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3 years ago

Find the value of x .

Mathematics

2 answers:

ohaa [14]3 years ago

7 0

Answer:

$x=18$

Step-by-step explanation:

$(4x-11)\\(2x+25)$

According to the Alternate Exterior Angles Theorem, "when two lines are cut by a transversal, the resulting alternate exterior angles are congruent."

This means that the two expressions above are to be set equal to each other because they are representative of two alternate exterior angles, which are congruent:

$4x-11=2x+25$

Add $11$ to both sides of the equation:

$4x=2x+36$

Subtract $2x$ from both sides of the equation:

$2x=36$

Divide both sides of the equation by the coefficient of $x$ , which is $2$ :

$x=18$

Check your work by substituting $18$ for $x$ in the initial equation:

$4(18)-11=2(18)+25$

$61=61$

It's correct!

zlopas [31]3 years ago

3 0

Answer:

Step-by-step explanation:

From the given figure, we can see that angle (4x - 11) will be equal to angle 1 since they are corresponding angles

We notice that angle 1 is vertically opposite to angle (2x + 25)

Hence,

angle (4x - 11) = angle 1 = angle (2x + 25)

So, we can say that angle (4x - 11) = angle (2x + 25)

Now, solving for x:

4x - 11 = 2x + 25

2x = 36

x = 18

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andrew11 [14]

Answer:

(i) The name of the part of the circle, OQ is a radius

(ii) The radius of the sector QOR is 21 cm

Step-by-step explanation:

The given figure is a sector of the circle O

∵ Any sector of a circle formed from 2 radii and an arc

∴ OQ is a radius

(i) The name of the part of the circle, OQ is a radius

The rule of the length of an arc of a circle is L = $\frac{\alpha }{360}$ × 2 π r, where

α is the angle of the sector

r is the radius of the circle

∵ The length of the arc QR is 22 cm

∴ L = 22

∵ The measure of the angle of the arc is 60°

∴ α = 60°

∵ π = $\frac{22}{7}$

→ Substitute them in the rule above

∵ 22 = $\frac{60}{360}$ × 2 × $\frac{22}{7}$ × r

∴ 22 = $\frac{22}{21}$ r

→ Divide both sides by $\frac{22}{21}$

∴ 21 = r

(ii) The radius of the sector QOR is 21 cm

5 0

2 years ago

A rectangular piece of metal is 25 in longer than it is wide. Squares with sides 5 in long are cut from the four corners and the

Licemer1 [7]

Answer:

The original length was 41 inches and the original width was 16 inches

Step-by-step explanation:

Let

x ----> the original length of the piece of metal

y ----> the original width of the piece of metal

we know that

When squares with sides 5 in long are cut from the four corners and the flaps are folded upward to form an open box

The dimensions of the box are

$L=(x-10)\ in\\W=(y-10)\ in\\H=5\ in$

The volume of the box is equal to

$V=(x-10)(y-10)5$

$V=930\ in^3$

$930=(x-10)(y-10)5$

simplify

$186=(x-10)(y-10)$ -----> equation A

Remember that

The piece of metal is 25 in longer than it is wide

$x=y+25$ ----> equation B

substitute equation B in equation A

$186=(y+25-10)(y-10)$

solve for y

$186=(y+15)(y-10)\\186=y^2-10y+15y-150\\y^2+5y-336=0$

Solve the quadratic equation by graphing

using a graphing tool

The solution is y=16

see the attached figure

Find the value of x

$x=16+25=41$

therefore

The original length was 41 inches and the original width was 16 inches

3 0

3 years ago

Please help, I added a photo to show the question. I’m so confused and I need help, so if you could show work I’d really appreci

Mashutka [201]

Angle A = 30 and its complement would be 60. This is because both angles must equal 90 degrees, and 30 + 60 = 90. Also in the directions it states Angle A must be half of its complement. 30 is half of 60. Sorry I don’t have any work, I just did it in my head!

Any questions? Hope this helps!

7 0

3 years ago

Read 2 more answers

A club is choosing 2 members to serve on a committee. The club has nominated 2 women and 4 men. Based on chance alone, what is t

tekilochka [14]

Answer:

53.33% probability that one woman and one man will be chosen to be on the committee

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the members are chosen is not important, so we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.