A graph is translated according to the following rule. Describe the translation.



(x, y) → (x, y – 3)



The graph is translated three units to the right.

The graph is translated three units to the left.

The graph is translated three units down.

The graph is translated three units up.

Answer:

6 cm

Step-by-step explanation:

Let k represent the scale factor between ΔABC and ΔDCA. Then ...

... CA = k·BC

... AD = k·CA

So, AD/BC = k·(k·BC)/BC = k² = 9/4

Then k = √(9/4) = 3/2, and ...

... CA = (3/2)·BC = (3/2)·(4 cm)

... CA = 6 cm

Final answer:

To find the length of diagonal AC in trapezoid ABCD, we utilize the properties of similar triangles created by the diagonal. Since triangles △ABC and △DCA are similar, we set up a proportion using the sides BC and AD, and solve for AC to find that AC is 6 cm.

Explanation:

The question asks us to find the diagonal AC of trapezoid ABCD where it's given that BC = 4 cm and AD = 9 cm, and triangles △ABC and △DCA are similar. To find AC, we can use the properties of similar triangles which dictate that corresponding sides are proportional. Let us consider that the trapezoid is split into two triangles by AC. The ratio of the smaller triangle's base to the larger triangle's base (BC:AD) must be the same as the ratio of any other pair of corresponding sides in these two similar triangles. Furthermore, the ratio of the longer leg of △ABC (which is AC) to its base BC is equal to the ratio of the longer leg of △DCA (which is also AC) to its base AD. Using these ratios, we can set up a proportion to solve for AC:

AC/BC = AC/AD

Since the length of AC is the same in both ratios, we can multiply both sides by BC*AD to get:

[tex]AC^2 = BC * AD[/tex]

By substituting the given values for BC and AD into the equation we get:

[tex]AC^2 = 4 cm * 9 cm[/tex]

[tex]AC^2 = 36 cm^2[/tex]

To find AC, we take the square root of both sides:

AC = √36 cm

AC = 6 cm

Hence, the length of diagonal AC is 6 cm.

Answer:

-6r+48

Step-by-step explanation:

(-6)(r)+(-6)(-8)

=-6r+48

Answer:

-6r +48

Step-by-step explanation:

The distributive property has us distribute the number on the outside to the numbers on the inside

-6(r-8)

-6 *r -6 * (-8)

-6r +48

Answer:

10.  1 right 2 acute 0 obtuse angles

11.   x=6

Step-by-step explanation:

10.  A triangle has 3 angles.

If it is a right triangle is has 1 right angle which is 90 degrees.

90 + x+y = 180  where x and y are the other 2 angles

Subtract 90 from both sides

x+y = 90

So the 2 angles that are left can only add to 90.

An obtuse angle is greater than 90 degrees, so we cannot have an obtuse angle.  Acute angles are less than 90 degrees.

A right angle is 90 degrees.  If one of the angles left is 90 degrees, the other one is zero, and that does not make a triangle.

So we must have 1 right angle and 2 acute angles  (no obtuse angles)

11.  Since the 2 sides are the same the triangle is isosceles.  That means the two angles have the same measurements.

90 + y+y = 180

y+y=90

2y = 90

y = 45

Each angle must equal 45 degrees

7x+3 = 45 degrees

Subtract 3 from each side

7x+3-3 =45-3

7x =42

Divide each side by 7

7x/7 =42/7

x =6

Answer: (B) -2, (E) 1, (F) 2

Step-by-step explanation:

   x³ - x² - 4x + 4

= x²(x - 1) - 4(x - 1)

= (x² - 4) (x - 1)

= (x - 2)(x + 2)(x - 1)

Set each factor equal to zero to find the roots:

  x - 2 = 0      x + 2 = 0       x - 1 = 0

       x = 2             x = -2           x = 1

Answer:

-2,1,2

Step-by-step explanation:

[tex]5x^2-(3xy-7x^2)+(5xy-12x^2)=5x^2-3xy+7x^2+5xy-12x^2=2xy\\\\ 2\cdot(-0.25)\cdot4=-2[/tex]

Answer:

-2

Step-by-step explanation:

5x^2-(3xy-7x^2)+(5xy-12x^2)

5x^2-3xy+7x^2+5xy-12x^2

[(5x^2+7x^2-12x^2)=0]

-3xy+5xy= -3(-.25)(4)+5(-.25)(4)

-3(-.25)(4)+5(-.25)(4)= 3-5= -2

-2

The maximum area of a rectangle inscribed in a semicircle of radius 8 cm is found by maximizing the product of its width and height, which occurs when the rectangle's height is half the radius. Using the Pythagorean theorem, the optimal dimensions are calculated, leading to a maximum area of approximately 27.71 cm².

To find the maximum area of a rectangle inscribed in a semicircle of radius 8 cm, we can employ a geometrical approach. Let the width of the rectangle be w and the height h. Because the rectangle is inscribed in a semicircle, the diagonal of the rectangle will be the radius of the semicircle, and the width of the rectangle will span from the midpoint of the diameter to a point on the circumference of the semicircle. Given the Pythagorean theorem, we have w² + h² = (2r)², where r is the radius. For our case, r = 8 cm.

