Given:
Max's house has two steps on the front porch.
Size of each step is the same.
To find:
The total vertical distance covered by the two steps.
Solution:
From the given figure, it is clear that,
Base length of each step = 6 in
Hypotenuse = 10 in
Let h be the vertical height of each step.
Using Pythagoras theorem, the vertical height of one step is
[tex]Base^2+Perpendicular^2=Hypotheuse^2[/tex]
[tex]6^2+h^2=10^2[/tex]
[tex]36+h^2=100[/tex]
[tex]h^2=100-36[/tex]
[tex]h^2=64[/tex]
Taking square root on both sides.
[tex]h=\pm\sqrt{64}[/tex]
[tex]h=\pm 8[/tex]
Height cannot be negative. So, h = 8 in.
Now,
Vertical height of 2 steps = [tex]2\times 8[/tex]
= [tex]16[/tex]
So, the total vertical distance covered by the two steps is 16 in.
Therefore, the correct option is A.
Can someone please help me with this, and give a thorough explanation?
Answer: x=68
Step-by-step explanation:
A. It’s asking what the last test must have to be (x) for all five tests to average out to an 80. This can be represent by:
(95+76+77+84+x)/5=80
The first four numbers are the existing test scores and x is the score you need. This is all divided by five so that you can find the average of all of these added together, which will equal 80, because that’s the grade you’re trying to get. Next, just solve for x:
= 95+76+77+84+x=80(5)
= 332+x=400
X=68
B. I got 74 for this one by using the same process as in part a, but I divided the left side by six and multiplied x by two: (95+76+77+84+2x)/6=80
But I’m not completely positive about this answer. A is definitely right though
Which is the mathematical symbol. HELP ASAP
Answer:
I would think D
Step-by-step explanation:
2(−5x+4)+4x−5=-3 i need help
2(-5x4)×4x-5=-3 its going to be x=1
What is 1200% as a simplified fraction>
Answer:
Step 1: Write down the percent divided by 100 like this: 1200% = 1200 / 100. Step 2: Multiply both top and bottom by 10 for every number after the decimal point: As 1200 is an integer, we don't have numbers after the decimal point. So, we just go to step 3.
Answer:
12/1 or 12
Step-by-step explanation:
33 POINTS! Find the area of the shape.
Answer:
The Answer is 41 cm.
Step-by-step explanation:
You have to add each side.
I read it wrong my anwser is wrong
Answer:
103.96
Step-by-step explanation:
justt solved it
Are 2(x + 1) and 2x + 1 equivalent expressions? explain.
I’m not in a hurry, take your time.
Answer:
Yes
Step-by-step explanation:
When you simplify 2(x+1). [MULTIPLY]
It comes 2x+1 so it is equivalent to 2x+1
Yes, 2(x + 1) and 2x + 1 are equivalent algebraic expression.
Given that,
To determine whether the 2(x + 1) and 2x + 1 are equivalent expressions.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let
y = 2 (x + 1) - - - - - -(1)
z = (2x + 1) - - - - - (2)
from equation1
y = 2 (x + 1)
using the PEMDAS rule, applying operation on the parenthesis 1st as distributive property,
now,
y = 2x + 1
Since the outcome of the equation is equal to equation 2.
Thus, 2(x + 1) and 2x + 1 are equivalent algebraic expression.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ2
PLZ HELP!!!! I HAVE A BAD GRADE IN MATH
Answer:
me too
Step-by-step explanation:
Answer: i think this question is asking for y=1/3x - 1
square root of 479/90
a question that is hard for me. I dont have my calculator
Answer:
the answer is 0.24317854031 hope this helps have a nice day please give me brainliest:))
Step-by-step explanation:
Answer:
0.24317854031
Step-by-step explanation:
1. Open your browser
3. Search up: square root of 479/90
4. Copy paste answer
5. Need I say more?
#1. How many three-letter words can be made from using the letters of the
word "GUARD" (no repeats)
Then notation:
I NEED HELP PLEASE !!!!
Answer: de
Step-by-step explanation:
The population of a city is modeled by the exponential function ƒ (x) = 689,254 · 2.40.014x, where x is the number of years after 2000. In what year will the city's population exceed one million?
