The diameter of a circle measures 17 mm. What is the measure of its radius ?

Answer:

The other solution is -0.56

Step-by-step explanation:

Quadratic equation :[tex]4x^2 + 45x + 24 = 0[/tex]

General quadratic equation : [tex]ax^2+bx+c=0[/tex]

Om comparing :

a=4

b = 45

c=24

Formula : [tex]x =\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

Substitute the values in the formula :

[tex]x=\frac{-45 \pm \sqrt{45^2-4(4)(24)}}{2(4)}\\x=\frac{-45 + \sqrt{45^2-4(4)(24)}}{2(4)},\frac{-45 - \sqrt{45^2-4(4)(24)}}{2(4)}\\x=-0.5613,-10.688[/tex]

So, One solution is −10.69.

So, Other solution is −0.56

Hence  the other solution is -0.56

The second solution to this equation is −0.56.

In the given quadratic equation 4x2 + 45x + 24 = 0, the quadratic formula is used to find the solutions, or roots, of the equation.

This formula is x = [-b ± sqrt(b² - 4ac)] / (2a).

For this specific equation, a is 4, b is 45, and c is 24.

Since it's already given that one root is -10.69, the other root should be obtained by substituting the values into the formula and choosing the alternative sign:

x = [-45 - sqrt(45² - 4*4*24)] / (2*4) this calculation would give −0.56, which is the other solution to the equation.

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Answer:

1. is -5/7

2. is 6/-9 OR 1/-3 (negative one third)

3. is 2

Step-by-step explanation:

Answer:

d = 0.

Step-by-step explanation:

First, use the distributive property and distribute the 5.

The equation is now 20d + 40 = 40.

Subtract 40 from both sides to isolate the variable.

The equation is now 20d = 0.

Now you're thinking, this can't be possible! But really, 0 / 20 is possible. The answer is d = 0.

Answer:B

Step-by-step explanation:

Mrs. Williams' family recycles 151.2 pounds of plastic in a year, and since 1 pound of plastic saves 7.4 yards of landfill space, their recycling efforts save approximately 1,118.88 yards of landfill space annually.

To find out how much landfill space Mrs. Williams family can save in a year, we can start by calculating how much plastic they recycle in a year. This can be done by multiplying the monthly amount by the total number of months:

12.6 (pounds per month) x 12 (months per year) = 151.2 pounds of plastic

Next, we use the fact that every pound of plastic recycled saves 7.4 yards of landfill space. So, we multiply the total pounds of plastic by the amount of space saved per pound:

151.2 (pounds of plastic) x 7.4 (yards per pound) = 1,118.88 yards

Therefore, Mrs. Williams family can save approximately 1,118.88 yards of landfill space per year by their recycling efforts.

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Answer:

b)

Step-by-step explanation:

Number of ping pong balls = 8 * number of golf balls

= 8*10

= 80

All three sides will be equal to 21.

So that is

3 + 7 + 9 + 2 = 21,

3 + 8 + 6 + 4 = 21 and

2 + 10 + 5 + 4 = 21

Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.

The operator that performs the arithmetic operations are called arithmetic operators.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

Given

Put the Number from 2 to 10 in the circle so that the sum of the Number on each side of a triangle is the same.

        3

    7      8

  9           6

2   10     5    4

So the numbers form a triangle and assume that a circle is drawn on the numbers.

If we add the numbers all the three sides will be equal to 21.

So that is

3 + 7 + 9 + 2 = 21,

3 + 8 + 6 + 4 = 21 and

2 + 10 + 5 + 4 = 21

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Answer:12 new, 24 used

Step-by-step explanation: i think this is right, sorry if not.

12 x 18= 216

9 x 24 = 216

216 + 216 = 432

Answer:

A=26.75

Step-by-step explanation:

A=1/2(2)(2)=2

A=1/2(5)(2)=5

A=1/2(2+2+5)(3.5)=15.75

A=2+5+15.75=26.75

The number of periods of REM sleep Georgia has in the 6 hours (390 minutes) as stated in the question is 8.667 periods.

Using the standard time conversion, the number of periods is 8 hours.

To determine the number of periods of REM sleep that Georgia has, we need to divide the total number of minutes of sleep by the interval at which she falls into the REM sleep.

From the given information:

The number of periods of REM sleep she has in 390 minutes of sleep is:

= 390 minutes/ 45 minutes

= 8.667 periods.

NOTE: We have only 360 minutes in 6 hours since 60 minutes = 1 hour.

= 360 minutes/ 45 minutes = 8 periods.

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Answer:

it is 3x+10

Step-by-step explanation:

The height of the building is 9x.

Speed is a measure of how quickly an object moves from one place to another. It is equal to the distance traveled divided by the time.

Given:

Time= 9s

Let the speed of penny be 'x'.

We know,

speed = distance / time

distance = speed* time

distance =  x *9

distance = 9x.

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Answer:

3,18

Step-by-step explanation:

Answer:

54kph

Step-by-step explanation:

Answer:

288

Step-by-step explanation:

a = 9

b = -1

c = -8

b^2 * -4 * ( a * c )

Just filing in the numbers given above:

-1^2 * -4 * ( 9 * -8 )

1 * -4 * ( -72)

1 * + 288 = 288

Answer:

2% hope it helpssss

Step-by-step explanation:

Answer:

2/8 or 1/4

Step-by-step explanation:

So pretty much you just turn the number into a fraction

Answer:

y = - 24

Step-by-step explanation:

[tex]y = (x - 4)(x + 6) \\ plug \: x = 0 \\ y = (0 - 4)(0 + 6) \\ y = ( - 4)(6) \\ y = - 24 \\ \purple{ \bold{ \therefore \: y - intercept = - 24}}[/tex]

Answer:

y = 11x

Step-by-step explanation:

First we find the slope

m = (y2-y1)/(x2-x1)

   = (11-0)/(1-0)

   = 11/1

=11

We know the y intercept is 0 ( the y value where x is zero)

We can use the slope intercept form of the equation for a line

y = mx+b where m is the slope and b is the y intercept

y = 11x+0

y = 11x

The bug crawl in total of 90 feet of distance .

A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangle triangle, is a triangle in which one angle is a right angle or two sides are perpendicular. The relation between the sides and other angles of the right triangle is the basis for trigonometry.

According to question

Ataut telephone wire extends from the top of a 40-foot tall telephone pole to a stake in the ground 9 feet away

So, according to diagram

AB= 9 feet

AC = 40 feet

BC =[tex]\sqrt{AB^{2} +AC^{2} }[/tex](Pythagoras theorem)

BC = [tex]\sqrt{9^{2} +40^{2} }[/tex]

BC=[tex]\sqrt{81 + 1600 }[/tex]

BC = [tex]\sqrt{ 1681 }[/tex]

BC= 41 feet

As bug start from the stake in the ground up the wire to the top of the

telephone pole. Then the bug crawled down to the bottom of the pole and back to the stake which means perimeter of right angle triangle.

Perimeter of triangle = AB + BC + AC

= 9 + 41 + 40

= 90 feet

Hence, the total distance travelled by bug is 90 feet .

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Answer:

The answer is 56.

Step-by-step explanation:

7 * 8 = 56

Answer:

x = ± 3, x = ± 2i

Step-by-step explanation:

Given

[tex]x^{4}[/tex] - 5x² - 36 = 0

Use the substitution u = x² then the equation is

u² - 5u - 36 = 0 ← in standard form

(u - 9)(u + 4) = 0 ← in factored form

Equate each factor to zero and solve for u

u - 9 = 0 ⇒ u = 9

u + 4 = 0 ⇒ u = - 4

This indicates there will be 2 real roots and 2 complex roots

Change back to find values of x, that is

u = 9 ⇒ x² = 9 ⇒ x = ± [tex]\sqrt{9}[/tex] = ± 3 ← real roots

u = - 4 ⇒ x² = - 4 ⇒ x = ± [tex]\sqrt{-4}[/tex] = ± 2i ← imaginary roots

Answer:

Step-by-step explanation:

The figure must also have the rotational symmetry of 180/270°.

In geometry, symmetry is defined as a balanced and proportionate similarity that is found in two halves of an object. It means one-half is the mirror image of the other half. The imaginary line or axis along which you can fold a figure to obtain the symmetrical halves is called the line of symmetry.

Types of symmetries are rotational symmetry, reflection symmetry, translation symmetry, and glide reflection symmetry. These four types of symmetries are examples of different types of symmetry on a flat surface called planar symmetry.

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Answer:

4 and 3 <------- That's the set I believe!

Answer:

Around 169.65.

Step-by-step explanation:

The formula is (pi)r^2*h

(pi)3^2*6

(pi)9*6

54(pi)

169.65

Answer:

7a²/16

Step-by-step explanation:

Area of the triangle PTS

½ × a × a

a²/2

Length of PS:

sqrt(a² + a²)

asqrt(2)

Length of MS:

¼asqrt(2)

Triangles MCS and TPS are similar

With sides in the ratio:

¼asqrt(2) : a

sqrt(2)/4 : 1

Area of triangle SMC:

A/(a²/2) = [(sqrt(2)/4)]²

2A/a² = 1/8

A = a²/16

Area of PTMC

= a²/2 - a²/16

= 7a²/16

Step-by-step explanation:

This is a much more interesting problem than what we usually see here.

Let's just start by assuming a=1 so we have two unit squares.

PMC and PTC are two congruent triangles, each right triangles with one leg of length 1 and a shared hypotenuse PC.

We'll put it on the grid at P(0,0), T(1,0).

Angle TPM is 45 degrees and PM=1 so

M(cos 45, sin 45) = M(1/√2, 1/√2)

MK has slope -1, thru M, so is

y = -x + √2

C's on that line at x=1, so C's x coordinate is 1, so its y coordinate is √2 - 1

C(1, √2 - 1)

OK, that's enough to compute the area.

P(0,0), T(1,0), C(1, √2 - 1), M(1/√2, 1/√2)

area(PMCT) = area(PTC) + area(PCM)= 2 area(PTC)

The area of a right triangle is half the product of its legs.

area(PMCT) = 2 (1/2) (1) ( √2 - 1)

area(PMCT) =  √2 - 1

When we have sides a, the area scales by a²,

Answer: a²(√2 - 1)

Answer:

[tex]28 cm^2[/tex]

Step-by-step explanation:

The formula for finding the area of a triangle is:

[tex]\frac{1}{2} bh[/tex]

The "b," is the base (7), and the "h," is the height (8):

[tex]\frac{1}{2} (7)(8)[/tex]

[tex]\frac{1}{2} (56)[/tex]

28

"The area of triangle [tex]IHC is $\boxed{\frac{1}{2} \times b \times h}$[/tex], where [tex]$b$[/tex] is the base of the triangle and[tex]$h$[/tex]is the height of the triangle.

To determine the area of triangle IHC, we need to know the lengths of the base and the height. The area of a triangle is given by the formula:

[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

In the case of triangle IHC, if we let b represent the length of the base IH, and h represent the length of the height from point H to side IH, then the area of triangle IHC can be calculated using these values.

Without specific numerical values for b and h, we cannot calculate a numerical area. However, if the values of b and h are provided, we can substitute them into the formula to find the area. For example, if b = 6 units and h = 4 units, then the area would be:

[tex]\[ \text{Area} = \frac{1}{2} \times 6 \times 4 = \frac{1}{2} \times 24 = 12 \][/tex]

Thus, the area of triangle IHC with a base of 6 units and a height of 4 units would be 12 square units. If the actual lengths of the base and height are different, those values should be substituted into the formula to calculate the correct area."

Answer:

0.06 or 6%

Step-by-step explanation:

Both bags have the numbers 5, 6, 7, 8, 9 and 10. Thus, there are 6 similar number in both bags.

The probability of picking the number 5 in both bags is:

P(5)= 1/10  * 1/10=  1/ 100

It is the same probability of picking the number 6 or 7 or 8 or 9 or 10 in both bags.

P ( 6)= 1/100

P ( 7 ) =  1 /100

P (8)=  1 /100

P ( 9 ) =  1 /100

P ( 10 ) = 1 /100

Answer:

13.04 units to the nearest hundredth.

Step-by-step explanation:

Use the Pythagoras theorem:

c^2 = a^2 + b^2  where a, b and c are the sides of  a right triangle with c the hypotenuse.

In our triangle ( x = length of the hypotenuse):

x^2 = 13^2 + 1^2

x^2 = 169 + 1 = 170

x = √170

= 13.04.

If we are doing this mentally the best we can do is say that the hypotenuse is a small amount greater than 13.

Answer:

2

Step-by-step explanation:

i think bc its on the middle but its ben a min since ive done it

Look at the attached screen shot. The population is 2 while the geometric mean is (Xg):4