Marlena has 3 straws. Two straws have the lengths
shown. She does not know the length of the shortest
straw, but when she forms a triangle with all three, the
triangle is obtuse. Which are possible lengths of the
shortest straw? Check all that apply.
5 inches
6 inches
7 inches
8 inches
9 inches​

Answer:

C

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

- 2x(- 4x - 3) - 9y²(- 4x - 3) ← distribute both parenthesis

= 8x² + 6x + 36xy² + 27y² → C

Answer:

150.6 ft^9

Step-by-step explanation:

The easisest way to solve this problem is to convert everything to the same unit

1 cu yd = (27 cu ft)

1 cu in = (0,000578704 cu ft)

The expression is

6cu yd* 9cu ft * 134cu in + 1cu yd* 12cu ft* 200cu in

=  6(27 cu ft) * 9cu ft * 134(0,000578704 cu ft) + 1(27 cu ft)* 12cu ft* 200(0,000578704 cu ft)

Please see attached image below

The answer is

150.6 ft^9

Answer:

see explanation

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y ), hence

F(- 1, 9) → F'(- 1, - 9)

G(- 2, 1) → G'(- 2, - 1)

H(- 7, 4) → H'(- 7, - 4)

Answer:

[tex]\large\boxed{\dfrac{V_{cone}}{V_{prism}}=\dfrac{1}{3}}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a cone:}\ V_{cone}=\dfrac{1}{3}B_cH_c\\\\B_c-base\ area\ of\ a\ cone\\H_c-height\ of\ a\ cone\\\\\text{The formula of a volume of a prism:}\ V_{prism}=B_pH_p\\\\B_p-base\ area\ of\ a\ prism\\H_p-height\ of\ a\ prism\\\\\text{The cone and the prism have the same base area and height.}\\\text{Therefore}\\\\V_{cone}=\dfrac{1}{3}BH\ \text{and}\ V_{prism}=BH\\\\\text{The ratio of the volume of the cone to the volume of the prism:}[/tex]

[tex]\dfrac{V_{cone}}{V_{prism}}=\dfrac{\frac{1}{3}BH}{BH}=\dfrac{1}{3}[/tex]

Answer:

See the image attached for answer

Step-by-step explanation:

Answer:

Frequency = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

We are given the following function and we are to find its frequency:

[tex]f (x) = 3 cos (\pi x) -2[/tex]

We know that the standard form of cosine function is [tex]y=Acos (Bx)+c[/tex]

where [tex]A[/tex] is the amplitude, [tex]B=\frac{2\pi}{\text{Period}}[/tex] while [tex]c[/tex] is the mid line.

Frequency is given by:

[tex]F=\frac{1}{P}[/tex] where [tex]F[/tex] is frequency and [tex]P[/tex] is the period.

Finding period by comparing the given function:

[tex]y=3cos(\pi x)-2[/tex]

[tex]Period - B = \pi[/tex]

Substituting B to get:

[tex]\pi =\frac{2\pi}{\text{Period}}[/tex]

[tex]\text{Period}=\frac{2\pi}{\pi}=2[/tex]

So, Period = 2.

Since frequency is [tex]\frac{1}{P}[/tex], therefore

Frequency = [tex]\frac{1}{2}[/tex]

The frequency is T / (2π).

To find the frequency of the function f(x) = 3 cos(T x) – 2, start by recognizing the standard form of a cosine function, which is f(x) = A cos(Bx + C) + D. Here, A, B, C, and D are constants with specific roles.

        f = ω / (2π)

        f = T / (2π)

Therefore, the frequency of the function f(x) = 3 cos(Tx) – 2 is T / (2π).

Answer:

The fraction = 9/35

To find the fraction, calculate the sum of 5 1/3 and 6 1/3, which is 35/3, then divide the final product, 3, by this sum. The fraction that when multiplied by the sum equals 3 is 9/35.

The question asks us to find the fraction when the product of the fraction and the sum of 5 1/3 and 6 1/3 is 3.

First, let's calculate the sum of 5 1/3 and 6 1/3:

5 1/3 can be written as (5*3 + 1)/3 = 16/3.

6 1/3 can be written as (6*3 + 1)/3 = 19/3.

Adding these fractions, we get (16/3) + (19/3) = (35/3).

So, we have the equation:

Fraction  imes (35/3) = 3

To find the unknown fraction, we divide both sides by 35/3:

Fraction = 3 / (35/3) = 3  imes (3/35) = 9/35

Therefore, the fraction we are looking for is 9/35.

Answer:

18

Step-by-step explanation:

2(15) - 3(4)

= 30 - 12

= 18

Answer:

87n+6*55n

Step-by-step explanation:

Answer:

The page numbers are 36 and 37.

Step-by-step explanation:

n + (n + 1) = 73

2n + 1 = 73

n = (73 - 1)/2

= 72/2 = 36

Follow below steps:

The sum of the page numbers on the facing pages of a book is 73. To solve this, we need to establish that facing pages in a book are always one number apart. If we call one page number x, then the other page number is x+1 because page numbers are consecutive.

Now, we can create the equation x + (x+1) = 73 to find the value of x. Solving this equation, we get:

2x + 1 = 73

2x = 73 - 1

2x = 72

x = 72 / 2

x = 36

Since x is the lower of the two page numbers, then the pages are 36 and 37.

Answer:

12.75 oz

Step-by-step explanation:

1 gallon is equivalent to 64 oz.

Writing and solving an equation of ratios, we get:

 1.5 oz       1 gal

----------- = ------------

     x          8.5 gal

Here we must cross-multiply to solve for x.

x(1 gal) = (1.5 oz)(8.5 gal) = 12.75 oz

Thus, x = 12.75 oz of cleaning product must be added to 8.5 gal of water to create the desired solution.

To make an all-purpose cleaner, you need 12.75 ounces of cleaner for 8.5 gallons of water.

This is determined by multiplying the ratio of 1.5 ounces per gallon by 8.5 gallons.

follow these steps:

Therefore, 12.75 ounces of cleaner will be added to 8.5 gallons of water.

Answer:

see explanation

Step-by-step explanation:

Given

[tex]log_{10}[/tex] x = 0.98, then

x = [tex]10^{0.98}[/tex]

Answer:

D. 96 inches

Step-by-step explanation:

Perimeter (P) = 2L + 2W , Where L is the length and W is the width.

20 ft = 2L + 2(2 ft)

2L = 20 ft - 4 ft = 16 ft

L = [tex]\frac{16}{2}[/tex] ft = 8 ft

1 ft = 12 inches

8 ft = ?

Cross-multiplying this gives; [tex]\frac{8}{1}[/tex] × 12 = 96 inches

Answer: D) 96 inches.

Step-by-step explanation: To calculate the lenght of James' rectangular yard, we need to isolate L from the given formula:

P=2L+2W

P-2W=2L

[tex]L=\frac{P-2W}{2}[/tex]

Now we replace the given values of P and W in the equation:

[tex]L=\frac{20feet-2*2feet}{2}[/tex]

[tex]L=\frac{20feet-4feet}{2}[/tex]

[tex]L=\frac{16feet}{2}[/tex]

[tex]L=8feet[/tex]

1feet=12inches so:

L=8feet*12inches/1feet

L=96 inches.

Answer:

x=-2 x=-8

Step-by-step explanation:

x2 + 10x + 16 = 0

(x + 2)(x + 8) = 0

x + 2 = 0 or x + 8 = 0

x = and x =

x=-2 x=-8

The value of (5.3x 10^4) (4.2x10^3) in scientific notation Option C 2.226 times 10^8

5.3×10^4  × 4.2 × 10^3

We multiply the numbers out front

5.3× 4.2 = 22.26

We add the exponents

10^(4+3) = 10^7

22.26×10^7

But we are not done yet because The number out front has to be between 1 and less than 10

Move the decimal 1 place to the left and add 1 to the exponent

2.226 × 10 ^(7+1)

=2.226×10^8.

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8.

Scientific Notation is the expression of a number n in the form a∗10b. where a is an integer such that 1≤|a|<10. and b is an integer too. Multiplication: To multiply numbers in scientific notation, multiply the decimal numbers.

The proper format for scientific notation is a x 10^b where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |a| < 10. b is the power of 10 required so that the scientific notation is mathematically equivalent to the original number.

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Answer:

0.0005 oz

Step-by-step explanation:

Usually, the greatest number that is allowed for approximation, assuming that the number itself is obtained by approximation, is the greatest possible error of it.

It is normally half the place value of the last digit in a number.

Like here we have [tex]10\frac{1}{8}[/tex] oz which is equal to [tex]10.125[/tex] oz. The last digit is 5 which is at the thousandth place (0.001) so the greatest possible error for this would be its half.

[tex]\frac{0.001}{2}[/tex] = 0.0005 oz

Answer: Inconsistent.

Step-by-step explanation:

The  equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

Solve for "y" in each equation:

Equation 1

[tex] x=-5-y\\\\y=-x-5[/tex]

Equation 2

[tex]4+y=-x+3\\\\y=-x+3-4\\\\y=-x-1[/tex]

You can notice that the slope of the Equation 1 is:

[tex]m_1=-1[/tex]

And the slope of the Equation 2 is:

[tex]m_2=-1[/tex]

Observe that [tex]m_1=m_2[/tex], then you can conclude that the lines are parallel and the System of equations has No solution.

When there is no solution the classification  of the system of equations is: "Inconsistent".

In the given scenarios: 1. Car speed (x) determines distance covered (y) in 30 minutes (y = 30x). 2. Tina's age (y) is 5 years more than Tim's age (x) (y = x + 5). 3. Chair cost (x) relates to table cost (y) as y = 2x. 4. Baking time for chocolate muffins (y) is 2 minutes longer than for vanilla muffins (x) (y = x + 2). These equations establish connections between variables in different real-world situations.

In these scenarios, we encounter different situations where certain variables and their relationships are described. Let's elaborate on each scenario and express it in a more detailed manner:

1. **Car Speed and Distance:** The speed of a car is represented by the variable 'x' in miles per hour. The total distance covered by the car in 30 minutes, denoted as 'y,' can be expressed using the formula: y = 30x. This equation relates the speed 'x' to the distance 'y' covered in a specific time period.

2. **Sibling Ages:** Tim's age, represented by 'x,' and Tina's age, represented by 'y,' are related. Tina's age is 5 years more than Tim's age, which can be expressed as y = x + 5. This equation defines the age difference between the siblings.

3. **Cost of Furniture:** In this scenario, the cost to produce a chair is 'x,' and the cost to produce a table is 'y.' The relationship is that the cost of producing a table is two times the cost of producing a chair, which can be expressed as y = 2x. This equation shows the cost relationship between chairs and tables.

4. **Muffin Baking Times:** The time required to bake a vanilla muffin is 'x,' and the time required to bake a chocolate muffin is 'y.' The relationship is that the time to bake a chocolate muffin is 2 minutes more than the time to bake a vanilla muffin, which can be expressed as y = x + 2. This equation establishes the time difference between baking these two types of muffins.

In summary, these scenarios involve different relationships and equations that connect variables and quantities in various real-world contexts, such as car speed and distance, sibling ages, furniture production costs, and muffin baking times. These equations help describe and quantify these relationships, making them useful for solving practical problems.

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Answer:

y=x-4

Step-by-step explanation:

Standard form is y=mx+b

the coordinates (0, -4) tell you that the y intercept is at -4 which means b will be -4. To find slope you have to find the change in y over the change is x. 1--4=5 and 5-0=5. 5/5 is 1 so the slope, or m, is 1. x stays the same since it's the variable. it'll become y=1x-4 and since you don't have to place a coordinate of one in front of a variable, you can just write it as y=x-4

Answer: X+5

Step-by-step explanation:

When you take out the 9 it should be 9(x+5) and when you take out the 9x on the bottom it gives you (x+5)+20 therefore x+5 is your GCF.

I hope this helps :)

The greatest common factor (GCF) of the numerator 9x+45 and the denominator x^2 +9x+20 of the provided rational expression is x+5.

The greatest common factor (GCF) is found by factoring both the numerator and the denominator and then identifying the largest factor that appears in both. For the provided rational expression 9x+45 over x2 +9x+20, let's factor both parts:

Comparing both factored forms, we can see that x+5 appears in both the numerator and the denominator, and it is the largest factor common to both. Therefore, the GCF of the numerator and the denominator is x+5.

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Answer:

B) 5.4 cm 2

Step-by-step explanation:

A==1/2 bh

5.4*2=10.8

10.8/2=5.4

The expression a/b is evaluated by dividing -6 by -2. Since both numbers are negative, the result is a positive 3.

The problem asks you to evaluate a/b with a=-6 and b=-2. The expression a/b means 'a divided by b'. Thus, to evaluate this expression, you simply divide -6 by -2. Remember that when you divide a negative number by another negative number, the result is positive. So, -6 divided by -2 equals 3.

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We substitute -6 for a, and -2 for b in the expression a/b, obtaining -6/-2, which equals 3 because division of two negative numbers yields a positive number.

To evaluate the expression a/b for a = -6 and b = -2, we can substitute the given values into the expression. This gives us -6 / -2. Dividing a negative number by another negative number gives a positive result. Therefore, -6 / -2 equals 3. The notion that dividing a negative number by another negative number results in a positive number is a fundamental rule in mathematics.

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Answer:

5:7

Step-by-step explanation:

Ratio of the areas of similar shapes is equal to the square of the scale:

A₂ / A₁ = r²

Ratio of the side lengths of similar shapes is equal to the scale:

s₂ / s₁ = r

Therefore:

A₂ / A₁ = (s₂ / s₁)²

25/49 = (s₂ / s₁)²

s₂ / s₁ = 5/7

The ratio of the side lengths is 5:7.

Answer:

5 : 7

Step-by-step explanation:

Given 2 similar figures then

ratio of sides = a : b

ratio of areas = a² : b²

Here the ratio of areas = 25 : 49, hence

ratio of sides = [tex]\sqrt{25}[/tex] : [tex]\sqrt{49}[/tex] = 5 : 7

Answer:

two ten-thousandths

Step-by-step explanation:

You would write 0.0002 as two ten-thousandths. However some people say it the easy way, zero point zero zero zero two.

Hope this helps!

Answer:

It would be 2 ten thousandths.

Step-by-step explanation:

It goes tenths, hundredths, thousands, 10 thousands in order as you move right 1 place value.  

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{4}{ h},\stackrel{1}{ k})\qquad \qquad radius=\stackrel{2}{ r} \\\\\\ (x-4)^2+(y-1)^2=2^2\implies (x-4)^2+(y-1)^2=4[/tex]

Answer:

B.2 1/41

Step-by-step explanation:

In a perfect square trinomial of the form ax+bx+c where a, b and c are constants, the value of (b/2)²=ac

In the provided equation the value of a=1, b=-3 c=?

Therefore, (-3/2)²=c since a-the coefficient of x²=1 and 1×c=c

c=2.25= 2 1/4

Thus the trinomial x² - 3x + 2 1/4 is a perfect square.

Answer:

B and C

Step-by-step explanation:

The denominator of the rational expression cannot be zero as this would make it undefined.

Equating the denominator to zero and solving gives the values that x cannot be.

solve

3x² - 75 = 0 ( add 75 to both sides )

3x² = 75 ( divide both sides by 3 )

x² = 25 ( take the square root of both sides )

x = ± [tex]\sqrt{25}[/tex] = ± 5 → B and C

Answer: 203.31

Step-by-step explanation:

Each bus have 214.42.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value

Give:

Total buses=9

Charges for tip= $ 100

Total money spends = $ 1829.82

Amount with tip = $ 1829.82+$ 100 = $ 1929.82

So, each bus have = 1929.82/9

                              = 214.42

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Answer:

B. y + 2 = ½(x + 3)

Step-by-step explanation:

Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE term of what they really are.

Answer:

option A.

y = (1/2)x - 2

Step-by-step explanation:

It is given that, line that passes through the points (2, –1) and (6, 1)

Slope m = (y₂ - y₁)/(x₂ - x₁)

 = (1 - -1)/(6 - 2)

 = (1 + 1)/4 = 2/4

 = 1/2

To find the equation of the line

Equation of a line passing through the points (x₁, y₁)  and  slope  m is given by,

(y - y₁)/(x - x) = m

Here (x₁, y₁) = (2, -1) and m = 1/2

(y - -1)/(x - 2) = 1/2

(y + 1) = (x - 2)/2

y = -1 + x/2 - 2/2

  =  -1 + x/2 - 1

 = x/2 - 2

The equation of the line is,

y = (1/2)x - 2

The correct answer is option A.

y = (1/2)x - 2