Write an equation in point-slope form of the line that passes through the point (4,7) and has a slope of -1.

Answer:

No, they are not copies of each other.

Step-by-step explanation:

<XNY and <ZHC are not the same sized angles. The shapes would have the same angles if they were just scaled down copies.

Answer:

3 and 4

Step-by-step explanation:

3 and 4 because you have to find two angles(in the triangle) that are far away of angles 1

which are 3 and 4

Answer: 3 and 4

Step-by-step explanation:

It would take approximately 19.65 years for an investment of $100,000 at a 7% annual interest rate to grow to $500,000. Rounded to two decimal places, the answer is 19.65 years.

To determine the number of years it will take for an investment of $100,000 at a 7% annual interest rate to grow to $500,000, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment ($500,000)

P = the initial principal amount ($100,000)

r = the annual interest rate (7% or 0.07)

n = the number of times that interest is compounded per year (assuming annually, so n = 1)

t = the number of years

Plugging in the values we know, we get:

$500,000 = $100,000(1 + 0.07/1)^(1*t)

Dividing both sides of the equation by $100,000 and simplifying:

5 = (1.07)^t

To solve for t, we can take the logarithm of both sides:

log(5) = log[(1.07)^t]

Using logarithmic properties, we can bring down the exponent:

log(5) = t * log(1.07)

Finally, we can solve for t by dividing both sides by log(1.07):

t = log(5) / log(1.07)

Using a calculator, we find:

t ≈ 19.65

Therefore, it would take approximately 19.65 years for an investment of $100,000 at a 7% annual interest rate to grow to $500,000. Rounded to two decimal places, the answer is 19.65 years.

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Answer:

x(x + 2) = 48

x^2 + 2x - 48 = 0

(x - 8)(x + 6) = 0

x = -8, so x + 2 = -6

x = 6, so x + 2 = 8

The numbers are -8 and -6, or 6 and 8.

Answer:

Option 2

Step-by-step explanation:

Answer:

6 + 2m

Step-by-step explanation:

You need to use the distributive property - multiply the outside number by each inside value or variable

So: 2 times 3 = 6 and 2 times m = 2m

Put it all back together: 6 + 2m

Answer:

6m

Step-by-step explanation:

Answer:

x < 7 /13

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

The percentage of scores that are greater than 154 on the test is approximately 0.13%.

To find the percentage of scores that are greater than 154 on a test with a normal distribution, we can use the properties of the standard normal distribution.

First, we need to standardize the value of 154 by converting it into a z-score. The formula for calculating the z-score is:

z = (x - μ) / σ

where x is the given value, μ is the mean, and σ is the standard deviation.

In this case, x = 154, μ = 109, and σ = 15.

Calculating the z-score:

z = (154 - 109) / 15

z = 45 / 15

z = 3

Now that we have the z-score, we can use a standard normal distribution table or a calculator to find the percentage of scores greater than 154.

Looking up the z-score of 3 in the standard normal distribution table, we find that the area to the left of z = 3 is approximately 0.9987.

Since we want to find the percentage of scores greater than 154, we subtract the area to the left from 1 to get the area to the right.

Area to the right = 1 - 0.9987 = 0.0013

Converting this to a percentage:

Percentage = 0.0013 * 100 = 0.13%

Therefore, approximately 0.13% of scores are greater than 154 on this test.

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The formula for the surface area of a cube in terms of its volume is [tex]SA(V) = 6V^(2/3)[/tex], and the domain of SA(V) is [0, ∞).

Let S represent the surface area of a cube, and let V represent its volume

. The formula for the surface area of a cube in terms of its volume is [tex]SA(V) = 6V^(2/3).[/tex]

The domain of SA(V) is all nonnegative real numbers, since the volume and surface area of a cube cannot be negative.

Volume of cube (V) = s³ where s is the length of any side of the cube.

Surface area of a cube (S) = 6s²

=[tex]6(V^(2/3))[/tex]

Formula for the surface area of a cube in terms of its volume is given as:

[tex]SA(V) = 6V^(2/3)[/tex]

State the domain of SA(V):

The domain of SA(V) is all nonnegative real numbers, since the volume and surface area of a cube cannot be negative.

In interval notation, the domain is [0, ∞).