Answer:
2036Step-by-step explanation:
Given the population of a city is modeled by the exponential function
ƒ (x) = 689,254 · 2.4e^0.014x, where x is the number of years after 2000
In order to determine the year that the city's population will exceed one million, we will substitute f(x) = 1,000,000 and find x first as shown:
1,000,000 = 689,254 2.4e^0.014x,
1000000/689,254 = 2.4e^0.014x,
1.4508 = 2.4e^0.014x,
1.4508 /2.4 = e^0.014x,
0.6045 = e^0.014x,
Apply ln to both sides
ln 0.6045 = lne^0.014x,
-0.5033 = 0.014x
x = -35.95
Since x cannot be negative, lets say x ≈ 36years
This means that the population will exceed one million after about 36 years. The year it will exceed this amount will be 2000+36 = 2036
Note that the exponential equation used was not correctly written but the same calculation can be employed for any exponential functions you might have.
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.
Use pi = 3.14.
What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.
Answer:
We can say that volume of cylinder (452.16) is greater than volume of cone (301.44).
Step-by-step explanation:
Diameter of cylinder = 8 inches
Diameter of cone = 8 inches
Height of cylinder = 9 inches
Height of cone = 18 inches
We need to find the relationship between the volume of this cylinder and this cone.
First we will find volume of the cylinder
The formula used is: [tex]Volume=\pi r^2h[/tex]
We have
Diameter of cylinder = 8 inches
Radius = d/2 = 8/2 = 4 inches.
Height of cylinder = 9 inches
Putting values and finding volume
[tex]Volume=\pi r^2h\\Volume=3.14\times (4)^2 \times 9\\Volume=452.16[/tex]
So, Volume of cylinder = 452.16 inches³
Now, we will find volume of the cone
The formula used is: [tex]Volume=\pi r^2\frac{h}{3}[/tex]
We have
Diameter of cone = 8 inches
Radius = d/2 = 8/2 = 4 inches.
Height of cone = 9 inches
Putting values and finding volume
[tex]Volume=\pi r^2\frac{h}{3}\\Volume=3.14 \times (4)^2 \times \frac{18}{3}\\Volume=3.14 \times (4)^2 \times 6\\Volume=301.44[/tex]
So, Volume of cone = 301.44 inches³
Now, comparing volume of both cylinder and cone.
Volume of cylinder = 452.16 inches³
Volume of cone = 301.44 inches³
We can say that volume of cylinder (452.16) is greater than volume of cone (301.44).
what does-25=1/3n-10 equal
Answer:
-45
Step-by-step explanation:
add 10 to -25, then divide 1/3 to that answer, which is -15. and you get -45
Answer: N=-45
Step-by-step explanation: Solve for n by simplifying both sides of the equation, then isolating the variable.
Identify the constant of proportionality
4 The triangles shown are similar. Find y.
180 degrees is equal to a triangle if we add 111 and 32 degrees it will get 143 degrees so we should subtract 143 from 180 degrees it will get 37
10(1.05)^x growth or decay
Answer:
growth
Step-by-step explanation:
Pleaseeeeee help. Picture attached
Answer:
Option C
Step-by-step explanation:
Given expression is [tex]y^{-\frac{4}{3}}[/tex].
Exponent of this expression is [tex](-\frac{4}{3})[/tex].
Option (A)
[tex]-\frac{4}{3}y[/tex]
Since, exponents and coefficients of both the expressions are different.
They are not equivalent.
Option (B)
[tex]-(\sqrt[3]{y})^4=-(y^{\frac{1}{3}})^4[/tex]
[tex]=-y^{\frac{4}{3}}[/tex]
Here, exponent is with positive notation [tex](+\frac{4}{3})[/tex] while in the original expression it is negative [tex](-\frac{4}{3})[/tex].
Therefore, both the expressions are not equivalent.
Option (C)
[tex]\frac{1}{(\sqrt[3]{y})^4}=(\sqrt[3]{y})^{-4}[/tex]
[tex]=y^{-\frac{4}{3}}[/tex]
Both the expressions are equivalent.
Option (D)
[tex]-(\sqrt[4]{y})^3=-(y)^{\frac{3}{4}}[/tex]
Exponents of both the expressions are different.
Therefore, not equivalent.
Option (E)
[tex]\frac{1}{(\sqrt[4]{x})^3}=(\sqrt[4]{x})^{-3}[/tex]
[tex]=y^{-\frac{3}{4}}[/tex]
Exponent of this expression is different from the original expression.
Therefore, not equivalent.
Option (C) will be the correct option.
One equation in a system of equations is y=4x-5 write a second equation to complete the system if the solution to the system is (3,7) PLSSS BE QUICK :))
Answer:
4y = -x + 31
Step-by-step explanation:
Given that one equation in a system of equations is y = 4x - 5 write a second equation to complete the system if the solution to the system is (3,7)
Since the solution of the system is (3, 7), that means the two lines of equations meet or intersect at point X = 3 and Y = 7
Let assume that the two equations are perpendicular to each other. Then, there slope can be expressed as
M1M2 = -1
Where M1 = 4
Find M2
4M2 = -1
M2 = -1 / 4
Using general linear equation
Y = MX + C
Let's find C by substituting Y, X and M2
7 = -1 /4( 3 ) + C
7 = -3/4 + C
C = 7 + 3/4
C = 31/4
Substitute C back into the equation
Y = -1/4X + 31/4
4y = -x + 31
Therefore, the second equation is
4y = -x + 31
Plz halp need an answer right away!
Answer:
20.56 cm
Step-by-step explanation:
3.5
Think About the Process Karen purchased a DVD player on sale. The original selling price was
$175.90. The sale price was $149.62. What is the first step in finding the percent markdown? Find
the percent markdown.
Ximena is typing a 2500 word essay. In 9 minutes she types 396 words, at this rate can Ximena type the essay in an hour?
Answer:
yes
Step-by-step explanation:
396÷ 9= 44
44×60= 2,640 > 2500
At the given rate, Ximena can type the 2,640 word essay in an hour.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that Ximena is typing a 2500 word essay. In 9 minutes she types 396 words,
The typing per word.
396÷ 9 = 44
Therefore,
44 × 60 = 2,640
Which is greater than 2500
Hence Ximena can type the 2,640 word essay in an hour.
More about the Algebra link is given below.
brainly.com/question/953809
#SPJ5
Please need answers please
Answer:
13
Step-by-step explanation:
-(-13) = 13
Answer:
13
Step-by-step explanation:
a - times - is a + so there you go I would use photo math if I was you
Solve the system of linear equations by substitution. 2x=y−10 x+7=y
Answer:
(-3, 4)
Step-by-step explanation:
2x = y - 10 (y = x +7) so
2x = x +7 - 10
2x = x -3
x = -3
-3 + 7 = y
4 = y
Step-by-step explanation:
2x = y - 10 and x + 7 = y.
By Substitution,
2x = (x + 7) - 10.
=> 2x = x - 3, x = -3.
Therefore y = (-3) + 7 = 4.
The pair of solutions are x = -3, y = 4.
What is 100,000,000x500,000,000
Answer:
5e+16
Step-by-step explanation:
2. Express the given statement as an algebraic expression.
Sum ofa and 5 divided by 8
Answer:
An algebraic expression for Sum of a and 5 divided by 8 is [tex]\mathbf{\frac{a+5}{8}}[/tex]
Step-by-step explanation:
We need to express the given statement as an algebraic expression.
Sum of a and 5 divided by 8
Basically, we are given the expression in English sentence and we have to write algebraic expression.
It can be done in two steps:
Sum of a and 5 = We know that sum is denoted by + sign. So, we get (a+5)
Sum of a and 5 divided by 8 = [tex]\frac{a+5}{8}[/tex]
So, An algebraic expression for Sum of a and 5 divided by 8 is [tex]\mathbf{\frac{a+5}{8}}[/tex]
What is the standard form of 2x2x2x2x2?
Answer:
The standard enthalpy of formation is the energy that would be involved if one mole of the substance were to be formed from its elements that were at standard conditions of temperature and pressure which are 25 degrees C and one atm pressure.
Step-by-step explanation:
The standard form of the given expression 2 × 2 × 2 × 2 × 2 is 2⁵.
The expression is given as follows:
2 × 2 × 2 × 2 × 2
When simplifying repeated multiplication of the same number, we use exponents as a concise representation.
The exponent denotes how many times the base is multiplied by itself. In this case, 2 is multiplied five times (2 × 2 × 2 × 2 × 2).
So, it is equal to 2⁵.
In this form, the base (2) is raised to the power of the number of times it is multiplied (5).
Thus, the standard form of 2 × 2 × 2 × 2 × 2 is 2⁵.
Learn more about the standard form here :
brainly.com/question/13139379
#SPJ6
Find the gradient of the line drawn bellow
We need a picture of the problem
[tex] - 2x - 4y = 10 \\ 2x + 4y = - 10[/tex]
please find the point of intersection
Answer:
They are the same slope
Step-by-step explanation:
When you convert both equations you get y=-[tex]\frac{1}{2\\}[/tex]x-[tex]\frac{5}{2}[/tex]
I need help with this question
Answer:
98 in.^2
Step-by-step explanation:
The lateral area is the sum of the areas of the 3 rectangular sides.
The triangular sides are the bases.
lateral area = 7.2 in. * 5 in. + 3 in. * 5 in. + 9.4 in. * 5 in.
lateral area = 36 in.^2 + 15 in.^2 + 47 in.^2
lateral area = 98 in.^2
5 + 5?
(hint: look at how many points you'll get)