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Mumz [18]
3 years ago
6

Determine the exact value of k so that the quadratic function f(x) = x2 - kx + 5 has only one zero.

Mathematics
2 answers:
galben [10]3 years ago
6 0
I like this question. When we factorise this question the brackets have to be identical.
5 has to be square rooted to become √5. From, FOIL we know that the last digit is times by the other last digit to find the 5, as our brackets are identical this number is the same. The square root of 5.
This number is doubled in identical brackets to find the middle number. so it is 2√5. As there is a minus number there the brackets are: (x-√5)(x-√5). Multiplying this out gives us: x²-2√5 x+5. k=2√5 (or -2√5, depending on if the minus is counted or not)
JulsSmile [24]3 years ago
3 0
f(x)=ax^2+bx+c\\\\\Delta=b^2-4ac\\\\if\ \Delta < 0-no\ zeros\\if\ \Delta=0-one\ zero\\if\ \Delta > 0-two\ zeros


f(x)=x^2-kx+5=0\\\\a=1;\ b=-k;\ c=5\\\\\Delta=(-k)^2-4\cdot1\cdot5=k^2-20\\\\one\ zero\ if\ \Delta=0\\\\therefore\\k^2-20=0\ \ \ \ |add\ 20\ to\ both\ sides\\\\k^2=20\\\\k=\pm\sqrt{20}\\\\k=\pm\sqrt{4\cdot5}\\\\\boxed{k=-2\sqrt5\ or\ k=2\sqrt5}
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Estimate -9 1/6 + 2 1/3 + (-1 7/8) I have more questions so if you want more just simply ask.
BigorU [14]

-8.70833333333 about but you can round to the nearest tenth (-8.7) or nearest whole number (-9)

4 0
3 years ago
-3q + 12 greater than equal too 4q - 30 solve for q
valentina_108 [34]

Solving the inequality -3q+12\geq 4q-30 the value of q is q\leq 6

Step-by-step explanation:

We need to solve the inequality: -3q+12\geq 4q-30 and find value of q

Solving:

-3q+12\geq 4q-30\\Adding\,\,-12\,\,on\,\,both\,\,sides:\\-3q+12-12\geq 4q-30-12\\-3q\geq 4q-42\\Adding\,\,-4q\,\,on\,\,both\,\,sides:\\-3q-4q\geq 4q-42-4q\\-7q\geq -42\\Divide\,\,both\,\,sides\,\,by\,\,7\\\frac{-7q}{7}\geq \frac{-42}{7}\\ -q\geq -6\\Multiply\,\,both\,\,sides\,\,by\,\,-1\,\,and\,\,reverse\,\,the\,\,inequality:\\q\leq 6

So, solving the inequality -3q+12\geq 4q-30 the value of q is q\leq 6

Keywords: Solving inequality

Learn more about solving inequality at:

  • brainly.com/question/7490805
  • brainly.com/question/9590016
  • brainly.com/question/2840217

#learnwithBrainly

6 0
3 years ago
Use the given transformation to evaluate the integral.
GuDViN [60]

For the transformation

\begin{cases}x=7u+v\\y=u+7v\end{cases}

the Jacobian is

\dfrac{\partial(x,y)}{\partial(u,v)}=\begin{bmatrix}7&1\\1&7\end{bmatrix}

with determinant

\det\left(\begin{bmatrix}7&1\\1&7\end{bmatrix}\right)=48

The vertices of the triangle in the u,v-plane are

(x,y)=(0,0)\implies(u,v)=(0,0)

(x,y)=(7,1)\implies(u,v)=(1,0)

(x,y)=(1,7)\implies(u,v)=(0,1)

Then the integral is

\displaystyle\iint_R(x-8y)\,\mathrm dA=-48\int_0^1\int_0^{1-v}(u+55v)\,\mathrm du\,\mathrm dv=\boxed{-448}

3 0
3 years ago
Please help and answer all the question too
IgorC [24]
To find the volume you use the formula—> length x width x height.

For the first problem you’ll solve 5 x 3 x 2 which is 30.

For the second one you’ll do the same thing. For this one you’ll do 3 x 3 x 2 which is 18.
4 0
2 years ago
Read 2 more answers
Which of the following theorems verifies that ABC~WXY?
Flura [38]

Answer:

ABC~WXY by AA

Step-by-step explanation:

In ΔABC

∠B = 90°

∠A = 27°

To Find ∠C

Angle sum property: The sum of all angles of triangle is 180°

∠A+∠B+∠C=180°

27°+90°+∠C=180°

∠C=180°-117°

∠C=63°

In ΔWXY

∠X = 90°

∠Y = 63°

We will use angle sum property

So, ∠W+∠Y+∠X=180°

90°+63°+∠W=180°

∠W=180°-(90°+63°)

∠W=27°

So, ∠A=∠W

∠B =∠X

∠C = ∠Y

So, ABC~WXY by Angle - Angle property.

Hence ABC~WXY by AA

3 0
3 years ago
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