Solve the quadratic equation
X^2+3x-70=0

Its pair factors are (1, 24), (2, 12), (3, 8), and (4, 6). The prime factorization of 24 gives 2 x 2 x 2 x 3 = 23 x 3, where 2 and 3 are the prime factors of 24. The sum of factors of 24 is 60. The correct answer is 24 = 2³×3

So, the prime factorization of 24 are 2 × 2 × 2 × 3 or 23 × 3, where 2 and 3 are the prime numbers. Learn more about factors and prime factors here with us in BYJU’S and also download BYJU’S – The Learning App for a better experience. What are the factors of 24? Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

There are many ways to factorization 24 but we have to pick one:

There is a picture of what the solution is to factorization of 24.

Therefore, the correct answer is 24 = 2³×3

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Therefore , the solution of the given problem of inequality comes out to be graph 2 shows the solution for this system.

In mathematics, an inequality is a linear connection or a collection of numbers even when there is no equal sign. Equity always comes after equilibrium. When two numbers are not equal, inequality exists. Between equality and inequality, there exist differences. The most common symbol was chosen because when parameters aren't the same or comparable (). Values can be compared using a variety of disparities, no matter how few or numerous they are.

Here,

Given :

=> x + y ≥ 5

and

=> - 3x + 2y ≤-2

So,

=> x ≥ 5- y

=> - 3(5- y) + 2y ≤-2

=> -15 + 3y + 2y ≤-2

=> 5y ≤ 13

=> y  ≤  13/5

and

=> x ≥ 5-  13/5

=>  x ≥  12/5

Therefore , the solution of the given problem of inequality comes out to be graph 2 shows the solution for this system.

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Answer:

X=10%

Y=30%

Step-by-step explanation:

The required percentages X and Y of copper and zinc in alloy A are given as 10% and 13.34%.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Percentage of copper in A = 1/2 [percentage of copper in ingot]
                                         = 1/2 × 20% = 10%

Percentage of zinc in A = 1/3 [percentage of zincin ingot]
                                    = 1/3 × 40% = 13.34%

Thus, the required percentages X and Y of copper and zinc in alloy A are given as 10% and 13.34%.

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The question seems to be incomplete,
Complete question.
Three specimens of Alloys A, B, and C containing copper and zinc are melted together to create an ingot containing 20% copper and 40% zinc. What are the percentages X and Y of copper and zinc in alloy A when copper is half of the copper in the ingot and zinc is 1/3 of the zinc in the ingot?

Without a coupon and paying $90 the customer was attended for 2 hours

When a customer with a coupon for 40% off the inspection fee pays $110 for a 4-hour repair the inspection fee is calculated

customer's pay =  (inspection fee * 40% off the inspection fee)  + charge per hour  * number of hours

40% off  means the customer paid 60% of the fees

let the inspection fee be x

110 = (x * 0.60)  + 20 * 4

110 = 0.6x + 80

110 - 80 = 4x

0.6x = 30

x = 50

a customer without a coupon

let the number of hours be y

customer's pay =  inspection fee + charge per hour  * number of hours

90 = 50 + 20 * y

90 = 50 + 20y

20y = 90 - 50

20y = 40

y = 2

the customer spent 2 hours

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The point that will be part of the linear regression line is (6,7).

The least-squares method is used to perform a linear regression on the given data points (6,7), (8,9), and (13,17). This method finds the line of best fit through the set of data points by minimizing the sum of the squares of the differences between the observed values and the predicted values from the line. To check whether a point is part of the regression line or not, we can substitute the x value of the point into the equation of the line and see if it gives the corresponding y value.

In this case, point (6,7) is part of the regression line because it satisfies the equation of the line.

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Triangle a is a shape that is formed by connecting three points.

Triangle is a geometric figure with three sides and three angles. It is one of the basic shapes in geometry. Triangles are either right, acute, or obtuse, depending on the size of each angle. The sum of the angles in a triangle is 180 degrees. Triangles can be classified into equilateral, isosceles, and scalene triangles, depending on the length of the sides. All three types of triangles have various applications in mathematics, physics and engineering.

In order to reflect triangle a in the x axis, triangle b must be a mirror image of triangle a. To achieve this, each point in triangle a must be reflected across the x axis. This is done by multiplying the y coordinate of each point in triangle a by -1. As a result, triangle b will have the same three points as triangle a, except that the y coordinates of each point in triangle b will be the opposite of what they are in triangle a.

After reflecting triangle a in the x axis to form triangle b, the next step is to rotate triangle b around the origin 90°. This can be achieved by finding the coordinates of each point in triangle b, then rotating each point around the origin. To do this, the x coordinates of each point in triangle b remain the same, while the y coordinates are multiplied by -1. As a result, triangle c will be formed as a 90° rotation of triangle b around the origin.

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The value of R when S = 13 and T = 63 is 4361.5

A variation is a relation between a set of values of one variable and a set of values of other variables.

If R varies directly with S and inversely with T . This statement is represented in the form:

R = KS/T.

K is called proportionality constant

When R = 45 ,S = 13 and T = 100, then K=

K = RT/S

K = 45×100/5

K = 4500/5= 900

When S = 13and T = 63, then

R = KT/S

R = 900× 63/13

R= 56700/13

R = 4361.5

Therefore when S = 13 and T = 63, the value of R is 4361.5

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Answer: The Midpoint of P and Q are (-0.5, -3.5)

Step-by-step explanation: To find the coordinates of the intersection points of the line and the curve, we can substitute the equation of the line into the equation of the curve and solve for x and y.

From the equation of the line: x - y = 3, we can see that y = x - 3

Substituting this into the equation of the curve:

3x^2 - (x-3)^2 + x(x-3) = 9

Now we can simplify and group

3x^2 - x^2 + 6x - 9 + x^2 - 3x = 9

3x^2 + 3x - 9 = 9

3x^2 + 3x = 18

3x(x+1) = 18

x(x+1) = 6

We can see that x = 2 and x = -3 are the solutions.

Substituting the x value back into the original equation of the line to find the y coordinate:

x = 2 => y = 2 - 3 => y = -1

x = -3 => y = -3 - 3 => y = -6

So the intersection points are (2,-1) and (-3,-6)

To find the midpoint of these two points, we take the average of their x and y coordinates:

x = (2 + -3) / 2 = -0.5

y = (-1 + -6) / 2 = -3.5

so the midpoint of the two intersection points is (-0.5, -3.5)

Answer:

Point, [tex](p,q)[/tex], is [tex](\frac{-1}{2} ,\frac{-7}{2} )[/tex].

Step-by-step explanation:

Given the equations  [tex]x-y=3[/tex]  and  [tex]3x^{2} -y^{2} +xy=9[/tex] . Find where they intersect and find the midpoint, [tex](p,q)[/tex], of the two intersection points. To find find points of intersection, you can either set up these equations as a system and solve algebraically or you can use a graphing calculator to graph the functions and see where they cross.

I will set up these equations as a system of equations,

[tex]\left \{ {{x-y=3} \atop {3x^{2} -y^{2} +xy=9}} \right.[/tex]

I will solve the top equation for [tex]x[/tex], and substitute it into the bottom.

[tex]x-y=3 = > x=3+y[/tex]

Now substitute [tex]x=3+y[/tex] for x into the bottom equation. Solve for y,

=> [tex]3x^{2} -y^{2} +xy=9[/tex]

=>[tex]3(3+y)^{2} -y^{2} +(3+y)y=9[/tex]

=> [tex]3(y^{2}+6y+9) -y^{2} +y^{2}+3y =9[/tex]

=>[tex]3y^{2}+18y+27 -y^{2} +y^{2}+3y =9[/tex]

=> [tex]3y^{2}+18y+27+3y =9[/tex]

=> [tex]3y^{2}+21y+27 =9[/tex]

=>[tex]\frac{3y^{2}+21y+27 =9}{3}[/tex]

=>[tex]y^{2}+7y+9 =3[/tex]

=>[tex]y^{2}+7y+6 =0[/tex]

=> [tex](y+1)(y+6)=0[/tex]

=>[tex]y=-1[/tex] or [tex]y=-6[/tex]

Now plug these values for [tex]y[/tex] into [tex]x=3+y[/tex].

When y=-1:

[tex]x=3+(-1)[/tex]

=> [tex]x=2[/tex]

When y=-6:

[tex]x=3+(-6)[/tex]

=> [tex]x=-3[/tex]

The solution to the system (points of intersection) is [tex](-3,-6)[/tex] and [tex](2,-1)[/tex]. I also attached a graph of the intersection points.

