Factorise the following:
a) x² + 6x +9
b) x² - 6x + 8
c) x² - 4x - 32
d) x² + x-42

Answer:

Step-by-step explanation: I'm not gonna give you the answer but i will explain what you need to do. First you need to draw a bar diagram and then you need to put the number equally. But first in part A is an easy question you only need to explain or tell the steps that you will do to solve the problem. For part C you only need to tell the answer but it says how how many got to fill equally so that means that there are gonna be equal number and an not so equal number. I hope this help you with your answer

The researcher's hypotheses for this study are:

H0: The mean birth weight of babies whose mothers did not see a doctor before delivery is equal to or greater than 3000 grams.

Ha: The mean birth weight of babies whose mothers did not see a doctor before delivery is less than 3000 grams.

In this case, the null hypothesis (H0) states that there is no difference in the mean birth weight of babies whose mothers did not see a doctor before delivery and the mean birth weight of 3000 grams. The alternative hypothesis (Ha) states that the mean birth weight of babies whose mothers did not see a doctor before delivery is less than 3000 grams.

To test these hypotheses, the researcher will need to collect data on the birth weights of babies whose mothers did not see a doctor before delivery and compare the mean birth weight to 3000 grams. If the mean birth weight is significantly less than 3000 grams, the researcher will reject the null hypothesis and accept the alternative hypothesis. If the mean birth weight is not significantly less than 3000 grams, the researcher will fail to reject the null hypothesis.

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Answer:

Factoring a polynomial means breaking it down into simpler parts that can be multiplied together to get the original polynomial. To factor a polynomial completely, we want to find all of its factors, including any that are in the form of a constant, a variable, or a combination of both.

Let's take a look at how to factor two of the given polynomials.

x^5 - x^3

We can factor out the greatest common factor (GCF) of x^3 to get:

x^5 - x^3 = x^3(x^2 - 1)

Now, we have a difference of squares, which we can factor using the formula:

a^2 - b^2 = (a + b)(a - b)

In this case, a = x and b = 1, so we get:

x^5 - x^3 = x^3(x + 1)(x - 1)

Therefore, the polynomial x^5 - x^3 can be completely factored as x^3(x + 1)(x - 1).

3x^2 - 75

We can factor out the GCF of 3 to get:

3x^2 - 75 = 3(x^2 - 25)

Now, we have a difference of squares, which we can factor as:

a^2 - b^2 = (a + b)(a - b)

In this case, a = x and b = 5, so we get:

3x^2 - 75 = 3(x + 5)(x - 5)

Therefore, the polynomial 3x^2 - 75 can be completely factored as 3(x + 5)(x - 5).

In general, to factor a polynomial completely, we should first look for any common factors that can be factored out using the GCF. Then, we can look for special patterns, such as differences of squares, sums or differences of cubes, or quadratic trinomials that can be factored using the quadratic formula or by factoring the sum or difference of two perfect squares. Finally, we can use trial and error or other methods to find any remaining factors that are not immediately obvious.

If you could label my answer brainliest, that would be awesome!

- Dante

The conversion value of Celsius to Fahrenheit for the value 30 Celsius is equal to 86 Fahrenheit.

Relation to convert the temperature from Celsius to Fahrenheit is equal to :

°F = 9 /5 ( ° C ) + 32.

Convert 30 Celsius  to Fahrenheit by substituting the value in the formula :

= 9 /5 ( 30° ) + 32

= 9 (6° ) + 32

= 54°  + 32

= 86°F

Therefore, the converted values for the 30Celsius to Fahrenheit is given by 86 Fahrenheit.

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False, every component of the matrix is multiplied by the same amount when you multiply a matrix by a number. A new matrix is created by this operation; it is known as a scalar multiple.

A rectangular matrix is a grouping of numbers in rows and columns. A matrix element/entry is the term used to describe each number in the matrix. The combination of a real number and a matrix is referred to as scalar multiplication.

Each entry/element of the matrix is multiplied by the specified scalar in scalar multiplication. Comparatively, matrix multiplication describes the result of two matrices. This operation is totally different. We can't just multiply the corresponding entries in two matrices to multiply them.

The first matrix must have exactly as many columns as the second matrix has rows in order to perform matrix multiplication. The resulting matrix has the same number of columns and rows as the second matrix, and its number of columns matches the number of rows in the first matrix.

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500 grams is equivalent to approximately 17.637 ounces.

Gram is a metric unit of weight equal to one thousandth of a kilogram.

Ounce is a unit of weight equal to one sixteenth of a pound or 16 drams or 28.349 grams.

Ounce is defined as exactly 28.349523125 grams and is equivalent to one sixteenth of an avoirdupois pound.

To convert 500 grams to ounces,

We can use the conversion factor that 1 ounce is equal to 28.3495 grams.

So, we can write:

500 grams = (500 ÷ 28.3495) ounces

500 grams = 17.637 ounces (rounded to three decimal places)

Therefore, 500 grams is equivalent to approximately 17.637 ounces.

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Knowing the absolute prices of goods X, Y and Z, we obtain their relative prices:

The relative price of a good is the price of that good in terms of another good. It is calculated by dividing the absolute price of one good by the absolute price of another good.

The relative price of X in terms of Y is calculated by dividing the absolute price of X by the absolute price of Y:

Relative price of X in terms of Y = Absolute price of X / Absolute price of Y

X/Y = $23 / $42

X/Y = 0.55

The relative price of Y in terms of Z is calculated by dividing the absolute price of Y by the absolute price of Z:

Relative price of Y in terms of Z = Absolute price of Y / Absolute price of Z

Y/Z = $42 / $56

Y/Z = 0.75

The relative price of Z in terms of X is calculated by dividing the absolute price of Z by the absolute price of X:

Relative price of Z in terms of X = Absolute price of Z / Absolute price of X

Z/X = $56 / $23

Z/X = 2.43

In conclusion, the relative price of X in terms of Y is 0.55, the relative price of Y in terms of Z is 0.75, and the relative price of Z in terms of X is 2.43.

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Answer:

[tex]\text{Area of larger $\triangle$} = 81 \:cm^2[/tex]

Step-by-step explanation:

Given.

Ratio of corresponding sides of two similar triangles = 2:3 or [tex]\dfrac{2}{3}[/tex]
Area of smaller triangle = 36 cm²

By the property of area of two similar triangle,
Ratio of area of both triangles = (Ratio of their corresponding sides)²

[tex]\dfrac{\text{Area of smaller $\triangle$ }}{\text{Area of larger $\triangle$ }} = \left(\dfrac{2}{3}\right)^2}[/tex]
[tex]\dfrac{36}{{\text{Area of larger $\triangle$ }}} = \dfrac{4}{9}[/tex]

Cross-multiplying we get
[tex]36 \times \dfrac{9}{4} = \text{Area of larger $\triangle$}\\\\81 = \text{Area of larger $\triangle$}\\\\\text{Area of larger $\triangle$} = 81 \:cm^2[/tex]

Answer:

A) 210 B) 0.18

Step-by-step explanation:

got it right

Your rate is 52.5 miles per hour, calculated by dividing the total distance traveled (200 miles) by the total time taken (4 hours).

To calculate this, take the total distance traveled (415 miles) and subtract the distance from Seattle at the start of the journey (215 miles). This gives you the total distance traveled, which is then divided by the total time taken (8 hours), giving you a rate of 52.5 miles per hour.

To better understand this concept, imagine driving from Seattle to Los Angeles. You know that Los Angeles is 800 miles from Seattle, and if you drive for 16 hours, you will reach your destination. In this case, your rate would be

The same principle applies here, which is why you can use the same formula to calculate your rate.

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Rhonda's claim that 8th graders performed better than 7th graders on the state English test seems to be supported, as the median and mode for the 8th graders are both higher than those for the 7th graders.

The 7th graders mode: 0 (since it appears twice in the sample)

The 7th graders median: 3.5 (since the scores are already sorted, the median is the average of the two middle scores, which are 3 and 4)

The 8th graders mode: 3 (since it appears twice in the sample)

The 8th graders median: 8.5 (since the scores are already sorted, the median is the average of the two middle scores, which are 7 and 10)

Based on these measures of center, Rhonda's claim that 8th graders performed better than 7th graders on the state English test seems to be supported, as the median and mode for the 8th graders are both higher than those for the 7th graders.

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The density of air in lb/ft³ based on the conversion using the formula is 0.08 lb/ft³.

We know that the density of air is 1.29 grams per litre. Now, to perform the conversion, we need to find the relation between grams and pounds and litre and feet.

So, we know that 1 gram is equal to 0.0022 pound and 1 litre is equal to 0.0353 cubic foot.

Therefore, keeping these values in the actual formula for conversion.

Density of air = 1.29 × 0.0022/0.0353

Performing division and multiplication on Right Hand Side of the equation

Density of air = 0.08 lb/ft³

Therefore, the density of air is 0.08 lb/ft³.

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The statements required for the prove are given in the explanation.

Vertical angles are two opposite angles which have equal values because they are formed by two straight lines intersecting at a point.

And a midpoint is a point which divides a line segment into two equal parts.

The required statements to prove that ΔTPR ≅ΔQPS are given below;

                 STATEMENT                                 REASON

1. P is the midpoint of TQ and RS                  Given

2. TP = QP, RP = SP                                        Definition of midpoint

3. <SPQ ≅ <RPT                                              Vertical angle theorem

4. ΔTPR ≅ΔQPS                                             Side-Angle-Side theorem

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The correct answer is (c) Understate change in the cost of living because consumers substitute toward goods whose relative prices are declining.

consumers do substitute toward goods whose relative prices are declining. This means that they are able to maintain their standard of living even if the overall cost of living increases. Therefore, the CPI tends to understate changes in the cost of living because it does not fully account for consumer substitution.  

The other options are not correct because:

a. The CPI does take into account quality changes by adjusting prices for changes in quality.

b. The CPI adjusts for changes in relative prices, so it does not overstate changes in the cost of living due to substitution effects.

d. The CPI includes services, but it may understate changes in the cost of living if the prices of services are increasing faster than the prices of goods.

e. The CPI includes a wide range of items, including volatile items such as fruit, vegetables, and petrol. However, the weights assigned to these items may change over time to reflect changes in consumer spending patterns.

The correct answer is (c) Understate change in the cost of living because consumers substitute toward goods whose relative prices are declining.

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If function [tex]f(x) = 7x - 8[/tex]  and  [tex]g(x) =4[/tex] then the answer is [tex](fog)(-1) = -36.[/tex]

In mathematics, a function is a relation between two sets of values, where each input value from the first set (called the domain) corresponds to exactly one output value in the second set (called the range). The output value of a function is determined by its input value and any relevant rules or formulas.

Formally, a function can be defined as follows: Let X and Y be two non-empty sets. A function f from X to Y is a rule or formula that assigns to each element x in X a unique element y in Y, denoted by f(x), such that for any two elements x1 and x2 in X, if x1 = x2, then f(x1) = f(x2). The set X is called the domain of the function, and the set Y is called the codomain or range of the function.

Functions can be represented graphically, algebraically, or in tabular form. The graph of a function shows how the output value of the function varies with the input value, and can be used to visualize the behaviour of the function. The algebraic representation of a function can be given by a formula or equation that expresses the output value in terms of the input value. A tabular representation of a function shows the input-output pairs in a table.

Functions are used in many areas of mathematics, science, engineering, and economics to model and describe relationships between variables. They are also used in practical applications, such as in computer programming, where they are used to define algorithms and data structures.

We need to find (fog)(-1) = f(g(-1)).

First, we find g(-1):

g(-1) = 4(-1) = -4

Then, we plug in g(-1) into f:

f(g(-1)) = f(-4) = 7(-4) - 8 = -36

Therefore, (fog)(-1) = -36.

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Answer:

[tex] \sf \: a) \: 27 = 9p \: ; p = 3[/tex]

Step-by-step explanation:

Given information,

→ Simon have 27 pieces of candy.

→ Each person will get 9 pieces.

Now we have to,

→ Find the required equation.

The equation will be,

→ 27 = 9p

→ 9p = 27

=> As each person (p) gets 9 pieces.

Then the value of p will be,

→ 9p = 27

→ p = 27 ÷ 9

→ [ p = 3 ]

Hence, option (a) is correct.

The chances of Renata being ready to complete kindergarten tasks when she enters school are about 1/2. The solution has been obtained by using the concept of probability.

What is probability?

To calculate the chance of an event, use the mathematical notion of probability. It only enables us to estimate the likelihood that an event will take place. On a scale of 0 to 1, where 0 represents impossible and 1 represents a certain event.

We are given that Renata is a 5-year-old girl from a poor family in the united states, who is about to enter kindergarten.

The chances of Renata being ready to complete kindergarten tasks when she enters school are about 1/2 because it is not necessary that she will be able to do all the tasks. She might be able to do and she might not be able to do.

So, there are equal chances of both.

Hence, chances of Renata being ready to complete kindergarten tasks are 1/2.

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Rana has 1 and 5/12 cups of chocolate chips left. Answer: $\boxed{\text{one and five-twelfths cups}}$.

How to find?

To find out how many cups of chocolate chips Rana has left, we need to subtract the amount she used in the cookie recipe from the amount she bought.

First, we need to convert both mixed numbers to improper fractions, so we can subtract them.

Three and three-fourths cups can be written as:

3\frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}

Two and one-third cups can be written as:

2\frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{7}{3}

Now, we can subtract:

\frac{15}{4} - \frac{7}{3} = \frac{45}{12} - \frac{28}{12} = \frac{17}{12}

Therefore, Rana has 1 and 5/12 cups of chocolate chips left. Answer: $\boxed{\text{one and five-twelfths cups}}$.

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The coordinates of point bbb are \left(\dfrac{2a+7c}{9}, 0\right)left( 9 2a+7c ​ , 0 right).

To find the coordinates of point bbb on \overline{ac}ac start overline, a, c, end overline, we need to use the formula for the division of a line segment in a given ratio. The formula is:

\begin{aligned} x &= \dfrac{x_1m+x_2n}{m+n} \\ y &= \dfrac{y_1m+y_2n}{m+n} \end{aligned}
Where m and n are the given ratio, and (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment.

In this case, the given ratio is \dfrac{2}{7}7 2 ​ start fraction, 2, divided by, 7, end fraction, and the coordinates of the two endpoints are (x1, y1) = (a, 0) and (x2, y2) = (c, 0).

Plugging in the values into the formula, we get:
\begin{aligned} x &= \dfrac{a \cdot 2 + c \cdot 7}{2+7} \\ y &= \dfrac{0 \cdot 2 + 0 \cdot 7}{2+7} \end{aligned}

Simplifying the equations, we get:
\begin{aligned} x &= \dfrac{2a+7c}{9} \\ y &= 0 \end{aligned}

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As a result, if the two angles' measurements are (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.

An angle is a geometric figure formed by two rays that have a common endpoint, called the vertex. The rays are also known as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees. Angles can also be measured in radians, which are another unit of angular measurement used in mathematics and physics. One radian is equal to the angle subtended by an arc of a circle that has a length equal to the radius of the circle. The size of an angle is determined by the amount of rotation that occurs between the two rays. This is typically measured relative to the positive x-axis, with counterclockwise rotations being considered positive and clockwise rotations being considered negative. Angles are used in a wide range of mathematical and scientific applications, including geometry, trigonometry, physics, engineering, and architecture. They are also used in many everyday situations, such as measuring the size of an opening or the angle of incidence of sunlight on a surface.

Here,

If the two angles are congruent, then they must have the same measure.

So we can set the expressions for the measures of the two angles equal to each other and solve for y:

3y + 11 = 11y + 15

Subtracting 3y from both sides:

11 = 8y + 15

Subtracting 15 from both sides:

-4 = 8y

Dividing both sides by 8:

y = -1/2

Therefore, if the measure of the two angles is (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.

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The expressions which are equivalent to 35 + 30s - 45t are:

5(7+6s−9t)

(−35−30s+45t)×(−1)

The correct answer options are options B and C

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

We have to determine equivalent expression:

35 + 30s - 45t

Check all options

A. 7⋅(5+30s−45t)

= 35 + 210s - 315t

False

B. 5(7+6s−9t)

= 35 + 30s - 45t

True

C. (−35−30s+45t)×(−1)

= 35 + 30s - 45t

True

D. 10×(3.5+3s−4.5)

= 35 + 30s - 45

False

E. ( 35/2 - 15s + 45/2t) ⋅ (-2)

= (17.5 - 15s + 22.5t) (-2)

= -35 + 30s - 45t

False

Therefore, the equivalent expression is an expression which has an equal value to each other.

Complete question:

Which expressions are equivalent to 35 + 30s - 45t?

A. 7⋅(5+30s−45t)

B. 5(7+6s−9t)

C. (−35−30s+45t)×(−1)

D. 10×(3.5+3s−4.5)

E. ( 35/2 - 15s + 45/2t) ⋅ (-2)

choose 2 answers

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The ratios are equivalent by simplifying is shown below.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

We have first ratio 3:1

and, second 6:2 on simplifying we get 3:1.

and, third 9: 3 on simplifying we get 3:1.

and, Fourth 12:4 on simplifying we get 3:1.

So, all the ratio gave same value on Simplification which shows the ratios are Equivalent.

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The compound interest of average family's health premiums will be approximately $12,593.25 in 2 years.

What is compound interest?

Compound interest is interest that is calculated not only on the initial principal but also on the accumulated interest of previous periods. This means that the interest earned each period is added to the principal, and then the interest is calculated on the new, higher principal for the next period. In other words, it is interest on interest. Compound interest can be contrasted with simple interest, which is calculated only on the principal amount. Compound interest can lead to significant growth in investment or debt over time, depending on the interest rate and the length of time.

Given by the question:
To solve the problem, we need to use the formula for compound interest:

[tex]A = P(1 + r)^n[/tex]

where A is the final amount, P is the initial amount, r is the annual interest rate as a decimal, and n is the number of years.

In this case, the initial amount is $11,430, the annual interest rate is 5% or 0.05, and we want to find the final amount in 2 years. So we have:

[tex]A = 11,430(1 + 0.05)^2[/tex]

[tex]A = 11,430(1.1025)[/tex]

[tex]A = 12,593.25[/tex]

Therefore, the average family's health premiums will be approximately $12,593.25 in 2 years.

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The value of given 1.86 meters after converting it into feet is equal to 6.1024 feet.

1 meter is equal to 3.28084 feet

⇒ 1.86 meters = ( 1.86 ) × ( 3.28084 ) feet

⇒ 1.86 meters =  6.1023624 feet

Round off the value upto four decimal places we get,

⇒ 1.86 meters =  6.1024 feet

Therefore, the unit of 1.77 meters after converted to feet the value is equal to 6.1024 feet ( approximately ) .

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the new coordinates of the room are Q(2.3125, 4.125), R(7.3125, 4.125), S(7.3125, 6.125), and T(2.3125, 6.125). the dimensions of the new room on the blueprint are 5.78125 inches by 2 inches and in feet 0.48 feet by 0.17 feet.

To find the new coordinates of the room, we can first calculate the dimensions of the original room and then increase them by 25%. The length of the room is the distance between points R and S, which is:

√(7-2)² + (4-4)² = 5 units

The width of the room is the distance between points Q and T, which is:

√(2-2)² + (6-4)² = 2 units

To increase the dimensions of the room by 25%, we can multiply the length and width by 1.25.

The new length is: 5 × 1.25 = 6.25 units

The new width is: 2 × 1.25 = 2.5 units

To find the new coordinates of the room, we can add half of the increase in each dimension to the original coordinates.

The new coordinates of Q are: (2 + 0.625/2, 4 + 0.25/2) = (2.3125, 4.125)

The new coordinates of R are: (7 + 0.625/2, 4 + 0.25/2) = (7.3125, 4.125)

The new coordinates of S are: (7 + 0.625/2, 6 + 0.25/2) = (7.3125, 6.125)

The new coordinates of T are: (2 + 0.625/2, 6 + 0.25/2) = (2.3125, 6.125)

Therefore, the new coordinates of the room are Q(2.3125, 4.125), R(7.3125, 4.125), S(7.3125, 6.125), and T(2.3125, 6.125).

To find the dimensions of the new room in inches on the blueprint, we can use the Pythagorean theorem: The new length is:

√(7.3125-2.3125)² + (4.125-4.125)² = 5.78125 units

The new width is: √(7.3125-7.3125)² + (6.125-4.125)² = 2 units

Therefore, the dimensions of the new room on the blueprint are 5.78125 inches by 2 inches.

To find the dimensions of the new room in feet in the new house, we can convert the dimensions to feet by dividing by 12:

The new length is: 5.78125 inches / 12 inches/ft = 0.48 ft

The new width is: 2 inches / 12 inches/ft = 0.17 ft

Therefore, the dimensions of the new room in the new house are 0.48 feet by 0.17 feet.

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Complete Question

A rectangular room has coordinates Q (2, 4), R(7, 4), 5 (7, 6), and T(2, 6) on the blueprint. The homeowner wants the dimensions of this room to be 25% larger. What are the coordinates of the new room? What are the dimensions of the new room, in inches, on the blueprint? What will the dimensions of the new room be, in feet, in the new house?

The five steps to solving an inequality are as follows:

1.Identify the inequality - In the equation, the inequality symbol should be identified first.

2.Isolate the variable - The inequality should be rearranged so that the variable is on one side, and all other terms are on the other side.

3.Simplify the inequality - Multiplication and division rules should be used to simplify the equation.

4.Solve the inequality - The simplified inequality can be solved for the variable.

5.Graph the solution - The solution should be graphed on a number line in order to visualize it.

In summary, solving an inequality requires the identification of the inequality symbol, the isolation of the variable, the simplification of the inequality, the solving of the inequality, and the graphing of the solution. Following these steps carefully will ensure that the inequality is solved accurately.

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The coordinate of point C which is 7 / 8 of the distance from M to J is 16 .

The first step is to find the distance between M and J to be :

= Coordinate of J - Coordinate of M

= 18 - 2

= 16

The distance that is 7 / 8 between M and J is :

= 16 x 7 / 8

= 14

The coordinate of C would be :

= Coordinate of M + 7 / 8 distance

= 2 + 14

= 16

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Answer:

The value of x can be 10

The value of y can be -4

Step-by-step explanation:

Assume the function is linear of the form
y = mx

When x = 5, y = -2

Simply multiply x by 2 and equivalently multiply -2 by 2

x = 5 x 2= 10

y = -2 x 2 = -4

Labro overlooks the Rieti Valley, which was frequently visited by which saint: Francis of Assisi.

Francis of Assisi spent a great deal of time in the Rieti Valley, where he established four sanctuaries that are stopping points for pilgrims following the Cammino di Francesco pathway. Francis is also said to have made the first live nativity scene during a visit to the valley in 1223.

Francis of Assisi, one of the Catholic Church's most loved and darling saints. St. Francis is known for his ministry to poor people and oppressed, his consideration for nature and animals, and establishing the Franciscan request.

His life and message were uncompromising and simple: voracity causes suffering for both the victims and the perpetrators.

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The simplified form of the expression x² - 8x +16 is (x - 8)²

Expressions are mathematical statements that involve operations, such as addition, subtraction, multiplication, and division. In this problem, we are given the expression x² - 8x + 16 and asked to simplify it.

The expression can be simplified by using factoring techniques. We can factor the expression as (x - 8)(x - 8), which can be further simplified as (x - 8)2. The simplified expression is (x - 8)²

Therefore, the simplified expression for x² - 8x + 16 is (x - 8)². This shows that the expression is a perfect square, which can be written as (x - 8)², where (x - 8) is the square root of the expression

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Complete Question:

Simplify the expression x² - 8x + 16