh}\\\\w=\dfrac{V}{lh}\\\\\text{We have}\\\\V=138.24\ in^3\\h=9.6\ in\\l=3.2\ in\\\\\text{Substitute:}\\\\w=\dfrac{138.24}{(3.2)(9.6)}=\dfrac{138.24}{30.72}=4.5\ in[/tex]

Answer:

g(-1) = 1

Step-by-step explanation:

Synthetic division is by far the fastest way to evaluate this function at x = -1.  Set up synth. div. as follows:

-1   )   1    6    12    8

              -1    -5    -7

     ----------------------

         1     5     7     1                

since the remainder is 1, g(-1) = 1

a) Finance Charge ≈ $18.01  the interest rate is 1.8 % per month.

b) The finance charge is approximately $18.01, and the new balance is approximately $1018.74.

To calculate the finance charge using the previous balance method, we'll need to follow these steps:

a) Find the finance charge on May 3:

Calculate the average daily balance for the billing period.

Average Daily Balance = (Total of daily balances) / (Number of days in the billing period)

Determine the number of days in the billing period (from April 3 to May 2). There are 30 days in this billing period.

Find the daily balances by considering the transactions during the billing period:

Daily balance from April 3 to May 2 = Previous balance on April 3 + Charges during the period - Payments during the period

Daily balance from April 3 to May 2 = $1495.39 + $305.34 - $800

Calculate the average daily balance:

Average Daily Balance = (Total of daily balances) / (Number of days in the billing period)

Average Daily Balance = [(1495.39 + 305.34 - 800) * 30] / 30

Average Daily Balance = $1000.73

Calculate the finance charge using the previous balance method:

Finance Charge = (Average Daily Balance) * (Monthly Interest Rate)

Finance Charge = $1000.73 * (0.018) [0.018 is the monthly interest rate as a decimal]

Finance Charge ≈ $18.01

b) Find the new balance on May 3:

New Balance = Previous balance + Charges during the period - Payments during the period + Finance Charge

New Balance = $1495.39 + $305.34 - $800 + $18.01

New Balance ≈ $1018.74

So, on May 3, the finance charge is approximately $18.01, and the new balance is approximately $1018.74.

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Final answer:

The finance charge on May 3 using the previous balance method is $26.92, assuming a monthly interest rate of 1.8%. The new balance on May 3, after adding the finance charge, additional charges, and subtracting the payment, is $1027.65.

Explanation:

To calculate the finance charge using the previous balance method, we take the balance due on the April 3 billing date, which was $1495.39, and apply the monthly interest rate of 1.8%. The charge is computed as follows:

Finance Charge = Previous Balance × Monthly Interest Rate
Finance Charge = $1495.39 × 0.018
Finance Charge = $26.91702

Since financial amounts are usually rounded to cents, the finance charge would be $26.92.

To find the new balance on May 3, we will take the previous balance and add the finance charge and any additional charges, then subtract any payments made. This looks like:

New Balance = Previous Balance + Finance Charge + Additional Charges - Payments
New Balance = $1495.39 + $26.92 + $305.34 - $800
New Balance = $1027.65

Therefore, the new balance on May 3 is $1027.65.

Answer:

Equation of line: y=3x-18

Step-by-step explanation:

Point: (4,-6) and slope = 3

[tex]y+6=3(x-4)[/tex]

y=3x-18

Answer:

y + 6 = 3(x - 4)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = 3 and (a, b) = (4, - 6), hence

y - (- 6) = 3(x - 4), that is

y + 6 = 3(x - 4) ← in point- slope form

Answer:

8

Step-by-step explanation:

Use the Pythagorean theorem.

a^2 + 6^2 = 10^2

a^2 + 36 = 100

a^2 = 64

a = 8

-3y = -6/5

-3y(5) = (-6/5)(5)

-15y = -6

y = -6/-15

y = 6/15

y = 2/5

[tex]42_x+53_x=125_x\\4\cdot x^1+2\cdot x^0+5\cdot x^1+3\cdot x^0=1\cdot x^2+2\cdot x^1+5\cdot x^0\\4x+2+5x+3=x^2+2x+5\\x^2-7x=0\\x(x-7)=0\\x=0 \vee x=7[/tex]

There is no numeral system with base 0, so [tex]x=7[/tex].

Answer:

Gary sold 5 paperback books

Step-by-step explanation:

each book is equal to $2 and $10 were made in Hardcover

So that only leaves us with ten unaccounted dollars

5x=10

Each book or (x) in this case is two dollars

so it will come out to be five books

Answer:

Option C. 15 cm

Step-by-step explanation:

The correct question is

A triangle has two sides that measure 8.7 cm and 12.3 cm. Which could be the measure of the third side?

A. 2.6 cm

B. 3.6 cm

C. 15 cm

D. 21 cm

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Analyze two cases

Let

x ----> the length of the third side

First case

x+8.7 > 12.3

x>12.3-8.7

x> 3.6 cm

Second case

12.3+8.7 > x

21 > x

Rewrite

x < 21 cm

Answer: 10 units.

