Find a and k so that the given points lie on the parabola (An algebraic solution is required)

Following the addition of both sides of the equation by 2/3, x is equivalent to 3/2(x-5)=-6.

An equation is a mathematical formula that joins two statements using the equal sign (=) to denote equality. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the terms 3x + 5 and 14 in the equation 3x + 5 = 14.

given

Add 2/3 to both sides of the equation.

(2/3(3/2⋅(x−5))=2/3⋅−6

Simplify the problem on both sides.

x − 5 = −4

Put all terms on the right side of the equation that don't contain x.

x = 1

Following the addition of both sides of the equation by 2/3, x is equivalent to 3/2(x-5)=-6.

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A. The equation of a tangent line to the circle through the point (- 6 , 8) is y = 0.75x + 12.50

B. The point of tangency of L with the circle is (9.81 , - 1.96).

The full question is in the attachment. The equation of a tangent line to the circle with radius r centered at the origin through the point (p , q)

px + qy = r²

- 6x + 8y = 10²

8y = 6x + 100

y = 6/8x + 100/8

y = 3/4x + 25/2

y = 0.75x + 12.50

The equation line y = mx + c has the slope or the gradient m. If two lines are parallel, the two lines have the same slope.

y = 5x + 7

The tangent line L to the circle with the gradient m and radius r

[tex]y \:=\: mx \pm r \: \sqrt{1 \:+\: m^2}[/tex]

[tex]y \:=\: 5x \pm 10 \: \sqrt{1 \:+\: 5^2}[/tex]

[tex]y \:=\: 5x \pm 10 \: \sqrt{1 \:+\: 25}[/tex]

[tex]y \:=\: 5x \pm 10 \: \sqrt{26}[/tex]

Because L has a negative y-intercept, it means when x = 0, y is negative. So the equation L

[tex]y \:=\: 5x \:+\: 10 \: \sqrt{26}[/tex]

The point x of tangency of L with the circle

x² + y² = r²

x² + (5x - 10 √26)² = 10²

x² + 25x² - 100√26 x + 2,600 = 100

26x² - 100√26 x + 2,500 = 0

[tex]x_{1.2} \:=\: \frac{-b \pm \sqrt{b^2 \:-\: 4ac}}{2a}[/tex]

[tex]x_{1.2} \:=\: \frac{100 \sqrt{26} \pm \sqrt{(- 100 \sqrt{26})^2 \:-\: (4 \times 26 \times 2,500)}}{2 \times 26}[/tex]

[tex]x_{1.2} \:=\: \frac{100 \sqrt{26} \pm \sqrt{260,000 \:-\: 260,000}}{52}[/tex]

[tex]x \:=\: \frac{100 \sqrt{26}}{52}[/tex]

[tex]x \:=\: \frac{50 \sqrt{26}}{26}[/tex]

x = 50/26 × √26

x = 9.81

The point y of tangency of L with the circle

[tex]y \:=\: 5x \:+\: 10 \: \sqrt{26}[/tex]

[tex]y \:=\: 5 \times \frac{50 \sqrt{26}}{26} \:+\: 10 \: \sqrt{26}[/tex]

[tex]y \:=\: \frac{250 \sqrt{26}}{26} \:+\:  \frac{260 \sqrt{26}}{26}[/tex]

[tex]y \:=\: \frac{- 10 \sqrt{26}}{26}}[/tex]

y = - 10/26 × √26

y = - 1.96

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Mid-point formula is used to determine the mid-point of a line segment. An example of the mid-point formula is discussed below.

What is the mid-point formula?

The centre of a line segment is known as the midpoint. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

The formula used to find this mid-point of the line is called the mid-point formula.

[tex](x_{m},y_{m} ) =(\frac{x_{1} +x_{2} }{2} ,\frac{y_{1} +y_{2} }{2})[/tex]

where, [tex](x_{m} ,y_{m})[/tex] = mid-point coordinates

            [tex](x_{1} ,y_{1})[/tex]   = first point coordinates

            [tex](x_{2} ,y_{2})[/tex]   = second point coordinates

An example of mid-point formula is given below.

