Answer:
[tex]x = \frac{ 5 \ + \ \sqrt{31}}{2} \ , \ x = \frac{ 5 \ - \ \sqrt{31}}{2}[/tex]
Step-by-step explanation:
[tex]2x^2 - 10x - 3 = 0 \\\\a = 2 \ , b = - 10 \ , \ c = - 3 \\\\x = \frac{-b^2\ \pm \ \sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{10 \ \pm \sqrt{(-10)^2 - ( 4 \times 2 \times -3)} }{2 \times 2}\\\\x = \frac{10 \ \pm \sqrt{(100 - ( -24 )} }{4}\\\\x = \frac{10 \ \pm \sqrt{(100 + 24 } }{4}\\\\x = \frac{ 10 \ \pm \sqrt{124}}{4}\\\\x = \frac{ 10 \ \pm \sqrt{4 \times 31}}{4}\\\\x = \frac{ 10 \ \pm \sqrt{2^2 \times 31}}{4}\\\\x = \frac{ 10 \ \pm2 \sqrt{31}}{4}\\\\x = \frac{ 5 \ \pm\sqrt{31}}{2}\\\\[/tex]
[tex]x = \frac{ 5 \ + \ \sqrt{31}}{2} \ , \ x = \frac{ 5 \ - \ \sqrt{31}}{2}[/tex]
Question and choices are in the photo please explain the answer
Answer: The correct option is B.
Step-by-step explanation:
(x+5)(2x-1)=3(x+5)
Multiply the parentheses
2x^2 - x + 10x - 5 = 3x + 15
Collect like terms
2x^2 + 9x - 5 = 3x + 15
Move the expression to the left hand side and change its sign, then equate it to 0
2x^2 + 9x - 5 - 3x -15 = 0
Collect like terms
2x^2 + 6x - 20 = 0
Divide each term of the equation by 2
x^2 + 3x - 10 = 0
Rewrite the expression in factorized form
x^2 + 5x - 2x - 10 = 0
Factor the expression
x(x + 5) - 2(x + 5) = 0
(x + 5) (x - 2) = 0
Separate into possible cases but when the product of factors equals 0, at least one factor is 0.
x + 5 = 0———equation (1)
x - 2 = 0———-equation (2)
Solve the equations
x + 5 = 0———equation (1)
Make x the subject
x = 0 - 5
x = -5
x - 2 = 0———equation (2)
Make x the subject
x = 0 + 2
x = 2
Hence, the possible values of x are -5 and 2.
Solve the system of equations algebraically by using substitution method:
-3x+3y=9
-x+y=3
Answer:
This system has infinite solutions and it would be much easier to solve it by elimination but substitution it is.
Step-by-step explanation:
-3x+3y=9
-x+y=3
Isolate either x or y in any of the equations. I'll go with the second.
y = 3+x
Now substitute this for y in the first equation.
-3x+3(3+x)=9
Distribute the 3
-3x+9+3x=9
Combine like terms:
9=9
0=0
It's infinite
mathhh raduiss please help
Solve the equation 6x^2 + 15x + 3= 2x^2 to the nearest tenth.
Answer:
x = -0.2 and x = -3.5
Step-by-step explanation:
Combine like terms in the given equation, by subtracting 2x^2 from both sides:
6x^2 + 15x + 3 = 2x^2
-2x^2 = -2x^2
----------------------------------
4x^2 + 15x + 3 = 0
This is a quadratic equation. We'll find the two solutions using the quadratic equation
-b ± √(b^2 - 4ac)
x = ---------------------------
2a
Here the coefficients of the quadratic are a = 4, b = 15 and c = 3.
Thus, the discriminant b^2 - 4ac is 15^2 - 4(4)(3), or +177
and from that we know we'll find two real, unequal roots.
-15 ± √177
The roots are: x = ------------------- , or x = -0.2 and x = -3.5
8
pls help me this is due in 30 minnutes
Answer:
The surface area is 88ft.
Just to let you know just in case if you have the same question is that the formula of finding the surface area of a rectangular prism is A = 2(wl + hl + hw)
please help me this is due in 30 minutes
Answer:
a
c
c
a
Step-by-step explanation:
✨HELP ASAP *Please*✨Theese figures are congruent. What series of transformations moves pentagon ABCDE onto pentagon A'B'C'D'E? Note: Rotations are clockwise Reflections are over the x-ory-axis.
A Rotation, translation
B. Reflection, translation
C. Reflection, rotation
D. Transation ansition
Answer: C
Brainliest Me
Reflection: Across the line y = -1
The A’ is your reflected shape. The red line is y=-1, or your line right reflection. To solve, I counted the distance from the red line on the original triangle, and then the same on the opposite side of the red line, and counted the same distance, plotting the points at the final spot.