Now to find the midpoint of the two intersection points, [tex]midpoint=(\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} )[/tex]

[tex](x_{1},y_{1}) = > (-3,-6)[/tex]

[tex](x_{2},y_{2}) = > (2,-1)[/tex]

=>[tex]midpoint=(\frac{-3+2}{2} ,\frac{-6+(-1)}{2} )[/tex]

=>[tex](\frac{-1}{2} ,\frac{-7}{2} )[/tex]

Thus, the point, [tex](p,q)[/tex], is [tex](\frac{-1}{2} ,\frac{-7}{2} )[/tex].

The degree of correlation required for significance reduces as the sample size increases. As a result, the correlation size needed to determine significance will be smaller.

The size of our sample and the sample size has an impact on the significance of a sample link. For results to be relevant for high sample sizes, a minimal correlation is required. Fewer correlations and linkages are required for significance as the sample size increases.

Each sampling distribution's variability declines with the sample number and gradually moves toward leptokurtic behavior. The sample distribution's range is smaller than the range of the initial population.

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To find the 95% confidence interval for the mean Sales on days that have 12 employees working, we would need to know the population standard deviation and the sample size. The formula for a 95% confidence interval for the mean is:

(sample mean) ± (critical value) x (standard deviation / sqrt(sample size))

Without the information about sample size, standard deviation and sample mean, it's not possible to find the exact 95% confidence interval for the mean Sales on days that have 12 employees working.

Similarly, to find the 95% prediction interval for Sales on a day with 12 employees working, we would need to know the population standard deviation, sample size, and the sample mean. The formula for a 95% prediction interval for a single observation is:

(sample mean) ± (critical value) x (standard deviation of the mean) x sqrt(1 + (1/sample size))

Again, without the information about sample size, standard deviation and sample mean, it's not possible to find the exact 95% prediction interval for Sales on a day with 12 employees working.

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Answer:

6358 mm

Step-by-step explanation: multiply the value of decimeters by 100,

we get 6300 mm and then we add the 58 mm in 6300 mm.

The equation of the straight line passing through the point (-4, -4) with slope 3 can be written as y = 3x + 8.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the line with slope 3 passing through the point (-4, -4)

The equation of the straight line passing through the point (-4, -4) with slope 3 can be written as follows. We can write -

y = 3x + c

For the point ( -4, -4), we can write -

- 4 = 3 x - 4 + c

c = - 4 + 12

c =  8

Therefore, the equation of the straight line passing through the point (-4, -4) with slope 3 can be written as y = 3x + 8.

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The inverse of f(x) = 2/3 x³ + 1 is f^-1(x) = (3/2)(x-1)^(1/3).

In other words, we can set y equal to the original equation and solve for x.

Let y = 2/3 x³ + 1

We can then subtract 1 from both sides to get y – 1 = 2/3 x³

We can then divide both sides by 2/3 to get (y – 1) • (3/2) = x³

Finally, we can take the cube root of both sides to get the inverse function:

x = (y – 1)¹/₃ • (3/2)¹/₃

Therefore, the inverse of f(x) = 2/3 x³ + 1 is x = (y – 1)¹/₃ • (3/2)¹/₃.

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Answer:

When you combine all the baking soda recipes from the recipes that use exactly 1 1/4 teaspoons, you will have the same amount of baking soda that was used in all the recipes.

Step-by-step explanation:

In other words, if you have X number of recipes that each use 1 1/4 teaspoons of baking soda, you will have X*1.25 teaspoons of baking soda in total.

It is important to notice that the question is asking about the amount of baking soda used in those exact recipes that calls for 1 1/4 teaspoons and not about the total amount of baking soda you would end up with after making all the recipes. Therefore, the total amount of baking soda you would have after making all the recipes would depend on how much was used in each recipe and how many were made .

i think i onestly i think maybe 7 cm.

Velocity, marginal cost, and acceleration are derivatives of displacement, cost, and velocity functions.

The velocity of an object or particle describes how far it has moved or displaced over time. If the function s(t) determines the position of an object, then the velocity is its first derivative. And, this is written as s'(t). The initial blank is therefore filled with velocity.

The cost difference between producing one more product or serving one more customer is known as the marginal cost. As a result, it can be calculated by dividing the change in overall costs by the change in energy output. So, the cost function's derivative is the marginal cost. If the cost function is c(x), then its derivative c'(x) is the marginal cost.  The second blank is filled with marginal cost.

