Answer:
19Step-by-step explanation:
Given the surdic expression [tex]\frac{2}{3\sqrt{5} + 2\sqrt{11}}\\[/tex], to rationalize the expression, we will have to multiply the numerator and denominator of the expression by the conjugate of the denominator as shown;
[tex]= \frac{2}{3\sqrt{5} + 2\sqrt{11}} * \frac{3\sqrt{5} - 2\sqrt{11}}{3\sqrt{5} - 2\sqrt{11}}\\\\= \frac{2(3\sqrt{5} - 2\sqrt{11})}{(3\sqrt{5} + 2\sqrt{11})(3\sqrt{5} - 2\sqrt{11})}\\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{9\sqrt{25}+6\sqrt{55}- 6\sqrt{55}-4\sqrt{121} } \\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{9(5)-4(11) }\\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{45-44 }\\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{1}[/tex]
Comparing the result [tex]\frac{6\sqrt{5} - 4\sqrt{11} }{1}[/tex] with the expression [tex]\frac{A\sqrt{B} + C\sqrt{D}}{E}[/tex], it can be seen that A = 6, B = 5, C = -4, D = 11 and E = 1
A+B+C+D+E = 6+5+(-4)+11+1
A+B+C+D+E = 11-4+12
A+B+C+D+E = 19
Hence the value of A+B+C+D+E is 19
URGENT!!! PLEASE help me with this question!
Answer:
[tex]\huge\boxed{x = 8,\ but\ x = 3\ is\ extraneous}[/tex]
Step-by-step explanation:
[tex]\sqrt{x+1}+5=x\\\\\text{Domain:}\ x+1\geq0\to x\geq-1\\\\\sqrt{x+1}+5=x\qquad\text{subtract 5 from both sides}\\\sqrt{x+1}=x-5\qquad\text{square both sides}\\(\sqrt{x+1})^2=(x-5)^2\qquad\text{use}\ (\sqrt{x})^2=x\ \text{and}\ (a-b)^2=a^2-2ab+b^2\\x+1=x^2-2(x)(5)+5^2\\x+1=x^2-10x+25\qquad\text{subtract}\ x\ \text{and}\ 1\ \text{from both sides}\\0=x^2-11x+24[/tex]
[tex]ab=24;\ a+b=-11\\a=-8;\ b=-3\\\\x^2-11x+24=0\\x^2-8x-3x+24=0\qquad\text{distribute}\\x(x-8)-3(x-8)=0\qquad\text{distribute}\\(x-8)(x-3)=0\\\\\text{The product is 0 if one of the factors is 0. Therefore}\\(x-8)(x-3)=0\iff x-8=0\ \vee\ x-3=0\\x-8=0\qquad\text{add 8 to both sides}\\\boxed{x=8}\in D\\x-3=0\qquad\text{add 3 to both sides}\\\boxed{x=3}\in D[/tex]
[tex]\text{For}\ x=8:\\\sqrt{8+1}+5=8\\\sqrt{9}+5=8\\3+5=8\\8=8\qquad\bold{CORRECT}\\\text{For}\ x=3:\\\sqrt{3+1}+5=3\\\sqrt4+5=3\\2+5=3\\7=3\qquad\bold{FALSE}[/tex]
Imagine if you won the jackpot! What are your chances to do so? What numbers would you pick? Would you take the annual installments or a reduced lump sum if you won?
Do you have numbers in mind? If so, jot them down (unless you want to keep them to yourself! If they are birthdays or numbers you use, you do not have to post, just describe). Have those numbers won before? In about 200 words.....I will give you an example then.. ...EXAMPLE:
Hello! I sometimes play and use birthdays/anniversaries for numbers. I do combinations of months and days for my kids, my husband, and myself. I do know that I would take the lump sum, instead of 30 payments. You end up taking the chunk out in taxes first, but in the long-haul, you save.
Step-by-step explanation:
Hi,
I like playing with the numbers. I do it either by playing games or by solving problems containing numbers. I also play to earn money for myself.
I use numbers form my date of birth, my telephone number, my street number, sometimes my house number to play lucky draws and try out my luck to win a jackpot. Sometimes I win and sometimes I loose.
So, I love to play with numbers.
Whenever I win, mostly I chose to take a lump sump amount so that I can immediately invest it in some other work to gain money.
A study was conducted on the effect of daytime running lights on cars. Researchers gathered data from a random sample of 3,248 drivers and measured
quite a few variables, in addition to the explanatory variable of daytime running lights and the response variable of less accidents. According to a
newspaper article summarizing the study, those cars that had daytime running lights were more likely to be operated by drivers who were confident and
attentive. Drivers whose cars did not have daytime running lights were about 22% more likely to have an accident. What conclusion can we draw from this
study? Explain.
