Answers
Answer:
In this case, you can use the concept of cosine to calculate y, and things are even easier when you have one of the special angles which is a 45° angle.
So we know that: cos45° = √2/2
This fact will always be true. In our case, we have:
cos45° = 7/y
Therefore, we have the equation:
7/y = √2/2
⇔ 14 = y√2
⇔ y = 14/√2
⇔ y = √196/√2 = √(196/2) = √98 = 7√2
So y is equal to 7√2
Answer:
7√2
Step-by-step explanation:
By observation, we can determine that because this is a right angle triangle with one of the internal angles = 45°, that the remaining unknown angle is also 45°, which makes this an isosceles triangle.
This means that x = 7
we can find y by using the Pythagorean equation:
y² = x² + 7²
y² = 7² + 7²
y² = 98
y = √98 = 7√2
Related Questions
Which point is on the graph of f(x)= 3 • 4^x?
Answers
The answer is C. (1, 12).
12 = 3 x [tex]4^{1}[/tex]
Answer:
Step-by-step explanation:
f(x)= 3 • 4^x
we can use the x coordinate of the points given in option to check what value do we get for y or f(x) .
so using the point from first option A :
x= 12
[tex]y=f(12)=3.4^{12}=50331648\neq 1[/tex]
for option B
x=0
[tex]y=f(0)=3.4^0=3[/tex]
option C
x=1
[tex]y = f(1)= 3.4^1=12[/tex]
so the correct option is C
Solve for x in the equation X2 - 10x+ 25 = 35.
Answers
Answer:
x = 5 ± sqrt(35)
Step-by-step explanation:
X^2 - 10x+ 25 = 35.
Factor the left hand side. This is the difference of squares. a^2 -2ab - b^2 = (a-b)^2 where a = x and b = 5
(x-5) ^2 = 35
Take the square root of each side
sqrt((x-5) ^2) =± sqrt(35)
x-5 = ± sqrt(35)
Add 5 to each side
x-5+5 = 5 ± sqrt(35)
x = 5 ± sqrt(35)
|
3. What is the next number in the sequence 20, 10, 5, 5/2
Answers
Answer:
[tex]\large\boxed{\dfrac{5}{4}}[/tex]
Step-by-step explanation:
[tex]a_1=20\\\\a_2=\dfrac{20}{2}=10\\\\a_3=\dfrac{10}{2}=5\\\\a_4=\dfrac{5}{2}\\\\a_5=\dfrac{\frac{5}{2}}{2}=\dfrac{5}{2}\cdot\dfrac{1}{2}=\dfrac{5}{4}[/tex]
A pair of jeans that originally cost $25.60 is 45% off .what is the sale price for the jeans?
Answers
Answer:
Step-by-step explanation:
45% off $25.60
= [tex]\frac{45}{100}[/tex] x $25.60
= $11.52 (Ans)
Answer:
$11.52
Step-by-step explanation:
$25.60 is 25.6 and 40% is 0.40
So do 25.6 * 0.40 and you get your answer of $11.52
Hope this helped ^-^
Lota points
44 is 25% of what
Answers
Answer:
176
Step-by-step explanation:
To find a number from a known percentage and a number, divide the given number by the percent.
[tex]\frac{v}{p}[/tex]
Where [tex]v[/tex] is the value given and [tex]p[/tex] is the percentage.
[tex]\frac{44}{0.25}=176[/tex]
Answer:
176
Step-by-step explanation:
1. Find the product (13 – x2)(x + 2).
-x3 - 2x2 + 13x + 26
Answers
Answer:
The product is -x³ - 2x² + 13x + 26
Step-by-step explanation:
* Lets revise how to find the product of two binomials
- If (ax ± b) and (cx ± d) are two binomials, where a , b , c , d are constant
their product is:
# Multiply (ax) by (cx) ⇒ 1st term in the 1st binomial and 1st term in the
2nd binomial
# Multiply (ax) by (d) ⇒ 1st term in 1st binomial and 2nd term in
2nd binomial
# Multiply (b) by (cx) ⇒ 2nd term in 1st binomial and 1st term in
2nd binomial
# Multiply (b) by (d) ⇒ 2nd term in 1st binomial and 2nd term in
2nd binomial
# (ax ± b)(cx ± d) = cx² ± adx ± bcx ± bd
- Add the terms adx and bcx because they are like terms
* Now lets solve the problem
- There are two binomials (13 - x²) and (x + 2)
- We can find their product by the way above
∵ (13)(x) = 13x ⇒ 1st term in the 1st binomial and 1st term in the
2nd binomial
∵ (13)(2) = 26 ⇒ 1st term in 1st binomial and 2nd term in
2nd binomial
∵ (-x²)(x) = -x³ ⇒ 2nd term in 1st binomial and 1st term in
2nd binomial
∵ (-x²)(2) = -2x² ⇒ 2nd term in 1st binomial and 2nd term in
2nd binomial
∴ The product of (13 - x²)(x + 2) = 13x + 26 - x³ - 2x²
- There is no like terms
- Lets arrange the terms from greatest power to smallest power
∴ The product is -x³ - 2x² + 13x + 26
Select the correct solution set. x + 17 ≤ -3
{x | x ≤ -20}
{x | x ≤ 14}
{x | x ≥ -20}
Answers
Answer:
{x | x ≤ -20}
Step-by-step explanation:
x + 17 ≤ -3
Subtract 17 from each side
x + 17-17 ≤ -3-17
x ≤ -20
Answer:
{x | x ≤ -20}
Guys please help!! Show your work! Any answers help
Answers
Answer:
I only know how to do the first and second one i'm not sure about the rest: V=Lwh
Step-by-step explanation:
so, (6)(6)(8)= 288ft^3
and (12)(16)(18)= 3456m^3
Hope i have helped you in some way!
The point-slope form of the equation of the line that passes through (–9, –2) and (1, 3) is y – 3 = (x – 1). What is the slope-intercept form of the equation for this line?
Answers
Answer:
the slope intercept form is: y = x+2
Step-by-step explanation:
The general form of point slope form is : y-y₁ = m(x-x₁)
The given equation is: y – 3 = (x – 1)
comparing we get,
m = 1
and solving the equation;
y-3 = x-1
Adding +3 on both sides
y = x-1+3
y=x+2
The general formula of slope-intercept form is : y = mx+b
where m is the slope and b is the y-intercept
so, y = x+2
where m =1 and b=2
so, the slope intercept form is: y = x+2
Answer:
the answer is y = y= 1/2x+2
Step-by-step explanation:
A sample data set has a mean of 122.3 and a standard deviation of 18.5. Convert a score of 168.4 to a z score and determine if the score is “usual” or “unusual.”
Answers
Answer:
[tex]Z=2.49[/tex] and this Z-score is “unusual.”
Step-by-step explanation:
To calculate the Z score use the following formula
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
Where
μ is the average
[tex]\sigma[/tex] is the standard deviation
x is the data to which we will calculate the z-score
In this case
[tex]\mu = 122.3\\\\\sigma= 18.5\\\\x =168.4[/tex]
So
[tex]Z=\frac{168.4-122.3}{18.5}[/tex]
[tex]Z=2.49[/tex]
A z-score is unusual if [tex]Z> 2[/tex] or [tex]Z < -2[/tex]
Finally
[tex]Z=2.49[/tex] and this Z-score is “unusual.”
Answer: 2.49 unusual
Step-by-step explanation:
A. Look at the diagram of the two squares shown below.
The Pythagorean theorem says that for any right triangle, the square of the length of the hypotenuse, c, is equal to the sum of the squares of the lengths of the legs (a and b): a2 + b2 = c2. Explain how the diagram shown above can be used to prove the Pythagorean theorem. Show your work.
B. Look at the small box shown below.
What is the length of the diagonal of the box shown? Leave your answer in radical form. Show your work and explain your steps.
Answers
Squares 1 and 2 have the same area because they're both (a+b) on a side.
Each of these squares is covered by four identical right triangle tiles, legs a,b, hypotenuse c.
In the first picture we see the uncovered part of the square, not covered by triangular tiles, is two squares, area [tex]a^2+b^2[/tex].
In the second picture the uncovered part of the square is a smaller square, area [tex]c^2[/tex].
We just moved the tiles around on the square, so the uncovered part is the same in both cases. So
[tex]a^2 + b^2 = c^2[/tex]
--------
The rectangular prism has a bottom rectangular base 6 by 8. So the diagonal is [tex]\sqrt{6^2+8^2}=\sqrt{100}=10[/tex].
The diagonal and the 7 cm side make a right triangle whose hypotenuse is the diagonal of the rectangular prism we seek.
[tex]\sqrt{10^2 + 7^2} = \sqrt{149}[/tex]
Answer: √149
write the equation in logarithmic form e^x=403.429
Answers
[tex]x=\ln 403.429[/tex]
Factor completely 5y^2-2y-3
Answers
Answer:
(5y+3)(y-1)
Step-by-step explanation:
5y^2-2y-3
I don't know if you like trial factors or not... but we can try that way
notice we have 5y^2
that can be written as 5y * 1y
Notice at the end we have -3
that can be written as -3*1
So possible answers could be:
(5y-3)(1y+1) =5y^2+5y-3y-3=5y^2+2y-3
So this was almost right.
If we just switch the signs the - and + there we will have got it
(5y+3)(1y-1)=5y^2-5y+3y-3=5y^2-2y-3 which is good
So the answer is (5y+3)(y-1)
To factor the quadratic equation 5y^2-2y-3 completely, find two numbers that multiply to -15 and add to -2, and use them to rewrite the middle term before factoring by grouping. The factors obtained are (5y - 3)(y + 1).
Explanation:The given quadratic equation to factor completely is 5y^2-2y-3. To achieve this, we are finding two numbers that multiply to the product of the coefficient of y^2 (which is 5) and the constant term (which is -3), and at the same time add up to the coefficient of the y term (which is -2).
The required pair of numbers is -3 and -1, because (-3)*(1) = -3 (the product of coefficient of y^2 and the constant term) and (-3)+(1) = -2 (the coefficient of the y term).
We rewrite the middle term and then factor by grouping:
Rewrite the equation: 5y^2 - 3y + y - 3Group the terms: (5y^2 - 3y) + (y - 3)Factor out the common terms: y(5y - 3) + 1(5y - 3)Since both terms have a common factor of (5y - 3), we can factor it out to get the final factored form: (5y - 3)(y + 1).Learn more about Factoring Quadratics here:https://brainly.com/question/30398551
#SPJ2
Can someone help me plz
Answers
Answer:
2p, since twice as long would hint to multiplication.
The functions f(x) and g(x) are shown in the graph
f(x)=x^2
What is g(x) ?
Answers
Answer:
[tex]g(x)=-x^{2}-4[/tex]
Step-by-step explanation:
we know that
The function g(x) is a vertical parabola open downward with vertex at (0,-4)
The equation of a vertical parabola into vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
I assume that g(x) is a reflection of the function f(x) over the line y=-2
so
a=-1 ---> because in the function f(x) the value of a is equal to 1
therefore
[tex]g(x)=-x^{2}-4[/tex]
What is square root of -98 + 71
Answers
Answer:
= 5.196 i
Step-by-step explanation:
The problem tells us to find the square root of -98 +71
√(-98 + 71)
= √(-27)
Which is an imaginary number
=√(-3^3)
Lets remember that, √(-1) = i
= i*3√(3)
= 5.196 i
Please see attached image for more information
The diagnals of a parallelogram are congruent. Which could be the parallelogram?
A. Trapezoid
B. Rectangle
C. Kite
D. Rhombus
Answers
Answer:
B. Rectangle
Step-by-step explanation:
All rectangles are parallelograms.
When a factor x − k is raised to an odd power, the graph crosses the x-axis at x = k.
When a factor x − k is raised to an even power, the graph only touches the x-axis at x = k.
Describe the graph of the function g(x) = (x − 1)(x + 4)3(x + 5)2.
The graph:
crossesdoes not intersecttouches the axis at (1, 0).
crossesdoes not intersecttouches the axis at (−4, 0).
crossesdoes not intersecttouches the axis at (−5, 0)
Answers
Answer:
The graph of [tex]g(x) = (x - 1) (x + 4)^3(x +5)^2[/tex] crosses the x-axis at (1,0) and (-4, 0). It touches the x-axis at (-5, 0).
Step-by-step explanation:
g(x):
[tex]g(x) = (x - 1) (x - (-4))^3(x - (-5)^2[/tex].
There are three factors:
(x - 1), where k = 1,(x - (-4)), where k = -4, and(x - (-5)), where k = -5.The first and second factors are raised to odd powers. The graph will cross the x-axis at all these two points:
(1, 0) as a result of the factor (x - 1), (-4, 0) as a result of the factor (x - (-4)).The third factor is raised to an even power. The graph will touch the x-axis at that point.
(-5, 0) as a result of the factor (x - (-5)).Answer:
crosses at (1,0)
crosses at (-4,0)
touches at (-5,0)
Got correct on ed
Step-by-step explanation:
Miss Wilson has spent $6 on breakfast using her debit card 5 mornings per week for the past 8 weeks. What is the change in Miss Wilson’s account balance from buying breakfast during this time? Write a multiplication expression. Then find and interpret the product
Answers
Answer:
(6x5) • 8
Step-by-step explanation:
We’ll I find it’s 6 dollars a day and their are 5 days that would be 30 but this went in for 8 weeks so it would be 30 x 8 which equal 240
Answer:
Required expression for amount spend on breakfast for 8 week is ( 6 × 5 ) × 8 and this amount is $ 240
Step-by-step explanation:
Given:
Amount spend on Breakfast using debit card = $6
Amount for breakfast spend for 5 mornings per week for past 8 weeks.
We need to write the multiplication expression for the given situation.
Amount spend on breakfast for a morning = $6
Amount spend on breakfast for 5 morning = 6 × 5
Amount spend on breakfast for 1 week = $ ( 6 × 5 )
Amount spend on breakfast for 8 week = ( 6 × 5 ) × 8
Required multiplication expression = ( 6 × 5 ) × 8
Answer of the multiplication = ( 6 × 5 ) × 8 = ( 30 ) × 8 = 240
Therefore, Required expression for amount spend on breakfast for 8 week is ( 6 × 5 ) × 8 and this amount is $ 240
A line passes through the points (−200,−4.03×10^4) and (50,9.7×10^3). Find the value of y when x=100. Write your answer in scientific notation.
Answers
Answer:
[tex]y=19.7*10^{3}[/tex]
Step-by-step explanation:
step 1
Find the slope
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex](-200,-4.03*10^{4}), (50,9.7*10^{3})[/tex]
convert to
[tex](-200,-40.3*10^{3}), (50,9.7*10^{3})[/tex]
substitute in the formula
[tex]m=\frac{9.7*10^{3}+40.3*10^{3}}{50+200}[/tex]
[tex]m=\frac{50*10^{3}}{250}[/tex]
[tex]m=200[/tex]
step 2
Find the equation of the line into point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex](x1,y1)=(50,9.7*10^{3})[/tex]
[tex]m=200[/tex]
substitute
[tex]y-9.7*10^{3}=200(x-50)[/tex] ----> equation of the line into point slope form
step 3
Find the value of y when x=100
substitute in the equation the value of x
[tex]y-9.7*10^{3}=200(100-50)[/tex]
[tex]y=200(50)+9.7*10^{3}[/tex]
[tex]y=19,700[/tex]
[tex]y=19.7*10^{3}[/tex]
When Quentin ordered a tennis racquet recently, he agreed to pay a 7% shipping and handling charge. If Quentin paid $9.45 in shipping and handling, bow much must the racquet have cost? Urgent!!!!!!!!!!!!!
Answers
Answer:
The cost of the racquet is [tex]\$135[/tex]
Step-by-step explanation:
Let
x-----> the cost of the racquet
we know that
The racquet represent the 100%
so
using proportion
[tex]x/100\%=\$9.45/7\%[/tex]
[tex]x=100\%*(\$9.45)/7\%[/tex]
[tex]x=\$135[/tex]
1. At a fundraiser dinner, the bill for 4 cups of coffee
and 6 spaghetti specials is $20.50, whereas the bill for 1 cup of coffee and 3 spaghetti
specials is $8.75.
Write
a system of 2 equations to model this problem. Let c stand for the price of a cup of coffee and let s stand for the price of a spaghetti
special.
Use the
substitution method to solve the system of equations.
What
would the bill be for 1 cup of coffee and 1 spaghetti special?
(Pls help!)
Answers
1- Writing the system of equations:
The price of a cup of coffee is denoted by c while the price of a spaghetti is denoted by s
We are given that:
4 cups of coffee and 6 spaghetti cost $20.5
This means that:
4c + 6s = 20.5 ................> equation 1
We are also given that:
1 cup of coffee and 3 spaghetti cost $8.75
This means that:
c + 3s = 8.75 .................> equation 2
2- Solving the equations using substitution methods:
From equation 2:
c = 8.75 - 3s ................> I
Substitute with I in equation 1 and solve for s as follows:
4c + 6s = 20.5
4(8.75 - 3s) + 6s = 20.5
35 - 12s + 6s = 20.5
35 - 6s = 20.5
6s = 14.5
s = $2.41667
Substitute with s in I to get c:
c = 8.75 - 3s
c = 8.75 - 3(2.41667) = 1.4999 = $1.5
3- getting price for 1 cup of coffee and 1 spaghetti:
c + s = 1.5 + 2.41667 = $3.91667
Hope this helps :)
At a busy street corner, one of every hundred jaywalkers will be hit when they cross. What is the probability of a jaywalker not being hit if he makes a round trip daily for thirty days? (0.01)30 (0.99)30 (0.9801)30
Answers
Answer: Last option
[tex]p = (0.9801) ^ {30}[/tex]
Step-by-step explanation:
the probability of a jaywalker being hit is
[tex]P = \frac{1}{100} = 0.01[/tex].
So the probability of a jaywalker not being hit is:
[tex]P '= 1-0.01[/tex]
[tex]P '= 0.99[/tex]
As in this experiment the probability of each trial is independent then, the probability that it is not a jaywalker will not be hit if it makes a round trip is:
[tex]P '= (0.99) (0.99) = 0.9801[/tex]
[tex]P '= 0.9801[/tex]
If this experiment is repeated for 30 days then the probability that it is not a jaywalker will not be hit if it makes a round trip is:
[tex]p = (0.9801) ^ {30}[/tex]
Which of the following equations can be used to find the length of angle LN in the triangle below?
HELP ASAP PLS
Answers
Answer:
Option A. [tex]LN^{2}=33^{2}-11^{2}[/tex]
Step-by-step explanation:
we know that
In the right triangle MNL
Applying the Pythagoras Theorem
[tex]MN^{2}=ML^{2} +LN^{2}[/tex]
substitute the values
[tex]33^{2}=11^{2} +LN^{2}[/tex]
[tex]LN^{2}=33^{2}-11^{2}[/tex]
8/9 and 7/8 common denominator
Answers
Answer: 72
Step-by-step explanation:
Rewriting input as fractions if necessary:
8/9, 7/8
For the denominators (9, 8) the least common multiple (LCM) is 72.
LCM(9, 8)
Therefore, the least common denominator (LCD) is 72.
Rewriting the original inputs as equivalent fractions with the LCD:
64/72, 63/72
which graph represents the solution of the inequality?
Answers
Answer:
The third graph.Step-by-step explanation:
[tex]14\leq2t+18\leq20\qquad\text{subtract 18 from all sides}\\\\14-18\leq2t+18-18\leq20-18\\\\-4\leq2t\leq2\qquad\text{divide all sides by 2}\\\\\dfrac{-4}{2}\leq\dfrac{2t}{2}\leq\dfrac{2}{2}\\\\-2\leq t\leq1\\\\\text{The third graph.}[/tex]
Which methods could you use to calculate the y-coordinate of the midpoint of
a vertical line segment with endpoints at (0,0) and (0, 15)
Answers
Answer:
Counting by hand
Dividing 15 by 2
Step-by-step explanation:
can some one help me please time
Answers
Answer:
The answer would be B. 2x+4 / x
For this case we have that by definition of composition of functions that:
[tex](f_ {0} h_ {0} g) = f (h (g (x)))[/tex]
So:
[tex]h (g (x)) = 4 (x-2) -1 = 4x-8-1 = 4x-9[/tex]
So:
[tex]f (h (g (x))) = \frac {4x-9 + 4} {4x-9} = \frac {4x-5} {4x-9}[/tex]
ANswer:
[tex](f_ {0} h_ {0} g) = \frac {4x-5} {4x-9}[/tex]
Option D
You invest $3000 in an account at 3.5% per year simple interest. How much will
you have in the account at the beginning of the 7th year?
A. $3735
B. $3720
C. $3540
D. $3630
Answers
Paul to Ava salaries ratio is 3:4. If Paul's salary is $87,000, what is Ava's salary?
Answers
Answer: $116,000
Step-by-step explanation:
Set up a ratio and then cross multiply and divide. See paper attached. (:
Final answer:
Ava's salary is calculated based on the given salary ratio of Paul to Ava (3:4). By dividing Paul's salary by 3, we find out how much one part of the ratio is worth and then multiply by 4 to find Ava's salary to be $116,000.
Explanation:
The question provided asks us to calculate Ava's salary based on the ratio of Paul to Ava's salaries which is 3:4. If Paul's salary is $87,000, we determine Ava's salary using the given ratio. Here is the step-by-step process:
Step 1: Understand the ratio, which tells us that for every 3 parts of Paul's salary, Ava gets 4 parts. This does not tell us the total amount, but how they share the total amount.
Step 2: Since Paul's salary is $87,000, and that represents 3 parts of the total, we divide $87,000 by 3 to find out what 1 part is: $87,000 / 3 = $29,000.
Step 3: Now that we know 1 part is $29,000, we can calculate Ava's salary which is 4 parts: $29,000 X 4 = $116,000.
Ava's salary is therefore $116,000.