By which rule are these triangles congruent?

The solution to given linear inequality, 6(x1.5) + 30 < 48, is x < 2

From the question, we are to solve the given linear inequality

The given linear inequality is

6(x1.5) + 30 < 48

First, we will write this inequality properly.

The inequality can be properly written as

6(1.5x) + 30 < 48

Now, we will solve the linear inequality

6(1.5x) + 30 < 48

Subtract 30 from both sides of the equation

6(1.5x) + 30 - 30 < 48 - 30

6(1.5x) < 18

Divide both sides of the inequality by 6

6(1.5x)/6 < 18/6

(1.5x) < 3
1.5x < 3

Divide both sides of the inequality by 1.5

1.5x/1.5 < 3/1.5

x < 2

Hence, the solution is x < 2

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Answer:

b.

-2/3

Step-by-step explanation:

2/3 + (-2/3)

2+-2/3

0

hope this helps :)

The sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be 12 cupcakes, 24 cupcakes, and 50 cupcakes will cοst rοughly $2.42, $2.33, and $2.58 per cupcake, respectively.

Tο cοmplete the assignment, use the tried-and-true straightfοrward methοdοlοgy, the real variables, and any pertinent details frοm the preliminary and specialized questiοns. In respοnse, custοmers might be given anοther οppοrtunity tο range sample the prοducts. In the absence οf such changes, majοr advances in οur knοwledge οf prοgrammes will be lοst.

Here,

We must divide the tοtal cοst by the quantity οf cupcakes in οrder tο determine the unit cοst οf each οptiοn:

Twelve cupcakes:

Unit cοst is calculated as Tοtal Cοst / Cupcakes.

=>  Unit cοst: $29 fοr 12 cupcakes.

=>  $2.42 is the unit cοst per cupcake.

Tο make 24 cupcakes:

Unit cοst is calculated as Tοtal Cοst / Cupcakes.

=> 24 cupcakes equals $56 fοr the unit.

=>  $2.33 is the unit cοst per cupcake.

50 cupcakes =

Unit cοst is calculated as Tοtal Cοst / Cupcakes.

=>  $129 fοr a unit οf 50 cupcakes.

=>  Unit cοst: $2.58 fοr each cupcake

As a result, 12 cupcakes, 24 cupcakes, and 50 cupcakes will cοst rοughly $2.42, $2.33, and $2.58 per cupcake, respectively.

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The value of x in the similar triangle is 6 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Therefore, let's use the similarity ratio to find the value of x in the similar triangle as follows:

Hence,

5 / 40 = x / 48

48 × 5 = 40x

240 = 40x

divide both sides by 40

x = 240 / 40

x = 6

Therefore,

x = 6

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Answer:

  3/2

Step-by-step explanation:

The composition of transformations has you dilate the line by a factor of 1/2, then by a factor of 3. Then the line is rotated about the origin.

The scale factor of the result will be the product of the dilation factors:

  (3)(1/2) = 3/2

The scale factor of the transformation is 3/2.

Answer:

3/2

Step-by-step explanation:

The composition of transformations has you dilate the line by a factor of 1/2, then by a factor of 3. Then the line is rotated about the origin.

The scale factor of the result will be the product of the dilation factors:

 (3)(1/2) = 3/2

The scale factor of the transformation is 3/2.

There are total 15 students per teacher and 8 students per tutor. For 100 students, total 13 tutors are required.

The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.

As per the given data provided in the question,

4 teachers  = 60 students

For 1 teacher = 60/4 = 15 students

Similarly,

6 tutors = 48 students

For 1 tutor = 48/6 = 8 students.

For total 100 students, total number of tutors = 100/8

= 12.5 or 13 tutors are required.

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Then it will take approximately 6.3 hours for the culture to grow to 80,000 bacteria

The given formula for the number of bacteria in a culture after t hours is:y = 5000(3)^tWe are required to find the number of hours it will take the culture to grow to 80,000.

This can be done by setting y equal to 80,000 and then solving for t.5000(3)^t = 80,000

Divide both sides by 5000:3^t = 16Now, we need to solve for t by taking the logarithm of both sides.

However, it is easier to use logarithmic properties to simplify the equation first.3^t = 2^4

Raise both sides to the power of (1/log3):log3(3^t) = log3(2^4)t = 4/log3(2)Using a calculator, log3(2) ≈ 0.631, so:t ≈ 4/0.631 ≈ 6.3.

