Solve for all values of xx by factoring.
x^{2}+5x-3= −4x−3

Answer: B

Step-by-step explanation:

Answer:

3.4 units

Step-by-step explanation:

The cross section of a right circular cone parallel to its base is a circle.

A three dimensional shape is a shape that has length, width and height. Examples of three dimensional shapes are cone, cylinder, prism and pyramid.

A two dimensional shape is a shape that have both length and width. Examples of two dimensional shape are circle, rectangle, square.

A cone is a three-dimensional solid geometric shape having a circular base and a pointed edge at the top

The cross section of a right circular cone parallel to its base is a circle.

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Answer:

10 ounces

Step-by-step explanation:

Answer:

  9.09 ounces

Step-by-step explanation:

The added water can be calculated by writing an equation for the amount of iodine in the diluted solution.

Let x represent the number of ounces of water added to the 60% solution. The total amount of iodine in the mixture is ...

  0.60(100) +0(x) = 0.55(100+x) . . . . . ounces of iodine in the mix

Simplify the equation:

  60 = 55 +0.55x

  5 = 0.55x . . . . . . . subtract 55

  x = 5/0.55 ≈ 9.09

9.09 ounces of pure water must be added to produce a 55% solution.

Answer:

1.89

Step-by-step explanation:

34 ÷ (14 − 5) × 2

34 ÷ (9) × 2

34 ÷ 18

1.89

Numerical expression:

numerical expression is a phrase involving numbers.

In mathematics, a numerical expression is a set of numbers that have been written together by utilizing arithmetic operators addition, subtraction, multiplication, and division.

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By  evaluating  the expression 34 ÷ (14 − 5) × 2  we get = 1.89

Children can use the acronym BODMAS to help them remember the proper sequence to carry out mathematical operations when solving problems. The abbreviation BODMAS stands for B-Brackets, O-Orders (powers/indices or roots), D-Division, M-Multiplication, A-Addition, and S-Subtraction.

A numerical expression is a sentence that uses numbers. A numerical expression in mathematics is a group of integers that have been combined using the addition, subtraction, multiplication, and division arithmetic operators.

Appling the BODMAS

= 34 ÷ (14 − 5) × 2

= 34 ÷ (9) × 2

= 34 ÷ 18

= 1.89

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The probability that the machine produces fewer than 3 defective widgets in a production run of 75 items is 0.041.

A probability refers to the ratio of favorable events to the n number of total events.

Also, it means the chance that a particular event (s) will occur expressed on a linear scale from 0 to 1 which can also be expressed as a percentage between 0 and 100%.

Given data

An industrial machine produces 3 widgets.

It has a 0.12 defective rate.

Defective rate fewer than 3

Total Probability = P of 2 defective + P for 1 defective

Total Probability = 2/74 + 1/73

Total Probability ≈ 0.04072565716

Total Probability ≈ 0.041

Therefore, the required probability for fewer than 3 defective rate is 0.041

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Answer:

i) a = 2, b = - 3, c =-6

Step-by-step explanation:

4x² - 12x + 3

4x² - 6x - 6x + 9 - 6

(2x - 3)(2x - 3) - 6

(2x - 3)² - 6

(2x + (- 3) )² - 6

In form of (ax + b)² - 6

a = 2, b = - 3, c =-6

a) 6x + 12 = 5x - 5y

6x-5x = -5y-12

x = -5y-12

b) 5a-10x = 9x+9

-10x-9x = 9-5a

-19x = 9-5a

x = 9-5a/-19

Answer: 0.25 or 25%

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

The length of the ladder is 75ft.

The longest side, or hypotenuse, of a right-angled triangle is the side that faces away from the right angle. The Pythagorean theorem asserts that the hypotenuse's square length equals the sum of the squares of the lengths of the other two sides, and this can be used to determine the hypotenuse's length.

The ladder makes an angle of 28° with the ground and the top of the ladder reaches 35ft

Therefore, we have:

Sineα = opposite/hypotenuse

Where:

Opposite = 35

Hypotenuse = Length

α = 28°

substitute values and solve for the length, as following:

Sine(28) = 35/Length

Length = 35/Sine(28)

Length = 75ft

Therefore,

The length of the ladder is 75 ft.

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The parabola represented by this graph has the following equation:

y = -16.67(x + 1)² + 2

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

A downward open parabola rises from (-2.4, 4) to (-1,2), and declines through (0.4, -4) on the coordinate plane, hence the vertex is given by:

(-1,2), hence the coefficients are h = -1 and k = 2, and the equation is:

y = a(x - h)² + k

y = a(x + 1)² + 2

We have that when x = -0.4, y = -4, hence the leading coefficient is found as follows:

y = a(x + 1)² + 2

-4 = a(-0.4 + 1)² + 2

a = -6/0.6²

a = -16.67

Hence the equation is:

y = -16.67(x + 1)² + 2

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[tex]\Large\texttt{Answer}[/tex]

[tex]180^\circ=\pi\:radians}[/tex]

[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]

[tex]\Large\texttt{Process}[/tex]

⇨ For converting from degrees to radians, use this conversion factor:

[tex]\bf{\cfrac{\pi}{180}}[/tex]

⇨ Convert

[tex]\bf{\cfrac{180}{1}\times\cfrac{\pi}{180}}[/tex]

⇨ The 180s cancel out, and we have:

[tex]\pi[/tex]

Hence

[tex]\bf{180^\circ=\pi\:radians}[/tex]

Hope that helped

Answer:  $10.8

Step-by-step explanation:  To do this, we need to find 90% of $12 because the cap is 10% off. We can do this by multiplying 12 by 0.9.  12 x0.9 = 10.8.

The angle it makes with the positive x axis in the xy plane is 61.3145 degrees.

In this question,

A normal vector to the plane is any vector that starts at a point in the plane and has a direction that is orthogonal (perpendicular) to the surface of the xy plane .

The magnitude of the xy plane, hypotenuse = 25 units

The x component of the xy plane, base = 12 units

Let θ be an angle, then the angle it makes with the positive x axis is

[tex]\theta = cos^{-1}(\frac{base}{hypotenuse} )[/tex]

⇒ [tex]\theta = cos^{-1}(\frac{12}{25} )[/tex]

⇒ [tex]\theta = cos^{-1}(0.48)[/tex]

⇒ [tex]\theta = 61.3145[/tex]

Hence we can conclude that the angle it makes with the positive x axis in the xy plane is 61.3145 degrees.

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Answer: x= 3.4

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

Answer:

x = 3.4

Step-by-step explanation:

[tex]10x - 4.5 + 3x = 12x -1.1 \\ 13x - 4.5 = 12x - 1.1 \\ 13x - 12x - 4.5 = 12x - 12x - 1.1 \\ x - 4.5 = - 1.1 \\ x - 4.5 + 4.5 = - 1.1 + 4.5 \\ x = 3.4[/tex]

The conic section will form an Ellipse.

The collection of all points in the plane that make up a circle are all equally spaced from a certain point known as the "centre," making the form a closed two-dimensional shape. The reflection symmetry line is created by all lines that traverse the circle. Additionally, it is symmetrical in rotation around the center at all angles.

A conic section is a curve formed when the surface of a cone and a plane connect. The hyperbola, parabola, and ellipse are the three forms of conic sections; the circle is a special case of the ellipse, though historically it was occasionally referred to as a fourth type.

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The points that are possible approximations for this system are; (2.2, -1.4) and (2.2, -1.35)

We are given the equations of the linear graphs as;

y = ⁷/₄x + ⁵/₂

y = ³/₄x - 3

Notice that the lines intersect each other and by definition, if the lines of the system of equations intersect, then the system has one solution. This means that the point of intersection of the lines is the solution of the system. It can be written as:

(x, y)

x is the x-coordinate .

y is the y-coordinate.

In this case, we can identify that:

- the x-coordinate of the point of intersection is between; x = 2 and x = 3

- The y-coordinate of the point of intersection is between y = -1 and y = -2

Based on the above, we can conclude that the points that are possible approximations for this system are; (2.2, -1.4) and (2.2, -1.35)

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Answer: B and C) 2.2, -1.4 and 2.2, -1.35

Step-by-step explanation:

Hope this helps!

Mark me brainliest!

Pls and Ty!

