Find all real numbers k for which the equation (k-5)x^2-kx+5=0 has exactly one real solution.
The equation [tex]k^2-20k+100=0[/tex] will have exactly one real solution when k=10.
Here, you will find k from the value of the discriminant for the given quadratic equation.
The standard form for a quadratic equation is: [tex]ax^{2}+bx+x=0[/tex]. Where: a, b, and c are your coefficients.
Then, the given equation [tex](k-5)x^2-kx+5=0[/tex] is a quadratic equation. Where:
[tex]a=k-5\\ \\ b=-k\\ \\ c=5[/tex]
The number of solutions for a quadratic equation is determined by the discriminant (D) that can be calculated from the expression: [tex]b^2-4a*c[/tex]. When:
D > 0 - the equation has two solutions;D = 0 - the equation has only one solution;D < 0 - there are no solutions for the equation. STEP 1 - Calculate the discriminant for the given equation.[tex]D=b^2-4a*c\\ \\ D=(-k)^2-4*(k-5)*5\\ \\ D=k^2-20*(k-5)\\ \\ D=k^2-20k+100[/tex]
STEP 2 - Find k.You should find the value for k for which the given equation has only one real solution. Therefore, D=0. For this, solve the quadratic formula for the equation [tex]D=k^2-20k+100=0[/tex] .
[tex]k_{1,2}=\frac{\(-b\pm \sqrt{(b)^2-4\cdot \:a\cdot \:c}}{2\cdot \:a}\\\ \\ k_{1,2}=\frac{\(20\pm \sqrt{(-20)^2-4\cdot \:1\cdot \:100}}{2\cdot \:1}\\ \\ k_{1,\:2}=\frac{20\pm \sqrt{0}}{2\cdot \:1}\\ \\ k=\frac{20}{2}=10\\[/tex]
Hence, k=10 for the equation [tex]k^2-20k+100=0[/tex] has exactly one real solution.
Read more about the number of solutions of quadratic equations:
https://brainly.com/question/7784687
solve algebraically using substitution or elmantion your choise -2x + 6y = -10 y = -4
Answer:
x = -7
Step-by-step explanation:
M is the midpoint. Find the value of X.
We have: SM = TM ( because M is the midpoint )
So: x + 12 = 8x - 2
=> x - 8x = -2 - 12
=> -7x = -14
=> x = (-14) / (-7) = 2
Answer: x = 2
Ok done. Thank to me :>
can you please help me
Answer:
i think it's 10
Step-by-step explanation:
i only had this lesson once ever soooo...
i tried tho
unit rate for $67.92 for 4 gallons
Answer:
$16.98 per gallon
Step-by-step explanation:
We can set up a equation using ratios:
[tex]\frac{67.92}{4}=\frac{x}{1}[/tex]
Solve by cross multiplication (multiply the numerator of the first fraction by the denominator of the second fraction and the denominator of the first fraction by the numerator of the second fraction):
67.92=4x
Divide both sides by 4 to isolate x
$16.98
What is the answer ?
To find :
angle of 3xHint :
first we have to find the value of xStep by step expansion:
x + 2x + 3x + 4x + 5x = 180°Why?
Reason: angles that are formed on a straight line is equal to 180°
15x = 180°x = 180°/15x = 12.°. value of x = 12
we need value of 3x
put the value of x in 3x
3 × 1236°REQUIRED ANSWER = 36°
Answer:
[tex]5x + 4x + 3x + 2x + x = 180° \\ 15x = 180° \\ x = 180° \div 15 \\ x = 12° \\ 3x = 12 \times 3 \\ 3x = 36°[/tex]
1. is 1 5/6 closer to 1 or 2
2. is 5 1/6 closer to 5 or 6
3. is 113 1/13 closer to 113 or 114
4. is 86 9/11 closer to 86 or 87
5. is 65 17/20 closer 65 or 66
6. is 19 3/25 closer to 19 or 20
7. is 71 41/50 closer to 71 or 72
Answer:
Convert fractions into decimal, round up if the decimal is 0.5 and/or higher, and round down if less than 0.5
Example for question 1: 5/6= 0.83 ← greater than 0.5, so round up to 2
Step-by-step explanation:
1. 2
2. 5
3. 113
4.86
5. 66
6. 19
7. 72
Which table contains a set of coordinate points that is not a function?
PLS HELP
Answer:
D
Step-by-step explanation:
-4 is listed twice with 2 different outputs
I need help on Number 16 Please! I’m lose I Will Give Brainiest!
