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4 years ago

35 + 70 = 35(1 + 2) Yes No

Mathematics

1 answer:

valkas [14]4 years ago

7 0

Answer:

yes

Step-by-step explanation:

35 (3) = 105

35=70 = 105

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Given f ( x ) = 3 x 2 + k x − 13 f(x)=3x 2 +kx−13, and the remainder when f ( x ) f(x) is divided by x + 4 x+4 is 15 15, then wh

Varvara68 [4.7K]

Answer:

k=5

Step-by-step explanation:

We are provided with function, f ( x ) = 3 $x^{2}$ + kx − 13

which is divided by x+4 gives 15.

Here,

since f(x) is divided by x+4 so we can put :

x+4 = 0

x= -4

Putting this in f(x) -----> f(-4)

f(x) = f(-4) = 3 ( $-4^{2}$ ) + k(-4) − 13

f(-4) = 3(16) - 4k - 13

f (-4) = 48 - 4k - 13 ------------------------------------------Equation 1

Since, when f(x) is divided by x+4 , the remainder is 15 so we can say,

f(-4) = 15

putting in equation 1

f (-4) = 15 = 48 - 4k - 13

48 -4k - 13 = 15

35 - 4k = 15

35 - 15 = 4k (Moving - 4k on right hand side and 15 on the left)

or 20 = 4k

or 4k = 20

k = $\frac{20}{4}$

4 0

4 years ago

Always, sometimes, or never true

Kitty [74]

I think it’s always because the absolute value is always positive.

8 0

4 years ago

Read 2 more answers

Suppose S and T are mutually exclusive events. Find P(S or T) if P(S) = 8/9 and P(T) = 1/10.

blsea [12.9K]

Answer:

$\textbf{$P(S \cap T) = \frac{89}{90}$ }\\$

Step-by-step explanation:

$\textup{Mutually events are events that cannot occur at the same time.}\\\textup{When you toss a coin you get only $head$ or only $tail$ but never both.}\\ \textup{In mathematical terms $P(A) \cup P(B) = 0$, where $A$ and $B$ are mutually exclusive events. }\\\textup{We know the formula:}\\$$ P(A \cup B) = P(A) + P(B) - P(A \cup B) $$\\\textup{When $A$ and $B$ are mutually exclusive, it will simply be:}\\$$ P(A \cup B) = P(A) + P(B) $$\\\textup{Now given:}\\ $P(S) = 8/9$ , $P(T) = 1/10$\\$

$\implies P(S \cup T) = \frac{89}{10}$

6 0

4 years ago

Find a solution x = x(t) of the equation x′ + 2x = t2 + 4t + 7 in the form of a quadratic function of t, that is, of the form x(

Temka [501]

The particular quadratic solution to the ODE is found as follows:

$x=at^2+bt+c$
$x'=2at+b$

$(2at+b)+2(at^2+bt+c)=t^2+4t+7$
$2at^2+(2a+2b)t+(b+2c)=t^2+4t+7$

$\begin{cases}2a=1\\2(a+b)=4\\b+2c=7\end{cases}\implies a=\dfrac12,b=\dfrac32,c=\dfrac{11}4$

Note that there's also the fundamental solution to account for, which is obtained from the characteristic equation for the ODE:

$x'+2x=0\implies r+2=0\implies r=-2$

so that $x_c=Ce^{-2t}$ is a characteristic solution to the ODE, and the general solution would be

$x=Ce^{-2t}+\dfrac{t^2}2+\dfrac{3t}2+\dfrac{11}4$

4 0

4 years ago

The sum of two number is 27. One number is 3more than the other number. Write and solve a system of equations to find the two nu

Sladkaya [172]

Answer:

One number is 15 and 3 less than that is 12 so that is your other number

3 0

4 years ago