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Refer to the images attached. Now I am guessing when it says "use geometry" was to graph it? I wasn't completely sure. I attached how I would normally evaluate that problem and a graph of the piecewise function. It has been a while since I have dealt with integrating piecewise function, please let me know what process you were supposed to use if you figure it out. Hope this helps you a bit, have a good one!

Check the picture below.

Answer:

Uhm, I see there's a pattern, but there are only 2 green boxes, whole there are 4 orange boxes in every figure.

Answer:

\(D = \frac{2}{3} (F+ G) \\ F + G = D \div \frac{2}{3} \\ \\ F+ G = D \times \frac{3}{2} \\ \\ F +G = \frac{3D}{2} \\ \\ G = \frac{3D}{2} - F\)

I hope I helped you^_^

The equation of the linear relationship in slope-intercept form is y = 2x - 8. Option A is the correct answer.

To determine the equation of the linear relationship in slope-intercept form based on the table, we need to find the slope and y-intercept.

By observing the table, we can calculate the slope by selecting any two points. Let's choose the points (0, -8) and (4, 0).

Slope (m) = (change in y) / (change in x)

= (0 - (-8)) / (4 - 0)

= 8 / 4

= 2

Now that we have the slope, we can find the y-intercept by substituting the values of one point and the slope into the equation y = mx + b and solving for b.

Using the point (0, -8):

-8 = 2(0) + b

b = -8

Therefore, the equation of the linear relationship in slope-intercept form is: y = 2x - 8. Option A is the correct answer.

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Answer:

its C

1.convert the mixed number to an improper fraction

(\(\frac{-20}{6\\}\) x \(\frac{2}{3}\) )

2. reduce the numbers with the greatest common factor (2)

\(\frac{-20}{3}\) x \(\frac{1}{3}\)

3. then multiply and get

\(\frac{-20}{9}\)

4. then reduce to get

-2\(\frac{2}{9}\)

Step-by-step explanation:

The correct option is,

The table represents a linear function because there is not a constant rate of change in the input and output values.

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The table is shown in figure.

Now,

For Table;

The equation of line is,

⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)

⇒ y - (-4) = (-2 - (-4)) / (- 1 - (-2))  (x - (-2))

⇒ y + 4 = 2/1 (x + 2)

⇒ y + 4 = 2 (x + 2)

⇒ y + 4 = 2x + 4

⇒ y = 2x

Thus, The table represents a linear function because there is not a constant rate of change in the input and output values.

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A positive value for n that makes the statement true is n = 1.5.

We need to find a positive value for n that satisfies the given inequality: 1 < 1 x n < 2.
Step 1: Choose a value of n such that it's greater than 1 when multiplied by 1.
Step 2: Ensure the chosen value also makes the product less than 2 when multiplied by 1.
Let's try n = 1.5:
1 x 1.5 = 1.5
Now, let's check if it satisfies the inequality:
1 < 1.5 < 2
Yes, it does. So, a positive value for n that makes the statement true is n = 1.5.

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Answer:

the answer is 77

Step-by-step explanation:

A measures 32 and B measures 109 so you subtract 109 and 32 and your answer will be 77

Answer: Find the Equation of a Line Given That You Know a Point on the Line And Its Slope. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.

Step-by-step explanation:

Answer:To find the lateral area and surface area of a cone with a diameter of 3.4 centimeters and a slant height of 6.5 centimeters, we first need to find the radius of the cone. The radius is half of the diameter, so it is 1.7 centimeters.

The lateral area of a cone is given by the formula LA = πrs, where r is the radius and s is the slant height. Plugging in the values we have, we get LA = π(1.7)(6.5) = 35.042 square centimeters.

The surface area of a cone is given by the formula SA = πr^2 + πrs, where r is the radius and s is the slant height. Plugging in the values we have, we get SA = π(1.7)^2 + π(1.7)(6.5) = 47.097 square centimeters.

Therefore, the lateral area of the cone is approximately 35.042 square centimeters and the surface area of the cone is approximately 47.097 square centimeters.

I hope this helps!