Step-by-step explanation:

The equation of the circle in Center-radius form is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Where the center is (h,k) and "r" is the radius.

The equation of the circle given is:

[tex]x ^2 + y^2 = 100[/tex]

You can observe that is written in Center-radius form.

Then, you can identify that:

[tex]r^2=100[/tex]

Knowing this, you need to solve for "r" to find the lenght of the radius.

This is:

[tex]r=\sqrt{100}\\\\r=10[/tex]

Therefore, the lenght of the radius is 10 units.

Answer:

Demand: q = -50p + 1200

Supply: q = 40p

Step-by-step explanation:

First let's define our variables.

q = quantity of T-shirts

p = price

We know that when p = 12, q = 600.  When p increases by 1, q decreases by 50.  So this is a line with slope -50 that passes through the point (12, 600).  Using point-slope form to write the equation:

q - 600 = -50 (p - 12)

Converting to slope-intercept form:

q - 600 = -50p + 600

q = -50p + 1200

Similarly, we know that when p = 9.75, q = 600 - 210 = 390.  When p increases by 1, q increases by 40.  So this is a line with slope 40 that passes through the point (9.75, 390).  Using point-slope form to write the equation:

q - 390 = 40 (p - 9.75)

Converting to slope-intercept form:

q - 390 = 40p - 390

q = 40p

Answer:

1) Are there 4 right angles? (90° angles)

2) Are there 2 sets of parallel lines?

3) Are there 2 sets of congruent lines?

4) Are there a set of congruent diagonals?

~

Answer:

[tex]\large\boxed{21x^4-14y^2=7(3x^4-2y^2)=7(x^2\sqrt3-y\sqrt2)(x^2\sqrt3+y\sqrt2)}[/tex]

Step-by-step explanation:

[tex]21x^4-14y^2=7(3x^4-2y^2)\\\\=7\bigg((\sqrt3)^2x^{2\cdot2}-(\sqrt2)^2y^2\bigg)\qquad\text{use}\ (a^n)^m=a^{nm}\ \text{and}\ (ab)^n=a^nb^n\\\\=7\bigg((x^2\sqrt3)^2-(y\sqrt2)^2\bigg)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=7(x^2\sqrt3-y\sqrt2)(x^2\sqrt3+y\sqrt2)[/tex]

[tex]\text{Hey there!}[/tex]

[tex]\text{1(96) = 96}[/tex]

[tex]\text{2(48) = 96}[/tex]

[tex]\text{4(24) = 96}[/tex]

[tex]\text{6(16) = 96}[/tex]

[tex]\text{8(12) = 96}[/tex]

[tex]\text{The factors of 96 are: 1, 2, 3, 4, 6,8, 12, 16, 24, 32, 48, 96}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

[tex]\$30[/tex]

Step-by-step explanation:

we have

[tex]p(t)=3x+2x-4x^{2}+21[/tex]

Find the amount of money that each girl spent

For t= 2 hours

[tex]p(2)=3(2)+2(2)-4(2)^{2}+21[/tex]

[tex]p(2)=10-16+21[/tex]

[tex]p(2)=\$15[/tex]

Find the amount of money that they spend together

Multiply by 2 the amount of money that each girl spent

[tex](2)\$15=\$30[/tex]

Shawna and Keisha spent $30 together when each of them went shopping for 2 hours.

It seems there might be a typo in the function p(t) you provided. It should be[tex]\( p(t) = 3t + 2t - 4t^2 + 21 \)[/tex], where t represents the number of hours spent shopping.

To find out how much money Shawna and Keisha spent together when each of them went shopping for 2 hours, we need to evaluate the function p(t)  at [tex]\( t = 2 \)[/tex] and then add the results.

Let's plug in t=2 into the function p(t):

[tex]\[ p(2) = 3(2) + 2(2) - 4(2)^2 + 21 \][/tex]

[tex]\[ = 6 + 4 - 16 + 21 \][/tex]

[tex]\[ = 10 - 16 + 21 \][/tex]

[tex]\[ = 15 \][/tex]

Multiply by 2 since $15 is for each girl = 2*$15= $30

Answer:

IbI

Step-by-step explanation:

The square root of [tex]\( b^2 \)[/tex] is [tex]\( b \),[/tex] as the square root of any positive number is its positive root.

The square root of [tex]\( b^2 \)[/tex]  can be calculated step by step as follows:

Step 1:

Understand the concept.

The square root of a number is a value that, when multiplied by itself, gives the original number. For any real number [tex]\( b \), \( b^2 \)[/tex]  represents [tex]\( b \)[/tex]multiplied by itself.

Step 2:

Apply the square root property.

The square root of [tex]\( b^2 \)[/tex]  is [tex]\( b \)[/tex] because [tex]\( b \times b = b^2 \).[/tex] The square root of any positive number is its positive root.

Step 3:

Interpret the result.

