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rjkz [21]
3 years ago
14

Factor: k^2 + 7x + 10 A:(k+10)(k+4) B:(k+2)(k+5) C:(k+2)(k-5) D:(k-2)(k-5)

Mathematics
2 answers:
Nata [24]3 years ago
7 0

Answer:

the answer is B. (k+2)(k+5)

ValentinkaMS [17]3 years ago
5 0

Answer:

a

Step-by-step explanation:

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Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,
torisob [31]

Answer:

32.66 units

Step-by-step explanation:

We are given that

y=6x^2+14x

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

\frac{dy}{dx}=12x+14

We know that length of curve

s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx

We have a=-2 and b=1

Using the formula

Length of curve=s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

dt=12dx

dx=\frac{1}{12}dt

Length of curve=s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt

We know that

\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C

By using the formula

Length of curve=s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}

Length of curve=s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}

Length of curve=s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})

Length of curve=s=\frac{1}{12}(13\sqrt{677}+\frac{1}{2}ln(26+\sqrt{677})+5\sqrt{101}-\frac{1}{2}ln(-10+\sqrt{101})

Length of curve=s=32.66

5 0
2 years ago
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!<br><br> What is [100(−4)^n-1} equal to?
nikklg [1K]

Answer:   -5100

<u>Step-by-step explanation:</u>

\sum^4_1[100(-4)^{n-1}]\qquad \rightarrow \qquad a_1=100\ \text{and r = -4}\\\\\\S_n=\dfrac{a_1(1-r^n)}{1-r}\\\\\\\\S_4=\dfrac{100(1-(-4)^4)}{1-(-4)}\\\\\\.\quad=\dfrac{100(1-256)}{1+4}\\\\\\.\quad=\dfrac{100(-255)}{5}\\\\.\quad=20(-255)\\\\.\quad=-5100\\

3 0
3 years ago
Rhonda bought a new laptop for $800. The laptop depreciates, or loses, 20% of its value each year. The value of the laptop at a
zhuklara [117]

As per the problem,

Rhonda bought a new laptop for $800.

The laptop depreciates, or loses, 20% of its value each year.

The value of the laptop at a later time can be found using the formula

A=P(1-r)^t.....(1)

Here we have

P=$800

r=20%=0.20

t=2 years

Substitute the values in equation (1) we get

A=800(1-0.2)^2\\ \\ \Rightarrow A=800(0.8)^2\\ \\ \Rightarrow A=800*0.64\\ \\ \Rightarrow A=512\\

The laptop be worth in two years will be $512.

6 0
2 years ago
A circle is centered at the point (7,1) and passes through the point (8,7). what is the radius
Scorpion4ik [409]
Easy

the radius is the distance from the center to a point on the circle

we are given
center=(7,1)
 a point=(8,7)
find the distance
distance formula
D=\sqrt{(x2-x1)^2+(y2-y1)^2}

so the distance between point and center is radius
D=\sqrt{(8-7)^2+(7-1)^2}
D=\sqrt{(1)^2+(6)^2}
D=\sqrt{1+36}
D=√37 units


radius is √37 units
7 0
3 years ago
I need help fast will give brainliest!!!
givi [52]

Answer:

C and D

Step-by-step explanation:

the answers are C and D.

6 0
3 years ago
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