what is X:
|4x−1|=3

|x|=−4

With a triangle, the sum of any two side lengths must be greater than the third side length. If this is not true, then the side lengths cannot make a triangle. Let's go through each set of side lengths and determine which would and wouldn't work.

a. 3, 4, 8 - will not make a triangle

3 + 4 = 7 > 8 = false

3 + 8 = 11 > 4 = true

4 + 8 = 12 > 3 = true

b. 7, 6, 12 - will make a triangle

7 + 6 = 13 > 12 = true

7 + 12 = 19 > 6 = true

6 + 12 = 18 > 7 = true

c. 5, 11, 13 - will make a triangle

5 + 11 = 16 > 13 = true

5 + 13 = 18 > 11 = true

11 + 13 = 24 > 5 = true

d. 4, 6, 12 - will not make a triangle

4 + 6 = 10 > 12 = false

4 + 12 = 16 > 6 = true

6 + 12 = 18 > 4 = true

e. 4, 6, 10 - will not make a triangle

4 + 6 = 10 > 10 = false

4 + 10 = 14 > 6 = true

6 + 10 = 16 > 4 = true

Hope this helps!

Given,

angle BAD = 2x

angle ADC = 79°

angle BCD = 32°

angle ABC = 5x

To Find,

The value of x.

Solution,

complex angle ABC = 360° - 5x

We know that the sum of all the angles of a quadrilateral is 360°.

By summing up all the given angles of the quadrilateral, we obtain

2x + 360° - 5x + 32° + 79° = 360°

or, -3x + 471° = 360°

or, -3x = 360° - 471°

or, -3x = -111°

or, x = -111°/-3

or, x = 37°

Answer,

The value of x is 37° .

Consider ∆JWZ and ∆JKZ

WZ~KJ (given)

/ WZJ~/ KJZ (given)

JZ~JZ (common)

Therefore,

∆JWZ~∆JKZ by SAS congruence rule.

JW~ZK by CPCT.

Answer:

XY ≈ 14.32

Step-by-step explanation:

XY² = XZ² + ZY²

XY² = 6² +13²

XY² = 36 + 169

XY² = 205

XY = \(\sqrt{205\\\)

XY ≈ 14.32

14)The sum of the tangent and the sine of the angle is obtained as 1.21.

15)The area of the segment is 95.6 m^2 while the perimeter of the segment is 11.047 m.

16)The angle opposite the largest side is  130°.

The trigonometric ratios are the ratios that are designated as cos, tan and sine. It is important to note that the  trigonometric ratios are particular to the right angled triangle. The meaning of the right angle triangle is that one of the angles in the triangle is about 90 degrees.

14)) We can find the hypotenuse by the use of the Pythagoras theorem that is used to find the parts of the right angle triangle.;

a = √2^2 + 3^2

a = √ 4 + 9

a = 3.6

We know that;

tan θ = 2/3 = 0.66

sin θ = 2/3.6 = 0.55

Then;

tan θ + sin θ

0.66 + 0.55

= 1.21

We can see by the use of the trigonometric ratios that we would obtain the sum of the sine and the tangent as 1.21.

15)

The area of the segment is obtained as;

Area of the triangle;

1/2r^2 sinθ

r= radius of the circle

θ = angle of inclination

1/2 * (10)^2 * sin 60

= 43.3

Area of the sector;

60/360 * 3.142 * (10)^2

= 52.3

Therefore the area of the triangle is;

43.3 +  52.3 = 95.6 m

b)The perimeter of the segment;

(2πr * θ/360) + 2rsin(θ/2)

(2 * 3.142 * 60/360) + (2 * 10 * sin (60/2))

1.047 + 10

= 11.047 m

16)

Using;

c^2 = a^2 + b^2 - 2abcos C

20^2 = 13^2 + 9^2 - 2(13 * 9) cos C

400 = 250 - 234cosC

400 - 250 = - 234cosC

150 =  - 234cosC

Cos C = -(150/234)

C = Cos-1-(150/234)

C = 130°

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Answer:

5 hours

Step-by-step explanation:

Subtract the amount the accountant charged for the 1st hour worked from the total earned:

127 - 35 = 92

Now divide 92 by 23 to find the number of hours he worked at the rate of $23 per hour:

92 ÷ 23 = 4 hours

Therefore, the account worked the 1st hour plus 4 more hours = 5 hours in total

Answer:

-7-63a

Step-by-step explanation:

-7(1 + 9a)

(use the distributive property of multiplication to simplify)

-7-63a

Answer:

See below for Part A.

Part B)

\(\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614\)

Step-by-step explanation:

Part A)

The parabola given by the equation:

\(y^2=4ax\)

From 0 to h is revolved about the x-axis.

We can take the principal square root of both sides to acquire our function:

\(y=f(x)=\sqrt{4ax}\)

Please refer to the attachment below for the sketch.

The area of a surface of revolution is given by:

\(\displaystyle S=2\pi\int_{a}^{b}r(x)\sqrt{1+\big[f^\prime(x)]^2} \,dx\)

Where r(x) is the distance between f and the axis of revolution.

From the sketch, we can see that the distance between f and the AoR is simply our equation y. Hence:

\(r(x)=y(x)=\sqrt{4ax}\)

Now, we will need to find f’(x). We know that:

\(f(x)=\sqrt{4ax}\)

Then by the chain rule, f’(x) is:

\(\displaystyle f^\prime(x)=\frac{1}{2\sqrt{4ax}}\cdot4a=\frac{2a}{\sqrt{4ax}}\)

For our limits of integration, we are going from 0 to h.

Hence, our integral becomes:

\(\displaystyle S=2\pi\int_{0}^{h}(\sqrt{4ax})\sqrt{1+\Big(\frac{2a}{\sqrt{4ax}}\Big)^2}\, dx\)

Simplify:

\(\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax}\Big(\sqrt{1+\frac{4a^2}{4ax}}\Big)\,dx\)

Combine roots;

\(\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax\Big(1+\frac{4a^2}{4ax}\Big)}\,dx\)

Simplify:

\(\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax+4a^2}\, dx\)

Integrate. We can consider using u-substitution. We will let:

\(u=4ax+4a^2\text{ then } du=4a\, dx\)

We also need to change our limits of integration. So:

\(u=4a(0)+4a^2=4a^2\text{ and } \\ u=4a(h)+4a^2=4ah+4a^2\)

Hence, our new integral is:

\(\displaystyle S=2\pi\int_{4a^2}^{4ah+4a^2}\sqrt{u}\, \Big(\frac{1}{4a}\Big)du\)

Simplify and integrate:

\(\displaystyle S=\frac{\pi}{2a}\Big[\,\frac{2}{3}u^{\frac{3}{2}}\Big|^{4ah+4a^2}_{4a^2}\Big]\)

Simplify:

\(\displaystyle S=\frac{\pi}{3a}\Big[\, u^\frac{3}{2}\Big|^{4ah+4a^2}_{4a^2}\Big]\)

FTC:

\(\displaystyle S=\frac{\pi}{3a}\Big[(4ah+4a^2)^\frac{3}{2}-(4a^2)^\frac{3}{2}\Big]\)

Simplify each term. For the first term, we have:

\(\displaystyle (4ah+4a^2)^\frac{3}{2}\)

We can factor out the 4a:

\(\displaystyle =(4a)^\frac{3}{2}(h+a)^\frac{3}{2}\)

Simplify:

\(\displaystyle =8a^\frac{3}{2}(h+a)^\frac{3}{2}\)

For the second term, we have:

\(\displaystyle (4a^2)^\frac{3}{2}\)

Simplify:

\(\displaystyle =(2a)^3\)

Hence:

\(\displaystyle =8a^3\)

Thus, our equation becomes:

\(\displaystyle S=\frac{\pi}{3a}\Big[8a^\frac{3}{2}(h+a)^\frac{3}{2}-8a^3\Big]\)

We can factor out an 8a^(3/2). Hence:

\(\displaystyle S=\frac{\pi}{3a}(8a^\frac{3}{2})\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big]\)

Simplify:

\(\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big]\)

Hence, we have verified the surface area generated by the function.

Part B)

We have:

\(y^2=36x\)

We can rewrite this as:

\(y^2=4(9)x\)

Hence, a=9.

The surface area is 1000. So, S=1000.

Therefore, with our equation:

\(\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big]\)

We can write:

\(\displaystyle 1000=\frac{8\pi}{3}\sqrt{9}\Big[(h+9)^\frac{3}{2}-9^\frac{3}{2}\Big]\)

Solve for h. Simplify:

\(\displaystyle 1000=8\pi\Big[(h+9)^\frac{3}{2}-27\Big]\)

Divide both sides by 8π:

\(\displaystyle \frac{125}{\pi}=(h+9)^\frac{3}{2}-27\)

Isolate term:

\(\displaystyle \frac{125}{\pi}+27=(h+9)^\frac{3}{2}\)

Raise both sides to 2/3:

\(\displaystyle \Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}=h+9\)

Hence, the value of h is:

\(\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614\)

You seem to have left out that 0 ≤ x ≤ h.

