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2 years ago

It takes Niamh 3 hours to drive from Ashdown to Bridgeton at an average speed of 50 mph.

Mathematics

1 answer:

Nadya [2.5K]2 years ago

6 0

Answer:

46.7

Step-by-step explanation:

3 × 50 = 150 miles

60 ÷ 40 = 1.5 h.

(150 + 60) ÷ (1.5 + 3) = 46.7 mph

(Speed × Time = Distance)

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After a storm, two street lights with the same length are leaning against each

Ray Of Light [21]

Answer:

c = 4.79 feet

Step-by-step explanation:

Given question is incomplete without a picture; find the question with the attachment.

Two poles AD and DB of same length are leaning against each other.

Distance between the poles (AB) = 45 feet

m(∠ADB) = 180°- (60 + 50)°

= 70°

By sine rule,

$\frac{sin50}{AD}=\frac{sin70}{45}=\frac{sin60}{DB}$

$AD=\frac{45\times (sin50)}{sin70}$

= 36.68 ft

Similarly,

DB = $\frac{45\times sin60}{sin70}$

= 41.47 ft

Now c = DB - AD

= 41.47 - 36.68

= 4.79 feet

4 0

3 years ago

Find the equation of the line specified. The slope is -4, and it passes through ( 5, 8).

ollegr [7]

Answer:

B. y= -4x + 28

Step-by-step explanation:

To find the equation of this line first put it into slope-point form, $y-y_{1} =m(x-x_{1})$ where $y_{1}$ and $x_{1}$ are the y and x coordinates and m is the slope. So plug in the information to get the equation, y-8=-4(x-5). Then solve for y,

First, distribute the -4

y-8=-4x+20

Next, add 8 to both sides

y=-4x+28

4 0

3 years ago

Read 2 more answers

In Exercises 40-43, for what value(s) of k, if any, will the systems have (a) no solution, (b) a unique solution, and (c) infini

svet-max [94.6K]

Answer:

If k = −1 then the system has no solutions.

If k = 2 then the system has infinitely many solutions.

The system cannot have unique solution.

Step-by-step explanation:

We have the following system of equations

$x - 2y +3z = 2\\x + y + z = k\\2x - y + 4z = k^2$

The augmented matrix is

$\left[\begin{array}{cccc}1&-2&3&2\\1&1&1&k\\2&-1&4&k^2\end{array}\right]$

The reduction of this matrix to row-echelon form is outlined below.

$R_2\rightarrow R_2-R_1$

$\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\2&-1&4&k^2\end{array}\right]$

$R_3\rightarrow R_3-2R_1$

$\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\0&3&-2&k^2-4\end{array}\right]$

$R_3\rightarrow R_3-R_2$

$\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\0&0&0&k^2-k-2\end{array}\right]$

The last row determines, if there are solutions or not. To be consistent, we must have k such that

$k^2-k-2=0$

$\left(k+1\right)\left(k-2\right)=0\\k=-1,\:k=2$

Case k = −1:

$\left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&-1-2\\0&0&0&(-1)^2-(-1)-2\end{array}\right] \rightarrow \left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&-3\\0&0&0&-2\end{array}\right]$

If k = −1 then the last equation becomes 0 = −2 which is impossible.Therefore, the system has no solutions.

Case k = 2:

$\left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&2-2\\0&0&0&(2)^2-(2)-2\end{array}\right] \rightarrow \left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&0\\0&0&0&0\end{array}\right]$

This gives the infinite many solution.

5 0

3 years ago

An investment made in the stock market decreased at a rate of 2.2% per year for 10 years. What is the current value of

never [62]

Answer:

$800,500 (nearest dollar)

Step-by-step explanation:

The given scenario can be modeled as an exponential equation.

General form of an exponential function:

$f(x)=ab^x$

where:

a is the initial value (y-intercept)
b is the base (growth/decay factor) in decimal form
x is the independent variable
y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

The initial value (a) is the value of the investment.

Therefore, a = 1,000,000.

If the investment decreases by 2.2% each year, then it will be 97.8% of the previous year.

Therefore, b = 97.8% = 0.978.

Substitute these values into the formula to create a general equation for the scenario:

$f(x)=1000000(0.978)^x$

(where x is the time, in years).

To find the value of the investment after 10 years, substitute x = 10 into the formula:

$\implies f(10)=1000000(0.978)^{10}=800500.1586$

Therefore, the value of the investment after 10 years is $800,500 (nearest dollar).

Learn more about exponential functions here:

brainly.com/question/27949445

brainly.com/question/27955470

3 0

2 years ago

Please help I need the right answer ill give brainliest pleaseee helpppp

drek231 [11]

Answer:

y=3x+1, or the second option

Step-by-step explanation:

We can see on the graph the line converges with the y-axis at (0, 1), so we can cross out the last two answers. Then we can also see that the slope is 3 on the graph and an equation that has x^2 must be a parabola. The answer is then narrowed down to the second option.

4 0

3 years ago

Read 2 more answers