Mr. John has $800 to be shared in the ratio of 5:3 what amount would each receive
​

Answer:

x=50°

Angle at A=108°

Step-by-step explanation:

If the triangle ABC is isosceles,then <ABC=<ACB=65°

We can now use angle properties to find <BAC

<BAC+65+65=180°

<BAC=180°-130=50°

Since line AB and CD are parallel,line AC is a transversal line which means <BAC=<ACD=x=50°

Therefore x=50°

For the parallelogram,

opposite interior angles are equal so <BAD=<BCD and <ABC=<ADC

3x+3x+2x+2x=360°

10x=360°

x=360°/10=36°

The angle at a=3x=3×36°=108°

Answer:

3. The vertex form of the function, f(x) = x² - 4·x - 17 is f(x) = (x - 2)² - 21

4. The solutions are, x = -2 + √10 and x = -2 - √10

5. The quadratic equation with vertex (3, 1) and a = 1 in standard form is given as follows;

f(x) = x² - 6·x + 10

Step-by-step explanation:

3. The function given in standard form is f(x) = x² - 4·x - 17, which is the form, f(x) = a·x² + b·x + c

The vertex form of the of a quadratic function can be presented based on the above standard form as follows;

f(x) = a(x - h)² + k

Where;

(h, k) = The coordinate of the vertex

h = -b/2a

k = f(h)

Comparing with the given equation, we have;

f(x) = a·x² + b·x + c = x² - 4·x - 17

a = 1

b = -4

c = -17

∴ h = -(-4)/(2 × 1) = 2

h = 2

k = f(h) = f(2) = 2² - 4 × 2 - 17 = -21

k = -21

The vertex form of the function, f(x) = x² - 4·x - 17 is therefore, given as follows;

f(x) = (x - 2)² - 21

4. The given equation for which we need to solve by completing the square is 2·x² + 8·x = 12

Dividing the given equation by 2 gives;

x² + 4·x = 6

Which is of the form, x² + b·x = c

Where;

a = 1

b = 4

c = 6

From which we add (b/2)² to both sides to get x² + b·x + (b/2)² = c + (b/2)²

Adding (b/2)² = (4/2)² to both sides of x² + 4·x = 6 gives;

x² + 4·x + 4 = 6 + 4

(x + 2)² = 10

x + 2 = ±√10

x = -2 ± √10

The solution are, x = -2 + √10 and x = -2 - √10

5. Given that the value of the vertex = (3, 1), and a = 1, we have;

The vertex, (h, k) = (3, 1)

h = 3, k = 1

Therefore, h = 3 = -b/(2 × a) = -b/(2 × 1)

∴ -b = 2 × 3 = 6

b = -6

k = f(h) = a·h² + b·h + c, by substitution, we have;

k = f(3) = 1 × 3² + (-6) × 3 + c = 1

∴ c = 1 - (1 × 3² + (-6) × 3) = 10

c = 10

The quadratic equation with vertex (3, 1) and a = 1 in standard form, f(x) a·x² + b·x + c is therefor;

f(x) = x² - 6·x + 10

Answer:

45

Step-by-step explanation:

Answer:

M(3.5 , 3.5)

J(3.5 , 14)

K(21 , 14)

L(21 , 3.5)

Step-by-step explanation:

M(1,1)

J(1,4)

K(6,4)

L(6,1)

multiply the coordinates by the scale factor of 3.5

M(3.5 , 3.5)

J(3.5 , 14)

K(21 , 14)

L(21 , 3.5)

Answer:

10 oz.

Step-by-step explanation:

There are 16 oz in 1 lb. So for the 10 lb. cake there is a total of 160 oz to start. If the cake is cut in half and then in 8 pieces. There will be a total of 16 pieces.

10 lb/whole cake

= 160 oz/2 halves

= 160 oz/16 slices

= 10 oz/slice

Each slice of icecream cake is 10 oz.

Answer:

x = -5 and y = 3

Step-by-step explanation:

There are two equations :

3x − 2y = −21 ....(1)

2x + 5y = 5 ......(2)

Multiply equation (1) by 2 and equation (2) by 3.

6x - 4y = -42 ...(3)

6x + 15y = 15 ....(4)

Subtract equation (4) from (3) :

6x - 4y - (6x + 15y) = -42 -15

-4y -15y = -57

-19y = -57

y = 3

Put y = 3 in equation (2) :

2x + 5(3) = 5

2x = 5-15

2x = -10

x = -5

So, the value of x is (-5) and y = 3.

Answer:

t = -3

Step-by-step explanation:

Simplify  7+4t+5t+177+4t+5t+17  to  24+9t24+9t.

24+9t=t

24+9t=t

2 Subtract 9t9t from both sides.

24=t-9t

24=t−9t

3 Simplify  t-9tt−9t  to  -8t−8t.

24=-8t

24=−8t

4 Divide both sides by -8−8.

-\frac{24}{8}=t

−

8

24

​

=t

5 Simplify  \frac{24}{8}

8

24

​

  to  33.

-3=t

−3=t

6 Switch sides.

t=-3

t=−3

−24x+16

Hope this helps!

Answer:

-24× + 16

Step-by-step explanation:

hope this helps :D

Based on the single letter that Peter picks and the single digit, the expected value in one turn for Star One is $-0.296262

First, find the probability that Peter picks the correct letter and the correct digit:
= Probability of picking letter x Probability of picking digit

= 1/26 x 1/10

= 0.3846%

The expected value per turn for Star One s:

= (0.3846% x 700) + ( (1 - 0. 3846%) x -3)

= $-0.296262

In conclusion, the expected value for a turn of Star One is $-0.296262.

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[tex]b-2<5\\b<5+2\\b<7[/tex]

Therefore, the answer is b < 7.

Answer: The measure of angle 1 is equaled to 20

Step-by-step explanation:

4x= 80 (You divide 80 by 4, which is 20), so the measure of angle 1 is 20.

Answer:

y = 5

Step-by-step explanation:

when the slope of a line is 0 because it does not incline

it is y = wherever the y value is

so in this case

it is

y = 5

Answer:

0.5 minutes

Step-by-step explanation:

Since we are provided the equation and the current height of the candle (which would be 25 inches) we can simply replace this current height with the variable h and then solve the rest of the equation to find out the value of m when the height of the candle is at 25 inches.

h = 32−14m

25 = 32−14m ... subtract both sides by 32

-7 = -14m ... divide both sides by -14

0.5 = m

Finally, we can see that after 0.5 minutes the candle would have melted down to 25 inches.

Answer:

self replicate

cloning site

lower molecular weight

selectable marker gene

Answer:

A. magnitude of 8 and direction angle equal to 0 degrees

Step-by-step explanation:

EDGE 2020

Answer:

The volume of the box is

V(x) = 4x^3 -72x^2+320x

Step-by-step explanation:

Here, we are interested in calculating the volume of the box

From what we can see, the shape of the box is a cuboid

Mathematically, the volume of a cuboid is l * b * h

Thus, what we have will be;

x * 20-2x * 16-2x

= x ( 20(16-2x) -2x(16-2x))

= x(320-40x-32x + 4x ^2)

= x(320-72x+4x^2)

= 320x-72x^2 + 4x^3

the volume v(x) will be;

V(x) = 4x^3 -72x^2+320x

Answer:

yes its linear

Step-by-step explanation:

Answer:

AC=44

Step-by-step explanation:

Two triangles are congruent

So the equation is

3z+17=6z-10

6z-3z=17+10

3z=27

z=9

So AC =

6.9-10

54-10

44

Answer:

9 cups of yellow paint

Step-by-step explanation:

A mixture of paint calls for 1/3 cups of red paint and 3/4 cups of yellow paint.

From the above question

1/3 cups of red paint = 3/4 cups of yellow paint

1 cup of red paint = x cups of yellow paint

Cross Multiply

1/3 × x = 3/4 × 1

x = 3/4 ÷ 1/3

x = 3/4 × 3/1

x = 9/4

x = 2 1/4 cups of yellow paint

Hence, 1 cups of red paint requires 2 1/4 cups of yellow paint

If there were 4 cups of red paint added to the mixture, how many cups of yellow paint would need to be added to keep a constant rate of proportionality?

1 cups of red paint = 2 1/4 cups of yellow paint

4 cups of red paint = x cups of yellow paint

Cross Multiply

x cups of yellow paint = 4 × 2 1/4 cups of yellow paint

= 4 × 9/4 cups of yellow paint

= 9 cups of yellow paint

Therefore, 4 cups of red paint requires 9 cups of yellow paint

The required surface area would be A= 2πr² + 710/r which represents area A as a function of its radius r, where r is measured in centimeters.

The can's surface area A and volume V are determined by the equation if the container has a radius of r and a height of h.

A= 2πr² + 2πrh and V = πr²h

The volume V of a 12 oz cola can is 355 cm³

Given that cola can is approximately cylindrical.

V = πr²h = 355 cm³

h = 355 / πr²

Substitute the value of h in the can's surface area A, we get

A= 2πr² + 2πr(355 / πr²)

A= 2πr² + 2(355/r)

A= 2πr² + 710/r

Therefore, the required surface area would be A= 2πr² + 710/r which represents area A as a function of its radius r, where r is measured in centimeters.

Learn more about the volume of cylinder here :

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Answer:

9.

Step-by-step explanation:

The top triangle is half in measurements then the bottom

Answer:

D. .................... . . . . . . . . . . . . .... . . . . . . . . .

Answer:

answer D 4.500..........