A square has side length x and a triangle has a base (3x - 2) and height (2x + 4). At what value of x will the two figures have the same area?
Show work and explain all steps.

Answer:

A.{7}^{15}

[tex]4.7475615 {}^{12}[/tex]

Step-by-step explanation:

[tex]( {7}^{5} ) {}^{3} = {7}^{5} =(16807) {}^{3}=4.7475615 {}^{12} [/tex]

Hope this helps ;) ❤❤❤

Answer:

43cm

Step-by-step explanation:

Given

Length of Log = 291cm

First Piece = 67cm

Second Piece = 181cm

Required

Determine the length of the third piece

Given that the log was cut into three;

this implies that;

Length of Log = First Piece + Second Piece + Third Piece

Substitute values for first piece, second piece and length of log;

[tex]291 = 67 + 181 + Third\ Piece[/tex]

[tex]291 = 248 + Third\ Piece[/tex]

Subtract both sides by 248

[tex]291 - 248 = 248 - 248 + Third\ Piece[/tex]

[tex]43 = Third\ Piece[/tex]

[tex]Third\ Piece = 43[/tex]

Hence, the length of the third piece is 43cm

Answer:

(-2 2/3,0)

(0,2)

Step-by-step explanation:

Just did it

Answer:

Step-by-step explanation:

the two points are(0,2), (-8/3,0)

Answer:

(2, 3 )

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines.

point of intersection = (2, 3 ) ← is the solution

Answer:

i am very sure that the answer is D which is domain does not change and the range changes.

Step-by-step explanation:

it is because always range value can varry more over when H(x) is equal to A and range is equal to B .

A=B

similarly

A= -B

Answer:

106°

Step-by-step explanation:

Given that the points B, C and D are colinear, it means that

2x + 40 = 5x + 10

collecting like terms

40 - 10 = 5x - 2x

3x = 30

x = 10

Hence the angle ∠E

= 5(10) + 10

= 60°

∠BCE = X + 4

= 10 + 4

= 14°

Given that the sum of angles in a triangle is 180°

∠D + 14 + 60 = 180

∠D = 180 - 74

= 106°

Answer:

The ratio of the volume of the larger sphere to the volume of the smaller sphere is

Step-by-step explanation:

Volume of a sphere is

[tex] \frac{4}{3} \pi {r}^{3} [/tex]

Where r is the radius

radius = diameter / 2

For First sphere

diameter = 8yards

radius = 8 / 2 = 4 yards

Volume of first sphere is

[tex] \frac{4}{3} \pi( {4})^{3} \\ \\ = \frac{256}{3} \pi \: {yd}^{3} [/tex]

For second sphere

diameter = 1064 yards

radius = 1064 / 2 = 532 yards

Volume of second sphere is

[tex] \frac{4}{3} \pi( {532})^{3} \\ \\ = \frac{602275072}{3} \pi \: {yd}^{3} [/tex]

Since the volume of the second sphere is the largest

Ratio of the second sphere to the first one is

[tex] \frac{602275072}{3} \pi \div \frac{256}{3} \pi \\ \\ = \frac{602275072}{3} \pi \times \frac{3}{256} \pi \\ \\ = \frac{602275072}{256} \\ \\ = \frac{ 2352637}{1} \\ \\ = 2352637: 1[/tex]

Hope this helps you

Answer: 69

Step-by-step explanation:

Answer:

(5,-6)

Step-by-step explanation:

ONE WAY:

If [tex]f(x)=x^2-6x+3[/tex], then [tex]f(x-2)=(x-2)^2-6(x-2)+3[/tex].

Let's simplify that.

Distribute with [tex]-6(x-2)[/tex]:

[tex]f(x-2)=(x-2)^2-6x+12+3[/tex]

Combine the end like terms [tex]12+3[/tex]:

[tex]f(x-2)=(x-2)^2-6x+15[/tex]

Use [tex](x-b)^2=x^2-2bx+b^2[/tex] identity for [tex](x-2)^2[/tex]:

[tex]f(x-2)=x^2-4x+4-6x+15[/tex]

Combine like terms [tex]-4x-6x[/tex] and [tex]4+15[/tex]:

[tex]f(x-2)=x^2-10x+19[/tex]

We are given [tex]g(x)=f(x-2)[/tex].

So we have that [tex]g(x)=x^2-10x+19[/tex].

The vertex happens at [tex]x=\frac{-b}{2a}[/tex].

