Answers
Step-by-step explanation:
5.
[tex](5 + 4 \sqrt{7} ){x}^{2} + (4 - 2 \sqrt{7} ) x- 1 = 0[/tex]
Simplify both radicals.
[tex](5 + \sqrt{112) {x}^{2} } + (4 - \sqrt{28} )x - 1 = 0[/tex]
Apply Quadratic Formula
First. find the discramnint.
[tex](4 - \sqrt{28} ) {}^{2} - 4(5 + \sqrt{112} )( - 1) = 64[/tex]
Now find the divisor 2a.
[tex]2(5 + \sqrt{112} ) = 10 + 8 \sqrt{7} [/tex]
Then,take the square root of the discrimant.
[tex] \sqrt{64} = 8[/tex]
Finally, add -b.
[tex] - (4 + 2 \sqrt{7} )[/tex]
So our possible root is
[tex] - (4 + 2 \sqrt{7} ) + \frac{8}{10 + 8 \sqrt{7} } [/tex]
Which simplified gives us
[tex] \frac{ 4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } [/tex]
Rationalize the denominator.
[tex] \frac{4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } \times \frac{10 - 8 \sqrt{7} }{10 - 8 \sqrt{7} } = \frac{ - 72 - 12 \sqrt{7} }{ - 348} [/tex]
Which simplified gives us
[tex] \frac{6 + \sqrt{7} }{29} [/tex].
6. The answer is 2.
9514 1404 393
Answer:
5. x = (6 +√7)/29; a=6, b=1, c=29
6. x = 2
Step-by-step explanation:
5.The quadratic formula can be used, where a=(5+4√7), b=(4-2√7), c=-1.
[tex]x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-(4-2\sqrt{7})+\sqrt{(4-2\sqrt{7})^2-4(5+4\sqrt{7}})(-1)}{2(5+4\sqrt{7})}\\\\=\dfrac{-4+2\sqrt{7}+\sqrt{16-16\sqrt{7}+28+20+16\sqrt{7}}}{10+8\sqrt{7}}=\dfrac{4+2\sqrt{7}}{2(5+4\sqrt{7})}\\\\=\dfrac{(2+\sqrt{7})(5-4\sqrt{7})}{(5+4\sqrt{7})(5-4\sqrt{7})}=\dfrac{10-3\sqrt{7}-28}{25-112}=\boxed{\dfrac{6+\sqrt{7}}{29}}[/tex]
__
6.Use the substitution z=3^x to put the equation in the form ...
z² -3z -54 = 0
(z -9)(z +6) = 0 . . . . . factor
z = 9 or -6 . . . . . . . . value of z that make the factors zero
Only the positive solution is useful, since 3^x cannot be negative.
z = 9 = 3^2 = 3^x . . . . use the value of z to find x
x = 2
Related Questions
What is the location of point F, which partitions the directed line segment from D to E into a 5:6 ratio? Negative one-eleventh One-eleventh Two-fifteenths Fifteen-halves.
Answers
The location of point F, which partitions the directed line segment from D to E into a 5:6 ratio is [tex]\frac{1}{11}[/tex].
The given parameters:
Partition of the line segment = 5:6The total segment of the directed line segment from D to E in the given ratio of 5:6 is calculated as follows;
total segment = 5 + 6 = 11
The value of each partition on the directed line segment is calculated as follows;
[tex]partition = \frac{1}{11} \times distance[/tex]
The distance between point D and point E is calculated as follows;
[tex]D = 5 - (-4)\\\\D = 5 + 4\\\\D = 9[/tex]
The partition of the two points (D to E) is calculated as follows;
[tex]partition = \frac{1}{11} \times 9 = 0.82[/tex]
Thus, we can conclude that, the location of point F, which partitions the directed line segment from D to E into a 5:6 ratio is [tex]\frac{1}{11}[/tex].
Learn more about partition of line segments here: https://brainly.com/question/4429522
Answer:
B
Step-by-step explanation:
edge2021
A man has a collection of 19 coins worth $2.55. There are twice as many nickels as dimes. If the rest are quarters, how many quarters are there?
Answers
Answer:
4
Step-by-step explanation:
Split 19 into two numbers, 9 and 10. If there are 10 nickels, there are 5 dimes. That means there rest are quarters and there are 4.
edit : im not american and have little knowledge of how much each are worth
Please help me solve these problems ASAP
Answers
Answer:
imagine having this
Step-by-step explanation:
can't relate
just times by 2 k:)))))))))
HELP ME PLEASE GUYS ! :)
Answers
Answer:
(12, 1)
Step-by-step explanation:
Arbitrarily choose y = 1. Then x - 6y = 6 becomes
x = 6(1) + 6, or x = 12.
Thus, one (of many) point on the graph is (12, 1).
Please help me evaluate f(x)=-52
Answers
Answer:
Axis interception points of -52 :
Y intercepts : (0,-52 )
What is the reciprocal of 3 1/3
Answers
Answer:
3/10
Step-by-step explanation:
make 3 and 1/3 to an improper fraction (3 multiplied by 3 plus 1) which is 10/3. the reciprocal is 3/10
Answer:
0.3
Step-by-step explanation:
Have a great day!