Answer:

Step-by-step explanation:

if x= -2, f(x)= -8

x= -1, y= -1

x=0, y=0

Answer:

6 - 16y

Step-by-step explanation:

2(3 – 8y) = 2 × 3 - 2 × 8y = 6 - 16y

In the analysis of variance study, if we consider 3 treatments, in which we have 4 observations for the first treatment, 5 observations for the second treatment, and 6 observations for the third treatment. Then, the degrees of freedom associated with SSE in each case is 2, 3, and 4, respectively.

Degrees of Freedom Associated with SSE

The number of degrees of freedom in statistics refers to the quantity of values that can fluctuate in a statistic's final calculation. Various amounts of data or information can be used to estimate statistical parameters.

In order to find the degrees of freedom associated with SSE in an Analysis of Variance (ANOVA) study, we subtract 2 from the number of observations. In n is the number of observations, then (n-2) gives the degrees of freedom associated with SSE.

Thus, for the first treatment, n = 4

⇒ Degrees of freedom = 4-2

= 2

For the second treatment, n = 5

⇒ Degrees of freedom = 5-2

= 3

For the third treatment, n = 6

⇒ Degrees of freedom = 6-2

= 4

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The equations with tangents at (0,0) are [tex]y = \frac{4}{7} x[/tex] and

[tex]y = -\frac{4}{7} x[/tex].

In this question,

The curves are x = 7 cos(t), y = 4 sin(t) cos(t)

Two tangents at (0, 0)

In this case, the parametric derivative of x and y are expressed in terms of t.

The first derivative dy/dx can be expressed as

[tex]\frac{dy}{dx}=\frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]

Now, dy/dt is obtained by differentiate y with respect to t,

[tex]\frac{dy}{dt}= 4[cos(t)(cos(t))+sin(t)(-sin(t))][/tex]

⇒ [tex]\frac{dy}{dt}= 4[cos^{2} (t)-sin^{2} (t)][/tex]

Now, dx/dt is obtained by differentiate x with respect to t,

[tex]\frac{dx}{dt} =7(-sin(t))[/tex]

⇒ [tex]\frac{dx}{dt} =-7sin(t)[/tex]

Thus, [tex]\frac{dy}{dx}=\frac{4[cos^{2}(t)-sin^{2}(t ) ]}{-7sin(t)}[/tex]

At (0,0) x = 0 and y = 0, Then

0 = 7 cos(t)

0 = 4 sin(t) cos(t)

and

cos(t) = 0

sin(t) cos(t) = 0

There are two values between -π and π which satisfy these equations simultaneously are

t = π/2

t = -π/2

The equation of a straight line given a point and its slope is

y-y₀ = m(x-x₀)

The two tangents lies at (0,0), so the equation becomes

y = mx

Then the two straight lines will be

y = m₁x  and

y = m₂x

For t = π/2,

[tex]m_1=\frac{dy}{dx}=\frac{4[cos^{2}(\frac{\pi }{2} )-sin^{2}(\frac{\pi }{2} ) ]}{-7sin(\frac{\pi }{2} )}[/tex]

⇒ [tex]m_1=-\frac{4[0-1]}{7(1)}[/tex]

⇒ [tex]m_1=\frac{4}{7}[/tex]

For t = -π/2,

[tex]m_2=\frac{dy}{dx}=\frac{4[cos^{2}(-\frac{\pi }{2} )-sin^{2}(-\frac{\pi }{2} ) ]}{-7sin(-\frac{\pi }{2} )}[/tex]

⇒ [tex]m_2=-\frac{4[0-1]}{-7(1)}[/tex]

⇒ [tex]m_2=-\frac{4}{7}[/tex]

Thus the equations with tangents at (0,0) are [tex]y = \frac{4}{7} x[/tex] and

[tex]y = -\frac{4}{7} x[/tex].

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Answer:

$279.25

Step-by-step explanation:

Multiply 6.50x43

[tex]w = 279.50 + (0.5 \times 6.50) \times (43 - 40)[/tex]

Multiply 0.5x6.50

[tex]w = 279.50 + 3.250 \times (43 - 40)[/tex]

Add 43-40

[tex]w = 279.50 + 3.250 \times 3[/tex]

Multiply 3.250x3

[tex]w = 279.50+ 9.750[/tex]

Solution

Answer:

100%, 20%, 60%

Step-by-step explanation:

250/250 = 100/100 = 100%

50/250 = 1/5 = 20/100 = 20%

150/250 = 3/5 = 60/100 = 60%

Answer:

Book 3

Step-by-step explanation:

So we have four statements:

1: Book 1 or Book 2

2: Book 3 or Book 4

3: Book 4

4: Not Book 3

We also have the condition that only 1 of the statements are correct, and more important, the other 3 are incorrect.

So it may be a bit difficult to see at first, but the solution, has to be book 3. The reason for this is if we assume statement 1, statement 2, or statement 3 is true, that would imply that the statement 4 is false, meaning the solution is in book 3.

If we assume that statement 2 is true, then statement 4 is false, meaning that book 3 has the solution, which aligns statement 2. It also aligns with statement 1 being false, because it's not book 1 or 2, and it also aligns with statement 3 being false, because the solution is not in book 4.

Let's look at why assuming any other statement to be true, leads to contradictions.

So let's assume the first statement is true, this means the solution is book 1 or 2. But this means the statement 4 is false, meaning book 3 has the solution. This contradicts the first statement which we assume is true, thus the first statement is not true.

Let's now assume the third statement is true, this means statement four is false meaning it's book 3, but this contradicts the third statement which says it's book 4. Thus this statement cannot be true

Let's assume the last option is true, this means book 3 has no solution, and since all the other are false, book 4 has no solution, book 3 or 4 has  no solution, book 1 or 2 has no solution either. This means that none of the books have solutions, and assuming one of the books does have a solution, this statement cannot be true.

m∠B = 57.52°, m∠B = 70.8°, AB = 46.03 km and AC = 39.08 ft. This can be obtained using the Laws of cosine formula and Laws of sine formula.

In a triangle ABC,

⇒ a² = b² + c² - 2bc cos A

⇒ b² = a² + c² - 2ac cos B

⇒ c² = a² + b² - 2ab cos C

where a, b and c are sides of a triangle and A, B and C are the angles of a triangle.

In a triangle ABC,

⇒ [tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]

where a, b and c are sides of a triangle and A, B and C are the angles of a triangle.

In the question we can use the laws of cosine formula and laws of sine formula,

5) Given that,

AB = c = 13 km

AC = b = 21 km

m∠A = 91°

By using Laws of cosine formula,

⇒ a² = b² + c² - 2bc cos A

a² = 21² + 13² - 2(21)(13) cos 91°

a² = 441 + 169 - 546 (-0.0174524064)    

a² = 610 + 9.52901391 = 619.529014

⇒ a = 24.89 km

By using Laws of sine formula,

⇒ [tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]

sin 91°/24.89 = sin B/21

sin B = 0.999847695×21/24.89 = 0.843583833

⇒ m∠B = 57.52°

6) Given that,

AB = c = 11 cm

BC = a = 13 cm

AC = b = 14 cm

By using Laws of cosine formula,

⇒ b² = a² + c² - 2ac cos B

14² = 13² + 11² - 2(13)(11) cos B

196 = 169 + 121 - 286 cos B

196 = 290 - 286 cos B

cos B = 94/286

cos B = 0.328671329

⇒ m∠B = 70.8°

7) Given that,

AC = b = 24 km

BC = a = 26 km

m∠C = 134°

By using Laws of cosine formula,

⇒ c² = a² + b² - 2ab cos C

c² = 26² + 24² - 2(26)(24) cos 134°

c² = 676 + 576 - 1248 (-0.69465837)

c² = 1252 + 866.933646 = 2118.93365

⇒ AB = c = 46.03 km

8) Given that,

AB = c = 26 ft

BC = a = 21 ft

m∠B = 112°

By using Laws of cosine formula,

⇒ b² = a² + c² - 2ac cos B

b² = 21² + 26² - 2(21)(26) cos 112°

b² = 441 + 676 - 1096 (-0.374606593)

b² = 1117 + 410.568826 = 1527.56883

⇒ AC = b = 39.08 ft

Hence m∠B = 57.52°, m∠B = 70.8°, AB = 46.03 km and AC = 39.08 ft.

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Using proportions, Nelly's total pay for last week was of £220.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From Monday to Friday, she worked 17 hours, hence:

On Saturday, she worked 5 hours, and was paid £16 per hour.

Hence her total payment is found as follows:

15 x 8 + 2 x 10 + 5 x 16 = £220.

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The limit of [tex]\lim_{x \to \infty} \frac{lnx}{x}[/tex]  using L'Hospital rule is 0.

According to the given question.

We have to find the limit of ln(x)/x when x approaches to infinity.

If we let x = ∞, we get an indeterminate form [tex]\frac{\infty}{\infty}[/tex] ie. [tex]\frac{ln(x)}{x} = \frac{\infty}{\infty}[/tex].

And, we know that whenever we get indeterminate form ∞/∞ we apply L'Hospital rule.

Therefore, defferentiating numerator ln(x) and x with respect to x.

[tex]\implies \frac{d(ln(x))}{dx} = \frac{1}{x}[/tex] and [tex]\frac{d(x)}{dx} =1[/tex]

So,

[tex]\lim_{x\to \infty}\frac{\frac{1}{x} }{1}[/tex]

[tex]= \lim_{x \to \infty} \frac{1}{x}[/tex]

As, x tends to ∞, 1/x tends to 0. Because ∞ is very large number and 1 divided by a very large number always approaches to 0 and it is very close to zero.

Therefore,

[tex]\lim_{x \to \infty} \frac{1}{x} = 0[/tex]

Hence, the limit of [tex]\lim_{x \to \infty} \frac{lnx}{x}[/tex] is 0.

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Answer:

11/20

Step-by-step explanation:

You could turn them all into equivalent fractions, but the common denominator would be 1,763,580.  Yuck.

Look at the relationship for the numerators to the denominators.  The only numerator that is more than half of its denominator is 11/20.  Half of 20 would be 10 and 11 has a larger value than 10, so as a decimal, it would be more than .5.  All of the other numerators are less than half, so that they have to less than .5.

If you changed all of the numbers to decimals, you would see that 11/20 has the largest value.

Answer: 63 Stickers

Step-by-step explanation:

Given information:

Ratio = Slade : Corbett = 5 : 2

Corbett has 27 fewer stickers

Set variables:

Let x be the number of stickers Corbett has

Let x + 27 be the number of stickers Slade has

Set proportional equation:

[tex]\frac{2}{5}~ =~\frac{x}{x~+~27}[/tex]

Cross multiply the system

[tex]2~(x~+~27)~=~5~*~x[/tex]

Simplify by distributive property

[tex]2~*~x~+~2~*~27~=~5x[/tex]

[tex]2x~+~54~=~5x[/tex]

Subtract 2x on both sides

[tex]2x~+~54~-~2x~=~5x~-~2x[/tex]

[tex]54~=~3x[/tex]

Divide 3 on both sides

[tex]54~/~3~=~3x~/~3[/tex]

[tex]{x=18}[/tex]

Add Corbett's and Slade's amounts together

Corbett = x = 18 stickers

Slade = x + 27 = 18 + 27 = 45 stickers

Total = 18 + 45 = [tex]\Large\boxed{63~Stickers}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

63 stickers

Step-by-step explanation:

Define the variables:

Given ratio:

Slade : Corbett = 5 : 2

Substitute the defined variables:

[tex]\implies \sf x : x - 27 = 5 : 2[/tex]

[tex]\implies \sf \dfrac{x}{x-27}=\dfrac{5}{2}[/tex]

Cross multiply:

[tex]\implies \sf 2x=5(x-27)[/tex]

Expand:

[tex]\implies \sf 2x=5x-135[/tex]

Subtract 5x from both sides:

[tex]\implies \sf -3x=-135[/tex]

Multiply both sides by -1:

[tex]\implies \sf 3x=135[/tex]

Divide both sides by 3:

[tex]\implies \sf x=45[/tex]

Therefore, Slade had 45 stickers.

Substitute the found value of x into the expression for the number of stickers Corbett had:

[tex]\implies \sf 45-27=18[/tex]

Therefore, Corbett had 18 stickers.

Total number of stickers = 45 + 18 = 63

The forces have a magnitude of 59 pounds, and their direction angles are zero.

Two forces of 17 and 42 pounds act horizontally on an object.

i.e

F1 = 17 pounds

F2 = 42 pounds

As the magnitude of the force represents the sum of all the forces

The direction is the same

Magnitude : 17 + 42 = 59 pounds

The Direction angles : 0

As they have the same direction so angle will be 0.

The forces have a magnitude of 59 pounds, and their direction angles are zero.

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Answer:59 and 0

Step-by-step explanation:

EDGE