Answers
Solve for the unknown variable using a pythagoras theorem:
Hypotenuse = 32+x
Opposite = 56
Adjacent = x
[tex]\begin{gathered} \text{Hyp}^2=\text{opp}^2+\text{adj}^2 \\ (32+x)^2=56^2+x^2 \\ (32+x)(32+x)=3136+x^2 \\ 1024+64x+x^2=3136+x^2 \\ \text{collect like terms} \\ 64x+x^2-x^2=3136-1024 \\ 64x=2112 \end{gathered}[/tex]Collect like terms
[tex]\begin{gathered} \frac{64x}{64}=\frac{2112}{64} \\ x=33 \end{gathered}[/tex]Therefore the correct value of x = 33
Related Questions
which number below comes first when the numbers are listed from least to greatest? Explain. Then write the numbers in order from least to greatest 1/6, -3, the square root of 5, -9 / 2, 4.6 which number comes first when the numbers are listed from least to greatest?A. 1/6B.-3C.-9/2D.Square root of 5E. 4.6
Answers
Answer:
The number that comes first when the numbers are listed from least to greatest is;
[tex]\frac{-9}{2}[/tex]And, arranging the numbers from least to greatest will give;
[tex]\frac{-9}{2},-3,\frac{1}{6},\sqrt{5},4.6[/tex]Explanation:
We want to arrange the number given below from least to greatest;
[tex]\frac{1}{6},-3,\frac{-9}{2},\sqrt{5},4.6[/tex]From the list of numbers, let us simplify each of them to their approximate decimal.
[tex]\begin{gathered} \frac{1}{6}=0.1667 \\ -3 \\ \frac{-9}{2}=-4.5 \\ \sqrt{5}=2.236 \\ 4.6 \end{gathered}[/tex]From the given number, the highest negative number will be the least number.
Because the higher a negative number the lower it becomes.
The highest negative is -4.5 followed by -3.
So, arranging from the least to the greatest we have;
[tex]-4.5,-3,0.1667,2.236,4.6[/tex]Rewriting it in its initial form we have;
[tex]\frac{-9}{2},-3,\frac{1}{6},\sqrt{5},4.6[/tex]Therefore, The number that comes first when the numbers are listed from least to greatest is;
[tex]\frac{-9}{2}[/tex]And, arranging the numbers from least to greatest will give;
[tex]\frac{-9}{2},-3,\frac{1}{6},\sqrt{5},4.6[/tex]What is the range of f(x) = 3x + 9?
{y | y < 9}
{y | y > 9}
{y | y > 3}
{y | y < 3}
Answers
The range of f(x) = 3x + 9
{y | y > 9}, Option B
This is further explained below.
What is the range?Generally, Based on the possibilities that have been presented to us, we may speculate that x is inside the exponent of 3.
Therefore, the formula for the function f(x) is really f(x) = 3x +9
Now that we have a function, we need to determine its range of values.
It is clear that the first component is an exponential term denoted by 3x, and that the second term is the number 9.
It is common knowledge that the product 3x will always be higher than 0.
As a result, the result of adding 3x to 9 will always be more than 9.
As a result, the range would be y more than 9.
In conclusion, option B "y | y > 9" is the range
Read more about range
https://brainly.com/question/28135761
#SPJ1
Answer: B
Step-by-step explanation: Trust
Polly surveyed 850 teenagers to find out their favorite type of music she found that 32% of teenagers to Vader like hard rock how many Teenage evade light Hard Rock
Answers
The survryed was on 850 teenagers
Number of teenage that evade light hard rock = 32% of 850
=32/100 x850
=272
54 is 120 percent of what number ?
Answers
Answer:
120% of 54 =
120% × 54 =
120/100 × 54 =
(120 ÷ 100) × 54 =
120 × 54 ÷ 100 =
6,480 ÷ 100 =
64.8
Percentage of 120% of 54
120% of 54 = 64.8
and to prove that we got the right answer do what we did above in reverse below
64.8 ÷ 54 =
1.2 =
1.2 × 100/100 =
(1.2 × 100)/100 =
120/100 =
120%
Step-by-step explanation:
y = 2x divided by 6?
Answers
Answer: I'm not sure if you're trying to find x or y, but y = x/3 and x = 3y
Step-by-step explanation:
Assume your salary is $24,000 per year and $50 for each computer you sell. What function represents your total pay for one year? Be sure to indicate any domain restrictions.
Answers
Let x represent the total amount of computers you sell in one year.
Since you get $50 for each computer, then, you would get 50x for x computers.
Additionally, your base salary is $24,000. Then, add 50x and 24,000 to find your total salary in a year.
If f(x) is a function that represents your salary depending on the amount of computers you sell, then:
[tex]f(x)=50x+24000[/tex]Notice that the amount of computers that you sell cannot be a negative number. Then, you must take into account the following restriction:
[tex]x\ge0[/tex]Therefore, the answer is:
[tex]f(x)=50x+24000\text{ for }x\ge0[/tex]Reflect triangle YWZ across line YW. Which of these is a valid reason why the image of Z will coincide with X?
Answers
Triangle WYZ
line YW
then YW is a bisector of, ZX
Solve the equation 3x - 4y = 16 for x.16 4OA. X-B. x1643C. X= 4y + 16O D. x= 3(16+47)
Answers
To solve for x, first, we add 4y to the equation:
[tex]\begin{gathered} 3x-4y+4y=16+4y, \\ 3x=16+4y\text{.} \end{gathered}[/tex]Now, we divide by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{16+4y}{3}, \\ x=\frac{16+4y}{3}\text{.} \end{gathered}[/tex]Answer:
[tex]x=\frac{16+4y}{3}\text{.}[/tex]2) seperate 90 into two parts (the sum of two numbers is 90)so that one part Cone number) is four times the other part (the other number)
Answers
The sum of two parts equal 90.
Also,
one part is 4 times the other part.
Let the normal part be "x", so the 4 times part would be "4x".
Their sum is 90, thus we can write:
[tex]x+4x=90[/tex]Solving for x (a part):
[tex]\begin{gathered} x+4x=90 \\ 5x=90 \\ x=\frac{90}{5} \\ x=18 \end{gathered}[/tex]The other part is:
90 - 18 = 72
So,
The two parts we separate 90 into are "18 and 72".
Read the problem below and find the solution. Use a model or act the
problem out to help solve it.
A group of 24 students have recess together. They are making teams to play
a game. Each team has to have exactly 5 players, and no one can be on more
than one team. How many teams can they make? (It is possible that not
everyone can be on a team.)
Answers
Answer:
possible
Step-by-step explanation:
a shelf is in the shape of a triangle. find the angle of the triangle if the measure of the angles are in the ratio of x:x:4x.x=4x=
Answers
ANSWER
30°, 30° and 120°
EXPLANATION
We want to find the measures of the angles of the triangle if the ratio of the angles is x : x : 4x
In other words, the ratio is 1 : 1 : 4
The total angle in a triangle is 180°.
Therefore, we have to find the value of x. To do this, we first find the total ratio:
[tex]\begin{gathered} 1+1+4 \\ =6 \end{gathered}[/tex]Now, find x by apply ratios. x is equal to 1/6 of the total angle of the triangle:
[tex]\begin{gathered} x=\frac{1}{6}\cdot180 \\ x=30\degree \end{gathered}[/tex]Now, find 4x:
[tex]\begin{gathered} 4\cdot x=4\cdot30 \\ =120\degree \end{gathered}[/tex]Therefore, the ratio of angles is:
[tex]30\degree\colon30\degree\colon120\degree[/tex]In other words, the angles are 30°, 30° and 120°.
Find the radius of a circle with a circumstance of 28π
Answers
We have the next formula to find the circumference of a circle
[tex]C=2\pi r[/tex]where C is the circumference and r is the radius
In our case we have
C= 28π
we substitute the value in the formula
[tex]28\pi=2\pi r[/tex]then we isolate the r
[tex]r=\frac{28\pi}{2\pi}=14[/tex]the radius is 14.
