Find the value of y in the equation y=-4x+9 when x=-3

Answer:

[tex]A = \left[\begin{array}{cccc}1&-1&-3&-5\\4&2&0&-2\\7&5&3&1\end{array}\right][/tex]

Step-by-step explanation:

A = (aij)

i representa a linha e j a coluna.

Tipo 3x4

Isto implica que a matriz tem 3 linhas e 4 colunas.

aij = 3i – 2j.

Primeira linha:

[tex]a_{1,1} = 3(1) - 2(1) = 1[/tex]

[tex]a_{1,2} = 3(1) - 2(2) = -1[/tex]

[tex]a_{1,3} = 3(1) - 2(3) = -3[/tex]

[tex]a_{1,4} = 3(1) - 2(4) = -5[/tex]

Segunda linha:

[tex]a_{2,1} = 3(2) - 2(1) = 4[/tex]

[tex]a_{2,2} = 3(2) - 2(2) = 2[/tex]

[tex]a_{2,3} = 3(2) - 2(3) = 0[/tex]

[tex]a_{2,4} = 3(2) - 2(4) = -2[/tex]

Terceira linha:

[tex]a_{3,1} = 3(3) - 2(1) = 7[/tex]

[tex]a_{3,2} = 3(3) - 2(2) = 5[/tex]

[tex]a_{3,3} = 3(3) - 2(3) = 3[/tex]

[tex]a_{3,4} = 3(3) - 2(4) = 1[/tex]

Matriz:

A matriz é dada por:

[tex]A = \left[\begin{array}{cccc}1&-1&-3&-5\\4&2&0&-2\\7&5&3&1\end{array}\right][/tex]

Answer:

Step-by-step explanation:

I always advise my students to make a table of information for these story problems because trying to keep track of the information otherwise is a nightmare. The table will look like this:

           d      =      r      *      t

m

c

m is motorcycle and c is car.

First thing we are told is that the ratio of m's speed to c's speed is 5:4; that means that we can divide 5/4 to find out how many times faster m is going than c.

5/4 = 1.25 so we have a couple of values to put into the table right away, along with the fact that they are both traveling the same distance of 160 miles.

             d      =     r      *      t

m        160     =   1.25r

c         160     =     r

The last thing we have to fill in is the time. If m travels a half hour less than c, c is driving a half hour more than m, right? Filling that in:

            d      =      r      *      t

m       160     =   1.25r   *     t

c        160     =      r       *  t + .5

Now we have our 2 equations. Looking at the top row of the table gives us the formula we need to solve this problem. It tells us, in other words, what we are going to be doing with these columns of numbers. Distance equals the rate times the time. For the motorcycle, the equation is:

160 = (1.25r)t  and that seems pretty useless since we still have 2 unknowns in there and you can only have 1 unknown in 1 equation. Let's see what the equation for the car is.

160 = (t + .5)r  Same problem.

Let's go back to the equation for the motorcycle and since we are looking for the rates of each, let's solve that equation for time in terms of rate (solve it for t):

[tex]t=\frac{160}{1.25r}[/tex] and sub that into the car's equation in place of t:

[tex]160=r(\frac{160}{1.25r})+.5r[/tex] and simplify. The r's to the left of the plus sign cancel out leaving us with:

[tex]160=(\frac{160}{1.25})+.5r[/tex] and divide those numbers inside the parenthesis to get:

160 = 128 + .5r and subtract 128 from both sides to get:

32 = .5r and finally divide by .5 to get

r = 64 miles/hour

The car goes 64 mph and the motorcycle goes 1.25 times that so,

m = 1.25(64) and

m = 80 mph

Answer:

x = -2; y = 1

Step-by-step explanation:

See picture below.

We are told matrices B is the inverse of matrix A.

The product of a matrix and its inverse is the identity matrix.

Answer:

x2 - 4x - 5 factored form is (x - 5)(x + 1)

Answer:

(x − 5)(x + 1)

Step-by-step explanation:

The answer above is correct.

Answer: (a) and (d)

Step-by-step explanation:

From the graph, vertex is at

Graph is same about the point [tex]x=2[/tex] . Therefore, axis of symmetry is the line [tex]x=2[/tex]

Y intercept is the place where curve intersect the Y-axis that is [tex](0,2)[/tex]

Option (a) and (d) are correct.

Answer:

The Sureset Concrete Company

The tons of gravel and sand that should be purchased each day are:

Sand = 800 tons

Gravel = 700 tons

Step-by-step explanation:

Two ingredients for producing concrete = sand and gravel

Cost of sand per ton = $6

Cost of gravel per ton = $8

Sand and gravel = 75% of the concrete

Therefore 25% (100 - 75%) will be made up of cement and water

Tons of concrete produced each day = 2,000

Sand and gravel = 1,500 (2,000 * 75%)

Sand <= 40% of 2,000 = 800 tons

Gravel => 30% of 2,000 = 700 (1,500 - 800) tons

To minimize costs,  800 tons of gravel and 700 tons of sand should be purchased each day.

Total cost incurred daily for both sand and gravel = $10,400 (800 * $6 + 700 * $8)

Answer:

y= -6

Step-by-step explanation:

the y-intercept is -6, which corresponds to point (0,-6)

remember that you're using the

y=mx+b format of an equation of a line where b is the y-intercept.

Also, if you make x=0, y will be -6.

Answer:

[tex]\sf \dfrac{1}{24}=0.0417=4.17\%\:\:(3\:s.f.)[/tex]

Step-by-step explanation:

Given information:

Contents of Jar 1:

Contents of Jar 2:

Probability Formula

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Therefore:

[tex]\sf P(white\:marble\:from\:Jar\:1)=\dfrac{4}{24}=\dfrac{1}{6}[/tex]

[tex]\sf P(white\:marble\:from\:Jar\:2)=\dfrac{20}{80}=\dfrac{1}{4}[/tex]

As the events are independent (i.e. drawing a marble from one jar does not influence or affect drawing a marble from the other jar), we can use the independent probability formula:

[tex]\sf P(A\:and\:B)=P(A) \cdot P(B)[/tex]

Therefore, the probability that a white marble will be drawn from both jars is:

[tex]\sf P(white\:marble\:from\:Jar\:1)\:and\:\sf P(white\:marble\:from\:Jar\:2)=\dfrac{1}{6} \cdot \dfrac{1}{4}=\dfrac{1}{24}[/tex]

#Jar 1

Total marbles =20+4=24

P(w)

#Jar 2

Total marbles=60+20=80

P(w)

P(w in total)

Answer:

9614

Step-by-step explanation:

Generic number with 4 digit

1000t + 100h + 10y + x

x = 3 + y

x = m - 5

h = 6

m = 9

if we substitute the value we have:

x = 9 - 5 = 4

4 = 3 + y

y = 1

Final number

9614

Answer:

Net present value= $25.17

Step-by-step explanation:

We are told that The last dividend paid was $1.55 and that the dividend growth rate is constant at 1.5% for 2 years.

Thus;

1) After 1st year;

1.55 × (1 + 0.015) = 1.57325 Div1

After 2nd year;

1.57325 × (1 + 0.015) = 1.59685 Div2

After that 2 years it grows at 6% Constant rate forever;

1.59685 × (1 + 0.06) = 1.69266 Div3

Let's now use the dividend formula which grows in perpetuity at a rate of "g" since required return is 12%:

Thus;

V = 1.69266/(0.12 - 0.06) = 28.211

Thus; Div2 = 28.211 + 1.59685 ≈ 29.80785

Now, using the financial calculator of the Cash Flow function, we have:

Div0 = 0

Div1 = 1.57325

Div2 = 29.80785

i% = 12

Net present value = (1.57325/(1 + 0.12)) + ((1.59685 + 28.211)/(1 + 0.12)²)

Net present value= $25.17

Answer:

answer is C

Step-by-step explanation:

General equation of a line is expressed as shown:

y = mx+c where;

m is the slope or gradient of the line

c is the intercept of the line

Given the equation of the line graph as y =2.5x

Comparing the given equation with the general equation, it is seen that m = 2.5 and c = 0 (since there is no value for the intercept)

Based on the explanation, the y-intercept of the graph is therefore 0

Answer:

B

Step-by-step explanation:

To find the x-intercept, substitute in

0 for y and solve for x

To find the y-intercept, substitute in 0 for x and solve for y

x-intercept(s): None

y-intercept(s): (0,1)

Answer:

A. The larger the sample size the better.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

We have to look at the standard error, which is:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

This means that an increase in the sample size reduces the standard error, and thus, the larger the sample size the better, and the correct answer is given by option a.

