Find a solution to the linear equation y=−x+7 by filling in the boxes with a valid value of x and y.

Answer:

a)x - 4y -14 =0

5x - y - 13 =0

Step-by-step explanation:

Using substitution method to solve equation above gives:

x - 4y - 14 =0 ....eq1

5x - y -13 =0 ....eqn2

From eqn1, making x the subject formula:

x - 4y - 14 =0

x - 4y =14

x = 14+4y ...eqn3

From eqn2, substitute value of x and solve for y:

5(14+4y)-y-13 =0

70+20y-y-13 =0

70+19y-13 =0

70 - 13 = -19y

57 = -19y

divide both sides by -19

-57/19 = -19y/-19, then

y = -3

From eqn1:

x = 14 + 4y

substitute the value of y in the expression above

x = 14 + 4(-3)

x = 14 + (-12)

x = 14 - 12

x = 2

Answer:

It would be B. Circle

Answer:

B. 3

Step-by-step Explanation:

To find the average rate of change of the exponential function represented by the table of values above can be calculated using the general formula for average rate of change of a function, which is given as [tex] m = \frac{f(b) - f(a)}{b - a} [/tex]

Where,

[tex] a = 1, f(1) = 7 [/tex]

[tex] b = 3, f(3) = 13 [/tex]

Plug in the above values in the average rate of change formula:

[tex] m = \frac{13 - 7}{3 - 1} [/tex]

[tex] m = \frac{6}{2} [/tex]

[tex] m = 3 [/tex]

Average rate of change is B. 3

Answer:

3

Step-by-step explanation:

Answer:

Step-by-step explanation:

The side lengths are equal - supposedly

30                          25

?                              ?

25 + ? = 45

-25        - 25

? = 20

45 - 30 = 15

The question mark should be equal to 15.

Hope this helps,

Kavitha

Answer:

2x - 4.

Step-by-step explanation:

4 less than twice a number is the same thing as a number times 2 minus 4. Let's say that the number is represented by x.

2 * x - 4 = 2x - 4.

Hope this helps!

Answer:

s = 0     OR     s = 2

Step-by-step explanation:

=> [tex]-s^2+2s = 0[/tex]

=> [tex]-s(s-2)=0[/tex]

So, Either:

=> -s = 0   OR    s-2 = 0

=> s = 0     OR     s = 2

Answer:

s=0,2

Step-by-step explanation:

-s^2+2s=0

Factor out -s

-s ( s-2) =0

Using the zero product property

-s =0  s-2 =0

s=0   s=2

Answer:

i think is 7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Recursively Defined Function               Sequence

f(1) = 13 f(n) = f(n - 1) + 26 for n ≥ 2         13, 39, 65, 91, ...

f(1) = 13 f(n) = 3 · f(n - 1) for n ≥ 2

f(1) = -24 f(n) = -4 · f(n - 1) for n ≥ 2

f(1) = 28 f(n) = f(n - 1) - 84 for n ≥ 2

f(1) = 28 f(n) = -4 · f(n - 1) for n ≥ 2         28, -112, 448, -1,792, ...

f(1) = -24 f(n) = 4 · f(n - 1) for n ≥ 2         -24, -96, -384, -1,536, ...

__

The initial values are easily seen. They match f(1). The recursive functions can be tested to see if they match the offered sequences.

  sequence 1 has a common ratio of 4 (not -4)

  sequence 2 has a common ratio of -4 (it is not arithmetic)

  sequence 3 has a common difference of 26 (it is not geometric)

Answer:

1 is sequence 3

5 is sequence 2

6 is sequence 1

(These r not included in the test, so don't use them)

 |

\ /

2 is no matching sequence

3 is no matching sequence

4 is no matching sequence

Step-by-step explanation:

PLATO

Answer:

[tex]\huge\boxed{slope=\dfrac{1}{2}=0.5}[/tex]

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points

[tex](-5;\ 3)\to x_1=-5;\ y_1=3\\(7;\ 9)\to x_2=7;\ y_2=9[/tex]

Substitute:

[tex]m=\dfrac{9-3}{7-(-5)}=\dfrac{6}{7+5}=\dfrac{6}{12}=\dfrac{6:6}{12:6}=\dfrac{1}{2}[/tex]

Answer:

1/2

Step-by-step explanation:

We can use the slope formula since we have 2 points

m = ( y2-y1)/(x2-x1)

    = (9-3)/( 7 - -5)

    = (9-3) /( 7+5)

   = 6/ 12

  = 1/2

Answer:

proper because the numerator is lower than the denominator

Answer:

59 accidents were investigated.

Step-by-step explanation:

The question above is a probability question that involves 2 elements: causes of accidents.

Let

A = Alcohol

E = Excessive speed

In the question, we are given the following information:

18 accidents involved Alcohol and Excessive speed =P(A ∩ E)

26 involved Alcohol = P(A)

12 accidents involved excessive speed but not alcohol = P( E ) Only

21 accidents involved neither alcohol nor excessive speed = neither A U B

We were given P(A) in the question. P(A Only) = P(A) - P(A ∩ E)

P(A Only) = 26 - 18

= 8

So, only 8 accident involved Alcohol but not excessive speed.

The Total number of Accidents investigated = P(A Only) + P( E only) + P(A ∩ E) + P( neither A U B)

= 8 + 12 + 18 + 21

= 59

Therefore, 59 accidents were investigated.

Answer:

Standard form = y = mx + c

m = Δy/Δx

m = 5/2

y = 5/2 x + c

Sub in (4,2)

2 = 10 + c

c = -8

y = 5/2 x - 8  

Step-by-step explanation:

Answer:

a)  Y = 350 + 130X

b) C. The symbol [tex]\hat {y}[/tex] represents the predicted value of price.

Step-by-step explanation:

The equation of a regression line is given as:

Y = a + bX

Where Y is the dependent variable, X is the independent variable, a is the intercept on the y axis when X = 0 and b is the slope of the regression line.

a)  The regression equation has a slope of 130 and a y-intercept of 350. From Y = a + bX, the equation of the regression line is:

Y = 350 + 130X

b) From the question x represents the ratings of different hotels in a certain area and [tex]\hat {y}[/tex] represents the price of the different hotels based on their ratings. Since a regression line is drawn, y represents the predicted value of price

Answer:

Q.2 [tex]4\sqrt2[/tex] units

Q.3 [tex]10\sqrt2[/tex] units

Step-by-step explanation:

Given that points:

C(-1, 3) and D (-5, 7)

E(0, -5) and F(10, -15)

To find:

Q.2. Distance between C and D

Q.3. Distance between E and F

Solution:

First of all, let us solve the question marked as number 2 in the attached image.

C(-1, 3) and D (-5, 7)

[tex]x_2 = -5\\x_1 = -1\\y_2 = 7\\y_1 = 3[/tex]

To find the distance 'd' between the points, we can use distance formula:

[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]d = \sqrt{(-5-(-1))^2+(7-3)^2}\\\Rightarrow d = \sqrt{(-4)^2+(4)^2}\\\Rightarrow d =\sqrt{16+16}\\\Rightarrow d =\sqrt{32} = 4\sqrt2\ units[/tex]

First of all, let us solve the question marked as number 3 in the attached image.

E(0, -5) and F(10, -15)

[tex]x_2 = 10\\x_1 = 0\\y_2 = -15\\y_1 = -5[/tex]

To find the distance 'd' between the points, we can use distance formula:

[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]d = \sqrt{(10-0)^2+(-15-(-5))^2}\\\Rightarrow d = \sqrt{10^2+(-10)^2}\\\Rightarrow d =\sqrt{100+100}\\\Rightarrow d =\sqrt{200} = 10\sqrt2\ units[/tex]

Please find attached image for the answers filled in the boxes.

Answer: Regression line equation:  [tex]\hat{y}=-1.008x+39.1704[/tex]

Step-by-step explanation:

Equation of least-squares regression line for predicting y :

[tex]\hat{y}=b_1x+b_o[/tex]

, where [tex]\text{Slope} (b_1)=r\dfrac{s_y}{s_x}[/tex] ,  [tex]\text{intercept}(b_0)=\bar{y}-b_1\bar{x}[/tex]

Given: [tex]\bar{x}=8.8,\ s_x=1.5,\ s_y=1.8,\ \bar{y}=30.3,\ r=-0.84[/tex]

Then,

[tex]b_1=(-0.84)\dfrac{ 1.8}{ 1.5}\\\\\Rightarrow\ b_1=-1.008[/tex]

Now,

[tex]b_0=30.3-(-1.008)(8.8)=30.3+8.8704\\\\\Rightarrow\ b_0=39.1704[/tex]

Then, Regression line equation:  [tex]\hat{y}=-1.008x+39.1704[/tex]

Answer: Choice C.  an = 8 + 9(n-1)

===========================================

Work Shown:

a1 = 8 is the first term

a7 = 62 is the seventh term

an = a1+d(n-1) = nth term of arithmetic sequence

a7 = a1+d(7-1) ... plug in n = 7; solve for d

62 = 8+d(6)

62 = 6d+8

6d+8 = 62

6d = 62-8

6d = 54

d = 54/6

d = 9 is the common difference

an = a1 + d(n-1)

an = 8 + 9(n-1) is the nth term of this arithmetic sequence

Answer:

Choice C.  an = 8 + 9(n-1)

Step-by-step explanation:

I just took the test

Answer:

  181.8 yd

Step-by-step explanation:

The law of cosines is good for this. It tells you for triangle sides 'a' and 'b' and included angle C, the length of 'c' is given by ...

  c^2 = a^2 +b^2 -2ab·cos(C)

For the given geometry, this is ...

  c^2 = 400^2 +240^2 -2(400)(240)cos(16°) ≈ 33,037.75

  c ≈ √33037.75 ≈ 181.8 . . . yards

Marsha's ball is about 181.8 yards from the hole.

