A girl 160 cm tall stands 360 cm from a lamp post at night. Her shadow from the light is 90 cm long. How high is the lamp post?

Answer:

J =2m -3

Step-by-step explanation:

2m is twice Monica's age

-3 represents 3 years younger

The answer is: 5 x ^2 + 2 x − 2

The 42 inches fishing rod is fit into the box.

Explanation:

Length of the box = 40 inch

Width of the box = 10 inch

Height of the box = 10 inch

Let us first find the diagonal of the base of the box and 'd' be the diagonal.

Diagonal formula:

[tex]d^2=l^2+w^2[/tex]

   [tex]=40^2+10^2[/tex]

   [tex]=1600+100[/tex]

[tex]d^2=1700[/tex]

Let r be the length from a bottom corner to the  opposite top corner.

To find r:

Using Pythagoras theorem,

[tex]r^2=s^2+h^2[/tex]

    [tex]=1700+10^2[/tex]

    [tex]=1700+100[/tex]

[tex]r^2=1800[/tex]

Taking square root on both side of the equation,

[tex]r=\sqrt{1800}[/tex]

r ≈ 42.43 inch

The length of the longest tube that will fit in the box is 42.43 inches.

Hence the 42 inches fishing rod is fit into the box.

To determine if the fishing rod will fit, compare the length of the fishing rod to the length of the box and check the other dimensions for a comfortable fit.

To determine if the fishing rod will fit inside the box, we need to compare the length of the fishing rod to the dimensions of the box. Since the fishing rod is 42 inches long, we need to check if 42 inches is less than or equal to the length of the box. If it is, then the fishing rod will fit.

Step 1: Compare the length of the fishing rod (42 inches) to the length of the box. If 42 inches is less than or equal to the length of the box, go to Step 2. Otherwise, the fishing rod will not fit.

Step 2: Check the other dimensions of the box to ensure that the fishing rod can fit without any issues. If the fishing rod can fit comfortably inside the box, then it will fit.

https://brainly.com/question/34796541

#SPJ3

Answer:

b

Step-by-step explanation:

you can break the 78 into 70 and 8, and multiply them separately by 6 and then add the two answers to get 468

Answer:

B

Step-by-step explanation:

literally the only equivalent equation

Answer:825000

Step-by-step explanation:

Answer:825000

Step-by-step explanation:

825*1000

Answer:

195in^2 is the correct answer.

Step-by-step explanation:

Answer:

cj sjx soiebxidhevdi hi

Answer: hi

Step-by-step explanation:

Lol

"Mitchael owes $8 to his bank, so he decides to add $60 in April at a rate of $2 per day. How many days Mitchael needs in order to get $28 in his account?"

Hello! Remember you have to write clear questions in order to get good and exact answers. The given equation doesn't make any sense so I'll assume the correct one is:

[tex]-8+60x=28[/tex]

So let's write a real world problem you could answer by solving the equation:

"Mitchael owes $8 to his bank, so he decides to add $60 in April at a rate of $2 per day. How many days Mitchael needs in order to get $28 in his account?"

So by isolating x (number of months):

[tex]x=\frac{28+8}{60} \\ \\ x=0.6 \ month \\ \\ \\ Since \ we \ need \ the \ number \ of \ days: \\ \\ April \ has \ 30 \ days, \ so: \\ \\ x-day=0.6\times 30=18 \ days[/tex]

So Mitchael would need 18 days in order to get $28 in his account

Method for solving system of linear equations: https://brainly.com/question/10185505

#LearnWithBrainly

To solve the equation -8+60=28, we follow basic arithmetic by adding the positive payment to the negative debt which gives us 52. This answer indicates an error in the original problem statement, as the expected balance does not match with the calculated one.

A real-world problem that could be answered by solving the equation -8+60=28 might involve a scenario where someone is tracking their financial transactions. Suppose you start with a debt of \(-8 dollars and then receive 60 dollars as a payment of some sort. The question could be to determine how much money you have after receiving the payment. To find out, you would solve the equation to see if your final balance is 28 dollars as expected.

Let's solve this step-by-step:

Add the amount received to the initial debt: \( -8 + 60 \).

