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JulsSmile [24]
3 years ago
6

the width of a rectangle is 7 cm less than twice its length. its area is 30 square cm. find the dimensions

Mathematics
1 answer:
spayn [35]3 years ago
5 0

Answer:

l = 6 cm

w = 5 cm

Step-by-step explanation:

l(2l - 7) = 30

2l^2 - 7l - 30

(2l + 5)(l - 6)

l = 6

2(6) - 7 = 5

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R is the interior of angle TUV. The measure of RUV=30degrees, the measure of TUV=3x+16, and the measure of TUR=x+10. Find x and
choli [55]

Given

R is the interior of ∠ TUV.

m∠ RUV=30degrees, m∠ TUV=3x+16, and m∠ TUR=x+10.

Find the value of x and the m ∠TUV.

To proof

As given in the question

m ∠TUV=3x+16, and m ∠TUR=x+10

thus

m∠ RUV =  m∠ TUV - m∠ TUR

            = 3x + 16 - x -10

            = 2x + 6

As given

m ∠RUV=30°

compare both the values

we get

30 = 2x + 6

24 = 2x

12 = x

put this value in the m ∠TUV= 3x+16

m ∠TUV= 12× 3 +16

            = 52°

Hence proved


7 0
3 years ago
Name the line and plane shown in the diagram. A.AB and plane ABD B.BA and plane DC C.AC and plane ABD D.AB and plane DA
elena-14-01-66 [18.8K]

Answer: The line is AB and the plane is ABD, the first option is the correct one.

Step-by-step explanation:

Ok, first some definitions.

A line is any line that crosses two colinear points. Particularly, you can see in the graph that the line crosses through A and B, so the line is AB.

A plane needs 3 non-colinear points (if the points where colinear, then the points may define a line). Other definition of plane is "a line and a point that is not in the line"

So, if our line is AB, then the possible planes are:

ABC and ABD.

then the correct option is:

Line AB and plane ABD, so the correct option is the first one.

6 0
3 years ago
EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi
Valentin [98]

If there is such a scalar function <em>f</em>, then

\dfrac{\partial f}{\partial x}=4y^2

\dfrac{\partial f}{\partial y}=8xy+4e^{4z}

\dfrac{\partial f}{\partial z}=16ye^{4z}

Integrate both sides of the first equation with respect to <em>x</em> :

f(x,y,z)=4xy^2+g(y,z)

Differentiate both sides with respect to <em>y</em> :

\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}

\implies\dfrac{\partial g}{\partial y}=4e^{4z}

Integrate both sides with respect to <em>y</em> :

g(y,z)=4ye^{4z}+h(z)

Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :

f(x,y,z)=4xy^2+4ye^{4z}+h(z)

\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}

\implies\dfrac{\mathrm dh}{\mathrm dz}=0

Integrate both sides with respect to <em>z</em> :

h(z)=C

So we end up with

\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}

7 0
3 years ago
A student has gotten the following grades on his tests. What is the minimum grade he must get on the last test in order to have
Schach [20]
Where are the following grades ? how am i supposed to answer without all parts of the question .
6 0
3 years ago
1. Olaf has 250 files saved on an external hard drive. Of those files, 12% are photos. (a) Write a percent equation to find the
Levart [38]
A.) Your percent equation would be 250 x 0.12(or 12%)= 30
b.) Olaf would have 30 photos on his external hard drive.
Hope This Helps!
~Cupcake
8 0
3 years ago
Read 2 more answers
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