A child measured 120 centimeters in a semiannual checkup with the doctor. What would be the child's height at the next office visit if the child grew by 2.51 centimeters?

AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

What is congruent ?

Congruent refers to having the same shape and size. In mathematics, two objects are said to be congruent if they are identical in shape and size, and can be superimposed onto one another. The symbol used to represent congruence is ≅. Congruence applies to various geometric objects, such as triangles, rectangles, circles, and more. When two objects are congruent, they have all corresponding angles equal and all corresponding sides equal in length.

Step 1: Statement: \($\angle DBE = \angle EBC$\)

Reason: Given that overline BE bisects \($\angle DBC$\)

Step 2: Statement: \($\angle DBC + \angle EBC = 180^\circ$\)

Reason: Angle sum property of a straight line.

Step 3: Statement: \($\angle ABC + \angle EBC = 180^\circ$\)

Reason: Angles on a straight line sum to \(180^\circ$, and $\overline{BE} || \overline{AC}$\) implies that \(\angle ABC$ and $\angle EBC$\) are co-interior angles.

Step 4: Statement: \($\angle ABC = \angle DBC$\)

Reason: From step 2 and step 3, \($\angle ABC + \angle EBC = \angle DBC + \angle EBC = 180^\circ$\). Thus, \($\angle ABC = \angle DBC$\).

Step 5: Statement: \($\triangle ABE \cong \triangle CBE$\)

Reason: By the angle-angle-side congruence criterion, since \($\angle DBE = \angle EBC$\) (from step 1) and \($\angle ABC = \angle DBC$\) (from step 4), and \($\overline{BE}$\) is common to both triangles.

Step 6: Statement: \($AB = BC$\)

Reason: By step 5, \($\triangle ABE \cong \triangle CBE$\), so corresponding sides are congruent, including \($\overline{AB} \cong \overline{BC}$\).

Therefore, AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

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Answer:

wait.

Step-by-step explanation:

what do u really mean by zombies

The producer of pottery is considering the addition of a new plant to absorb the backlog of demand that currently exists. The primary location being considered will have fixed costs of $5500 per month. The cost of producing a single unit of pottery is expected to be $20, and it is expected that each unit will be sold for $30.

To meet the demand, 1500 units of pottery must be produced every month. Should the producer add the new plant?In order to decide whether or not to add the new plant, the producer must first calculate the breakeven point (BEP). This is the point where the costs of producing the pottery will be equal to the revenue earned from selling it. Any production beyond this point will result in profits for the producer.

Here is how to calculate the breakeven point: BEP = fixed costs ÷ (price per unit - variable costs per unit)BEP = $5500 ÷ ($30 - $20)BEP = 5500 ÷ 10BEP = 550 units per month Now that we know that the breakeven point is 550 units per month, we can determine whether or not the new plant is worthwhile. Since the demand is for 1500 units of pottery per month, the producer will need to produce more than the breakeven point in order to earn a profit. Therefore, the new plant should be added since it will produce 1500 units per month, resulting in a profit of $15,000 per month.

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Answer:

i believe you would have 8 cookies. i feel like this isnt the correct answer and there is some sorta subliminal message in this question

Step-by-step explanation:

The company's claim can be evaluated using a hypothesis test. The null hypothesis, denoted as H0, assumes that the true proportion of chips that do not fail in the first 1000 hours is 55% or lower.

Ha stands for the alternative hypothesis, which assumes that the real proportion is higher than 55%. This test has a significance level of 0.01.

A sample of 800 chips was taken based on the information provided, and it was discovered that 60% of them do not fail in the first 1000 hours. A one-sample percentage test can be used to verify the assertion.  The test statistic for this test is the z-score, which is calculated as:

\(\[ z = \frac{{p - p_0}}{{\sqrt{\frac{{p_0(1-p_0)}}{n}}}} \]\)

If n is the sample size, p0 is the null hypothesis' assumed proportion, and p is the sample proportion.

If we substitute the values, we get:

\(\[ z = \frac{{0.6 - 0.55}}{{\sqrt{\frac{{0.55(1-0.55)}}{800}}}} \]\)

The z-score for this assertion is calculated, and we find that it is approximately 2.86.

