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LuckyWell [14K]
3 years ago
7

In the diagram, transversal t cuts parallel lines a and b. Which equation is necessarily true?

Mathematics
2 answers:
Svetllana [295]3 years ago
4 0
B is the correct answer
hoa [83]3 years ago
3 0

Answer:

The correct answer is option B.  

m<3 = m<6

Step-by-step explanation:

From the figure we an see that, a and b are parallel lines and line t is the traversal on the lines.

<u>To find the correct option</u>

From the given figure we get

Corresponding angles are,

<1 & <5,  <2&<6, <2&<7 and <4 &<8

Alternate interior angles are,

<3 & <6  and <4 &<5

Alternate interior angles are equal.

m<3 = m<6

Therefore the correct answer is optionB

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A Cashier has fifteen $5 bills . How Much does he have in $5 bills
Mila [183]
Lets make a known and an unknown chart:

KNOWN: Fifteen $5 bills.

UNKNOWN: How much is that?

So to find the answer to this, we are going to do 5+5+5+5+5+5+5+5+5+5+5+5+5+5+5=??
The answer is $75.
~Hope I helped!~
4 0
3 years ago
3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k
Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt

Evaluate the integral to solve for y :

\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt

\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x

\displaystyle y = x^3+2x^2+kx - 2

Use the other known value, f(2) = 18, to solve for k :

18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}

Then the curve C has equation

\boxed{y = x^3 + 2x^2 + 2x - 2}

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2

The slope of the given tangent line y=x-2 is 1. Solve for a :

3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1

So, the point of contact between the tangent line and C is (-1, -3).

7 0
2 years ago
Two architects bid for a small government project, both
blondinia [14]

Answer:

10 hours

Step-by-step explanation:

let x be the total number of hours

Amazing design total charge = 45x+250

super structures total charge = 60x+100

both companies charge the same amount when both equation equals

45x+250=60x+100

60x-45x=250-100

15x=150

x=10

therefore at 10 hours both companies will charge the same amount

4 0
2 years ago
A savings and loan association needs information concerning the checking account balances of its local customers. A random sampl
Marina86 [1]

Answer:

The 99% confidence interval for the true mean checking account balance for local customers is ($439.29, $888.99).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 14 - 1 = 13

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 13 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.99}{2} = 0.995. So we have T = 3.0123

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 3.0123\frac{279.29}{\sqrt{14}} = 224.85

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 664.14 - 224.85 = $439.29

The upper end of the interval is the sample mean added to M. So it is 664.14 + 224.85 = $888.99.

The 99% confidence interval for the true mean checking account balance for local customers is ($439.29, $888.99).

4 0
3 years ago
5x+9=2x+7+3x-15
andrew11 [14]

Answer:

No Solutions

Step-by-step explanation:

Step 1:

5x + 9 = 2x + 7 + 3x - 15  Equation

Step 2:

5x + 9 = 5x - 8   Add and Subtract

Step 3:

9 = - 8    Subtract 5x on both sides

Answer:

9 ≠ - 8       9 cannot equal - 8

Hope This Helps :)

3 0
3 years ago
Read 2 more answers
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