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1 year ago

Given ΔADC and ΔAEB, What is AE?

Mathematics

1 answer:

chubhunter [2.5K]1 year ago

4 0

Answer:

AE = 43.2 units

Step-by-step explanation:

As per the given question image, it can be seen that in the $\triangle ADC \text { and }\triangle AEB :$

1. $\angle B = \angle C = 90^\circ$

2. $\angle A$ is common to both the triangles.

3. Two angles are common, so the third angle $\angle E$ is also equal to $\angle D$ .

All the three angles in the $\triangle ADC \text { and }\triangle AEB$ are equal to each other, hence the triangles are similar.

As per the property of similar triangles, the ratio of their sides will be equal.

AB : AC = AE : AD

AC = 88 units

BC = 55 units

AB = AC - AB = 33 units

Let side AE = $x$ units

Side AD = AE + ED

So, AD = $x + 72$

Using the ratio:

$\dfrac{AB}{AC} = \dfrac{AE}{AD}\\\Rightarrow \dfrac{33}{55} = \dfrac{x}{x+72}\\\Rightarrow 55x = 33 \times 72\\\Rightarrow x = \dfrac{3\times 72}{5}\\\Rightarrow x = 43.2\ units$

So, AE = 43.2 units

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Consider the trinomial 9x2 + 21x + 10. What value is placed on top of the X? What value is placed on the bottom of the X? What i

inna [77]

Answer: 1) Value is placed on top of the X =90

2) Value is placed on the bottom of the X =21

3) Factored form will be (3x+5)(3x+2)

Step-by-step explanation:

Since we have given that

$9x^2 + 21x + 10$

As we know the quadratic form :

$ax^2+bx+c=0$

1) Value is placed on top of the X is given by

$a\times c=9\times 10=90$

2) Value is placed on the bottom of the X is given by

$b=21$

3) Factorised form:

We will use "Split the middle term":

$9x^2 + 21x + 10\\\\=9x^2+15x+6x+10\\\\=3x(3x+5)+2(3x+5)\\\\=(3x+2)(3x+5)$

Hence, Factored form will be

(3x+5)(3x+2)

7 0

2 years ago

Read 2 more answers

Suppose the firm in this example considers a second product that has a unit profit of $5 and requires 2 hours of production time

user100 [1]

The question is incomplete, here is the complete question

Recall the production model from Section 1.3:

Max 10x

s.t. 5x ≤ 40

x ≥ 0

Suppose the firm in this example considers a second product that has a unit profit of $5 and requires 2 hours for each unit produced. Assume total production capacity remains 40 units. Use y as the number of units of product 2 produced. . Show the mathematical model when both products are considered simultaneously.

Answer:

Max Profit: 10x + 5y

5x + 2y ≤ 40

x ≥ 0, y ≥ 0

Explanation:

x= number of units of product 1 produced

y = number of units of product 2 produced

Since the first product, x, has a unit profit of $10 and Max1 is 10x

Second product, y, has a unit profit of $5, Max2 = 5y

The maximum profit when both products are considered simultaneously is 10x + 5y

Max Profit = 10x + 5y

Time required for each unit of x is 5hours

Therefore, time required for x units is 5x hours

Time required for each unit of y is 2hours

Therefore, time required for y units is 2y hours

Time required for the simultaneous production of both products is 5x + 2y

Since production capacity remains 40 units, 5x+2y ≤40

NB: The values of x and y cannot be negative

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1 year ago

Employees in the marketing department of a large regional restaurant chain are researching the amount of money that households i

kap26 [50]

Answer:

The z-score for the group "25 to 34" is 0.37 and the z-score for the group "45 to 54" is 0.25.

Step-by-step explanation:

The data provided is as follows:

25 to 34 45 to 54

1329 2268

1906 1965

2426 1149

1826 1591

1239 1682

1514 1851

1937 1367

1454 2158

Compute the mean and standard deviation for the group "25 to 34" as follows:

$\bar x=\frac{1}{n}\sum x=\frac{1}{8}\times [1329+1906+...+1454]=\frac{13631}{8}=1703.875\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{8-1}\times 1086710.875}=394.01$

Compute the z-score for the group "25 to 34" as follows:

$z=\frac{x-\bar x}{s}=\frac{1851-1703.875}{394.01}=0.3734\approx 0.37$

Compute the mean and standard deviation for the group "45 to 54" as follows:

$\bar x=\frac{1}{n}\sum x=\frac{1}{8}\times [2268+1965+...+2158]=\frac{14031}{8}=1753.875\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{8-1}\times 1028888.875}=383.39$

Compute the z-score for the group "45 to 54" as follows:

$z=\frac{x-\bar x}{s}=\frac{1851-1753.875}{383.39}=0.25333\approx 0.25$

Thus, the z-score for the group "25 to 34" is 0.37 and the z-score for the group "45 to 54" is 0.25.

8 0

1 year ago

3) George walks away from his house. He walks 25 km west and then

Romashka-Z-Leto [24]

Answer:

29.15 km

Step-by-step explanation:

Given;

George walks; 25km west and then 15 km south

Resolving the directions to x and y axis;

North and South represent positive and negative y axis.

East and West represent positive and negative x axis respectively.

25km west

Rx = -25 km

15 km south

Ry = -15 km

The resultant displacement from the house is;

R = √(Rx^2 + Ry^2)

Substituting the values;

R = √((-15)^2 + (-25)^2)

R = √(225+625)

R = √(850)

R = 29.15 km

Therefore, he is 29.15 km from house

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1 year ago

three positive numbers are in Arithmetic Progression (A.P). the sum of the squares of the three numbers is 155. while the sum of

Alecsey [184]

Given:
Three numbers in an AP, all positive.
Sum is 21.
Sum of squares is 155.
Common difference is positive.

We do not know what x and y stand for. Will just solve for the three numbers in the AP.
Let m=middle number, then since sum=21, m=21/3=7
Let d=common difference.
Sum of squares
(7-d)^2+7^2+(7+d)^2=155
Expand left-hand side
3*7^2-2d^2=155
d^2=(155-147)/2=4
d=+2 or -2
=+2 (common difference is positive)

Therefore the three numbers of the AP are
{7-2,7,7+2}, or
{5,7,9}

6 0

2 years ago