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.

Answer:

This assumes the question should read:

"The average of 5 girls is 16 [not 6] yrs. the average of 4 of them is 16½. what is d age of d fifth gal​

The age, d, is 14 years.

Step-by-step explanation:

When the girl with age d is not included, the average goes up to 16.5 years.   Let's define GroupA as the sum of the ages of the 4 girls whose average age is 16.5 years.  d is the age of the girl that is removed from the average.

We know that all the girls (GroupA + d) have an average age of 16 years:

(GroupA + d)/5 = 16 years  [Add the ages for all the girls (GroupA and d) and divide by 5 to obtain the average age for the larger group].

We know that when d is removed, the average for the 4 remaining girls (GroupA) is 16.5 years:

(GroupA)/4 = 16.5 years

This tells us the sum of the ages for GroupA:

GroupA = 4*(16.5)

GroupA total = 66 years

From above:       (GroupA + d)/5 = 16 years

Since GroupA = 66 years,    (66 years + d)/5 = 16 years

(66 years + d) = 90 years

d = 14 years

Using the circle theorems, the value of z is 45

From the question, we are to determine the value of z

From the given information,

KM is a diameter

∴ ∠KLM = 90° (Angle in a semicircle)

Also, ΔKLM is isosceles

∴ ∠KML = ∠MKL (Base angles of an isosceles triangle)

Then,

∠KML + ∠MKL + ∠KLM = 180° (Sum of angles in a triangle)

2× ∠KML + 90° = 180°

2× ∠KML = 180° - 90°

2× ∠KML = 90°

∠KML = 90°/2

∠KML = 45°

Now, we can observe that

z° = ∠KML (Angles in alternate segment)

But,

∠KML = 45°

∴ z = 45

Hence, the value of z is 45

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Answer: 1 1/2

Step-by-step explanation:

1 4/5 = 9/5

1 1/5 = 6/5

[tex]\frac{9}{5} / \frac{6}{5}\\ \\\frac{9}{5} * \frac{5}{6}\\ \\\frac{45}{30} \\ \\1\frac{1}{2}[/tex]

[tex]~~~~~~\dfrac{3x+15}{6-x} = 0\\\\\implies 3x +15 = 0\\\\\implies 3x = 0-15\\\\\implies 3x = -15\\\\\implies x = -\dfrac{15}3\\\\\implies x = -5[/tex]

Answer:

the answer=  -5

The equation that is equivalent to the given equation is 4x = 68. No answer is correct

Equations are two expressions equated to each other. Given the equation below;

- 4(x - 5) + 8x = 91 - 3

Expand

-4x + 20. + 8x = 88

Collect the like terms

4x + 20 = 88
4x = 88 - 20

4x = 68

Hence the equation that is equivalent to the given equation is 4x = 68

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Applying the leg rule, the value of x in the given right triangle is: A. 6.

The leg rule for solving a right triangle having an altitude is expressed as:

hypotenuse/leg = leg/part.

In the image given we have the following:

Hypotenuse = 4 + 5 = 9 units

Leg = x

Part = 4

Plug in the values into the leg rule formula:

9/x = x/4

(x)(x) = (9)(4)

x² = 36

x = √36

x = 6 units.

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Answer:The entire area would be 12 square meters.

Step-by-step explanation:

2 x 6 square meters =  12 square meters. which is the entire area.

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Answer:

The point will be plotted on Y axis

The value of the expression f(5) + j(-2)  is -8 where f(x)=12-3x and j(x)=x² + 4x - 1

The expression is given as:

f(5) + j(-2)

Where f(x)=12-3x and j(x)=x² + 4x - 1

Calculate f(5) and j(-2)

f(5)= 12 - 3(5) = -3

j(-2) = (-2)² + 4(-2) - 1 = -5

So, we have:

f(5) + j(-2)  = -3 - 5

Evaluate

f(5) + j(-2)  = -8

Hence, the value of the expression f(5) + j(-2)  is -8

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Surface area is all the area of all sides while volume is the amount of space (a substance) occupies in a solid.

For example:

A cube has a length,breadth and height of 5cm,find:

a) surface area of the cube;

b) and the volume of the cube.

a) area of one side of the cube = 5 x 5

                                                    = 25cm²

Total surface area = 25cm x 6 (a cube has 6 sides)

                               = 150cm²

b) volume of cube = length x breadth x height

                              = 5 x 5 x 5

                              = 125cm³

Hope this helps you :]

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The sample space S =  {1, 2, 3, 4, 5, 6} describing all possible outcomes and outcomes for the event of rolling the number 2 is E = {2}

It is defined as the space in which all possible outcomes are represented in a list form for a particular event.

We have:

A number cube with faces labeled from 1 to 6 will be rolled once.

Let S is the sample space:

As we know, the sample space is the set of all possible outcomes:

S = {1, 2, 3, 4, 5, 6}

The total number of outcomes:

n(S) = 6

The outcomes for the event of rolling the number 2.

E = {2}

n(E) = 1

Thus, the sample space S =  {1, 2, 3, 4, 5, 6} describing all possible outcomes and outcomes for the event of rolling the number 2 is E = {2}

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[tex] \rm \: {2x}^{2} + x - 6[/tex]

[tex] \rm \: {2x}^{2} + 4x - 3x - 6[/tex]

[tex] \rm \: {2x} \times (x + 2)- 3x \times (x + 2)[/tex]

[tex] \rm \: (x + 2) \times (2x - 3)[/tex]

Answer:

B: Save $10

Step-by-step explanation:

A: $14.80, B: $12, C:$18.70, D: $16.50

Answer:

9³

Step-by-step explanation:

We know that,

[tex]a^b[/tex] ÷ [tex]a^c[/tex] = [tex]a^b^-^c[/tex]

By following the above, let us solve the given question.

Let us solve now.

⇒ 9⁵ ÷ 9²

⇒ 9⁵⁻²

⇒ 9³

The time it would take for the bacteria to reach 1119 is 5.83 hours

Given the function:

[tex]Pt= P_0e^k^t[/tex]

To find the exponential growth;

80 = [tex]50e^k^*^3[/tex]

[tex]k= 1.6/3\\k= 0.533[/tex]

If there is a constant growth, then to get to 1119:

1119= [tex]50e^0^.^5^3^3^*t[/tex]

3.8 = 0.533*t

t= 5.83 hours

Therefore, it would take 5.83 hours for the bacteria to increase to 1119.

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Answer:

3/7

Step-by-step explanation:

Probability=Number of possible items÷Number of total items.

We will make the possible item 3 because we are looking for the probability whether a boy will be picked.

The number of total items will therefore be: the number of boys + the number of girls; that will be 3+4 =7.

So the probability of picking a boy will be 3/7

THANK YOU.

Answer: The surface area = 2040.

Step-by-step explanation: Have a great day!

The area of the rectangle is 64.8 square .inch

A rectangle is a polygon with four sides , opposite sides are parallel and equal.

It is given that

A rectangle is divided into exactly 20 congruent squares

If they are lined up the Length is 36 inches

Therefore the length of each square or the side of the square = 36/20

= 1.8 inch

The area of the rectangle will be

20* Side of square * Side of square

=20*1.8*1.8

= 64.8 square inch

The area of the rectangle is 64.8 square .inch

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Answer:

3.14 × 16 is 18,84

Method in picture

[tex]{\color{aqua}{\boxed{\mathfrak{LordKeyarga23}}\:}}[/tex]

The value of the multiplication of the numbers 3.14 and 16 will be 50.24.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The numbers are given below.

3.14 and 16

Then the multiplication of the numbers 3.14 and 16 will be given by putting a cross sign between them. Then we have

⇒ 3.14 x 16

⇒ 50.24

The value of the multiplication of the numbers 3.14 and 16 will be 50.24.

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Answer:

2 days

Step-by-step explanation:

275 miles times 0.05 = $13.75 for mileage

200-13.75=186.25 left

186.25/63.41(daily fee)= 2.93

She can rent it for 2 days

The graph third represents the provided situation first line increases and then constant then again increases and becomes constant.

A line graph is a graph made up of segments of straight lines that connect the depicted data points.

We have:

Keisha ran to swim practice but needed to stop by her friend Natasha’s house on the way. She stayed at Natasha’s house for 15 minutes, and together they ran the rest of the way to practice, where they stayed for 1 hour.

Based on the information given we can say graph third represents the situation.

First Keisha ran to swim practice so the line first increases and then she  but needed to stop by her friend Natasha’s house on the way. She stayed at Natasha’s house for 15 minutes which means the line should be constant.

Again they both ran so line increases.

Then they both stayed for 1 hour, so the line should be constant.

Thus, the graph third represents the provided situation first line increases and then constant then again increases and becomes constant.

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Answer:

Step-by-step explanation:

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3900\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &9 \end{cases} \\\\\\ A=3900\left(1+\frac{0.075}{1}\right)^{1\cdot 9}\implies A=3900(1.075)^9\implies A\approx 7477.23[/tex]

Step-by-step explanation:

[tex] \sin {}^{2} ( - 300) \cos {}^{2} (120) + \cos {}^{2} ( - 240) \sin {}^{2} (390) = \frac{1}{4} [/tex]

[tex] \sin {}^{2} (60) \cos {}^{2} ( {}^{} 120) + \cos {}^{2} (120) \sin {}^{2} (30) [/tex]

[tex] \frac{3}{4} \frac{1}{4} + \frac{1}{4} \frac{1}{4} [/tex]

[tex] \frac{3}{16} + \frac{1}{16} = \frac{4}{16} = \frac{1}{4} [/tex]

Answer:

11,000

Step-by-step explanation:

10% of 10,000 is 1,000 so 5% is 500 and add 2 of 5% you get 1,000 and add it to the old price thus you get 11,000.

Triangle RST is reflected across the x-axis and translated 5 units to the left to form triangle R"S"T"

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Triangle RST is reflected across the x-axis and translated 5 units to the left to form triangle R"S"T"

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Answer:

  410 g

Step-by-step explanation:

Radioactive decay can be modeled by an exponential equation. The amount remaining (y) after a time period (t) can be expressed in terms of the initial amount (a) and the half-life (h).

  y = a(1/2)^(t/h)

__

We can use this equation with the given values to find the amount remaining.

  y = (680 g)(1/2)^((19 yrs)/(26 yrs)) ≈ (680 g)(0.602583)

  y ≈ 410 g

About 410 grams of element X will remain after 19 years.