Which value completes the table? A. -17 b. -3 c. 1 d. 3

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

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:

The number of child tickets = 39

Step-by-step explanation:

It is given that,child admission is $5.20 and adult admission is $8.60

Total sales = $868.00

To find the number of child tickets

Le 'x' be the number of children then number of adults = 2x

(x * 5.20) + (2x * 8.60) = 868

5.2x + 17.2x = 868

22.4x = 868

x = 868/22.4

 = 38.75 ≈ 39

Therefore the number of child tickets = 39

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:

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:

8

Step-by-step explanation:

Use the Pythagorean theorem.

a^2 + 6^2 = 10^2

a^2 + 36 = 100

a^2 = 64

a = 8

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.

Answer:

d

Step-by-step explanation:

In an axiomatic system, the definition is 'the accepted meaning of a term'. An axiom is an accepted unproven fact. A fact proven by using logic is a theorem.

In an axiomatic system, the phrase that best describes the 'definition' would be option A - 'the accepted meaning of a term.' An axiomatic system is a sort of framework within mathematics where definitions, axioms, and propositions work together. A definition in this context offers the precise description or meaning of a term used within that mathematical system.

An axiom (option B) would most accurately be described as an accepted fact that is not proven, but instead accepted as truth within an axiomatic system (option C). A fact proven by using logic, on the other hand, would be a theorem (option D).

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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.

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:

[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:

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:

[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]

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:

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:

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

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:

The width of the base = the volume ÷ (length × height)

w = V/lh

Step-by-step explanation:

* Lets take about how to re-arrange any formula

- The formula of the volume of the rectangular prism is:

  V = lwh, where l is the length of the base , w is the width of the

  base and h is the height of the prism

- To find the formula of the width from the formula of the volume,

  we must isolate the width in one side and all other dimensions in

  other side

∵ V = lwh ⇒ divide both sides by l and h

∵ V/(lh) = (lwh)/(lh) ⇒ cancel lh up with lh down

∴ V/(lh) = w

∴ w = V/(lh)

∴ w = V ÷ (lh)

* The width of the base = the volume ÷ (length × height)

Answer:

Width=[tex]\frac{Volume}{(Length)*(height)}[/tex]

Step-by-step explanation:

You only have to clear the start of the formula:

V=L*W*H

Since lenght and height are multiplying the width of the base you have to clear them and take them to the other side of the equation dividing:

[tex]\frac{V}{l*h}[/tex]

So you can calculate the width of the base by dividing the volume between the product of the Height times the length.

[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]

[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:

$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.

The answer to 4+4 is 8

4+4=8

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:

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

-3y = -6/5

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

-15y = -6

y = -6/-15

y = 6/15

y = 2/5

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:

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:

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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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