We can infer a cause-and-effect relationship because the sample was selected randomly.
We cannot infer a cause-and-effect relationship because we do not have a control group.
We can infer a cause-and-effect relationship because multiple variables were included.
We cannot infer a cause-and-effect relationship because treatments were not assigned randomly.
We cannot infer a cause-and-effect relationship because the treatments imposed were not blocked correctly.
Answer:
The correct option is;
We cannot infer a cause and effect relationship because we do not have a control group
Step-by-step explanation:
The treatment in research involves giving stimulus known as treatment to a group or portion of the sample which are then known as the treatment group while the remaining portion of the the sample are exempted from the stimulus. A successful treatment manipulation is one where members of the treatment group perform higher in the measured metrics of the research than members of the control group.
Given that the researchers gathered data from a random sample of drivers and measurement of several variables including the explanatory variable of the of the research without subjecting a sample to a treatment or having a control group we cannot infer a cause and effect relationship as there are no control group
In a competition, a school awarded medals in different categiories.40 medals in sport 25 medals in danceand 212 medals in music, if the total of 55 students got medals and only 6 students got medals in the three categories ,how many students get medals in exactly two of these categories?
Answer:
210
Note: this answer might be incorrect because of the value of music (212). This doesn't make logical sense.
Step-by-step explanation:
Hello,
This question can easily be solved through the use of a venn diagram.
Total number of students = 55
Number of medals in sport = 40 = A
Number of medals in dance = 25 = B
Number of medals in music = 212 = C
Number of students that got award in the three categories = (AnBnC) = 6
n(AuBuC) = 55
n(AnB) + n(BnC) + n(AnC) - 3n(AnBnC) =
n(AnB) + n(AnB) + n(AnC) -3×6 ......equation (i)
n(AuBuC) = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)
Therefore,
n(AnB) + n(BnC) + n(AnC) = n(A) + n(B) + n(C) + n(AnBnC) - n(AuBuC)
n(A) + n(B) + n(C) + n(AnBnC) - n(AuBuC) - 18
40 + 25 + 212 + 6 - 55 - 18 = 210
Note: this answer might be incorrect because of the value of C (music)
Find m
A. 82
B. 32
C. 98
D. 107
Answer: A. 82
Step-by-step explanation:
The measure of <BAD can be found by simply adding 25(<BAC)+57(<CAD) = 82.
[tex]\mathrm{BAD}=\mathrm{BAC}+\mathrm{CAD}=25^{\circ}+57^{\circ}=82^{\circ}[/tex].
Hope this helps.
Evaluate the expression 2x – xy for x=− 1/2 and y=8
Answer:
3
Step-by-step explanation:
2x-xy
2(-1/2)-(-1/2)(8)
-1+4
=3
If f (x) = StartRoot x minus 3 EndRoot, which inequality can be used to find the domain of f(x)?
Answer:
[tex]x\geq 3[/tex] is the inequality to find the Domain of f(x)
Step-by-step explanation:
When we have a function where the variable "x" is inside a square root, we find its Domain by looking for all those values x for which the function is defined for the root, which means all the x-values that make the expression inside the root larger than or equal to zero, avoiding the values smaller for which the square root is not defined.
Therefore, in this case , for
[tex]f(x)=\sqrt{x-3}[/tex]
we ask for the x-values that verify:
[tex]x-3\geq 0\\x\geq 3[/tex]
where we have isolated x on one side of the equal sign.
This would be the definition of the Domain of the function.
Answer:
The answer is C
Step-by-step explanation:
Randomization in an experiment means that the experimental units or
subjects are selected as a simple random sample from the whole population
under study.
Answer:
Randomization allows a sample or small groups with similar characteristics to determine a probability or to hypothesize an event, that is why this type of samples is important in an experiment, that is, to carry it out in a random way.
Step-by-step explanation:
For example;
If a crop at a certain time of year, for example in summer, is affected by a certain fungus, to know if it is really the time of year that affects this problem, random samples of the same crop with the same characteristics and put it to the test at another time of the year to see if the weather is really a risk factor in the spread of this fungus.
What are the points
Answer:
Step-by-step explanation:
x-y=6
(0,-6),(6,0)
4x+y=4
(0,4),(1,0)
point of intersection:
Answer:
for first eq
three points are (7,-1) (6,0) and (5,1)
for second eq
three points are (1,0) (0,4) and (-1,8)
point of intersecton is (2,-4)
Step-by-step explanation:
check by substituting if u want
hope i helped
pls give brainliest
im trying to level up
There are 20 girls and 26 boys on the tennis team . What is the ratio of the number of girls to the total number of players on the team
Answer:
10:23
Step-by-step explanation:
Total number of players on the team = 20 + 26 = 46 players
Number of girls = 20
Ratio of the number of girls to the number of players on the team = 20/46 = 10/23 = 10:23
Ratio is 10:23
To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that
What is the answer now in two minutes
Answer:
sqrt(6)
Step-by-step explanation:
In a 45-45-90 right triangle, the ratio of the lengths of the sides is
1 : 1 : sqrt(2)
u = sqrt(3) * sqrt(2) = sqrt(6)
Answer:
√6 meters
Step-by-step explanation: In a 45° right triangle, the two sides of the 90° angle are equal. a^2+b^2=c^2
2(√3)^2 = 6
√c^2 = √6.