For 1-3 write an equivalent expression
1.) -3(7+5g)
2.) (x+7)+3y
3.) 2/9-1/5*x
Answers
Answer:
1) –(3 • 7 • 3 • 5 • g)
2) 7+x+3⋅y
3) 2/9 – x/5
Hope you could get an idea from here.
Doubt clarification - use comment section.
9. On a certain day the temperature in New
York City was 4°C and the temperature
in Austin was 10°C. How many degrees
lower was the temperature in New York
City?
Answers
Answer:
it is 6°. because 10 degree - 4 degree = 6 degree
Is 1:4 equivalent to 12:3
Answers
Answer: no
Step-by-step explanation:
first, we have to simplify when finding if they are equivalent or not.
1:4 = 0.25
12:3 = 4:1
Answer:
Yes (if your doing fractions)
Step-by-step explanation:
If you didn’t know how to simplify you could see the greatest possible multiple that 3 and 12 share. So 3 is the greatest possible multiple because 3x4=12. So you do the denominator and numerator to divide 3 and eventually you will get 1/4. (Sorry if I’m not accurate)
please help me i will give you a brainlist thingy thanksss
Answers
I could not see the first question so i couldn't answer.
2) Draw a horizontal line and cut it in half with a vertical angle. 4 equal quarters will form. There each quarter is 90° (right angle is exactly 90°angle)
3) Just add the two angles.
x =13+19
x= 32° (Answer)
4) We must know the other angle value in order to find x. So considering both the angles are equal,
2x = 44
x= 22° (Answer)
5) Yes, x = 80° because the line cutted is a straight line and the value of a straight line is 180°
6) Supplementary angles total 180°
Complementary angles total 90°
7)Opposite angles is equal when two straight lines intersect. So,
14x - 16 = 12x + 22
14x-12x=22+16
2x= 38
x= 19° (Answer)
8) Corresponding angles
9) 140°
Solve with elimination:
10a + 4b = 18
7a + 14 = b
solve for b
Answers
Might help not sure if it’s correct
10a+4(7a+14)=18
(we use the distributive since we have 4 times of b)
when we solve it, we get a is -1
plug in -1 for a
7(-1)+14=7
b=7
plug it back in
10(-1)+4(7)=18
18=18
Hope this helps! :)
What is the height of a triangle with an area of 67. 5 square meters and a base of 9 meters?.
Answers
The height of the triangle is 15 meters.
A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
Types of triangles
Right triangle Equilateral triangle Isosceles triangle Scalene triangleArea of a triangle = 1/2 (base x height)
height = (2 x area ) / base
(2 x 67.5) / 9
= 135 / 9
= 15 meters
Please find attached an image of a triangle. A similar question was answered here: https://brainly.com/question/7655890
The list below shows the temperature Elizabeth recorded at 11:00 p.m. for
four days last January.
Monday: 15°F
Tuesday: 20°F
Wednesday: -20°F
Thursday: -5°F
On which of the days did Elizabeth record the lowest (coldest) temperature?
O Monday
O Tuesday
Submit Answer
O Wednesday
O Thursday
Answers
Wednesday reported -20 compared to the other days recording -5, 15, and 20 degrees. In this case, Wednesday had the coldest temperature.
Answer: Wednesday
Step-by-step explanation: Think of it like this; all temperatures are cold for us human beings. The question is being asked which days did Elizabeth record the lowest (coldest) temperature.
You can put this figures into a number line. Any number going to the right of a number line is an increase. So Monday and Tuesday can be eliminated. Any number going the left of a number line is decreasing. - 5 is very cold but -20 is colder than -5. Therefore, the lowest (coldest) temperature is -20 which was Wednesday,
Hope this explanation helps.
Suppose you were given this table. Select all of the true statements.
x y
6 3
12 6
18 9
24 12
The ratio of x to y is the slope.
The ratio of y to x is the slope.
The equation of the graph is y = 2x.
The equation of the graph is y = 12
1\2x
Answers
Answer:
The ratio of y to x is the slope
The equation of the graph is y = 1/2x
Step-by-step explanation:
In this scenario, we see that 1/2 of x always equals y, so the y-intercept is 0. This means that the slope is equal to 1/2, and that is the ratio of y to x.
Find the value of x
Answers
Answer:
x = 16°Step-by-step explanation:
[tex]3x + 46 + 93 + 47 + 4x + 62 + 3x = 360 \\ 7x + 248 = 360 \\ 7x = 360 - 248 \\ 7x = 112 \\ x = \frac{112}{7} \\ x = {16}^{o} [/tex]
If you received 5 one hundred dollar bills, 7 one thousand dollar bills and 7 one dollar bills, how much money did you get? Write the number in standard form.
Answers
Answer:
$7,507
Step-by-step explanation:
What does geometric progression mean?