Find the mid-point of a line whose end coordinates are (3,5) and (6,10).

From the question, we can write,

                [tex](x_{1} ,y_{1}) = (3,5)\\(x_{2} ,y_{2}) = (6,10)[/tex]

Then as discussed above, we can find the mid-point using the formula,

             [tex](x_{m},y_{m} ) =(\frac{x_{1} +x_{2} }{2} ,\frac{y_{1} +y_{2} }{2})[/tex]

                [tex]x_{m} = \frac{x_1 + x_2}{2} = \frac{3+6}{2} = 4.5[/tex]

                [tex]y_{m} = \frac{y_{1} + y_{2}}{2} = \frac{5+10}{2} = 7.5[/tex]

Therefore the mid-point of the given line found using the mid-point formula is (4.5, 7.5).

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The scientific notation for the answer to 1.9×10⁷*3×10⁶ is 5.7×10¹³.

An exponent is a number or letter placed above and to the right of the base of a mathematical statement. It denotes that the base will be raised to a specific level of power. Exponents are classified into four types: positive, negative, zero, and rational. Positive exponents indicate how many times a base may be multiplied by itself. The number of times a number is multiplied by itself is referred to as its exponent. For instance, 2 to the third (written as 23) means: 2 x 2 x 2 = 8. 2 x 3 = 6 does not equal 23. Keep in mind that a number raised to the power of one is itself.

Here,

=1.9×10⁷*3×10⁶

=5.7×10⁽⁷⁺⁶⁾

=5.7×10¹³

The scientific notation for the result of 1.9×10⁷*3×10⁶ is 5.7×10¹³.

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A triangle can not have three sides whose lengths are 3.2 cm 5.3 cm 9.4 cm

We know that the triangle inequality theorem states that for any triangle the sum of any two sides of a triangle is greater than or equal to the third side.

Here, we have been given the three measurements.

Let a = 3.2 cm, b =  5.3 cm and c = 9.4 cm

Consider the sum of sides a and b,

a + b

= 3.2 + 5.3

= 8.5cm

< 9.4

= c

i.e., a + b < c

Acctording to triangle inequality theorem, a, b, c can not be the sides of triangle, as the sum of two sides that measure 3.2 cm and 5.3 cm is not greater than or equal to the third side which measures 9.4 cm

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Answer:

$4.45

Step-by-step explanation:

First, we try to find the slope of the table. We can do this by doing the following-  [tex]\frac{Change \ in \ y }{Change \ in \ x}[/tex]

When we do this, we find that the slope (or the change in y / change in x) is equal to 5.27

Now we subtract this from the slope of the price of steak at Store B which is 9.72

[tex]9.72-5.27 = 4.45[/tex]

You get 4.45 which is $4.45 or 4 dollars and 45 cents.

Algebra Formulas for Class 8

Some essential 8th-class formulas related to Algebra are:

Algebraic Identities For Class 8

(a + b)2 = a2 + 2ab + b2

(a − b)2 = a2 − 2ab + b2

(a + b) (a – b) = a2 – b2

(x + a) (x + b) = x2 + (a + b)x + ab

(x + a) (x – b) = x2 + (a – b)x – ab

(x – a) (x + b) = x2 + (b – a)x – ab

(x – a) (x – b) = x2 – (a + b)x + ab

(a + b)3 = a3 + b3 + 3ab (a + b)

(a – b)3 = a3 – b3 – 3ab (a – b)

I tried my best!

b. √60 is equivalent to 60^1/2

60^1/2 represents the square root of 60. The square root of a number is a value that when multiplied by itself, gives the original number. So in this case, √60 * √60 = 60. Therefore, the equivalent of 60^1/2 is √60.

Option a, 60/2 is not equivalent, because it is not the value that when multiplied by itself gives 60.

Option c, 1/60^2 is not equivalent, because it is not the value that when multiplied by itself gives 60.

Option d, 1/√60 is not equivalent, because it is not the value that when multiplied by itself gives 60.

It is important to note that 60^1/2 is not the same as (60^1)^1/2, the first one is finding the square root of 60 while the second one is finding the 1/2 power of 60 which is not the same thing.

