Answers
x=-13
x=2
Answer:
Solution given:
5-2x=[tex]\sqrt{2x²+x-1}-x[/tex]
keep square root alone
5-2x+x=[tex]\sqrt{2x²+x-1}[/tex]
5-x=[tex]\sqrt{2x²+x-1}[/tex]
squaring both side
(5-x)²=2x²+x-1
25-10x+x²=2x²+x-1
2x²+x-1-25+10x-x²=0
x²+11x-26=0
doing middle term factorisation
for this
coefficient of first and last terms should be multiplied
here
1*26=26
factor product
26=2*13*1
remember that check the sigh of last term
in here it is - so
we need to get 11 by subtracting factor of 26
we get
13-2=11
keep 13-2 value in place of 11
x²+(13-2)x-26
now
distribute
x²+13x-2x-26=0
take common from each two term
x(x+13)-2(x+13)=0
(x+13)(x-2)=0
either
x=-13
or.x=2
Answer:
A and B
Step-by-step explanation:
we would like to solve the following equation:
[tex] \rm\displaystyle 5 - 2x = \sqrt{ {2x}^{2} + x - 1 } - x[/tex]
to do so isolate -x to the left hand side and change its sign:
[tex] \rm\displaystyle 5 - 2x + x = \sqrt{ {2x}^{2} + x - 1 } [/tex]
simplify addition:
[tex] \rm\displaystyle 5 - x = \sqrt{ {2x}^{2} + x - 1 } [/tex]
square both sides:
[tex] \rm\displaystyle (5 - x {)}^{2} = (\sqrt{ {2x}^{2} + x - 1 } {)}^{2} [/tex]
simplify square of the right hand side:
[tex] \rm\displaystyle (5 - x {)}^{2} = {2x}^{2} + x - 1 [/tex]
use (a-b)²=a²-2ab+b² to expand the left hand side:
[tex] \rm\displaystyle {x}^{2} - 10x + 25= {2x}^{2} + x - 1 [/tex]
swap the equation:
[tex] \rm\displaystyle {2x}^{2} + x - 1 = {x}^{2} - 10x + 25[/tex]
isolate the right hand side expression to the left hand side and change every sign:
[tex] \rm\displaystyle {2x}^{2} + x - 1 - {x}^{2} + 10x - 25 = 0[/tex]
simplify:
[tex] \rm\displaystyle {x}^{2} + 11x - 26= 0[/tex]
rewrite the middle term as 13x-2x:
[tex] \rm\displaystyle {x}^{2} + 13x - 2x - 26= 0[/tex]
factor out x:
[tex] \rm\displaystyle x({x}^{} + 13)- 2x - 26= 0[/tex]
factor out -2:
[tex] \rm\displaystyle x({x}^{} + 13)- 2(x + 13)= 0[/tex]
group:
[tex] \rm\displaystyle (x- 2)(x + 13)= 0[/tex]
by Zero product property we obtain:
[tex] \displaystyle \begin{cases}x- 2 = 0\\ x + 13= 0 \end{cases}[/tex]
solve for x:
[tex] \displaystyle \begin{cases}x = 2\\ x = - 13 \end{cases}[/tex]
to check for extraneous solutions we can define the domain of equation recall that a square root of a function is always greater than or equal to 0 therefore
[tex] \rm\displaystyle 5 - x \geq0[/tex]
solve the inequality for x:
[tex] \rm\displaystyle x \leqslant 5[/tex]
since 2 and -13 is less than 5 both solutions are valid for x hence,
[tex] \displaystyle \begin{cases}x _{1} = 2\\ x_{2} = - 13 \end{cases}[/tex]
and we're done!
Related Questions
find the missing side of the triangle.
Answers
Answer:
x = 17
Step-by-step explanation:
x ^2 = 8^2+ 15^2
√x^2 =√64+225
x=17
Answer:
17cm.
Step-by-step explaination:
The given triangle is a right angled triangle.
