1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dafna1 [17]
3 years ago
11

Solve by Factoring

Mathematics
1 answer:
Bad White [126]3 years ago
3 0
1)
k^2=21+4k\\\\ k^2-4k-21=0\\\\ (k^2-2\cdot 2k+4)-4-21=0\\\\ (k-2)^2-25=0\\\\ (k-2)^2=5^2\\\\ |k-2|=5\\\\\ k-2=5 \vee k-2=-5\\\\ k=7\vee k=-3

2)
-4k = 3k-7k

k^2=21+4k\\\\k^2-4k-21=0\\\\k^2+3k-7k-21=0\\\\ k(k+3)-7(k+3)=0\\\\(k+3)(k-7)=0\\\\ k+3=0 \vee k-7=0\\\\ k=-3\vee k=7

3)

k^2=21+4k\\\\k^2-4k-21=0\\\\a=1 , b=4 , c=-21 \\\\ \Delta=b^2-4ac=4^2-4\cdot 1\cdot (-21)=16+84=100\\\\ \sqrt\Delta=10\\\\ k_1=\frac{-b-\sqrt\Delta}{2a}=\frac{-(-4)-10}{2\cdot 1}=\frac{4-10}{2}=-3\\\\ k_2=\frac{-b+\sqrt\Delta}{2a}=\frac{-(-4)+10}{2\cdot 1}=\frac{4+10}{2}=7
x\in \{-3, \ 7\}

Answer B


You might be interested in
During one calendar year, a state trooper issued a total of 375 citations for warnings and speeding tickets. Of these, there wer
timama [110]

Answer:

169 Speeding Tickets, 206 Warnings.

Step-by-step explanation:

If there were 37 more warnings than tickets, then the first thing you want to do is remove that from the total by subtracting it: 375-37 = 338.

You then halve this to split them into tickets and warnings: 338/2 = 169.

Lastly, you add back the 37 more warnings, giving you 169 speeding tickets and 206 warnings.

6 0
3 years ago
When the p-value is used for hypothesis testing, the null hypothesis is rejected if _____
pashok25 [27]

Answer:

B

Step-by-step explanation:

Here, we are to give the reason why we would reject the null hypothesis during the hypothesis testing.

In considering whether to accept the null hypothesis or reject the null hypothesis, we have to take into consideration two things.

The p-value and the alpha value. The p-value refers to the probability which is directly obtainable from the standard score which is referred to as the z-score while the alpha refers to the level of significance.

Now, when the p-value is less than alpha, we simply reject the null hypothesis and accept the alternative hypothesis. In a case however, we have the value of p greater than or equal to the significance level alpha, we simply accept the null hypothesis in this case.

The question asks for a rejection case and this can happen only when the p-value is less than the level of significance alpha

5 0
3 years ago
The length of a rectangular field is 6 metres longer than its width. If the area of the field is 72 square metres, What are the
Mnenie [13.5K]

Answer:

The length is 12metres, the width is 6metres

Step-by-step explanation:

Suppose the width is x, the length is x+6

The square is 72. The square of rectangular field is equal to product of length and width.

so x(x+6)=72

x^2+6x-72=0

a=1 b=6 c=-72

D= b^2-4ac= 6*6+288= 36+288= 324

sqrtD= 18

x1= (-b-sqrtD)/2a=(-6-18)/2= -12 (it is negative, but width is only positive. So this root doesn't match)

x2=(-b+sqrtD)/2a= (-6+18)/2= 12/2=6 - the width

The length is 6+6=12

5 0
3 years ago
You reflect triangle PQR, with vertices P(-2, -4), Q(-3, -1), and R(-4, -4), across the y-axis to get triangle P′Q′R′. What are
inna [77]

Answer:

D

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
X-y=-6 what the x int y int and slope
tangare [24]
I know the y intercept is -1 and the x intercept is 1 but im not sure what the slope is.
8 0
3 years ago
Other questions:
  • URGENT!!!!!!!!!!!The graph shows the recorded heights of a plant in a soil experiment.
    15·2 answers
  • Which of the following is equal to log 6
    12·2 answers
  • What is the price per ounce for 10 ounces and the cost is $1.75
    9·1 answer
  • 1/2n + 1/2n + 1/2n = 7<br> what is the value of n? include a check to check your answer.
    5·1 answer
  • Divide. round your answer to the nearest tenth 26,290.28÷6
    6·1 answer
  • HELP ME PLEASE I'll give brainiest
    6·1 answer
  • Factorize x²+7x+10. Show working please
    10·1 answer
  • Mrs. Gomez likes to put 3 tablespoons on every 2 1/2 cups of ice cream she eats if she has 5 cups of ice cream how much tablespo
    5·2 answers
  • Type the correct answer in the box. Use numerals instead of words.
    9·1 answer
  • Suppose f(x) = x2. What is the graph of g(x) = f(4x)?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!