Acceleration is the time-dependent derivative of velocity. If v(t) is the velocity, then the acceleration is v'(t). The third blank is filled with acceleration.

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When Rollins read books it is a expression in which the  number of books he has completed is, N  =  P/( a × b )

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

In given problem,

we have to make relationship between number of books he has completed, how many pages he can read per minute and daily how many minutes he reads book.

suppose,

the number of books he has completed  = N

pages he can read per minute = a

time spent on reading per day = b

Total page in a book = P

N  =  P/( a × b )

Hence, The expression is  N  =  P/( a × b )

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Substituting into the formula for the perimeter of a rectangle, the perimeter is [tex]2\left(n+3 \frac{1}{2} n +4 \frac{1}{2} \right)=2n+7n+9=\boxed{9n+9}=\boxed{9(n+1)}[/tex]

A sine function that has an amplitude of 2, a midline of 4 and a period of 2/3 is write as:

The sine function is written considering the general formula in the form

sine function, y = A sin wx + b

where

A = amplitude

w = 2π / period

b  = midline

In the problem the values available are

A = 2

b = 4

period = 2/3

substituting the known values

sine function, y = A sin wx + b

sine function, y = 2 sin (2π / 2/3) x + 4

sine function, y = 2 sin (3π) x + 4

sine function, y = 2 sin 3πx + 4

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Answer:

k = 58

Step-by-step explanation:

k = 15 litres + remaining petrol

Remaining petrol:

The car travels 8 km/litre.

344 km / (8 km/litre) = 43 litre

The car uses 43 litres to travel 344 km.

k = 15 + 43

k = 58

Answer:

3 1/2 cups of oats = 28 grams of fiber

Step-by-step explanation:

1 whole cup equals 8 grams (add halves for this)

8 x 3 = 24

24 + additional 4 from the remaining half makes 28 grams of fiber total.

The value of the logarithm equation is given by x = [ ln ( 4 ) - 5 ] / 4

The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm

The properties of Logarithm are :

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

Given data ,

Let the logarithm equation be represented as A

Now , the value of A is

e⁽ ²ˣ ⁺ ⁵ ⁾ = 4   be equation (1)

On simplifying the equation , we get

Taking logarithm on both sides of the equation , we get

2x + 5 = ln ( 4 )

On simplifying the equation , we get

ln ( 4 ) = 2x + 5

Subtracting 5 on both sides of the equation , we get

2x = ln ( 4 ) - 5

Divide by 2 on both sides of the equation , we get

x = [ ln ( 4 ) - 5 ] / 4

Hence , the equation is  x = [ ln ( 4 ) - 5 ] / 4

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The lines y = x + 3 and y = 2 · x + 2 pass through point (1, 4) on Cartesian plane.

In this problem we must graph two lines that pass through point (x, y) = (1, 4). Lines can be represented by equations of following form:

y = m · x + b

Where:

We must choose two slope-intercept combinations to generate two different lines: (x, y) = (1, 4)

Line 1

4 = m · 1 + b

4 = m + b

m = 1

4 = 1 + b

b = 3

y = x + 3

Line 2

4 = m · 1 + b

4 = m + b

m = 2

4 = 2 + b

b = 2

y = 2 · x + 2

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Answer:

Step-by-step explanation:43

Answer: C

Because 5(x - 4) is equal to 5 times x and 5 times -4, which is 5x - 20

Answer:

I think it's b. when you have a negative and a negative it becomes a positive

Answer:

[tex]\sf \frac{2A-hb}{h}=c[/tex]

Step-by-step explanation:

[tex]\sf A=\frac{1}{2}h(b+c)[/tex]

First, multiply both sides by 2.

[tex]\sf 2A=h(b+c)[/tex]

Solve the brackets.

[tex]\sf 2A=hb+hc[/tex]

Subtract h b from both sides.

[tex]\sf 2A-hb=hc[/tex]

Divide both sides by h.

[tex]\sf \frac{2A-hb}{h}=c[/tex]

Answer: x⁰⁄₂ + 0 = y or x⁰⁄₂ = y

Step-by-step explanation:

Equation of a line is mx+b=y

m=slope

The slope is ʸ⁄ₓ or in this case ⁰⁄₂

b=where the line cross the y-axis which is 0, when it is 0 there is no use in write +0 after the equation, as there is no difference, but it is your choice