Answer:

[tex]P(A\cup B \cup C)=89[/tex]

Step-by-step explanation:

From the question we are told that:

Believed in UFO's [tex]A=42[/tex]

Believed in Ghosts [tex]B=45[/tex]

Believed in Bigfoot [tex]C=21[/tex]

Believed in UFO's & Ghosts [tex]A&B=11[/tex]

Believed in Ghosts & Bigfoot [tex]B&C=6[/tex]

Believed in UFO's & Bigfoot [tex]A&B=4[/tex]

Believed in ALL [tex]A&B&C=2[/tex]

Generally with a well detailed Set diagram of the Number of People that that believed in at least one of them is mathematically given by

 [tex]P(A\cup B \cup C)=n(A\cap C)-n(B\cap C) +n(A\cap B \cap C)[/tex]

 [tex]P(A\cup B \cup C)=42+45+21-11-6-4+2[/tex]

 [tex]P(A\cup B \cup C)=89[/tex]

Answer:

Face card= 12/52

(52 cards in a deck and 12 are face cards)

Red face card= 6/12

(12 face cards in a deck cards in a deck and 6 are red face cards)

Black face card= 6/52

(6 are black)

Black card= 26/52

(52 cards in a deck and 26 are black)

Red card= 26/52

(26 are red)

Answer:

a) A

b) C and E

c) C, D and F

d) two

e) Equal

Answer:

0.6836

Step-by-step explanation:

(weight - mean weight) = 48

Variance, s² = 204,304

Sample size, n = 89

We need to obtain the Zscore :

Zscore = (X - mean) / standard Error

Zscore = (weight - mean weight ) / (s/√n)

s = √204304 = 452

The difference from the meanncoukdnbe either to the right or left :

Zscore = - 48 / (452/√89) OR 48 / (452/√89)

Zscore = - 48 / 47.911904 OR - 48 / 47.911904

Zscore = - 1.002 or 1.002

P(Z < - 1.002) = 0.1582 (using Z table)

P(Z < 1.002) = 0.8418

P(Z < 1.002) - P(Z < - 1.002)

0.8418 - 0.1582

= 0.6836

Step-by-step explanation:

s+u

Add t: You will need to introduce brackets

(s+u) + t

Add v: Introduce another v

((s/u) + t) + v

Answer:

B.

Step-by-step explanation:

I don't know for a fact but i think its B. Sorry if I got it wrong.

Answer:

See below

Step-by-step explanation:

Hi there!

We're given that ΔABC≅ΔXYZ

When two triangles are congruent, their corresponding parts are congruent

Because of that, it means vertex A in ΔABC is congruent to vertex X in ΔXYZ, vertex B is congruent to vertex Y, and vertex C is congruent to vertex Z

Since we don't have a picture of the triangles given, we can use the names of the triangles to find the corresponding parts

so, to find the corresponding congruent angle to <BCA:

B is the first letter in the angle, and the corresponding letter in ΔXYZ is Y.

C is the second letter in the angle, and the corresponding letter is Z.

A is the last letter in the angle, and the corresponding letter is X

so that means <YZX is congruent to <BCA

now let's do the same for <ZYX

Z is the first letter in the angle, and the corresponding letter that's in the same place in ΔABC is C

Y is the second letter in the angle, and the corresponding letter is B

X is the last letter in the angle, and the corresponding letter is A

So that means <CBA is congruent to <ZYX

Now to find corresponding sides:

We can still use the names of the triangles, ΔABC and ΔXYZ

so to find the corresponding side to AB,

in ΔABC, AB makes up the first and second letter of the name of the triangle

The corresponding side must also make up the first and second letter of the name of the triangle

in ΔXYZ, the letters X and Y make up the first and second letter

so that means XY must be corresponding to AB

finally,

we need to find the segment congruent to YZ

in ΔXYZ, YZ makes up the second and third letter of the name of the triangle

the corresponding side must also make up the second and third letter of the name of the triangle

in ΔABC,  the letters B and C make up the second and third letter in the triangle

So that means BC must be congruent to YZ

Hope this helps!

Answer:

Hence the value of p is 0.04746.