From y² = 4ax, we get that the top half of the parabola (the part that lies in the first quadrant above the x-axis) is given by y = √(4ax) = 2√(ax). Then the area of the surface obtained by revolving this curve between x = 0 and x = h about the x-axis is

\(2\pi\displaystyle\int_0^h y(x) \sqrt{1+\left(\frac{\mathrm dy(x)}{\mathrm dx}\right)^2}\,\mathrm dx\)

We have

y(x) = 2√(ax)   →   y'(x) = 2 • a/(2√(ax)) = √(a/x)

so the integral is

\(4\sqrt a\pi\displaystyle\int_0^h \sqrt x \sqrt{1+\frac ax}\,\mathrm dx\)

\(=\displaystyle4\sqrt a\pi\int_0^h (x+a)^{\frac12}\,\mathrm dx\)

\(=4\sqrt a\pi\left[\dfrac23(x+a)^{\frac32}\right]_0^h\)

\(=\dfrac{8\pi\sqrt a}3\left((h+a)^{\frac32}-a^{\frac32}\right)\)

Now, if y² = 36x, then a = 9. So if the area is 1000, solve for h :

\(1000=8\pi\left((h+9)^{\frac32}-27\right)\)

\(\dfrac{125}\pi=(h+9)^{\frac32}-27\)

\(\dfrac{125+27\pi}\pi=(h+9)^{\frac32}\)

\(\left(\dfrac{125+27\pi}\pi\right)^{\frac23}=h+9\)

\(\boxed{h=\left(\dfrac{125+27\pi}\pi\right)^{\frac23}-9}\)

Answer:

c. 51=h−17

Step-by-step explanation:

the other ones dont make since and C is the only one that does.

Answer:

a = 2/5

Step-by-step explanation:

a + 1/10 = 5/10

Subtract 1/10 from both sides of the equation.

a + 1/10 = 5/10

-1/10 -1/10

a = 4/10

This answer is not incorrect but we usually need to simplify it if possible.

4/10 can be reduced to 2/5.

a = 2/5

Answer:

a=2/5

Step-by-step explanation:

To solve this, we first need to isolate the a so we can solve from there

First, we subtract 1/10. But whatever we do to one side we have to do to the other side. So when we subtract 1/10 from the left side we cancel it out and we subtract 1/10 from the right side so 5/10-1/10

So our equation becomes…

a=5/10-1/10

We can simplify this to…

a=4/10

4/10 is equal to 2/5

So that is our final answer

Now since we have nothing else to do that is our final answer

PLEASE AWARD BRAINLIEST I REALLY NEED TO LEVEL UP!

Answer:

$134.71

Step-by-step explanation:

This is a simple interest question

A = P(1 + rt)

A = Amount after t months or years

P = Principal or amount saved

r = interest rate = 5.18% = 0.0518

t = time.in years = 18 months

= 1 year and 6 month

= 1.5 year

A = $125( 1 + 0.0518 × 1.5)

A = $125 ( 1 + 0.0777)

A = $125(1.0777)

A = $134.71

Answer:

  a = -5/11

Step-by-step explanation:

You want to solve the equation -1/4-a-4=7/4a-3.

The first step in solving this 3-step equation can be to add the opposite of (-a) so that the variable 'a' appears only on one side of the equation:

  -1/4 -a -4 +a = 7/4a -3 +a

  -17/4 = 11/4a -3 . . . . . . . . . . . simplify

The second step is to add the opposite of the constant (-3) so that the constant is on one side of the equation, and the variable is on the other side.

  -17/4 +3 = 11/4a -3 +3

  -5/4 = 11/4a . . . . . . . . . . simplify

The third step is to multiply by the inverse of the coefficient of the variable:

  (4/11)(-5/4) = (4/11)(11/4a)

  -5/11 = a . . . . . . . . . . . . . . . simplify

  -1/4 -(-5/11) -4 = (7/4)(-5/11) -3

  -17/4 +5/11 = -35/44 -3

  (-187 +20)/44 = (-132 -35)/44

  -167/44 = -167/44 . . . . . . answer checks OK

\({ \large{ \implies{ \sf 2 {}^{x} = 64}}}\)

\({ \large{ \implies{ \sf{2 {}^{x} = 2 {}^{6} }}}}\)

\({ \large{ \therefore{ \rm{x = 6 } \: \: \: ans.}}}\)

Answer:

1,200

Step-by-step explanation

Multiply 720 and 100 = 72,000

Divide by 60 = 1,200

Answer:

The answer is 1,200

Step-by-step explanation:

First Multiply 720 and 100 which = 72,000

Then Divide 72,000 by 60 = 1,200

Answer:

1. Two ribbons, A and B. One third of A is equal to all of B. Draw a tape diagram to show the ribbons.

2. Half Robert’s piece of wire is equal to 2/3 of Maria’s wire. The total length of their wires is 10 feet. How much longer is Robert's wire than Maria's?

