Which expression represents the sum of the expression below?
( 1/5 x -5) + (2/5 x +1)

The triangles are congruent if all three sets of comparable sides are present. The side-side-side shortcut is a congruence technique (SSS). Side-angle-side (SAS), which uses two sets of sides and an angle between them that is known to be congruent, is another shortcut.

SSS, which stands for "side, side, side," denotes that there are two triangles with identical angles on all three sides. The triangles are congruent if their third sides are the same as those of another triangle. The triangles are congruent if two pairs of corresponding angles and the included sides are both true. This standard is called angle-side-angle (ASA).

Angle-angle-side (AAS) is another criterion that takes into account the congruence of two pairs of angles as well as the non-included side. SSS stands for "side, side, side," which signifies that we have two triangles with equal sides on all three sides. SAS, ASA, and AAS are acronyms for these rules. "Side, Angle, Side" stands for two triangles whose two sides and one included angle are known to be equal.

Learn more about SSS Visit: brainly.com/question/3999145

#SPJ4

Answer:

49

Step-by-step

step 1 subtract 10 -3

step 2 multiply 7 x 7

that's your answer

Answer:

49

Step-by-step explanation:

Step 1:

a = 3; b = 2; c = 10         Given

Step 2:

\((c-a)^{b}\)         Equation

Step 3:

\(( 10 - 3)^{2}\)        Input values

Step 4:

( 7 ) ²           Parentheses

Answer:

49

Hope This Helps :)

we have the numbers

1/2 and 2/5

the given fractions don't have the same denominator

so

Find out an equivalent fraction

1/2 -----> multiply by 5/5

(1/2)*(5/5)=5/10

2/5 ----> multiply by 2/2

(2/5)*(2/2)=4/10

Now compare the fractions

5/10 is greater than 4/10

so

The light post height is around 9.71 feet tall 

We are ready to utilize comparative triangles to get it this issue.

The stature of the young lady and the light post diagrams facilitate comparing sides, and the length of the girl's shadow and the confinement from the energetic lady to the light post shape the other facilities.

Since the triangles are comparative, the degree of comparing sides must rise.

Let's call the height of the light post "x". At that point we are ready to set up the taking after degree:

The stature of youthful woman/length of girl's shadow

= stature of light post / apportioned from energetic lady to light post

Stopping inside the given values, we get:

4 / 3.5 = x / 8.5

Moving forward with this condition, able to cross-multiply and light up for  x:

4 * 8.5 = 3.5 * x

34 = 3.5x

x = 34 / 3.5

x ≈ 9.71

In this way, the light post is around 9.71 feet tall.

To know more about height-related problems refer to this:

https://brainly.com/question/12446886

#SPJ4

The profit-maximizing number of units, rounded to the closest whole number, is 23.

To find the profit-maximizing number of units, we need to determine the quantity that maximizes the profit function. Profit is calculated by subtracting the cost function from the revenue function.

The revenue function is given by multiplying the price per unit by the quantity sold. In this case, the price per unit is $47. Therefore, the revenue function can be expressed as R(q) = 47q.

The profit function (P) can be defined as the difference between the revenue function and the cost function:

P(q) = R(q) - C(q)

Substituting the given revenue function R(q) = 47q and cost function C(q) = q^2 + 2q + 94, we have:

P(q) = 47q - (q^2 + 2q + 94)

Expanding and simplifying the expression, we get:

P(q) = -q^2 + 45q - 94

To find the profit-maximizing quantity, we need to find the value of q that maximizes the profit function P(q). One way to determine this is by finding the vertex of the parabolic profit function.

The vertex of a parabola defined by the quadratic function P(q) = -q^2 + 45q - 94 can be found using the formula:

q = -b / (2a)

In this case, a = -1 and b = 45. Substituting these values into the formula, we have:

q = -45 / (2*(-1))

q = -45 / -2

q = 22.5

Since the number of units (q) must be a whole number, we can round the value to the nearest whole number. Therefore, the profit-maximizing number of units is approximately 23.

Learn more about parabola at: brainly.com/question/11911877

#SPJ11

Answer:

$19.68

Step-by-step explanation:

To find out how much it'll cost Melissa to buy the ribbon, we simply need to find all the side lengths (the perimeter) and then multiply then by the cost.