Answer:
[tex]16. - 3 + \frac{p}{7} = - 5[/tex]
[tex] - 3 + p = - 5 \times 7[/tex]
[tex] - 3 + p = - 35[/tex]
[tex]p = - 35 + 3[/tex]
[tex]p = - 32[/tex]
[tex]\qquad\huge\underline{\boxed{\sf AnSwEr}}[/tex]
- 32[tex]\qquad\huge\underline{\boxed{\sf SoLuTiOn}}[/tex]
Multiply both the sides by '7'[tex]\sf\longmapsto \frac{7( - 3 + p)}{7} = 7( - 5)[/tex]
Now simplify it ;[tex]\sf\longmapsto - 3 + p = - 35[/tex]
Add 3 to both the sides .[tex]( - 3 + p + 3 = - 35 + 3[/tex]
Hence , simplified[tex]\sf\longmapsto p \: = - 32[/tex]
Hope it helps ~
If a and b are independent events, p(a)=0. 20, and p(b)=0. 80, what is p(b|a)?.
Answer:
P(B | A) = 0.80
Step-by-step explanation:
For independent events A and B, P(B | A) = P(B)
Therefore, P(B | A) = 0.80
Which of the distributions is left skewed? A graph shows the horizontal axis numbered 12 to 120. The vertical axis is numbered 1 to 5. The graph shows an upward trend. A graph shows the horizontal axis numbered 22 to 121. The vertical axis is numbered 1 to 3. The graph shows a downward then upward trend. A graph shows the horizontal axis numbered 78 to 100. The vertical axis is numbered 1 to 3. The graph shows a downward trend. A graph shows the horizontal axis numbered 60 to 100. The vertical axis is numbered 1 to 3. The graph shows an upward then downward trend.
You can use the fact that left skewed distribution's graph will have upward values first like a mountain but leaned on left side and then plane low value or no values.
The distribution which is left skewed out of the given distributions is
Option D: A graph shows the horizontal axis numbered 60 to 100. The vertical axis is numbered 1 to 3. The graph shows an upward then downward trend.
How to identify left skewed graph?A skewed distribution is a distribution having bias on one of the two sides (either left or right).
It is like leaning mountain on one side(left or right).
A left skewed graph(also called negatively skewed graph) will have upward movement first (and fast) and then downward trend(slowly and sort of elongated)
A right skewed graph(also called positively skewed graph) will have downward movement first(slowly rising) and then upward trend(fast and abrupt like end on the right)
Thus,
The distribution which is left skewed out of the given distributions is
Option D: A graph shows the horizontal axis numbered 60 to 100. The vertical axis is numbered 1 to 3. The graph shows an upward then downward trend.
Learn more about left skewed distributions here:
https://brainly.com/question/1604092
Answer:
Option A
Step-by-step explanation:
The price of dinner was 24.80. The sales tax was 8℅. The server was given a 15℅ tip. What was the total cost of the meal?
please help me with these
Hope you could understand.
If you have any query, feel free to ask.
Answer:
iii. a
iv. d
Step-by-step explanation:
iii.
Area Small Semicircles:
(3.14)(3)² 3.14(9) 28.26Area Large Semicircles:
(3.14)(14.5)²(3.14)(210.25)660.185Area rectangle:
6 * 29 174Area Garden:
28.26 + 660.185 + 174862.445 ≈ 862Units: m²
A = [tex]\boxed{862} \text{m}^2[/tex]
iv.
Area Field :
600m * 400m = 240000 m²Price per m² = ₹2.50
Total Price :
240000 * ₹2.50 = 6,00,000P = ₹[tex]\boxed{6,00,000}[/tex]
-Chetan K
Find an equation for the line that passes through the points (-5, 6) and (1, -4).
Answer:
[tex]y = \frac{ - 5}{3} .x + \frac{ - 7}{3} [/tex]
HELP!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
H: [tex]x\leq -5[/tex]
Step-by-step explanation:
[tex]-4x+10\geq 5x+55\\-4x\geq 5x+45\\-9x\geq 45\\x\leq -5[/tex]
Remember when dividing by a negative number across the inequality the direction of the inequality flips.
Solve showing all work
Y=x^2+3
y=x+5
Answer:
x=2 , x=(-1)
Step-by-step explanation:
y=x^2+3----------1
y=x+5-------------2
1=2
x^2+3 = x+5
x^2-x-2=0
(x-2)(x+1)=0
x=2 , x=(-1)
Answer this please!!
Answer:
A is the answer
Step-by-step explanation:
look at a picture of a triangle prism...
*) Complete the equation. 2/8=
help me pls
2 ÷ 8
2/8 = 2 ÷ 8
both represent same
Gretchen works at a department store. She earns a 12% commission
on the perfume that she sells and a 6% commission on the clothes
that she sells. Gretchen sells $350 worth of perfume and $700 worth of clothes
in one day. What is her commission that day?
Answer: $84
Step-by-step explanation:
Total Commission = Commission for Perfume + Commission for clothes
=12% of sales + 6% of sales
=12% of 350 + 6% of 700
=(350x12/100)+(700x6/100)
=(4200/100)+(4200/100)
=42+42
=$84
Help me please asap!!
Answer:
In order: y = 29, 8, -1, 2, 17
Step-by-step explanation:
Simply plug in what x equals to get the coordinating y!
When x = -2 6(-2)² - 3(-2) - 1 = 29
When x = -1 6(-1)² - 3(-1) - 1 = 8
When x = 0 6(0)² - 3(0) - 1 = -1
When x = 1 6(1)² - 3(1) - 1 = 2
When x = 2 6(2)² - 3(2) - 1 = 17
What is the converse and the truth value of the converse of the following conditional? If an angle is a right angle, then its measure is 90.
need help, really not good with anything in math
Answer:
D. 40.Step-by-step explanation:
Find the reciprocal of 1/40:
1/40= 40/1= 40.That's really it.
Your answer is 40 (D).
4. Round 155 to the nearest ten.
155
++++++++++
150
155
160
Answer:
160
because when the digit at one's place of a no. is 5 or more than 5 then it will proceed to next nearest tens not previous.
1) Cathy borrows $3280 at 0.3% simple interest per month. When Cathy pays the loan back 9 years later, what is the total amount that Cathy ends up repaying? Answer:
Answer:
Step-by-step explanation:
we calculate how much 0.3% is from 3280
y=3280*0.3/100=9.84$
months in 9y
12*9=108
the interest of 9y
108y=1062.72$
the sum of interest + the money borrowed
1062.72+3280=4342.72$
2+2 equals what. please answer.
Answer: 4
Step-by-step explanation: i do not know if this answer is true i am 1.2% sure it is correct
why do u give such hard questions.
Pls help. Multiply 2/3×1/2
Answer
2/6 = 1/3
Step-by-step explanation:
2 x 3 = 6
2 x 1 = 2
2/6 = 1/3
The soccer coach gave Brandon $16 to buy juice boxes from the grocery store. The juice boxes come in pack of 16 and cost $1.75 per pack. Alex was given $21 to buy almonds at the grocery store. Almonds are sold in cans of 200 and cost $2.59 per can.
Brandon buys as many cases of juice boxes as he can afford. Alex buys as many cans of almonds as he can afford.
How many complete snack bags can they make? Explain or show your thinking.
Answer:
64 complete snack bags.
Step-by-step explanation:
Brandon has $16 maximum to spend. 16 juices come in a pack for $1.75 per pack, so 16 divided by $1.75 ≈ 9. We want to see how many of those 9 packs of 16 juices we can get into the snack bags, so we need to multiply 16 x 9 = 144 juices.
Alex has $21 maximum to spend. 200 almonds come in a can for $2.59 per pack, so 21 divided by $2.59 ≈ 8. We want to see how many of those 8 cans of 200 almonds we can get into the snack bags, so we need to multiply 200 x 8 = 1600 almonds.
This piece of information was omitted from the original question:
[Brandon and Alex are making snack bags for their soccer club. Each soccer player will get a snack bag that will have 2 juice boxes and 25 almonds.]
Based on this omission, only 2 juice boxes can fit in a snack bag and only 25 almonds respectively. Thus, we divide.
144/2 = 72 juices
1600/25 = 64 almonds
Therefore, there would be 64 complete snack bags that can hold 2 juices and 25 almonds without overflow.
What is the vertex of the graph of the quadratic function f(c) = x2 + 8x + 10?
Vertex is at (4,−6)and the axis of symmetry is x=4
Evan used base-10 blocks to model the product of 3 and 0.51.
How can Evan use this model to determine the product?
HURRY WORTH 80 POINTS!
Enter your answers in the boxes to correctly complete each statement.
The model shows a total of
tenths and
hundredths. After regrouping, there is 1 whole,
tenths, and
hundredths, so the product is
Basketball shoes are on sale for 22% off. What is the regular price if the sale price is $42?
Answer:
x =53.85
Step-by-step explanation:
Let x be the original price
If the price is 22% of, you will pay 100% -22% = 78%
x * 78% = 42
Change to decimal form.
78x = 42
Divide each side by .78.
78x/.78 = 42/.78
Rounding to the nearest cent
x =53.85
say the regular price is "x", which is the 100% value of the shoes, but today they're 22% off, that means 100% - 22% = 78%, so the sale price is really 78% of the regular price, we know that's 42 bucks, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 42&78 \end{array}\implies \cfrac{x}{42}=\cfrac{100}{78}\implies \cfrac{x}{42}=\cfrac{50}{39} \\\\\\ 39x=2100\implies x=\cfrac{2100}{39}\implies x\approx 53.85[/tex]