Using Pythagorean Theorem,
a² + b² = c²
Putting the given values in the equation;
(15)² + (8)² = c²
225 + 64 = c²
289 = c²
17² = c² (square root of 289 = 17)
17 = c
c = 17
Therefore, the missing side of the triangle is equal to 17 cm.
what is 2,034,627 rounded to the nearest ten thousand
Answers
Answer:
rounded to the nearest ten thousand
2,034,627
2,030,000
On a baseball field, the pitcher's mound is 60.5 feet from home plate. During practice, a batter hits a ball 214 feet at an
angle of 36° to the right of the pitcher's mound. An outfielder catches the ball and throws it to the pitcher. Approximately
how far does the outfielder throw the ball?
Answers
9514 1404 393
Answer:
169 ft
Step-by-step explanation:
The law of cosines can be used to find the distance from the outfielder to the pitcher. It tells you for triangle ABC, the length of side c can be found from ...
c² = a² +b² -2ab·cos(C)
Here, we hve a=60.5, b=214, and C=36°. Then the desired distance is ...
c = √(60.5² +214² -2·60.5·214·cos(36°)) ≈ √28507.56 ≈ 168.84
The outfielder throws the ball about 169 feet.
Rationalize the denominator and simplify:
a) (√3 - √2)/( √3+√2)
b) (5+2√3)/(7+4√3)
c) (1+√2)/(3 - 2√2)
Answers
Answer:
A) (√3-√2)/(√3+√2)
Step-by-step explanation:
i think so
The sum of a rational number and an irrational number is irrational.
Always true,sometimes true, never true
Answers
=========================================================
Explanation:
We can prove this by contradiction.
Let's say
A = some rational numberB = some irrational numberC = some other rational numberand
A+B = C
We'll show that a contradiction happens based on this.
If A is rational, then A = p/q where p,q are two integers. The q cannot be zero.
If C is rational, then C = r/s for some other integers. We can't have s be zero.
Note the following
A+B = C
B = C - A
B = r/s - p/q
B = qr/qs - ps/qs
B = (qr - ps)/qs
B = (some integer)/(some other integer)
This shows B is rational. But this is where the contradiction happens: We stated earlier that B was irrational. A number cannot be both rational and irrational at the same time. The very definition "irrational" literally means "not rational".
In short, I've shown that if A+B = C such that A,C are rational, then B must be rational as well.
The template is
rational + rational = rational
Therefore, we've shown that if A is rational and B is irrational, then C cannot possibly be rational. C is irrational.
Another template is
rational + irrational = irrational
Alexandra is trying to factorise fully15y + 30. Rebecca says the answer is 3(5y + 10) Victoria says the answer is 5(3y + 6) Alexandra says both Rebecca and Victoria are incorrect, why?
Answers
Answer:
Step-by-step explanation:
They are not wrong exactly. Their answers are just incomplete. They did not take the factoring process to it's end.
Victoria could pull out another three.
Rebecca could pull out another five.
The answer is 15(y + 2)
Answer:
because: 3(5y + 10)=15y+30 (Distributive property between addition and multiplication )
the same we have 5(3y + 6)=15y+30
Step-by-step explanation:
PLS HELP ME ON TTHIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION WHILE YOU ANSWER THE QUESTION!!
Which of the following is not a step in creating a box plot?
A. Order the data
B. Find the values for the five-number summary
C. Create a number line
D. Add all of the numbers in the data set and divide by the number of data items in the set
Answers
9514 1404 393
Answer:
D (compute the mean)
Step-by-step explanation:
A box plot is a visual representation of the 5-number summary of a set of data. It is plotted against a number line.
The 5-number summary of the data set is most easily determined from an ordered set of the data, so ordering the data is usually the first step. Since the 5-number summary is plotted against a number line, the next steps are finding the 5-number summary, and creating a suitable number line.
__
The business of adding the data and dividing by the number of data items is a description of computing the mean of the data. That value is not part of the 5-number summary, and is not needed in the creation of the box plot.
Factorize:
6 + 13mn + 7m² n²
explanation
Answers
Answer:
1(6+13mn+7m^2n^2)
Step-by-step explanation:
The coefficients and variables in this equation have a common factor of 1, therefore the equation will go back to it's original state if you use 1 as the common factor.
I hope this helps and sorry if am wrong
The question is
"Mia has a large bag of sweets, If i share the sweets equally among 1,2,3,4,5 or 6 people, there will always be 1 sweet left over"
with step by step pls :(
Answers
Answer:
61
or
421
Step-by-step explanation:
Find the L.C.M. of 2,3,4,5,6 and add 1.
2| 2-3-4-5-6
-------------------
2| 1-3-2-5-3
---------------------
3| 1-3-1-5-3
----------------------
5| 1-1-1-5-1
----------------------
| 1-1-1-1-1-1
L.C.M.=2×2×3×5=60
reqd. number=60+1=61
if i distribute between 2,3,4,5,6 people then reqd number is 61
if Mia is also among those people or she gets also share
then the people are2,3,4,5,6 or 7
L.C.M. of 2,3,4,5,6,7=60×7=420
so reqd number is 420+1=421
how do i convert y = 6x into y = mx + b form?
Answers
Answer:
it already is in that form
y = 6x
technically Y = 6x + 0 could be the answer...
but in math we tend to not rite "obvious" information
to reduce clutter and confusion
+1[tex]x^{1}[/tex] is technically correct but we drop the + sign for positive numbers
and also drop the exponent if it is a 1 ... similarly
+1[tex]x^{1}[/tex] + 0 + 0 + 0 would also be silly and we don't write the zeros
+1[tex]x^{1}[/tex] + 0 + 0 + 0 = x
Step-by-step explanation:
G(x)=3x+2 encontrar el dominio, codominio y haga tabla de valores
Answers
Answer:
x=
[tex]x = \frac{2}{g - 3} [/tex]
explainion is shown in picture above. Hope this helps
Given g(x) = -x + 4, find g(5).
Answers
Answer:
g(5) = -1
Step-by-step explanation:
Let x = 5.
[tex]g(5)=-(5)+4\\g(5)=-5+4\\g(5)=-1[/tex]
Answer:
-1
Step-by-step explanation:
g(x)= -x+4
then substitute 5 on x
=-(5)+4=-1
What is x in the diagram below?
Answers
Answer:
3rd option, 2√10
Step-by-step explanation:
x²=4×10
or, x=√(4×10)
or, x=2√10
Answer: C, 2√10
Step-by-step explanation:
Solve the inequality 8 + n > 4.
Answers
Answer:
n>-4
Step-by-step explanation:
8+n>4
n>4-8
n>-4
Answer:
-4
Step-by-step explanation
Subtract 8 from 4 to get -4.
N = -4
God Bless.
In a math class of 28 students, 14 boys and 14 are girls. On a unit test, 5 boys and 9 girls made an A grade. A student is chosen at random from the class. What is the probability of choosing a girl or an A student?
A. 0.82
B. 0.68
C. 0.14
D. 0.50
Answers
Answer:
The probability of choosing a girl is 1/2.
The probability of choosing an A student who is a BOY is 5/28.
1/2 = 14/28, and 14/28 + 5/28 = 19/28. This can be simplified to 0.68
Thus, the answer is B. 0.68
Let me know if this helps!
The required probability of choosing a girl or an A student is 0.82. Option A is correct.
Given that,
In a math class of 28 students, 14 boys and 14 are girls. On a unit test, 5 boys and 9 girls made an A grade.
A student is chosen at random from the class. What is the probability of choosing a girl or an A student is to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Total sample space = 28
Number of girls = 14
Number of boys = 14
Number of girls A grade student = 9
probability of a girl = 14/28 = 0.5
probability of A grader girl = 9 / 28 = 0.32
Now the probability of choosing a girl or an A grader girl student,
= 0.32 + 0.5
= 0.82
Thus, the required probability of choosing a girl or an A student is 0.82. Option A is correct.
Learn more about probability here:
brainly.com/question/14290572
#SPJ5
(1)
A piece of wire is bent to form a square of area 121 cm?
Calculate:
a)
The length of each side of the square
b)
The perimeter of the square
Answers
Step-by-step explanation:
that is really a problem ?
come on !
you know, the area of a square is side length × side length = length²
that is basically all of us learn as the very first thing when we are learning about squaring and multiplication.
how do we get the regular side length out of length² ?
we pull the square root. you have a calculator (at least on your computer, cell phone,...).
sqrt(121) = .... .... .... 11 ! tada !
and the perimeter of a square ... you really have to ask ?
it is the way all around the whole square. you need to go along every one of the 4 sides.
so, it is side length × 4 = 11×4 = 44 cm
again - you really needed help with THAT ?
Please help me to solve this two questions
Answers
Answer:
c.8,625grams of flour
4a. X=12
Y=30
Z=60
Step-by-step explanation:
For c. , You have to convert the mixed numbers to fractions.
2¾ cups of flour= 2×4=8
8+3=11
Answer: 11/4 (11 over 4)
You multiply the 2 (whole number) by the 4 (bottom number) and then you get *8*
You then take the 8 (which was your answer) and add 3. This will give you 11
You take the 4 and use it as your denominator (bottom number) for the 11. So no need to find a denominator, because you just use the 4
For the fruit cake, she uses *1½* cups of flour more than carrot cake
Calculation:
1½ converted to an improper fraction= 1×2=2
2+1=3
Answer: 3/2 (3 over 2)
"Customer orders *3* carrot cakes and *4* fruit cakes
How many cups of flour are required to bake for the cakes ordered by the customer?"
11/4÷3= 8,25grams
3/2÷4= 0,375grams
8,25+0,375=8,625grams in total
*Feel free to correct me as I might be wrong!*
Opal can make 9 beaded bracelets per hour, and Lynette can make 6 per hour. Together how many hours should it take them to make 45 beaded bracelets?
Answers
Answer:
I'm pretty sure it is 3 hours.
Step-by-step explanation:
Well, when you add 9 plus 6, you get 15. Then you divie 45 by 15, which gives you three. Hope this helps. Good luck :D
help meh please I'm bad at math
Answers
Answer:
4050 cubic feet
Step-by-step explanation:
We would break this figure down into the square pyramid on the top and the cube on the bottom.
Volume of the cube:
l*w*h
= 15*15*15
= 3375.
Volume of the square pyramid:
a^2*(h/3)
= 15^2*(9/3)
= 225*3
= 675
Now we add the two to get the final answer:
3375+675=4050
The figure is 4050 cubic feet.
I hope this helped! :D
Answer:
Step-by-step explanation:
Cube:
Volume = length x width x height
V = 15 * 15 * 15
(Simplified version): 15³
V = 3,375ft³
Triangle:
Volume = 1/2 * base * height * length
V = 1/2 * 15 * 9 * 15
V = 1,012ft³
Add them both up to get our answer
3,375ft³ + 1,102ft³
4,477ft³
Therefore the volume of the figure is 4,477ft³
Find an equation for y (in terms of β and α). Then find tan y.
Answers
Answer:
See belowStep-by-step explanation:
Angle opposite to 6 is complementary of α:
90 - αSimilarly, angle opposite to side 4 of the triangle in the right side is:
90 - βSum of the interior angles of the triangle on the bottom:
90 - α + 90 - β + γ = 180γ = α + βtan γ = tan (α + β)From the smaller triangles we get:
tan α = 4/6 = 2/3tan β = 3/4Use the identity below and find the value of tan γ:
tan (α + β) = (tan α + tan β)/(1 - tan α tan β)tan γ = tan (α + β) = (2/3 + 3/4) / (1 - 2/3*3/4) =(17/12) / (1/2) = 17/6 = 2 5/6Help anyone can help me do this question,I will mark brainlest.
Answers
Answer:
[tex]344 {cm}^{2} [/tex]
Step-by-step explanation:
[tex]area \: of \: the \: square \\ = 40cm \times 40cm \\ = 1600 {cm}^{3} \\ [/tex]
[tex]area \: of \: the \: circle \\ = \pi {r}^{2} \\ = 3.14 \times {(20)}^{2} \\ = 3.14 \times 400 \\ = 1256 {cm}^{2} \\ [/tex]
[tex]area \: of \: shaded \: region \\ = 1600 {cm}^{2} - 1256 {cm}^{2} \\ = 344 {cm}^{2} \\ [/tex]
find the values of x and y.
Answers
Answer:
x=15.75 y=59
Step-by-step explanation:
In total there is 360 degrees. We know y is 59 so we will replace it with that.
59+59=118. 360-118=242. 242/2=121. 29+29=58. So we can subtract that to equal 63. Now 63=4x. We can divide so 2x=31.5. x=15.75.
Therefore, 15.75=x and 59=y
I hope this helped ^^.
8 0/1 as a improper fraction
Answers
Hey there!
8 0/1
8 * 1 + 0/1
= 8 + 0/1
= 8/1
Therefore your answer is most likely: 8/1
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Can anyone help?
For what values of K does the equation (2k+1)x^2 +2x= 10x - 6 have two real and equal roots?
Answers
For the equation (2k + 1)x² + 2x = 10x - 6 to have two real and equal roots, the value of k = 5/6.
Since the equation is (2k + 1)x² + 2x = 10x - 6, we collect subtract 10x from both sides and add 6 to both sides.
So, we have (2k + 1)x² + 2x - 10x + 6 = 10x - 6 - 10x + 6
(2k + 1)x² - 8x + 6 = 0
For the equation, (2k + 1)x² + 2x = 10x - 6 to have two real and equal roots, this new equation (2k + 1)x² - 8x + 6 = 0 must also have two real and equal roots.
For the equation to have two real and equal roots, its discriminant, D = 0.
D = b² - 4ac where b = -8, a = 2k + 1 and c = 6.
So, D = b² - 4ac
D = (-8)² - 4 × (2k + 1) × 6 = 0
64 - 24(2k + 1) = 0
Dividing through by 8, we have
8 - 3(2k + 1) = 0
Expanding the bracket, we have
8 - 6k - 3 = 0
Collecting like terms, we have
-6k + 5 = 0
Subtracting 5 from both sides, we have
-6k = -5
Dividing through by -6, we have
k = -5/-6
k = 5/6
So, for the equation (2k + 1)x² + 2x = 10x - 6 to have two real and equal roots, the value of k = 5/6.
Learn more about quadratic equations here:
https://brainly.com/question/18162688
If the functions f(x) and g(x) are
increasing on an interval, is the
interval? how about f(x) – g(x)?
Answers
Answer:
The difference will be increasing too
Step-by-step explanation:
If f(x) and g(x) is increasing in nature then
f(b) < f(a) and g(b) < g(a) for any a and b in the interval.
Subtracting these 2 equations, we get
f(b) - g(b) < f(a) - g(a) for any a and b in the interval.
Which means f-g is increasing in the interval (a, b) but as a and b were random real numbers we took, f(x) - g(x) will be increasing for an interval
Translate this phrase into an algebraic expression.
the quotient of 14 and a number
Answers
Answer:
Step-by-step explanation:
Let the number be x
14 ÷ x = [tex]\frac{14}{x}[/tex]
Answer:
14 / x
Step-by-step explanation:
quotient = /
14 = 14
a number = the variable, let's call it x
Brainliest please!
4cosx - 2cos2x - cos4x=1
Answers
Answer:
x = 360°
Answered by GAUTHMATH
which is the right equation
Answers
Answer:
C
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 = [tex]\frac{2}{3}[/tex] x + 1 ← is in slope- intercept form
with slope m = [tex]\frac{2}{3}[/tex]
Parallel lines have equal slopes , then
the slope of a parallel rail has slope = [tex]\frac{2}{3}[/tex]
The only equation with this slope is
y = [tex]\frac{2}{3}[/tex] x + 3 ← could represent the path of the second rail → C
help me please!!!!!!!!
Answers
Answer:
BC = 29.4
Step-by-step explanation:
30² = 20² + BC² -2•20•BC•cos(108)
900 = 400 +BC² -12.4•BC
900 -400 = BC² -12.4•BC
BC² -12.4•BC -500 = 0
Solve the equation using Bhaskara and you'll find two possible values for BC, which are:
BC = -17 and BC = 29.4
A negative number doesn't make sense because it is a side of a triangle, so we choose BC = 29.4
Which number best represents the slope of the graphed line?
A. -5
B. -1/5
C. 1/5
D. 5
Answers
Answer:
A. -5
Step-by-step explanation:
First of all this is a line that shows a negative slope.
Secondly, the formula for slope is rise/ run.
5 is your rise and 1 is your run, therefore: -5/1
And this can be reduced to : -5