I need help on this problem can anyone help me on this
Answer:
Step-by-step explanation:
Finding solutions in a problem like this requires factoring. That means we need to do whatever we have to to isolate the x term. Of course, we have to do it in order of operations but backwards. Begin by adding 2 to both sides to get
[tex](x+4)^2=9[/tex] Now we have to undo the squaring on the left by taking the square root of both sides:
[tex]\sqrt{(x+4)^2}=[/tex] ±[tex]\sqrt{9}[/tex] Taking the square root of a square cancels out both, and of course the square root of 9 is + or - 3:
x + 4 = ±3
The 2 solutions are
x = -4 + 3 which is -1, and x = -4 - 3 which is -7. Choice (3) is the one you want.
roatate triangle p 90* clockwise about the point (2,-1)
Answer:
hope this helps
Step-by-step explanation:
A baker uses 20
cups of flour to make 4 loves of bread. Use this information for the picture below!
Answer:
60 cups
Step-by-step explanation:
We can use ratios to solve
20 cups x cups
--------------- = -------------------
4 loaves 12 loaves
20 * 12 = 4 *x
240 = 4x
Divide by 4
240/4 = 4x/4
60 =x
60 cups
please help! ten points! thank you
Determine the relationship between the two triangles and whether or not they can be
proven to be congruent.
Helppp!!!and thanks.
Answer:
Step-by-step explanation:
12inches/foot , 12x132=1,584 inches
Consider angle θ in Quadrant II, where sinθ = 4/5 . What is the value of cosθ?
Answer:
3/5
Step-by-step explanation:
sin theta=opposite/hypotenuse
4/5=opposite/hypotenuse
therefore opposite=4 and hypotenuse=5
for adjacent
using pythagoras theorem
a^2+b^2=c^2
opposite^2 + adjacent^2 =hypotenuse^2
4^2 + adjacent^2 =5^2
16 + adjacent^2 =25
adjacent^2 =25-16
adjacent =[tex]\sqrt{9[/tex]
adjacent=3
cos theta=adjacent/hypotenuse
=3/5
therefore the value of cos theta is 3/5
In ΔHIJ, the measure of ∠J=90°, IH = 5, HJ = 4, and JI = 3. What is the value of the tangent of ∠I to the nearest hundredth?
The required triangle is possible, the value of the tangent of ∠I is 1.33.
What are trig ratios?If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to estimate the measures of one (or both) of the acute angles.
In a right triangle, the tangent of one of the acute angles is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, we are looking for the tangent of ∠I.
Using the Pythagorean theorem, we can find the length of the third side, HJ, of the right triangle:
HI² = HJ² + IJ²
5² = 4² + 3²
25 = 16 + 9
tan(∠I) = opposite/adjacent = HJ/ JI = 4/3
Rounding to the nearest hundredth, we get:
tan(∠I) ≈ 1.33
Therefore, if the triangle is possible, the value of the tangent of ∠I is 1.33.
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Pedro spins the pointer of a spinner 10 times. The pointer lands on the color blue 7 times. Write a fraction to represent the part of Pedro's spins that were blue?
Answer:
7/10
Step-by-step explanation:
Out of the ten spins seven landed on blue.
I hope this helps :)
Answer:
The fraction that would represent the part of Pedro's spins that were blue would be [tex]\frac{7}{10}[/tex].
Step-by-step explanation:
In a fraction, there is a numerator and a denominator. In order to get a fraction that would represent the part of Pedro's spins that were blue, you need to put the number of times the pointer landed on blue as a numerator and the total number of spins as the denominator. Therefore a fraction that would represent the part of Pedro's spins that were blue would be [tex]\frac{7}{10}[/tex].
What is the exact time t, in years, needed for the balance of an account that earns 5% annual 8. Interest compounded continuously to triple?
Answer:
It takes 22.52 years for the balance to triple in value.
Step-by-step explanation:
Continuous compounding:
The amount of money earned using continuous compounding is given by the following equation:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which A(0) is the initial amount of money and r is the interest rate, as a decimal.
Interest rate of 5%.
This means that [tex]r = 0.05[/tex], and thus:
[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]A(t) = A(0)(1+0.05)^t[/tex]
[tex]A(t) = A(0)(1.05)^t[/tex]
Time for the balance to triple?
This is t for which [tex]A(t) = 3A(0)[/tex]. So
[tex]A(t) = A(0)(1.05)^t[/tex]
[tex]3A(0) = A(0)(1.05)^t[/tex]
[tex](1.05)^t = 3[/tex]
[tex]\log{(1.05)^t} = \log{3}[/tex]
[tex]t\log{1.05} = \log{3}[/tex]
[tex]t = \frac{\log{3}}{\log{1.05}}[/tex]
[tex]t = 22.52[/tex]
It takes 22.52 years for the balance to triple in value.
Find the measure of the arc
Answer:
104, 52 degrees
Step-by-step explanation:
A whole circle is 360 degrees.
So ark YX = 360-110-146=104
Z=1/2*YX=52
A square pyramid has a base with a side length
of 8 feet and lateral faces with heights of 6 feet.
What is the lateral area of the pyramid?
Answer:
160.
Step-by-step explanation:
The area of the base is 64 since each side is 8, 8x8 is equal to 64. Then you have the lateral faces with a length of 8, and a height of 6, which is 48, but since they are triangles, you divide by 2, finally add 24+24+24+24+64 and your final answer is 160.
need the answer asap i will give you brainliest
Answer:
d
Step-by-step explanation:
Someone help with this please you have to classify and construct the triangles
Answer:
The first triangle would be D - Right.
Explanation :
Acute angles can't have a single angle greater or equal to [tex]90^o[/tex]
Equiangular triangles have every single angle equivalent.
Obtuse angles have only angles greater than [tex]90^o[/tex]
Right triangles have 1 right angle (90 degrees)
=============================================
The second triangle would be an obtuse triangle (A)
Here's an example of an obtuse angle :
(As you can see, it doesn't need to have all 3 sides obtuse, just one)
The selected accounts from the Blue Door Corporation's accounting records are presented below for the year ended December 31, 2015: Advertising expense $ 55,000 Interest revenue $ 30,000 Common stock 250,000 Inventory 67,000 Cost of goods sold 1,085,000 Rent revenue 24,000 Depreciation expense 125,000 Retained earnings 535,000 Dividends 150,000 Salaries and wages expense 675,000 Freight-out 25,000 Sales discounts 8,500 Income tax expense 70,000 Sales returns and allowances 41,000 Insurance expense 15,000 Sales revenue 2,400,000 Interest expense 70,000 Prepare a multiple-step income statement.
Solution :
Sales Revenue
Sales $ 2,400,000
Less:
Sales discount $ 8,500
Sales returns and allowances $ 41,000
$ 48,500
Net Sales $ 2,350,500
Cost of goods sold $ 1,085,000
Gross profit $ 1,265,500
Operating expense :
Salaries expenses $ 675,000
Advertising expenses $ 55,000
Depreciation expense $ 125,000
Freight expense $ 25000
Insurance expense $ 15,000
Total operating expenses $ 895,000
Operating income $ 370,500
Non operating income
Interest revenue $ 30,000
Rent revenue $ 24,000
$ 54,000
Non Operating expenses :
Interest expense $ 70,000
Income before income tax $ 354,500
Income tax expense $ 70,000
Net income $ 284,500
Solve the rational equation by multiplying both sides by the LCD. Check your results for extraneous
solutions.
3
2 + 5x + 6
2-1
x + 2
7
x + 3
is a solution.
x=
0
is an extraneous solution.
RETRY
Intro
Answer:
x = 7 is a solution
x = -2 is an extraneous solution
^ CORRECT ANSWER
Step-by-step explanation:
The rational equation is solved and the solutions are 7 and the extraneous solution is x = -2
What is rational function equation?A rational equation can be defined as an equation that involves at least one rational expression
A rational function is a function of the form f( x )=P( x ) / Q( x ) ,
f( x ) = P( x ) / Q( x ) , where P( x ) and Q( x ) are both polynomials.
A rational function f ( x )=P( x ) / Q( x )
f( x ) = P( x ) / Q( x ) may have a vertical asymptote
The domain is the set of all real numbers for which Q( x ) ≠ 0
Given data ,
Let the rational equation be represented as A
Now , the value of A is
( 3 / ( x²+5x+6 ) ) + ( ( x-1) / (x+2) ) = 7 / (x+3) be equation (1)
On simplifying , we get
A rational function is a function of the form f( x )=P( x ) / Q( x ) ,
f( x ) = P( x ) / Q( x ) , where P( x ) and Q( x ) are both polynomials.
So , multiplying both sides by ( x²+5x+6 ) , we get
3 + x² + 2x - 3 = 7x + 14 be equation (2)
On further simplification , we get
x² - 5x - 14 = 0
On factorizing the equation , we get
x² - 7x + 2x - 14 = 0
Taking the common factors , we get
x ( x - 7 ) + 2 ( x - 7 ) = 0
( x + 2 ) ( x - 7 ) = 0
So , the two solutions of x are x = 7 and x = -2
Hence , the solutions of rational equation are x = 7 and x = -2
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anyone help? Math infinite series
Which of the following infinite geometric sequences will have a related convergent series?
{16, 20.8, 27.04, 35.15,…}
{44, 44, 44, 44, …}
{5, 6, 7.2, 8.64,…}
(120, 96, 76.8, 61.44...)
