Answers
7[tex]\sqrt{2}[/tex]
Step-by-step explanation:The triangle shown is a 45-45-90 triangle. This name comes from the fact the 3 angle measurements are 45, 45, and 90 degrees.
If needed, you could find the missing angle using the equation: 180 - (45 + 90) = x.
Special Right Triangles
Special right triangles allow us to use formulas and shortcuts to find missing sides easily. Another type of special right triangle is the 30-60-90 triangle. While both of these are special right triangles, they have different formulas.
Formulas
All 45-45-90 triangles have 2 types of sides: the legs (a and b) and the hypotenuse (c).
c = b[tex]\sqrt{2}[/tex]b = a a = bIn these triangles, both of the legs are congruent.
Solving for c
Since we are given b, we can just plug the b-value into the formula that solves for c.
c = 7[tex]\sqrt{2}[/tex]The answer cannot be simplified further, so this is the final answer.
Answer:
Second option
Step-by-step explanation:
It is a right triangle isosceles
a = b = 7
c = hypotenuse
[tex]c =\sqrt{7^{2}+7^{2} } =\sqrt{49+49} =\sqrt{2(49)}=7\sqrt{2}[/tex]
Hope this helps
Related Questions
What is the exact value of sin (165 degrees)
Answers
Answer:
Step-by-step explanation:
(√6 - √2)/4
Which ordered pairs make both inequalities true? Check all that apply
Answers
Answer:.
Step-by-step explanation:
√2/√2+√3-√5 rationalise the denominator
Answers
answer is
(2√6+√15+6)/12
Which is mostly likely to be the first step in solving a system of nonlinear equations by substitution
Answers
Answer: To solve a system of equations by substitution, we can rewrite a two-variable equation as a single variable equation by substituting the value of a variable from one equation into the other. Let’s start by solving the system of equations that we looked at above: x=4 x = 4 y+x=12 y +x = 12
Step-by-step explanation:
Answer:
Isolating a variable in one of the equations.
Step-by-step explanation:
Weekly wages at a certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$350 and $400.
[ ? ]%
Answers
4
12 + 17 < -18 *
True
False
Answers
12+ 17 = 29
4 * -18 = -72
so the answer would be false, since 29 is greater than -72
w and x are whole numbers
w>60
x<50
Work out the smallest possible value of x-z
Answers
Using the given information, the smallest possible value of x - z is 12
Evaluating an expressionFrom the question, we are to determine the smallest possible value of x - z
From the given information,
w and x are whole numbers
and
w > 60
x < 50
∴ w = 61, 62, 63, 63, 65, ...
x = 49, 48, 47, 46, 45, ...
Then,
The smallest possible value of x - z is
x - z = 61 - 49
x - z = 12
Hence, the smallest possible value of x - z is 12
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5x + 13y=232
12x + 7y= 218
Answers
Answer:
x=10, y=14
Step-by-step explanation:
added in the picture
Trey graphs the equations y = –x2 + 2x + 3 and y = x2 – 2x + 3 to solve the equation –x2 + 2x + 3 = x2 – 2x + 3. His graph is shown below.
What are the solution(s) of –x2 + 2x + 3 = x2 – 2x + 3?
Answers
The solution of the equation -x^2 + 2x + 3 = x^2 - 2x + 3 are the x-coordinates of common points on the graphs are x=0 and x=2.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
As we can see from the attached graph these graphs intersect at points (0,3) and (2,3).
The system of equation are;
[tex]y = x^2 + 2x + 3 \\y = x^2 - 2x + 3[/tex]
So,
[tex]-x^2 + 2x + 3 = x^2 - 2x + 3 \\\\2x^2 - 4x = 0\\\\2x ( x - 2) = 0[/tex]
Then the solutions of the equation are x=0 and x=2.
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Answer:
0 and 2
Step-by-step explanation:
b on edge
John bought 8 watches for $56 and his friend victor bought 7 watches for $63. whose watch is expensive ?
Answers
Victor =$9 each watch
63*8= 504
56*7=382.
John bought 56 for 382
Victor bought 56 for 504.
if x=p+2 and y=p-3, show that x+y+1=2p and x-y-5=0
Answers
If [tex]x=p+2[/tex] and [tex]y=p-3[/tex], then
[tex]x+y = (p+2) + (p-3) = 2p - 1 \implies x+y+1=2p[/tex]
and
[tex]x-y = (p+2)-(p-3) = 5 \implies x-y-5=0[/tex]
as required.