3. Half Sarah’s wire is equal to 2/5 of Daniel’s. Chris has 3 times as much as Sarah. In all, their wire measures 6 ft. How long is Sarah’s wire in feet?

The solution is Option A.

The coordinate of the triangle after the translation is given by A' ( 0 , -3 ) with 4 units right and 4 units down

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the coordinate of the triangle be represented as A

Now , the coordinate A = A ( -4 , 1 )

Now , the coordinate of the triangle after translation is A' ( 0 , -3 )

when there is a translation of the coordinate A by 4 units to the right , we get

A to 4 units right = A ( -4 + 4 , 1 )

The new coordinate of A = A ( 0 ,  1 )

Now , A to 4 units down , we get

The coordinate of A' = A' ( 0 , 1 - 4 )

The coordinate of A' = A' ( 0 , -3 )

Hence , the translated coordinate is A' ( 0 , -3 )

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Answer:

\(x = 2.5\)

Step-by-step explanation:

Given

The attached figure

Required

Find x

To solve for x, we make use of the following equivalent ratio

\(x :3.5 = 5 : 7\)

Express as fractions

\(\frac{x}{3.5} = \frac{5}{7}\)

Make x the subject

\(x= \frac{5}{7}*3.5\)

\(x= \frac{5}{2}*1\\\)

\(x = 2.5\)

What Yoshi uses is the multiplication property of equality, so the correct option is B.

The step that Yoshi did is:

(1/2)*s = 112

s = 112*(2/1) = 224.

What Yoshi does there is multiplicating both sides by the inverse of (1/2), so it is cancelled in the left side and the variable is isolated.

What he is using there is "Multiplication property of the equality".

Then that is what he should have written, the correct option is B.

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Answer:

been a while, so I'd check w someone else too, but hope this helps

Step-by-step explanation:

Answer:

5(4) + 5(8)

Step-by-step explanation:

Through destributive property, 5 is multiplied by both 4 and 8

Answer:

the person above is right thank and five star them

Step-by-step explanation:

Answer:

Step-by-step explanation:

I could only find 4

m    n

5     10

6       6

8       4

12      8

I wouldn't know how to find the 5th one if there is such a thing.

I did this with a computer language (delphi). There is no proof that I can think of.

Answer:

1 2 3 4 5

4 8 12 16 20

Step-by-step explanation:

the x is 4 therefore, count by 4.

Answer:

It's the first one: 7 to the fourth over 3 to the tenth.

Step-by-step explanation:

Answer:

I think it is the first one

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

1. Area of a circle is pi x R^2

Area = 3.14 x 18^2

Area = 3.14 x 324= 1017.36 sq. In.

The blade covers 122 out of 360 degrees.

1017.36 x 122/360 = 345 square inches.

2.

Like above.

Area =3.14 x 75^2 = 17,662.5 square feet

17662.5 x 80/360 = 3,925 square feet.

the value of variable x in the rhombus is Option (c) 25.

A parallelogram is a particular instance of a rhombus. opposite sides and angles of the rhombus are parallel and equal. The rhombus has equal-length sides on each side, and its diagonals meet at right angles to form its shape as square. The rhombus is sometimes called as a diamond or rhombus.

Let O be the intersection point of the line AC and the line BD in the rhombus.

This two lines intersect at a 90° angle in the center. ( Property of Rhombus)

∠AOD=90°

∠AOD+∠OAD+∠ODA=180° (triangle sum property)

90°+x+x+40°=180°

2x=180°-130°

x=25

Hence the value of x=25.

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Answer:

-4

Step-by-step explanation:

The remainder when P(x) is divided by (x + 2) is P(-2) which is - 4

The true statement is; II. Option D

From the information given, we have that;

I. The set of all second-degree polynomials with the standard operations is a vector space

II. The set of all first-degree polynomial functions 'mx' with the standard operations is a vector space

III. The set of second quadrant vectors with the standard operations is a vector space

Note that;

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Answer:

.1

Step-by-step explanation:

Answer:

Point Q is represented by the ordered pair (-2,9)