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3 years ago

In the diagram below of triangle MNPMNP, QQ is a midpoint of \overline{MN}

Mathematics

1 answer:

trasher [3.6K]3 years ago

8 0

Answer:

Given that MNP is a triangle. Q is the midpoint of MN and R is the midpoint of NP.

The length of QR is 4x -11 and the length of MP is 9x - 29.

We need to determine the measure of MP.

Value of x:

The value of x can be determined using the triangle midsegment theore

Applying the theorem, we have;

Substituting the lengths, we get;

Subtracting both sides by 8x, we have;

Adding both sides of the equation by 29, we get;Thus, the value of x is 7.

Measure of MP:

The measure of MP can be determined by substituting x = 7 in the length of MP.

Thus, we have;

Thus, the measure of MP is 34.

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A line is drawn so that it passes through the points (-3, -1) and (4, 2).

marishachu [46]

Answer:

(A) $\boxed{\bold{y=\frac{3}{7}x+\frac{2}{7}}}$

(B) $\boxed{\bold{2 \ = \ \frac{3}{7} * \ 4 \ + \ \frac{2}{7} }}$

Explanation:

(A) Slope: y = mx + b

m = 3/7

b = 2/7

Slope = $\bold{\frac{y_2-y_1}{x_2-x_1}}$

$\bold{\left(x_1,\:y_1\right)=\left(-3,\:-1\right),\:\left(x_2,\:y_2\right)=\left(4,\:2\right)}$

M = $\bold{\frac{2-\left(-1\right)}{4-\left(-3\right)}: \ \frac{3}{7} }$

Y intercept

$\bold{y=\frac{3}{7}x+b}$

Plug in $\bold{\left(-3,\:-1\right)\mathrm{:\:}\quad \:x=-3,\:y=-1}$

$\bold{-1=\frac{3}{7}\left(-3\right)+b}$

Isolate B

$\bold{-1=\frac{3}{7}\left(-3\right)+b}$

b = $\bold{\frac{2}{7} }$

(B) 4 = x, 2 = y

2 = 3/7 * 4 + 2/7

5 0

4 years ago

Read 2 more answers

At what point does the curve have maximum curvature? Y = 4ex (x, y) = what happens to the curvature as x → ∞? Κ(x) approaches as

MAXImum [283]

Answer-

At $x= \frac{1}{2304e^4-16e^2}$ the curve has maximum curvature.

Solution-

The formula for curvature =

$K(x)=\frac{{y}''}{(1+({y}')^2)^{\frac{3}{2}}}$

Here,

$y=4e^{x}$

Then,

${y}' = 4e^{x} \ and \ {y}''=4e^{x}$

Putting the values,

$K(x)=\frac{{4e^{x}}}{(1+(4e^{x})^2)^{\frac{3}{2}}} = \frac{{4e^{x}}}{(1+16e^{2x})^{\frac{3}{2}}}$

Now, in order to get the max curvature value, we have to calculate the first derivative of this function and then to get where its value is max, we have to equate it to 0.

${k}'(x) = \frac{(1+16e^{2x})^{\frac{3}{2} } (4e^{x})-(4e^{x})(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})}{(1+16e^{2x} )^{2}}$

Now, equating this to 0

$(1+16e^{2x})^{\frac{3}{2} } (4e^{x})-(4e^{x})(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x}) =0$

$\Rightarrow (1+16e^{2x})^{\frac{3}{2}}-(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})$

$\Rightarrow (1+16e^{2x})^{\frac{3}{2}}=(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})$

$\Rightarrow (1+16e^{2x})^{\frac{1}{2}}=48e^{2x}$

$\Rightarrow (1+16e^{2x})}=48^2e^{2x}=2304e^{2x}$

$\Rightarrow 2304e^{2x}-16e^{2x}-1=0$

Solving this eq,

we get $x= \frac{1}{2304e^4-16e^2}$

∴ At $x= \frac{1}{2304e^4-16e^2}$ the curvature is maximum.

6 0

3 years ago

Albert sells furniture. His base salary is $300 per week, plus 5.5% commission. If his total sales for last week were $2950, wha

Andreas93 [3]

Answer:

16225

Step-by-step explanation:

You need to multiply

5 0

3 years ago

Solve |-4b-8|+|-1-b^2|+2b^3. b= -2 show steps please .

evablogger [386]

Ok, first put in the -2 for each b. That gives:
|-4(-2)-8|+|-1(-(-2))^2|+2(-2)^3
Let's do each section.
The first section is |-4(-2)-8)|
-4 times -2 is 8, minus 8 is 0. The absolute value of 0 is still 0.
Now we move on to |-1(-(-2))^2)|
First we do exponents
-(-2) is 2, and 2^2 is 4. 4 times -1 is -4. The absolute value of -4 is 4
Now the last section, 2(-2)^3
Exponents first: (-2)^3 is -2 * -2 * -2, which is -8.
-8*2=-16.
0+4+(-16)=-12

7 0

3 years ago

The ratio of 6:5 can be expressed as

Helen [10]

Answer:

the ratio of 6:5 can be expressed as 6/5

7 0

3 years ago