Therefore, the formula for the surface area of a cube in terms of its volume is[tex]SA(V) = 6V^(2/3)[/tex], and the domain of SA(V) is [0, ∞).

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Answer:

.05 + .23 + .37 + P(D) = 1

.65 + P(D) = 1

P(D) = .35 = 35%

Answer:   2286 ^2  ft

Step-by-step explanation:

Answer:

the answer is 3182540.hope this helps

3.65 is less than [tex]3\frac{3}{4}[/tex]

First, you must change the mixed number into a decimal so you can compare the two numbers.

[tex]3\frac{3}{4} = 3.75[/tex]

Then, you must compare the terms.

3.65 < 3.75

3.65 is less than [tex]3\frac{3}{4}[/tex]

Answer:

= 11-33+7

= 11+7-33

= 18-33

= -15

Step-by-step explanation:

if we multiple + by - then it becomes -

if we multiple - by - then it becomes +

by this way I have done

I hope this will help u .

Answer:

The remainder is -1

The binomial is not a factor of the polynomial

Step-by-step explanation:

In the algebraic division, there are 4 terms

The remainder theorem:

Let us use it to solve the question

∵ The dividend is x² - 2

∴ f(x) = x² - 2

∵ The divisor is x - 1

∴ (x - h) = (x - 1)

∴ h = 1

Let us find f(1)

∵ f(1) = (1)² - 2 = 1 - 2 = -1

∴ f(1) = -1

∴ The remainder is -1

∵ f(1) ≠ 0

∴ x - 1 is not a factor of x² - 2

∴ The binomial is not a factor of the polynomial

Answer:

The midpoint is ( -1/2, -2)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2

( 1+-2)/2 = -1/2

To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2

( 0+-4)/2 = -4/2=-2

The midpoint is ( -1/2, -2)

Answer:

Hey mate here is ur answer.....

Step-by-step explanation:

63

Sixty Three

hope it helps you,

follow me.....

Answer:

sixty three

Step-by-step explanation:

Perpendicular to y=-3/7 and passes through (2/3,1/2):Finding the equation of a line perpendicular to a given line and passing through a particular point is one of the fundamental topics of analytical geometry. Let's take a look at the steps that are required to solve this problem.

Step 1: Understand the problem The first step in solving any mathematical problem is to understand the problem and the information given. In this case, we're given the equation y=-3/7 and the point (2/3,1/2), and we're asked to find the equation of a line that is perpendicular to the given line and passes through the given point.

Step 2: Find the slope of the given lineTo find the slope of the given line, we need to convert the equation into slope-intercept form (y=mx+b), where m is the slope and b is the y-intercept. y=-3/7x + bTo do this, we must rearrange the equation in terms of y. y= (-3/7)x + bComparing it with y = mx + b format, we have m = -3/7. Therefore, the slope of the given line is -3/7.

Step 3: Find the slope of the perpendicular lineThe slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. The negative reciprocal of -3/7 is 7/3.

Step 4: Use the point-slope formula to find the equation of the lineThe point-slope formula for a line is y-y1=m(x-x1).We know that the point (2/3,1/2) lies on the line. Therefore, x1=2/3 and y1=1/2.Substituting these values, we get: y - 1/2 = 7/3(x - 2/3)Multiplying through by 3, we get: 3y - 3/2 = 7x - 14/3Rearranging, we get: 7x - 3y = 8/3Therefore, the equation of the line that is perpendicular to y=-3/7 and passes through (2/3,1/2) is 7x - 3y = 8/3.

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Answer:

Her grade must be an 89 or better

Step-by-step explanation:

to find the average you add all the numbers than divide but the total numbers of numbers so when she had the first two test her average was an 78.5 if she has an 85 it is close to the 80's but still less than but if she has a 90 she is averaged to be about 85 so if she gets an 89 she has an exact average of 82

Answer:

8(.4) + .4a - a = .6(8)

3.2 - .6a = 4.8

.6a = 1.6, so a = 2 2/3 quarts

Answer: C. 1.276 x 107

Step-by-step explanation:

Correct on e d g e n u i t y!

Answer:

C

Step-by-step explanation:

I just took the asignment.

The given equation has two real and distinct roots.

The formula for the discriminant is b² - 4ac. For the given equation, 3x² + 4x - 7 = 0,

the value of a = 3, b = 4 and c = -7.Substituting these values in the formula for discriminant, we get:$$\begin{aligned}b^2-4ac&=4^2-4\times3\times(-7) \\&=16+84 \\&=100 \end{aligned}$$

Hence, the value of discriminant is 100.Using the value of the discriminant, we can determine the nature of roots. If the discriminant is positive, then the roots are real and distinct.

If the discriminant is zero, then the roots are real and equal.

If the discriminant is negative, then the roots are imaginary and conjugate.In this case, the discriminant is positive (100), so the roots will be real and distinct.

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Answer:

16 < w < 21

Step-by-step explanation:

Given that :

Width if mirror = w

Length of mirror = l

L = 6 + w

Perimeter of mirror < 96 and > 76

Possible width of the mirror

Perimeter of a rectangle :

2(l + w)

2(6 + w + w)

= 2(6 + 2w)

= 12 + 4w

Hence,

76 < perimeter < 96

76 < 12 + 4w < 96

76 - 12 < 4w < 96 - 12

64 < 4w < 84

16 < w < 21

Answer:

c) 14

Step-by-step explanation:

2*6 + 1 + 1

following PEMDAS, the multiplication comes first.

2 * 6 = 12

12 + 1 + 1

14

Answer:

0.6

Step-by-step explanation:

subtract 4.5 from 3.9

The given data provides information about an IC engine, including the mass of the connecting rod (mrod), length of the connecting rod (Lord), center of gravity of the rod (Cg), mass of the piston (Mp), piston area (Ap), engine speed (3000 RPM), and gas pressure at various points in the indicator diagram. We are asked to determine the torque of the engine at top dead center (TDC).

To calculate the torque of the engine at TDC, we need to consider the forces acting on the connecting rod and the piston. The torque can be determined using the equation:
Torque = Force × distance
First, we calculate the force acting on the connecting rod. The force can be obtained using the equation:
Force = Mass × acceleration
The acceleration can be determined using the equation:
Acceleration = (Change in velocity) / time
Since the engine speed is given as 3000 RPM, we convert it to radians per second:
Angular Velocity = (3000 RPM) × (2π radians / 1 minute) × (1 minute / 60 seconds) = 100π radians/second
We can calculate the change in velocity by subtracting the velocity at TDC from the velocity at the given point on the indicator diagram. Then we divide the change in velocity by the time period.
Next, we can determine the distance from the center of the crankshaft to the center of the connecting rod (crank radius) using the given length of the connecting rod and the position of the center of gravity of the rod.
Finally, we can calculate the torque at TDC by multiplying the force acting on the connecting rod by the crank radius.
By following these calculations, we can determine the torque of the engine at top dead center (TDC) based on the given data.

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The answer of 5+7-2+5=15

The surface area of the paraboloid z = 1 - x^2 - y^2 that lies above the plane z = -4 is 3π√5 square units.

The paraboloid z = 1 - x^2 - y^2 lies above the plane z = -4. To find the surface area of this paraboloid, we need to calculate the area of its intersection with the plane z = -4 and subtract it from the total surface area of the paraboloid.

To find the intersection, we set z = -4 and solve for x and y:

-4 = 1 - x^2 - y^2

x^2 + y^2 = 5

This is the equation of a circle with radius √5 centered at the origin. The area of this circle is π(√5)^2 = 5π.

To find the total surface area of the paraboloid, we use the formula for the surface area of a surface of revolution:

S = 2π∫a^b f(x)√(1 + (f'(x))^2) dx

In this case, we want to revolve the curve z = 1 - x^2 - y^2 around the z-axis. Solving for y in terms of x and z, we get:

y = ±[tex]\sqrt(1 - x^2 - z)[/tex]

We can now use this formula to calculate f(x):

f(x) = 2sqrt(1 - x^2 + 4)

f'(x) = (-2x) / sqrt(1 - x^2 + 4)

Substituting these into the formula for surface area, we get:

S = 2π∫-√5^√5 2*[tex]\sqrt(1 - x^2 + 4) / \sqrt(1 - x^2 + 4) dx[/tex]

Simplifying, we get:

S = 4π∫-√5^√5 dx

S = 8π√5

Subtracting the area of the intersection with the plane, we get:

S = 8π√5 - 5π

S = 3π√5

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