We already know two of the side lengths: 6 and 8. To find the third, remember that the question tells us that the triangle is a right triangle. Therefore, we can use the Pythagorean Theorem. The unknown side is the longest side. Therefore:

\(a^2+b^2=c^2\)

Substitute 6 for a and 8 for b. This gives us:

\((6)^2+(8)^2=c^2\)

Solve for c. Square the values:

\(36+64=c^2\)

Add:

\(100=c^2\)

Take the square root of both sides:

\(c=10\)

Therefore, our unknown side is 10 feet.

Therefore, the sum of our side lengths or the perimeter is:

\(P=6+8+10\)

Add:

\(P=24\text{ feet}\)

This means that the total cost will be:

\(T=\frac{0.82\text{ dollars}}{\text{foot}}\cdot24\text{ feet}\)

Multiply. The foot/feet cancel:

\(T=24(0.84)\text{ dollars}\)

Multiply:

\(T=\$19.68\)

So, it will cost Melissa a total of $19.68 to buy the ribbon.

And we're done!

Edit: Typos

Answer:

The table that shows the relationship between the time in seconds, x, and the height of the balloon in feet, y is H. This table shows that for every 10 seconds that pass, the height of the balloon increases by 20 feet. This is consistent with the information given in the question that after 5 seconds the height of the balloon is 20 feet and it continues to rise at the same rate.

Step-by-step explanation:

Answer:

62.83in

Step-by-step explanation:

C=2 π r = 2• π • 10= 62.83185in

The circumference of a circle with a radius of 10 inches is 62.8 inches

Circumference is the distance around the perimeter of a circular object. It is defined as the length of the circle that is found by multiplying the diameter of the circle by π (pi), which is approximately equal to 3.14.

The formula for the circumference of a circle is given by: C = 2πr,

Given that,

A circle having radius 10 inches.

The circumference = ?

Substituting the given value of the radius, we get:

C = 2π(10) = 20π

To find the circumference to the nearest tenth of an inch, we can substitute the value of π as 3.14 (an approximation of π accurate to two decimal places).

Therefore,

C = 20π ≈ 20(3.14) = 62.8 inches (rounded to one decimal place)

To know more about circumference check:

https://brainly.com/question/4268218

#SPJ2

The required average speed of the given train is 42 km/hour.

Speed is what it means. the speed at which an object's location changes in any direction.

The distance traveled in relation to the time it took to travel that distance is how speed is defined.

As speed simply has a direction and no magnitude, it is a scalar quantity.

So, we have:

63/x + 72/6+x = 3

63(x+6)+72x/x(x+6) = 3

63x + 378 + 72x/x²+6x = 3

378 + 135x = 3x² = 18x

3x² - 117x - 378 = 0

x² - 39x - 126 = 0

x² - 42x + 3x - 126 = 0

x(x-42)+3(x-42) = 0

(x+3)(x-42) = 0

x = 42, -3

As speed cannot be zero, the first average speed is 42 km per hour.

Therefore, the required average speed of the given train is 42 km/hour.

Know more about speed here:

https://brainly.com/question/13943409

#SPJ1

Correct question:

A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed. If it takes 3 hours to complete total journey, what is its original average speed?

Answer:

y'=6,-2    z'=2,-1

Step-by-step explanation:

Translations are x+4, y-4

We can apply this to the others.

y'=2+4,2-4

y'=6,-2

z'=-2+4/3-4

z'=2,-1

The final answer is A. ∇f(-3,1) = (-6(-3) - 3(1), -3(-3) - 4(1)) = (15, -5).

                                B.  the gradient of f at the point P is (15, -5).

                                C.  the directional derivative of f at P in the direction of u is 39/5.

A. The gradient of f is a vector that points in the direction of maximum increase of the function, and its magnitude is the rate of change of the function in that direction. It is computed by taking the partial derivatives of the function with respect to each variable and putting them together as a vector:

∇f(x,y) = (∂f/∂x, ∂f/∂y) = (-6x - 3y, -3x - 4y)

So, in this case, the gradient of f is:

∇f(-3,1) = (-6(-3) - 3(1), -3(-3) - 4(1)) = (15, -5)

B. Evaluating the gradient at the point P means plugging in the values x = -3 and y = 1 into the expression for ∇f(x,y):

(f)(-3,1) = (-6(-3) - 3(1))i + (-3(-3) - 4(1))j = (15)i - 5j

So, the gradient of f at the point P is (15, -5).

