X 6.1.31<br> Sohe the given equation.<br> ).<br> (Type an integer or a simplified fraction)

The cost of 7 chairs and 2 tables is equal.If the cost of 6 chairs and 5 tables is 10575, find the cost of 12 chairs.

Igoryamba

Answer:

5400

Step-by-step explanation:

Let x represent the cost of a chair and y represent the cost of a table. We can use this to set up a system of equations:

7x=2y

6x+5y=10575

We can solve this system using substitution.

Start by rewriting the first equation in terms of x.

$7x=2y\\\text{Divide both sides by 7}\\x=\frac{2}{7}y$

Substitute this into the second equation:

$6(\frac{2}{7}y)+5y=10575\\\frac{12}{7}y+5y+10575\\\frac{12}{7}y+\frac{35}{7}y=10575\\\frac{47}{7}y=10575$

Multiply both sides by 7

$47y=74025$

Divide both sides by 47

$y=1575$

This means...

$7x=2(1575)\\7x=3150$

Divide both sides by 7

$x=450$

One chair costs 450. Now, multiply this number by 12 to find the cost of 12 chairs.

$450*12=5400$

12 chairs cost 5400.

7 0

2 years ago

Determine if the triangles are congruent by HL, SAS, SSS, AAS, or

Tom [10]

Asa. the side is in the middle of the angles

3 0

3 years ago

(cot^2x - 1)/(csc^2x) = cos2x

Alex787 [66]

Answer:

Step-by-step explanation:

The idea here is to get the left side simplified down so it is the same as the right side. Consequently, there are 3 identities for cos(2x):

$cos(2x)=cos^2x-sin^2x$ ,

$cos(2x)=1-2sin^2x$ , and

$cos(2x)=2cos^2x-1$

We begin by rewriting the left side in terms of sin and cos, since all the identities deal with sines and cosines and no cotangents or cosecants. Rewriting gives you:

$\frac{\frac{cos^2x}{sin^2x} -\frac{sin^2x}{sin^2x} }{\frac{1}{sin^2x} }$

Notice I also wrote the 1 in terms of sin^2(x).

Now we will put the numerator of the bigger fraction over the common denominator:

$\frac{\frac{cos^2x-sin^2x}{sin^2x} }{\frac{1}{sin^2x} }$

The rule is bring up the lower fraction and flip it to multiply, so that will give us:

$\frac{cos^2x-sin^2x}{sin^2x} *\frac{sin^2x}{1}$

And canceling out the sin^2 x leaves us with just

$cos^2x-sin^2x$ which is one of our identities.

5 0

3 years ago

How many times does 15 goes into 2

Whitepunk [10]

Answer:

7

Step-by-step explanation:

2,4,6,8,10,12,14 that is howni got my answer

4 0

3 years ago

Read 2 more answers

The final margin of an NFL football game is approximately normally distributed, with a mean equal to the gambling point spread a

nika2105 [10]

Answer:

The Giants had 0.1949 = 19.49% probability of winning initially.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mean equal to the gambling point spread and a standard deviation of 14 points. The Patriots had been favored by 12 points.

This means that $\mu = 12, \sigma = 14$

What does that fact imply about the Giants' initial (i.e., pre-game) chances of winning

P(X > 0): Probability of Patriots winning.

P(X < 0): Probability of Giants winning.

So we want to find P(X < 0), which is the pvalue of Z when X = 0. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{0 - 12}{14}$

$Z = -0.86$

$Z = -0.86$ has a pvalue of 0.1949

The Giants had 0.1949 = 19.49% probability of winning initially.

7 0

3 years ago

X 6.1.31 Sohe the given equation. ). (Type an integer or a simplified fraction)