How many solutions are there to the equation below?
8(x-3) = 7x- 20

Answer:

[tex]c < 4[/tex]

Step-by-step explanation:

Move the constant to the right-hand side and change its signs:

[tex]c < 16 - 12[/tex]

Subtract the numbers:

[tex]c < 16 - 12 = c < 4[/tex]

Answer:

4c^2+7c-5=0

4c^2+7c=5

4c^2+7c=5

4c^2+7c-5=0\quad :\quad c=\frac{-7+\sqrt{129}}{8},\:c=\frac{-7-\sqrt{129}}{8}\quad \left(\mathrm{Decimal}:\quad c=0.54472\dots ,\:c=-2.29472\dots \right)

Hope This Helps!!!

Answer:

C) c = -7 ± √129 / 8

Step-by-step explanation:

x = (-b ± √ (b² – 4ac) ) / 2a

[quadratic formula]

where ax² + bx + c = 0.

[quadratic / square trinomial]

given 4c² + 7c – 5 = 0,

↓ ↓ ↓

a b c

where c = x,

c = (-b ± √ (b² – 4ac) ) / 2a.

c = (-(7) ± √ ((7)² – (4)(4)(-5)) ) / 2(4)

c = (-7 ± √ (49 – (-80)) ) / 8

c = (-7 ± √ (129) ) / 8

c = -7 ± √129 / 8

domain is  (- infinity, infinity)

range is (- infinity, infinity)

Answer:

4√2 and 5+4√2

Step-by-step explanation:

Let the two numbers be x ad y

Smaller = y

Bigger = x

If a positive real number is 5 more than another, then;

x = 5 + y ... 1

When - 10 times the smaller is added to the square of the larger, the result is 57, then;

-10y + x² = 57 ...2

Substitute 1 into 2;

-10y + (5+y)² = 57

-10y + 25+10y+y² = 57  

y²+25 = 57

y² = 57 - 25

y² = 32

y = √32

y = 4√2

Since x = 5 + y

x = 5 + 4√2

Hence rhe numbers are 4√2 and 5+4√2

Answer:

a) 0.0171 fluid ounces.

b) 0% probability that the average fill volume of 22 bags is below 5.95 ounces

c) The mean should be of 6.153 fluid ounces.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, we get the probability that the value of the measure is greater than X.

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.

Standard deviation of 0.08 fluid ounces.

This means that [tex]\sigma = 0.08[/tex]

(a)What is the standard deviation of the average fill volume of 22 bags?

This is s when n = 22. So

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

[tex]s = \frac{0.08}{\sqrt{22}}[/tex]

[tex]s = 0.0171[/tex]

(b)The mean fill volume of the machine is 6.16 ounces, what is the probability that the average fill volume of 22 bags is below 5.95 ounces?

We have that [tex]\mu = 6.16[/tex]. The probability is the p-value of Z when X = 5.95. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{5.95 - 6.16}{0.0171}[/tex]

[tex]Z = -12.3[/tex]

[tex]Z = -12.3[/tex] has a p-value of 0.

0% probability that the average fill volume of 22 bags is below 5.95 ounces.

(c)What should the mean fill volume equal in order that the probability that the average of 22 bags is below 6.1 ounces is 0.001?

[tex]X = 6.1[/tex] should mean that Z has a p-value of 0.001, so Z = -3.09. Thus

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]-3.09 = \frac{6.1 - \mu}{0.0171}[/tex]

[tex]6.1 - \mu = -3.09*0.0171[/tex]

[tex]\mu = 6.153[/tex]

The mean should be of 6.153 fluid ounces.

Answer:

Step-by-step explanation:Bó tay

Answer:

5/6 + 11/6 = 16/ 6

Step-by-step explanation:

Distance between any Teo labeled tick marks =

(1 - 2/3) / 2 = 1/3 ÷ 2 = 1/3 * 1/2 = 1/6

From the left :

2/3 + 1/6 = 5/6

5/3 + 1/6 = 11/6

5/6 + 11/6 = (5 + 11) / 6 = 16/6

5/6 + 11/6 = 16/ 6

Answer:

Step-by-step explanation:

Answer:

B) $85,167

Step-by-step explanation:

u got discount 45% so u just have to pay 55% of it

cost = 55% x $154,85 = $85,1675

Answer:

DE = 24

Step-by-step explanation:

The midsegment DE is half the length of the third side AC , that is

DE = [tex]\frac{1}{2}[/tex] AC = [tex]\frac{1}{2}[/tex] × 48 = 24

Answer:

The answer for thid equation is x = -5/3

Answer:

x = [tex]\frac{1}{3}[/tex]   y = -1

Step-by-step explanation:

x = 0 to solve for y

[tex]y=3x-1[/tex]

[tex]y=3(0)-1[/tex]

[tex]y=-1[/tex]

y = 0 to solve for x

[tex]y=3x-1[/tex]

[tex]0=3x-1[/tex]

Add 1 to both sides

[tex]1=3x[/tex]

Divide by 3 to isolate x

[tex]\frac{1}{3} =x[/tex]

The values of variables, such as the height of the table can be found by writing equations of their relationships

The height of the table is 105 cm

The reason the above height value is correct is as follows;

Known parameters:

The diagram shows a table, a cat and a mice

Let x, represent the height of the table, let y represent the height of the cat, and let z represent the height of the mice

From the given diagram, we have;

Height of the table + Height of the cat - Height of the mice  = 120 cm

∴ x + y - z = 120...(1)

Height of the table + Height of the mice - Height of the cat   = 90 cm

∴ x + z - y = 90...(2)

Adding equation (1) to equation (2) gives;

x + y - z + (x + z - y) = 120 + 90 = 210

x + y - z + (x + z - y) = 210

However;

x + y - z + (x + z - y) = x + x + y - y - z + z = 2·x

∴ x + y - z + (x + z - y) = 2·x = 210

x = 210/2 = 105

Therefore;

The height of the table, x = 105 cm

Learn more about word problems leading on simultaneous equations here:

https://brainly.com/question/16513646

Answer:

10

Step-by-step explanation:

Total pizza topped with pepperoni, sausage or pepperoni and sausage = 33

Number of pizzas with pepperoni = 29

Number of pizzas with pepperoni and sausage = 15

Pizza with pepperoni only = 29 - 15 = 14

Pizza with sausage only = 33 - 29 = 4

Pepperoni only than sausage only :

14 - 4 = 10

Answer:

6

Step-by-step explanation:

The product of three consecutive numbers is divisible by ​6

Let us say the numbers are x, x+1 , x+2

if x = 1,

Product of the three consecutive numbers,

(1)(2)(3)

=> 6, which is divisible by 6

if x = 2,

Product of the three consecutive numbers,

(2)(3)(4)

=> 24, which is divisible by 6

Similarly if we take any 3 consecutive numbers their product will be divisible by 6.

Answer:

Y= -x^2+12x-36

Step-by-step explanation:

Answer:

C. -2x +3y-6=0

this is the answer

Answer:

Yes, because they are identical to eachother

Step-by-step explanation:

The statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.

a quadrilateral is a four-sided polygon, having four edges and four corners.

DEFG is a parallelogram.

A parallelogram is a simple quadrilateral with two pairs of parallel sides.

The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

DF=FG is a true statement.

The diagonal passing through a parallelogram are equal in length.

EF=DG is a true statement

The opposite sides of a parallelogram are equal.

∠DEG ≅ ∠FGE are congruent angles.

Because the opposite angles of a triangle are equal in meausure.

Hence, the statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.

To learn more on Quadrilateral click:

https://brainly.com/question/29934440

#SPJ2

Answer:

split the other three in half

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

We can find the slope using the slope formula

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

    = ( -2 - -2)/(2 - -6)

   = (-2+2)/(2 +6)

    = 0/8

   = 0

Answer:

Slope is 0

Step-by-step explanation:

Slope formula is (y2-y1)/(x2-x1)

-2 - (-2)/2 - (-6)

0/8

0

Answer:

She bought 7 coach tickets and 7 first class tickets.

Step-by-step explanation:

1. Set the equations up using y to represent first class and x to represent coach:

x + y = 14

370x + 1140y = 10,570

2. Use a graphing calculator to graph the equations and find the point where they intersect.  The intersection point will tell you the number bought:

Answer:

Sarah bought y = 8 first class tickets.

Step-by-step explanation:

You can set up a system of equations for this problem. Let x = number of coach tickets and y = number of first class tickets. Then:

330x + 1220y = 12730    (cost of coach tickets plus cost of first class tickets is total budget)

x + y = 17    (number of coach tickets plus number of first class tickets is total number of people)

Solve the second equation for y to get y = 17 - x, then plug that into the first equation and solve for x:

330x + 1220(17 - x) = 12730

330x + 20740 - 1220x = 12730

-890x + 20740 = 12730

-890x = -8010

x = 9

 Sarah bought x = 9 coach tickets. Plug that into the second equation and solve for y:

9 + y = 17

y = 8

Sarah bought y = 8 first class tickets.

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

120 times

Step-by-step explanation:

On a dice, there are 6 sides.

Since one of these sides is a 5, the chance of rolling a five is 1/6.

Find how many times Malachy can expect to roll a five by multiplying 720 by 1/6:

720(1/6)

= 120

So, Malachy can expect to roll a five 120 times

Answer:

Uuuzu7ggijjrudidjdiwisiwiwieie

Answer:

.60 + .40 + 3.00 = 4.00

Step-by-step explanation:

Answer:

$ 4

Step-by-step explanation:

six dimes (.10 each) = .60

8 nickels (.05 each)= .40

3 dollars (1.00 each) = 3.

Add together

Answer:

h=A-πr²÷2πr

Step-by-step explanation:

Making h subject

A=2πrh+πr²

A-πr²=2πrh

A-πr²÷2πr=h

h=A-πr²÷2πr

Answer:

The answer is [tex]h=\frac{A+-\pi r^{2} }{2\pi r}[/tex].

Step-by-step explanation:

To solve for (h), start by subtracting ([tex]\pi r^{2}[/tex]) from both sides, and the equation will look like [tex]A-\pi r^{2}= 2\pi rh+\pi r^2-\pi r^2[/tex]. The next step is to simplify the equation, which will look like [tex]A-\pi r^{2} =2\pi rh[/tex].

Next, divide both sides of the equation by [tex]2\pi r[/tex], and it will look like [tex]\frac{A-\pi r^{2} }{2\pi r} =\frac{2\pi rh}{2\pi r}[/tex]. Finally, simplify the equation, and the answer will be [tex]h=\frac{A+-\pi r^{2} }{2\pi r}[/tex].

Answer:

y = -4x+14

Step-by-step explanation:

First find the slope

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

m = (2-10)/(3-1)

   =-8/2

   = -4

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = -4x+b

Substitute a point into the equation

10 = -4(1)+b

Add 4 to each side

14 = b

y = -4x+14

Answer:

A dilation by a factor of three about Point T followed by a translation of two units downwards.

Step-by-step explanation:

When transforming functions, we will reflect/dilate the figure first and then translate it. This is directly from the order of operations.

Since we are trying to determine the transformation that was performed, we can try to map ΔS'T'U' onto ΔSTU. We can start by translating the figure and then determining any reflections/dilations.

First, we can translate ΔS'T'U' up two units to map T' onto T. This is represented by the black triangle in the image below. Let the black triangle be ΔS''T''U''. (T'' and T are the same point.)

Next, notice that from Point T'' to U'', we move nine units right and six units up.

From Point T to Point U, we move three units right and two units up.

Likewise, from Point T'' to S'', we move six units left and nine units up.

From Point T to Point S, we move two units left and three units up.

Therefore, to map ΔS''T''U'' onto ΔSTU, we dilate ΔS''T''U'' about Point T by a factor of 1/3.

Hence, by reversing the transformations, to acquire ΔS'T'U', we can see that we will dilate ΔSTU by a factor of three about Point T and then a perform a translation of two units downwards.

Answer: c<2

Step-by-step explanation:

-6c<-12

c<-12/-6

c<2