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Answer: -3

Step-by-step explanation:

The given equation is:

-2p-4 = 2

Let's add 4 to each side of the equation.

You'll get

-2p = 6

Now let's divide both sides by -2, and you get

p = -3

It is possible to construct a triangle whose sides are 17 cm 15 cm and 8 cm because the sum of two sides are greater than third sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 17 cm 15 cm and 8 cm.

The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.

To check this we firstly add the 17 and 15.

17 + 15 > 8

32 > 8

Now we add 17 and 8

17 + 8 > 15

25 > 15

Now we add 15 and 8

15 + 8 > 17

23 > 17

It is possible to construct a triangle whose sides are 17 cm 15 cm and 8 cm because the sum of two sides are greater than third sides.

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Answer:

your answer is D

Step-by-step explanation:

I literally just finished the quiz on edge

Answer:

Step-by-step explanation: First we start by using the order of operations and do -2 + 16 which is 14. Then we do multiplication left to right, do 3 x 6 = 18x2 =36 +14 =50

Answer:

the answer is C should be

Step-by-step explanation:

the answer is C should be, I'm in middle school btw

Substitution property is a property in algebra that helps in substituting the value of a quantity/variable into an algebraic expression to solve a given mathematical problem.

The substitution property is a notion in algebra that is used for substituting the value of a given variable or a quantity into an expression to find the value of the unknown.

In other words, we can express that the substitution property is utilised to replace the value of a quantity in an equation or an expression to solve a mathematical problem.

For example, Using the substitution property of equality, find the value of the algebraic expression g(x) = sin x + cos x if x = 45°.

We will replace x with 45° in the expression. So we have

g(45°) = sin 45° + cos 45°

= 1/√2 + 1/√2

= 2/√2

= √2

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The predicted sales for week 6 is 740

In the case of linear regression using excel formula, we can find the intercept and the slope value for the regression model.

The equation of linear regression is similar to the slope formula what we have learned before in earlier classes such as linear equations in two variables.

Forecast[tex]$=\mathrm{A}+\mathrm{B}(\mathrm{x})$[/tex]

Where A is the intercept of the data, B is the slope, and X is the period.

Intercept [tex]=[/tex] INTERCEPT (Range Y, Range X)

The above data generates the equation.

Now the data corresponds to an intercept value of 698 and a slope of 8.

Therefore, for period [tex]$6, x=6$[/tex]

The equation [tex]$=698+(8 * 6)=746$[/tex]

The intermediate calculations are in the table below:

PERIODUNITSFORECAST

____________________

1            700      706

2           724       714

3           720       722

4           728       730

5                         738

6                         740

Therefore, the predicted sales for week 6 is 740.

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Judy needs 1 5/8 yards area more of flannel to stitch the kirt.

To find how much more fabric Judy needs, we need to subtract the amount she already has from the amount she needs.

Judy needs 2/3 yard of flannel

Judy has 3/8 yard of flannel

To subtract these fractions, we first need to convert them to the same denominator.

2/3 yard = 4/6 yard

3/8 yard = 6/8 yard

4/6 yard - 6/8 yard = (24 - 24)/48 = 0/48

To simplify, 0/48 = 0

Therefore, Judy needs 0 yards more of flannel.

However, Judy needs 2/3 yard of flannel to stitch the kirt. Since she has 3/8 yard, we can subtract the two to find how much more fabric she needs.

2/3 yard - 3/8 yard = (16 - 12)/24 = 4/24

To simplify, 4/24 = 1/6

Therefore, Judy needs 1 1/6 yards area more of flannel to stitch the kirt.

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The equation have infinite solutions.

What does a math equation mean?

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

                    Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

We can proceed to solve this equation by collecting like terms and then dividing through to know the coefficient of x.

 12x + 1 = 3(4x + 1) - 2

   12x + 1 =  12x + 3 - 2

     12x + 1 =   12x + 1

The equation have infinite solutions.

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How many solutions exist for the given equation?

12x + 1 = 3(4x + 1) – 2

If we expand the bracket, -20 -2 = -22.

