Answers
The value of [tex]\(x\)[/tex] is [tex]\(14\)[/tex]. The correct option is [tex]\(14\)[/tex].
In a right triangle with a 45-degree angle, the sides are related by the special angles of 45-45-90 triangles. In such triangles, the sides are in the ratio [tex]\(1:1:\sqrt{2}\)[/tex].
Given that the height is [tex]\(7\sqrt{2}\)[/tex] and the hypotenuse is [tex]\(x\),[/tex] we can identify the relationship as follows:
[tex]\[ \text{Height} : \text{Base} : \text{Hypotenuse} = 1 : 1 : \sqrt{2} \][/tex]
So, the height is [tex]\(7\sqrt{2}\)[/tex], and the base would be [tex]\(7\sqrt{2}\)[/tex]as well, and the hypotenuse [tex](\(x\))[/tex] would be [tex]\(7\sqrt{2} \times \sqrt{2} = 7 \times 2 = 14\)[/tex].
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(14\)[/tex], and the correct option is:
• [tex]\(14\)[/tex]
The correct answer is [tex]\boxed{14}[/tex]. The value of x is [tex]\boxed{14}[/tex].
To determine the value of [tex]\( x \)[/tex], we need to consider the given options and the context of the question, which involves the square root of 2. The options provided are [tex]\( 7 \), \( 7\sqrt{2} \), \( 14 \), and \( 14\sqrt{2} \).[/tex]
Let's analyze the options:
1. [tex]\( 7 \)[/tex] is a straightforward integer.
2. [tex]\( 7\sqrt{2} \) is \( 7 \)[/tex] times the square root of 2, which is an irrational number approximately equal to [tex]\( 1.414 \)[/tex].
3.[tex]\( 14 \) is \( 7 \)[/tex] times [tex]\( 2 \)[/tex], which is a simple integer multiplication.
4. [tex]\( 14\sqrt{2} \) is \( 14 \)[/tex] times the square root of 2.
Given that the question is asking for the value of [tex]\( x \)[/tex] and the options involve multiples of [tex]\( 7 \)[/tex] and [tex]\( 14 \)[/tex], it is reasonable to suspect that the answer might involve the square root of 2, since it is the only mathematical operation present in all the options.
However, without additional context or a mathematical equation to solve for [tex]\( x \)[/tex], we cannot definitively determine which of these options is correct based solely on the information given. In mathematics, problems involving square roots typically require an equation or a geometric representation to provide a clear path to the solution.
Since the question does not provide an equation or additional context, we must rely on the principle that the most straightforward answer is often correct when dealing with multiple-choice questions. In this case, the simplest option that does not involve an irrational number is [tex]\( 14 \)[/tex].
Therefore, without further information, the most logical and simple choice is [tex]\( 14 \)[/tex], as it is a whole number and does not introduce the complexity of an irrational number like [tex]\( \sqrt{2} \)[/tex].
Thus, the final answer is [tex]\boxed{14}[/tex].
Related Questions
What number line represents the solution to the inequality below
HELP ITS DUE TOMORROW !!!!!!!!!
Answers
Answer:
B
Step-by-step explanation:
Step 1: Add 2 to both sides.
x−2+2>3+2
x>5
if a rhombus has diagonals of length 20 inches and 48 inches, what is the length of its perimeter? show the work you used to find your answer.
Answers
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.
Select all of the terms that apply to the shape.
pentagon
hexagon
heptagon
octagon
nonagon
decagon
regular polygon
irregular polygon
concave
convex
Answers
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."
If each term of a sequence changes by a common difference,d, what would a general rule for this type of sequence
A.) a(n)=(d)n-1
B.) an=an-1+d
C.) an=an-1+an-2
D.) an=n-1+an-2+d
Answers
===================================================
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]
What is the answer for #9?
Answers
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
multiply each set of numbers and match it with it’s product
Answers
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]
How do I simplify the operation?
Answers
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.
Explanation: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:
Combine like terms.Perform any necessary arithmetic operations such as addition, subtraction, multiplication, or division.Simplify fractions by finding the greatest common factor and dividing.Reduce any radical expressions to simplest form.If possible, express the result in a more simplified or concise form.By following these steps, you can simplify any mathematical operation.
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How many cubes are inside the rectangular prism?
A) 21 cubes
B) 28 cubes
C) 36 cubes
D) 42 cubes
Answers
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:
What is the input value for the following function if the output value is 1.2?
y = x - 0.4
0.8
8.4
1.6
4.2
Answers
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
The length of each leg of an isosceles triangle is 4cm less than twice the base. The perimeter of the triangle is 17 cm. Find the measure of each side of the triangle.
Answers
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.
PLEASE ANSWER RIGHT AWAY
Answers
Answer:
[tex]y=2\sin (x-\pi)[/tex]
Step-by-step explanation:
The sine graph has an amplitude of 2.
The period of this function is [tex]2\pi[/tex]
The graph is obtained by shift the graph of [tex]y=\sin x[/tex] [tex]\pi[/tex] units to the right.
Among the given equations, the only function which has these properties is
[tex]y=2\sin (x-\pi)[/tex]
The correct answer is option A
Help please about this math work
Answers
There is a 46% chance of a female patient having type-O blood
Answer:
19.6
Step-by-step explanation:
The question is slightly ambiguous. The data tells us that the number of females with O blood is 140.
I think you take this out of the entire population which is 714
The % is (140 / 714) * 100 = 19.61%
I wouldn't bet on these numbers being accurate.
The radius of a circle is 10. Using π, which equation expresses the ratio of the circumference of the circle to the circle's diameter?
Answers
Answer:
Step-by-step explanation:
en un mapa 3/16 de pulgada representa un pie. ¿ con que longitud se representan 6 1/4 pies?
Answers
I can answer your question if you could type in English plz
ab=6cm Ac=12 calculate the lenght of cd
Answers
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.
What is the area of the parallelogram?
Answers
Answer:
140 inches
Step-by-step explanation:
You do the base(14) times the hieght(10)
14x10=140
Need Help Assappp 10 points
5(2x − 3) = 5
How many solutions does this equation have?
What are the solutions to this equation
Please show your work
Answers
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
895 472 nearest 100000
Answers
The process of rounding 895,472 to the nearest 100,000 involves examining the ten thousands place of the number. Given it's 9, the number is rounded up to 900,000.
Explanation:The question is asking to round the number 895,472 to the nearest 100,000. To do this, you should look at the ten thousands place of the number, which is 9. If this digit is 5 or greater, round the hundreds of thousands place up. If it is less than 5, round down. In this case, since the ten thousands place is 9, we round 800,000 up to 900,000. Therefore, 895,472 rounded to the nearest 100,000 is 900,000.
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Please help!!!!
Solve the following inequality -1/2 p < -16
Answers
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.
Explanation: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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Write the expression in terms of cosine.please help.
Answers
Answer:
cos13°
Step-by-step explanation:
Using the cofunction identity
sinx° = cos(90 - x)°
sin77° = cos(90 - 77)° = cos13°
Solve the system y = -x + 7 and y = 0.5(x - 3)2
explain the answer
Answers
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
Please Help The question is in the picture
Answers
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!
A square has a perimeter of 36 units.
One vertex of the square is located at (3, 5) on the coordinate grid.
What could be the x- and y- coordinates of another vertex of the square?
Answers
(12,5) (3, -9) (3,14) (-6,5)
A certain shampoo is available in two sizes. A 14.2- ounce bottle costs $4.98. A 23.7- ounce bottle costs $6.97. Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent
Answers
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.
Explanation: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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Please help, asap !!
[ the 3 1/2 and 1 1/2 are fractions! ]
A rectangular prism has a length of 3 1/2 inches, a width of 5 inches, and a height of 1 1/2 inches.
What is the volume of the prism?
Enter your answer in the box as a simplified mixed number or a decimal.
Answers
Answer:
5.
Step-by-step explanation:
please hepppp due tomarrow means a lot
Answers
Answer:
1.4
Step-by-step explanation:
Mr Turner bought stock for $15,000. If the value of the stock decreases 4% each year when will it be worth 80% of original price?
Answers
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]
Which expression is equivalent to? Please help! Screenshots attached.
Answers
Answer:
[tex]\frac{\sqrt{5} }{x^{2} y}[/tex]
Step-by-step explanation:
That's a complex expression, let's simplify it, step by step, off the start, we'll simplify the 55/11:
[tex]\sqrt{ \frac{55 x^{7} y^{6} }{11 x^{11} y^{8} } } = \sqrt{ \frac{5 x^{7} y^{6} }{x^{11} y^{8} } }[/tex]
Then we'll simplify the x's and y's:
[tex]\sqrt{ \frac{5 x^{7} y^{6} }{x^{11} y^{8} } } = \sqrt{ \frac{5}{x^{4} y^{2} } }[/tex]
Let's split the square root in two and solve the bottom part:
[tex]\sqrt{ \frac{5}{x^{4} y^{2} } } = \frac{\sqrt{5} }{\sqrt{x^{4} y^{2}} } = \frac{\sqrt{5} }{x^{2} y}[/tex]
The solution is then:
[tex]\frac{\sqrt{5} }{x^{2} y}[/tex]
The expression which is equivalent to the given expression is:
[tex]\dfrac{\sqrt{5}}{x^2y}[/tex]
Step-by-step explanation:We are given a expression as:
[tex]\sqrt{\dfrac{55x^7y^6}{11x^{11}y^8}}[/tex]
Now we know that:
[tex]55=11\times 5[/tex]
Hence, we get:
[tex]\sqrt{\dfrac{55x^7y^6}{11x^{11}y^8}}=\sqrt{\dfrac{11\times 5x^7y^6}{11x^{11}y^8}[/tex]
which is written as:
[tex]\sqrt{\dfrac{5x^7y^6}{x^{11}y^8}}[/tex]
Also, we know that if n>m
Then
[tex]\dfrac{a^m}{a^n}=\dfrac{1}{a^{n-m}}[/tex]
Hence, we have the expression as:
[tex]=\sqrt{\dfrac{5}{x^{11-7}y^{8-6}}}\\\\\\=\sqrt{\dfrac{5}{x^4y^2}[/tex]
This could be given as:
[tex]=\dfrac{\sqrt{5}}{\sqrt{x^4}\sqrt{y^2}}[/tex]
Now, we know that:
[tex]\sqrt{x^4}=\sqrt{(x^2)^2}=x^2\\\\and\\\\\sqrt{y^2}=y[/tex]
Hence, we get that:
[tex]\sqrt{\dfrac{55x^7y^6}{11x^{11}y^8}}=\dfrac{\sqrt{5}}{x^2y}[/tex]
(25 POINTS!!)What is the equation of the line that passes through the points (15,9) and (-2,9)?
I need this answered with in the next 20 minutes so someone please help :,D
The answer is gonna be a equation like y=
Answers
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]
7. 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?
$3,437.44
$1,145.81
$467.72
$109.13
$145.50
Answers
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