Step-by-step explanation:
Since x² + kx + (k + 3) is tangent to the x-axis, the quadratic function has a repeated root.
The discriminant is zero, so b² - 4ac = 0.
=> k² - 4(1)(k + 3) = 0
=> k² - 4k - 12 = 0
=> (k - 6)(k + 2) = 0
Hence k = 6 or k = -2.
The value of k is -2 and 6.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
x² + kx + (k + 3) is tangent to the x-axis.
This means,
The equation has roots.
Now,
The determinant of the equation is equal to zero.
D = b² - 4ac
x² + kx + (k + 3) is in the form of ax² + bx + c.
a = 1
b = k
c = k + 3
Now,
D = 0
k² - 4(k + 3) = 0
k² - 4k - 12 = 0
k² - (6 - 2)k - 12 = 0
k² - 6k + 2k - 12 = 0
k(k - 6) + 2(k - 6) = 0
(k + 2) (k - 6) = 0
k + 2 = 0
k = -2
k - 6 = 0
k = 6
Thus,
k = -2 and 6.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ2
Which of the following is a solution of x^2 -10x = -36?
-5 - i √10
5 + i √61
-5 - i √11
5 + i √11
graph the image of triangle UVW after a reflection across the line x = -1
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Reflection over the line x = -1 alters the x-coordinates, but leaves the y-coordinates alone. The image point is as far horizontally from the reflection line as the pre-image point is.
Each new x-coordinate is the old one subtracted from twice the x-value of the line of reflection:
(x, y) ⇒ (-2-x, y)
U(-8, -6) ⇒ U'(6, -6)
V(-3, -6) ⇒ V'(1, -6)
W(-4, -1) ⇒ W'(2, -1)
Suppose that Gx=f(x+11). Which statement correctly describes the graph? please hurry!
Given:
[tex]g(x)=f(x+11)[/tex]
To find:
The correct statement for the given transformation.
Solution:
The translation is defined as
[tex]g(x)=f(x+a)+b[/tex] .... (1)
Where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
We have,
[tex]g(x)=f(x+11)[/tex] ... (2)
On comparing (1) and (2), we get
[tex]a=11>0[/tex]
So, the graph of f(x) translated 11 units to the left.
Therefore, the correct option is A.
4 (3u - 1) - 4u = 76*
u=?
Answer: 12u-4-4u=76
Step-by-step explanation: Use distributive property and PEMDAS, that might help.
how many half's are in a whole
Answer:
Two
Step-by-step explanation:
Because 1/2 plus 1/2 equals 1 witch would be the final half to make one whole
I AM IN A TEST AND I NEED THE ANSWER SOON!!! PLEASEE!!!
THANK YOU SO MUCH!!
Question in picture below will give brainly
Answer:
only student ll (2)
Step-by-step explanation:
PLEASE HELP I GIVE BRAINLIEST
Answer:
y = 11
Step-by-step explanation:
Perimeter = 6 + 5y + y + 2 + 4y + 3
= 10y + 11
10y + 11 = 121
10y = 121 - 11
= 110
y = 110 ÷ 10
y = 11
if x =20 and y =40 then x and y are
Answer:
Are directly proportional
HELP ME PLEASE !!! please
Answer:
(0,0) and (60,0)
Step-by-step explanation:
because they are the points on the x-axis
The points (5,-2) and (9, r) lie on a line with slope 3/2. Find the missing coordinate r.
Farmer Bob wants to build a rectangular pigpen with side lengths of 3x2+4x-1 ft and 2x2-5x+9 ft. How much fencing will he need to
O A 5x2-x+8 ft
OB. 10x2+18x+16 ft
O C. 10x2-2x+16 ft
OD. 5x2+9x+8 ft
Answer:
b
Step-by-step explanation:
Please help me solve this question will give you braisnlt !