Step-by-step explanation:

The test statistic is

[tex]Z=(\bar x-\mu)/(s/vn)\\\\=(355-390)/(115/ \sqrt(30))\\\\=-1.667[/tex]

The p-value= P(Z<-1.67) =0.04746. (from standard distribution table)

Therefore p-value =0.04746.

Answer:

1984

Step-by-step explanation:

Answer:

La hipotenusa del triángulo mide 5 metros, el ángulo (a) mide 53,13º y el ángulo (b) mide 36,87º.

Step-by-step explanation:

Dado que del triángulo rectángulo se conocen sus dos catetos, uno mide 4 metros y el otro 3 metros, para hallar su hipotenusa y sus ángulos interiores se deben realizar los siguientes cálculos:

4^2 + 3^2 = X^2

16 + 9 = X^2

√25 = X

5 = X

sen(a) = 4/5

(a) = 53,13º

(b) = 180 - (90º+53,13º)

(b) = 36,87º

Así, la hipotenusa del triángulo mide 5 metros, el ángulo (a) mide 53,13º y el ángulo (b) mide 36,87º.

Answer:

The original graph was shifted 2 units to the left and 5 units down.

Step-by-step explanation:

y = |x|

From this, we go to: y = |x - 2|.

When we want to shift a function f(x) a units to the left, we find f(x - a). So first, the graph was shifted 2 units to the left.

y = |x - 2|.

From this, we go to: y = |x - 2| - 5.

Shifting a function f(x) down b units is the same as finding f(x) - b, so the second transformation was shifting the graph 5 units down.

Answer:

median

Step-by-step explanation:

Q is at the midpoint of RS and so PQ is a median

A median is a segment from a vertex to the midpoint of the opposite side.

We want to define what type of line is PQ (the line that passes through points P and Q) by looking at the given image, one can easily see that the line PQ is a median, now let's explain why.

First, let's analyze the image:

In the image, we can see that P is one vertex of the triangle, and Q is the midpoint of the segment RS (you can see that RQ = 4 and QS = 4) , where R and S are the other two vertexes of the triangle.

Particularly, we can define a median of a triangle as the line that passes through the midpoint of one side of the triangle and by the vertex that does not belong to that side.

With that definition, we can see that PQ is a median because Q is the midpoint of one side of the triangle and P is the vertex that does not belong to that side.

If you want to learn more, you can read:

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9514 1404 393

Answer:

  $150 in 4%, $850 in 6%

Step-by-step explanation:

The fraction that must earn the highest rate is ...

  (5.7 -4.0)/(6.0 -4.0) = 1.7/2 = 0.85

That is 0.85 × $1000 = $850 must be invested at 6%. Matches the last choice.

_____

If you let x represent the amount that must earn 6%, then the total interest earned must be ...

  x·6% +(1000 -x)·4% = 1000·5.7%

  x(6 -4) = 1000(5.7 -4) . . . . . . multiply by 100, subtract 4·1000

  x = 1000·(5.7 -4)/(6 -4) = 850 . . . . as above

Answer:

B. 14

Step-by-step explanation:

It's asking for function f + function g. Then it wants you to use 2 as the x value. So you have:

(f+g)(x) = 2x^2 + 3x + x - 2

(f+g)(x) = 2x^2 + 4x -2

Then using 2 as x:

(f+g)(2) = 2(2^2) + 4* 2 -2

(f+g)(2) = 8 + 8 - 2

(f+g)(2) = 14

Hope that helps, and let me know if I did any of that wrong.

The answer is They left a 20% tip, so the service was probably above average.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

First step is to the amount of the sales tax.

If 100% is $73.89,

5.8% will be x (tax):

100% : $73.89 = 5.8% : x.

x = $73.89 * 5.8% : 100%.

x = $4.28.

Now, we have the price for meals, sales tax, and the total amount of money left, so we can calculate how much the tip is:

$93.00 - $73.89 - $4.28 = $14.83.

So, the tip is $14.83.

Let represent it as percent.

If $73.89 is 100%, $14.83 will be x.

$73.89 : 100% = $14.83 : x.

x = $14.83 * 100% : $73.89.

x = 20%.

So, they left a 20% tip, so the service was probably above average.

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Answer:

b=2

Step-by-step explanation: