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Marianna [84]
3 years ago
8

The length of the segment between the points $(2a, a-4)$ and $(4, -1)$ is $2\sqrt{10}$ units. What is the product of all possibl

e values for $a$? LOTS OF POINTS AND BRAINLIEST TO CORRECT ANSWER!
Mathematics
1 answer:
True [87]3 years ago
5 0

Answer:

-3

Step-by-step explanation:

The length of a segment is

sqrt( ( y2-y1)^2 + (x2-x1) ^2) = 2 sqrt(10)

sqrt( ( a-4 - -1)^2 + (2a -4) ^2) = 2 sqrt(10)

sqrt( ( a-4 +1)^2 + (2a -4) ^2) = 2 sqrt(10)

Combine like terms

sqrt( ( a-3)^2 + (2a -4) ^2) = 2 sqrt(10)

Square each side

( a-3)^2 + (2a -4) ^2) = 4 *(10)

FOIL the left side

a^2 -6a +9   + 4a^2 -16a +16 = 40

Combine like terms

5a^2 -22a +25 = 40

Subtract 40 from each side

5a^2 -22a -15 =0

Factor

(a - 5) (5 a + 3) = 0

Using the zero product property

a-5 =0   5a +3 = 0

a = 5       5a = -3

a=5     a = -3/5

The product of the terms is

5 * -3/5 = -3

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The value of f(2) is 1

Step-by-step explanation:

4 0
3 years ago
At 3:30 in the afternoon in mid-September the Kimball Tower casts a shadow about 290 feet long when the sun's rays come down at
ioda

Answer:

203 feet.

Step-by-step explanation:

Please find the attachment.

Let h represent the height of the building.

We have been given that at 3:30 in the afternoon in mid-September the Kimball Tower casts a shadow about 290 feet long when the sun's rays come down at an angle about 35 degrees above the horizontal.    

We know that tangent relates opposite side of a right triangle to its adjacent side.

\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}

Upon substituting our given values in above formula, we will get:

\text{tan}(35^{\circ})=\frac{h}{290}

290*\text{tan}(35^{\circ})=\frac{h}{290}*290

290*0.70020753821=h

h=290*0.70020753821

h=203.0601860809

h\approx 203

Therefore, the building is approximately 203 feet high.

 

3 0
4 years ago
an ice cream shop has a total of 48 flavors of ice cream and toppings. if there are 16 flavors of ice cream, how many toppings c
Tanzania [10]

Answer:

B

Step-by-step explanation:

There are 48 flavors and toppings. Since 16 are flavors, 32 are toppings. Dividing the 32 topping equally between 8 children is 4 toppings per child.

32 ÷ 8 = 4

3 0
3 years ago
Determine the relationship between the two triangles and whether or not they can be proven to be congruent.
forsale [732]

Answer:

The answer would be A

Step-by-step explanation:

Both congruent sides are pairs

8 0
3 years ago
Read 2 more answers
Can someone please help me with this?
dsp73

Answer:

S_{13} = 403

Step-by-step explanation:

the sum to n terms of an arithmetic series is

S_{n} = \frac{n}{2} (a + l) ← a is the first term and l the last term

here a = - 5 and l = 67 , then

S_{13} = \frac{13}{2} (- 5 + 67) = 6.5 × 62 = 403

3 0
2 years ago
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