(a) Draw the graph of y=x²+x-5 for values of x ranging from -4 to +3. Use a scale of 1cm to 1 unit on both axes. (b) On the same graph draw the line y = 2(x-1). From your graph: (c) find the roots of the equation x²+x-5=0 (d) deduce the roots of the equation x²+x-7=0 (e) deduce the roots of the equation x²+x-5=2(x-1) (f) state the minimum value of x2+x-5.​

Answer:

[tex] \frac{3}{4} + \frac{1}{3} \\ \frac{ \: \: 9 \: \: + \: \: 4 \: \: }{12} \\ \frac{13}{12} [/tex]

The probability of the couple having at least one girl is 0.875 0r 87.5 % by probability method. So, the option C is correct.

Having at least 1 girl out of 3 children means that there can be 1, 2 or 3 girls out of the 3 children.

So having at lest 1 girl out of 3 children is the same as saying that all 3 children are not boys.

The probability that all 3 children are boys would be

chance that child 1 is a boy * chance that child 2 is a boy * chance that child 3 is a boy = 0.5 * 0.5 * 0.5 = 0.125

since given that there is equal chance of both.

And the probability that NOT all 3 children are boys would be

100% - probability that all 3 children are boys = 1 - 0.125 = 0.875.

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Answer:

see explanation

Step-by-step explanation:

1

20% of 35

= [tex]\frac{20}{100}[/tex] × 35

= 0.2 × 35

= 7

(2)

60% of 70

= [tex]\frac{60}{100}[/tex] × 70

= 0.6 × 70

= 42

(3)

45% of 80

= [tex]\frac{45}{100}[/tex] × 80

= 0.45 × 80

= 36

Answer:

busy work lol. its = not smart

Step-by-step explanation:

The value of x is 15 and the angles in the pentagon are 105,49,90,33,83

What is interior angles in a pentagon ?

The interior angles in a pentagon are the angles which are inside the pentagon and sum of the interior angles in a pentagon is 540 degrees.

Given ,

From the figure we can say that it is pentagon.

And the sum of exterior angles in a pentagon is always 360 degrees.

SO,

7x+49+6x+33+83 = 360

13x + 165 = 360

13x = 360 - 165

13x = 195

x = 195 / 13

x = 15

So, the angles could be 7x = 7*15 = 105  and 6x = 6*15 = 90

Therefore, The value of x is 15 and the angles in the pentagon are 105,49,90,33,83 .

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After finding the ratio, the population of Illinois than Alaska is 20 times greater.

The population of Alaska is approximately 6.5 x [tex]10^5[/tex] people.

The population of Illinois is about 1.3 x [tex]10^7[/tex] people.

We have to find how many times greater is the population of Illinois than Alaska.

We will use their population ratio to determine how many times the population of Illinois is greater than the population of Alaska.

Ratio = Population of Illinois's /Population of Alaska

Ratio = 1.3 x [tex]10^7[/tex]/6.5 x [tex]10^5[/tex]

Now simplifying.

Ratio = 0.2 x [tex]10^2[/tex]

Ratio = 20

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According to the area value, the amount required to be paid for the showroom is $2000.85

The term area in math is known as the region bounded by the shape of an object or it is the space covered by the figure or any two-dimensional geometric shape.

Here we have know that Warehouse Space A Includes 8000 sq. Ft. Of showroom and workshop space and it rents for. 85 cents per month and an additional 25. Cents per sq. Ft, per month for operations expenses.

While we looking into the question, we know that the following are known,

Area = 8000 square feet.

Rent = 85 cents.

Additional expenses = 25 cent per square feet.

Then the total expense is calculated as,

=> 85 + (8000 x 25)

=> 200085 cents.

When we convert into dollars, then we get,

=> One dollar = 100 cents.

Then the resulting value is

=> $2000.85

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The trigonometric equation 7cos(9x) - 1 = 17 has an undefined solution.

The trigonometric equation for this problem is defined as follows:

7cos(9x) - 1 = 17

Isolating the cosine, we have that:

7cos(9x) = 18

cos(9x) = 18/7

Now we isolate x applying the arc cosine, which is the inverse of the cosine, as follows:

9x = arccos(18/7)

9x = undefined.

The solution is undefined because the arccosine only exists for values between -1 and 1, as the cosine of an angle is always going to assume a value between -1 and 1.

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Answer:

1050$

Step-by-step explanation:

= 75

75 ___ × 60

75 ___ × 60 100

75 ___ × 60 100= 3

75 ___ × 60 100= 3 ___ × 60

75 ___ × 60 100= 3 ___ × 60

75 ___ × 60 100= 3 ___ × 60 4

75 ___ × 60 100= 3 ___ × 60 4= 45

Answer:

x=-1 y=-1

Step-by-step explanation:

i am lazy to type

Answer:{x = -1}{y = -1}

Step-by-step explanation:

subtract the two equations

{6x - 5y = -1                       ^

{6x + 4y = -10                      ^

determine the sign

6x - 5y - (6x +4y) = -1 - (-10) ^

simplify

6x - 5y - 6x - 4y = -1 + 10 ^

substitute

y = -1      ^

solve the equation

6x + 4 x (-1) = -10  ^

write the solution

x = -1                     ^

The net external force acting on the freely falling ball is 43.12 N.

We are provided with the following information:

Mass of bowling ball (m) = 5.5kg

Distance travelled by the ball (h) = 12m

Time taken by the ball = 1.75 s

To calculate the net force acting on the ball, we first need to calculate the acceleration experienced by the ball under free fall.

We can determine the acceleration using the formula,

d= ut + (1/2)at^2

since, the ball was initially at rest, u=0.

Thus, formula becomes,

d= (1/2)at^2.

Therefore, a= 2d/t^2

=> a= 2*12/(1.75)^2

=> a=24/ 3.0625

=> a= 7.84 m/s^2

Now, according to Newton's 2nd law of Motion,

[tex]F_{net} = mass * acceleration[/tex]

[tex]F_{net}[/tex] = 5.5 * 7.84 N =  43.12 N

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The fraction 1/4b + 1/4 = -1/2 is simplified to b = -12/4

A fraction can be defined as the part of a whole variable, or number.

The types of fractions are;

From the information given, we have that;

1/4b + 1/4 = -1/2

Now, collect iike terms

1/4b = -1/2 - 1/4

find the lowest common denominator

1/4b = -2 -1 /4

Add the numerators

1/4b = -3/4

Now, divide both sides by the coefficient of b

b = -3/4 × 4/1

Multiply the values

b =-12/4

Hence, the value is - 12/4

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Answer:

525 minutes

Step-by-step explanation:

Let us find the temperature of each furnace after 't' minutes.

Furnace1:

Temperature in furnace1 is reducing at rate of 3.5°C per minute.

Rate of cooling after t minute = 3.5*t = 3.5t

We have to subtract 3.5t from 1200°C as it is cooling.

Temperature of furnace1 after 't' minutes = 1200 - 3.5t

Furance2:

Temperature in furnace2 is increasing at rate of 0.5°C per minute.

Rate of heating after t minute = 0.5*t = 0.5t

We have to add 3.5t from 900°C as it is getting heated.

Temperature of furnace1 after 't' minutes = 900 +0.5t

After some minutes, both furnace reach the same temperature.

              900 + 0.5t = 1200 - 3.5t

    900 + 0.5t + 3.5t = 1200

                           4t   = 1200 + 900

                           4t   = 2100

                             t =  2100 ÷ 4

                             [tex]\boxed{t = 525 \ minutes}[/tex]

The total cot of the building (original cot of $6,552,000 le the Accumulated Depreciation of $4,550,000 pre-adjutment) divided by the new life of 35 year equal the annual depreciation amount of $188,514.29. The econd journal entry would therefore debit Building for $5,552,000 ($188,514.29 x 10 year) and credit Accumulated Depreciation for the same amount.

The journal entry to record the tructural repair and the related  adjutment i:

Debit: Accumulated Depreciation $1,000,000

Credit: Building $1,000,000

Debit: Building $5,552,000

Credit: Accumulated Depreciation $5,552,000

The first journal entry record the cot of the tructural repair. The $1,000,000 tructural repair cot reduce the value of the building, and therefore the amount debited to Accumulated Depreciation will equal the amount credited to Building.

The econd journal entry adjust the Accumulated Depreciation for the change in the life of the building. Since the life of the building wa extended 10 year, the Accumulated Depreciation need to be reduced by 10 year of depreciation. The total cot of the building (original cot of $6,552,000 le the Accumulated Depreciation of $4,550,000 pre-adjutment) divided by the new life of 35 year equal the annual depreciation amount of $188,514.29. The econd journal entry would therefore debit Building for $5,552,000 ($188,514.29 x 10 year) and credit Accumulated Depreciation for the same amount.

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A number that is less than 5 / 8 but is greater than 1 / 9 is A. 0. 5.

To find the number that is less than 5 / 8 but greater than 1 / 9, first convert both fractions to decimals.

5 / 8 in decimals is:

= 5 / 8

= 0. 625

1 / 9 in decimals is:

= 1 / 9

= 0. 111

The number from the given options that is less than 5/8 but greater than 1/9 is therefore 0. 5 as it is less than 5 / 8 but more than 1 / 9.

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The options for the question include:

The given scatter plot depicts the exponential function. Therefore, option 1 f(x) = 2ˣ is the correct one.

A scatter plot is a particular kind of graphic diagram that uses Cartesian coordinates to show the values of two variables for a collection of data.

We write y as the function of x as y=f(x). Here, f is considered the name of the function and x is the value of the function. To check which function depicts the given scatter plot, we have to substitute the values for x and find the function. Then, plot the graph.

By doing we get, the plot for f(x) = 2ˣ is equivalent to the given scatter plot. Because this graph depicts the exponential function where the graph passes through the point (0,1). Therefore, option 1 correctly depicts the given plot. Option 2 depicts the identity function and 4 depicts squaring or quadratic function.

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The two non-right angles in a right angled triangle balance each other out because the right angle already takes up 90 degrees of the triangle's 180 total angles. We refer to two angles as complementing each other when their sums equal 90 degrees.

The right angle, or 90°, is always one angle. The hypotenuse is the side with the 90° angle opposite. The longest side is always the hypotenuse. The sum of the other two inner angles is 90 degrees. Base and perpendicular are the names of the other two sides that are close to the right angle. The Pythagorean Theorem is a triangle formula.

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The distance between Tim and Jan rounded to the nearest tenth is 21.4 miles.

The formula used in this problem is the Pythagorean Theorem. The Pythagorean Theorem states that the square of the hypotenuse (the longest side of a right triangle) is equal to the sum of the squares of the other two sides. This can be shown as A2 + B2 = C2.

In this problem, we need to find the hypotenuse, which is the distance between Tim and Jan. To do this, we will use the Pythagorean Theorem. First, we need to find the sum of the squares of the distances traveled by Tim and Jan.

For Tim, the square of 8 miles plus the square of 15 miles equals 289. For Jan, the square of 5 miles plus the square of 12 miles equals 169. Adding these together gives a total of 458. We then take the square root of 458 and get 21.38. This is the answer we are looking for, the distance between Tim and Jan rounded to the nearest tenth is 21.4 miles.

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Probability that 2 or more of the statistics courses are in same slot is 0.28.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

probability that 2 or more of the statistics courses are in same slot

=1-P(all 3 are in different slots)

=1-P(select 3 from 10 slots and arrange them)

=1-(10*9*8)/10^3

=0.28

Therefore, probability that 2 or more of the statistics courses are in same slot is 0.28.

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Answer:

[D] -45 + 54x

Step-by-step explanation:

Base on the given we can use the distributive property to solve this:

Distributive property ⇒ Multiply outside numbers with each term inside the parenthesis.

-9 (5 - 6 x )  → {-9 × 5 = -45 } {-9 × -6x = 54x}

Now let's put it together;

-45 + 54x

Hence, [D] -45 + 54x is the correct answer.

RevyBreeze

Answer: There are none

Step-by-step explanation:

The polynomial for the north side of the house will be 2x^2+9x-32.

What are polynomials?

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x^2+x-12. In this example, there are three terms: x^2, x and -12.

Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial.

Now,

As the north side will be the sum of 5x-4,x^2-23 and 4x-5

so the polynomial for north will also be the sum of  5x-4,x^2-23 and 4x-5.

Hence,

          Polynomial for north side= 5x-4 + x^2-23 + 4x-5

         Polynomial for north side   =2x^2+9x-32

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Since they are not the same, they are not the exact same circles.  In other words they are similar.

Since the center point does not affect the size of the circle.

Now, According to the question:

Figures can be proven similar if one, or more, similarity transformations

reflections, translations, rotations, dilations can be found that map one

figure onto another.

To prove all circles are similar, a translation and a scale factor from a

dilation will be found to map one circle onto another

Lets solve the problem

Circle A has center (1 , 1) and radius 4

The standard form of the equation of the circle is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex] , where (h , k) are the coordinates the center

and r is the radius

Equation circle A is [tex](x -1)^2 + (y - 1)^2 = (4)^2[/tex]

Equation circle A is : [tex](x -1)^2 + (y - 1)^2 = 16[/tex]

[tex]x^{2} +1-2x+y^2+1-2y=16\\\\x^2 +y^2-2x-2y+2=16\\\\x^2 +y^2-2x-2y-14=0\\\\x^2+y^2= 14+2x+2y[/tex]

Circle B has center (-4 , -2) and radius 3

Equation circle B is [tex](x - (-4))^2 + (y - (-2))^2 = (3)^2[/tex]

Equation circle B is [tex](x +4)^2 + (y +2)^2 = 9[/tex]

[tex]x^2+16+8x+y^2+4+4y=9\\\\x^{2} +y^2+20+8x+4y=9\\\\x^2+y^2+8x+4y+11=0[/tex]

By comparing between the equations of circle A and circle B

As you can see, if we try to equate the [tex](x^2 + y^2)'s[/tex], the values of them are not the same.  Since they are not the same, they are not the exact same circles.  In other words they are similar.

You can also compare the radii as well, since the center point does not affect the size of the circle.

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92 is the most reasonable estimate for the number of Gamin Middle School athletes whose favorite sport is hockey.

A reasonable estimate does not exceed the original numbers in a problem.

Reasonableness can be defined as checking to verify that the result of the solution or the calculation of the problem is correct or not, either estimating or plugging in your result to check it

The most reasonable estimate for the number of Gamin Middle School athletes whose favorite sport is hockey.

Estimate= population size x sample proportion.

population size=114

sample proportion=10/45

Estimate=114*10/45

Estimate=92.

Therefore, 92 is the most reasonable estimate for the number of Gamin Middle School athletes whose favorite sport is hockey.

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Answer: The pH of blood is a measure of its acidity or basicity and is related to the concentration of hydrogen ions (H+) in the blood. The pH of 7.371 indicates that the blood is slightly basic. Carbonic acid (H2CO3) is a weak acid that dissociates into bicarbonate (HCO3-) and hydrogen ions (H+) in water. The carbonic acid concentration of 1.5 indicates the concentration of H2CO3 in the blood.

The concentration of bicarbonate (HCO3-) in the blood can be approximated by using the relationship between the pH, carbonic acid concentration and the bicarbonate concentration. The Henderson-Hasselbalch equation, which relates the pH and the pK of a buffer, to the ratio of the buffer's conjugate base to its acid form is:

pH = pK + log [HCO3-]/[H2CO3]

The pK of carbonic acid is 6.1 and the concentration of H2CO3 is given as 1.5.

Plugging these values into the Henderson-Hasselbalch equation,

7.371 = 6.1 + log [HCO3-]/1.5

Solving for [HCO3-],

[HCO3-] ≈ 25.8 mM

The approximate concentration of bicarbonate (HCO3-) in the person's blood is 25.8 mM.

Please note that this is an approximation, the actual value may vary depending on the person's health condition.

Step-by-step explanation:

As per the Pythagoras theorem the length in feet of Brad's "line of sight" to the base of the flagpole 25 feet².

In math the term called Pythagoras theorem is states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

The standard form of the Pythagoras theorem is written with the help of the triangle ABC as,

=> AC² = AB² + BC²

where AC refers the hypotenuse and AB and BC refers the sides of the triangle.

Here we know that it follows from the task content that the length in feet of Brad's line of sight to the base of the flag pole is to be determined.

And here we also know that the flag pole in discuss is said to be 15 feet high.

And here we have also identified that Brad is at the same height as the pole and is at a horizontal distance of 20 feet from the top of the pole.

Then the length is calculated as,

=> l² = 15² + 20²

=> l² = 225 + 400

=> l² = 625

=> l = 25.

Hence the length of the line of sight is 25 feet.

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It saves time, doesn't need to be changed if a row or column is added to the range, and adjusts the range when the function is copied to another cell.

Based on the values in another column, we'll discover how to add up a column of numerical data. We are attempting, for instance, to assess product sales based on the typical customer rating. Thus, each of our products has an average rating of 9.8, 7.2, 6.1, and so on because customers score our products on a scale of 1 to 10. The sales totals for goods with ratings of 9 to 10, 7 to 8, and so forth should be calculated.

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The factored form of 6 + 27 is 3(2 + 9) using GCF.

The greatest common factor, which is the product of two or more numbers, is the biggest number (GCF). A natural number is created by dividing them by the biggest number (factor). There are a few factors that both share once all the number's components have been identified. The greatest common factor is the one with the largest number among the common factors. The highest common factor is another name for the GCF (HCF)

The given expression is:

6 + 27

Take the factors of the individual numbers:

6 = 1, 2, 3, 6

27 = 1, 3, 9, 17

Take the common factor from both the numbers, in this case it is 3.

Now, factor out the number from the given expression:

6 + 27

3(2 + 9)

Hence, the factored form of 6 + 27 is 3(2 + 9) using GCF.

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The solution of equation f(x)=g(x) is 2.

a formula that illustrates the relationship between the two expressions on either side of a sign. Usually, it has one variable and an equal sign. similar to 2. 2x - 4 = 2. The equals sign (=) in equations indicates that two expressions are equal. Point-slope, standard, and slope-intercept equations are the three main types of linear equations.

The "left hand side" and "right hand side" of the equation refer to the expressions on each side of the equals sign. The right side of an equation is frequently thought of as zero.

Given : f(x)=g(x)

          1/x = (x-1)^2-1

          1 = x (x-1)² - 1

          x (x-1)² = 2

         x ( x² + 1 - 2x ) = 2

         x³ + x - 2x² = 2

         x³ + x - 2x² - 2 = 0

         x³ - 2x² + x - 2= 0

        x²(x-2) + 1(x-2) = 0

       (x² +1) + (x-2) = 0

So,   x = 2 .

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Reason:

The negative out front is distributed to each term inside the parenthesis.

This will flip the sign of each term.

For more information, search out "distributive property".