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:
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A school bought 45 band uniforms and 18 musical instruments. If the
uniforms cost $89 each, what was the total cost of the uniforms?
Answer:
45 times 89
Step-by-step explanation:
The instuments are irrelevant and are only there to distract you.
Answer:
45 times 89 equals 4005
Step-by-step explanation:
4cosx - 2cos2x - cos4x=1
Answer:
x = 360°
Answered by GAUTHMATH
find the values of x and y.
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 ^^.
Jerry sold 320 tickets for the school play. He sold x adults tickets for $8 each and y child tickets for $5 each. He sold $1900 worth of tickets. Write a system of equations to model the situation.
What is the equation?
Answer:
x + y = 320
8x + 5y = 1900
Step-by-step explanation:
The equation x + y = 320 represents how 320 tickets were sold in total, from combining the adult and child tickets sold.
Since adult tickets are $8 each, the money from adult ticket sales can be represented by 8x.
The money from child ticket sales can be represented by 5y.
The equation 8x + 5y = 1900 represents how $1900 worth of tickets were sold.
So, the system of equations for the situation is:
x + y = 320
8x + 5y = 1900
Answer:
y = 220
x = 100
Step-by-step explanation:
x + y = 320
8x + 5y = 1900
x = 320 - y
8(320 - y) + 5y = 1900
2560 - 8y + 5y = 1900
2560 -3y = 1900
-2560 -2560
-------------------------
-3y = -660
----- -------
-3 -3
y = 220
x + 220 = 320
-220 -220
----------------------
x = 100
Explain the steps necessary to convert a quadratic function in standard form to vertex form.
Answer:
A quadratic function in standard form is converted to vertex form by completing the square. The first two terms are used to create a perfect square trinomial after a zero pair is added. The zero pair is found by taking half of the x-term coefficient and squaring it. The original constant term and the negative value of the zero pair are then combined.
Step-by-step explanation:
Answer:
A quadratic function in standard form is converted to vertex form by completing the square. The first two terms are used to create a perfect square trinomial after a zero pair is added. The zero pair is found by taking half of the x-term coefficient and squaring it. The original constant term and the negative value of the zero pair are then combined.
Step-by-step explanation:
Sample response
find the missing side of the triangle.
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.
Could you please please help me with these questions this is my last attempt and it's due today
Answer:
70.20%
Step-by-step explanation:
Since you seem to be in a rush, let's go for a concise answer.
Let's add 146 and 344 to get 490, and do 344 / 490. This gives us the decimal proportion of ice cream cones that was sold. 344 / 490 = 0.70204.
Excellent. To get the percentage, let's multiply 0.70204 by 100 to get 70.204%. Rounding this to the nearest hundredth gives us 70.20%.
Hope this helps!
Note: This question seems to be badly worded, your 42.44% is correct if it's percentage of ice cream bowls in ice cream cones. I'm assuming that it's the percentage of all ice cream. :)
Review the table of values for function f(x).
Which number is the value of f^-1(-2)?
O -8
O -7
O 1/8
O 1
Answer:
1/8
Step-by-step explanation:
f^-1 part makes it into a fraction
Translate this phrase into an algebraic expression.
the quotient of 14 and a number
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!
Between which two numbers does 46 lie?
A.
between 8 and 9
B.
between 6 and 7
C.
between 5 and 6
D.
between 7 and 8
Answer:
So the sqrt(46) is between 6 and 7
Step-by-step explanation:
sqrt(46)
5*5 = 25
6*6=36
7*7=49
So the sqrt(46) is between 6 and 7
Please help me to solve this two questions
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!*
If you open an already created budget Excel spreadsheet, what is one feature it has when calculating amounts?
A) There isn't an already created budget Excel spreadsheet.
B) Formulas are already included that will calculate the totals for you.
C) You need to create formulas by yourself to calculate the totals.
D) You can use a calculator to add the numbers.
Formulas are already included that will calculate the totals for you.
Find the measure of the indicated angle to the nearest degree.
Answer:
? ≈ 37°
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex] , then
? = [tex]cos^{-1}[/tex] ([tex]\frac{4}{5}[/tex] ) ≈ 37° ( to the nearest degree )
5. PLEASE HELP ME
Write the equation in standard form. Then factor the left side of the equation.
2x2 + 7x = 15
A. (2x – 3)(x + 5) = 0
B. (2x + 3)(x + 5) = 0
C. (2x + 5)(x – 3) = 0
D. (2x – 5)(x + 3) = 0
Answer:
7x=11
Step-by-step explanation:
do it
The water level in a plastic pool changed
by −8 gallons each hour due to a small
hole in the bottom. After 6 hours, the pool
contained 132 gallons. How much water
was in the pool originally?
Answer: 180 gallons
Step-by-step explanation:
If you take 8 times 6 you get 48, now take 132 plus 48 and you get 180.(hope this helped):)
Write the name of the definition, postulate, property or theorem that justifies the statement about the diagram.
