If
\[x^2 - 7x + c = (x + a)^2\]for some constants $a$ and $c,$ then find $c.$

A number multiplied by 1 is the number itself. So,1 is a factor of every number.

1 is the factor of every number as one divides every number exactly, without leaving any remainder behind, and gives the quotient as the number itself.

1 is the greatest factor of itself and the smallest factor of any other number.

There are some properties of factors one:

To know more about common factors:

https://brainly.com/question/219464

#SPJ4

It takes 10 minutes for the two lines to have filled an equal number of barrels

Each line will have filled 90 barrels

Let “x” be the number of minutes

The old conveyer line has filled 20 barrels of paint, and is filling more at a rate of 7 barrels per minute

Thus, a equation is framed as follows:

Old conveyor: 20 + 7(number of minutes)

Old conveyor: 20 + 7x ------- eqn 1

A worker just switched on a newer line that can fill 9 barrels per minute

Thus, a equation is framed as follows:

New conveyor: 9(number of minutes)

New conveyor: 9x -------- eqn 2

In a little while, the two lines will have filled an equal number of barrels.

Thus, eqn 1 must be equal to eqn 2

Thus it takes 10 minutes for the two lines to have filled an equal number of barrels

Substitute x = 10 in any one of equations

Substitute in eqn 2

9x = 9(10) = 90

Thus each line will have filled 90 barrels

To learn more about number of barrels to refer:

https://brainly.com/question/17556725

#SPJ1

[tex]8 = c - - 3 \\ 8 = c + 3 \\ c = 8 - 3 \\ c = 5[/tex]

Answer:

it is c=5

Step-by-step explanation:

here is how you get the answer

8=c−−3

8=c+3

c=8−3

c=5

Check the picture below.

Answer:

Step-by-step explanation:

beaucoup pour votre aide !

Pour résoudre cette expression, nous allons appliquer la distributivité, c'est-à-dire multiplier chaque terme entre parenthèses par le nombre devant les parenthèses.

On commence par 4x + [3 - (7-x)], ce qui donne:

4x + (3 - 7 + x)

Ensuite, nous pouvons appliquer la distributivité à 4x-(x-2):

4x + (3 - 7 + x) - (4x - x + 2)

Enfin, nous pouvons réorganiser les termes pour simplifier l'expression:

4x + 3 - 7 + x - 4x + x - 2

En réarrangeant, nous obtenons:

-2 - 4 + 5x

Donc, l'expression complète est: -2 - 4 + 5x.

Answer:

Step-by-step explanation:

The two equations that have the solution x = 2 when x is substituted for 2 are:

Equation 1: 2 + 3x = 10

2 + 3(2) = 10

2 + 6 = 10

8 = 10

Equation 2: 2x + 4 = 10

2(2) + 4 = 10

4 + 4 = 10

8 = 10

3P=C-5 is the equation relating the number of carrots that Pio has compared to Claudine, Pio has 5 carrots when Claudine has 20 and  if pio has 10 then the number of carrots with Claudine are 35

Two or more expressions with an Equal sign is called as Equation.

Rustam has three times as many carrots as Pio

R=3P

Where  is Rustam, P is Pio and C is Claudine.

Rustam has 5 fewer carrots that Claudine.

R=C-5

3P=C-5 is the equation relating the number of carrots that Pio has compared to Claudine.

Now let us find the number of carrots Pio has when Claudine has 20

3P=20-5

3P=15

Divide both sides by 3

P=5

Pio has 5 carrots when  Claudine has 20.

Now if pio has 10 then the number of carrots with Claudine

3(10)=C-5

30+5=C

35=C

Hence, 3P=C-5 is the equation relating the number of carrots that Pio has compared to Claudine, Pio has 5 carrots when Claudine has 20 and  if pio has 10 then the number of carrots with Claudine are 35

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

The Cartesian product that I read about is a mathematical concept that is used to combine two sets together in a specific way. The Cartesian coordinate system, on the other hand, is a way of representing points in a two-dimensional plane using a set of numerical coordinates.

The relationship between the two is that the Cartesian product is used to create the set of all possible coordinates that can be used in the Cartesian coordinate system. The Cartesian product of two sets, say set A and set B, is the set of all ordered pairs (a, b) where a belongs to set A and b belongs to set B.

When we graph a point in the Cartesian coordinate system, we are picking a specific point from the set of all possible points that can be created using the Cartesian product of the set of x-coordinates and the set of y-coordinates.

In other words, the Cartesian product is the foundation of the Cartesian coordinate system. It provides a set of all possible points that can be graphed using that system.

To know more about cartesian products refer to:

brainly.com/question/29329368

#SPJ4

The length of segment $\overline{ab}$ is 12 + 4$[tex]\sqrt{11}[/tex]$ units.

What is right triangle ?

A right triangle is a type of triangle that has one angle that measures exactly 90 degrees, also known as a right angle. The side opposite the right angle is called the hypotenuse and it is the longest side of the triangle. The other two sides are called legs, and one of them is the base and the other one is the height.

We know that the medians are 6 and $2\sqrt{11}$ units, respectively.

Therefore, the length of $\overline{ab}$ is twice the median length from $a$ to segment $\overline{bc}$ + twice the median length from $b$ to segment $\overline{ac}$

so the length of $\overline{ab}$ = 2(6) + 2($2[tex]\sqrt{11}[/tex]$) = 12 + 4$\sqrt{11}$

so the length of $\overline{ab}$ = 12 + 4$[tex]\sqrt{11}[/tex]$ units.

Hence , The length of segment $\overline{ab}$ is 12 + 4$[tex]\sqrt{11}[/tex]$ units.

To learn more about right triangle visit : brainly.com/question/29285631

#SPJ4

Answer:540

Step-by-step explanation:

Answer:

540

Step-by-step explanation:

When multiplying two numbers and one is a decimal you multiply both of them by 10 to keep whole number denominators.

[tex]\frac{324}{0.6}[/tex]

[tex]10* \frac{324}{0.6}[/tex]

[tex]\frac{3240}{6}[/tex]

[tex]\frac{3240}{6} = 540[/tex]

Answer:

1. 37, 44, 51

2. 24, 19, 14

3. 36, 49, 64

Step-by-step explanation:

The first rule is add 7

The second rule is subtract 5

The third rule is add 2 to every difference

Answer:

Nicholas has 5 boys, and Paul has 1 boy

Step-by-step explanation:

We will use 3 different variables, p, j, and n. Along with this, if there is a subscript on a variable, it will be either b or g, meaning boy or girl. If there is no subscript, it means both genders. We will start by translating our sentences into linear equations, giving us:

[tex]p + j + n = 15[/tex]              (1st Equation)

[tex]p_{g} = j_{b} = 3[/tex]              (2nd Equation)

[tex]j = p + 1 (p = 4)[/tex]              (3rd Equation)

[tex]n_{b} = n_{g} +4[/tex]              (4th Equation)

[tex]n_{g} = p_{b}[/tex]              (5th Equation)

Whew! That was a lot.  We know that Paul has 4 children, which means Johnson has 5 children. Which means Nicolas has 6 children. We know that Paul's girl count is 3 (second equation), meaning that 4 - 3 = Paul has 1 boy. Then, we know that Nicholas has:

b = g + 4 and b + g = 6

So, we substitute the first equation into the second equation, giving us:

g + 4 + g = 6

2g = 2

g = 1

So, Nicholas has one girl, meaning he has 5 boys.

So, Nicholas has 5 boys, and Paul has 1 boy.

Hope this helped!

The degree of the measure of the exterior angle is 141 3/7°.

the term exterior angle in triangle is defined as angles that are parallel to the inner angles of a polygon but lie on the outside of it

Here we know that A square and a regular heptagon are coplanar and share a common side AD.

And then here we need to find each of the interior angle of the regular heptagon.

As we all know that here we have to use the formula that gives the interior angle measure for a regular polygon with any number of sides is 180(n-2)/n where n is the number of sides.

According to the given formula here we have a regular heptagon's interior angle measures is calculated as

=> 180(7-2)/7 = 128 4/7.

Here we also know that the angle A and D would be 128 4/7 degrees.

Here the next step is to Find angle BAC.

For that here we have to know that a square's interior angle is 90 degrees and a heptagon's is 128 4/7 degrees.

Now we have to subtract those from 360 degrees to find angle BAC then we get the expression like the following,

=> Angle BAC = 360 - (angle A + 90)

=> 360 - (128 4/7 + 90)

When we simplify this one then we get the resulting value as,

=> 360 - 218 4/7 = 141 3/7 degree

To know more about angle here,

https://brainly.com/question/4316040

#SPJ4

The equation showing the total cost for purchasing x tickets is given as y = 12.5x + 7

An equation is a expression that shows the relationship between numbers and variables.

The standard form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Let y represent the total cost for x tickets.

From the table, using the points (2, 32) and (6, 82):

y - 32 = [(82 - 32)/(6 - 2)](x - 2)

y - 32 = 12.5(x - 2)

y = 12.5x + 7

The equation is given as y = 12.5x + 7

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

Step-by-step explanation:

Given that w=5 and x=9, we can substitute these values into the expression to find the value of the expression:

7w-x

= 7(5) - 9

= 35 - 9

= 26

So the value of the expression when w=5 and x=9 is 26

An answer option which distinguishes the element that needs to be adjusted on the chart in the following scenario is: C. x-axis value.

In an experiment, there are two (2) main types of variables and these include the following:

In Mathematics, an independent variable can be defined as the variable that is being manipulated by an experimenter or researcher. This ultimately implies that, an independent variable is typically considered to be the cause in an experiment and it is represented by the x-axis value on a graph.

In this scenario, we can reasonably infer and logically deduce that the independent variable (x-axis value) represents the element that should be adjusted on Donna's demographic chart on population growth.

Read more on independent variable here: brainly.com/question/82796

#SPJ1

The least positive integer value of x is 1

We can start by expressing the expression (2x)^2 2372x 37^2 as a multiple of 47.

47 | (2x)^2 2372x 37^2

Since 47 is a prime number, we can use the property that a multiple of a prime number is a number that can be divided by that prime number without leaving a remainder.

So, we need to find the least positive integer value of x such that (2x)^2 2372x 37^2 is divisible by 47.

We can start by assuming (2x)^2 2372x 37^2 as (2x)^2 2372x 37^2 = 47*k, where k is any integer.

We can start testing values of x starting from 1,

x=1 : (21)^2 * 23721 * 37^2 = 4 * 74 * 1369 = 47 * 2028,

x=2 : (22)^2 * 23722 * 37^2 = 16 * 148 * 1369 = 47 * 6912,

and so on.

So the least positive integer value of x such that (2x)^2 2372x 37^2 is a multiple of 47 is x=1.

To learn more about trigonometry visit: brainly.com/question/29002217

#SPJ4

The solution to the given system is (2, 3, 5). This can be determined by solving the system of equations using elimination.

First, add the first equation to the second equation to eliminate the y-term:

5x + z = 7

Next, add the third equation to the first equation to eliminate the x-term:

3y + z = 3

Finally, substitute the expression for z into the expression for x and solve for y:

y = 3

Now that we have the values for x and y, substitute them into one of the original equations to solve for z:

2(2) - 3(3) + z = 0

z = 5

The solution is (2, 3, 5).

Answer:

Step-by-step explanation:

The correct answer is: 4x4 + 8x2y2 – 3x3y – 7xy3. This is the standard form for the polynomial, where the terms are written in descending order. The terms in this polynomial are the 4x4 term, the 8x2y2 term, the -3x3y term, and the -7xy3 term.

The bacteria count after 5 hours, given the initial bacteria count and the rate that the bacteria are disappearing is 59 bacteria

First, find the rate at which the bacteria are disappearing from the culture dish every hour. This rate is:

= 100 % - 90 %

= 10 %

This means that every hour, 10% of the bacteria are removed from the culture dish on account of the antibiotic.

In five hours therefore, the bacteria count on the culture dish would be:

= Starting number of bacteria x ( 1 - rate of decrease per hour) ^ number of hours

= 100 x ( 1 - 10 %) ⁵

= 100 x 90 %⁵

= 59 bacteria

In conclusion, after 5 hours of the antibiotic working on the culture dish, the number of bacteria left would be 59 bacteria.

Find out more on bacteria count at https://brainly.com/question/27176993

#SPJ1

Answer: B. [tex]x^{2} - 16x + 64 = -21 + 64[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

The dimensions of the garden will be 4m by 3m. To determine the dimensions of the garden, we need to use the formula A = l x w, where A is the area of the garden (12m), l is the length of the garden and w is the width of the garden.

We can then rearrange the formula to solve for either l or w. We can rearrange the formula to solve for l by dividing both sides of the equation by w: A/w = l.

We know that the area is 12m, so we can substitute 12m for A in the equation. We need to find the dimensions that use the least amount of fencing, so let's set w equal to 3m. We can then substitute 3m for w in the equation and solve for l: 12m/3m = 4m.

Therefore, the dimensions of the garden are 4m by 3m.

(i × j) × k = 0, is the vector, not with determinants, but by using properties of cross products.

The procedure for multiplying two vectors is called the cross product of the two vectors. The sign(×) of multiplication between two vectors indicates a cross product. It is a three-dimensional system-defined binary vector operation.

A cross product in three dimensions is a binary operation on two vectors. It generates a vector that is parallel to both vectors. A and B together form a vector product, which is represented by the symbol a b. The vector that results from it is parallel to both a and b. Cross products and vector products are similar terms.

As we know,

i × j = | i | × | j | × sin 90° × k

or, i × j = 1 × 1 × 1 × k

or, i × j = k

thus,  (i × j) × k = k × k

or,  (i × j) × k = 0

To know more about cross products refer to:

https://brainly.com/question/29178479

#SPJ4

function f(x) is said to be discontinuous at a point ‘a’ of its domain D if it is not continuous there. The point ‘a’ is then called a point of discontinuity of the function.

he function of the graph which is not connected with each other is known as a discontinuous function.

A function f(x) is said to have a discontinuity of the first kind at x = a,

if the left-hand limit of f(x) and right-hand limit of f(x) both exist but are not equal.

f(x) is said to have a discontinuity of the first kind from the left at x = a,

if the left hand of the function exists but not equal to f(a)

There are three types of discontinuity.

Jump Discontinuity

Infinite Discontinuity

Removable Discontinuity

To know more about Discontinuity visit brainly.com/question/28783981

#SPJ4

The total amount in an account to the nearest cent after 3 years if the interest is compounded annually on an investment of $5600 at 7.65% is $6,986.02

To find the total amount in the account after 3 years, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the total amount, P is the initial investment (principal), r is the annual interest rate (expressed as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $5600, r = 0.0765, n = 1 (because the interest is compounded annually), and t = 3. Plugging these values into the formula gives:

A = 5600(1 + 0.0765)^3

A = $6,986.02

So, the total amount in the account after 3 years, to the nearest cent, would be $6,986.02

To know more on compound interest

https://brainly.com/question/13155407

#SPJ4

The probability that Susan will select 3 "good" eggs are 8C3*3/4 and the probability that Susan will select at least one "bad" egg. is 8C1*1/4

Probability is a measure of how likely something is to occur. Calculating probability involves dividing the total number of outcomes by the number of possible ways an event may occur.

The probability is equal to the variety of possible outcomes. the total number of outcomes that might occur. For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of flipping a coin and receiving heads is 1 in 2. (a head or tail). Writing P(heads) = 12

Hence,

The probability that Susan will select 3 "good" eggs are 8C3*3/4 and the probability that Susan will select at least one "bad" egg. is 8C1*1/4

To learn more about probability, click the following link:-

https://brainly.com/question/24756209

#SPJ1

Answer:

1÷(5/2×(2×(8-2/5)-1))

1÷(5/2×(2×(6/5)-1))

1÷(5/2×(12/5-1))

1÷(5/2×7/5)

1÷(35/10)

1÷35/10

1×10/35

10/35

2/7

Answer: 16.8

Step-by-step explanation:

[tex]\frac{5.8}{r}=\tan 19^{\circ}\\\\\frac{r}{5.8}=\frac{1}{\tan 19^{\circ}}\\\\r=\frac{5.8}{\tan 19^{\circ}}}\\\\r \approx 16.8[/tex]