Maximum area occurs when the rectangle's area is maximized. The area of the rectangle is A = w × h. By using the relation obtained from the Pythagorean Theorem, and knowing that for a rectangle inscribed in a semicircle the height will be half the radius when the area is maximized, we find h = r/2 = 4 cm. Substituting back into the Pythagorean Theorem, we find w = √(8² - 4²) = √64 - 16 = √48 = 4√3 cm. Therefore, the maximum area of the rectangle is A = w × h = 4√3 × 4 = 16√3 cm². This is approximately 27.71 cm².

This question combines geometry and basic principles of optimization to find the maximum area of a geometric shape within defined constraints, showcasing the application of mathematical reasoning in problem-solving.

a= [tex]\pi[/tex] [tex]r^{2}[/tex]

The area of a pizza with a diameter of 10 inches is 78.5.

Answer:

Either 177 or 188 buttons

Step-by-step explanation:

2134/12=177.83

Lisa can place 177 buttons into each jar when she distributes 2,134 buttons equally among 12 jars.

To determine the number of buttons Lisa can distribute into each jar, we perform a simple division: dividing her total button count, 2,134, by the number of jars, which is 12. This calculation results in approximately 177.83 buttons per jar. However, since you can't have a fraction of a button, we must round down to the nearest whole number, which is 177. Consequently, each jar will be filled with exactly 177 buttons. This fair distribution ensures that all 12 jars are equally supplied, making it practical and straightforward for Lisa to organize her collection.

https://brainly.com/question/2273245

#SPJ3

Answer:

i took a long time figuring it out lol but here it is let me know if you got them all correct

Step-by-step explanation:

A) 3.6 × 10^(-1)   B) 3.1 × 10^(6)  C) 5.3 × 10^(-6)  D) 4.2 × 10^(-1)

Answer:

Yes, the triangles are similar.

x=7.2

Step-by-step explanation:

Similar triangles are triangles which have the same shape not not the same size. This can be seen when triangles have the same exact angle measures. The triangles in number 4 have the exact same angle measures and are therefore similar. Because they are similar, their sides have a special relationship. They are proportional on each triangle. We can set a proportion to find an unknown length.

A proportion is a ratio between two related quantities. We will write a proportion from one triangle side to the corresponding side on the other.

[tex]\frac{3}{5} =\frac{x}{12} \\[/tex]

We can cross multiply and isolate x to solve.

[tex]\frac{3}{5} =\frac{x}{12}\\3(12)=5(x)\\36=5x\\\frac{36}{5} =\frac{5x}{5} \\7.2=x[/tex]

Answer:

[tex]s = \sum^5_1 {(2h)(\frac{2}{3})^i},[/tex]

Step-by-step explanation:

The initial height of the ball is h

After the first bounce the height is [tex]\frac{2}{3}h[/tex]

After the second bounce the height is [tex]\frac{2}{3}(\frac{2}{3})h[/tex]

After the i-th rebound the height is [tex](\frac{2}{3}) ^ i[/tex]

Then, distance s traveled by the ball is the sum of the heights reached between the first and fifth bounces.

[tex]s = 2 [\frac{2}{3}h + \frac{2}{3}(\frac{2}{3})h +, ..., + (\frac{2}{3}) ^ n h][/tex]

The equation is multiplied by 2 because the distance the ball travels when it goes up is the same as it travels down.

Finally the distance is a geometric series as shown:

[tex]s = \sum^5_1 {(2h)(\frac{2}{3})^i},[/tex]

The total distance traveled by the ball between the first and sixth bounce is [tex]\( \frac{23}{3}h \)[/tex] feet.

Step 1: Find the distance traveled during the first fall:

- The ball is dropped from a height of [tex]\( h \)[/tex] feet.

- So, the distance traveled during the first fall is [tex]\( h \)[/tex] feet.

Step 2: Find the distance traveled during each subsequent bounce:

- After each bounce, the ball reaches a height that is [tex]\( \frac{2}{3} \)[/tex] of the height from which it previously fell.

- During each bounce, the ball travels twice the distance of the height it reached.

- Therefore, during each bounce, the total distance traveled is [tex]\( \frac{4}{3}h \)[/tex] feet.

Step 3: Find the total distance traveled between the first and sixth bounce:

- Since we're asked for the distance between the first and sixth bounce, we have 5 subsequent bounces.

- The total distance traveled between the first and sixth bounce is the sum of the distance traveled during the first fall and the total distance traveled during the subsequent five bounces.

- So, it's [tex]\( h + 5 \times \left(\frac{4}{3}h\right) \)[/tex]feet.

Step 4: Calculate the total distance:

- Substitute the values and calculate: [tex]\( h + \frac{20}{3}h = \frac{23}{3}h \)[/tex]feet.

Therefore, the total number of feet the ball travels between the first and sixth bounce is [tex]\( \frac{23}{3}h \).[/tex]

Answer:

[tex]a_{17}[/tex] = - 3

Step-by-step explanation:

to find the 17 th term substitute n = 17 into the explicit formula

A(17) = 77 + (16 × - 5 ) = 77 - 80 = - 3

the answer is -3

have a blessed day!