Answer:

181.8 yds

Step-by-step explanation:

I got it correct on founders edtell

Answer:

(-2, -(2pi)/3)

Step-by-step explanation:

a p ex

In da pic :)))))))))

Answer:

y = -15

Step-by-step explanation:

x-5y=-15x−5

Let x = -5

-5 -5y = -15 * -5 -5

Combine like terms

-5 -5y = 75-5

-5 -5y = 70

Add 5 to each side

-5y = 75

Divide by -5

y = -15

Answer:

201 miles

Step-by-step explanation:

Base fee =  $15.95

Mileage fee = $ 0.95  per/mile

Paid = $206.90

Distance= ?

--------------

Equation to calculate miles:

Answer:

A=64340 dollars

Step-by-step explanation:

A=p(1+r)^t     p principal, t= time period, r is the rate

A=21000(1+0.0775)^15= 64339.61

A=64340 dollars

Answer:

There is sufficient evidence to support the claim that the standard deviation is less than 14.7.

Step-by-step explanation:

From the question we are told that that the null hypothesis is

       [tex]H_o : \sigma < 14.7[/tex]

Now given from the question that this null hypothesis was rejected, it mean, in non technical term that there is sufficient evidence to support the claim that the standard deviation is less than 14.7.

Answer:

18.4°

Step-by-step explanation:

Use law of cosine.

a² = b² + c² − 2bc cos A

11² = 20² + 28² − 2(20)(28) cos A

121 = 1184 − 1120 cos A

cos A = 0.949

A = 18.4°

Answer:

Step-by-step explanation:

A linear graph with y values (height of tree) going up 2.5 with each increase of x (growing season)

This is the model that best fits the graph describing a growth of a plant

Answer:

9 miles

Step-by-step explanation:

Let's say that the speed that Jeremy's father drives Jeremy through traffic is x. When there is no traffic, Jeremy's father drives 18 miles per hour faster than his speed in traffic, x. This would make the speed that Jeremy's father drives Jeremy to school without traffic, 18 / 60 + x. This is as it is 18 miles per hour faster, not 18 miles per minute faster.

Now recall the formula Speed = Distance / Time, or S = D / T. We want the distance here ( How far (in miles) from Jeremy's home to school ) so let's isolate D here in this formula,

S = D / T ⇒ D = S [tex]*[/tex] T - and as you know, the distance from Jeremy's home to school is the same, with or without traffic. So, we can consider case 1 : Jeremy's " distance traveled " in traffic, and case 2 : Jeremy's " distance traveled " without traffic, and make them equal to one another.

20 [tex]*[/tex] x = 12 [tex]*[/tex] ( 18 / 60 + x ),

20x = 3.6 + 12x,

8x = 3.6,

x = 0.45 - Now the distance is 20 [tex]*[/tex] x, and hence 20 [tex]*[/tex] 0.45 = 9 miles

Answer:

d.

Step-by-step explanation:

[tex]f(g(x))=3(g(x))^2-12=3(5x+3)^2-12=3(25x^2+30x+9)-12=75x^2+90x+27-12=75x^2+90x+15[/tex]

Answer:

-0.5

Step-by-step explanation:

σM=σ/√N

=9/√36

=9/6

=3/2=1.5

Z=(x-μ)/σ/√N

=(19.5-24)/9/√36

=-4.5/1.5=-3

The probability that the sample mean will be larger than 19.5 = -0.5

P(>19.5)=P(Z>-3)= -0.5

Answer:

a)the proportion of student is 0.1082

b)

H1: p = .08

H2: p not equal to 0.08

H1: p =0 .08

H2: p < .08

H1: p =0 .08

H2: p >0 .08

c)z=1.45

d) the p value is 0.1470

e)null hypothesis cannot be accepted,There is no enough evidence to reject the  null hypothesis.

Step-by-step explanation:

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Answer:

10

Step-by-step explanation:

To find 20% of 50 you need to times 20 with 50 and divide by 100.

20×50÷100

=10

Answer:

T(n) = 5n + 20

Step-by-step explanation:

1 candy has a mass of 5 g.

n candies have a mass of 5n grams.

The box has a mass of 20 grams.

total mass = mass of candies + mass of box

T(n) = 5n + 20

n         T(n)

0           20

25         145

50         270

75          395

100        520