Car A is traveling east at a steady speed of 50 miles per hour. After 2 hours, it is 140 miles east of Johnstown.
Car B is traveling east on the same road. its distance east of Johnstown is represented by the graph.
Where were the two cars in relation to each other when they began traveling?
Answers
The two cars in relation to each other when they began travelling will be car B was 20 miles east of car A. Then the correct option is A.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
Car A is travelling east at a steady speed of 50 miles per hour.
Then the equation of car A is given as
y = 50x + C
where x be the number of miles and x be the number of hours.
Then we have
After 2 hours, it is 140 miles east of Johns town.
Then we have
y = 50x ..1
Car B is travelling east on the same road. its distance east of Johns town is represented by the graph.
Then the equation of car B will be
y = [(120 - 20) / (2 - 0)]x + 20
y = 50x + 20 ...2
Then the two cars in relation to each other when they began travelling will be car B was 20 miles east of car A.
Then the correct option is A.
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Answer:
Car A was 20 miles east of car B.
Step-by-step explanation:
If the point (7, 3) is on the graph of an equation, which statement must be true?
Answers
Answer:
The values x = 7 and y = 3 make the equation true.
Step-by-step explanation:
hope this helps
The enrollment for a new program is 1,500 students. the program is expected to grow at a rate of 0.03. what is the expected enrollment in 7 years? round to the nearest whole number.
Answers
The expected enrolment in 7 years is 1845.
What is the expected enrolment?The formula for calculating future value of the number of students is an exponential equation with this form:
FV = P (1 + r) ^n
FV = Future populationP = Present populationR = rate of growth of the populationN = number of years1500 x (1.03)^7 = 1845
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Scientists are using a computer simulation to test ideas about climate on Earth. Looking at one period of time in the simulation, they notice that more energy entered the Earth system than exited. How might the amount of carbon dioxide have changed to cause this, and how would this have changed the energy in the Earth system? In the simulation,
A. Carbon dioxide decreased, leading to less energy in the Earth system and less energy absorbed by Earth’s surface.
B. Carbon dioxide decreased, leading to more energy in the Earth system and more energy absorbed by Earth’s surface.
Carbon dioxide increased, leading to less energy in the Earth system and less energy absorbed by Earth’s surface.
D. Carbon dioxide increased, leading to more energy in the Earth system and more energy absorbed by Earth’s surface.
Answers
Answer:
Step-by-step explanation:
ore energy entered the Earth system than exited due to the greenhouse effect, solar energy trapping systems like solar panel, etc.
How CO₂ changed the energy in the Earth system due to many reasons:-
Carbon dioxide forces the Earth's energy budget out of balance by absorbing thermal infrared energy radiated by the surface. It absorbs thermal infrared energy with wavelengths in a part of the energy spectrum that other gases, such as water vapor, co₂, etc.
The greenhouse effect also increases energy in the earth's system.
An increase in the amount of carbon dioxide creates an overabundance of greenhouse gases that trap additional heat.
These greenhouse gas emissions have increased the greenhouse effect and caused the earth's surface temperature to rise.
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Can someone help me with fill the blanks of this pls? It’s about geometry
Answers
Answer:
see below
Step-by-step explanation:
2: letter at the vertex, placing a letter or number inside .... , or by using 3 letters
3:
WXY
WXZ
YXZ
4: X
A bike store rents bikes for $9 an hour in addition to a helmet rental fee of $15. If
Emmanuel paid $51, for how many hours did he rent the bike?
Answers
Answer:
4 hours
Step-by-step explanation:
First we need to subtract the one pay fee (the helmet rental fee, $15)
So 51 - 15 = 36
Then we need to divide 36 by the amount of money it costs for each hours to find how many hours he rented the bike
So 39/9 = 4
find x ratio y... help please, i have a test tomorrow.
thanks
Answers
Answer:
27/4
Step-by-step explanation:
added in the picture
If 5 hours at a computer terminal costs $25, what is the cost of 6 hours?
A. $30
B. $45
C. $150
D. $12
Answers
Answer:
30 dollars
Step-by-step explanation:
25/5 = 5 dollars per hour
so 6 hours would be 5 * 6 = 30 dollars
Answer:
It would be B
Step-by-step explanation:
First, we need to find out the unit rate
5/25=1/5
Therefore, that means in one hour the cost would be $5
Since you are going from one hour to 6 hours you need to multiply both numbers by 6
Since 5x6=30, it would be 30$ :)
p=f/a, where f=70 and a=20 f is increased by 10 a is increased to by 10
Answers
Answer:
P=3.5
P=2.667
Step-by-step explanation:
p=f/a
P=70/20
P=3.5
then f is increased by 10
f=70+10=80
and a is increased by 10
a=20+10
a=30
therefore; P=f/a
P=80/30
P=2.667
A hiking club is planning a hike in the mountains. They estimates that it will take 3.5 hours to walk 6km. How long will it takes the group to walk 24km?
Answers
Answer:
14
Step-by-step explanation:
First divide 24 and 6 to find how much 6's there are in 24.
24/6=4
Now, we take that number and multiply it by 3.5 to find how long it will take the group to walk 24km.
3.5*4=14.
It will take the group 14 hours to walk 24 km.
Hope this helps!
If not, I am sorry.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Which is the correct representation of the inequality?
Here we have.
-3(2x - 5) < 5*(2 - x)
First, we need to isolate x in one side, let's expand both sides:
-6x + 15 < 10 - 5x
15 - 10 < 6x - 5x
5 < x
This will be represented with a number line where we have an open circle at 5, and an arrow that goes to the right. So the correct option is:
"A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right."
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What is the quadratic equation for 0=-2x+3x^2
Answers
x = 2/3 , 0 .
Question :
[tex] {3x}^{2} - 2x = 0[/tex]
use quadratic formula :
[tex]x = \frac{( - b)± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
Solution :
[tex]a {x}^{2} + bx + c = 0 \\ a = 3 \\ b = - 2 \\ c = 0[/tex]
[tex]x = \frac{ - ( - 2)± \sqrt{ { (- 2)}^{2} - 4 \times 3 \times 0} }{2 \times 3} \\ \\ x = \frac{2± \sqrt{4 - 0} }{6} \\ \\ x = \frac{2± \sqrt{4} }{6} \\ \\ x = \frac{2± 2}{6} [/tex]
separate into two equations :
[tex]x = \frac{2 + 2}{6} = \frac{4}{6} = \frac{2}{3} .[/tex]
[tex]x = \frac{2 - 2}{6} = \frac{0}{6} = 0.[/tex]
the values of x are 2/3 and 0 .
Teresa is factoring this polynomial by grouping. Which common factors should be used in the next step of factoring?
10x3+3x2−20x−6
(10x3+3x2)+(−20x−6)
x2 and −2x
2x2 and −2x
x2 and −2
2x2 and −2
Answers
Answer: [tex]x^2[/tex] and [tex]-2[/tex]
Step-by-step explanation:
original :
[tex](10x^3+3x^2)+(-20x-6)[/tex]
factored :
[tex]x^2(10x+3)+-2(10x+3)[/tex]
Answer :
[tex]x^2[/tex] and [tex]-2[/tex]
Using Newton-Raphson method to find the approximate root of the equation x log_{10}x=1.2
( Carry out three iterations ). [tex] \\ \\ [/tex]
Thank uh!