C. The directional derivative of f at P in the direction u is the rate of change of f as we move along the line passing through P in the direction of u. It is computed by taking the dot product of the gradient of f at P with the unit vector in the direction of u:

Duf(p) = ∇f(-3,1) · u/|u| = (15, -5) · (3/5, 4/5)/|(3/5, 4/5)|
= (45/5, -20/5) · (3/5, 4/5)/√(9/25 + 16/25)
= 39/√25
= 39/5

So, the directional derivative of f at P in the direction of u is 39/5.

To learn more about derivatives, visit https://brainly.in/question/1044252

#SPJ11

Answer:

true

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

To represent the situation, you would have to do 14÷3 because there are 3 cats that eat 14 pounds of food in a week and to figure out how much a cat eats in a week, you would have to divide.

\(\text{For angle N,}\\\\PQ= \text{Perpendicular.}\\\\QN = \text{Hypotenuse.}\\\\\text{Now,}\\\\\sin N = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\\~~~~~~~=\dfrac{QP}{QN}\)

The diagonal of the parallelogram be 10 cm or 8 cm.

A parallelogram is just a quadrilateral with two parallel sides (and therefore opposite angles equal).

For the given case.

The sides of the 3  cm and 5 cm. As, these two side are the adjacent sides of the parallelogram, the diagonal formed will be the closing side of the triangle.

As, the diagonal is the longest side of the triangle, thus its value must be greater than other side.

This is possible with the diagonal values of 10 cm and 8 cm.

Thus, 10 cm and 8 cm are the correct values for the diagonal of parallelogram.

To know more about the parallelogram, here

https://brainly.com/question/970600

#SPJ9

Answer:

80% of 75 = 60

Step-by-step explanation:

first make 80% a decimal so 0.8 because 80/100 = 0.8

the multiply 0.8 by 75

this will give you 60

Therefore Helen's necklace has 60 blue beads

Therefore, Two slices of bacon had 96 less calories than three slices of roasted turkey.

a formula that illustrates the connection between two expressions on either side of a sign. It usually only has one variable and an equal sign. like this: 2x – 4 = 2.

Here,

One piece of bacon has 42 calories in it.

There are 60 calories in 1 slice of turkey.

2 slices of bacon are 2 calories each (42)

So 84 calories in 2 slice of bacon

3 slices of roasted turkey have 3 calories each slice (60)

Three slices of roasted turkey have 180 calories each.

180-84 is the difference in the amount of calories.

96 calories are added due to the calorie difference.

Two slices of bacon had 96 less calories than three slices of roasted turkey.

To know more about equation , visit

https://brainly.com/question/10413253

#SPJ4

There are 12 identical marbles in a bag, and Suzy is going to select 9 marbles from the bag at random.

The problem asks how many possible outcomes there are.

To begin with, we need to understand the concept of combinations. A combination is a way to select a subset of objects from a larger set, without regard to the order of the objects. For example, if we have four marbles (A, B, C, and D), there are six possible combinations of two marbles: AB, AC, AD, BC, BD, and CD.

In this problem, we have 12 marbles and we are choosing 9 of them. To find the total number of combinations, we can use the formula for combinations:

nCr = n! / r!(n-r)!

where n is the total number of objects, r is the number of objects we are choosing, and ! represents factorial (i.e. multiplying a number by all the positive integers less than it).

So, plugging in our numbers:

12C9 = 12! / 9!(12-9)! = 12! / 9!3! = (121110) / (321) = 220

Therefore, there are 220 possible outcomes if Suzy selects 9 marbles at random from a bag containing 12 identical marbles.

To learn more about combinations click brainly.com/question/13715183

#SPJ11

Answer:

See below

Step-by-step explanation:

32.  w + 5 = -20

       w = -20 - 5

       w = - 25

33.  x - 17 = -32

       x = -32 + 17

       x =  - 15

34.  t + 7.2 = 1.65

       t = 1.65 - 7.2

       t = - 5.55

35.  -0.4 = g - 4.9

       g = - 0.4 + 4.9

       g = 4.5

36.  y - 2/5 = 1 3/5

       y = 1  3/5  +   2/5

       y =  1   5/5  or   2

37.  -5 1/6 = 2 1/3 + p

       p =  - 5 1/6  -  2  1/3  convert 1/3 to x/6 for a common denominator

1/3 converts to 2/6

        p =  -5  1/6  -  2  2/6

        p =  - 7   3/6    or   - 7  1/2

38.  You were given that

Simone =  $65.35 + Dan

Simone =  Carly - 37.50

Carly = 127.75

So Simone = 127.75 - 37.50  =  90.25

Simone = 65.35 + Dan   or Dan = Simone - 65.35

Dan = 90.25 - 65.35 = 24.90

The velocity of a particle = i + 2t j

The acceleration of a particle = 2 j

The speed of a particle = \(\sqrt{1 + 4t^{2} }\)

Here,

The position function is, \(r (t ) = ti + t^{2} j +2k\)

We have to find, the velocity, acceleration, and speed of a particle with the given position function.