In order to determine whether there is sufficient data to support the company's claim, we compare the computed z-score with the essential value. At a significance level of 0.01 the critical value for a one-tailed test is approximately 2.33.

Because the estimated z-score (2.86) is larger than the determining value (2.33), we reject the null hypothesis. Therefore, the company's assertion that more than 55% of the chips do not fail in the first 1000 hours of use is supported by sufficient data at the 0.01 level.

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=πr^2h

=π(5)^2*11

=25*11π

=275π yd^3

Answer:

C=36

Step-by-step explanation:

Answer:

c = 36

Step-by-step explanation:

so our equation is 21 = 5/6c - 9

first we need to get rid of the 9. in order to do this, we have to do the opposite of the action shown. so in this case, we would add 9 to both sides. we add it to both sides to keep the equation balanced and equal.

adding 9 to 21 gives us 30. so our equation would then be 30 = 5/6c

now we need to get the c by itself. so we divide by 5/6 because in the original equation the 5/6 and the c are being multiplied to each other.

when we devide 5/6c by 5/6, it cancels out. leaving us with c. 30 divided by 5/6 will in turn gives 36. and there is your answer.

Answers: Angle ABE = 117 And DBE = 27

The table of values is

X |f(x)

-6 | 11

-3 | 7

0 | 4

3 | -1

The value of f(6) is -5

The y-intercept is 3

From the question, we have the following parameters that can be used in our computation:

4x + 3y = 9

Make y the subject

So, we have

y = 3 - 4/3x

We have the x values to be

x = -6, -3, 0, and 3

Substitute the known values in the above equation, so, we have the following representation

y = 3 - 4/3 * -6 = 11

y = 3 - 4/3 * -3 = 7

y = 3 - 4/3 * 0 = 4

y = 3 - 4/3 * 3 = -1

We have

y = 3 - 4/3x

This means that

f(6) = 3 - 4/3 * 6

f(6) = -5

For the y-intercept, we set x = 0

So, we have

f(0) = 3 - 4/3 * 0

f(0) = 3

So, the y-intercept is 3

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Answer:

\(\displaystyle 10c - 6a = 110\)

Step-by-step explanation:

We are given the equation:

\(\displaystyle 3x^3 - 25x^2 -50x = 0\)

Where a, b, and c are solutions to the equation and where a < b < c, we want to determine the value of 10c - 6a.

To find the solutions of the equation, we can factor:

\(\displaystyle \begin{aligned} 3x^3 - 25x^2 -50x & = 0 \\ \\ x(3x^2 - 25x -50) & = 0 \\ \\ x(3x+5)(x-10) & = 0 \end{aligned}\)

From the Zero Product Property:

\(\displaystyle x = 0 \text{ or } 3x + 5 = 0 \text{ or } x - 10 = 0\)

Solve for each case:

\(\displaystyle x = 0 \text{ or } x = -\frac{5}{3} \text{ or } x = 10\)

We can see that -5/3 < 0 < 10. Thus, a = -5/3, b = 0, and c = 10.

Therefore:

\(\displaystyle \begin{aligned} 10c - 6a & = 10(10) - 6\left(-\frac{5}{3}\right) \\ \\ &= 100 + 10 \\ \\ & = 110 \end{aligned}\)

The total amount of almonds and walnuts that the customer bought is 5 lb 3 oz.

To calculate the total amount of almonds and walnuts, we need to convert the weights to a common unit and then add them together.

First, let's convert 1 pound 15 ounces of almonds to a common unit. There are 16 ounces in a pound, so 1 pound 15 ounces is equal to 1 pound + 15 ounces/16 = 1 pound 0.9375 ounces.

Next, let's convert 3 pounds 5 ounces of walnuts to a common unit. Similarly, 3 pounds 5 ounces is equal to 3 pounds + 5 ounces/16 = 3 pounds 0.3125 ounces.

Now, we can add the weights of almonds and walnuts together:

1 pound 0.9375 ounces + 3 pounds 0.3125 ounces = 4 pounds 1.25 ounces.

Finally, we can simplify this to the mixed unit form:

4 pounds + 1.25 ounces = 4 pounds 11 ounces.

Therefore, the total amount of almonds and walnuts that the customer bought is 4 lb 11 oz.

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The annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily is approximately 64.04%.

To determine the annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (6.63%)
n = the number of times interest is compounded per year (365 for daily compounding)
t = the number of years (8)
Plugging in the values, we have:
A = 1200(1 + 0.0663/365)^(365*8)
Calculating this, we get A ≈ $1,968.49.
To find the annual percentage yield, we need to find the interest earned:
Interest = A - P = $1,968.49 - $1200 = $768.49
Now, we can find the annual percentage yield using the formula:
Annual percentage yield = (Interest / P) * 100
Plugging in the values, we have:
Annual percentage yield ≈ ($768.49 / $1200) * 100 ≈ 64.04%
Therefore, the annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily is approximately 64.04%.

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Yes, the room heater will fit into the robust box, which is 45 cm in width and 90 cm in height.

The cylindrical, which is frequently a lobed solid, comprises one of the most simple curvature geometric forms. In simple geometry, it is known as a prism with a circle as its basis. The term "cylinders" is also used to refer to an infinitely curved surface in a number of modern domains of topology and geometries. A "cylinder" is a two half object made up of curved surfaces with circle tops and bases. A cylinder is a two half solid figure with two bases that are both similar circles connected at its height, which is controlled by the separation of the legs from the center. Cans of iced drinks and the wicks from toilet paper are example of cylinders.

given

r = d/2 = 40/2 = 20 cm

v = pi *r*r*h

100 = 3.14 * 20*20 *h

100 = 1256*h

h = 0.08 cm

strong box = surface area of cuboid = 45 * 90

= 4050 cm2

surface area of water heater = A=2πrh+2πr2=2·π·20·0.08+2·π·202

≈2523.3

Yes, the room heater will fit into the robust box, which is 45 cm in width and 90 cm in height.

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Answer:

25°

Step-by-step explanation:

A supplementary angle refers to two angles that measure up to 180° degrees when added together.

Let x = one of the angles

Let y = 115°

\( x + y = 180^{\circ} \)

\( x = 180 - y\)

\( x = 180 - 115\)

x = 65°

To find the complementary angle;

A complementary angle refers to two angles that measure up to 90° degrees when added together.

Let a = one of the angles.

Let b = 65°

\( a + b = 90^{\circ} \)

\( a = 90 - b\)

\( a = 90 - 65\)

a = 25°

Therefore, the complement of an angle whose supplement is 115 degrees is 25 degrees.

Answer:

The least common multiple of 5 and 7 is 35

Step-by-step explanation:

Because 5 x 7 is 35

Answer:

The Least common multiple ( LCM) of 5 and 7 is 35

Step-by-step explanation:

We list the first few multiples of 5 and 7a and identify the common multiples .

The least among the common multiples is the LCM of 5 and 7.

LCM 5 and 7

Multiples of 5: 5,10,15,20,25,30,35,40,45

Multiples of 7: 7,14,21,28,35,42,49

The Least common multiple of 5 and 7 is 35 .

l hope it helps ❤❤

Info given

We have a total of people given (82). We also know that we have 54 children of under 12 years and under some children were under 3 years

We define x as the number of children under 3 years.

We want to find C for the total cost. We don't have the unitary prices but we can assume it as C1 (over 3 and lower than 12) and C2(adults) for children and adults.

Solution:

With C the total amount collected and C1 and C2 described above.

The ferryman should transport the goat first, then return alone to bring the wolf, leaving the goat on the right bank. Finally, he should transport the cabbage and leave it with the wolf.

In order to solve this puzzle, the ferryman must make a series of careful moves to ensure the safety of the wolf, goat, and cabbage. The first step is to transport the goat to the right bank, leaving it there. The ferryman then returns to the left bank alone.

He takes the wolf across the river, but before leaving it on the right bank, he brings the goat back to the left bank. Now, the goat and cabbage are on the same side, while the wolf remains on the right bank.

The ferryman transports the cabbage to the right bank, leaving it there, and then returns alone to the left bank. Finally, he takes the goat across the river one last time, completing the puzzle. This sequence of moves ensures that the wolf and goat are never left alone together, nor are the goat and cabbage.

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Answer:

ok so x*0.85=150

so x=176

Hope This Helps!!!

The non zero vector orthogonal to the plane through P,Q and R is ⟨0,18,−9⟩

A non-zero vector orthogonal to the plane through the points P, Q, and R can be found by taking the cross product of two vectors that lie in the plane. One way to do this is to take the difference vector of two of the points, and then take the cross product of that difference vector with the difference vector of the third point.

For example, we can use the difference vector QP = (-2,1,3) - (1,0,1) = (-3,1,2) and the difference vector RP = (4,2,5) - (1,0,1) = (3,2,4)  

The cross product of these two vectors is:

(-3,1,2) x (3,2,4) =⟨0,18,−9⟩

so the non-zero vector orthogonal to the plane through the points P, Q, and R is ⟨0,18,−9⟩

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Answer:

3

Step-by-step explanation:

5.75 - (1.75 × 2) = 2.25

2.25 ÷ 0.75 = 3

Answer: Cindy bought 3 children books.

Step-by-step explanation:

$1.75 + $1.75 = $3.50

$5.75 - $3.50 = $2.25

$2.25 ÷ $ 0.75 = 3

The total area of the solid figure is 90 square inches + 27sqrt(3) / 4 square inches.

To find the total area of the solid figure, we need to determine the areas of each face and then add them together.

The solid figure consists of a rectangular prism with dimensions 3" x 3" x 6" and a pyramid on top with an equilateral triangle base.

First, let's find the area of the rectangular prism. The rectangular prism has two identical square faces with side length 3" and four rectangular faces with dimensions 3" x 6". The total area of the rectangular prism can be calculated as:

Area of the square faces: 2 * (3" * 3") = 2 * 9 square inches

Area of the rectangular faces: 4 * (3" * 6") = 4 * 18 square inches

Total area of the rectangular prism: 2 * 9 + 4 * 18 = 18 + 72 = 90 square inches.

Next, let's find the area of the triangular pyramid. The base of the pyramid is an equilateral triangle with side length 3". The height of the pyramid is 3". The formula to find the area of an equilateral triangle is (sqrt(3) / 4) * (side length)^2. Plugging in the values, we have:

Area of the triangular pyramid: (sqrt(3) / 4) * (3" * 3") * 3" = (sqrt(3) / 4) * 9 * 3 = (sqrt(3) / 4) * 27 = 27sqrt(3) / 4 square inches.

Now, we can find the total area of the solid figure by adding the area of the rectangular prism and the area of the triangular pyramid:

Total area = Area of rectangular prism + Area of triangular pyramid

Total area = 90 square inches + 27sqrt(3) / 4 square inches.

Thus, the total area of the solid figure is 90 square inches + 27sqrt(3) / 4 square inches.

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Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

Answer:

y=2/3x-2

Step-by-step explanation:

EXPLANATION

Since we have that the cost per linear foot is $110, and by applying the Pytagorean Theorem, we can get the value of the new street as shown as follows:

Where shorter leg = 6 , larger leg = 9 and Hypotenuse = New Street

Substituting terms:

Applying the square root to both sides:

Simplifying:

Representing the length in ft units:

Finally, the cost per linear foot will be:

The cost of the street will be of $6,284,256

Answer:

10x - 10 = 180

Step-by-step explanation:

Simplify:

\(\boxed{\text{The answer is 10x - 10 = 180}}\)

-Chetan K

Answer/Step-by-step explanation:

You add the angle measures up so (7x-1)+(3x-9)=180

Add the variables together and the numbers together.

10x-10=180

Answer:

26

Step-by-step explanation:

The first will lay 12 in 12 days

the second will lay 6 in 12 days

and the third will lay 8 eggs in 12 days

12+6+8=26

Answer:

34 Eggs in total

Step-by-step explanation:

Since one hen lays one egg each day over a 12 day period, the hen would lay 12 total eggs.

With this information, you can apply it to another hen

Since another hen lays one egg every 2 days, take the 12/2 and you will get 6.

With the hen that lays two eggs every three days, there are 12 days total, so it would lay 2 eggs for a total of 4 days (12/3=4). 2*8 = 16

12+6+16 = 34

Answer: 74.52 if the question is how far she swims

Step-by-step explanation: