A ladder is resting against a wall. The top of the ladder touches the wall at a height of 9 ft. Find the length of the ladder if the length is 3 ft more than its distance from the wall.

Solving the exponential function, it is found that the times that will take to have the desired measures are given by:

a) 3.6 hours.

b) 38.51 hours.

c) 56.98 hours.

The function is given by:

[tex]A(t) = 140(0.5)^{\frac{t}{19.255}}[/tex]

Solving for t, we have that:

[tex](0.5)^{\frac{t}{19.255}} = \frac{A(t)}{140}[/tex]

[tex]\log{(0.5)^{\frac{t}{19.255}}} = \log{\frac{A(t)}{140}}[/tex]

[tex]\frac{t}{19.255} = \frac{\log{\frac{A(t)}{140}}}{\log{0.5}}[/tex]

[tex]t = 19.255\frac{\log{\frac{A(t)}{140}}}{\log{0.5}}[/tex]

In item A, we have that A(t) = 123, hence:

[tex]t = 19.255\frac{\log{\frac{123}{140}}}{\log{0.5}}[/tex]

t = 3.6 hours.

In item B, we have that A(t) = 35, hence:

[tex]t = 19.255\frac{\log{\frac{35}{140}}}{\log{0.5}}[/tex]

t = 38.51 hours.

In item C, we have that A(t) = 18, hence:

[tex]t = 19.255\frac{\log{\frac{18}{140}}}{\log{0.5}}[/tex]

t = 56.98 hours.

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[tex]~~~~~1-x < 5\\\\\implies -x < 5-1\\\\\implies -x < 4\\\\\implies x > -4\\\\\text{Interval notation:}~ (-4, \infty)[/tex]

Answer: SAS similarity theorem

Proportional relationship:

[tex]\sf \dfrac{AB}{AC} = \dfrac{AM}{AN}[/tex]

insert values

[tex]\rightarrow \sf \dfrac{21+9}{14+6} = \dfrac{21}{14}[/tex]

simplify

[tex]\rightarrow \sf 1 = 1[/tex]

L.H.S = R.H.S

The triangles are congruent and follows the rule SAS similarity theorem.

The triangles has/starts from the same angle, corner (A).

Answer:

5,000,000^2

Step-by-step explanation:

half of 10,000,000 sqrt of 2

Answer:

25 in x 15 in

Step-by-step explanation:

Given:

Let width = [tex]x[/tex]

Therefore, length = 3/5 [tex]x[/tex]

First create an equation for the area of the picture based on the given information for its width and length:

[tex]\begin{aligned} \implies \textsf{Area of original picture} & = \sf width \times length\\& = x\left(\dfrac{3}{5}x\right)\\& = \dfrac{3}{5}x^2\end{aligned}[/tex]

We are told the area of the enlarged picture is 375 in².  Therefore, substitute this into the equation and solve for [tex]x[/tex] to find the width of the enlarged picture:

[tex]\begin{aligned}\textsf{Area} & = 375\\ \implies \dfrac{3}{5}x^2 & = 375\\ x^2 & =375 \cdot \dfrac{5}{3}\\ x^2 & =625\\ x & = \sqrt{625}\\ x& = 25\end{aligned}[/tex]

Therefore, the width of the enlarged picture is 25 in.

Substitute the found value of [tex]x[/tex] into the expression for length to find the length of the enlarged picture:

[tex]\begin{aligned}\sf Length & = \dfrac{3}{5}x\\\\\implies \sf Length & = \dfrac{3}{5}(25)\\\\& = 15\: \sf in\end{aligned}[/tex]

Therefore, the dimensions of the enlarged picture are 25 in x 15 in.  The width is 25 in and the length is 15 in, as the length is 3/5 of the width.

Answer:

correct

Step-by-step explanation:

Answer:

  3 and 1/2 half-cups

Step-by-step explanation:

We are asked to find the number of half-cups that will equal 1 3/4 cups.

__

Let the desired number be represented by n. Then we require ...

  n × 1/2 = 1 3/4 . . . . some number of 1/2-cups will give 1 3/4 cups

Using a common denominator, we have ...

  n × 2/4 = 7/4

Multiplying by the inverse of the coefficient of n gives ...

  n × 2/4 × 4/2 = 7/4 × 4/2

  n = 7/2 = 3 1/2 . . . . . simplify

That is, Donna can measure 1 3/4 cups of sugar by using her 1/2-cup measure 3 times, and filling it half-full for the final 1/4 cup she needs.

She needs 3 1/2 half-cups to get the correct amount.

Answer:

180

Step-by-step explanation:

The required ratio is 2:1.

We have given that,

4.5:2.25

Since we have given that

We need to find the ratio in the form of n:1.

A ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14.

so, it becomes,

[tex]=\frac{4.5}{2.25}:1\\\\=2:1[/tex]

Hence, the required ratio is 2:1.

Express the ratio in the simple form

4.5:3 1/2.

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For the given exponential function there will be an exponential growth of 7%.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

we have

[tex]f(x) = 4200(1.07)^x[/tex]

This is an exponential function of the form

[tex]f(x)=ab^x[/tex]

where

a -  is the initial value

b -  is the base

If b > 1 ----> is a exponential growth

0 < b < 1 ----> is a exponential decay

r is the per cent rate

b = 1 + r

In this problem we have

a = 4200

b = 1.07

We can see that 1.07 > 1 -----> is a exponential growth

Find out the per cent rate

b = 1 + r

r = 1.07 - 1

r = 0.07

r = 7 x 100 = 7%

Therefore the given exponential function there will be an exponential growth of 7%.

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Answer:

6 is the answer

Hope that helps.
Let me know if im wrong :)

Step-by-step explanation:

The attached graph represents the graph of the inequality

The points on the line are given as:

(-3,-7) and (0,2)

Start by calculating the linear equation using:

[tex]y = \frac{y_2 -y_1}{x_2 -x_1}(x -x_1) + y_1[/tex]

This gives

[tex]y = \frac{2 + 7}{0 + 3}(x -0) + 2[/tex]

Evaluate the fraction expression

y = 3(x -0) + 2

Evaluate the difference

y = 3x + 2

From the question, we understand that the line of the inequality is a dashed line and the left of the line is shaded.

This means that the inequality is greater than i.e. >

So, we have:

y > 3x + 2

See attachment for the graph of the inequality

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Answer:

$25

Step-by-step explanation:

the fruit vendor sold 75-10 = 65 kg of bananas. 65*28 = 1820 dollars. so the fruit vendor earned 1820 dollars.

since she lost 55 dollars, 75 * cost = 1875, divide by 75 to get cost = 25

Considering the constant rate of change, it is found that table 1 represents a linear function.

A linear function is modeled by:

y = mx + b

In which:

From the concept of the slope, we have that the rate of change of a linear function is constant, that is, when x changes by 1, y has to change always by the same amount, which happens in table 1, with a constant rate of change of 1/2 = 0.5.

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Based on the angle-angle similarity theorem, the piece of additional information can be used to prove ΔCEA ≅ ΔCDB is: A. ∠BDC and ∠AED are right angles.

Based on the angle-angle similarity theorem, if two triangles have two pairs of corresponding angles that are congruent, then both triangles are similar.

In the diagram given, we can establish that the two triangles have one pair of congruent angles, ∠CEA ≅ ∠CDB.

Thus, an additional information that is needed to prove that both triangles are similar is: A. ∠BDC and ∠AED are right angles.

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Answer: A. ∠BDC and ∠AED are right angles

Step-by-step explanation:

Answer:

Rhombus

Step-by-step explanation:

The first and third points have the same y-coordinate along with the second and fourth. None have the same x-coordinate. This figure has two sets of parallel sides but no right angles.

Answer:

[tex]\frac{4}{n^{2} }[/tex]

Step-by-step explanation:

(2nm⁻³) * 2m³n⁻³

First, focus on the coefficients, 2*2 = 4.

Now the n, n * n⁻³ = n⁻²

Now the m, m⁻³ * m³ = m⁰ = 1

Now multiply altogether, 4n⁻²(1) = [tex]\frac{4}{n^{2} }[/tex]

Answer:

Mean: 4

Median : 4

Mode: 1, 2, 3, 4, 5, 6, 7

Step-by-step explanation:

Measure of center is:

Mean: Average

Median: Middle number

Mode: Often number

Mean: Add all number then divide by the total number in data set.

1 + 2 + 3 + 4 + 5 + 6 + 7 = 28

28/7 = 4

Median: Middle number

1,2,3,4,5,6,7

Mode: most often number

1,2,3,4,5,6,7

Kavinsky

Answer:

(a)no mode

(b)mean= 4

(c)median= 4

Step-by-step explanation:

the measure of centre are the mode, mean and median

mode: this is the heighest occuring number or the number with the heighest frequency.

mean: this is the average number. it's obtained by adding the data values in a set of numbers and dividing the sum by the number of data items.

meadian: this is the middle number when the data is ordered or when the data is arranged in ascending or descending order.

from the data,

mode: no number occured more than the other. therefore, there is no mode

mean = 1+2+3+4+5+6+7 = 28/7= 4

median= 1,2,3,4,5,6,7

the middle numbers is 4

Answer:

The probability of it rolling 5 or above is 45%

Step-by-step explanation:

I have passed the test of it

Answer:

the answer is d

Step-by-step explanation:

1st day : 7 × 10 = 70

5 × 7 = 35 70+ 35= 105

2nd day : 7 × 10 = 70

2 × 7 = 14 70+14 = 84

The area of the parallelogram in the given diagram is 103.68 cm²

From the question, we are to determine the area of the given parallelogram

The area of a parallelogram can be calculated by using the formula,

A = bh

Where A is the area

b is the base

and h is the perpendicular height

From the given diagram,

b = 14.4 cm

h = 7.2 cm

Putting the parameters into the equation, we get

A = 14.4 × 7.2

A = 103.68 cm²

Hence, the area of the parallelogram in the given diagram is 103.68 cm²

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the degrees Fahrenheit is -9

A customer that uses an internet plan that costs $10 per month is expected to give a customer rating of 6

We start by calculating the regression equation of the table of values using a graphing calculator.