Calculate the sum which gives us \( 52 \).

Therefore, after receiving the payment, you have 52 dollars.

To answer the original equation, the final balance should be 28 dollars; however, the solution we found is 52 dollars, indicating there might be a mistake in the original problem statement or the transactions recorded.

Answer:

x=4.16

Step-by-step explanation:

12x -18 +4 = 16+18

12x-16= 16+18

12x-16=34

      +16 +16

12x=50

50/12

4.16

Answer:

[tex](F+G)x=2x^2+4x-16[/tex]

[tex]Domain[/tex] [tex]=(-\infty,\infty)[/tex]

Step-by-step explanation:

Given that

[tex]F(x)=2x^2+3x-15[/tex]

and  [tex]G(x)=x-1[/tex]

then   [tex](F+G)x = F(x)+G(x)[/tex]

[tex]=(2x^2+3x-15)+(x-1)\\=2x^2+3x-15+x-1\\\\(F+G)x=2x^2+4x-16[/tex]

Domain

since it is a polynomial of degree [tex]2[/tex], the domain will be whole real line  

[tex]domain[/tex] [tex]=(-\infty,\infty)[/tex]

Final answer:

To perform the function operation (F+G)(X), add the functions f(x) and g(x) together to get (F+G)(X) = 2x² + 4x - 16. The domain of this function is all real numbers.

Explanation:

To perform the function operation (F+G)(X), where f(x) is given as 2x² + 3x - 15 and g(x) is x - 1, we simply add the two functions together:

(F+G)(X) = f(x) + g(x)

(F+G)(X) = (2x² + 3x - 15) + (x - 1)

This simplifies to:

(F+G)(X) = 2x² + (3x + x) - (15 + 1)

(F+G)(X) = 2x² + 4x - 16

The domain for this new function is all real numbers, since there are no restrictions such as division by zero or taking the square root of a negative number that would limit the values that x can take.

The additive inverse is the idea of adding a negative number, which is the same as subtraction. Example: 2 + (-3) = 2-3

Based on the example above, if we start off with 3 and add on its additive inverse -3, then 3 + (-3) = 3-3 = 0. In general, x + (-x) = x-x = 0. So adding any number with its additive inverse gets you 0 every time.

-----------------------------------------------

Extra info:

Answer:

0.073

Step-by-step explanation:

The question is about growth function and you are asked to find out the growth rate. Growth function has a format of

y = a(1+r)^t

Where

y= future value = S(t)

a= current value = 273

r= growth rate

t= time =t

Since its a growing function, the r will be positive. If its decay function then the r will be negative. As you can see, the growth rate value is located inside the parentheses. The growth rate of the function should be:

(1+r)= (1.073)

r= 1.073- 1

r= 0.073

7.0267

Step-by-step explanation:

The clue here is that the decimal point follows after the "and"

For example,

One and one thousandth = 1 + 1/1000 = 1.001

One and two hundred sixty-three thousandths = 1+ 263/1000 = 1.263

Hence;

seven and two hundred sixty-seven ten thousandths= 7+ 267/10000= 7.0267

Learn More

Decimal points form :https://brainly.com/question/232702

Keywords : hundred, ten thousandths,decimal

#LearnwithBrainly

The equations used to find the length of leg of triangle are:

[tex]0.5x(x+2) = 24\\\\x^2+2x-48=0\\\\x^2+(x+2)^2 = 100[/tex]

Solution:

From given,

Area of right triangle = 24 square feet

Also from given figure in question (attached below )

base = x and height = x + 2

The area of triangle is given by formula:

[tex]Area = \frac{1}{2} \times base \times height[/tex]

Substituting the values we get,

[tex]24 = \frac{1}{2} \times x \times (x+2)\\\\24 = 0.5x(x + 2)\\\\48 = x(x+2)\\\\x^2 + 2x - 48 = 0\\\\[/tex]

Also, the above equation can be written as,

[tex]x^2 + (x+2)^2 =100[/tex]

Thus the equations used to find the length of leg of triangle are:

[tex]0.5x(x+2) = 24\\\\x^2+2x-48=0\\\\x^2+(x+2)^2 = 100[/tex]

Answer:

A, D, E

Step-by-step explanation:

From the answer above, but the letters to make it easier :)

Answer:

x = 15

Step-by-step explanation:

Step 1:  Distribute

3x - 5(x) - 5(2) = -40

3x - 5x - 10 = -40

Step 2:  Combine like terms

-2x - 10 = -40

Step 3:  Add 10 to both sides

-2x - 10 + 10 = -40 + 10

Step 4:  Divide both side by -2

-2x / -2 = -30 / -2

x = 15

Answer:

8

Step-by-step explanation:

12+15=27 27+3=30 30+6+4=40 40/5=8

Answer:

the answer is 8

Step-by-step explanation:

12+15+6+4+3 / 5 = 8

Answer:

Step-by-step explanation:

zxy or xyz or z×x×y

Final answer:

The mathematical expression for 'the product of z, x, and y' is simply 'zxy' or 'z  times x  times y', which indicates that the three variables are being multiplied together to form a product.

Explanation:

To translate "the product of z, x, and y" into a mathematical expression, we represent multiplication using either the multiplication sign (times) or simply by juxtaposition (placing the variables next to each other). Thus, the product of the variables z, x, and y is represented as z  imes x  imes y or simply as zxy. This expression shows that z, x, and y are being multiplied together to give a Mathematical Result.

In mathematics, when expressions are evaluated and produce the same value, they are known as equivalent expressions. For example, the expression (5 - 3xy) is evaluated by following the order of operations, which in this case involves subtracting the product of 3 and xy from 5. If x, y, and z are treated as three independent variables, it is also possible to represent their product in the form of a Multiple or Product, like so: xyz.

To solve the equation (3x+1)+(4x-5)=8x-9, we simplify and solve for x, obtaining x=5 as the solution. Verification by substitution confirms that our solution is correct.

To find the value of X for the equation (3x+1)+(4x-5)=8x-9, we first simplify both sides of the equation by combining like terms. On the left side, we combine the x terms and the constant terms: 3x + 4x + 1 - 5. This simplifies to 7x - 4. The right side of the equation remains as 8x - 9.

Next, we set the simplified left side of the equation equal to the right side: 7x - 4 = 8x - 9. To solve for x, we can subtract 7x from both sides to get x on one side of the equation, resulting in -4 = x - 9. Adding 9 to both sides gives us x = 5 as the solution.

To verify, we substitute x=5 back into the original equation: (3(5)+1)+(4(5)-5) = 15 + 1 + 20 - 5 = 31, and on the right side, 8(5) - 9 = 40 - 9 = 31, which confirms our solution since both sides equal 31.

Answer:

x= 14√3

y= 28√3

Step-by-step explanation:

Please see attached picture for full solution.

(tan30° and cos30° are special angles so there's an exact value to it in which we can memorise.)

In this case, by Pythagoras's Theorem, you should ensure that:

[tex] {y}^{2} = 42^{2} + {x}^{2} [/tex]

✓ Let's check:

[tex]{y}^{2} = (28 \sqrt{3} )^{2} \\ y^{2} = 2352 \\ {x}^{2} + {42}^{2} = ( 14\sqrt{3})^{2} + 1764 = 2352[/tex]

This satisfies Pythagoras' Theorem :)

For this kind of questions, first label the adjacent side, opposite side and the hypotenuse side of the triangle.

Cosine angle= adjacent/ hypotenuse

Sine angle= opposite/ hypotenuse

tangent angle= opposite/ adjacent

Then substitute the known side and angle to find the unknown side.

Answer:

165 people

Step-by-step explanation:

If there are 105 woman then there are going to be 60 men because 105/7=14, so you multiply 4*15 and get 60. 60 + 105= 165. So the total employees will be 165.

The total number of employees is the sum of men and women, which is 105 (women) + 60 (men) = 165 employees.

To find the total number of employees, calculate the number of men from the given ratio 4:7 and the number of women (105), and then add the number of men to the number of women to get the total.

The question is about finding the total number of employees in a company given the ratio of men to women and the number of women.

Let's use the provided ratio of men to women, which is 4 to 7, to calculate the number of men.

Since there are 105 women, and the ratio dictates that for every 7 women there are 4 men, we divide 105 by 7 to find the number of units that represent women, which is 15.

We then multiply this by 4 (the number of men) to find the number of men, which is 60.

105 + 60 = 165

Answer:

The only correct statement is ii) In Grade 8,  17% of the students liked

running.

Step-by-step explanation:

Favorite Sports

                    Swimming        Running      Volleyball      Total

Grade 8            0.24                0.17             0.05               0.46

Grade 9            0.18                 0.14             0.22               0.54

Total                  0.42                0.31            0.27                 1

i.) In Grade 8 14 students liked swimming.

   This cannot be said with accuracy as the total number of students is not

   known.

ii) In Grade 8,  17% of the students liked running.

   This statement is TRUE.

iii)  In Grade 9, 31% of students liked volleyball.

    This statement is NOT TRUE.  In Grade 9,  22% of the students liked

     volleyball.

iv)  In Grade 9, 22 students liked volleyball.  

    This cannot be said with accuracy as the total number of students is not

   known.

  The only correct statement is ii) In Grade 8,  17% of the students liked

  running.

Answer:

In Grade 8,  17% of the students liked running.

Answer:

Its 111ft. tall if thats what your asking.

Step-by-step explanation:

100+11=111

The answer is: [tex]83.66^\circ[/tex]. The angle of elevation that the ladder makes with the ground is approximately [tex]\( 83.66^\circ \)[/tex].

To solve the problem, we need to find the angle of elevation that the ladder makes with the ground when it is resting on top of the hook and ladder truck. We are given that the ladder is 100 feet long and its base is 11 feet from the ground.

We can use trigonometry to solve for the angle of elevation (θ). The tangent of the angle of elevation is the ratio of the opposite side (height from the ground to the top of the ladder) to the adjacent side (the distance from the base of the ladder to the point on the ground directly below the top of the ladder).

Let's denote:

- The length of the ladder as [tex]\( L \)[/tex], which is 100 feet.

- The distance from the base of the ladder to the point on the ground directly below the top of the ladder as [tex]\( d \)[/tex], which is 11 feet.

- The height from the ground to the top of the ladder as [tex]\( h \)[/tex].

Using the Pythagorean theorem, we can find [tex]\( h \)[/tex]:

[tex]\[ h^2 + d^2 = L^2 \][/tex]

[tex]\[ h^2 + 11^2 = 100^2 \][/tex]

[tex]\[ h^2 = 100^2 - 11^2 \][/tex]

[tex]\[ h^2 = 10000 - 121 \][/tex]

[tex]\[ h^2 = 9879 \][/tex]

[tex]\[ h = \sqrt{9879} \][/tex]

[tex]\[ h \approx 99.39 \text{ feet} \][/tex]

Now, we can find the angle of elevation using the tangent function:

[tex]\[ \tan(\theta) = \frac{h}{d} \][/tex]

[tex]\[ \theta = \arctan\left(\frac{h}{d}\right) \][/tex]

[tex]\[ \theta = \arctan\left(\frac{99.39}{11}\right) \][/tex]

[tex]\[ \theta \approx \arctan(9.03545455) \][/tex]

[tex]\[ \theta \approx 83.66^\circ \][/tex]

Therefore, the angle of elevation that the ladder makes with the ground is approximately [tex]\( 83.66^\circ \)[/tex].

The final answer is:

[tex]\[ \boxed{83.66^\circ} \][/tex]

The complete question is:

A 100 ft ladder rests on top of a hook and ladder truck with its base 11 feet from the ground. When the angle of elevation of the ladder is 81°, how high up the building will the ladder reach?

Final answer:

The slope of the line passing through the points (10,4) and (-2, 17) is calculated using the slope formula and is approximately -1.08.

Explanation:

To find the slope for the line passing through the two points (10,4) and (-2, 17), we use the slope formula which is (change in y)/(change in x) or (y2 - y1) / (x2 - x1). Applying this formula to our points:

m = (17 - 4) / (-2 - 10)

m = 13 / -12

m = -1.0833...

So, the slope of the line that passes through the points (10,4) and (-2, 17) is approximately -1.08.

Answer:

A.)

Step-by-step explanation:

It has the best graph that matches the table

The Y-axis is the number of students who got that grade

The X-axis is the number grade

Answer:

There will be 8 columns

Step-by-step explanation:

So first you get 48 and divide it by 6 then you get 8 as your answer

Final answer:

To determine the number of columns in a 48-bead array with 6 rows, divide the total beads by the number of rows, which results in 8 columns.

Explanation:

The student has arranged 48 beads into an array with 6 rows. To find out how many columns there are, we divide the total number of beads by the number of rows. Therefore:

Divide 48 by 6.

48 ÷ 6 equals 8.

Thus, there are 8 columns of beads.

Each row has the same number of beads, so with 6 rows and 8 columns, we can visualize the array as a rectangle where every row contains 8 beads.

Answer:

6 cups

Step-by-step explanation:

did the math

For two cups of boiling water, 6 cups of sugar would be needed

The first step is to determine how many cups of sugar that would be needed for one cup of boiling water

The number of cups of sugar needed for a cup of boiling water = cups of sugar / cups of boiling water

2 ÷  [tex]\frac{2}{3}[/tex]

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

The second step is to determine the number of cups of sugar that would be needed with two cups of boiling water

Cups of sugar needed for 2 cups of water = cups of sugar needed for one cups of boiling water x 2

3 cups x 2 cups = 6 cups

In order to determine the cups of sugar needed for two cups of boiling water, first determine the number of cups of sugar needed for a cup of boiling water. Use the figure determined to find the cups of sugar needed for 2 cups of water

A similar question was solved here: https://brainly.com/question/16614723?referrer=searchResults

Answer:

1. B. x = 11

2. E. [tex]m\angle BEF=140^{\circ}[/tex]

3. D. 4.3 in

4. D. 40.8 ft

Step-by-step explanation:

1. By Angle Addition Postulate,

[tex]m\angle KLM=m\angle KLV+m\angle VLM[/tex]

Since

[tex]m\angle KLV=34^{\circ}\\ \\m\angle KLM=14x+19\\ \\m\angle VLM=12x+7,[/tex]

then

[tex]14x+19=34+12x+7\\ \\14x-12x=34+7-19\\ \\2x=22\\ \\x=11[/tex]

2. By Angle Addition Postulate,

[tex]m\angle FED=m\angle DEB+m\angle BEF[/tex]

Since

[tex]m\angle FED=14x+8\\ \\m\angle DEB=22^{\circ}\\ \\m\angle BEF=13x-3,[/tex]

then

[tex]14x+8=22+13x-3\\ \\14x-13x=22-3-8\\ \\x=11[/tex]

Therefore,

[tex]m\angle BEF=(13\cdot 11-3)^{\circ}=(143-3)^{\circ}=140^{\circ}[/tex]

3. The area of trapezoid is

[tex]A_{trapezoid}=\text{Midsegment}\times \text{Height}[/tex]

From the diagram,

[tex]\text{Smaller base}=1.2\ in\\ \\\text{Bigger base}=4.2\ in,[/tex]

then

[tex]\text{Midsegment}=\dfrac{1.2+4.2}{2}=2.7\ in[/tex]

Since the area of trapezoid is [tex]11.6\ in^2,[/tex] then

[tex]11.6\ in^2 =2.7\ in\times \text{Height}\\ \\\text{Height}=\dfrac{11.6\ in^2}{2.7\ in}\approx 4.3\ in[/tex]

4. Use formula for the area of the circle to find the radius of the circle:

[tex]A_{circle}=\pi r^2[/tex]

So,

[tex]132.7=\pi r^2\\ \\r^2=\dfrac{132.7}{\pi}\\ \\r=\sqrt{\dfrac{132.7}{\pi}}\ ft[/tex]

Now, find the circumference of the circle:

[tex]C=2\pi r\\ \\C=2\pi \cdot \sqrt{\dfrac{132.7}{\pi}}=2\sqrt{132.7\pi}\approx 40.8\ ft[/tex]