Compute the value of each expression 7−17
Answer: -10
Step-by-step explanation:
7 - 17 = -10. An easy way to do this (with only two terms) is to just flip it, and do 17 - 7 = 10, then make 10 negative(-10)
Hope it helps <3
Which relationships have the same constant of proportionality between yyy and xxx as the following graph?
The constant of proportionality is 3. The relationship that will have the same constant of proportionality will also have a slope of 3
For us to determine the constant of proportionality of the given graph, we must first find the equation of the line.
The standard equation of a line is expressed as y = mx + b
m is the slopeb is the y-interceptUsing the coordinate points (0, 0) and (2, 6)
Get the slope "m"
[tex]m=\frac{6-0}{2-0}\\m=\frac{6}{2}\\m=3[/tex]
Since the line passed through the origin, the y-intercept is 0
Get the required equation:
y = mx + b
y = 3x + 0
y = 3x
From the equation, the constant of proportionality is 3. The relationship that will have the same constant of proportionality will also have a slope of 3
Learn more here: https://brainly.com/question/13441754
2/3 x (-6/7 + 4/5) = (2/3 x 4/5) x (-6/7) : verify
Answer:
No they can't be equal
Step-by-step explanation:
L.H.S. :-
2/3 × ( -6/7 + 4/5 )
=> 2/3 × -2/35
=> -4/105
R.H.S
(2/3 × 4/5) × -6/7
=> 8/15 × -6/7
=> -48/105
L.H.S IS NOT EQUAL TO R.H.S.
geometric sequence 1 on mymaths
Answer:
start with 97 and multiply each term by 0.5
3.03 cells
Step-by-step explanation:
1. The colony begins with 97 cells. The cells split into two which is the same as multiplying by 0.5.
2. Multiply 97 by 0.5 5 times for 5 minutes.
97 · 0.5 · 0.5 · 0.5 · 0.5 · 0.5 = 3.03
If you vertically stretch the exponential function, f(x) = 2^x, by a factor of 4, what is the equation of the new function?
Answer:
f( x ) = 4( [tex]2^x[/tex] )
Step-by-step explanation:
If we vertically stretch a graph by a factor of 4, the " exponential slope " extending from the x - axis, should increase by a factor of 4 as well.
Therefore, the previous function is expressed by the following ...
f( x ) = [tex]2^x[/tex] ... then this new function should be -
f( x ) = 4( [tex]2^x[/tex] )
The equation of this new function is f( x ) = 4( [tex]2^x[/tex] )
The measure of each exterior angle of a regular polygon is 30 degrees. How many sides does the polygon have
Answer:
12 sides
Step-by-step explanation:
To find the number of sides, use a formula.
[tex]\frac{360}{\theta }=n[/tex]
θ is the measure of each exterior angle of the regular polygon.
n is the number of sides of the regular polygon.
[tex]\frac{360}{30} =12[/tex]
Cheryl is planning to go to a four-year college in two years. She develops a monthly savings plan using the estimates shown. What should her monthly savings be? (rounded to the nearest cent)
Answer:
$541.67 per month
Step-by-step explanation:
Tuition and other expenses = $8,250 per semester.
There are two semesters in a year
She has 4 years to spend
Total semester=4years*2semesters
=8 semesters
4 years in college which is a total of 8 semesters.
Total Tuition and other expenses = $8,250 * 8
= $66,000
She needs a total of $66,00 to complete her college
Assistance from parents=$15,000
Financial aid(per semester)=$4750
Total financial aid=$38,000
Total assistance=
Assistance from parents+ financial aid
=$15000+$38,000
=$53,000
Total savings=Total amount needed - Total assistance
=$66,000 - $53,000
=$13,000
She needs to save $13,000 in two years
There are 12 months in one year
2 years=2*12=24 months
Monthly savings=Total savings/24 months
=$13,000/24
=$541.666666
To the nearest cent
=$541.67
Answer: $541.67
Step-by-step explanation: Got it right on TTM.
What is the value of x?
Answer:
The Answer is 180
Step-by-step explanation:
Please answer this in two minutes
Answer:
60°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relation between sides of a right triangle and angles.
Tan = Opposite/Adjacent
tan(T) = SU/ST
tan(T) = (5√51)/(5√17) = √3
Now, the arctangent function is used to find the angle whose tangent is √3.
T = arctan(√3) = 60°
Find the measure of arc JKM if angle KLM = 50 degrees.
Answer:
180°
Step-by-step explanation:
Answer:
180 = arc JKM
Step-by-step explanation:
Angle JM is a straight line so the angle is 180
Central Angle = Intercepted Arc
angle JM = arc JKM
180 = arc JKM
Bengus the expert blacksmith forged 32 swords from copper, twice as many swords from iron, and 19 swords from mythril. Estimate how many swords Bengus forged.
Answer: 115 swords
Step-by-step explanation:
He forged 32 swords from copper, 2*32 from iron and 19 from mythril. Thus, he forged 32+(32*2)+19, or 32+64+19, or 115 swords.
Hope it helps <3
Answer:
110
Step-by-step explanation:
no need
PLEASE ANSWER ASAP WITH AN EXPLANATION
The eighth grade class at Seven Bridges Middle School has 93 students. Each student takes a current events class, a foreign language class, or both a current events class and a foreign language class. There are 70 eighth graders taking a current events class, and there are 54 eighth graders taking a foreign language class. How many eighth graders take only a current events class and not a foreign language class?
Answer:
39 students
Step-by-step explanation:
let x represent the number of students taking both current event and foreign language
there are : 70 eight grader taking current event and 54 taking foreign
70+54-x=93
-x=93-124
x= 31 students taking both
number of eighth graders take only a current events class and not a foreign language class: 70-31=39 students
help me really urgent
Determine the equation of a sine function that would have a range of {y|6<=y<=9} and a period of 60 degrees
Answer:
6 ^ 5743yy^€_*$%_$/_/^€^=÷/_#×
Marta is solving the equation x2+x=3 by completing the square what number should be added to both sides of the equation to complete the square?
Answer:
C = 1/4
Step-by-step explanation:
When solving a quadratic equation, there are steps to follow and I'll highlight them here.
Assuming we have an equation
ax² + bx + c = 0
Step 1
If a is not equal to 1, divide all through by a
x² + bx + c = 0
Take c to the other side of the equation
x² + bx = c
Step 2
Add (b/2)² to both sides of the equation
x² + bx + (b/2)² = c + (b/2)²
In our original question,
We had x² + x = 3
a = 1 , b = 1 c = 3
Using step two, we would have
(b / 2)² = (½)² = ¼ (which is the answer)
Now back to the steps
Step 3
We factor our left side of the equation so as to have a perfect square
[x + (b/2)]² = c + (b/2)²
Step 4
Take the square root of both sides of the equation and solve for x
x + b/2 = ±√[c + (b/2)²]
The answer to the question is ¼
Answer:
1/4
Step-by-step explanation:
The sketch shows a triangle and its
exterior angles. Find the measure of
angle IAC.
Show all your calculations. Justify your
answer.
MDHA = 128"
MZHCA = 46°
Answer:
∠ IAC = 98°
Step-by-step explanation:
The sum of the exterior angle = 360°
∠ HCB = 180° - 46° = 134° ( adjacent angles )
Thus
∠ IAC + 128° + 134° = 360°, that is
∠ IAC + 262° = 360° ( subtract 262° from both sides )
∠ IAC = 98°
Answer:
<IAC=°98
Step-by-step explanation:
<DHA + CHA = 180 SUPPLEMENTARY ANGLE
128 +CHA=180
<CHA=52
<CHA + <HAC+<ACH=180 b/c it is triangle
46 +52+HAC= 180
<HAC= 180-98
<HAC= 82
<HAC + <IAC= 180. Supplementary angle
82+<IAC=180
<IAC=180-82
<IAC=98
What is 37 ÷ 100 × 9 =
Answer: 3.33
Step-by-step explanation:
Multiplication and division should be solved left to right.
[tex]37/100*9\\\\Divide(100)\\\\0.37*9\\\\Multiply(9)\\\\3.33[/tex]
Hope it helps <3
Answer:
=37/100×9=.
=divide 37 by 100
=0.37 ×9
=3.33
PLEASE HELP!!!
A calculator was used to perform a linear regression on the values in the table. The results are shown to the right of the table.
Image attached
Answer: C
explanation: a p e x
Explanation:
Start with the template they give, which is y = ax+b. From here, replace 'a' with -2.9 and b with 13.5 to get the answer y = -2.9x + 13.5
The r and r^2 values aren't used to form the regression line. Instead, they are ways to see how good a fit we have. Since r is fairly close to -1, this means we have a really strong negative correlation. All of the points are close or around the same straight line with a negative slope (that slope being -2.9).