Solve for x: −8 < x − 1 < 5

−7 < x < 6

7 < x < 6

−7 > x > 6

7 > x > 6

Answer:

\(area = (7 \times 1) + (5 \times 1) + (8 \times 1) \\ = 7 + 5 + 8 \\ = 20 \: {m}^{2} \)

To find the equation of a line that passes through the points (5, -3) and (-2, -4) in standard form, we can use the point-slope form of a linear equation and then convert it to standard form.

Determine the slope (m) of the line using the formula:

   m = (y2 - y1) / (x2 - x1)

For the given points (5, -3) and (-2, -4), we have:

   m = (-4 - (-3)) / (-2 - 5) = (-4 + 3) / (-2 - 5) = -1 / (-7) = 1/7

Use the point-slope form of a linear equation:

   y - y1 = m(x - x1)

Using the point (5, -3), we have:

   y - (-3) = (1/7)(x - 5)

Simplifying:

   y + 3 = (1/7)(x - 5)

Convert the equation to standard form:

Multiply both sides of the equation by 7 to eliminate the fraction:

   7y + 21 = x - 5

Rearrange the equation to have the x and y terms on the same side:

   x - 7y = 26

The equation of the line in standard form that passes through the points (5, -3) and (-2, -4) is x - 7y = 26.

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Answer: 36 shingles can be placed on the north part of the house.

Step-by-step explanation:

Given: Length of each shingle = \(1\dfrac23\) feet = \(\dfrac53\) feet.

The north part of the house has a roof line that is 60 feet across.

Then, the number of  shingles can be placed  on the north part of the house = (Length of roof line in north part) ÷ (Length of each shingle)

\(=60\div \dfrac{5}{3}\\\\=60\times\dfrac{3}{5}\\\\=12\times3=36\)

Hence, 36 shingles can be placed on the north part of the house.

Answer:

Domain = (-∞, ∞) Range = (-∞, ∞)

End Behavior: As X -> -∞, Y -> -∞ | As X -> ∞, Y -> ∞

Inflection Point: (2,0)

Step-by-step explanation:

Answer:

Ali has 1528. She has 1146 more cards than Max. In total, there are 1910 cards.

Step-by-step explanation:

382 x 4 = 1528

1528 - 382 = 1146

1528 + 382 = 1910

Answer:

Answer:

The sale price will be:  $215.10

Step-by-step explanation:

We know that:

Sale price = Regular price × (100% - Discount %)

                 = Regular price × (100% - 10%)

                 = 239 × 90%

                 = 239 × 0.9

                 = 215. 10 $

Therefore, the sale price will be:  $215. 10        

Answer:

x to the 4th power+ 87x + 34

Step-by-step explanation:

The probability of observing no positive reading if all suspects are telling the truth is d. 0.59. Probability theory is a branch of mathematics that is used to model and analyze random events.

Probability can be used to predict the likelihood of different outcomes in a wide range of situations, from games of chance to scientific experiments to everyday events. Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.

To solve this problem, we need to calculate the probability of observing no positive readings given that all suspects are telling the truth, which is equal to the probability that all 5 suspects receive a negative reading on the lie detector test. Since the lie detector will show a positive reading 10% of the time when a person is telling the truth, the probability that a suspect will receive a negative reading when telling the truth is 1 - 10% = 90%. Therefore, the probability that all 5 suspects will receive a negative reading when telling the truth is:

(90%)^5 = (0.9)^5 = 0.59049.

The correct answer is therefore (d) 0.59.

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The domain of the square root function is x greater-than-or-equal-to 0, since the function is defined for all non-negative x-values or x-values greater than or equal to zero.

The domain of the square root function graphed below can be determined by looking at the x-values of the points on the graph.

From the given information, we can see that the curve starts at (0, -1) and goes through (1, -2) and (4, -3).

The x-values of these points are 0, 1, and 4.

Since the square root function is defined for any non-negative x-values or x-values more than or equal to zero, its domain is x greater-than-or-equal-to 0.

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Answer:

i think they are 23, 50, and 64!

Step-by-step explanation:

Thomas' installment payment that he pays in one fortnight is approximately k523.08.

To calculate Thomas' installment payment, we need to consider the principal amount (k10,000) and the interest rate (36%).

First, let's calculate the total amount to be repaid at the end of the year, including the interest. The interest is calculated as a percentage of the principal amount:

Interest = Principal × Interest Rate

= k10,000 × 0.36

= k3,600

The total amount to be repaid is the sum of the principal and the interest:

Total Amount = Principal + Interest

= k10,000 + k3,600

= k13,600

Now, we need to calculate the number of fortnights in a year. There are 52 weeks in a year, and since each fortnight consists of two weeks, we have:

Number of Fortnights = 52 weeks / 2

= 26 fortnights

To find the installment payment for each fortnight, we divide the total amount by the number of fortnights:

Installment Payment = Total Amount / Number of Fortnights

= k13,600 / 26

≈ k523.08

Therefore, Thomas' installment payment that he pays in one fortnight is approximately k523.08.

It's important to note that this calculation assumes equal installment payments over the course of the year. Different repayment terms or additional fees may affect the actual installment amount. It's always advisable to consult with the bank or financial institution for accurate information regarding loan repayment.

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Answer:

Step-by-step explanation:

7       1          x         3       1

        2                             2

= 105        =      26     1

      4                          4

Result in decimals: 26.25

Calculation steps:

7     1         x        3      1

      2                          2

=  15    x    7

   2           2

=  15 × 7

    2 × 2

=  105             =  26     1

     4                            4

Answer:

50

Step-by-step explanation:

<d + <e = <f

Answer:

2x

Step-by-step explanation:

5, 10, 20, 40, 80

each step is multiplying by 2, therefore the sequence is 2x

Answer:

The length of the pool is \(L=24\:ft\).

Step-by-step explanation:

The area of a rectangle is given by \(A=L\cdot W\) where L is the length, W is the width.

If the length of the pool is 9 feet more than it’s width, this means that \(L=9+W\)

We know that the area of a rectangular swimming pool is 360 \(\:ft^2\). So we simple insert the length (\(L=9+W\)), width ( \(W\)) and area (360) into the formula and  solve the resulting equation.

\(360=\left(9+W\right)W\\\\360=9W+W^2\\\\9W+W^2=360\\\\W^2+9W-360=0\)

\(\mathrm{Solve\:with\:the\:quadratic\:formula}\\\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)\(\mathrm{For\:}\quad a=1,\:b=9,\:c=-360:\quad W_{1,\:2}=\frac{-9\pm \sqrt{9^2-4\cdot \:1\left(-360\right)}}{2\cdot \:1}\\\\W=\frac{-9+\sqrt{9^2-4\cdot \:1\left(-360\right)}}{2\cdot \:1}= 15\)

\(W=\frac{-9-\sqrt{9^2-4\cdot \:1\left(-360\right)}}{2\cdot \:1}= -24\)

A length cannot be negative. So \(W=15\) and the length of the pool is \(L=9+15=24\:ft\)

Recall that for all x,

cos²(x) + sin²(x) = 1

So we have

sin(x) = ± √(1 - (60/61)²) = ± 11/61

Recall the double angle identity,

sin(2x) = 2 sin(x) cos(x)

From here, we get

sin(2x) = 2 (± 11/61) (60/61) = ± 1320/3721

In case you meant to ask about sin²(x), we get

sin²(x) = 1 - cos²(x) = 121/3721

The area of the triangle with the given vertices is 11.5 square units.

The area of a triangle can be calculated using the coordinates of its vertices using the following formula.

To find the area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), we can use the following formula:

A = (x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂))/2

Using this formula with the given vertices (0, 6), (2, −3), and (3, 4), we get:

A = (0(-3 − 4) + 2(4 − 6) + 3(6 − (-3)))/2

A = (0 - 4 + 27)/2

A = 23/2

A = 11.5

Therefore, the area of the triangle with the given vertices is 11.5 square units.

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Answer:

C.

Step-by-step explanation:

the one u had highlighted

Answer:

Because f(g(x)) = g(f(x)) = x, f and g are inverse functions.

Step-by-step explanation:

f(g(x)) = f(\(\frac{1}{4}\sqrt{x}\)) = \(16(\frac{1}{4}\sqrt{x} ) ^{2} = 16(\frac{1}{16}x)=x\)

g(f(x)) = g \((16x^{2}) = \frac{1}{4}\sqrt{16x^{2} } = \frac{1}{4}(4x) = x\)

Answer:

X

X

are

Step-by-step explanation:

Answer:

none of these

Step-by-step explanation:

the side lengths are are 2√5/5, 2, and 4.

sin(x) = opp/hyp

sin(x) = 2/2√5

Answer:

f(-4) = -1

f(-1) = -4

f(1) = 4

Step-by-step explanation:

We need to find the y value for the x values

f(-4) means find the y value for x= -4

f(-4) = -1

f(-1) = -4

f(1) = 4

Answer:

The word or phrase that describes the probability that Arianna will roll a number between 1 and 6 (including 1 and 6) is "certain." The reason for this is that a standard six-sided die always has a number between 1 and 6 on each face, and if the die is fair and unbiased, then the probability of rolling a number between 1 and 6 is 1, or 100%. Therefore, option (b) "certain" is the correct choice.

The domain of the relation S is the set of all x-values from the ordered pairs in the relation. In this case, the given ordered pairs are (3, p), (3, 0), (4, g), and (1, 4).

To find the domain, we collect all the unique x-values from these ordered pairs.

From the given pairs, we have x = 3, x = 4, and x = 1. However, note that (3, p) and (3, 0) have the same x-value of 3. When considering the domain, we only need to list unique x-values.

Therefore, the domain of the relation S can be expressed as:

domain = {1, 3, 4}

Moving on to the range of the relation S, it refers to the set of all y-values from the ordered pairs.

From the given pairs, we have y = p, y = 0, y = g, and y = 4. Similarly, we need to consider only unique y-values when determining the range.

Thus, the range of the relation S can be expressed as:

range = {0, 4, g, p}

It's important to note that the specific values of g and p are not given in the question. So, in the range, g and p are considered as distinct symbols representing unknown values.

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Answer:

Step-by-step explanation:

We can write the information as equations. We will use variables x and y to find the two numbers

Equation 1: The sum of two numbers is 526

x + y = 526

Equation 2: The difference is 176

x - y = 176

With two variables and two equations, we can first find one variable by elimination:

(See image)

and then substitute y into either equation to find x:

(See image)

The constant of proportionality in the box to match the table will be 2/3. Then the last option is correct.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The table is given below.

x      y

0     0

3      2

6      4

9      6

The variable 'y' is directly proportional to the variable 'x'. Then we have

y ∝ x

y = k x

At (9, 6), the value of the constant 'k' is given as,

6 = 9k

k = 6 / 9

k = 2/3

The proportionality is given as,

y = (2/3) x

The constant of proportionality in the box to match the table will be 2/3. Then the last option is correct.

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Answer:

The measure of angle D and A must be equal.

Step-by-step explanation:

    ASA means angle-side-angle.  So you must have two angles and the side between them be congruent to the other triangle.  We already know Angle C and F are congruent and Side lengths AC and FD are congruent.  So we just need the angles on the other side of the side lengths.

Answer:

each ticket is $8.75

Step-by-step explanation:

c=8$8.75

The equation that can be used to determine the cost of each movie ticket is C = $48.50 / 6.

Total cost of the 6 movie tickets = (6 x cost of each ticket) - value of one coupon

50.50 = 6C - $2

Combine similar terms

$50.50 - $2 = 6C

$48.50 = 6C

Divide both sides of the equawtion by 6

C = $48.50 / 6

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Option 2 is the correct graph for the function f(x) = \(4[(1/2)^{x}]\) .

Given ,

f(x) = \(4[(1/2)^{x}]\)

Mathematically the graph will of exponential in nature.

So,

Let us assume few values to understand the nature of graph.

Firstly,

Let x= 1

f(x) = \(4[(1/2)^{1}]\)

f(x) = 2

Let x = 2

f(x) = \(4[(1/2)^{2}]\)

f(x) = 1

Let x = 3

f(x) = \(4[(1/2)^{3}]\)

f(x) = 0.5

Thus from these values of f(x) corresponding to the values of x second graph will be correct .

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