Answer:
960 in (or 80 ft)
Step-by-step explanation:
First, we should convert all of the feet measurements to inches so we have equal units of measurements:
50 ft = 600 in
5 ft 4 in = 64 in
40 in = 40 in
Now we can solve this problem with a simple proportion:
h / 600 = 64 / 40
600 * 64 = 40h
38400 = 40h
960 in = h
***also h = 80 ft
By setting up a proportion of corresponding sides from similar triangles, we find that the flagpole's height is roughly 80 feet.
Explanation:This is a problem of similar triangles. The flagpole and its shadow form one triangle, and the woman and her shadow form a smaller, similar triangle. Since the triangles are similar, the ratio of corresponding sides should be equal. In this case, we have:
height of the flagpole / shadow of the flagpole = height of the woman / shadow of the woman
We can plug the provided values into this equation:
height of the flagpole / 50 feet = 5.33 feet / 3.33 feet
To solve for the height of the flagpole, we cross-multiply and divide, giving us:
height of the flagpole = (5.33 feet / 3.33 feet) * 50 feet
Following that logic, the height of the flagpole is approximately 80 feet tall.
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How do you write 825 in scientific notation
Answer:
8.25 * 10^2
Step-by-step explanation:
825 = 8.25 * 100 = 8.25 * 10^2
8.25×10 to the power of 2
Sarah walks 3.1 kilometers on Monday and 1.35 kilometers on Tuesday. On Wednesday she walks 2.4 times as far as she walked on the previous two days combined. How far does Sarah walk on Wednesday?
Answer:10.68
Step-by-step explanation:
3.1 + 1.35 = 4.45 4.45 × 2.4 = 10.68
Answer:
10.68
Step-by-step explanation:
i worked it out on a piece of paper but this is my answer
The cruising speed of the bullet train will be no less than 130 miles per hour.
Use s to represent the train's cruising speed (in miles per hour).
The representation of the speed will be s ≥ 130.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
The problem raises the following statement: "The cruising speed of the bullet train will be at least 130 miles per hour"
Which means that the train has a speed of 130 miles for now or higher, knowing this we can pose the inequality.
Knowing that "s" is the train's cruising speed (in miles per hour), we have to:
s ≥ 130
This would be the inequality that the statement represents.
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Final answer:
The variable 's' represents the train's cruising speed in mph, and the given condition is translated into the inequality 's ≥ 130', indicating the speed is at least 130 mph.
Explanation:
To represent the cruising speed of the bullet train using a variable, we can assign s to indicate the train's cruising speed in miles per hour. Given the statement 'The cruising speed of the bullet train will be no less than 130 miles per hour,' we can translate this into an inequality: s ≥ 130. This inequality means that the value of s, the train's cruising speed, must be greater than or equal to 130 mph.
PLEASE HELP
The total cost f(x), in dollars, for renting a moving van for a week and driving it x miles is shown below:
f(x) = 90 + 0.13x
What is the value of f(200), and what does f(200) represent?
Answer:
f(200) =116
f(200) is the cost to rent the moving van and drive it 200 miles
Step-by-step explanation:
f(x) = 90 + 0.13x
Let x = 200
f(200) = 90+ .13(200)
=90+26
=116
f(200) is the cost to rent the moving van and drive it 200 miles
what is the answer to the equation: 7x + 4x +2
1. Collect like terms
(7x + 4x) + 2
2. Simplify
11x + 2
How does a compass allow you to draw perfect circles?
Answer:
it makes like a guide to go around to end up as a circle
-angie:) pls mark me brainliest!
Step-by-step explanation:
Doubling the radius of a sphere increases the surface area by a factor of ?
Answer:
4π(2r)² = 4π(4r²) = 4(4πr²)
Doubling the radius of a sphere increases the surface area by a factor of 4.
The correct factor is 4. Doubling the radius of a sphere increases the surface area by a factor of 4.
