Find the value of each unknown variable in the given figures ?

Answer:

a² - 14a - 15 = 0 (quadratic equation)

Emily's age = 15 years

Tuli's age = 15 - 10 = 5 years

Step-by-step explanation:

let

Emily age = a

Tuli age =  a - 10

Two years ago their ages will be as follows.

Emily's age = a - 2

Tuli's age = a - 10 - 2 = a - 12

The product of their ages 2 years ago is 39.

(a - 2)(a - 12) = 39

a² - 12a - 2a + 24 - 39 = 0

a² - 14a - 15 = 0 (quadratic equation)

To get a

a² + a - 15a - 15 = 0

a(a + 1) - 15(a + 1)

(a + 1)(a - 15)

a = -1 or 15

we can only use 15 as it is positive.

Answer:

  33.7 m at 1.7 seconds

Step-by-step explanation:

For quadratic ax^2+bx+c, the line of symmetry (x-coordinate of the vertex) is ...

  -b/(2a)

For your quadratic, the vertex (highest point) is reached at time ...

  t = -(17)/(2(-4.9)) = 17/9.8 ≈ 1.7 . . . . seconds

__

The height at that time is ...

  f(17/9.8) = (-4.9(17/9.8) +17)(17/9.8) +19 = 289/19.6 +19 ≈ 33.7 . . . meters

_____

Comment on the function evaluation

We have used the "Horner form" of the function to make evaluation easier.

  f(t) = (-4.9t +17)t +19

Answer:

The perimeter of the field is 21 yards

Step-by-step explanation:

See attachment 1 for the coordinates plane.

The question is best solved using an attachment.

To calculate the perimeter of the fence, we simply add the sides of the rectangle.

Attachment 2 is a labelled diagram of attachment 1.

From 2, we have that

Perimeter = A + B + C + D + E + F

Where A to F represent the length of each sides of the fence

From coordinates geometry,

A = 5

B = 4

C = 6½

D = 1½

E = 1½

F = 2½

So,

Perimeter = 5 + 4 + 6½ + 1½ + 1½ + 2½

Perimeter = 21

Hence, the perimeter of the field is 21 yards

Answer:

Acute.

Step-by-step explanation:

Using the Triangle Inequality Theorem you know that the sum of the lengths of two sides of a triangle are greater than the length of the third side.

Using this we can narrow it down that this DOES have a solution, since 10+12>15.

Now, we can determine if this triangle is a right triangle using the Pythagorean Theorem. C is the longest length.

If c^2= a^2+b^2, then it is a right triangle.

If c^2< a^2+b^2 then it is an acute triangle.

If c^2>a^2+b^2 then it is an obtuse triangle.

We can now substitute. (A and B are interchangeable, but C is the longest length.

A=10

B=12

C=15

A^2=100

B^2=144

C^2=255

We can now figure out that this triangle is acute because A^2+ B^2 (244) < C^2 (255).

Hope this helps!

Answer:

S(a) = 27,5036  squared units

Step-by-step explanation:

Shaded area is :

S(a)  =  Area of the circle  - area of the regular pentagon      (1)

A(c) = area of the circle

A(c) = π*(r)²    ⇒  A(c) =  π*(6)²     ⇒   A(c) =  36*π   ⇒ A(c) = 113,0976 squared units

Area of a regular pentagon:

a) If we draw a straight line between the center and each vertex we get  5 triangles, and if we draw the apothem for each side, we get 10 triangles. We will calculate the area of one  of these triangles

The first 5 triangles has a central angle equal to 72⁰ according to:

360/5  =  72

When we divide these triangles in two triangles by means of the apothem, each central angle will be of 36⁰, then

sin 36⁰  =  0,58778  and cos 36⁰ = 0,809017    and   sin 36⁰ =  x/6      here x is half of the side of the regular pentagon. Then

0,58778  =  x/6

x = 6*0,58778

x =  3,52668 units of length  

and cos 36⁰ = a/6      where a is the apothem, then

0,809017  = a / 6     ⇒   a  = 6*0,809017

a =  4,8541 units of length

Now we are in conditon to calculate area of the triangles as:

A(t) = (1/2)*b*h

A(t) = (1/2)*x*a     ⇒ A(t) = 0,5* 3,52668*4,8541

A(t) = 8,5594 squared units

Finally we have 10 of these triangles, then

Area of regular pentagon is : 10*A(t) squared units

A(p) = 85,594 squared units

Now plugging these values in equation (1) we get the shaded area

S(a) =  113,0976 - 85,594

S(a) = 27,5036  squared units

Answer:

miss him :(

Step-by-step explanation:

Answer:

:( RIP

Step-by-step explanation:

Answer:

$352.48

Step-by-step explanation:

500 = P(1+6/100)^6

500 = P(1.141851912)

P = 500 / 1.1418519112 = 352.48

Answer:

The radius of a cone is [tex]\dfrac{3}{\sqrt{\pi} }\ \text{units}[/tex].

Step-by-step explanation:

The formula of the volume of a cone is given by :

[tex]V=\dfrac{1}{3}\pi r^2 h[/tex]

r is radius of cone

h is height of cone

We have,

Volume of a cone is 3x cubic units and height is x units. Putting the values of volume and height such that,

[tex]r=\sqrt{\dfrac{3V}{\pi h}}\\\\r=\sqrt{\dfrac{3\times 3x}{\pi x}} \\\\r=\sqrt{\dfrac{3\times 3}{\pi}}\\\\r=\sqrt{\dfrac{9}{\pi}}\\\\r=\dfrac{3}{\sqrt{\pi} }\ \text{units}[/tex]

So, the radius of a cone is [tex]\dfrac{3}{\sqrt{\pi} }\ \text{units}[/tex].

Answer:

C. $290

Step-by-step explanation:

The expected cost is:

E = 1686.50 − (0.057) (24500)

E = 290

Answer:

Answers are below

Step-by-step explanation:

Percent means "out of 100" so 35% is 35/100. We can simplify this fraction by dividing the numerator and denominator by 5. 35/100 / 5 = 7/20.

7/20 multiply the numerator and denominator by 5.

7/20 x 5 = 35/100

If this answer is correct, please make me Brainliest!

Answer:

b and c

Step-by-step explanation:

Answer:9/4

Step-by-step explanation:

3/4 + (1/3/1/6) - (1/2)

3/4 + (1/3 ➗ 1/6) - 1/2

3/4 + (1/3 x 6/1) - 1/2

3/4 + ((1x6)/(3x1)) - 1/2

3/4 + (6/3) - 1/2

3/4 + 2 - 1/2

(3+8-2)/4

9/4

Answer:

[tex]z=\frac{46300-50000}{\frac{9800}{\sqrt{28}}}=-1.998[/tex]  

Now we can calculate the p value using the alternative hypothesis with this probability:

[tex]p_v =P(z<-1.998)=0.0229[/tex]  

The p value for this case is significantly lower than the value of [tex]\alpha=0.05[/tex] so then we can reject the null hypothesis at this signficance level and we have enough evidence to conclude that the true mean for the deluxe tire is less than 50000 and the claim is not correct.

Step-by-step explanation:

Information given

[tex]\bar X=46300[/tex] represent the sample mean for the lifespans

[tex]\sigma=9800[/tex] represent the population standard deviation

[tex]n=28[/tex] sample size  

[tex]\mu_o =50000[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

z would represent the statistic    

[tex]p_v[/tex] represent the p value

System of hypothesis

The idea for this case is verify if the deluxe tire averages at least 50,000, so then the system of hypothesis are:

Null hypothesis:[tex]\mu \geq 50000[/tex]  

Alternative hypothesis:[tex]\mu < 50000[/tex]  

We know the population deviation so then the correct test stattistic would be:

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{46300-50000}{\frac{9800}{\sqrt{28}}}=-1.998[/tex]  

Now we can calculate the p value using the alternative hypothesis with this probability:

[tex]p_v =P(z<-1.998)=0.0229[/tex]  

The p value for this case is significantly lower than the value of [tex]\alpha=0.05[/tex] so then we can reject the null hypothesis at this signficance level and we have enough evidence to conclude that the true mean for the deluxe tire is less than 50000 and the claim is not correct.

Answer:

$675.00

Step-by-step explanation:

4500 x 0.05 x 3 = 675

Answer:23.55

Step-by-step explanation:

radius=r=5

Φ=360-90

Φ=270

π=3.14

Length of arc=Φ/360 x 2 x π x r

length of arc=270/360 x 2 x 3.14 x 5

Length of arc=0.75 x 2 x 3.14 x 5

Length of arc=23.55

Answer:

23.55 units

Step-by-step explanation:

Hope this helps!

Answer:

Step-by-step explanation:

A= 2(5*2) + 2(1*4) + (3*5) + 2(2*3) + (1*3) + (4*3) + (6*3) = 88 cm^2

Answer:

0.1875 and 0.12

Step-by-step explanation:

3/4x1/4 is 0.1875. 3/5 x 1/5 is 0.12

Answer:

1)0.1875

2)0.12

Step-by-step explanation:

Answer:

3/8

Step-by-step explanation:

add 5+1+3=9

and there is 3 cheese pizza so its 3 over 8.

Answer:

3/9

Step-by-step explanation:

Answer:

You move right 3, and down 7

Answer: a

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The appropriate test is a t-test for slope. The test statistic is t = 2.68 and the p-value is 0.005. Because the p-value, 0.005, is less than α=0.05 we have convincing evidence that there is a positive linear relationship between the amount of water received and how tall the sunflower plants grew.

Answer:

about 27.42

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

C. (2x+3)(x+5)

Step-by-step explanation:

We need to use FOIL for this

First

Outer

Inner

Last

Let's see the answers of our options:

A. (2x+1)(x+15) = 2x²+30x+x+15 = 2x²+31x+15

B. (2x+15)(x+1) = 2x²+2x+15x+15 = 2x²+17x+15

C. (2x+3)(x+5) = 2x²+10x+3x+15 = 2x²+13x+15

D. (2x+5)(x+3) = 2x²+6x+5x+15 = 2x²+11x+15

Only option C simplifies to 2x²+13x+15

Answer:

Brown house driveway; larger by 5 feet

Step-by-step explanation:

Lets convert yds to ft

We know 3 ft = 1yd

3*7 = 21

so 7yds = 21 ft

Add the 9 ft

7yds 9ft = 21+9 = 30 ft

The house with the 35 ft driveway is longer by (35-30)  or 5 ft

Answer:

The cost of the game is $7 .

Step-by-step explanation:

By looking at the graph, the line at x = 4 is equals to y = 7

Answer:

Step-by-step explanation:

Area of sector = angle/360 * pi * r^2

5.5pi = angle/360 * pi * 9

5.5 = angle/360 * 9

angle = (5.5 * 360)/9 = 40 * 5.5 = 220

Answer:

The p-value is 0.0013. He should reject the null in favor of the alternative.

Step-by-step explanation:

We are given that Members of a soccer team suspect the coin used for the coin toss at the beginning of their games is unfair. They believe it turns up tails less often than it should if it were fair.

The coach of the team decides to flip the coin 100 times and count the number of tails. His trial results in 35 tails.

Let p = proportion of occurrence of tail.

SO, Null Hypothesis, [tex]H_0[/tex] : p = 0.50     {means that it turns up tails equal to that it should if it were fair}

Alternate Hypothesis, [tex]H_A[/tex] : p < 0.50      {means that it turns up tails less often than it should if it were fair}

The test statistics that would be used here One-sample z-test for proportions;

                            T.S. =  [tex]\frac{\hat p-p}{\sqrt{\frac{ p(1-p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of tails occurrence = [tex]\frac{35}{100}[/tex] = 0.35

            n = sample of trails = 100

So, the test statistics  =  [tex]\frac{0.35-0.50}{\sqrt{\frac{0.50(1-0.50)}{100} } }[/tex]    

                                     =  -3

The value of z test statistics is -3.

Also, P-value of the test statistics is given by;

                P-value = P(Z < -3) = 1 - P(Z [tex]\leq[/tex] 3)

                              = 1 - 0.9987 = 0.0013

Since, the P-value of test statistic is less than the level of significance as 0.0013 < 0.01, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that it turns up tails less often than it should if it were fair.

Answer:

32

Step-by-step explanation:

Answer: 32

Step-by-step explanation:

Answer:

f(n) = f(n - 1) + 2(n - 1) for n [tex]\geq[/tex] 1

Step-by-step explanation:

Answer:   a

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

It would still be 10° because dilation doesn't change angles

Answer:

61%

Step-by-step explanation:

First we need to add the two numbers,38 and 23.Then we will get 61.To convert a number into a probability . we will have to take change the value.100 turns into 1 and 61 turns in to 0.61.Then to convert it into a percentage, which will give us our answer 61%.