What is Velocity of a particle with the given position function?

The instantaneous velocity v(t) of a particle is the derivative of the position with respect to time. That is, v(t)=dx/dt.

Now,

The position function is, \(r (t ) = ti + t^{2} j +2k\)

The velocity of a particle = \(\frac{d r(t)}{dt}\)

\(r (t ) = ti + t^{2} j +2k\)

\(\frac{d r(t)}{dt} = i + 2t j\)

The acceleration of a particle = \(\frac{d^{2} r(t)}{dt^{2} }\)

\(r (t ) = ti + t^{2} j +2k\)

\(\frac{d r(t)}{dt} = i + 2t j\)

\(\frac{d^{2} r(t)}{dt^{2} }= 2j\)

The speed of a particle = \(| \frac{d r(t)}{dt}| = |v(t)|\)

\(\frac{d r(t)}{dt} = i + 2t j\)

\(|v(t)|=\sqrt{1 + 4t^{2} }\)

Hence, The velocity of a particle = \(i + 2t j\)

The acceleration of a particle = \(2 j\)

The speed of a particle = \(\sqrt{1 + 4t^{2} }\)

Learn more about the velocity visit:

https://brainly.com/question/18566194

#SPJ4

Answer:

C

Step-by-step explanation:

A six back has a value of 35 cents per bun,

you may find this by dividing 2.10 by 6  and getting .35 per

while a 8 pack 3.12 divided by 8 is .39

so it is more economical or correct to get C. 8 six packs for 35 cents a bun

Answer:

Step-by-step explanation:

dad hates me sorry bye

Checking for approximate normality in the population is essential for constructing a valid confidence interval, particularly when dealing with small sample sizes. This ensures the accuracy and reliability of the interval in estimating the true population parameter.

It's important to check whether the population is approximately normal before constructing a confidence interval because the accuracy and validity of the interval depend on the underlying distribution of the population. Here's a step-by-step explanation:

1. A confidence interval is a range of values within which the true population parameter (e.g., mean or proportion) is likely to fall, with a certain level of confidence (e.g., 95% or 99%).

2. The process of constructing a confidence interval relies on the Central Limit Theorem, which states that, for large sample sizes, the sampling distribution of the sample mean will be approximately normal, regardless of the population distribution.

3. However, for small sample sizes, the distribution of the population needs to be approximately normal in order to obtain an accurate confidence interval. This is because the normality assumption is crucial for the proper interpretation of the interval.

4. If the population is not approximately normal, the confidence interval may not provide a reliable estimate of the true population parameter, leading to incorrect conclusions and potentially invalid results.

Learn more about Central limit theorem here: brainly.com/question/18403552

#SPJ11

Answer:

The car was traveling for 1.5 hours.

Step-by-step explanation:

Given that distance d, in kilometers, that a car travels at a speed of 80 km per hour , for t hours, is given by the equation d=80t.

Here wee need to find the time if the car has gone 120 kilometers.

That is

            d = 120 km

we need to find t.

            d=80t

           120 = 80 x t

The car was traveling for 1.5 hours.

Some triangle pairs are congruent triangles but some others are not, because:

A pair of triangles is congruent if they have one of these criterias:

Let's explore each triangle pairs we have:

Pair 1

We know that both triangle have a vertical angle on its connection, hence both angles are congruent. They also have another pair of corresponding angles and 1 pair of corresponding sides between the angles .

Pair 1 meet ASA rules --> Congruent triangles

Pair 2

Pair 2 has 1 corresponding angle and 2 pairs of corresponding sides

Pair 2 meets SAS rules --> congruent triangles

Pair 3

We know that both triangle have a vertical angle on its connection, hence both angles are congruent. They also have another pair of corresponding angles and 1 pair of corresponding sides between the angles.

Pair 3 meet ASA rules --> Congruent triangles

Pair 4

Pair 4 has 3 corresponding sides and meets SSS rules --> congruent triangles

Pair 5

Pair 5 only has 2 corresponding sides --> not congruent triangles

Pair 6

We know that both triangle have a vertical angle on its connection, hence both angles are congruent. They also have another pair of corresponding angles and 1 pair of corresponding sides not between the angles.

