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Rama09 [41]
3 years ago
12

Which systems of equations have exactly one solution?

Mathematics
1 answer:
fenix001 [56]3 years ago
4 0
1.
y=2x \\ y=2x+1 \\ \\
2x=2x+1 \\
2x-2x=1 \\
0=1 \\
not \ true - no \ solution

2.
x=5 \\
y=-4 \\
already \ solved - one \ solution

3.
y=x+6 \\
y-6=x \\ \\
y=x+6 \\
y=x+6 \\ \\
x+6=x+6 \\
x-x=6-6 \\
0=0 \\
true - infinitely \ many \ solutions

4.
y=3x+4 \\
y=3 \\ \\
3=3x+4 \\
3-4=3x \\
-1=3x \\
x=-\frac{1}{3} \\ \\
(x,y)=(-\frac{1}{3},3) - one \ solution

The answer is 2 and 4.
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Eva8 [605]
The answer is D. $756
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Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. Find cos(θ) and csc(θ).
insens350 [35]

Answer:

\cos{\theta} = \dfrac{1}{52}

\csc{\theta} = \dfrac{52}{\sqrt{2703}}

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

\sec{\theta} = \dfrac{1}{\cos{\theta}}

we can substitute the value of sec(θ) in this equation:

52 = \dfrac{1}{\cos{\theta}}

and solve for for cos(θ)

\cos{\theta} = \dfrac{1}{52}

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by \theta = \arccos{\left(\dfrac{1}{52}\right)} = 88.8^\circ

b) since right triangle is mentioned in the question. We can use:

\cos{\theta} = \dfrac{\text{adj}}{\text{hyp}}

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

  • length of the adjacent side = 1
  • length of the hypotenuse = 52

we can find the third side using the Pythagoras theorem.

(\text{hyp})^2=(\text{adj})^2+(\text{opp})^2

(52)^2=(1)^2+(\text{opp})^2

\text{opp}=\sqrt{(52)^2-1}

\text{opp}=\sqrt{2703}

  • length of the opposite side = √(2703) ≈ 51.9904

we can find the sin(θ) using this side:

\sin{\theta} = \dfrac{\text{opp}}{\text{hyp}}

\sin{\theta} = \dfrac{\sqrt{2703}}{52}}

and since \csc{\theta} = \dfrac{1}{\sin{\theta}}

\csc{\theta} = \dfrac{52}{\sqrt{2703}}

4 0
3 years ago
Kaden works 5 days. The median number of hours he works is 3. The mean number of hours he works is 4.
alisha [4.7K]

Answer:

(a) 1, 2, 3, 6, 8

Step-by-step explanation:

Given

Median = 3

Mean = 4

Required

The sequence of hours worked each day

<em>See attachment for options</em>

From the question, we understand that:

Median = 3

This means that, the middle number is 3 (when sorted)

So, we can conclude that (b) and (c) cannot be true because their middle numbers are 6 and 5 respectively

Next, is to determine the mean of (a) and (d)

The mean of a data is calculated as:

\bar x = \frac{\sum x}{n}

So, we have:

(a)

\bar x = \frac{1+ 2+ 3+ 6+ 8}{5}

\bar x = \frac{20}{5}

\bar x = 4

(d)

\bar x = \frac{1+ 2+ 3+ 4+ 5}{5}

\bar x = \frac{15}{5}

\bar x = 3

Option (a) is true, because it has:

Median = 3

Mean = 4

7 0
3 years ago
James, Priya, and Siobhan work in a grocery Store. James makes $9.00 per hour. Priya makes 40% more than James, and Siobhan make
wolverine [178]

Answer:

<em>* Siobhan's profit at the grocery store ⇒ $ 10.8 *</em>

Step-by-step explanation:

See below;

Priya's 40% profit in the grocery store ⇒ 40/100 * 9 = 2/5 * 9 = 18/5 ⇒ $ 3.6,

Priya's profit at the grocery store ⇒ 9 + 3.6 ⇒ $ 12.6,

Siobhan's 15% of Priya's profit from the store ⇒ 15/100 * 12.6 = $ 1.8

Siobhan's profit at the grocery store ⇒ 12.6 - 1.8 = $ 10.8

<em>* Siobhan's profit at the grocery store ⇒ $ 10.8 *</em>

4 0
3 years ago
1.2cm represents 24 km. it is approximately 5 cm from knight rock to storm bay on the map. what is the actual distance in kilome
Kipish [7]

Answer:

about 120

Step-by-step explanation:

4 0
3 years ago
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