Using the graphing calculator, we have:

y = 0.04x + 5.75

When the cost is $10 per month, it means that

x = 10

So, we have:

y = 0.04 * 10 + 5.75

Evaluate

y = 6.15

Approximate

y = 6

Hence, a customer that uses an internet plan that costs $10 per month is expected to give a customer rating of 6

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[tex]~~~~~~\dfrac{2x-3}{4} = 3x\\\\\implies 2x-3 = (3x)(4)\\\\\implies 2x -3 = 12x \\\\\implies 12x -2x = -3\\\\\implies 10x = -3\\\\\implies x = -\dfrac{3}{10}[/tex]

Answer:

x = -3/10

Step-by-step explanation:

Given :

[tex]\frac{2x-3}{4} = 3x[/tex]

============================================================

Multiply both sides with 4 :

⇒ [tex]4 \times \frac{2x-3}{4} = 4 \times 3x[/tex]

⇒ 2x - 3 = 12x

============================================================

Subtract 2x from both sides :

⇒ 2x - 3 - 2x = 12x - 2x

⇒ -3 = 10x

⇒ x = -3/10

Answer:

[tex]f(x) = \frac{x^{2} -5x-6}{x^{2} -4}[/tex]

Step-by-step explanation:

Let's factorize the 1st option :

⇒ [tex]f(x) = \frac{x^{2} -5x-6}{x^{2} -4}[/tex]

⇒ [tex]f(x) = \frac{x^{2}+x-6x-6 }{(x+2)(x-2)}[/tex]

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

===============================================================

Finding the zeros :

⇒ Factors of numerator should be equated to 0

=============================================================

Solution :

[tex]f(x) = \frac{x^{2} -5x-6}{x^{2} -4}[/tex]

Answer:

first option

Step-by-step explanation:

the zeros are determined by the numerator of the rational function.

given that the zeros are x = - 1 and x = 6 , then the corresponding factors are

(x + 1) and (x - 6) , that is

(x + 1)(x - 6) ← expand using FOIL

= x² - 5x - 6

the rational function is then

f(x) = [tex]\frac{x^2-5x-6}{x^2-4}[/tex]

Answer:

6^a+v

Step-by-step explanation:

a^m * a^n = a^(m+n)

so, 6^a * 6^v = 6^a+v

Answer:

[tex] {6}^{a+v} [/tex]

Step-by-step explanation:

We want to find the value of

[tex]{6}^{a} \times 6 ^{v} [/tex]

We can do so by using basic exponent laws.

Multiplying exponents with the same base law:

(note that the base is the number under the exponent, in this case both bases have a value of 6 so we use this law)

[tex]a ^{m} \times {a}^{n} = {a}^{m+n} [/tex]

Explanation of law : We simply keep the bases the same and add the exponents.

Applying this law to 6^a * 6^v

We acquire

6^a * 6^v

==> keep the bases the same and add the exponents

6^a+v

Answer: They are vertical angles​

Step-by-step explanation:

Intersecting lines form vertical angles.

The total surface area of the remaining solid is 48(4+✓3) centimeters square.

Through a regular hexagonal prism whose base edge is 8 cm and the height is 12 cm, a hole in the shape of a right prism.

The formula for the total surface area will be:

= Total surface area=2(area of the base)+ parameter of base × height

where,

Height= 8cm

Parameter of base=12(2) = 24

Area of the base= 6×✓3/4×4² = 64✓3/4

The surface area of the remaining solid will be:

= 2(64✓3/4) + 24 × 8

= 2(64✓3/4 + 192

With the hole is a rhombus prism with the following parameters:

diagonal 1 = 6, diagonal 2 = 8, height = 12

The volume is:

V1 =0.5 × d1 × d2 × h

V1 = 0.5 × 6 × 8 × 12

V1 = 96

The dimensions of the hexagonal prism are:

Base edge (a) = 8

Height (h) = 12

The volume is

V2 = (3✓(3)/2)a²h

V2 = (3✓3)/2) × 8² × 12

V2 = 1152✓3

The remaining volume is

V = V2 -V1

V = 1152✓3 - 96

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An angle cannot be the complement of one angle and the supplement of another angle at the same time. Then the given statement is false.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

An angle cannot be the complement of one angle and the supplement of another angle at the same time.

Then the given statement is false.

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