Pair 6 meet AAS rules --> Congruent triangles

Pair 7

We know that both triangle have a vertical angle on its connection, hence both angles are congruent. Pair 7 also has another 2 corresponding angles. In total, pair 7 has 3 corresponding angles.

Pair 7 is not congruent triangles because three corresponding angles might have different size of sides. A pair of triangles can be congruent only if there is at least one pair of corresponding side between them.

Pair 8

We know that both triangle have a vertical angle on its connection, hence both angles are congruent. Pair 8 also has another 2 corresponding angles. In total, pair 8 has 3 corresponding angles.

Pair 8 is not congruent triangles because three corresponding angles might have different size of sides. A pair of triangles can be congruent only if there is at least one pair of corresponding side between them.

Learn more about Congruent Triangles here: brainly.com/question/22062407

#SPJ1

2. Using proportion, the value of x = 38, the length of FC = 36 in.

3. Applying the angle bisection theorem, the value of x = 13. The length of CD = 39 cm.

The Angle Bisector Theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides of the triangle.

2. The proportion we would set up to find x is:

(x - 2) / 4 = 27 / 3

Solve for x:

3 * (x - 2) = 4 * 27

3x - 6 = 108

3x = 108 + 6

Simplifying:

3x = 114

x = 114 / 3

x = 38

Length of FC = x - 2 = 38 - 2

FC = 36 in.

3. The proportion we would set up to find x based on the angle bisector theorem is:

13 / 3x = 7 / (2x - 5)

Cross multiply:

13 * (2x - 5) = 7 * 3x

26x - 65 = 21x

26x - 21x - 65 = 0

5x - 65 = 0

5x = 65

x = 65 / 5

x = 13

Length of CD = 3x = 3(13)

CD = 39 cm

Learn more about Angle Bisector Theorem on:

https://brainly.com/question/30459648

#SPJ1

(a) The probability that both dice have the same number is 1/6.

(b) The probability that the sum of the dice is 10 is 3/36 = 1/12.

(c) The probability that the sum of the dice is 10 is 7/64.

(a) There are 6 possible outcomes for each die, there are 6 x 6 = 36 possible outcomes when rolling two dice.

There are 6 outcomes where both dice have the same number (1-1, 2-2, 3-3, 4-4, 5-5, 6-6).

So, P(both dice have the same number) = 6/36 = 1/6.

(b) To find the probability that the sum of the dice is 10, we can list all the possible outcomes that add up to 10: (4-6, 5-5, 6-4).

So, P(sum of the dice) = 3/36 = 1/12.

(c) When rolling two eight-sided dice, there are 8 x 8 = 64 possible outcomes.

To find the probability that the sum of the dice is 10, we can list all the possible outcomes that add up to 10: (2-8, 3-7, 4-6, 5-5, 6-4, 7-3, 8-2).

P(sum of the dice is 10) = 7/64.

Learn more about probability here:

brainly.com/question/11234923

#SPJ4

Answer:

Step-by-step explanation:

its the second one

The total number of sides of a regular polygon with each exterior angle of measure 30 degrees is equal to 12.

Let us consider 'n' be the number of sides of the regular polygon.

Let 'y' be the measure of each of the exterior angle of regular polygon.

y = 30 degrees

Measure of each of the exterior angle of regular polygon 'y'

= ( 360° ) / n

⇒ n = ( 360° / y )

Substitute the value we get,

⇒ n = ( 360° / 30° )

⇒ n = 12

Therefore, the number of sides of a regular polygon with each of the exterior angle 30 degrees is equal to 12.

Learn more about regular polygon here

brainly.com/question/12092158

#SPJ4

The above question is incomplete, the complete question is:

How many sides does a regular polygon have when each exterior angle measures 30 degrees?

The capacity of fish tank in quarts is 246.

Therefore the answer is 246.

A pint is a unit of volume in the US customary system of measurement and is equal to 16 fluid ounces. A quart is also a unit of volume in the US customary system of measurement and is equal to 32 fluid ounces or 2 pints.

There are 2 pints in 1 quart, so to convert from pints to quarts, we need to divide by 2.

The capacity of the fish tank in pints is 492.

Therefore, the capacity of the fish tank in quarts is

= 492 pints / 2 pints per quart

= 246 quarts

So, the capacity of the tank in quarts is 246 quarts.

To know more on pints quarts conversion

https://brainly.com/question/17732315

#SPJ4