=====================================================
Explanation:
A sequence is simply a list of values. There may or may not be a pattern to the list, though usually in a math class your teacher would use a pattern.
A series is where we add partial sums of a certain sequence to form a new sequence. For example, let's say A = {44, 44, 44, ...} is one sequence and we could form a list of partial sums to be B = {44, 88, 132, ...} The 88 is from adding the first two terms of sequence A together. The 132 is from adding the first three terms of sequence A. This process is continued forever.
For a series to be convergent, the terms must approach some finite single value. They likely won't actually reach this value but they should get closer and closer (think of it like an asymptote). When I formed series B shown above, note how the terms keep growing. It turns out they won't stop growing either and that means the series diverges to positive infinity. So we rule out choice B. The same happens for choices A and C as well.
To make sure the series approaches some finite value, the underlying sequence its based on must have the terms approaching 0. Choice D seems to have this happen. The terms of the sequence are getting smaller and smaller. Adding on smaller pieces will produce terms in a series that would likely get us closer to some finite target.
Keep in mind that not all decreasing sequences have a converging series. A famous example would be the harmonic sequence {1, 1/2, 1/3, 1/4, ...} which its series does not converge. The proof of this lengthy so I'll leave it out.
In the case of choice D, it is a geometric sequence with a = 120 as the starting term and r = 0.8 as the common ratio. The series converges to
S = a/(1-r) = 120/(1-0.8) = 600
The triangles below are similar.
Triangle S R P. Angle S is 54 degrees, R is 41 degrees, P is 85 degrees. Triangle X Y Z. Angle X is 54 degrees, Z is 41 degrees, and Y is 85 degrees.
Which similarity statements describe the relationship between the two triangles? Check all that apply.
Triangle P R S is similar to triangle X Y Z
Triangle R S P is similar to triangle Z X Y
Triangle S R P is similar to triangle X Z Y
Triangle P S R is similar to Triangle Z Y X
Triangle R P S is similar to triangle Z Y X
Triangle S P R is similar to triangle X Z Y
Answer:
Triangle RSP is similar to triangle ZXY
Step-by-step explanation:
to be similar triangles the order of the angles must match.
Angle R is 41° so is angle Z
angle S is 54° so is angle X
angle P is 85° so is angle Y
Tracy's team won 75% of their games last year. They played 12 games. How many games did they win?
Answer:
9 games.
Step-by-step explanation:
You need to find 75% of 12. 75% is equal to three fourths. 12 divided by 4 is 3, so one fourth of 12 is 3. 3 times 3 is 9, so three fourths (75%) of 12 is 9.
For the given table of values for a polynomial function, where must the zeros of the function lie?
A. between 2.0 and 2.5 and between 4.0 and 4.5
B. between 2.5 and 3.0 and between 4.0 and 4.5
C. between 2.0 and 2.5 and between 3.5 and 4.0
D. between 2.5 and 3.0 and between 3.5 and 4.0
Answer:
(B). between 2.5 and 3.0 and between 4.0 and 4.5.
Step-by-step explanation:
According to the Question,
If the value of the function is 0 at x=c, then c is a root or zero of the function. It means the graph of function intersects the x-axis at its zeroes.From the given table it is clear that the value of function are
x | f(x) | Sign
2.0 | 2.8 | Positive
2.5 | 1.1 | Positive
3.0 | –0.8 | Negative
3.5 | –1.2 | Negative
4.0 | –0.3 | Negative
4.5 | 0.7 | Positive
The sign of values of function changes in interval 2.5-3.0 and 4.0-4.5. It means the graph of function must intersect the x-axis in intervals 2.5-3.0 and 4.0-4.5. So, the zeros of the function lie between 2.5 and 3.0 and between 4.0 and 4.5.Therefore, the correct option is B.
Libby wants to buy 290 raspberry yogurts. They are sold in packs of 4. How many packs does she need to buy?
Answer:
73 packs
Step-by-step explanation:
Find how many packs she has to buy by dividing 290 by 4, since each pack has 4 yogurts.
290/4
= 72.5
Since we need a whole number answer, round this up:
72.5
= 73
So, Libby will need to buy 73 packs
Which best describes the incenter of a triangle?
• A. The point where the three altitudes of the triangle intersect
•
B. The point where the perpendicular bisectors of the three sides of
the triangle intersect
•
C. The point where the three medians of the triangle intersect
•
D. The point where the three angle bisectors of the triangle intersect
SUBMIT
Answer:
The statement that best describes the incenter of a triangle is that, it is the point where the three angle bisectors of the triangle intersect. In geometry, an incenter of a triangle is described as the triangle center.
Step-by-step explanation:
follow me
Answer:
D. The point where the three angle bisectors of the triangle intersect
Step-by-step explanation: