Answer:
Explanation:For any right triangle, the longest side is called the hypotenuse. Therefore, by Pythagorean theorem it is true that:
[tex]x^2=a^2+b^2[/tex]
Where:
x: Hypotenuse
a, b: The other two sides.
For instance, if we have a right triangle whose sides measure:
[tex]a=3 \\ \\ b=4[/tex]
Then, the hypotenuse can be found as:
[tex]x=\sqrt{3^2+4^2} \\ \\ c=\sqrt{25} \\ \\ c=5[/tex]
Which statement about fractions that are equivalent to 1 is correct?The denominator is greater than the numerator. The denominator is equal to the numerator. The numerator is greater than the denominator. The denominator is twice the numerator.
The denominator is equal to the numerator.
Step-by-step explanation:
For a fraction to be equal to 1, the value of denominator and the value of numerator should be same.For instance, the fraction 2/2 = 1 because the number in the denominator is 2 and the numerator is also 2.Both cancel out each other that is equal to 1.i need help with thissss!!
Answer: D
Step-by-step explanation:
Paul's Current score is 42, x = paul's awaiting score
Paul's score has to be greater than 174
Current score plus awaiting score must be greater than 174
Answer:
d. 42 + p > 174
Step-by-step explanation:
Since Paul needs to score more than 174, the sign needs to be > and not ≥ because he does not want to equalize the score of 174.
Since he currently has a score of 42, he needs to add another score. Assuming the next score he needs is p,
42 + p is the equation.
£150 is divided between David, Mark & Henry so that David gets twice as much as Mark, and Mark gets three times as much as Henry. How much does David get?
Answer:
David receives £90
Step-by-step explanation:
Let David's share be D
Let Mark's share be M
Let Henry's share be H
From the question, we obtained the following data:
David gets twice as much as Mark i.e
D = 2M
M = D/2
Mark gets three times as much as Henry i.e
M = 3H
H = M/3
H = (D/2) /3
H = D/6
The sum of their shares is £150 i.e
D + M + H = 150
D + D/2 + D/6 = 150
Multiply through by 6 to clear the fraction
6D + 3D + D = 900
10D = 900
Divide both side by the coefficient of D i.e 10
D = 900/10
D = 90
Therefore, David receives £90
A cereal company packages 305.50 lbs of cereal an hour. Each cereal box contains 3.25 lbs of cereal. How many boxes of cereal are packaged in an 812 -hour day?
A
A) 752 boxes
B) 757 boxes
C
C) 799 boxes
D) 858 boxes
In an 812-hour day, a cereal company that packages 305.50 lbs of cereal an hour would package approximately 76,331 boxes of cereal, given each box contains 3.25 lbs of cereal. The provided options in the question do not match this result.
The subject of this question is Mathematics, specifically division used in a real-world context regarding a cereal company's packaging process. To find the number of cereal boxes produced in an 812-hour day, we need to divide the total weight of cereal packed in a day by the weight of cereal in each box.
Firstly, we find out the total amount of cereal produced by multiplying the hourly rate by the number of hours. This will give us: 305.50 lbs/hour x 812 hours = 248,071 lbs.
Next, we divide the total amount of cereal by the weight of cereal in each box to find the number of boxes. Therefore, 248,071 lbs ÷ 3.25 lbs/box = 76,331 boxes.
None of the options (A) 752 boxes, (B) 757 boxes, (C) 799 boxes, (D) 858 boxes match our result. There might be an error in the question or the choices provided.
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How can you determine whether a triangle is a right triangle
Answer:
if there is a right angled square shape at the angle
Answer: MARK BRAINLIEST!!!!!!!!!
Because its the only triangle that has a 90 degree angle
Step-by-step explanation:
what Is x if y=2x+7?
Answer:
x = (y - 7)/2
Step-by-step explanation:
from the question given y=2x+7 , so we are to find the value of x now we first make x the subject of the formulae from y=2x+7
y=2x+7............. equation 1
y- 7 = 2x
divide both sides by 2
(y-7)/2= 2x/2
x = (y - 7)/2
to check if your answer is correct
put the value of x in to equation 1
y=2x+7............. equation 1
y = 2[ (y-7)/2] + 7
y = y - 7 + 7
y = y.......... proved
What is the solution of the system of equations?
5x + 4y = -22
2x – 3y = 5
Answer:
y = 3
x =7
Step-by-step explanation:
to solve this system of equations using substitution method we say, let
5x + 4y = -22 .................... equation 1
2x – 3y = 5...................... equation 2
from equation 2
2x - 3y = 5
2x = 5 + 3y
divide both sides by 2
we have;
2x/2 = (5+3y)/2
x =(5+3y)/2................................ equation 3
put x = (5+3y)/2 in equation 1
5x + 4y = -22 .................... equation 1
5(5+3y)/2 + 4y = -22
(25 + 15y)/2 + 4y = -22
multiply through by 2
25 + 15y + 8y = -44
25 + 23y = -44
collect the like terms
23y = -44 - 25
23y = -69
divide both sides by 23
23y/23 = -69/23
y = 3
put the value of y= 3 into equation 3
x =(5+3y)/2................................ equation 3
x = (5+3(3)]/2
x = 5+9/2
x =14/2
x =7
there are 110 calories per 28.4 grams of cereal X. find how many calories are in 42.6 grams of the cereal
Answer:
165 calories
Step-by-step explanation:
110 cal/28.4 g in Cereal X
How m any cals in 42.6 g of Cereal X
110/x=28.4/42.6
28.4x=4686
x=165
Therefore, 165 calories
The number of calories in 42.6 grams of cereal X will be 165 calories.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
There are 110 calories per 28.4 grams of cereal X. Then the number of calories in each gram is calculated as,
Rate = 110 / 28.4
Rate = 275 / 71 calories per gram
Then the number of calories in 42.6 grams of the cereal X will be given as,
⇒ (275 / 71) x 42.6
⇒ 275 x 0.60
⇒ 165
The number of calories in 42.6 grams of cereal X will be 165 calories.
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4. A health club manager wants to determine
whether the members would prefer a new
sauna or a new steam room. The club surveys
50 of its 600 members. What is the population
of this study?
Answer: 600 members of the club
Step-by-step explanation:
In a statistical study , a population is a large group of observations by the researcher's point of view regarding the objective of the study.A sample is a subset of the population that represents the entire population.
Here , we are given that ,
The club surveys 50 of its 600 members.
Clearly , Population = 600 members of the club
Sample = 50 members
Hence, the population of this study is "600 members of the club " .
15 arches decreased by 80%
If it decreases by 80٪, then only 20٪ remains.
15×20٪=15×20/100=15×0.2=3
Answer: 3
Answer:
3 arches
Step-by-step explanation:
Given
15 arches decreased by 80%.
First get 80% of 15 arches
That’s 80%/100% x 15
0.8 x 15
12 arches
Now subtract 12 arches from 15 arches to get the decrease
Decrease = (15 - 12) arches
= 3 arches
Therefore, 80% decrease of 15 inches is equal to 3 arches
please help 100points and BRAINLYEST!!!!!!!!
Drag each value to the correct location on the table.
Identify whether each cube root or square root lies between 2 and 3, 4 and 5, or 9 and 10.
Answer:
sqrt of 7 goes between 2 and 3
Square root of 20 goes between four and five
Square root of 90 goes between nine and 10
The 101 goes between 4 &5
The 3 90 goes between 4&5
The 3 20 goes between two and three
And 3 800 goes between 9&10
A circle has a circumference of 18. It has an arc of 6. What is the central angle of the arc, in degrees?
Answer:
Step-by-step explanation:
C=2πr
18=2×3.14×r
18=6.28r
r=2.88
Arc of a circle
A=®/360°πr
6=®/360°×3.14×r
®=239°
6
Answer:
120
Step-by-step explanation:
Oxnard Petro Ltd. is buying hurricane insurance for its off-coast oil drilling platform. During the next five years, the probability of total loss of only the above-water superstructure ($320 million) is .30, the probability of total loss of the facility ($820 million) is .30, and the probability of no loss is .40. Find the expected loss. (Input the amount as a positive value.) Expected Loss
Answer:
Expected loss = $342 million.
Step-by-step explanation:
The formula to compute the expected loss is:
[tex]E(Loss)=\sum Loss\ amount\times P (Loss)[/tex]
Given:
P (Loss) Amount of loss
0.30 $320 million
0.30 $820 million
0.40 $0
Compute the expected loss as follows:
[tex]E(Loss)=\sum Loss\ amount\times P (Loss)\\=(0.30\times320)+(0.30\times820)+(0.4\times0)|_{in\ millions}\\=96 +246+0\\=\$342\ million[/tex]
Thus, the expected loss is $342 million.
Multiply (x^2 + 2x + 3)(4x^2 - 2x + 1)
Answer:
4x^4 + 6x^3 + 9x^2 − 4x + 3
Step-by-step explanation:
Simplify the expression. 4x^4 + 6x^3 + 9x^2 − 4x + 3
Answer:
4x^4 + 6x^3 + 9x^2 - 4x + 3
Step-by-step explanation:
Distribute (x^2 + 2x + 3)(4x^2 - 2x + 1)
You will get 4x^4 - 2x^3 + x^2 + 8x^3 - 4x^2 + 2x + 12x^2 -6x + 3
Then you need to combine like terms
And you will get the answer:
4x^4 + 6x^3 + 9x^2 - 4x + 3
You've been given a twenty dollar bill that you need to break into smaller bills and coins in order to make change. You break it into three (3) five-dollar bills, and three (3) one-dollar bills. How many quarters do you need to complete the conversion?
Answer:
8 quarters
Step-by-step explanation:
You need to break the $20 into smaller bills. The smaller bills value has to be equal to $20. So far you have three $5 bills and three 1$ bills, so the current value is 3*$5 + 3*$1= $18
The value you need to add more will be $20- $18= $2
You need to add $2 more value to the smaller bills and you want to do it using quarters($0.25). The number of the quarter you need will be: $2/ $0.25= 8 quarters
Let's start by calculating the total value of the five-dollar bills and one-dollar bills:
You have 3 five-dollar bills, and each is worth $5, so:
3 five-dollar bills × $5 per bill = $15
You also have 3 one-dollar bills, and each is worth $1, so:
3 one-dollar bills × $1 per bill = $3
Now, let's add the value of the five-dollar bills and one-dollar bills together:
$15 (from five-dollar bills) + $3 (from one-dollar bills) = $18
You started with a twenty-dollar bill, which is worth $20, so we subtract the total value of the bills you have from $20 to find out how much is left to reach $20:
$20 (initial amount) − $18 (value of bills) = $2
You need to make up this remaining $2 with quarters. Since each quarter is worth $0.25 (25 cents), we divide the remaining amount by the value of each quarter to find out how many quarters you need:
$2 ÷ $0.25 per quarter = 8 quarters
Therefore, you need 8 quarters to complete the conversion to $20.
3 fifths÷7 eighths please help
Answer:
24/35
Step-by-step explanation 3/5 times 8/7 equals 24/35
does anyone know what 2/3 x= 8. So the question is what does x equal too
Answer:
x = 12
Step-by-step explanation:
⅔x = 8
x = 8 × 3/2
x = 12
Answer:
12
Step-by-step explanation:
8 divided by 2/3 = 12.01 so 12.
Which expression is equivalent to 2(a+2b)- a-2b
Answer:
a + 2b
Step-by-step explanation:
Perform the indicated multiplication.
This results in 2a + 4b - a - 2b, whiin in turn reduces to
a + 2b
Solve for x: 4/7 = x-1/12
To solve for x in the equation 4/7 = x-1/12, combine the fractions, cross multiply, and solve to find x=3 and x=-7.
Explanation:Solve for x: 4/7 = x-1/12
To solve for x, first combine the fractions on the right side: 4/7 = (12x - 1)/12. Then, cross multiply to get 12*4 = 7*(12x - 1). Solve for x to find x=3 and x=-7.
By substituting these values back into the original equation, which is x is equal to (12x-1)/12, you can verify these solutions.
his season, Lisa's lacrosse team has won $\frac 23$ of their home games (games played at Lisa's school), but just $\frac 25$ of their away games (games played at other schools). In total, Lisa's team has won $26$ games out of $49$ games they have played. How many home games has Lisa's team played?
Answer:
24 Home games
Step-by-step explanation:
let [tex]x[/tex] denote the number of home games played, and [tex]y[/tex] denote the number of home games played. We are given the total number of games played as 49
and total wins as 26.
The problem can be expressed in equation form as:[tex]\frac{2}{3}x+\frac{2}{5}y=26[/tex]...[tex]eqtn1[/tex]
Total games is expressed as [tex]x+y=49[/tex]...[tex]eqtn2[/tex]
Rewrite equation 1 to remove fractions:
[tex]\frac{2}{3}x+\frac{2}{5}y=26\\=>5x+3y=195\\[/tex]
Solve for x to obtain total home games played.
Making [tex]x[/tex] the subject in eqtn 2:
[tex]x=49-y[/tex]
Substitute for [tex]x[/tex] in eqtn1:
=>
[tex]5(49-y)+3y=195\\-5y+3y=195-245\\-2y=-50\\y=25[/tex]
To obtain [tex]x[/tex], replace y value in eqtn2:
[tex]x+y=49\\y=25\\Therefore\\x=49-25\\x=24[/tex]
Home games played is 24
Write the first six terms of the sequence.
a = -n²+6
en oo
4, 2, 0, -2, -4,-6
5, 2, -3, -10, -19, -30
2, -3, -10, -19, -30, -43
6, 5, 2, -3, -10, -19
Step-by-step explanation:
1st term = -n²+6
= -(1)²+6
= -1+6
=5
2nd term = -(2)²+6
= -4+6 = 2
3rd term= -(3)²+6
=-9+6 = -3
4th term= -(4)²+6
= -16+6 = -10
5th term = -(5)²+6 = -25+6 = -19
6th term = -(6)²+6 = -36+6 = -30
5,2, -3,-10,-19, -30
optionB
Triangle 1 has vertices at (A,B), (C,D), and (E,F). Triangle 2 has vertices at (A,3B), (C,3D), and (E,3F). What can you conclude about triangle 2?