To understand why the surface area increases by a factor of 4 when the radius is doubled, let's consider the formula for the surface area of a sphere, which is given by:
[tex]\[ A = 4\pi r^2 \][/tex]
where A is the surface area and [tex]\( r \)[/tex] is the radius of the sphere.
Now, if we double the radius, the new radius becomes [tex]\( 2r \)[/tex]. Substituting this into the formula for surface area, we get:
[tex]\[ A_{\text{new}} = 4\pi (2r)^2 \][/tex]
[tex]\[ A_{\text{new}} = 4\pi \cdot 4r^2 \][/tex]
[tex]\[ A_{\text{new}} = 16\pi r^2 \][/tex]
To find out how much the surface area has increased, we take the ratio of the new surface area to the original surface area:
[tex]\[ \text{Factor of increase} = \frac{A_{\text{new}}}{A} \][/tex]
[tex]\[ \text{Factor of increase} = \frac{16\pi r^2}{4\pi r^2} \][/tex]
[tex]\[ \text{Factor of increase} = 4 \][/tex]
Therefore, when the radius of a sphere is doubled, the surface area increases by a factor of 4.
The city of Arachna has a spider population that has been doubling every year. If there are about 100,000
spiders this year, how many will there be 4 years from now?
Answer:
1,600,000
Step-by-step explanation:
100,000x2x2x2x2
Answer:160000
Step-by-step explanation:
,
If the area of a triangle with a base measuring 22 feet is 93.5 square feet, find its height
Answer:
I think it is 8.5
Step-by-step explanation:
The height of the triangle is 8.5 feet
To find the height of a triangle when the area and the base are known, we use the formula Area = 1/2 x base x height, where A is the area, b is the base, and h is the height. Given that the area of the triangle is 93.5 square feet and the base measures 22 feet, we can rearrange the formula to solve for h: h = 2 × Area/Base
h = 2×93.5/22
h=187/22
h = 8.5 feet
Therefore, the height of the triangle is 8.5 feet.
A science class has a total of 34 students. The number of females is 16 less than the number of males. How many males and how many females are in the class?
Answer:
25 and
9
Step-by-step explanation:
Let the number of males be A and that of females be B
Total number of students = 34
Number of females B = A - 16
Remember males and females = 34
That’s
A + B = 34
We now have two equations
Equation one:B = A - 16
Equation two: A + B = 34
Substitute A - 16 for B in equation 2
We have,
A + B = 34
A + A - 16 = 34
2A - 16 = 34
Add 16 to both sides
2A - 16 + 16 = 34 + 16
2A = 50
Divide both sides by 2
2A/2 = 50/2
A = 25
Now put 25 as A in any of the equations to get B
Using equation one , we have
B = A - 16
B = 25 - 16
B = 9
There are 25 males and 9 females in the class
I need help ASAP!! Please no decimals
Answer:
-3/4 is plotted 3 little tabs left of 0
5/4 is plotted 1 little tab right of 1
Slide the green dot from 0 to plot the number at the correct
location.
Plot V5
Plot the numbers on the number line.
V5, V8, V13
Which inequalities are true? Check all that apply
0 V5 <3
V8 > 3
V8 < 513
013 = 3.6
2.2< V5 <2.3
3.6 > 3> 3.7
The true inequalities are √5 < 3, 2.2 < √5 < 2.3, and 3.6 > √13 > 3.7. The false inequalities are √8 > 3 and √13 = 3.6. The truth value of √8, √13 is inconclusive due to the incomplete expression. These comparisons highlight the relative magnitudes of square roots in the given range of numbers.
The given numbers √5, √8, and √13 can be compared using various inequalities to determine their relative magnitudes. First, √5 is less than 3, as √5 is approximately 2.24. However, √8 is not greater than 3, as it is approximately 2.83, rendering the second inequality false.
The inequality √8, √13 is incomplete, making it impossible to determine its truth value without a specific comparison operator. Moving on, √13 is not equal to 3.6; in fact, it is approximately 3.61, making the statement false.
On the other hand, the range-based inequality 2.2 < √5 < 2.3 holds true, as √5 is approximately 2.24, falling within the given range. Similarly, the range-based inequality 3.6 > √13 > 3.7 is true since √13 is approximately 3.61, falling within the specified range.
In summary, √5 < 3, 2.2 < √5 < 2.3, and 3.6 > √13 > 3.7 are true inequalities, while √8 > 3, √13 = 3.6, and √8, √13 are inconclusive or false based on the provided information. These comparisons highlight the relative sizes of square roots within the given numerical context.
rewrite each expression by factoring out the greatest common factor 9b+12
Answer:
3(3b +4)
Step-by-step explanation:
The greatest common factor (GCF) of 9 and 12 is 3, so you're being asked to factor that out.
9b +12 = 3(3b +4)
_____
The GCF can be found a couple of ways. One of them is to list the prime factors and identify those that are common.
9b = 3 × 3 × b
12 = 2 × 2 × 3
For these two terms, the only common factor is 3.
please help me on this math problem
Answer:
-21/8 or -2 5/8
Step-by-step explanation:
When dividing fractions by other fractions you use keep change flip, you keep the first fraction, change the division into multiplication and you flip the second fraction. We do this because we don't have to convert the fractions into decimals this was and its easier with fractions.
The problem changes to
3/8 times -7/1
Now we multiple the numerators together and the denominators together and then put it back into a fraction
3 * -7 = -21
8 * 1 = 8
-21/8
If you need it as a mixed number it is
-2 5/8
1000(1+0,05 )^4 *x=1500
The answer is supposed to be x=ln(1.5)/4ln(1.0125)
I'm currently at 4log¹'⁰¹²⁵(1.0125)=log¹'⁰¹²⁵(1.5)
What did I do wrong?
The correct answer is [tex]\( x = \frac{\ln(1.5)}{4\ln(1.05)} \).[/tex]
Let's analyze the given equation step by step:
Given the equation [tex]\( 1000(1+0.05)^4 \cdot x = 1500 \)[/tex], we want to solve for [tex]\( x \).[/tex]
First, simplify the left side of the equation by calculating
[tex]\( (1+0.05)^4 \):\( (1+0.05)^4 = (1.05)^4 \).[/tex]
Now, the equation becomes:
[tex]\( 1000 \cdot (1.05)^4 \cdot x = 1500 \).[/tex]
Next, divide both sides by [tex]\( 1000 \cdot (1.05)^4 \) to isolate \( x \):[/tex]
[tex]\( x = \frac{1500}{1000 \cdot (1.05)^4} \).[/tex]
Simplify the right side by dividing 1500 by 1000:
[tex]\( x = \frac{1500}{1000} \cdot \frac{1}{(1.05)^4} \),[/tex]
[tex]\( x = 1.5 \cdot \frac{1}{(1.05)^4} \).[/tex]
Now, to express [tex]\( x \)[/tex] in terms of natural logarithms, we take the natural logarithm of both sides:
[tex]\( \ln(x) = \ln(1.5 \cdot \frac{1}{(1.05)^4}) \).[/tex]
Using the property of logarithms that [tex]\( \ln(ab) = \ln(a) + \ln(b) \)[/tex], we can split the right side:
[tex]\( \ln(x) = \ln(1.5) - \ln((1.05)^4) \).[/tex]
Applying the power rule of logarithms, [tex]\( \ln(a^b) = b\ln(a) \)[/tex], we get:
[tex]\( \ln(x) = \ln(1.5) - 4\ln(1.05) \).[/tex]
To solve for [tex]\( x \)[/tex], exponentiate both sides to remove the natural logarithm:
[tex]\( e^{\ln(x)} = e^{\ln(1.5) - 4\ln(1.05)} \),[/tex]
[tex]\( x = e^{\ln(1.5)} \cdot e^{-4\ln(1.05)} \),[/tex]
[tex]\( x = 1.5 \cdot \frac{1}{e^{4\ln(1.05)}} \),[/tex]
[tex]\( x = 1.5 \cdot \frac{1}{(e^{\ln(1.05)})^4} \),[/tex]
[tex]\( x = 1.5 \cdot \frac{1}{(1.05)^4} \).[/tex]
Now, we have arrived back at the expression we had for [tex]\( x \)[/tex] earlier:
[tex]\( x = 1.5 \cdot \frac{1}{(1.05)^4} \).[/tex]
To find the numerical value of [tex]\( x \)[/tex], we can use the expression involving natural logarithms:
[tex]\( x = e^{\ln(1.5) - 4\ln(1.05)} \).[/tex]
This is equivalent to:
[tex]\( x = \frac{e^{\ln(1.5)}}{e^{4\ln(1.05)}} \),[/tex]
[tex]\( x = \frac{1.5}{1.05^4} \).[/tex]
Finally, to express [tex]\( x \)[/tex] as a single logarithm, we can use the change of base formula for logarithms:
[tex]\( x = \frac{\ln(1.5)}{\ln(1.05^4)} \),[/tex]
[tex]\( x = \frac{\ln(1.5)}{4\ln(1.05)} \).[/tex]
This is the correct expression for [tex]\( x \)[/tex] in terms of natural logarithms. The mistake in the original attempt was likely in the manipulation of the logarithms, where the properties of logarithms were not correctly applied. The correct step is to use the quotient rule of logarithms, [tex]\( \ln(\frac{a}{b}) = \ln(a) - \ln(b) \)[/tex], and the power rule, [tex]\( \ln(a^b) = b\ln(a) \)[/tex], to arrive at the correct expression for [tex]\( x \).[/tex]
What are the solutions of x^2-2x+5=0
Answer:
1 + 2i and 1 – 2i
A processing machine crushes 3 1/4 kilograms of dry fruits in 3/4 minute. What is the rate, in kilograms per minute, at which the machine crushes dry fruit?
A. 3/13
B. 16/39
C. 2 7/16
D. 4 1/3
(PLEASE INCLUDE STEP BY STEP)
Answer:
D
Step-by-step explanation:
Kg : min
3¼ : ¾
13/4 : 3/4
13 : 3
13/3 : 1
13/3 = 4 ⅓
8 divided by 6040 fill in the blank
Answer:
0.00132450331
Step-by-step explanation:
just divide lol
To solve 8 divided by 6040, perform the division, resulting in approximately 0.0013245.
To solve the problem of 8 divided by 6040, follow these steps:
1. Recognize this as a division problem: 8 ÷ 6040.2. Since 8 is smaller than 6040, the quotient will be less than 1.3. Perform the division by dividing 8 by 6040: 8 ÷ 6040 ≈ 0.0013245Therefore, 8 divided by 6040 equals 0.0013245.please help me again
Answer:
y = 5
Step-by-step explanation:
The sum of all three angle measures of a triangle is ALWAYS equivalent to 180 degrees. Using this information, (4y + 10) + 75 + (3x) = 180
This is also an equilateral triangle, meaning those bottom two angles will be equivalent. 75 = 3x
So you can plug in the value for 3x into the first equation: (4y + 10) + 75 + 75 = 180
First, simplify the equation by adding the 75 and 75 together: (4y + 10) + 150 = 180
Now, subtract 150 from both sides of the equation: 4y + 10 = 30
Then subtract 10 from both sides: 4y = 20
And divide both sides by 4: y = 5
I hope this helps!
Answer:
y = 5
Step-by-step explanation:
75 / 3 = 3x / 3
25 = x
75 + 3(25) + 4y + 10 = 180
75 + 75 + 4y + 10 = 180
4y + 160 - 160 = 180 - 160
4y / 4 = 20 / 4
y = 5
Answer: y = 5
Charles earns an annual salary of $61,870. If he is paid weekly, much would his pay be each week?
Please take a look and help if you can!
Answer:
see explanation
Step-by-step explanation:
1
The area of a rectangle = length × width
2
To find the width, divide the area by the length
3
width = [tex]\frac{area}{length}[/tex] = [tex]\frac{3x^2+9x}{3x}[/tex]
To simplify divide each term on the numerator by 3x
= [tex]\frac{3x^2}{3x}[/tex] + [tex]\frac{9x}{3x}[/tex] = x + 3 ← width
Kayla purchased a used truck that had 27,544 kilometers on it. Later on, she sold the truck when it had 80,452 kilometers on it. How many kilometers did Kayla put on the truck
Answer:
Kayla put 52,908 km on the truck.
Step-by-step explanation:
Subtract 27,544 km from 80,452 km to answer this question:
80,452 km
- 27,544 km
-------------------
52,908 km
Kayla put 52,908 km on the truck.
I need help. Pls fill in all the black
Answer:
12 * 6 = (10 + 2) * 6
= (10 * 6) + (2 * 6)
= 60 + 12
= 72
Answer: 2 is the answer in the first line
2 is the answer in the second line
12 is the answer in the third line
72 is the answer in the fourth line
Step-by-step explanation:
12 x 6= (10 + ?? ) x 6 :: subtract 10 from 12 on the left hand side, that is, 12 - 10 = 2
(10 x 6) + (?? x 6) : since 2 is the answer in the first line, this is factored. And it is still 2
60 + ?? : multiply 2 x 6 = 12
??: Add 60 + 12 = 72
I hope this helps, mark as brainliest please
what is two thirds times negative one
Answer:
-1/3
Step-by-step explanation:
2/3 times -1 is -1/3
It is -2/3 or negative two thirds
Skylar is filling a barrel with water. The graph shows the relationship between time in minutes and the gallons of water in the barrel. Write an inequality showing the times there will be more than 10 gallons in the barrel. Explain your answer.
Answer:
t>15
Step-by-step explanation:
What is a equivalent expression for 5times v+6
Answer:
5v +30
Step-by-step explanation:
[tex]5(v + 6) \\ = 5v + 5 \times 6 \\ = 5v + 30[/tex]
Jacks tent is shaped like an isosceles triangle. The height of the tent measures 7 feet and the diagonal side measures 9 feet. Find the length of the base
Answer:
The length of the tent's base is [tex]8\sqrt{2}[/tex].
Step-by-step explanation:
Given : Jacks tent is shaped like an isosceles triangle. The height of the tent measures 7 feet and the diagonal side measures 9 feet.
To find : The length of the base ?
Solution :
Let x denote the length of the tent's base.
Refer the attached figure below.
Using Pythagorean Theorem,
[tex]9^{2} =7^{2} +(\frac{x}{2} )^2[/tex]
[tex]81=49+\frac{x^{2} }{4}[/tex]
[tex]324=196+x^{2}[/tex]
[tex]x^{2} =128[/tex]
Taking square root on both sides,
[tex]x=\sqrt{128}[/tex]
[tex]x=8\sqrt{2}[/tex]
Therefore, the length of the tent's base is [tex]8\sqrt{2}[/tex].
Answer:
5/2
Explanation:<3
The students at Porterville Elementary sold raffle tickets, each for the same price, for a fundraiser. The equation below shows how much money was raised with t tickets sold. $1,530 = $17t
Two sides of a triangle measure 5 inches 6 inches. jason says the triangle wust be scalene is jason correct?
Answer:
He is incorrect
If there was 2 sides of 6 inches, the base can be 5 inches and it could be an isoscles triangle
Step-by-step explanation:
He is incorrect, the third side could be 5.
The point U (-2,0) is translated 1 unit up. What are the coordinates of the resulting point, U’?
Answer:
Point U' (-2, 1)
Step-by-step explanation:
When moving up and down on a graph, this affects the y coordinate only.
Since it is moving up 1 unit, we have to add 1 to the y coordinate. So U' will end up being (-2, 1).
Answer:
U x 1U = -3 , 1
Step-by-step explanation:
U=1 x=1
y= -2 x 0 =-2
0=-2x-2 +1
y=-2x2+1
y=-4-1
y=-3