A torch and a battery cost 2. 50 altogether. The torch costs 1. 50 more than the battery. What fraction of the total price is the torch?Give your answer in its simplest form

For [tex]f(x)[/tex], the axis of symmetry is the vertical line passing through the vertex. Matching with vertex form, we see the vertex of the graph of [tex]f(x)[/tex] has coordinates [tex](4,2)[/tex]. Thus, the axis of symmetry has equation [tex]x=4[/tex].

Similarly, for [tex]h(x)[/tex], the axis of symmetry is the vertical line passing through the vertex. The vertex of the graph of a quadratic function is either the minimum or maximum point (it depends on the leading coefficient of the function). Here, there is a maximum point, which has coordinates [tex](-2,2)[/tex]. Thus, the axis of symmetry has equation [tex]x=-2[/tex].

The solutions for the equation are b = 0, 3.

What is the cubic equation?

A three-degree equation is referred to as a cubic equation. All cubic equations have roots that are either three real roots or one real root and two imaginary roots. Polynomials are referred to as cubic polynomials if they have a degree of three. The opposite of cubing an integer is finding the cube root of that number. It can be determined by first determining how the given integer can be divided into prime factors, and then by using the cube root formula.

To find the solution for the equation 5/3b³ - 2b² - 5, we can factor it or use the quadratic formula.

One way to factor it is to note that it is a cubic equation in terms of b, and can be written as:

5/3b³ - 2b² - 5 = (5/3b³ - 2b²) - 5 = (5/3b³ - 2b²- 5b) + (5b)

= (5/3b)(b² - 3b) + 5

So, b=0 is one solution, but we can also factor the remaining quadratic equation (b² - 3b) = 0,

b=0 and b=3 are the solutions for the equation.

Hence, the solutions for the equation are b = 0, 3.

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By solving a system of equations we will see that the quadratic equation is:

y = 3*x^2 - 10*x - 4

We know that a general quadratic function can be written as:

y = a*x^2 + b*x + c

Here we know that the equation passes through (0, -4), replacing these values:

-4 = a*0^2 + b*0 + c

-4 = c

Then the quadratic equation is:

y = a*x^2 + b*x - 4

Now we can use the other two points (-3, -7) and (2, -12), replacing these values we will get a system of equations:

-7 = a*(-3)^2 + b*(-3) - 4

-12 = a*(2)^2 + b*(2) - 4

We can simplify these equations to get:

-3 = 9a + 3b

-8 = 4a + 2b

We can isolate b on the second equation to get:

2b + 4a = -8

2b = -8 - 4a

b = (-8 - 4a)/2

b = -4 - 2a

Now we can replace that in the other equation to get:

-3 = 9a + 3*(-4 - 2a)

-3 = 9a -12 - 6a

-3 + 12 = 3a

9 = 3a

9/3 = a

3 = a

And the value of b is:

b = -4 - 2a

b = -4 - 2*3

b = -4 - 6 = -10

Then the quadratic equation is:

y = 3*x^2 - 10*x - 4

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Answer:

ΔMDA ≅ ΔMBC by ASA

Step-by-step explanation:

∠DMA ≅ ∠BMC          

MD ≅ MB

∠MDA ≅ ∠MBC

Two angles are congruent and the sides in between the congruent angles are equal. So, the two triangles are congruent by Angle Side Angle congruency.

Answer:

2x+6=x+4

2x-x = 4-6

x= -2

Answer:

x=-2

Step-by-step explanation:

cuz , if u added them together the sum would be -2+6=4 , is that ur question? or I've answered smth that has nothing to do?

The actual height of the house is 0.910 feet.

When both the original dimensions and the new dimensions are known, the scale factor may be determined. When employing the scale factor, there are two terms that must be understood. When a figure's size is increased, we refer to this as scaling up, and when its size is decreased, we refer to this as scaling down.