(A)Triangle 2 is not congruent to triangle 1 because the transformation applied was not a rigid motion.
(B)Triangle 2 is congruent to triangle 1 because a reflection is a rigid motion.
(C)Triangle 2 is not congruent to triangle 1 because it is not a translation of triangle 1.
(D)You cannot tell because you do not know where the points are in the plane.
Answer:
Step-by-step explanation:
A
Answer:
Answer A
Step-by-step explanation:
How do you find the slop from this?
Answer:
Look at the rise over run
itd be 10/10 or 1
create a pattern for the rule a x 3+2
it is 3+2 = 5 plus a = 5a
j divided by 9 is 5.
Solve for j.
j=
Answer:
j = 45
Step-by-step explanation:
j/9 = 5
Multiply both sides by 9: j = 45
The required value of j will be 45 when j divided by 9 is 5.
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation.
For example, 62÷31 = 2
To solve for j, we are trying to find the value of j that makes the equation "j / 9 = 5" true.
We can start by setting up the equation:
j / 9 = 5
This equation says that the result of dividing j by 9 is equal to 5.
To solve for j, we can multiply both sides of the equation by 9, the denominator of the fraction on the left-hand side:
j = 9 × 5
= 45
This shows that j = 45 is the solution to the equation. In other words, if we substitute 45 for j in the equation "j / 9 = 5", the equation becomes true:
45 / 9 = 5
Therefore, the value of j that makes the equation "j / 9 = 5" true is 45.
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John and Liz are sharing a large pizza. John ate 1/3 of the pizza, and Liz ate 1/4 of the pizza. How much of the pizza is left?
Answer:
5/12
Step-by-step explanation:
Final answer:
After John ate 1/3 of the pizza and Liz ate 1/4, we convert these fractions to have a common denominator of 12, resulting in 4/12 + 3/12 = 7/12 eaten. Subtracting this from the whole gives us 5/12 of the pizza remaining.
Explanation:
John and Liz are sharing a large pizza. To determine how much of the pizza is left after John has eaten 1/3 and Liz has eaten 1/4, we need to add those fractions together and subtract the sum from the whole pizza, which is 1 (representing the entire pizza).
First, we find a common denominator, which in this case is 12, so we convert 1/3 to 4/12 and 1/4 to 3/12. Adding these fractions, we get 4/12 + 3/12 = 7/12.
Now we subtract the portion eaten from the whole pizza: 1 - 7/12 = 5/12 of the pizza is left.
A ball is thrown in the air from a ledge. Its height in tesspresented by
R -16(x^2
- 5x-6), where x is the number of seconds since the ball has
been thrown. The height of the ball is 0 feet when it hits the ground.
How many seconds does it take the ball to reach the ground?
Answer:
6 .74 seconds
Step-by-step explanation:
The height of the ball is given by the equation:
[tex]R(x) = - 16( {x}^{2} - 5x - 6)[/tex]
When the ball hit the ground, then;
[tex]R(x) = 0 \\ - 16( {x}^{2} - 5x - 6) = 0 \\ {x}^{2} - 5x - 6 = 0 \\ x = -0.74 \: Or \: 6.74[/tex]
We discard x=-0.74 since time is not negative.
Therefore the ball hit the ground after 6.74 seconds.
Help please! Thank you
Which expression is equivalent to StartRoot negative 80 EndRoot?
Answer:
[tex]4i\sqrt{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{-80}[/tex]
[tex]\sqrt{80*i^2}[/tex]
i^2 is -1
[tex]i\sqrt{80}[/tex]
[tex]i\sqrt{4^2 * 5}[/tex]
[tex]4i\sqrt{5}[/tex]
Answer: [tex]4i\sqrt{5}[/tex]
Answer:
[tex]4i\sqrt{5}[/tex]
Step-by-step explanation:
A carpenter needs 3 minutes to cut a board into 5 equal sections. If each cut takes the same length of time, at what rate is the carpenter cutting?
Answer:
3/180= 60 seconds = 1m/per cut or 60 sec/per cut.
Step-by-step explanation:
This is 3 cuts executed from a board to get 5 parts.
Answer:
he cuts 1.6 section of a board in one minute
Step-by-step explanation:
They're telling you that it takes 3 minutes for the carpenter to cut one board into 5 qual section. Therfore how many sections he's cutting in one minute divide the 5 by three. With that you will have the rate