Each leg of a 45°-45°-90° triangle measures 12 cm.
What is the length of the hypotenuse?
4
45°
45°
6 cm
62 cm
12 cm
12 cm
12 cm
12V3 cm

[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]

For this case we must solve the following quadratic equation:

[tex]2x ^ 2 -7x -15 = 0[/tex]

We must apply the following formula:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

We have to:

[tex]a = 2\\b = -7\\c = -15[/tex]

Substituting we have:

[tex]x = \frac {- (- 7) \pm \sqrt {(- 7) ^ 2-4 (2) (- 15)}} {2 (2)}\\x = \frac {7 \pm \sqrt {49 + 120}} {4}\\x = \frac {7 \pm \sqrt {169}} {4}\\x = \frac {7 \pm13} {4}[/tex]

Thus, the solutions are:

[tex]x_ {1} = \frac {7 + 13} {4} = \frac {20} {4} = 5\\x_ {2} = \frac {7-13} {4} = \frac {-6} {4} = - \frac {3} {2}[/tex]

ANswer:

[tex]x_ {1} = 5\\x_ {2} = - \frac {3} {2}[/tex]

Answer:

{-3/2, 5} would be the right choice

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:

[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:

Option B

Step-by-step explanation:

we know that

The volume of a solid is the amount of space occupied by a solid object. The volume of solid is expressed as cubic units.

therefore

It is the amount of three -dimensional space inside the solid

Answer:

B. It is the amount of three-dimensional space inside the solid.

Step-by-step explanation:

Volume is defined as the amount of three-dimensional space enclosed by a close surface. Volume is the product of the three dimensions of a body. The SI unit of volume is m³.

eg. Volume of cube = a³

Volume of cuboid = L×B×H

Volume of sphere = [tex]\frac{4}{3}\pi r^3[/tex]

Volume of cylinder = πr²h

Volume of cone = [tex]\frac{1}{3}\pi r^2h[/tex]

Answer:

(1,-1)

Step-by-step explanation:

A translation of (x,y) ⟶ (x + 4, y – 2) means that the coordinates of the pre-image have moved four units to the right and two units down.

To get the coordinates of the pre-image rom the image, we must reverse the procedure.

That is, we must go two units up and four units to the left.

The coordinates of Point P' are (5, -3), so those of P must have been (1, -1).

Answer:

(1,-1) is the answer

Step-by-step explanation:

Hope this helps

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.

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:

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]

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:

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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-3y = -6/5

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

-15y = -6

y = -6/-15

y = 6/15

y = 2/5

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:

x ≈ 50.8

Step-by-step explanation:

Given

sin80° = [tex]\frac{50}{x}[/tex]

Multiply both sides by x

x × sin80° = 50 ( divide both sides by sin80° )

x = [tex]\frac{50}{sin80}[/tex] ≈ 50.8 ( to 1 dec. place )

Answer:

[tex]\large\boxed{x\approx50.77}[/tex]

Step-by-step explanation:

[tex]\text{Look at the picture.}\\\\\sin80^o\approx0.9848\\\\\text{Substitute it the the equation}\ \sin80^o=\dfrac{50}{x}:\\\\0.9848=\dfrac{50}{x}\\\\\dfrac{9848}{10000}=\dfrac{50}{x}\qquad\text{cross multiply}\\\\9848x=(10000)(50)\\\\9848x=500000\qquad\text{divide both sides by 9848}\\\\x\approx50.77[/tex]

Answer:

16/9

Step-by-step explanation:

Step 1 : {Apply exponent rule}

Step 2: repeat

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:

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

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.

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:

The answer should be: B. (9,3)

Answer:  B. (9,3)

Step-by-step explanation:

To solve this problem, we start organizing the equation to the Slope intercept form:

[tex]y=5(x-9)+3[/tex]

[tex]y=5x-45+3[/tex]

[tex]y=5x-42[/tex]

Where 5 is the positive slope of the line, and -42 is the y-axis intercept. knowing the y-intercept, we may infer that choices C or D are incorrect, because values must be lower than -42. Thus, we replace the x value of choices A and B to verify which one applies:

Choice A

[tex]y=5(3)-42[/tex]

[tex]y=-27[/tex]

[tex]27\neq 9[/tex]

Choice B

[tex]y=5(9)-42[/tex]

[tex]y=3[/tex]  Correct!

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:

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:

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: 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.

The equation that represents the given situation is 3x - (50 - x) - 0.5(50 - x) = 110. This equation is derived from the fact that Desiree gets 3 points for each correct answer, 1 point deducted for each wrong answer, and 0.5 point deducted for each unanswered question.

The equation that represents the given situation is 3x - (50 - x) - 0.5(50 - x) = 110.

This eqUation is derived from the fact that Desiree gets 3 points for each correct answer, 1 point deducted for each wrong answer, and 0.5 point deducted for each unanswered question.

By solving the equation, you can find the value of x, which represents the number of questions Desiree answered correctly.

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:

∠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

The answer to 4+4 is 8

4+4=8