Find AC for question two

Answer:

The length of the other leg is [tex]3.21\ units[/tex]

Step-by-step explanation:

I will assume that the triangle is a right triangle

In a right triangle the legs are perpendicular

so

The area of a right triangle is equal to

[tex]A=\frac{1}{2}(a)(b)[/tex]

where

a and b are the legs of the triangle

In this problem we have

[tex]a=39.2\ units[/tex]

[tex]A=63\ units^{2}[/tex]

substitute the values

[tex]63=\frac{1}{2}(39.2)(b)[/tex]

[tex]126=(39.2)(b)[/tex]

[tex]b=126/(39.2)=3.21\ units[/tex]

This problem involves the uses of the Pythagorean Theorem as well as the use of Sine.

To start we need to identify what we know and what we don't know. We know that there are two triangles. We are given 2 sides lengths and an angle in one and only an angle in the other. They share one side meaning when we are given 2 sides in one triangle it will be easy to get the third side. What we don't know is the side length of CB DB or CD. We need to find CB in order to find CD.

Pythagorean Theorem for side length CB:

12^2-6^2=√108

√108=10.4 (average)

So CB is equal to 10.4

Sine Calculation for side length CD:

Since we have angle 56* we will use the length we found which will be the opposite side from the angle and then input x for our hypotenuse CD in order to solve.

sin 56* = 10.4/x

sin 56* × x = 10.4/x × x

sin 56*x = 10.4

/sin 56*      /sin 56*

x = 12.544....

or 12.6 (average)

So, to conclude, our answer for CD is 12.6cm.

Hope I helped!

Answer:

12.7 cm

Step-by-step explanation:

Given information: AB=6cm AC=12cm.

Pythagoras theorem: In a right angle triangle

[tex]hypotenuse^2=base^2+perpendicular^2[/tex]

Using Pythagoras in triangle ABC we get

[tex](AC)^2=(AB)^2+(BC)^2[/tex]

[tex](12)^2=(6)^2+(BC)^2[/tex]

[tex]144-36=(BC)^2[/tex]

[tex]108=(BC)^2[/tex]

Taking square root on both sides.

[tex]\sqrt{108}=BC[/tex]

Law of sine:

[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

Using law of sin we get

[tex]\dfrac{CD}{\sin (90)}=\dfrac{\sqrt{108}}{\sin (55)}[/tex]

[tex]\dfrac{CD}{1}=\dfrac{\sqrt{108}}{\sin (55)}[/tex]         [tex][\because \sin 90^{\circ}=1][/tex]

[tex]CD=12.6866616739[/tex]

Approx the data to three significant figures.

[tex]CD\approx 12.7[/tex]

Therefore, the length of CD is 12.7 cm.

Answer:

68

Step-by-step explanation:

48+2+20

Answer:

cos13°

Step-by-step explanation:

Using the cofunction identity

sinx° = cos(90 - x)°

sin77° = cos(90 - 77)° = cos13°

Let's use the point-slope formula...

y-y1=m(x-x1)

m is the slope.

y--9=7(x--2)

Subtracting a negative number is the same as adding a positive number...

y+9=7(x+2)

y+9=7x+14

Let's subtract 9 from both sides...

-9+y+9=7x+14-9

y=7x+5

The formula is now in the format of...

y=mx+b

This is known as slope-intercept.

m is the slope.

b is the y-intercept, the value of y when x=0.

Standard formula is...

Ax+By=C

Neither A nor B equal zero.

A is greater than zero.

y=7x+5

Let's move 7x to the left side of the equation.  It becomes negative.

-7x+y=5

Let's multiply both sides by -1 to render A greater than zero.

-1(-7x+y)=(5)(-1)

7x-y=-5

This is the equation in standard form.

[tex]

\text{d stands for distance between two points} \\

d(A, B)=\sqrt{(\Delta{x})^2+(\Delta{y})^2} \\

\text{or simply} \\

d(A, B)=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\

\text{now put in the data} \\

d(A, B)=\sqrt{(-2-15)^2+(9-9)^2} \\

d(A, B)=\sqrt{(-17)^2} \\

d(A, B)=\boxed{17} \\

[/tex]

Answer:

Perimeter of Rhombus = 104 inches  

Step-by-step explanation:

To find the Perimeter of Rhombus we use the formula

Perimeter of rhombus = 4*Length

We need to find the length of rhombus.

if the rhombus has diagonals, it makes four right angled triangles (as shown in figure).