So the equivalent expression would be -22.

The expression 5(-4) means to take the number -4 and multiply it by 5.

Since multiplication is distributive, this is the same as -4 * 5 which results in -20.

And -20 -2 is -22.

So the equivalent expression is -22.

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Located in Ennis, Montana, Madison Valley Bank provides services to residents of Madison County and the surrounding region. Madison deposited $463 into a bank savings account with a 2% annual interest rate.

Although inflation doesn't stop, it does get better. We don't want it to completely end, in fact. The Federal Reserve, the US central bank tasked with reducing the rate of inflation through a series of interest rate hikes, has set a target of about 2%. As a result, albeit not by as much, prices will still increase. At an interest rate of 8% compounded semi-annually, a $1,000 investment made now will be worth $1,480.24 after five years.

Calculator for future inflation in the US: In 2025, $106.09 is expected to be the same as $100 in terms of purchasing power. Future inflation of 3% per year is used as the basis for this computation. A 3.00% future inflation rate is predicted. when $54,855.74 is the same as $30

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The final balance on the card is $15350.92, rounded to the nearest penny.

The correct option is D.

Interest that compounded continuously to the principal amount. This interest rate provides exponential growth to a period of time.

Formula of continuous compound interest rate;

P(t) = P₀[tex]e^{rt}[/tex], where P₀ is the principal amount, r is the interest rate and t is the time period.

Given:

A customer uses a store credit card to purchase a boat for $10,500.

The store credit card offers an annual interest rate, compounded continuously, of 18.99% with no payments due for the first two years.

That means,

P₀ = $10500, r = 18.99 and t = 2.

So,

P(t) = P₀[tex]e^{rt}[/tex]

Substituting the values,

P(t) = (10500)[tex]e^{(0.1899)(2)}[/tex]

P(t) = (10500)(1.46199)

P(t) = 15350.917

P(t) = $15350.92

Therefore, the final amount is $15350.92.

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Answer: Zero or negative Zero

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

2a + 2 = 2

2a = 2 - 2

2a = 0

a = 0/2

a = 0

The solution of the division of 4 2/9 by the number 1 1/3 is

Mixed fractions are type of fractions which consist of a whole number part and a fractional part.

Mixed fractions are of the form a b/c where a is the whole number part and b/c is the fractional part.

The given fractions are 4 2/9 and 1 1/3.

First we have to change the mixed fraction into improper fraction.

4 2/9 = (4 × 9 + 2) / 9 = 38/9

1 1/3 = (1 × 3 + 1) / 3 = 4/3

Dividing these,

4 2/9 ÷ 1 1/3 = 38/9 ÷ 4/3

                     = (38/9) × (3/4)

                     = 38 / (3 × 4)

                     = 19/6

                     = 3 1/6

Hence the solution of the division of the mixed fractions given is 3 1/6.

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Answer:2095.23

Step-by-step explanation:

By solving the linear equation in x Abebi receives $37.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. Here, A is a coefficient, B is a constant, and x is a variable.

On identifying the information given in the problem we have:

Abebi, Bella, and Chuku share $112. Abebi receives $x. Bella receives $12 less than Abebi. Chuku receives twice as much as Bella.

On setting up an equation using the information given:

We know that the total amount shared is $112 and we want to find out how much Abebi receives, represented by x.

We know that:

Bella receives $12 less than Abebi =(x - 12)

Chuku receives twice as much as Bella =(2 * (x - 12))

So we can set up the equation as:

x + (x - 12) + (2 * (x - 12)) = 112

On simplifying the equation:

x + x - 12 + 2x - 24 = 112

Combining like terms:

4x - 36 = 112

On solving for x we get:

Add 36 to both sides:

4x = 148

Divide both sides by 4:

x = 37

On interpreting the solution we get:

By solving the linear equation in x Abebi receives $37.

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As we know that Trinomial means a polynomial with three terms.

Therefore, option (c) x²y -xy² +y² is correct.

Given polynomials are:

(а) -7z

(b) z² – 4y²

(c) x²y – xy² + y²

(d) 12a – 9ab + 5b – 3.

To Find :  Which one is Trinomial.

Monomial:

A monomial is defined as an expression with one non-zero term. It consists of various parts such as variables, coefficients and orders. A unary variable is the character it contains. A coefficient is a number that is multiplied by a monomial variable. The monomial degree is the sum of the exponents of all variables.

Binomial:

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-no question and each has a Boolean result of Success (probability p) or failure. A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a series of results is called a Bernoulli process. For one trial, d. H. n = 1, binomial distribution is Bernoulli distribution. The binomial distribution is the basis for the common binomial test of statistical significance.

Trinomial:

A ternary expression is an algebraic expression with three terms. An algebraic expression consists of variables and constants in one or more terms. These expressions use symbols or operations such as +, –, ×, and ÷ as separators. Trinomials fall into this algebraic expression, along with monomials, binomials, and polynomials.

In Short :

Monomial - A polynomial with single Term

Binomial - A polynomial with 2 terms

Trinomial  - A polynomial with  3  terms

Based on the information:

(а) -7z    only one term hence Monomial  

(b) z² – 4y²     Two terms Hence Binomial

(c) x²y – xy² + y²    Three terms hence Trinomial  

(d) 12a – 9ab + 5b – 3.   Four terms hence quadrinomial.

So correct option is c)  x²y – xy² + y²    

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if ΔEFG, e = 75 cm, m∠G=141° and m∠E=16° then length of g is 171.24 cm

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that ΔEFG, e = 75 cm, m∠G=141° and m∠E=16°

We need to find the length of g.

Because two angles are given, F = 180 – (141 +16 )

m∠F=180-157F=23

Now let us apply the sine rule

SinE/e=SinF/g

Sin16/75=sin23/g

g=171.24 cm

Hence, if ΔEFG, e = 75 cm, mm∠G=141° and mm∠E=16° then length of g is 171.24 cm

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Answer: The y-intercept of the line perpendicular to the line y = -3/4x+5 that includes the point (-3,-3) is -21/4. Thus option D is correct.

Step-by-step explanation: The line is a general straight line y=mx+c where c is the y-intercept and m is the gradient or the slope.

In this equation, m= -3/4. Putting the value of m, y and x in the equation gives

-3=3/4(-3) + c

-3= 9/4 +c

solving for c we get,

c= -3-9/4

c = - 21/4

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The process for converting 2D data to 3D data involves a few steps. First, a 3D model needs to be created, which is typically done using a 3D modeling software such as Blender or 3DS Max.

Data in math is information that can be used to draw conclusions or make decisions. It is typically collected, analyzed, and presented in the form of numbers, graphs, or tables. Data can be used to compare and contrast different scenarios, identify trends and patterns, or make predictions about the future. Data can also be used to help researchers develop hypotheses and develop models to explain phenomena.

Once the model is created, the data needs to be imported into the software in a format that can be used by the software, such as an .obj or .3ds file. The data can then be manipulated within the software to create the 3D model. Finally, the 3D model can be exported in a variety of file formats, such as .stl, .fbx, or .dae, that can be used for 3D printing, virtual reality, and other applications.

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To  write coordinates in quadratic forms,

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According to given data, we can prove that Statement 1 is increasing function, Statement 2 is Decreasing Function, and Statement 3 is Constant Function.

1. The linear function that describes the relationship between the input value (number of days) and the output value (total number of texts sent) is y = 60x, where y is the total number of texts sent and x is the number of days. The graph of this function is increasing because as the number of days increases, the total number of texts sent also increases at a constant rate of 60 texts per day.

2. The linear function that describes the relationship between the input value (number of days) and the output value (total number of texts remaining for the month) is y = 500 - 60x, where y is the total number of texts remaining for the month and x is the number of days. The graph of this function is decreasing because as the number of days increases, the total number of texts remaining for the month decreases at a constant rate of 60 texts per day.

3. The linear function that describes the relationship between the input value (number of days) and the output value (total cost of texting each month) is y = 50, where y is the total cost of texting each month and x is the number of days. The graph of this function is constant because the cost of texting is the same regardless of the number of days.

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