When Dylan travels 8 miles due north, the distance between the homes of the parents and grandparents is thus 9 miles.
what is pythagoras theorem ?The hypotenuse side of a right-angled triangle's square is equal to the sum of its other two sides, according to Pythagoras' Theorem. The perpendicular, base, and hypotenuse of this triangle are its three named sides. With the aid of the Pythagorean Theorem, we may determine the side lengths of a right triangle by adding the areas of three intersecting squares. The base for more intricate trigonometry ideas, such as the Pythagorean theorem's opposite, is provided by this theorem, which is a very helpful tool.
given
by pythagoras theorem
[tex]c^{2} = a^{2} + b^{2} \\c^{2} = 8^{2} + 5^{2} \\c^{2} = 64 + 25 \\c^{2} = 89 \\c = 9[/tex]
The homes of the parents and grandparents are thus 9 miles apart in a straight line.
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It takes 34 of an hour to paint a single shutter. It takes 9 hours to paint 12 pairs of shutters. The number of hours, y, that it takes to paint xshutters shows either a direct or inverse variation. What is the equation that relates x and y?
The equation that relates x and y for the given data is y = (3/4)x.
The relationship between the number of shutters (x) and the number of hours (y) is an inverse variation because as the number of shutters increases, the number of hours required to paint them decreases and vice versa.
An inverse variation is a relationship between two variables in which their product is always equal to a constant value. Mathematically, it can be represented by the equation: y = k/x where k is a constant and x and y are the variables in question.
Hence, the equation that relates x and y can be found using the information given:
y = (9 hours) / (12 shutters) * x shutters
y = (3/4)x is the required equation.
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May someone please help me.
Answer: x=9
Step-by-step explanation:
Here the given angles are,
50,80,6x-4
The sum of the angles of a triangle is 180 degrees and hence
50+80+6x-4=180
130+6x-4=180
126+6x=180
6x=180-126
6x=54
x=54/6
x=9
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Gwen scans a photo that is 4inches wide by 6 inches long into her computer. If she scales the length down to 3inches how wide should the similar photo be?
The similar photo should be 4.5 inches wide.
What is scale factor?Direct variation of a quantity {y} with respect quantity {x} means that the value of {y} increases as the the value of {x} increases. Mathematically -
y = Kx
K = y/x
where -
{K} is scale factor. It also tells by how many times is {y} greater than {x}.
Given is that Gwen scans a photo that is 4 inches wide by 6 inches long into her computer. Now, she scales the length down to 3 inches.
We can write -
y₁/x₁ = y₂/x₂
6/4 = 3/x₂
x₂ = 6 x 3/4
x₂ = 6 x 0.75
x₂ = 4.5
Therefore, the similar photo should be 4.5 inches wide.
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Find the difference of (6x2 + 3x – 5) and (4x² – 2x + 3).
Answer:
2x^2 + 5x - 8
Step-by-step explanation:
6x^2 + 3x - 5
- (4x^2 - 2x + 3)
--------------------------
2x^2 + 5x - 8
the cylinder below has a volume of 80 cm³. what is the value for r?
Answer:
r= 7.09 cm (3s.f.)
Step-by-step explanation:
[tex]\boxed{volume \: of \: cyinder = \pi {r}^{2}h }[/tex]
Given: h= 5cm, volume= 80cm³
πr²(5)= 80
Divide both sides by 5π:
[tex] {r}^{2} = \frac{80}{5\pi} [/tex]
Simplify:
[tex] {r}^{2} = 16\pi[/tex]
Square root both sides:
[tex]r = \sqrt{16\pi} [/tex]
r= 7.09 cm (3s.f.)
Tom is adding soil to his raised garden bed. The depth of the soil is currently 8 inches, and for each bag of soil he adds, the depth will increase by 1/2 of an inch. You can use a function to describe the depth of the soil in the garden bed after Tom adds x bags of soil.
Write an equation for the function. If it is linear, write it in the form h(x)=mx+b. If it is exponential, write it in the form h(x)=a(b)^x.
The function that describes the depth of the soil is h(x) = -(1/2)x + 8.
Where x is the number of bags of soil.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Depth of the soil = 8 inches
One bag of soil increases by 1/2 of an inch.
Now,
The function denotes the depth of the soil.
h(x) = -(1/2)x + 8
Where x is the number of bags of soil
Thus,
The function is h(x) = -(1/2)x + 8.
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Points E and Flie on a circle, centre O.
The radius of the circle is 10 cm.
The area of the shaded sector is 65cm².
Diagram not drawn to scale
Calculate the size of angle EOF
(3 marks)
The measure of the angle of the shaded sector with an area of 65 cm² is 74.5°
What is an equation?An equation is used to show the relationship between numbers and variables.
The area of a two dimensional shape is the amount of space it occupies.
The area of a sector in a circle is given by:
Area = (Ф/360) * π * radius²
Where Ф is the sector angle
Given that sector area is 65 cm², radius is 10 cm, hence:
Area = (Ф/360) * π * radius²
Substituting gives:
65 = (Ф/360) * π * 10²
Ф = 74.5°
The measure of the angle is 74.5°
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Solve the following quadratic equation, leaving your answer in exact form:
2e²-8e +7= 0
Pls can anyone help it would rrly help out
Answer:
The two answers would be 0 and ln (7)
Step-by-step explanation:
Hope it helps:)
Which side is adjacent to
Answer:
from B-A is adjacent
because of the 90 degree
rewrite in y=mx+b form and show ur work 2x+y=3x-7
heyy! i’ll give brainliest please help.
Answer:
the city at a lower altitude would have a colder climate
40 mi
9 mi
What is the length of the hypotenuse?
Answer:
[tex] = \sqrt{ {40}^{2} + {9}^{2} } \\ = \sqrt{1681} \\ = 41 \: mi[/tex]
50 PTS 50 PTS 50 PTS help.
Answer:
x = 90
Step-by-step explanation:
The diagram shows that angles 1 and 4 correspond with each other. Given that the two lines should be parallel, corresponding angles have the same answer. When corresponding angles cross at the same relative location (known as the junction), they will have the same angle measure.
So, set the 1st and 4th angles equal to each other.
3x-160 = x+20
2x = 180
x=90
Answer:x=90
Step-by-step explanation:Angles 1 and 4 must be equal to each other, as they are corresponding angles, so you set 3x-160 equal to x+20 and after solving, you get x is equal to 90.
If the radius of a circle is 2 yards, what is the circles area?
Answer:
12.56 yards
Area of Triangle: [tex]\pi r^2[/tex]
So, [tex]\pi[/tex][tex]2^2[/tex]
Finally, 3.14*4 = 12.56
Step-by-step explanation:
what is 30x30x30x30 plz i need help
Answer:
810000
Step-by-step explanation:
Please tell me someone know I have to go back to school tomorrow
An equation for the function g(x) when g(x) = f(-x) is g(x) = -x/3 - 6, which is shown in the graph attached below.
What is a reflection?In Mathematics, a reflection can be defined as a type of transformation which moves every point of the geometric figure by producing a flipped, but mirror image of the geometric figure.
In Geometry, a reflection across the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
By reflecting the given function across the across the y-axis (y = x), we have the following:
f(x) = x/3 - 6
g(x) = f(-x)
g(x) = -x/3 - 6.
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For which values of x does each expression make sense? square root of x-2 over square root of x-3
the answer is x>3
this is the answer becuase x-3 cannot be 0 because tou cant divide by zero and it cant be negative because it is in the square root notation which cant be negative without the use of inaginary numbers
helppp me plss its due tonight!!
Answer:
B.
Step-by-step explanation:
Nelly put the batch of pies in the oven at 6:17 AM when they go into the oven the internal temperature of the pies is 60 Fahrenheit the temperature increases at a rate of 2.5 Fahrenheit per minute if Nelly wants the internal temperature of the pie to reach 160 Fahrenheit at what time should she take them out of the oven?
Answer:
Nelly should take out the pies after 64 mins or an hour and four minutes.
Step-by-step explanation:
whats 1.5 divided by 1.5
Answer:
1
hope this helped
Step-by-step explanation:
Answer:
so 1.5 ÷1.5= 1
Step-by-step explanation:
PLEASE HELPPP I TOLD MY MOM I WOULD BE DONW ITH THIS CLASS TODAY SO SHE WOULDNT YELL AT ME BUT I HAVE 54 ASSIGNMENTS
Which expression is equivalent to 12x2+x−20
If two algebraic expressions are equivalent, then they both have the same result when the same value of the variable is entered. 12x2 + x + 20 is the same as the given expression.
What other expression is the same as 3 5?6/10, 9/15, 12/20, etc. are fractions that are identical to 3/5. The value of equivalent fractions remains unchanged when lowered. Explanation: The numerator and denominator of equivalent fractions can be written by multiplying or dividing them both by the same value.
The given quadratic expression 12x^2+x-20
now, 12x^2 + 16x - 15x - 20
4x (3x+4) - 5(3x+4)
(4x-5) (3x+4)
the root of the equation is (4x-5) (3x+4)
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Find the volume of the right prism with a cylindrical hole. Round to the nearest tenth.
Answer:
11.2
Step-by-step explanation:
First, you get the volume of the right prism by multiplying the length times the width times the height, which is 2.5 cubed. Then we subtract the volume of the cylindrical hole. We do this by doing pi times the radius squared times the height, which is pi times 0.75 squared times the height. This will yield 11.2 cubic millimeters.
plzz help asap, I'll mark you the brainliest if you tell me how to solve this with step by step explanation ❤❤
if x+y+z=1 and 1/x+1/y+1/z=0
what is x²+y²+z²=?
A) 0
B) 1
C) 2
D) 3
Answer:
B
Step-by-step explanation:
Given
[tex]\frac{1}{x}[/tex] + [tex]\frac{1}{y}[/tex] + [tex]\frac{1}{z}[/tex] = 0 , then
[tex]\frac{yz+zx+xy}{xyz}[/tex] = 0 , so
yz + zx + xy = 0
Now
(x + y + z)² = x² + y² + z² + 2(xy + yz + zx) , that is
1² = x² + y² + z² + 2(0) , thus
x² + y² + z² = 1
The population of a city is 5876000 in 1980. By 1990 it increased by 10.8%. In the 1990s it increased a further 4.7%. What was the population in the year 2000?
Answer: I think it's 6816606.576
Step-by-step explanation: Hope this helps?
A 15-foot ladder is leaning against a building so that the top of the ladder is at a height of 12 feet.
building
Answer:
12
Step-by-step explanation:
Answer:12
feet
Step-by-step explanation:
Help is for today!!!
Ayuda es para hoy.!!
Answer:
x=20 degrees
Step-by-step explanation:
So, lets recall some things.
First off, opposite angles are the same.
So this would make x equal 20.
But lets test this.
When you look at a X, or any other sort of two lines that cross each other, can you ever think of a time when one side is not the same as the other? No.
This is because when you change one angle, since the lines are crossed together, it will change the opposite angle. This change will always be constant as long as the two lines connect at the same point
So if you changed a 10 degree angle of two lines, so that it was 30, this would change for the other line.
I attached a image below.
I hope this explains this to you and helps! :D
==================================================================
Respuesta:
x = 20 grados
Explicación paso a paso:
Entonces, recordemos algunas cosas.
En primer lugar, los ángulos opuestos son iguales.
Entonces esto haría que x sea igual a 20.
Pero probemos esto.
Cuando miras una X, o cualquier otro tipo de dos líneas que se cruzan, ¿puedes pensar alguna vez en un momento en el que un lado no sea igual que el otro? No.
Esto se debe a que cuando cambia un ángulo, dado que las líneas se cruzan, cambiará el ángulo opuesto. Este cambio siempre será constante siempre que las dos líneas se conecten en el mismo punto
Entonces, si cambia un ángulo de 10 grados de dos líneas, de modo que sea 30, esto cambiaría para la otra línea.
Adjunto una imagen a continuación.
¡Espero que esto te explique esto y te ayude! :D
How do you find the value of x in a two step equation?
Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.
Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.
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lacy work 15 hours last week she was paid $127.50 what is your hourly pay
Given:
Lacy work 15 hours last week and she was paid $127.50.
To find:
The hourly pay of Lacy.
Solution:
We have,
15 hours pay = $127.50
To find the hourly pay of Lacy, we need to divide total pay by number of hours.
[tex]\text{Hourly pay}=\dfrac{\text{Total pay}}{\text{Number of hours}}[/tex]
[tex]\text{Hourly pay}=\dfrac{127.50}{15}[/tex]
[tex]\text{Hourly pay}=8.5[/tex]
Therefore, the hourly pay of Lacy is $8.50.
Put 38200 in standard Form
Answer: Thirty-eight thousand two hundred.
Step-by-step explanation: You'd get Thirty-eight thousand two hundred because the standard form is writing out the number using letters. So, we should break this down:
38,000 + 200 is a good strategy to divide big numbers.
So, 38,000 = Thirty-eight thousand
And 200 = two hundred
So, combine it and you get Thirty-eight thousand two hundred or Thirty-eight thousand and two hundred. (it's the same thing)