Compare [tex]x^2-10x+19[/tex] to [tex]ax^2+bx+c[/tex] to determine [tex]a,b,\text{ and } c[/tex].

[tex]a=1[/tex]

[tex]b=-10[/tex]

[tex]c=19[/tex]

Let's plug it in.

[tex]\frac{-b}{2a}[/tex]

[tex]\frac{-(-10)}{2(1)}[/tex]

[tex]\frac{10}{2}[/tex]

[tex]5[/tex]

So the [tex]x-[/tex] coordinate is 5.

Let's find the corresponding [tex]y-[/tex] coordinate by evaluating our expression named [tex]g[/tex] at [tex]x=5[/tex]:

[tex]5^2-10(5)+19[/tex]

[tex]25-50+19[/tex]

[tex]-25+19[/tex]

[tex]-6[/tex]

So the ordered pair of the vertex is (5,-6).

ANOTHER WAY:

The vertex form of a quadratic is [tex]a(x-h)^2+k[/tex] where the vertex is [tex](h,k)[/tex].

Let's put [tex]f[/tex] into this form.

We are given [tex]f(x)=x^2-6x+3[/tex].

We will need to complete the square.

I like to use the identity [tex]x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2[/tex].

So If you add something in, you will have to take it out (and vice versa).

[tex]x^2-6x+3[/tex]

[tex]x^2-6x+(\frac{6}{2})^2+3-(\frac{6}{2})^2[/tex]

[tex](x+\frac{-6}{2})^2+3-3^2[/tex]

[tex](x+-3)^2+3-9[/tex]

[tex](x-3)^2+-6[/tex]

So we have in vertex form [tex]f[/tex] is:

[tex]f(x)=(x-3)^2+-6[/tex].

The vertex is (3,-6).

So if we are dealing with the function [tex]g(x)=f(x-2)[/tex].

This means we are going to move the vertex of [tex]f[/tex] right 2 units to figure out the vertex of [tex]g[/tex] which puts us at (3+2,-6)=(5,-6).

The [tex]y-[/tex] coordinate was not effected here because we were only moving horizontally not up/down.

Answer:

[tex]\huge\boxed{f(x - 2) = x + 6}[/tex]

Step-by-step explanation:

f(x) + n - shift the graph n units up

f(x) - n - shift the graph n units down

f(x + n) - shift the graph n units to the left

f(x - n) - shift the graph n units to the right

===========================================

f(x) = x + 8

shift the graph 2 units to the right

f(x - 2) = (x - 2) + 8 = x - 2 + 8 = x + 6

Answer:

64° aka D

Step-by-step explanation:

∠J + ∠L + ∠LKJ = 180°

58° + 58° + ∠LKJ = 180°

116° + ∠LKJ = 180°

∠LKJ = 180° - 116°

=  64°

hope i helped

-lvr

Answer:

49.87% of the population has a heart rate between 68 and 77.

Step-by-step explanation:

We are given that the mean of the data for the resting heart of adults is 68 beats per minute and the standard deviation is 3 beats per minute.

Let X = the data for the resting heart of adults

The z-score probability distribution for the normal distribution is given by;

                          Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 68 beats per minute

           [tex]\sigma[/tex] = standard deviation = 3 beats per minute

Now, the percentage of the population that has a heart rate between 68 and 77 is given by = P(68 < X < 77)

    P(68 < X < 77) = P(X < 77) - P(X [tex]\leq[/tex] 68)

    P(X < 77) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{77-68}{3}[/tex] ) = P(Z < 3) = 0.9987

    P(X [tex]\leq[/tex] 68) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{68-68}{3}[/tex] ) = P(Z [tex]\leq[/tex] 0) = 0.50

The above probability is calculated by looking at the value of x = 3 and x = 0 in the z table which has an area of 0.9987 and 0.50 respectively.

Therefore, P(68 < X < 77) = 0.9987 - 0.50 = 0.4987 or 49.87%

Answer:

The perimeter of the big rectangle is 38 cm

Step-by-step explanation:

Rectangle 1 and rectangle 2 share the same width, let their width be a cm while Rectangle 3 and rectangle 4 share the same width, let their width be b cm

Rectangle 1 and rectangle 3 share the same length, let their length be x cm while Rectangle 2 and rectangle 4 share the same length, let their length be y cm

The perimeter of a rectangle = 2(length + breadth).

For rectangle 1:

Perimeter = 2(a + x) = 10

a + x = 5            1)

For rectangle 2:

Perimeter = 2(a + y) = 20

a + y = 10          2)

For rectangle 3:

Perimeter = 2(b + x) = 28

b + x = 14         3)

For rectangle 4:

Perimeter = 2(b + y) = 18

b + y = 9         4)

Adding equations 1, 2, 3 and 4 gives:

a + x + a + y + b + x + b + y = 5 + 10 + 14 + 9

a + a + b + b + x + x + y + y  =38

2a + 2b + 2x + 2y = 38

2((a + b) + (x + y)) = 38

For the big rectangle, let its width = c = a + b and its length be d = x + y

The perimeter of the big rectangle = 2 (c + d)

Therefore:

2((a + b) + (x + y)) = 38

2(c + d) = 38 cm = The perimeter of the big rectangle

The perimeter of the big rectangle is 38 cm

Answer:

[tex]\boxed{6\sqrt{6} }[/tex]

Step-by-step explanation:

[tex]\sqrt{12} \sqrt{18}[/tex]

Multiply square roots.

[tex]\sqrt{12 \times 18}[/tex]

[tex]\sqrt{216}[/tex]

Simplify square root.

[tex]\sqrt{36} \sqrt{6}[/tex]

[tex]6\sqrt{6}[/tex]

Answer:

900L per minute

Step-by-step explanation:

1- 70 - 20 = 50

2- in this 50 min the 45000L was drowned

3- 45000L / 50 = 900L

.. ..

Answer:

a) 4 : 1 : 10

b) 25 : 9 : 13

c) 18 : 11 : 3

d) 2000 : 20 : 1

Step-by-step explanation:

We are to put the values in the form a : b : c

a) 40 ml, 1/100 l, 0.1 l

Put them all in ml (1 l = 1000 ml)

40ml, 10 ml, 100 ml

Therefore:

40 : 10 : 100

In lowest terms, 4 : 1 : 10

b) 2 1/2 kg, 900 g, 1.3 kg

Put them all in grams, (1 kg = 1000 g):

2500 g, 900 g, 1300 g

Therefore:

2500 : 900 : 1300

In lowest terms, 25 : 9 : 13

c) 1.5 hrs, 55 minutes, 1/4 hrs

Put them all in minutes (1 hour = 60 minutes)

90 minutes, 55 minutes, 15 minutes

Therefore:

90 : 55 : 15

In lowest terms, 18 : 11 : 3

d) 60 cm, 6 mm, 0.03 cm

Put them all in mm (1 cm = 10 mm)

600 mm, 6 mm, 0.3 mm

Therefore:

600 : 6 : 0.3

In lowest terms, 2000 : 20 : 1  (Divide by 0.3 because a ratio cannot be decimal)

Answer:

Hey there!

That would be the square root of 36, or 6.

Hope this helps :)

Answer:

Volume of cone = 130 cm³

Step-by-step explanation:

Given:

Volume of cylinder = 390 cm³

dimensions of cylinder = dimensions of cone

Find:

Volume of cone

Computation:

Volume of cylinder = πr²h

390 = πr²h

124.090909 = r²h

So,

Volume of cone = (1/3)πr²h

Volume of cone = (1/3)(22/7)r²h...........[124.090909 = r²h]

Volume of cone = (1/3)(22/7)(124.090909)

Volume of cone = 130 cm³

Answer:

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer:

b is the right option

Step-by-step explanation:

According to the line of best fit, the coin would land heads up about 52.73 times in 100 flips, which we can round to 53.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

We can use linear regression to find the line of best fit for the given data, which will give us a linear equation that models the relationship between the number of coin flips and the number of times the coin lands heads up.

Using a calculator or statistical software, we can find that the line of best fit for the given data is:

y = 0.4975x + 2.9825

where y is the number of times the coin lands heads up, and x is the number of coin flips.

To find how many times the coin would land heads up in 100 flips, we can substitute x = 100 into the equation and solve for y:

y = 0.4975(100) + 2.9825

y = 49.75 + 2.9825

y ≈ 52.73

Therefore,

According to the line of best fit, the coin would land heads up about 52.73 times in 100 flips, which we can round to 53.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ7

Answer:

[tex]\boxed{\sf Option \ 3}[/tex]

Step-by-step explanation:

When x is -2, F(x) is undefined.

When x is -1, F(x) is -3.

If we see the third option,

[tex]F(x)=\sqrt{x+1} -3[/tex]

When x is -2, we get the square root of -1, which is undefined.

When x is -1, we get the square root of 0, which is just 0, 0-3 is -3.

Answer:

x < 6

Step-by-step explanation:

open circle < or >, closed circle ≤ or ≥

Answer:

Test statistic = 3.863

Step-by-step explanation:

We are told that most adults would erase all of their personal information online if they could. Since the word "most" is used, it means more than 50% or 50 percent.

So, p_o = 0.5

Also, we are told that 58 % of them would erase all of their personal information online if they could.

Thus, p^ = 0.58

Number of randomly selected adults; n = 583

The test statistic formula for hypothesis test for proportion is given by:

z = (p^ - p_o)/[√[p_o(1 - p_o)/n]

Plugging in the relevant values, we have;

z = (0.58 - 0.5)/[√[0.5(1 - 0.5)/583]

z = 0.08/0.02070788416

z = 3.863

Answer: M^10

Step-by-step explanation:

since the base number is the same, just add up the exponents: 2+5+3=10

Answer:

Step-by-step explanation:

If its like M^2 x M^5 x M^3 (exponents)

then just add 2+5+3=10

so M^10

Its a rule when the bottom (M) is the same you add the exponents.

If its 2M x 5M x 3M then you multiply

2x5x3=30

so 30M

Hope this helps!

Answer:

Step-by-step explanation:

[tex]A = (-2, -4) \\ B = (-8, 4) \\ d = (\sqrt{( {x_2 - x_1})^{2} + ({y_2 - y_1})^{2} } [/tex]

[tex]x_1 = - 2 \\ y_1 = - 4 \\ x_2 = - 8 \\ y_2 = 4[/tex]

[tex]d = \sqrt{ {( - 8 - ( - 2)}^{2} + {(4 - ( - 4))}^{2} } \\ d= \sqrt{ {( - 6)}^{2} + {8}^{2} } \\ d = \sqrt{36 + 64} \\ [/tex]

[tex]d = \sqrt{100} \\ d = 10[/tex]

Answer:

10

Step-by-step explanation:

Answer:

4000 nm

Step-by-step explanation:

Conversion from meters to nanometers: 1 meter is 1(10⁹) nm

Step 1: Convert 0.000004 to scientific notation

0.000004 = 4(10⁻⁶)

Step 2: Convert by multiplication

4(10⁻⁶) x 1(10⁹) = 4000 nm

Answer:

x=1.94

x = - 1.94

Step-by-step explanation:

8x² + 5 = 35

Subtract 5 from each side

8x² + 5-5 = 35-5

8x²  = 30

Divide each side by 8

8x² /8 = 30/8

x² = 15/4

Take the square root of each side

sqrt( x²) = ±sqrt(15/4)

x = ±sqrt(15/4)

x=1.93649

x = - 1.93649

To the nearest hundredth

x=1.94

x = - 1.94

Answer:

1.94

Step-by-step explanation:

[tex]8x^2+5=35\\8x^2=30 \\x^2=30/8\\x^2=3.75\\\sqrt{3.75} \\[/tex]

≈ ±1.94

Answer:

[tex]x^{2}[/tex]

Step-by-step explanation:

because x^{2} represents the quadratic equation, so I don't think it will affect it

Answer:

Since Manish hit the target 25 - 5 = 20 times, he earned 15 * 20 = ₹ 300. Since he missed 5 times, he lost 5 * 5 = ₹ 25, therefore, he only earned 300 - 25 = ₹ 275.

Answer:

Manish hit the target=25-5=20times

He he earned=15×20=₹300

Since he missed 5 times he lost 5×5=₹25

Therefore,he only earned 300-25=₹275

I HOPE YOU LIKE IT. THIS IS THE CORRECT ANSWER

Answer: -5

Step-by-step explanation:

A coefficient is a number that a variable is multiplied by.

Hope it helps <3

Answer:

well technically, there are two coefficients

the coefficient of (b^2) is 1 and the coefficient of b (itself) is -5.

But if you sre just looking for the coefficient ot just plain b, it is -5

Step-by-step explanation:

the reason I say the coefficient to (b^2) is 1 because if there is no number in front of the variable, it is automatcally assumed to be 1.

now, as for just plain b, it is -5 because the sign, positive or negative, before a number coefficient gets attached to that number.  so, the entire term is -5b, which makes the coefficient to just plain b to be -5