Use the Pythagorean Theorem to find the missing measure when a = 24 and b = 7.
Answers
To start, we know the a and b values which are 24 and 7. As according to the formula, we square them which gives us 576+49=c^2
Then we simplify: 625=c^2
And solve for c= 25 (c represents the missing length)
Related Questions
Many food products are packaged in a variety of sizes. The list below gives the sizes and costs of fruit juice drinks at one store. $1.92 single-serving multi-pack (serves 6) $1.12 one quart (serves 4) $2.16 two quarts (serves 8) $3.52 one gallon (serves 16) Type your responses here: 1. Choose two different sizes and give an advantage for buying each.
Answers
The first one is advantageous because when it is desired that this be brought some place, it will not be very bulky and not heavy because among the given, this is the smallest. Also, one gallon can be chosen because it does serve many people at a relatively lower price than the other given.
divide using synthetic division (2x^3 + 14x^2 - 58x) / (x + 10) 58 POINTS!!!!
Answers
-20 -60
2 -6 -118
So it's 2x^2 -6x The remainer is -118
Set x + 10 = 0
So that's how I get -10
I then multiplied -10 x 2 to get -20 and placed it below 14. -20 + 14 is -6. -6 x -10 is -60. -58 + -60 is -118. 2 remains the same since you didn't do anything with.
Since you started with 2x^3 and this is division, you immediately know the first term will start with x^2 so that's how I get 2x^2. The ending number, in this case -118, is always the remainder.
what 3 digits are in the ones/units period 4,083,817
Answers
digit 8 is in the hundreds place, digit 1 is in the tens place, and digit 7 is in the ones or units place.
Brainest Answer is appreciated.
Using the formula for volume of a cone, express r in terms of V, h and pi
Answers
The volume of the cone is one-third of the volume of the cylinder which is equal to the product of area of the base and the height. The equation is,
V = (1/3)(pi)(r^2)h
Dividing both sides of the equation by (1/3)(pi)(h) will give us,
3V/(pi)(h) = r^2
Taking the square-root of both sides,
r = sqrt(3V/(pi)(h))
Answer:
[tex]r = \sqrt{\displaystyle\frac{3V}{h\pi}}[/tex]
Step-by-step explanation:
We are given the following information in the question.
Using the formula for volume of cone, we have to express r in terms of V, h and pi.
Formula:
[tex]\text{Volume of cone, V} = \displaystyle\frac{1}{3}\pi r^2 h\\\\\text{where r is the radius of cone, h is the height of radius}[/tex]
Now, we have to evaluate r, the radius of cone.
Rearranging the terms, we have,
Working:
[tex]V = \displaystyle\frac{1}{3}\pi r^2 h\\\\r^2 = \frac{3\times V}{\pi\times h}\\\\r^2 = \frac{3V}{h\pi}\\\\r = \sqrt{\frac{3V}{h\pi}}[/tex].
Thus, r in form of V, h and pi can be written as:
[tex]r = \sqrt{\displaystyle\frac{3V}{h\pi}}[/tex]
Isa's calculator displays a number as 7.3579 E8. What is this number in standard form? Enter your answer in the box.
Answers
7.3579 x 10⁸ in standard form.
Answer: 7.3579 x 10⁸.
yvonne made 2 3/4 quarts of punch. Write 2 3/4 as a decimal
Answers
8+3=11
11/4
I hope this helped
2 3/4 as a decimal is 2.75.
Hope this helps!
Elizabeth bought 4 drinks and some nachos. The nachos cost $6, and she spent a total of $18. How much did each drink cost? Use d to represent the cost of each drink. A. ; each drink cost $4. B. ; each drink cost $6. C. ; each drink cost $2. D. ; each drink cost $3.
Answers
Answer:
D. ; each drink cost $3
Step-by-step explanation:
Given that Elizabeth bought 4 drinks and some nachos.
Total amount spent = [tex]18[/tex]$
She can buy only in integers the drinks i.e.1,2,or 3
Nachos also she can buy 1,2...