Since the square root of [tex]\( b^2 \)[/tex] is [tex]\( b \),[/tex]  regardless of the value of \( b \), the square root of [tex]\( b^2 \)[/tex] is simply [tex]\( b \)[/tex] . This property holds true for any real number [tex]\( b \).[/tex]

So, the square root of [tex]\( b^2 \)[/tex] is [tex]\( b \).[/tex]

Answer:

-7

Step-by-step explanation:

4x-12=16+8x

-12-16=8x-4x

-28÷4=x

x=-7

Answer:

-7 :)

Step-by-step explanation:

The answer to 4+4 is 8

4+4=8

Answer:

D

Step-by-step explanation:

we can use the formula of tan(A-B) to solve this equation .

The formula is

[tex]tan(A-B)= \frac{tanA-tanB}{1+tanA.tanB}[/tex]

In our question , A is x and B is [tex]\frac{\pi }{3}[/tex]

so when we apply these in the question we get

[tex]tan(x-\frac{\pi }{3} )=\frac{tanx-tan\frac{\pi }{3} }{1+tanx.tan\frac{\pi }{3} }[/tex]

Now since [tex]tan\frac{\pi }{3} = \sqrt{3}[/tex]

we get

[tex]tan(x-\frac{\pi }{3} )=\frac{tanx-\sqrt{3}  }{1+\sqrt{3} tanx.} }[/tex]

so correct option is

D

Answer:

∠ACB==50°

b=15.6 units

c=11.9 units

Step-by-step explanation:

step 1

Find the measure of angle BCA

we know that

The sum of the interior angles of a triangle must be equal to 180 degrees

∠ABC+∠BAC+∠ACB=180°

substitute the given values

90°+40°+∠ACB=180°

∠ACB=180°-130°=50°

step 2

Find the measure of side b

Applying the law of sines

a/sin(∠BAC)=b/sin(∠ABC)

substitute the given values

10/sin(40°)=b/sin(90°)

b=10/sin(40°)

b=15.6 units

step 3

Find the measure of side c

Applying the law of sines

c/sin(∠ACB)=a/sin(∠BAC)

substitute the given values

c/sin(50°)=10/sin(40°)

c=[10/sin(40°)]*sin(50°)

c=11.9 units

ANSWER:

C=11.9

ABC=90 deg.

BAC=40 deg.

A=10

Answer:

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Step-by-step explanation:

slope formula

Answer:

[tex]\frac{rise}{run}[/tex]

Step-by-step explanation:

The slope of a line is calculated by dividing the rise by the run.

In the attached example, the rise is 1 and the run is 2, so the slope is 1/2.  The rise is the distance the line goes up.  The run is the distance the line goes to the right for each (rise) units.  The line below goes up 1 and right 2 over and over again.

The complete statements of the expression are

How to complete the statements in the expression

From the question, we have the following parameters that can be used in our computation:

5x - 8(3y + 13) - 1

Consider an expression

Ax + b

Where x is the variable, we have

Using the above as a guide, we have the following:

In the first term, 5 is a coefficient

In the second term, (3y+ 13) is a factor

In the third term, -1 is a constant

Question

Use the given expression to complete the statements.

5x– 8(3y + 13) – 1

In the first term, 5 is a _____

In the second term, (3y+ 13) is a ______

In the third term, -1 is a ______

so the company has an overhead of $600, usually that involves premises leasing and industrial equipment for the manufacturing of the product, that's cost.  The cost to make each item is 50 cents, so if the company produces "x" items, their cost is 0.5x total.

so our cost equation C(x) = 0.5x + 600   <---- items' cost plus overhead.

the company sells the product for 85 cents, so if they sell "x" items, their total revenue or income will be 0.85x.

so our revenue equation is simply R(x) = 0.85x.

as you already know, the break-even point is when.... well, you break even, no losses but no gains either, how much you take in is the same amount that you shelled out, namely R(x) = C(x).

[tex]\bf \stackrel{R(x)}{0.85x}=\stackrel{C(x)}{0.5x+600}\implies 0.35x=600\implies x=\cfrac{600}{0.35} \\\\\\ x\approx 1714.285714285714\implies \stackrel{\textit{rounded up}}{x=1714}[/tex]

Answer:

3.0 cm

Step-by-step explanation:

The Law of Sines states the relationship between the sides and the angles of non-right (oblique) triangles.

In the given triangle,the following relation holds;

[tex]\frac{4.7}{sin(95)}=\frac{a}{sin(40)}\\\\a=\frac{4.7}{sin(95)}*sin(40)\\\\a=3.03[/tex]

Answer:

Option C. a = 3.0 cm

Step-by-step explanation:

We have to find the value of a from the given triangle ABC.

By applying sine rule in ΔABC

[tex]\frac{sin95}{4.7}=\frac{sin40}{a}[/tex]

Now we cross multiply in the given equation.

a(sin95°) = 4.7(sin40°)

a(0.9962) = 4.7(0.6428)

a = [tex]\frac{4.7(0.6428)}{0.9962}[/tex]

a = 3.03 cm ≈ 3.0 cm

Therefore, a = 3.0cm Option C. will be the answer.