The following are the statement justifications and explanatory reasons ;
(a) AD + DB = AB; Is justified by segment addition postulate
Reason
Segment addition postulate states that let A and B represent two points,
Then a third D can be on the line joining A and B, if and only if the
relationship between the points is according to the equation, AD + DB = AB
only
(b) m∠1 + m∠2 = m∠CDB; Is justified by angle addition postulate
Reason
Angle addition postulate states that given that a point B lies between an angle m∠AOC, then we have;
m∠AOC = m∠AOB + m∠BOC
(c) ∠2 ≅ ∠6; Is justified by vertically opposite angles theorem
Reason
Vertical angles formed by the crossing of two lines are always equal
(d) If D is the midpoint of [tex]\overline{AB}[/tex], then AD = [tex]\dfrac{1}{2}[/tex]×AB; Definition of midpoint
Reason
The midpoint of a line is the point that is of equal distance from both ends of the of the line. It is the point halfway between the endpoints
(e) If [tex]\underset{DF}{\rightarrow}[/tex] bisects ∠CDB then ∠1 ≅ ∠2; Definition of angle bisector
Reason
An angle bisector is a ray or line that divides an angle into two angles that are congruent
(f) m∠ADF + m∠FDB = 180°; Linear pair postulate
Reason
The linear pair postulate states that where we have two angles that form a linear pear (their addition forms a straight line), then the two angles are supplementary (their sum is 180°)
(g) ∠ADF and ∠4 are supplements, then m∠ADF + m∠4 = 180°; Definition of supplementary angle
Reason
Supplementary angle are defined as angles that when added together, have a sum of 180°
(h) If ∠4 is complementary to ∠5, and ∠6 is complementary to ∠5, then ∠4 ≅ ∠6; Transitive property
Reason
Transitive property states that given three real numbers, a, b, and c, if a = b and c = b, then a = c
Learn more about angle properties postulates, and theorems here;
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A straight line PQ cuts the x andy axis at M and N respectively. If the points A(-3,5) and B(4,7) lies on PQ , calculate
1.the coordinate of M and N
2./AB/, correct to one decimal place
3.The eqation PQ
I need answers urgently.
pls
A rectangle has a perimeter of 50m, the ratio between the two side is 32 . Caculator the area of that rectangle?
Answer:
Area of rectangle = 150 cm
Step-by-step explanation:
Given the following data;
Ratio = 3:2 Perimeter = 50mTo find the area of the rectangle;
First of all, we would determine the dimensions (length and width) of the rectangle;
For length;
Length, L = 2x
For width;
Width, W = 3x
Mathematically, the perimeter of a rectangle is given by the formula;
P = 2(L + W)
50 = 2(2x + 3x)
50 = 2(5x)
50 = 10x
x = 50/10
x = 5
Length, L = 2x = 2 * 5 = 10 cm
Width, W = 3x = 3 * 5 = 15 cm
Now, we would find the area of the rectangle;
Mathematically, the area of a rectangle is given by the formula;
Area of rectangle = length * width
Area of rectangle = 10 * 15
Area of rectangle = 150 cm
True or False:
4x and 4x2 are like terms
Actually its false
In algebra 4x and 4x² are two different terms and are not like terms.
Must click thanks and mark brainliest
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
What is the solution set of 7x 2 + 3x = 0?
{0, 3/7}
{0, -3/7}
{0, -4/7}
Answer:
the answer is b when we have two positives it makes a negitive therefore its b
Step-by-step explanation:
PLEASE SOMEONE HELP ME ANSWER THIS !!!!
Write the equations of the linear and exponential functions that pass through the points (0, 15) and (1, 5)
Linear Equation, y = mx+b
Exponential Equation, y = a(b)^x
PLEASE ANSWER IT I HAVE AN IMAGE ATTACHED IF NEEDED !!!!
Step-by-step explanation:
Part A: Linear Equation.
One of the points is (0,15). This means 0,15 is the y intercept so b=15.We can find the slope
[tex] \frac{5 - 15}{1 - 0 } = \frac{ - 10}{1} = - 10[/tex]
So our equation is
[tex]y = - 10x + 15[/tex]
Part B: Exponential Equation
We know that
[tex]15 = a \times b {}^{0} [/tex]
B to the zero power is 1 so
[tex]15 = a[/tex]
This means a =15. Now let find b.
[tex]5 = 15 \times b {}^{1} [/tex]
[tex] \frac{1}{3} = b[/tex]
So the equation is
[tex]y = 15( \frac{1}{3} ) {}^{x} [/tex]
would you Rather geometry
Walk on a line or A line segment
why?
Which number best represents the slope of the graphed line?
A. -5
B. -1/5
C. 1/5
D. 5
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
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?
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.
PLS HELP ME ON THIS ANSWER I WILL MARK YOU AS BRAINLIEST IF YOU KNOW TGE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
LOL
Answer:
D. The over 30s have a larger range and interquartile range than the under 30s
Step-by-step explanation:
In a data set, the range is the difference between the maximum and minimum. So, the range for under 30s is 20, while the range for over 30s is 24. Additionally, the interquartile range is the difference between Q3 and Q1. For a boxplot, Q3 is the line where the box ends and Q1 is the line where the box begins. Therefore, the IQR for the under 30s is 8, and the IQR for over 30s is 11. So, D must be correct.
Whats different for the functions
Simplify (Asap️ )
please answer this if you know
(full steps required )
(please no spam answers)
see the attachment hope this helps you
Can someone help me with this question pls
Answer:
D
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = - 94 and d = a₂ - a₁ = - 112 - (- 94) = - 112 + 94 = - 18 , then
S₁₀ = [tex]\frac{10}{2}[/tex] [ (2 × - 94) + (9 × - 18) ]
= 5(- 188 - 162)
= 5 × - 350
= - 1750
Help anyone can help me do this question,I will mark brainlest.
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]