1. base angles

2. centroid

3. altitude of a triangle

4. orthocenter

5. vertex angle

6. median of a triangle

7. base of an isosceles triangle

Answer:

1.Base angles.

2.Centroid.

3.Altitude of a triangle.

4. Orthocenter.

5.Vertex angle.

6.Median of triangle.

7. Base of an isosceles triangle.

Step-by-step explanation:

1. Base angles: The two angles that include the base of an isosceles triangle.

2. Centroid: A point on the interior of a triangle in which the three medians of the triangle intersect.

3.Altitude of a triangle:A segment from a vertex perpendicular to the opposite side.

4.Orthocenter: A point in which the three altitudes of the triangle intersect .It is possible for the orthocentre to occur on the triangle ,on the interior of the triangle or on the exterior of the triangle.

5.Vertex of angle:The angle formed by the two equal sides of an isosceles triangle.

6.Median of triangle:A segment from a vertex to the midpoint of the opposite side .

7.Base of an isosceles triangle: The third , unequal side of an isosceles triangle.

Answer:

False

Step-by-step explanation:

If the value is a root of the polynomial, then the remainder will be 0. This means that the root as a factor will multiply to make the polynomial.

Answer:

Independent:  time (minutes)

Dependent: Distantce (inches)

Step-by-step explanation:

Answer:

3216/8 is = to 402

Step-by-step explanation:

So I am not sure what you are asking sorry

Answer:

It is D 100%

Step-by-step explanation:

Answer:

100 degrees

Step-by-step explanation:

Remark

The endpoints of the smaller diagonal of a kite, intersect the vertexes of 2 equal angles. Put in simpler language, if x is at the top of the kite and x is the vertex of the larger angle between the top and bottom angles, then the other two angles (left and right) are equal.

In still simpler language. <W = <Y

Equation

<X + <W + <Z + <Y = 360               All quadrilaterals have 360 degrees for their interior angles.

Givens

Solution

Answer

Answer:

100

Step-by-step explanation:

Angle ZWX and angle ZYX are congruent.

360 = 120 + 4x + 10x + 10x

360 = 120 + 24x

240 = 24x

10 = x

The measure of angle ZYX is equal to 10(10) = 100°

Answer:

41%

Step-by-step explanation:

To calculate the percent error:

Gregory predicted 310 and 220 actually came.

1. 310-220=90

2. 90/220=0.41

3. 0.41(100)=41%

Answer:

the percent error is 41%

Step-by-step explanation:

Answer:

Water - 62.5 pounds per cubic foot

18.25 cubic feet would weigh 18.25 * 62.5 =

1,140.625 pounds.

Step-by-step explanation:

Answer:

13.863 years

Step-by-step explanation:

Initial deposit is $2,000.

The rate of interest is 5% compounded continuously.

The account balance of the savings account after t years by an exponential function:  

A(t) = $2,000 ∙ e^0.05t.

It says to find out the time when it takes for the initial deposit to double, i.e. A(t) = $4,000

Mathematically, we can set them equal and solve for t as follows:-

A(t) = $2,000 ∙ e^0.05t = $4,000.

e^(0.05t) = 4000/2000 = 2

0.05t Ln(e) = Ln(2)

t/20 = Ln(2)

t = 20 * Ln(2) = 13.86294361

So, it takes 13.863 years for the initial deposit to double.

Answer:

hope it hepls

Step-by-step explanation:

for an experiment you need to dissolve 0.05 moles of NaCl in one liter of water. how much NaCl must you weigh out?

2.9 i just took the test

To find the amount of NaCl required, multiply the number of moles by the molar mass of NaCl. Hence, you need approximately 2.922 g of NaCl to get 0.05 moles.

To find out how much NaCl you would need to weigh out, we need to convert moles to grams using the molar mass of NaCl. Knowing that the molar mass of NaCl is 58.44 g/mol, we could get the mass by multiplying the number of moles by the molar mass.

So, it would be 0.05 moles * 58.44 g/mol = 2.922 g of NaCl. You would need to weigh out approximately 2.922 grams of NaCl (assuming precision up to three decimal places) to get the required 0.05 moles needed for the experiment.

This is a typical example of applying concepts of molality and molarity in chemical solutions, where you need to accurately determine the amount of solute to use to achieve a precise molar concentration.

https://brainly.com/question/12127540

#SPJ3

The original selling price if, A dress is selling for $100 after a 20 percent discount is $125.

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

Given:

A dress is selling for $100 after a 20 percent discount,

Calculate the original price as shown below,

Original price - 20% original price = 100

Original price(1 - 0.2)  = 100

Original price  = 100 / 0.8

Original price  = $125

Thus, the original price is $125.

To know more about percentages:

brainly.com/question/20818421

#SPJ5

Answer:

x = -11

Step-by-step explanation:

h(x) = 17 + x/6

times 6

6 = x + 17

subtract 17

-11 = x

Answer:

H x − x 6 = 17

Step-by-step explanation:

Answer: s = 324/4 = 81 yards

Answer:

s=81 yards

Step-by-step explanation: