Josie’s best friend is getting married and she wants to buy her something from her online wedding registry. She wants to buy some sets of dishes (d) that cost $35 each. Because she’s buying online, she must pay a shipping fee of $10. Josie wants to spend $150 or less. How many sets of dishes can Josie buy?

The roots the the given quadratic equation, will be -1/3 and -5 so the factors will be (3x+1)(x+5). As the value of roots is known, so the value of quadratic equation will be zero (0) for both the roots.

As per the question statement, we are supposed to fill the gaps to factorize the quadratic equation given :

3x² + 16x + 5 = (3x + _)(x + _)

We need to solve the expression for finding out its factors.

y = 3x² + 16x + 5

y = 3x² + 15x + x + 5

y = 3x(x + 5) + 1(x + 5)

y = (3x + 1)(x + 5)

Therefore, the  roots the the given quadratic equation, will be -1/3 and -5 so the factors will be (3x+1)(x+5). As the value of roots is known, so the value of quadratic equation will be zero (0) for both the roots.

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Answer:

[tex]y+1=\frac{1}{2}(x-6)[/tex]

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals, so the slope of the line to be found is 1/2.

Substituting into point-slope form, the equation is

[tex]y+1=\frac{1}{2}(x-6)[/tex]

The most appropriate choice for for linear equation will be given by -

Gain in weight of Max = 7.69 pounds

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Let the gain in weight be x pounds

Weight of Max in the month of September = 3.04 pounds

Weight of Max today = 10.73 pounds

By the problem,

                          3.04 + x = 10.73

                                     x = 10.73 - 3.04

                                     x = 7.69

Gain in weight of Max = 7.69 pounds

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Answer:

3

Step-by-step explanation:

1 = 1

The graph of the inequaity expression is added as an attachment

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The mathematical statement is given as

"2.5 greater than the product of -0.5 and a number"

Product means times

So, we have the following representation

"2.5 greater than the product of -0.5 and a number" ⇒  2.5 greater than -0.5 * a number

Let the number be x

So, we have

"2.5 greater than the product of -0.5 and a number" ⇒  2.5 greater than -0.5x

Greater than is represented by >

So, we have

"2.5 greater than the product of -0.5 and a number" ⇒  2.5 > -0.5x

Next, we plot the graph of the inequality expression

See attachment for the graph of the inequality expression

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Step-by-step explanation:

a distance on a coordinate grid is always the Hypotenuse of a right-angled triangle with the differences of the x coordinates and the y coordinates as the legs.

so, per Pythagoras

distance² = (x diff)² + (y diff)²

we have here a distance 17. 17² = 289.

to get integer coordinates the lengths of the legs must be integer numbers.

what 2 squared integer numbers can be added to get 289 ?

I found after subtracting 4, 9, 16, 25, 36, 49 and finally 64 (the squares of 2, 3, 4, 5, 6, 7, 8) that

289 - 64 = 225, which is also a square number (15²).

so, we get the possible integer coordinates of Q to be

(-4 + 8, 7 + 15) = (4, 22)

in this case the shorter leg has the length 8, and the longer leg the length 15.

the shorter leg is in this case horizontal, because it is the x coordinate difference. and Q is again as described (4, 22).

if we make the shorter leg vertical, that means it is the y coordinate difference. and Q is then

(-4 + 15, 7 + 8) = (11, 15)

The first thing we have to know is that 1 kilogram is equal to 1000 grams

if we have 5.4 kilograms

Answer:

250

Step-by-step explanation:

[tex](x + \frac{1}{3} ) + (x + \frac{1}{5} ) = 1 \\ x + x + \frac{1}{3} + \frac{1}{5} = 1 \\ 2x(15) + \frac{1}{3} (15) + \frac{1}{5} (15) = 1(15) \\ 30x + 5 + 3 = 15 \\ 30x = 15 - 5 - 3 \\ 30x = 7 \\ \frac{30x}{30} = \frac{7}{30} \\ x = \frac{7}{30} [/tex]

ATTACHED IS THE SOLUTION

Answer:

First Choice:

(1.4)(0.18)²

Step-by-step explanation:

Using the negative exponent rule

[tex]\left(\dfrac{a}{b}\right)^{-1} = \dfrac{b}{a}[/tex]

we get

[tex]\left(\dfrac{5}{7}\right)^{-1} = \dfrac{7}{5}[/tex]

[tex]\dfrac{7}{5} = 1.4\\\\[/tex]

Therefore
[tex]\left(\dfrac{5}{7}\right)^{-1}\left(0.18\right)^2\\\\= (1.4)(0.18)^2[/tex]

Answer:

1.) -4

2.) 3/5 and 6/10 are both equal to 0.6

Step-by-step explanation:

1.) 16(1/4 - 1/2)

For this one you can either distribute the 16 and solve or just subtract the fractions and solve.  I like the first method personally:

16/4 - 16/8

4 - 8

-4

2.) Fractions can be looked at as dividing the top (numerator) by the bottom (denominator).  If we put each of the answer choices into our calculator and divide, we get 3/5 and 6/10.  Note that 2/3 = 0.66, but that is not the same as 0.6.

40° is the value of the angle ∠QPR.

So, PQ ⊥ PS then, ∠QPS = 90°.

According to the given figure: ∠QPR + ∠RPS = ∠QPS

Then,

So, ∠QPR = 7x - 9°

Substitute x = 7 as:

Therefore, 40° is the value of the angle ∠QPR.

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$2580\\ P=\textit{original amount deposited}\dotfill & \$2400\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 2580=2400[1+(\frac{r}{100})(1)] \implies \cfrac{2580}{2400}=1+\cfrac{r}{100}\implies \cfrac{43}{40}\implies \cfrac{100+r}{100} \\\\\\ \cfrac{4300}{40}=100+r\implies \cfrac{215}{2}=100+r\implies \cfrac{215}{2}-100=r\implies \boxed{\stackrel{\%}{7.5}=r}[/tex]

Answer:

7.5%

Step-by-step explanation:

Answer:

1:2

Step-by-step explanation:

For every triangle there are two squares.

The most appropriate choice for LCM will be given by

After the year 2005, France and America will be in recession in the year 2029

What is LCM?

Suppose a and b are two numbers. LCM of a and b is the lowest common multiple of a and b. LCM of a and b is the lowest number that is divisible by both a and b.

Here,

France has a recession every 6 years.

America has a recession every 8 years.

Florence works out when France and America will both be in recession.

It will be possible in the year which is a common multiple of 6 and 8

In the year 2005, both France and America were in recession

France and America will both be in recession again after (LCM of 6 and 8) years

Now,

6 = 2 x 3

8 = 2 x 2 x 2

LCM of 6 and 8 = 2 x 2 x 2 x3

                          = 24

France and America will both be in recession again after 24 years  

After the year 2005, France and America will be in recession in the year (2005 + 24) = 2029

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The difference between the freezing point of seawater and the freezing point of nitric acid is 40 °C.

As per the question, we can write

The freezing point of seawater = −2 °C.

The freezing point of nitric acid = −42 °C.

We were asked to calculate the difference between the freezing point of seawater and the freezing point of nitric acid. We can find the difference between the freezing point of seawater and the freezing point of nitric acid by following the steps mentioned below;

The difference between the freezing point of seawater and the freezing point of nitric acid = Freezing point of Seawater - Freezing point of nitric acid

The difference between the freezing point of seawater and the freezing point of nitric acid = -2 - (-42) = 40 °C.

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Multiply both sides of the equation by 20, the lowest common denominator of 4,5.

Multiply 5 and 12 to get 60.

Swap the sides so that all the terms of the variables are on the left side.

Divide both sides by 4.

Divide 60 by 4 to get 15.

The base of the parallelogram is 3

The height of the parallelogram is 8

Let the base be represented as (x+2)

Let the height be represented as (x-2)

The area of the parallelogram is 24

The first step is to get two numbers that can be multiplied together to get 24

= 3 × 8

The two numbers are 3 and 8

Hence the base is 3 and the height is 8

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The coordinates of the point that at 7/8 from a to b are (5, -5/8)

On the segment, we have the following endpoints

A = (-2, 2)

B = (6, -1)

Also, we have the line ratio to be

Ratio, m : n = 7/8

Express the ratio as a ratio

So, we have

m : n = 7 : 8 - 7

Evaluate the difference

So, we have

m : n = 7 : 1

The coordinate of the point at the given distance is then calculated as

Point = 1/(m + n) * (mx2 + nx1, my2 + ny1)

So, we have

Point = 1/(7 + 1) * (7 * 6 + 1 * -2, 7 * -1 + 1 * 2)

Evaluate the products

So, we have

Point = 1/8 * (42 -2, -7 + 2)

Evaluate the sum and the difference

So, we have

Point = 1/8 * (40, -5)

Evaluate the products

So, we have

Point = (5, -5/8)

Hence, the coordinates of the point that is 7/8 of the distance from a to b are (5, -5/8)

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Answer:

Step-by-step explanation:

6x-2x-8=12  

4x-8=12    (add 6x and -2x)

4x=20         (8+12=20)

x=5   (4 divide by 20 =5)

The Confidence Interval for a Population Proportion is 0.69 ± 1.13

(-0.44 to 1.82)

Confidence Interval:

Confidence Interval means a range of values that is determined through the use of observed data, calculated at a desired confidence level that may contain the true value of the parameter being studied.

Given,

n = 130 and

p= 0.69,

construct a 99% confidence interval.

Here we need to find the confidence interval.

According to the formula, the confidence interval is,

We know that,

Sample Size: 130

Sample Mean: 0.69

Confidence Level: 99%

99% Confidence Interval: 0.69 ± 1.13

(-0.44 to 1.82)

"With 99% confidence the population mean is between -0.44 and 1.82, based on 130 samples."

Margin of Error: 1.13

(to more digits: 1.13)

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Calculate identity exponents using the exponent of the quotient, degree of exponent, and the law of zero exponent equations and evaluate numerical equations with integer exponents.

The following is an equivalent numeric expression with an integer exponent that uses the quotient, the quotient, zero-degree rule, and the identity exponent, and evaluates the numeric expression.

[tex]2^{5} \\[/tex] × [tex]2^{6}[/tex] = [tex]2^{11}[/tex], using the product of powers.

2² × 2³ = (2×3)² = 6², using the power of a product.

[tex](2^{2})^{6}[/tex] = [tex]2^{12}[/tex], using the power of a power.

The seven laws of exponents are the power rule, the power ratio rule, the power rule, the power rule, the power quotient rule, the power zero rule, and the negative exponent rule. Arithmetic questions, as well as how to multiply, divide and add powers.

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The associative property let us associate different terms or factors in order to solve some expression.

We have to find the expression in which this property is more useful.

The only expression where the associative may be helpful is C, as we can associate this way:

(43 + 60) + 40 = 43 + (60 + 40) = 43 + 100 = 143

In the other expression there is no advantage in applying this property.

Answer: C

iven

adiius of circle = 3 ft

ind

rea and circumference of a circle

xplnanation

Circumference of a circle is given by

Area of circle =

inal ANnswer

ircumference =

Area =

The total number of different numbers which Toby could have picked according to the task content as given is; 1,000.

It follows from the task content that the number of different numbers which Toby could have picked given the conditions is to be determined.

On this note, since the required number is to be greater than 49,999 and must be a 5-digit number, the numbers which he could pick would range from;

49,999 - 99,999.

Hence, there are 5000 numbers in between.

Additionally, since the number must be a multiple of 5, the total number of multiples of 5 from 5,000 consecutive numbers is;

= 5,000/5

= 1000 different numbers.

Therefore, Toby could pick any of 1000 different numbers.

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Answer:

[tex]x + 53 + 86 = 63 \\53 - 86 = 33[/tex]

The solutions to the question are

The given parameters are:

Sides = 3

Fourth side = barn wall

Perimeter = 120 m

Next, we sketch the dog pen using the above parameters (see attachment)

Here, we have

P = 120m

Also, we have

P = 2x + y

This gives

2x + y = 120

Make y the subject

y = 120 - 2x

The area is calculated as

A = xy

So, we have

A = x(120 - 2x)

Hence, the area is A = x(120 - 2x)

See attachment for the graph of A = x(120 - 2x)

We have

A = x(120 - 2x)

Expand

A = 120x - 2x^2

Differentiate

120 - 4x= 0

So, we have

4x = 120

This gives

x = 30

Hence, the value of x that gives maximum area is 30

Recall that

y = 120 - 2x

So, we have

y = 120 - 2 * 30

Evaluate

y = 60

Hence, the dimensions is 30 by 60

From the graph, we have

x = 0 to 60

Hence, the domain of the function is 0 <= x <= 60

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