If x is the no of nachos and d the cost of drink, we get
[tex]6x+4d=18[/tex]
If x=1, d =3
x=2, d = 1.50
d=3, d=0 (which is not possible)
Hence d can take values either as 3 or 1.50
Out of the options given 3 is only there.
D. ; each drink cost $3
The equation for the cost in dollars of producing computer chips is y =.000015x^2-.03x+35. Where x is the number of chips produced . Find the number of chips that minimizes the cost. What is the cost for that number of chips?
Answers
1000 chips minimize the production cost in the given equation, and the minimum cost for producing these chips is $20.
Explanation:To find the number of chips that minimizes the cost in the given quadratic equation, y = 0.000015x^2 - 0.03x + 35, we can use the vertex formula for a parabola, which is derived from the general quadratic equation.
The general form of a quadratic equation is y = ax^2 + bx + c, and the x-coordinate of the vertex, which gives us the number of chips that minimizes the cost, can be found using x = -b/(2a). For our equation, a = 0.000015 and b = -0.03.
Substituting the values of a and b into the vertex formula:
x = -(-0.03)/(2 * 0.000015)x = 0.03/0.00003x = 1000 (number of chips)Now, we plug this value back into the original equation to find the minimum cost:
y = 0.000015(1000)^2 - 0.03(1000) + 35y = 15 - 30 + 35y = $20 (cost for producing 1000 chips)This gives us the minimum cost and the number of chips that lead to this cost. Therefore, 1000 chips minimize the cost, and the minimum cost for producing these chips is $20.
Jack wants to fill a rectangular box with sand. The length of the sand box is 3 feet, width is 6 inches, and height is 2.4 inches. Each bag of sand contains 0.15 cubic foot of sand. How many bags of sand will Jack need to fill the box completely?
[1 foot = 12 inches]
Numerical Answers Expected!
Answers
To find the answer you first have to find the volume of the rectangular box which can be found using the formula length times width times height (remember that the numbers have to have the same unit so it would look like 3 times .5 times .2 if you convert them all the feet). the volume of the box is equal to .3
Then you could set the volume of the box equal to .15x to find how many boxes he would need. The formula would be .15x=.3
Divide by .15 to get x alone and you get 2 for the answer.
The number of bags of sand that Jack need to fill the box completely are:
2
Step-by-step explanation:The length(l) of the sand box is 3 feet, width(w) is 6 inches, and height(h) is 2.4 inches.
Also,
1 foot=12 inches
This means that:
1 inch=1/12 foot
i.e.
6 inches=0.5 feet
i.e.
w=0.5 feet
and
h=2.4 inches
i.e. h=0.2 feet
Now, we find the volume of the rectangular box.
The volume of the rectangular box is given by:
Volume=lwh
Hence,
Volume=3×0.5×0.2
i.e.
Volume=0.3 cubic feet.
Also, the volume of one bag of sand= 0.15 cubic feet
This means that the number of bags of sand that will fill the box completely is:
(Volume of rectangular box) / (Volume of one bag of sand)
= 0.3/0.15
=2
Hence, number of bags =2
Solve 6e^(x)-4e^(-x)=5. Solve for x and please describe how you got your answer.
Answers
For the given equation 6eˣ-4e⁻ˣ=5 the value obtained after solving the equation will be x =0.29.
What is an exponential function?It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x, where a is a constant and a>1
It is given that,
6eˣ-4e⁻ˣ=5
Multiplying complete equation by eˣ
eˣ(6eˣ-4e⁻ˣ)=5(eˣ)
6(eˣ)(eˣ) - 4(e⁻ˣ)(eˣ) =5(eˣ)
6e²ˣ-4 = 5(eˣ)
6e²ˣ-5eˣ -4 = 0
Suppose y = eˣ
6y² - 5y -4 = 0
After solving the equation we get y = 4/3 and y = -1 / 2.As a result,
eˣ = 4/3
x = log(4/3)
x = 0.29
Thus, for the given equation 6eˣ-4e⁻ˣ=5 the value obtained after solving the equation will be x =0.29.
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what times what equals 108
Answers
12 times 9 = 108, 18 times 6 = 108, 27 times 4 = 108 and 36 times 3 = 108.
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number.
Given that, what times what equals 108,
Below is a list of all the different ways that what times what equals 108.
12 times 9 equals 108
18 times 6 equals 108
27 times 4 equals 108
36 times 3 equals 108
54 times 2 equals 108
108 times 1 equal 108
Hence, 12 x 9 = 108. 18 x 6 = 108. 27 x 4 = 108. 36 x 3 = 108.
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There are multiple pairs of numbers that multiply to 108, such as 1 × 108, 2 × 54, 3 × 36, 4 × 27, 6 × 18, and 9 × 12. Therefore, any pair of these factors will correctly answer the question.
To determine what times what equals 108, we need to identify the factors of 108.
1 × 108 = 108
2 × 54 = 108
3 × 36 = 108
4 × 27 = 108
6 × 18 = 108
9 × 12 = 108
There are multiple pairs of numbers that, when multiplied together, equal 108. Therefore, any of these factor pairs are valid answers to the question.
For example, 9 times 12 or 6 times 18 are pairs that satisfy this condition.
Prove algebraically that the difference between the squares of any two consecutive integers is equal to the sum of these two integers.
Answers
Then, the consecutive integer (the number that follows) should be x+1.
The statement wants us to prove;
(x+1)²-x²=x+(x+1) <-- solve left hand side
x²+x+x+1²-x²
2x+1 (solution for left hand side)
Now solve for right hand side.
x+(x+1)= 2x+1
As noticed, the LHS=RHS (left hand side= right hand side), therefore, the difference of squared consecutive numbers subtracted is equal to the sum of the two integers.
Hope I helped :)
Approximately 55% of the 750 pupil student body voted for Suresh for student body president. How many students voted for him?
Answers
Karli's shadow is 60 inches long. A nearby fire hydrant casts a shadow 40 inches long. If Karli is 48 inches tall, what is the height of the fire hydrant?
Answers
Assume that you own a ruby. Apply the law of detachment to the following conditional statement:
If you have a ruby, then it you have at least $1000.
Which of these statements is true, according to the law of detachment?
You have a ruby.
Someone buys the ruby for $1000.
You sell the ruby.
You have at least $1000.
Answers
The statement fourth "You have at least $1000" is correct if you have a ruby, then it you have at least $1000.
What is the law of syllogism?Legal syllogism is a legitimate concept that deals with the law and how it is applied, specifically a type of argument that uses deductive reasoning to determine whether a given act is legal.
We have:
Assume that you own a ruby. Apply the law of detachment to the following conditional statement:
The statement is:
If you have a ruby, then it you have at least $1000.
As we know, the law of detachment, we must let go of attachment to both the desired end and all possible routes to get there in order to actualize our wants.
Thus, the statement fourth "You have at least $1000" is correct if you have a ruby, then it you have at least $1000.
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Given the statement 'If you have a ruby, then you have at least $1000.' and the fact that you have a ruby, the Law of Detachment leads to the conclusion 'You have at least $1000.'
Explanation:The Law of Detachment (also known as Modus Ponens) in logic says that if a conditional statement ('if p then q') is true and the first part of the statement (p) is true, then the second part of the statement (q) is true. Let's apply it to your statement.
The original statement is 'If you have a ruby, then you have at least $1000.' You confirmed the first part 'You have a ruby.' So, according to the Law of Detachment, the resulting correct statement would be 'You have at least $1000.' The other statements about selling or someone buying the ruby are irrelevant to the Law of Detachment.
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If the sum of six consecutive even integers is 390 what is the smallest of the six integers
Answers
first because we dont know the values of the 6 numbers we have to lay it out like this.
x
x+2
x+4
x+6
x+8
x+10
-------- (then we add it together)
6x+30 = 390 (the sum of the 6 numbers)
using this equation we find out what x is
so we do 390-30 to find what 6x is, which is 360
because now we know that 6x=360, we divide 360 by 6 to find out what x is
360 divided by 6 =60..... x = 60
so now we know that the smallest integer is 60
to check the answer we could add the 6 numbers which are:
60+62+64+66+68+70=390 :)
so the smallest integer is 60
find the perimeter of ABC with vertices A (1,1), B (7,1), and C (1,9)
Answers
Answer:
24 unit
Step-by-step explanation:
Given,
The vertices of the triangle ABC are,
A (1,1), B (7,1), and C (1,9),
By the distance formula,
[tex]AB=\sqrt{(7-1)^2+(1-1)^2}=\sqrt{6^2}=6\text{ unit}[/tex]
[tex]BC=\sqrt{(1-7)^2+(9-1)^2}=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10\text{ unit}[/tex]
[tex]CA=\sqrt{(1-1)^2+(1-9)^2}=\sqrt{8^2}=8\text{ unit}[/tex]
Thus, the perimeter of the triangle ABC = AB + BC + CA = 6 + 10 + 8 = 24 unit
How is 2 and 7 tenths written as a decimal?
Answers
is 2.7 because 2 is in the ones place and 7 is in the tenths place
so 2.7 is the answer
hope this helps
Find the distance between A (0,1) and B (-4,6) to the nearest tenth
Answers
(0,1)...x1 = 0 and y1 = 1
(-4,6)...x2 = -4 and y2 = 6
now we sub
d = sqrt (( -4 - 0)^2 + (6 - 1)^2)
d = sqrt ((-4^2) + (5^2))
d = sqrt (16 + 25)
d = sqrt 41
d = 6.4 <===
which graph represents a circle with equation x2 + y2 = 9
Answers
x^2+y^2=r^2
where r^2 is the radius squared.
Looking at your equation, x^2+y^2=9, the radius is 3 (sqrt of 9 is 3)
Therefore, the graph B would be correct since the radius of the circle at all points is 3.
Hope I helped :)
Answer: The correct option is (B). Its image is attached below.
Step-by-step explanation: We are given to select the graph that represents the circle with equation as follows:
[tex]x^2+y^2=9~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that the standard equation of a circle with center at the point (h, k) and radius r units is given by
[tex](x-h)^2+(y-k)^2=r^2.[/tex]
From equation (i), we have
[tex]x^2+y^2=9\\\\\Rightarrow(x-0)^2+(y-0)^2=3^2.[/tex]
Comparing the above equation with the standard equation of a circle, we get
Center, (h, k) = (0, 0) and radius, r = 3 units.
We draw the graph of the circle with center at the origin (0, 0) and radius 3 units in the attached figure below.
We see that the graph of the circle is same as the one provided in option (B).
Thus, option (B) is CORRECT.
Which gas is plotted using the y-axis on the right?
Answers
twenty-two pencils cost $0.60 less than $5 what is the cost per pencil?
Answers
4.40/22=0.2.
So the cost per pencil is 0.2 or 20 cents!
Check: 0.2*22=4.4
Hope this helps!
Can u plz mark me as brainliest? I really need it!
Solve 81^x = 27^x+2
X=1
X=2
X=5
X=6
Answers
After 2 months of living at his new apartment, Henry had 2 cats. Six months later, Henry still had 2 cats. Which of the graphs below models Henry's cat population?
I know it is just a straight line but I need to know if its horizontal or vertical..
Answers
Since the time keeps increasing but the number if cats do not, I would think that it is a horizontal line.
Hope this helps!
Your fortune is "404 error : Fortune not found. Would you like to try again?"
Answer:
The graph with the horizontal line.
PLEASE HELP: When two-thirds of an even number is added to one-quarter of the next consecutive even number, the result is 28. What are the numbers?
Answers
______________________________________
The two (2) consecutive even numbers are: "x" and "(x+2)" .
We are asked to find these numbers.
If we can solve for "x" (one of these numbers); we can solve for "(x+2)" by adding "2" to "x".
_________________________________________
→ (⅔) x + (¼) (x + 2) = 28 ; Solve for "x" ;
_________________________________________
Note the distributive property of multiplication:
_________________________________________
a(b+c) = ab + ac ;
a(b − c) = ab − ac ;
__________________________________________
As such: " + (¼) (x + 2) = (¼) x + (¼) (2) = (¼) x + ½ ;
__________________________________________
Rewrite the equation: → (⅔) x + (¼) (x + 2) = 28 ;
as: " → (⅔) x + (¼) x + ½ = 28 ;
Multiply the entire equation by "12" ; to get rid of the fractions:
→ 12 * { (⅔) x + (¼) x + ½ = 28 } ;
→ (24/3) x + (12/4)x + (12/2) = 28*(12) ;
→ 8x + 3x + 6 = 336
→ 11x + 6 = 336 ;
Subtract "6" from each side of the equation:
→ 11x + 6 − 6 = 336 − 6 ;
→ 11x = 330 ;
Divide each side of the equation by "11" ;
to isolate "x" on one side of the equation; & to solve for "x" ;
→ 11x / 11 = 330 / 11 ;
→ x = 30 ;
____________________________________________
The next consecutive even integer is:
"(x + 2)" ; which equals: "30 + 2 = 32" .
____________________________________________
The numbers are: "30" and "32" .
____________________________________________
Let us check our answer, by plugging the value for "x" in the original equation; to see if it holds true:
____________________________________________
→ (⅔) x + (¼) (x + 2) = 28 ;
→ (⅔) (30) + (¼) (30 + 2) = ? 28 ? ;
→ (60/3) + (¼)*(32) = ? 28 ? ;
→ 20 + 8 = ? 28 ? ; Yes!
____________________________________________
∠E∠E and ∠F∠F are vertical angles with m∠E=9x+12m∠E=9x+12 and m∠F=3x+24m∠F=3x+24 .
What is the value of x?
Answers
Since ∠E and ∠F are vertical angles, they are congruent, meaning that m∠E = m∠F
Plugging in the equations that were originally given, we can form the equation 9x + 12 = 3x + 24
Subtract both sides of the equation by 3x
6x + 12 = 24
Subtract 12 from both sides
6x = 12
Divide both sides by 6
x = 2
This should be your answer. Have an awesome day! :)
Maria started with $10. She has been saving $3 dollars each week to buy a softball bat. The amount of money Maria has depends on how many weeks she has been saving. Which expression represents Maria after x weeks?
A) f(x) = 10x + 3
B) f(x) = 3x + 10
C) f(x) = 10x - 3
D) f(x) = 3x - 10
Answers
algebra- you make a large pot of soup. You freeze the soup in small and medium containers. A small container holds 4 ounces and a medium container holds 6 ounces. The soup can fill 6 small containers and 10 medium containers.
A.Write an equation in standard form that models the possible combinations of small and medium containers that the soup can fill.
B. Graph the equation from part (a)
C. Find four possible combination.
Answers
A. Let us say that:
s = number of small containers
m = number of medium containers
From the given data, the total volume of soup is:
total soup = 4 ounces * 6 + 6 ounces * 10 = 84 ounces
So the equation is:
4s + 6m = 84
B. We rewrite the equation explicit to one variable, here we choose s:
4s = 84 – 6m
s = 21 – 1.5m
Then we assign several values for m starting at 0 to get the corresponding value of s then plot the graph. See the graph attached.
C. From the graph, we choose the pair of s and m that are whole numbers. The four possible combinations are:
21 small containers, 0 medium containers
15 small containers, 4 medium containers
9 small containers, 8 medium containers
3 small containers, 12 medium containers
?/48=7/8 what is the numerator
Answers
What key would you use is 10 students chose cartoons