Given:

Scale : 14 inch = 3 feet

So, 1 inch is represented by

= 3/14

So, 4.25 inch represented as

= 3/14 x 4.25

= 0.910 feet

Hence, the actual height is 0.910 feet.

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The increase in the temperature for an increase of 5 chirps per minute is 41.7 Fahrenheit.

What is Linear relationship?

A Linear relationship, describes a straight-line relationship between two variables.

Given that, There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature.  A biologist gives the model = 25.2 + 3.3x, where x is the number of chirps per minute.

there is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. a least-squares fit of some data collected

Here x = 5, putting it in the given model,

Temperature = 25.2 + 3.3 (5) = 41.7 F

Hence, the required prediction of increase in temperature is 41.7 F

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Formula questions are those questions which require an answer that is numerical in value, including a specific value or a set of values.

These questions require you to apply certain mathematical formulas and use numeric data to come up with solutions. It will contain random numerical data that will be changed and the student has to find a solution for the same. Any numeric value can be modified and hence, the answer is not fixed. There can be different answers depending on the set of numbers presented in the formula question. The answer can be found by using the necessary formulas that exist.

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Answer:

j+k=468

j=52 + j

are the correct equations

If Pham burgers has beginning net fixed assets of $684218 , ending net fixed assets of $679426 and depreciation expense of $48859 , then the net capital spending for the year is $44067  .

For the Pham burgers , the Beginning Net Fixed Assets is = $684218 ;

the ending net fixed assets for Pham burgers is = $679426  ;

the depreciation expense for Pham burgers is = $48859 ;

the tax rate is 21% , which is not relevant for this question ;

The Net capital Spending for the year can be calculated using the formula :

[tex](Ending \; Net \; Fixed \;Assets - Beginning \; Net\; Fixed \; Assets) + Depreciation[/tex] ;

substituting the required values ,

we get ;

Net Capital Spending for year is = ($679426 - $684218) + $48859 ;

On simplifying ,

we get ;

= $44067 .

Therefore , the Net Capital Spending for the year is $44067  .

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Answer:

565.004, 565.040, 565.4

Step-by-step explanation:

Answer:

where t is in hours since midnight and f(t) represents thousands of gallons of water. The amount of treated water at any given time, t, can be modeled by g(t) = 30e^cos(/2)a) Define a new function, a(t), that would represent the amount of untreated water inside the plant, at any given time, t.b) Find a′ (t).c) Determine the critica

The solution to the system in given tables of line 1 and line 2, using linear equation is (b) (0,5)

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

from the table of line 1, the equation of line is

y = 2x +5.

from the table of line 2, the equation of line is

y = 5 - x

to find the solution of the system, we compare both of the equation, we get

2x + 5 = 5 - x

add x from both side, we get

3x + 5 = 5

subtract 5 from both side, we get

3x = 0

So that, x = 0

putting the value of x in the equation of line 2

y = 5 - x

y = 5 - 0

y = 5

The solution to the system in given tables of line 1 and line 2 is (0,5)

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Conversing the conditional statement we get the answer as, if x is odd, then x+ 1 is even.

Two pieces make up a conditional statement: an assumption in the "if" clause and a conclusion in the "then" clause. Conversing, changes the hypothesis and conclusion to create the conditional statement's opposite.

The converse of the first conditional statement is:

If x is odd, then x + 1 is even.

If x is not odd, then x + 1 is not even.

If x + 1 is even, then x is odd.

If x + 1 is not even, then x is not odd.

Hence, in converse of the conditional statement we switch the hypothesis and the conclusion of the statements.

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Answer: 1478 = Pedro
1196 = Ricky

Step-by-step explanation: 2674-282 = 2392/2 = 1196 = Ricky
1196+282 = 1478 = Pedro

The difference in values of the two houses when they are each 15 years old is given as follows:

$22,000.

The home values are modeled using linear functions, which in slope-intercept form are given as follows:

y = mx + b.

In which the parameters are given as follows:

For House A, the points are given as follows:

(3,150) and (8, 180).

Then the slope is given as follows:

m = (180 - 150)/(8 - 3)

m = 6.

Hence:

y = 6x + b

When x = 3, y = 150, hence the intercept b is given as follows:

150 = 18 + b

b = 132.

Then the function for the value of the home after x years is given as follows:

y = 5x + 132.

Meaning that the value of the home after 15 years is given as follows:

y = 5(15) + 132

y = $222,000.

For House B, the points are given as follows:

(1,130) and (5, 150).

Then the slope is given as follows:

m = (150 - 130)/(5 - 1)

m = 5.

Hence:

y = 5x + b

When x = 1, y = 130, hence the intercept b is given as follows:

130 = 5 + b

b = 125.

Then the function for the value of the home after x years is given as follows:

y = 5x + 125.

Meaning that the value of the home after 15 years is given as follows:

y = 5(15) + 125

y = $200,000.

The difference is then given as follows:

$222,000 - $200,000 = $22,000.

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Answer: We know that T is the midpoint of VW, which means that ZW = ZV. So we can say that ZV = ZW = 41°.

Also, we know that Y is the midpoint of UW, so the angle ZYU is half of ZUW. So we can say that ZYU = ZUW/2.

We know that X is the midpoint of UV, so the angle ZXU is half of ZUV. So we can say that ZXU = ZUV/2.

Since Y is the midpoint of UW, ZYU + ZXU = ZUW/2 + ZUV/2 = ZUW/2 + (ZUW - ZXU)/2 = ZUW/2 + (ZUW - ZUV/2)/2 = ZUW/2 + (ZUW - ZUW/2)/2 = ZUW/2 + ZUW/4 = (3/4)ZUW

We know that X is the midpoint of UV, so ZXU + ZVU = ZUV/2 + ZUV = ZUV

The angle ZTYW is supplementary to the angle ZXU + ZVU + ZYU so mZTYW = 180 - ( ZXU + ZVU + ZYU)

Therefore, mZTYW = 180 - ( ZUV + (3/4)ZUW + 41)

mZTYW = 180 - (56 + (3/4)56 + 41) = 180 - (56 + 42 + 41) = 180 - 139 = 41 degrees

Step-by-step explanation:

Our confidence interval is (66, 102).

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.

Now, here:

Mean, μ = 84

Standard deviation, σ = 9

It is a 95% confidence interval. We know that, within 2 standard deviations of the mean lies 95% of the population. Hence, z = 2.

Now, calculating μ - z.σ and μ + z.σ to find the intervals.

μ - z.σ  = 84 - 2x9 = 66

μ + z.σ = 84 + 2x9 = 102

Thus, our confidence interval is (66, 102).

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Answer:

65.9

Step-by-step explanation:

The equation x² – 12x = 30 (x>0) promises that we can determine possible values of x if we solve the equation.  So let's start there:

We can factor the equation or solve it with the quadratic equation.

Factor

  x² – 12x = 30

  x² – 12x - 30 = 0

I don't see an easy factor solution.  One possibility is to first rewrite the equation as

  (x-12)x-30 = 0

  (x-6)^2 - 66 = 0

 -(-x+[tex]\sqrt66}[/tex]+6)(x+[tex]\sqrt{66}[/tex]-6)

The roots are:

x = 6-[tex]\sqrt{66}[/tex] and

x = 6+[tex]\sqrt{66}[/tex]

Since x>0, only the second root is valid:  x = 6+[tex]\sqrt{66}[/tex]

x = 6 + (8.12)

x = 14.12

[That was painful]

Quadratic Equation

Solving with the quadratic equation gives values of:

14.12, and -2.12  Again, only the positive value is valid:  14.12

[The quadratic approach was far easier than factoring, in this case]

==

Since we established x = 14.12, (x − 6)² bcomes:

  (14.12 − 6)²

 (8.12)² = 65.9

The transformation for the graph f(x) to h(x) is a vertical transformation of 2 units.

The graph is given below.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

f(x) = x

h(x) = x + 2

h(x) = f(x) + 2

Now,

f(x) → h(x)

The transformation from f(x) to h(x) is a vertical translation of 2 units.

i.e

f(x) → f(x) + 2

The graph is given below.

The blue line is the function.

The red line is the parent function.

Thus,

The transformation of the function is f(x) → f(x) + 2.

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The point-slope form of the horizontal line (-6,0) is y = 0.

Here given point (-6,0).

If the line is horizontal, the slope is zero.

Then the formula in slope-point form, ( y - y 1 ) = m ( x - x 1 )

By substituting,

This is equivalent to y - 0  = 0 ( x - (-6)).

y - 0 = 0

y = 0

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Answer:

[tex] \sf \: 9(x + 2)[/tex]

Step-by-step explanation:

Given expression,

→ 9x + 18

Let's factorise the expression,

→ 9x + 18

→ (9 × x) + (9 × 2)

→ 9(x) + 9(2)

→ 9(x + 2)

Hence, the factor is 9(x + 2).

The simplified form of the expression given is 4.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given is a logarithmic expression.

㏒ 10⁸ - ㏒ 10⁴

We have a rule for logarithms ㏒ aᵇ = b ㏒ a

So the expression becomes,

㏒ 10⁸ - ㏒ 10⁴ = 8 ㏒ (10) - 4 ㏒ (10)

The value of log 10 is 1.

㏒ 10⁸ - ㏒ 10⁴ = 8 - 4 = 4

Hence the expression can be simplified to 4.

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Answer:

N/A

Step-by-step explanation:

1. subtract 3 from both sides to isolate the square root and its coefficient

5√(5-x) = - 10

2. divide both sides by 5 to isolate the square root

√(5-x) = -2

this means that the square root of something would be negative, which is not possible

The zeros of the quadratic function are: x = -3 or x = -4.

The quadratic function is:

f(x) = 2x² + 14x + 24

Set the function equal to 0

2x² + 14x + 24 = 0

Common 2 from the left side,

⇒2(x² + 7x +12) = 0

Factorize the left side

⇒2(x + 3)(x + 4) = 0

Set factors equal to 0 and we get

  x + 3 = 0 or, x + 4 = 0

⇒x = 0-3 or, x = 0-4

⇒x = -3  o, x = -4

Thus,

The zeros of the quadratic function are: x = -3 or x = -4.

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Answer:

A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are coefficients and x is the variable.

The roots of a quadratic equation are the values of x that make the equation equal to zero.

Given that the roots of the quadratic equation are (3+√5) and (3-√5), we can set the quadratic equation equal to zero and substitute the roots for x:

ax^2 + bx + c = 0

(x - (3+√5))(x - (3-√5)) = 0

(x - 3 - √5)(x - 3 + √5) = 0

(x - 3 - √5)(x - 3 + √5) = (x-3)^2 - (√5)^2 = (x-3)^2 - 5 = 0

x^2 - 6x + 9 - 5 = 0

x^2 - 6x + 4 = 0

So the quadratic equation whose roots are (3+√5) and (3-√5) is x^2 - 6x + 4 = 0

Step-by-step explanation:

The predicted number of sit ups each person can do in 12 seconds, using a proportional relationship model are;

Janet 18 sit ups

Paulo 10 sit ups

Shah 9 sit ups

A proportional relationship is one in which the values of the output variable are a constant multiple of the values of the variables in the set of the input values.

The data for the number of sit ups each person can do with time are as follows;

1. Janet does 3 sit ups in 2 seconds

2. Paulo does 5 sit ups in 6 seconds

3. Shah does 3 sit ups in 4 seconds

The rates at which each person does sit ups, using a proportional relationship between the number of sit ups and time and the the constant of proportionality in the proportional relationship is the rate of sit ups per person which are;

Rate = (Number of sit ups)/(Time)

The rate at which Janet does sit ups = (3 sit ups)/(2 seconds), m = 1.5 sit ups/second

Rate at which Paulo does sit ups = (5 sit ups)/(6 seconds), m = (5/6) sit ups/second

Rate at which Shah does sit ups = (3 sit ups)/(4 seconds), m = (3/4) sit ups/second

The number of sit ups each person can do, n, in a specified time, t, can be found using the formula;

n = m × t

Where;

n = The number of sit ups

m = The rate at which the person does sit ups

t = The time duration

Therefore, the number of sit ups each person can do in 12 seconds are therefore;

The number of sit ups Janet can do in 12 seconds is; n = 1.5 × 12 = 18

Janet can do 18 sit ups in 12 seconds

Number of sit ups Paulo can do in 12 seconds is; n = (5/6) × 12 = 10

Paulo can do 10 sit ups in 12 seconds

Number of sit ups Shah can do in 12 seconds is; n = (3/4)×12 = 9

Shah can do 9 sit ups in 12 seconds

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Answer:

1.3 * c + 1.5

Step-by-step explanation:

(5.2c-7) + (-3.9c + 8.5)

5.2 * c - 7 - 3.9 * c + 8.5

1. add constants ( - 7 and 8.5)

5.2 * c - 3.9 * c + 1.5

2. add both of the coefficients of c

when a variable is multiplied by a coefficient, we can add another coefficient * variable combination if the variable is the same. for example, 1 * x + 2 * x = 3 * x by adding the 1 and 2 together

similarly, 5.2 * c - 3.9 * c = (5.2 - 3.9) * c = 1.3 * c

1.3 * c + 1.5

The fraction 1/9 is greater than the fraction 1/11.

Comparing fractions involves a set of rules related to the numerator and the denominator. When any two fractions are compared, we get to know the greater and the smaller fraction.

To compare unlike fractions:

Step 1: Observe the denominators of the given fractions: .

Step 2: Now, let us convert them in such a way that the denominators become the same.

Step 3: Compare the fractions:

Step 4: The fraction with the larger numerator is the larger fraction.

The given fractions are 1/9 and 1/11.

Here, LCM of denominator 9 and 11 is 99

Then, fractions becomes 11/99 and 9/99

11/99>9/99

1/9>1/11

Therefore, the fraction 1/9 is greater than the fraction 1/11.

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Answer:

---------------------------------

Given equation:

Recall the identity for a square of a sum:

Complete the square by adding the missing part:

Answer:

x = -2, x = -4

Step-by-step explanation:

Given quadratic equation:

[tex]x^2+6x+8=0[/tex]

Solve by the method of Completing the Square.

Step 1

When completing the square for a quadratic equation in the form ax²+bx+c=0, the first step is to move the constant to the right side of the equation:

[tex]\implies x^2+6x=-8[/tex]

Step 2

Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:

[tex]\implies x^2+6x+\left(\dfrac{6}{2}\right)^2=-8+\left(\dfrac{6}{2}\right)^2[/tex]

Simplify:

[tex]\implies x^2+6x+3^2=-8+3^2[/tex]

[tex]\implies x^2+6x+9=-8+9[/tex]

[tex]\implies x^2+6x+9=1[/tex]

Step 3

Factor the perfect square trinomial on the left side:

[tex]\implies (x+3)^2=1[/tex]

Step 4

Square root both sides:

[tex]\implies \sqrt{(x+3)^2}=\sqrt{1}[/tex]

[tex]\implies x+3=\pm1[/tex]

Step 5

Subtract 3 from both sides:

[tex]\implies x+3-3=\pm1-3[/tex]

[tex]\implies x=-4, -2[/tex]

Therefore, the solutions of the given quadratic equation are:

[tex]x=-4, \;\; x=-2[/tex]

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