Answer:
[tex]s = 54m +160[/tex]
Step-by-step explanation:
Given: The attachment
Required: Determine the equation
We start by picking any two equivalent points on the table:
[tex](m_1,s_1) = (2,268)[/tex]
[tex](m_2,s_2) = (4,376)[/tex]
Next, we determine the slope, M:
[tex]M = \frac{s_2 - s_1}{m_2 - m_1}[/tex]
[tex]M = \frac{376 - 268}{4-2}[/tex]
[tex]M = \frac{108}{2}[/tex]
[tex]M = 54[/tex]
The equation is then calculated as:
[tex]s - s_1 = M(m - m_1)[/tex]
Where:
[tex]M = 54[/tex]
[tex](m_1,s_1) = (2,268)[/tex]
So, we have:
[tex]s - 268 = 54(m - 2)[/tex]
Open bracket
[tex]s - 268 = 54m - 108[/tex]
Collect like terms
[tex]s = 54m - 108 + 268[/tex]
[tex]s = 54m +160[/tex]
Hence, the equation is: [tex]s = 54m +160[/tex]
how are <1 and <2 related
Answer:
They are adjacent
Step-by-step explanation:
The ratio of boys to girls on Rowan’s swim team is 2:3. If there are 24 boys on the team, how many girls are there?
Answer:
36 girls
Step-by-step explanation:
2x=24
x=12
3(12) = y
y= 36
Difference in Roth IRA and Traditional IRAs, pension plans, 401Ks
Answer:
Contributions to a 401(k) are pre-tax, meaning they are deposited before your income taxes are deducted from your paycheck. However, when in retirement, withdrawals are taxed at your then-current income tax rate. Conversely, there is no tax savings or deduction for contributions to a Roth IRA
Can someone help with this please? I think it has to do with the Pythagorean theorem.
Answer:
2 sqrt(13)
Step-by-step explanation:
We can use the Pythagorean theorem
The x value between A and B is 4 units and the y value is 6 units
The distance is
d = sqrt( x^2 + y^2)
= sqrt( 4^2 + 6^2)
= sqrt( 16+36)
= sqrt(52)
= sqrt(4*13)
= 2 sqrt(13)
A realtor is trying to predict the selling price of houses in Greenville (in thousands of dollars) as a function of Size (measured in thousands of square feet) and whether or not there is a fireplace (FP is 0 if there is no fireplace, 1 if there is a fireplace). The regression output is provided below. Some of the information has been omitted.Sources of variation SS df MS FRegression 3177.17 2 1588.584 Residual 17 17.71713 Total 3478.36 19 How many predictors (independent variables)were used in the regression?
A) 20
B) 18
C) 3
D) 2
Answer: B) 18
Step-by-step explanation: It is also widely used for predicting the value of one dependent variable from the values of two or more independent variables. When there are two or more independent variables, it is called multiple regression
The number of independent variables or predictors present in the regression model is 3.
The number of independent variables can be obtained from an ANOVA table of the degree of freedom column of corresponding to RegressionThe Regression degree of Freedom usually denoted as k - 1 ; where k is the number of independent variables. From the ANOVA table given ; k - 1 = 2 The value of k = 2 + 1 = 3 ; Therefore, the value of k in the regression table is 3.Therefore, the number of predictors in the regression is 3.
Learn more :https://brainly.com/question/18405415
ABCD is a square.
Solve for x
The graph of an equation shown below: based on the graph, which of the following represents the solution to the equation? (-2, -3) (2, 1) (1, 2) (-3, -2)
What is the quotient of 4/5 divided by 17/9
Answer:
0.42352941176
Step-by-step explanation:
hope this helps
The value of quotient will be 0.42.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The expression is,
''4/5 divided by 17/9''
Now,
Since, The expression is,
''4/5 divided by 17/9''
Hence, After solving we get;
⇒ 4/5 ÷ 17/9
⇒ 4/5 × 9/17
⇒ 36/85
⇒ 0.42
Thus, The value of quotient = 0.42
Learn more about the divide visit:
brainly.com/question/844312
#SPJ2
Harley bought a one year $1000 treasury bond. He paid $950 for the treasury bond. What is his rate of return? Round to one decimal, such as: 6.7%.
0.053%
53%
5.3%
5%
Answer: 5.3%
Step-by-step explanation:
The formula to compute rate of return is given by :-
Rate of return = [tex]\dfrac{\text{Selling price - investing price }}{\text{ investing price}}\times100[/tex]
[tex]=\dfrac{1000-950}{950}\times100\%\\\\=\dfrac{50}{950}\times100\%\\\\=\dfrac{100}{19}\%\\= 5.3\%[/tex]
Hence, his rate of return = 5.3%
Steel is an alloy of iron and carbon (98% iron, 2% carbon). Stainless steel is steel and chromium, (90% steel, 10% carbon). What amount of iron, carbon, and chromium are needed for 500 kg of stainless steel?
500 kg x 90% = 500x 0.9 = 450 kg of Steel is needed.
450 kg x 98% = 450 x 0.98 = 441 kg of iron needed.
450 x 0.02 = 9 kg of carbon is needed for the steel.
50 kg of chromium is needed.
Chromium is 10% carbon, 50x 0.1 = 5 kg of carbon is needed for the chromium.
Total iron = 441 kg
Total carbon = 9 + 5 = 14 kg
Total chromium = 50 kg
Drag the item from them item bank to its corresponding match
Will mark brainless
Answers, in order:
1. Acute
2. Congruent
3. Supplementary angles
4. Vertical angles
5. Adjacent angles
6. Adjacent supplementary angles
7. Alternate interior angles
8. Alternate exterior angles
9. Consecutive interior angles
10. Corresponding angles
11. Straight angle
A prom ticket at Smith high school is $120 time is going to save money for the ticket by walking his neighbors dog for $15 per week.Tom has already saved $15 write an in equality that represents the situation.
Answer:
120 = 15x + 15
Step-by-step explanation:
what you have to do is find the amount of weeks needed to walk the dog until you get around 120. so if two weeks is equal too 30 dollars you can multiply it by that amount. 30 = 2.So 30 times what = 120 or 15 times what = 120. also dont forget that tom has saved thirty dollars in advance
x + 5y = 8
3x = 24 - 157
Answer:
1) x+5y=8 (that’s a basically simplified already)
2) -44 1/3
Step-by-step explanation:
1) Since its in it’s most simplified form, leave it like that.
2) Solve it, combine like terms, and then just divide 3 on both sides to isolate variable
Lines a, b, c, and d are distinct lines in the same plane. Decide if lines a and d are parallel, perpendicular, or if there is not enough information
Answer:
A. Parrellel
Step-by-step explanation:
it is parrellel because if you look between b and c you can
see that it is a parrellel line
Which of these tables represents a function?
Answer:
W
Step-by-step explanation:
The table that will represent a function is the table where every x-value (domain) has exactly one y-value (range).
Table W represents a function because each x-value has exactly only one y-value.
The other tables have two y-values assigned to a one x-value.
Answer:
W
Step-by-step explanation:
If two rectangles are similar, what is the length of side x? Give your answer to one decimal place. Rectangle 1: A = 13.4ft B = 4.6ft Rectangle 2: A = 87.1 ft B = x
Answer:
x = 29.9 ft
Step-by-step explanation:
Given:
Rectangle 1 ≈ Rectangle 2
In Rectangle 1
A = 13.4 ft
B = 4.6 ft
In Rectangle 1
A = 87.1 ft
B = x ft
Find:
Value of x
Computation:
Rectangle 1 ≈ Rectangle 2
So,
13.4 / 4.6 = 87.1 / x
x = [(87.1)(4.6)] / 13.4
x = 29.9 ft
A baseball player batted 544 times in a season, with a batting average of 0.294. Using the formula below, find the number of hits he made.
The batting average formula is a=h/n where a is the batting average, h is the number of hits, and n is the number of times at bat.
Answer:
Calculate Batting Average
Calculating a baseball player's batting average is not a difficult task at all. A batting average represents the percentage of at bats that result in hits for a particular baseball player. The formula is:
Hits / At Bats = Batting Avg.
That's all there is to it. For example, if Justin Upton gets 155 hits in a season and has 554 at bats, his batting average would be 155/554, or .280. The batting average is usually represented not as a percentage (i.e. 28.0%), but instead as a decimal number with three places after the decimal. A batting average of 1.000 means that the player gets a hit every time he comes to bat, and an average of .000 means the player has no hits.
It should also be noted that not every time a batter comes to the plate counts as an at bat. Plate appearances that do not count as at bats include walks, hit-by-pitches, sacrifices, etc.
Here's one last example: Albert Pujols gets 35 hits in 113 at bats in May, so his batting average would be calculated as 35 divided by 113, which is .310 for the month of May.
Step-by-step explanation:
Answer:
160
Step-by-step explanation:
The previous answer response to this question was too long and complicated. Just follow the things you know from the question and use the formula.
a=h/n, a is the batting average, h is the number of hits, and n is the number of times at bat. Use substitution to make your formula now look like this:
0.294 = h/544.
Now you have to get h by itself. To do that, you do the opposite of division: multiply. What you do to one side, you do to the other.
544(0.294 = h/544)544 ⇒ h = 544 x 0.294.
Your result should be 159.936; round to the nearest whole number ⇒ 160.