Since 4 triangles are made so, each side of triangle is half of the length of the diagonal.

In our case: Length of diagonals are: 20 and 48

but the Length of sides of triangle will be: 10 and 24

To find the side of rhombus, we can use Pythgoras theorem since the triangles are right angled.

c² = a²+b²

c² = (10)² + (24)²

c² = 100 + 576

c² = 676

√c²= √676

c = 26

So, the length of side of rhombus is 26 inches

Perimeter = 4*length

                = 4*26

                = 104 inches

Perimeter of Rhombus = 104 inches.  

The length of the perimeter of the rhombus is 104 inches.

To find the perimeter of a rhombus with given diagonal lengths of 20 inches and 48 inches, we can use the properties of rhombuses:

Step 1. Relationship between diagonals in a rhombus:

The diagonals in a rhombus cut each other at right angles. Let the diagonal lengths be [tex]\( d_1 \)[/tex] and [tex]\( d_2 \)[/tex].

Step 2. Formula to find side length from diagonals:

The following formula can be used to find the side length ( s ) of a rhombus:

[tex]\[ s = \frac{1}{2} \sqrt{d_1^2 + d_2^2} \][/tex]

where [tex]\( d_1 = 20 \)[/tex] inches and [tex]\( d_2 = 48 \)[/tex] inches.

Step 3. Calculate the side length:

[tex]\[ s = \frac{1}{2} \sqrt{20^2 + 48^2} \][/tex]

[tex]\[ s = \frac{1}{2} \sqrt{400 + 2304} \][/tex]

[tex]\[ s = \frac{1}{2} \sqrt{2704} \][/tex]

[tex]\[ s = \frac{1}{2} \times 52 = 26 \text{ inches} \][/tex]

Step 4. Calculate the perimeter:

The perimeter ( P ) of a rhombus, with all sides equal, is determined by:

[tex]\[ P = 4 \times s = 4 \times 26 = 104 \text{ inches} \][/tex]

Therefore, the length of the perimeter of the rhombus is 104 inches.

Answer:

B

Step-by-step explanation:

Step 1: Add 2 to both sides.

x−2+2>3+2

x>5

Answer:

[tex]5.5\ years[/tex]

Step-by-step explanation:

we know that

In this problem we have a exponential function of the form

[tex]f(x)=a(b^{x})[/tex]

where

x is the time in years

f(x) is the value of the stock

a is the initial value

b is the base

r is the rate

b=(1-r)

we have

[tex]a=\$15,000[/tex]

[tex]r=4\%=4/100=0.04[/tex]

[tex]b=(1-0.04)=0.96[/tex]

substitute

[tex]f(x)=15,000(0.96^{x})[/tex]

80% of original price is equal to

[tex]f(x)=0.80(15,000)=12,000[/tex]

so

For f(x)=12,000 ------> Find the value of x

[tex]12,000=15,000(0.96^{x})[/tex]

[tex](12/15)=(0.96^{x})[/tex]

Apply log both sides

[tex]log(12/15)=log(0.96^{x})[/tex]

[tex]log(12/15)=(x)log(0.96)[/tex]

[tex]x=log(12/15)/log(0.96)[/tex]

[tex]x=5.5\ years[/tex]

Answer:

The base = 5, The legs are 6 each.

Step-by-step explanation:

Let the Base=x, Let the legs = (2x-4)

Perimeter = sum of all the sides = x + (2x-4) + (2x-4) = 5x-8 when you combine the like terms.

You know that the Perimeter = 17 cm. So, 17=5x-8.

Now you can solve for x. Once you do that, you can put your value of x into the leg equations.

17=5x-8

17+8=5x-8+8

25=5x

x=5

The Base is x=5 cm long, The Legs are each 2x-4=2(5)-4=10-4=6 cm long.

The Perimeter is x + (2x-4) + (2x-4) = 5 + 6 + 6 = 17.

Answer:

Step-by-step explanation:

The only solution is x=2

5(2x-3)=5

Divide each term by 5 and simplify

2x−3=12x-3=1

Move all terms not containing x

to the right side of the equation.

2x=42x=4

Divide each term by 2

x=2

Answer:

The given solution has only one solution which is x=2

Step-by-step explanation:

Given the equation

[tex]5(2x-3)=5[/tex]

we have to find the solution of above equation.

Equation is

[tex]5(2x-3)=5[/tex]

Divide by 5 throughout the equation

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

[tex]2x-3=1[/tex]

Adding 3 on both sides

[tex]2x=4[/tex]

Dividing throughout by 2, we get

[tex]x=\frac{4}{2}=2[/tex]

Hence, the given solution has only one solution which is x=2

===================================================

Explanation:

The idea is that for any term, we add on the common difference d to get the next term. For example, the sequence {3, 7, 11, 15, 19, 23, ...} has us add on 4 each time so d = 4 in this case.

3+4 = 7

7+4 = 11

11+4 = 15

and so on. The nth term is represented by the notation[tex]a_n[/tex] while the term just before the nth term is written as [tex]a_{n-1}[/tex]

So adding d onto the term just before the nth term gets us the nth term which is how we end up with [tex]a_n = a_{n-1}+d[/tex]

This is the recursive form of the arithmetic sequence. The closed form is written as [tex]a_n = a_1 + d(n-1)[/tex]

Answer:

140 inches

Step-by-step explanation:

You do the base(14) times the hieght(10)

14x10=140

(12,5) (3, -9) (3,14) (-6,5)

Answer:

x=5, x=-1

Step-by-step explanation:

Since both equations are equal to y, we can set them equal to each other

y = -x + 7 and y = 0.5(x - 3)2

-x + 7 = 0.5(x - 3)^2

Distribute the right hand side by Foiling

-x+7 =.5 ( x^2 -3x-3x+9)

Combine like terms

-x+7 = .5( x^2 -6x+9)

Distribute the .5

-x+7 = .5x^2 -3x+4.5

Add x to each side

-x+x+7 = .5x^2 -3x+x+4.5

7 =  .5x^2 -2x+4.5

Subtract 7 from each side

7 -7= .5x^2 -2x+4.5-7

0 = .5x^2 -2x-2.5

Multiply by 2 to clear the decimals

0 = x^2 -4x -5

Factor

0 = (x-5) (x+1)

Using the zero product property

x-5=0  x+1 =0

x=5, x=-1

So, tangents are equal to each other when they come to a point. So, all you have to do is set 3x+10 and 7x-6 equal to each other. 3x+10=7x-6 subtract 3x from both sides 10=4x-6 and now add 6 to both sides to get 16=4x, divide by 4 on each side and x=4. If you could give me brainliest that would be super helpful!

Answer:

1.4

Step-by-step explanation:

I think that it’s n>7

i think it’s 7 bc u gotta distribute the 5 w the n and 8 and then it equals to 5n+40>75 then just subtract 40 from each side and then ur left w 5n>35, divide each side by 5 and u get n>7

Answer:

option A is correct...

Step-by-step explanation:

just got done with that question and am now on my 10th, wish me luck!

To solve the inequality -1/2 p < -16, multiply all parts of the inequality by '-2' and reverse the inequality sign, yielding 'p' > 32. Therefore, any real number greater than 32 will satisfy the original inequality.

For solving the inequality -1/2 p < -16, you want to find the value of 'p' where the inequality holds true. To do that, you should remove the fraction from the inequality. You can do this by multiplying every part of the inequality by '-2', however, remember that when you multiply or divide by negative numbers in an inequality, the direction of the inequality sign changes.

So, (-1/2 p) * -2 becomes 'p' and -16 * -2 becomes 32, reversing the inequality sign results in 'p' > 32.

In terms of a solution set, this implies that any real number greater than 32 will satisfy the original inequality -1/2 p < -16.

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Answer:

the 23.7 ounce bottle is the better price because the 14.2 ounce bottle is $0.35 and the 23.7 ounce bottle is $0.29.

Step-by-step explanation:

you simply divide the cost by the ounces and get the unit price

To find the unit price for each size, divide the cost of the shampoo by the number of ounces. The 23.7-ounce bottle is the better buy based on the lower unit price.

To find the unit price for each size, divide the cost of the shampoo by the number of ounces in each bottle. For the 14.2-ounce bottle, the unit price is $0.35 per ounce ($4.98 / 14.2). For the 23.7-ounce bottle, the unit price is $0.29 per ounce ($6.97 / 23.7).

To determine which size is the better buy based on the unit price, compare the unit prices. Since the 23.7-ounce bottle has a lower unit price ($0.29 per ounce) compared to the 14.2-ounce bottle ($0.35 per ounce), the larger size is the better buy.

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Answer:

1/2

Step-by-step explanation:

A die has 6 sides, in which 3 numbers (2 , 4 , 6) are even.

Simplify: 3/6 = 1/2

There is a 1/2 chance that blue is even and green is even.

~

Answer:

See below.

Step-by-step explanation:

This is a skewed distribution so the best measure of centre is the median.

The best measure of spread  is the IQR because of the skewed distribution.

Hi, hope this helps you out. I understand how this can be confusing. Have a great day! :)

Answer:

[tex]\frac{10y - 11}{(y - 1)(y - 2)( y + 1)}[/tex]

Step-by-step explanation:

1. Factor [tex]y^2 - 3y + 2[/tex]:

How-to:

After breaking the expression into groups, you're left with [tex](y^2 - y) + (-2y + 2)[/tex]. Factor out y from [tex]y^2 - y[/tex][tex]: y(y - 1)[/tex]. Factor out [tex]-2[/tex] from [tex]-2y + 2: -2(y - 1)[/tex]  = [tex]y( y - 1) - 2(y - 1)[/tex].  Finally, factor out common terms (in your case, y -1 ) and you're left with: [tex](y - 1)(y - 2)[/tex] Now you have [tex]\frac{3}{(y - 1)(y - 2)} + \frac{7}{y^2 - 1}[/tex]

2. Find the least common multiple of [tex]( y - 1)(y - 2), (y + 1)(y - 1)[/tex].

How-to:

Find an expression comprised of factors that appear in [tex]( y - 1)(y - 2), (y + 1)(y - 1)[/tex]. You'll find [tex](y - 1)(y - 2)(y + 1)[/tex]. Adjust your fractions based on the LCM and you'll get [tex]\frac{3(y + 1)}{(y - 1)(y - 2)(y + 1)}  + \frac{7 (y - 2)}{(y + 1)(y - 1)(y - 2)}[/tex]

3. Since the denominators are equal, combine the fractions above. You'll get [tex]\frac{3(y + 1) + 7(y - 2)}{(y - 1)(y - 2)(y + 1)}[/tex]

4. Expand [tex]\frac{3(y + 1) + 7(y - 2)[/tex] and you'll get [tex]10y - 11[/tex]. This is your new numerator.

Finally, your simplified operation is: [tex]\frac{10y - 11}{(y - 1)(y - 2)( y + 1)}[/tex]

To simplify an operation in mathematics, follow these steps: combine like terms, perform arithmetic operations, simplify fractions, and express the result in a simplified form.

When simplifying an operation in mathematics, you want to reduce the expression or equation to its simplest form. This may involve combining like terms, performing any necessary arithmetic operations, or simplifying fractions. Here are the steps to simplify an operation:

By following these steps, you can simplify any mathematical operation.

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To calculate Nick's monthly mortgage payment, determine the loan amount, convert the interest rate to a monthly rate, and use the formula for fixed mortgage payments. The monthly payment for Nick's mortgage is $467.72.

The monthly payment can be calculated using the loan amount, interest rate, and loan term.

Calculate the loan amount: $145,500 × 75% = $109,125.

Convert the annual interest rate to a monthly rate: 3.15% ÷ 12 = 0.2625%.

Plug the values into the formula for fixed mortgage payments: [tex]$109,125*\frac{0.002625*(1+0.002625)^{30*12}}{(1+0.002625)^{30*12}-1}[/tex]

The monthly payment for Nick's mortgage is $467.72.

The correct answer is option C. The monthly payment for Nick's mortgage is $467.72.

First, we calculate the mortgage amount, which is 75% of the purchase price:

[tex]\[ \text{Mortgage amount} = \frac{75}{100} \times \$145,500 = \$109,125. \][/tex]

Next, we convert the annual interest rate to a monthly interest rate:

[tex]\[ \text{Monthly interest rate} = \frac{3.15\%}{12} = \frac{0.0315}{12} \approx 0.002625. \][/tex]

Now, we use the formula for the monthly payment (M) on a fixed-rate mortgage, which is given by:

[tex]\[ M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}, \][/tex]

where P is the principal loan amount, r is the monthly interest rate, and n is the number of payments (30 years times 12 months per year).

So, we have:

[tex]\[ P = \$109,125, \][/tex]

[tex]\[ r = 0.002625, \][/tex]

[tex]\[ n = 30 \times 12 = 360. \][/tex]

Plugging these values into the formula gives us:

[tex]\[ M = \$109,125 \times \frac{0.002625(1 + 0.002625)^{360}}{(1 + 0.002625)^{360} - 1}. \][/tex]

Calculating this expression yields:

[tex]\[ M \approx \$467.72. \][/tex]

The complete question is:

Nick's new home had a purchase price of $145,500. He got a 30-year fixed mortgage for 75% of the purchase price. The interest rate on the loan is 3.15%. What is his monthly payment?

A. $3,437.44

B. $1,145.81

C. $467.72

D. $109.13

E. $145.50​

Answer:

D.) 42 cubes

Step-by-step explanation:

Instead of counting each cube, you can find the volume.

The formula to find volume is ( Volume = Length x Width x Height)

                                                  ( V= 2 x 7 x 3)

2 x 7 x 3 = 42 cubes

I hope this helped you ; )

Answer:

21

Step-by-step explanation:

Answer:

1. [tex]1. (\frac{5}{16}) (-2) (-4) (\frac{-4}{5})= -2 \\2. (2\dfrac{3}{5}) (\frac{7}{9})=(\frac{91}{45})\\3. (\frac{2}{3})(-4)(9)= -24\\4. (\frac{-3}{4}) (\frac{7}{8})=(\frac{-21}{32})[/tex]

Step-by-step explanation:

These are simple multiplication questions of fractions. We multiply numerator with numerators and denominators with denominators. If numerator and denominator is both divisible by same number we can divide them for simplification.

1. [tex](\frac{5}{16}) (-2) (-4) (\frac{-4}{5})[/tex]

[tex]=(\frac{-10}{16}) (-4) (\frac{-4}{5})\\=(\frac{40}{16}) (\frac{-4}{5})\\=(\frac{-160}{80}) \\dividing\,\, numerator\,\, and\,\, denominator\,\, by\,\, 80\,\,\\= -2[/tex]

2. [tex](2\dfrac{3}{5}) (\frac{7}{9})[/tex]

Converting mixed form into fraction form,

[tex]=(\frac{13}{5})(\frac{7}{9})[/tex]

Multiplying numerators with each other and denominators with each other

[tex]=(\frac{13*7}{5*9})\\=(\frac{91}{45})[/tex]

3. [tex](\frac{2}{3})(-4)(9)[/tex]

Multiplying these terms with each other:

[tex]=(\frac{2*-4}{3})(9)\\=(\frac{-8}{3})(9)\\=(\frac{-8*9}{3})\\=(\frac{-72}{3})\\[/tex]

Dividing numerator and denominator with 3

[tex]=-24[/tex] 

[tex]4. (\frac{-3}{4}) (\frac{7}{8})\\=(\frac{-3}{4}) (\frac{7}{8})\\=(\frac{-3*7}{4*8})\\=(\frac{-21}{32})[/tex]

Answer:

see explanation

Step-by-step explanation:

Given

x² + 10x + 14 = - 7 ( subtract 14 from both sides )

x² + 10x = - 21

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(5)x + 25 = - 21 + 25

(x + 5)² = 4 ( take the square root of both sides )

x + 5 = ± 2 ( subtract 5 from both sides )

x = - 5 ± 2

x = - 5 - 2 = - 7, or x = - 5 + 2 = - 3

-------------------------------------------------

The equation can also be solved by factoring

x² + 10x + 14 = - 7 ( add 7 to both sides )

x² + 10x + 21 = 0 ← in standard form

(x + 7)(x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x + 3 = 0 ⇒ x = - 3

I can answer your question if you could type in English plz

Answer:

1.6; exercise answer: 28

Step-by-step explanation:

It is just simple "plug in and evaluate".

Output → y

Input → x

I am joyous to assist you anytime.

Answer:

1.6

Step-by-step explanation

plz dont report people have been reporting me for no reason so if you dont report thanks

i know this because homework

Answer:

Hexagon

Regular polygon

Convex

Step-by-step explanation:

Hexagon is the name of the shape.

A regular polygon is a polygon with equal sides.

Convex means "A shape with no indentations."

Answer:

5.

Step-by-step explanation: