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2 years ago

The graph of the function f(x) = (x - 3)(x + 1) is shown.

Mathematics

2 answers:

salantis [7]2 years ago

8 0

Answer:

Step-by-step explanation:

nekit [7.7K]2 years ago

5 0

Answer:it’s A

Step-by-step explanation:

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A building is 964 feet tall. Two people are standing on the ground directly west of the building. The

Lina20 [59]

Answer:

The distance from both of them = 1463.925 ft

Step-by-step explanation:

The building is 964 ft tall . 2 people are standing on the ground directly west of the building. The first person looks up at an angle of 62° to the top of the building while the second person did same at an angle of 26°. The distance between them can be computed below.

The illustration forms a right angle triangle . Using the SOHCAHTOA principle let us find the distance of the second person from the building

tan 26° = opposite/adjacent

tan 26° = 964/adjacent

adjacent tan 26° = 964

adjacent = 964/tan 26°

adjacent = 964/0.48773258856

adjacent = 1976.49290328 ft

The distance from the second person to the building = 1976.493 ft

Distance of the first person to the building

tan 62° = opposite/adjacent

tan 62° = 964/adjacent

adjacent tan 62° = 964

adjacent = 964/tan 62°

adjacent = 964/1.88072646535

adjacent = 512.567892122

distance from the first person to the building = 512.568 ft

The distance from both of them = 1976.493 ft - 512.568 ft = 1463.925 ft

5 0

2 years ago

Given vectors u = (−1, 2, 3) and v = (3, 4, 2) in R 3 , consider the linear span: Span{u, v} := {αu + βv: α, β ∈ R}. Are the vec

julia-pushkina [17]

Answer:

$(2,6,6) \not \in \text{Span}(u,v)$

$(-9,-2,5)\in \text{Span}(u,v)$

Step-by-step explanation:

Let $b=(b_1,b_2,b_3) \in \mathbb{R}^3$ . We have that $b\in \text{Span}\{u,v\}$ if and only if we can find scalars $\alpha,\beta \in \mathbb{R}$ such that $\alpha u + \beta v = b$ . This can be translated to the following equations:

1. $-\alpha + 3 \beta = b_1$

2. $2\alpha+4 \beta = b_2$

3. $3 \alpha +2 \beta = b_3$

Which is a system of 3 equations a 2 variables. We can take two of this equations, find the solutions for $\alpha,\beta$ and check if the third equationd is fulfilled.

Case (2,6,6)

Using equations 1 and 2 we get

$-\alpha + 3 \beta = 2$

$2\alpha+4 \beta = 6$

whose unique solutions are $\alpha =1 = \beta$ , but note that for this values, the third equation doesn't hold (3+2 = 5 $\neq$ 6). So this vector is not in the generated space of u and v.

Case (-9,-2,5)

Using equations 1 and 2 we get

$-\alpha + 3 \beta = -9$

$2\alpha+4 \beta = -2$

whose unique solutions are $\alpha=3, \beta=-2$ . Note that in this case, the third equation holds, since 3(3)+2(-2)=5. So this vector is in the generated space of u and v.

4 0

2 years ago

If PQR ~ QST, find the value of x

MaRussiya [10]

Answer:

I don't understand.

Step-by-step explanation:

5 0

1 year ago

Write a system of equations to describe the situation below, solve using elimination or substitution.

tangare [24]

X= mountain dew y= coke

-(5x+5y=1160)
8x+5y=1523

-5x-5y=-1160
+
8x+5y=1523

3x=363
3 3

x=121 g of sugar in Mt. Dew

8x+5y=1523 plug in 3 in x

24+5y-24= 1523-24

5y= 1499
5 5

y= 299.8 grams of sugar in coke

4 0

3 years ago

The population of turtles is doubling every 3 months. If there are 400 turtles now, how many will there

QveST [7]

First we need to know how many months is 2 years. To answer that we multiply the number of months in a year by 2 and get 48 months.

Every 3 months the population of turtles doubles, but to get how many times the population doubles, you need to divide 48 months by 3 to get 16.

So population of 400 will get doubled 16 times in the following two years.

We construct the following equation where $p$ is the final population,