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

6x -8y = - 16y

6x = -8y

8y = 17x + 4

-8y = -17x - 4

6x = -17x - 4

23x = -4

x = -4/23

Answer:

0.625

Step-by-step explanation:

5/8=0.625

Answer:

0.625

Step-by-step explanation:

because 1/8 is 0.125 just multiply by 5 it'll be

0.625

\(\\ \sf\longmapsto XY+YZ=XZ\)

\(\\ \sf\longmapsto 7a+5a=6a+24\)

\(\\ \sf\longmapsto 12a=6a+24\)

\(\\ \sf\longmapsto 12a-6a=24\)

\(\\ \sf\longmapsto 6a=24\)

\(\\ \sf\longmapsto a=\dfrac{24}{6}\)

\(\\ \sf\longmapsto a=5\)

Value of a is 4 and value of YZ is 20 units

Step-by-step explanation:

Given:

Y is between point X and Z

Value of line XY = 7a

Value of line YZ = 5a

Value of line XZ = 6a + 24

Find:

Value of "a" and line YZ

Computation:

We know that

XY + YZ = XZ

So,

7a + 5a = 6a + 24

12a = 6a + 24

6a = 24

a = 4

Value of a = 4

So,

Value of line YZ = 5a

By putting value of a

Value of line YZ = 5(4)

Value of line YZ = 20 units

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Step-by-step explanation:

(3h - 5)(5h + 4) =   3h * 5h    +   3h * 4     - 5*5h    - 5 *4

                              =    15h^2        - 13h    -20

\((3h-5)(5h+4)\)

\(=(3h+-5)(5h+4)\)

\(=(3h)(5h)+(3h)(4)+(-5)(5h)+(-5)(4)\)

\(=15h^2+12h-25h-20\)

Answer:

Work done lifting the bucket and rope to the top of the building is 4005.75 Joules

To express this concept mathematically, the work W is equal to the force f times the distance d, or W = fd. If the force is being exerted at an angle θ to the displacement, the work done is W = fd cos θ.

Initially bucket hold = 25kg. Sand

Sand leaks 0.1 kgs each meter it is lifted

At height x meter bucket hold = (25 - 0.1x) kg of sand

Length of rope = 15 meter

density of rope = 0.4kg / meter

weight of rope = 15 (0.4) = 6kg.

At height x meter, weight of rope = (6 - 0.4x)

Total weight at height x meter = (25-0.1x) + (6-0.4x)

                                                   = (31 - 0.5x) kg

force = (31-0.5x) g Newtons. = [(31-0.5x) 9.8] Newton

Work = force × displacement

\(Work= \int_{0}^{15}9.8(31-0.5x)dx\)

          \(=9.8[31x-0.5 \frac{x^2}{2} ]_{0}^{15}\)

          \(=9.8[31(15)-0.25(15)^2]-0\)

          \(=4005.75 joules\)

Hence, work done 4005.75 Joules

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Answer:

Step-by-step explanation:

First you need to find the slope. Y1 - y2/m1-m2.

7--5=12 .....3--1=4

So 12/4=3 Your slope is 3.

Next the equation is y=mx+b.

Y= 3x+b. Then fill in y-coordinate and sole.

Use one from ordered pair. So 7 or -5 can be used.

Using 7

Y=3x+7 is your answer/equation.

The required probability of drawing a red marble from the bag and any specific card from the deck is 1/156.

There are 12 marbles in the bag, and 4 of them are red, so the probability of drawing a red marble is 4/12, or 1/3.

There are 52 cards in the deck, and the probability of drawing any specific card is 1/52.

This probability assumes that the events are independent, meaning that the outcome of one event does not affect the outcome of the other event.

In this case, drawing a marble from the bag and drawing a card from the deck are independent events, so their probabilities can be multiplied.

Therefore, the probability of drawing a red marble from the bag and any specific card from the deck is (1/3) x (1/52) = 1/156.

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Answer:

Step-by-step explanation:

The solution is, The area of Rhombus B is 9 times bigger than the area of Rhombus A.  The reason is that 2 dimensions were tripled, so x3 x3 = 9 times bigger.

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

here, we have,

Rhombus A:

Area = 35 square inches

base = 7 inches

height = 5 inches

Rhombus B:

Area = 315 square inches

base = 21 inches (7 x 3)

height = 15 inches (5 x 3)

A = 21 x 15

so, we get,

The area of Rhombus B is 9 times bigger than the area of Rhombus A.  The reason is that 2 dimensions were tripled, so x3 x3 = 9 times bigger.

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complete question:

Rhombus A has base of 7 inches and an area of 35 square inches. Rhombus B has a Base and Height that are three times the base and height of Rhombus A. Find the area of Rhombus b and compare it to the area of rhombus A Explain

Answer:

i hop you will know the answer soon

Step-by-step explanation:

sorry i dont know