Answers
Step-by-step explanation:
[tex] \large\tt\underline\blue{a} \underline\pink{n} \underline\green{s} \underline\red{w}\underline \purple{e} \underline\orange{r}[/tex]
A geometric progression is a sequence in which any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r.
It takes 2 yards of material to
make 6 scarves, how many yards of material are needed to make 24
scarves?
Answers
Hope this helped
Under her cell phone plan, Janelys pays a flat cost of $46.50 per month and $5 per gigabyte. She wants to keep her bill under $70 per month. Write and solve an inequality which can be used to determine g, the number of gigabytes Janelys can use while staying within her budget.
Answers
Answer:
Less than 4.70 GB
Step-by-step explanation:
Let x = # of GB that Janelys uses that month. Since Janelys wants to pay less than $70 given that the flat rate for subscribing to that company's data per month is $46.50 and each GB costs $5 to use, the inequality can be written as:
5x + 46.50 < 70
5x < 23.50 Subtract $45.60 from each side.
x < 4.70 GB Divide 5 from each side.
Thus, (if it is whole numbers) Janelys can use 4 GB while staying within her budget or (if decimals are fine) anything less than 4.70 GB. Hope this helped! :D
A line passes through the points (0, 2) and (2, 10). What is its equation in slope-intercept form?
Answers
Answer:
y = 4x + 2Step-by-step explanation:
The slope-intercept form:
y = mx + b, where m is the slope, b is the y-interceptFind the slope using given points:
m = (10 - 2)/(2 - 0) = 8 / 2 = 4The y-intercept is given with point (0, 2):
b = 2The line is:
y = 4x + 2[tex]\\ \sf{:}\Rrightarrow m=\dfrac{10-2}{2-0}=\dfrac{8}{2}=4[/tex]
Put in slope intercept form
[tex]\\ \sf{:}\Rrightarrow y=mx+b[/tex]
[tex]\\ \sf{:}\Rrightarrow 2=4(0)+b[/tex]
[tex]\\ \sf{:}\Rrightarrow 2=b[/tex]
Equation of the line
[tex]\\ \sf{:}\Rrightarrow y=4x+2[/tex]
What is the value of (225 ÷ 0.25) – 11.875 written to two decimal places.(2d.p.)
Answers
888.125 is the answer just use your calculator
Answer:
Step-by-step explanation:
888.13
2
Which is the equation of a line that has a slope of 3 and passes through point
(-3,-1)?
2
1o -+1
O y=-3x+1
O y=-x+3
O y=-x-1
=
O y=-x-3
Answers
Answer:
Step-by-step explanation:
We'll start with the slope intercept form of a straight line equation:
y = mx + b, where x is the slope and b the y-intercept. The slope we are given is 3, so:
y = 3x + b
We need a value of b that will force the line to go through (-3,-1). Do this by entering that point in the equation and solving for b:
y = -3x + b
-1 = 3(-3) + b
b = 8
y = 3x + 8
Hey y’all please help me with this question.
Answers
Answer:
-g-8>9 answer
since g is -18 and we have (-)g we will have +18
+18-8+10
now we have 10 and it will be bigger the the 9.
Answer:
-g-8≥9
Step-by-step explanation:
Just ask!
Hope this helps.
HELP ME WITH THIS PLEASEEE !
Answers
Answer:
38.525 in²
Step-by-step explanation:
The area formula for a triangle is useful here.
A = 1/2bh . . . . . . b=base length; h=height
A = 1/2(11.5 in)(6.7 in) = 38.525 in²
The area is 38.525 square inches.
60 more boys than girls attended the school picnic. If at most 230 boys attended the picnic, how many girls attended?
Answers
Answer:
!70 girls
Step-by-step explanation:
230 - 60 = 170
hope this helps
How i can answer this question, NO LINKS, if you answer correctly i will give u brainliest!
Answers
Count them all together you will get 16!
The round off value of 38.23 to the nearest whole number is?
Answers
Answer:
38
Step-by-step explanation:
38.23 is closest to 28, because neither the .2 or .03 is high enough to round the last whole number up
Answer:
Rounding 38.23 to the nearest whole number would be 38
Step-by-step explanation:
Rounding 38.23 to the nearest whole number would be 38 because the extra 0.23 is less than 0.50
If it was 0.50, the answer would go up to 39.
i was wondering if u convert 38 inches to centimeters what would it be i told my teacher there is no correct answer for it
Answers
Answer:
96.52 cm
Step-by-step explanation:
Your teacher is incorrect, probably telling you this to avoid you wasting time
Answer:
96.52 cm
Step-by-step explanation:
1 inch is 2.54 cm
so 38 inch will be 2.54*38
96.52 cm
The accompanying table shows the value of a car over time that was purchased for 14000 dollars, where x is years and y is the value of the car in dollars. Write an exponential regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, determine the value of the car, to the nearest cent, after 12 years.
Answers
Your bill from Acme Supply Company is marked "3/15, net 30." The amount of the bill is $289.95. If you pay the bill within 15 days, how much should you tender?
Answers
Answer:
$8,698.50
Step-by-step explanation:
289.95x30= $8,695.50