Answers
Answer:
[tex]x \approx 2.740646096[/tex]
Step-by-step explanation:
Given:
[tex]x\log_{10}x=1.2[/tex]
Rewrite so that it's equal to zero:
[tex]\implies x\log_{10}x-1.2=0[/tex]
Therefore:
[tex]\implies f(x)=x\log_{10}(x)-1.2[/tex]
Differentiate the function:
Use the product rule to differentiate [tex]x\log_{10}(x)[/tex]:
[tex]\textsf{Let }u=x \implies \dfrac{du}{dx}=1[/tex]
[tex]\textsf{Let }v=\log_{10}(x) \implies \dfrac{dv}{dx}=\dfrac{1}{x \ln 10}[/tex]
[tex]\begin{aligned}\implies \dfrac{dy}{dx} & = u\dfrac{dv}{dx}+v \dfrac{du}{dx}\\& = \dfrac{x}{x \ln 10}+\log_{10}(x)\\& = \dfrac{1}{\ln 10}+\log_{10}(x)\end{aligned}[/tex]
[tex]\implies f'(x)=\dfrac{1}{\ln 10}+\log_{10}(x)[/tex]
[tex]\implies f'(x)=\dfrac{1+\ln 10 \log_{10}(x)}{\ln 10}[/tex]
Newton-Rhapson iteration formula
[tex]x_{n+1}=x_n-\dfrac{f(x_n)}{f'(x_n)}[/tex]
Substitute the function and its derivative into the formula, replacing x with [tex]x_n[/tex]:
[tex]\implies x_{n+1}=x_n-\dfrac{x_n\log_{10}(x_n)-1.2}{\dfrac{1+\ln 10 \log_{10}(x)}{\ln 10}}[/tex]
[tex]\implies x_{n+1}=x_n-\dfrac{x_n\ln 10\log_{10}(x_n)-1.2\ln 10}{1+\ln 10 \log_{10}(x_n)}[/tex]
Therefore, the iteration formula is:
[tex]x_{n+1}=x_n-\dfrac{x_n\ln 10\log_{10}(x_n)-1.2\ln 10}{1+\ln 10 \log_{10}(x_n)}[/tex]
Let [tex]x_0=3[/tex]
Substitute this into the formula and carry out 3 iterations:
[tex]\implies x_{1}=3-\dfrac{3\ln 10\log_{10}(3)-1.2\ln 10}{1+\ln 10 \log_{10}(3)}=2.746149035[/tex]
[tex]\implies x_2=2.740648841[/tex]
[tex]\implies x_3= 2.740646096[/tex]
MARKING BRAINLIEST TO THE FIRST CORRECT ANSWER If triangle BCD was reflected over the x-axis, what would be the coordinates of the new triangle's vertices?
Answers
If BCD was reflected over the x axis then the coordinates will be B(-1,0) C(-1,2) and D(-4,1).
Given BCD is a triangle having coordinates (-1,0),(-1,-2),(-4,-1).
When the triangle is reflected over the x axis then all the values of y will change from negative to positive and the values of x remains same because in the second and third quadrant the values of x remains same and in the second quadrant the values of y used to be positive and in the third quadrant the values of y used to be negative.
So coordinates of B will change from (-1,0) to (-1,0)
coordinates of C will change from (-1,-2) to (-1,2)
coordinates of D will change from (-4,-1) to (-4,1)
New coordinates will be (-1,0) (-1,2) (-4,1).
Hence if BCD was reflected over x axis the new coordinates will be (-1,0) (-1,2) (-4,1).
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Assembly of a television set in the factory is set to 45 minutes. Some workers take a shorter time (t) at this while some take longer. However, each varies no more than 8 minutes. Which inequality below represents this scenario?
Answers
Answer:
a
Step-by-step explanation:
PLEASE HELP ME WITH THIS
Answers
Answer:
Decreases
Step-by-step explanation:
A negative correlation means the y is big when the x is small. As x gets bigger, y gets smaller.
Question 3 of 21
Which of the following are the domain and range that represent the inverse of
the function f(x), given the mapping diagram of f(x) below?
Answers
Answer: C
Step-by-step explanation:
The inverse of a function maps the domain onto the range.
What are the exact solutions of x2 − 3x − 5 = 0? (1 point) a x = the quantity of negative 3 plus or minus the square root of 29 all over 2 b x = the quantity of 3 plus or minus the square root of 29 all over 2 c x = the quantity of 3 plus or minus the square root of 11 all over 2 d x = the quantity of negative 3 plus or minus the square root of 11 all over 2
Answers
x = the quantity of 3 plus or minus the square root of 29 all over 2. Then the correct option is B.
What is the solution of the quadratic equation by formula method?The quadratic equation is given as ax² + bx + c = 0.
Then the solution is given as
[tex]\rm x = \dfrac{-b\pm \sqrt{b^2 - 4ac}}{2a}[/tex]
The quadratic equation is given below.
x² – 3x – 5 = 0
Then the solution of the equation will be
[tex]\rm x = \dfrac{-(-3)\pm \sqrt{(-3)^2 - 4 *1*(-5)}}{2*1}\\x = \dfrac{3 \pm \sqrt{29}}{2}[/tex]
Then the correct option is B.
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