Jan and her brother mel go to different schools. Jan goes 6 kilometer east from home. Mel goes 8 kilometer north. How many kilometer apart are their schools.
Answers
Jan goes 6 km east from her home, and Mel goes 8 km north from the same home. So we need to find the distance between both schools, and we do such using the Pithagorean theorem, since we are in the presence of a right angle triangle for which we know the two legs, and need to find the measure of the hypotenuse.
I am going to represent the problem with a diagram below, so you see the right angle triangle I am talking about.
So the two legs are represented by the distances each student travels, and the segment in red is the distance between the schools which appears as the HYPOTENUSE of the right angle triangle.
Therefore, we use the Pythagoras theorem for the hypotenuse:
[tex]\begin{gathered} \text{Hypotenuse}=\sqrt[]{leg1^2+\text{leg}2^2} \\ \text{hypotenuse}=\sqrt[]{6^2+8^2} \\ \text{Hypotenuse}=\sqrt[]{36+64} \\ \text{Hypotenuse}=\sqrt[]{100}=10 \end{gathered}[/tex]Therefore, the distance between the schools is 10 km
metres> -21,23Sup10f3: Wandere first rareAnswerTeir wiced data prosto w will be whermerson is us. There will stand er is danfromGoethe type of boundary lineDashedEnter two points on the boundary lineSelect the repon you wish to be shaded:
Answers
Given
[tex]\begin{gathered} x>-2 \\ y\ge3 \end{gathered}[/tex]The graph
[tex]\begin{gathered} x>-3\text{ the pink colour} \\ y\ge3\text{ the blue colour} \end{gathered}[/tex]Two boundary points
[tex]\begin{gathered} \lparen-2,3) \\ \lparen-2,0) \end{gathered}[/tex]help meeeeeeeeee pleaseee !!!!!
Answers
The solution of the composition functions are represented as follows;
(fog)(x) = [tex]\sqrt{-2x+3}[/tex](g o f)(x) = -2√x + 3How to solve composite functions?Composite functions are when the output of one function is used as the input of another.
In other words, a composite function is generally a function that is written inside another function.
Therefore, the composite function can be solved as follows:
f(x) = √x
g(x) = - 2x + 3
Hence,
(fog)(x) = f(g(x)) = [tex]\sqrt{-2x+3}[/tex]
(g o f)(x) = g(f(x)) = - 2√x + 3 = -2√x + 3
Therefore, the composite function expression is as follows:
(fog)(x) = [tex]\sqrt{-2x+3}[/tex](g o f)(x) = -2√x + 3learn more on composite function here: https://brainly.com/question/24464747
#SPJ1
What is the GCF of 42 and 70
Answers
To find the GCF of 42 and 70,
List the prime factors of each numbers,
The prime factors of 42 and 70 is
[tex]\begin{gathered} 42\Rightarrow2\times3\times7 \\ 70\Rightarrow2\times5\times7 \end{gathered}[/tex]42 and 70 share the common factors below
[tex]2\text{ and 7}[/tex]Multiply the common factors to find the GCF
The GCF of 42 and 70 will be
[tex]\text{GCF}=2\times7=14[/tex]Hence, the GCF of 42 and 70 is 14
Can someone help me with this?
Answers
x to the zeroth power - 3x +5
A volleyball drops 8 meters and bounces up 2 meters.
Use the expression |-8 + 2 to find the total distance
the volleyball travels. The total distance the volleyball travels is
✓meters.
Answers
The volleyball travelled a total distance of 10 meters
How to determine the total distance travelled by the volleyball?From the question, the given parameters are
Initial height = 8 meters
Height of bounce = 2 meters
The expression of the total distance is represented as
Total distance = |-8| + 2
Remove the absolute symbol
Total distance = 8 + 2
Evaluate the sum
Total distance = 10
Hence, the total distance travelled by the volleyball is 10 meters
Read more about distance at
https://brainly.com/question/24571540
#SPJ1
tell whether the fractions are equivalent
Answers
Step 1:
Equivalent fractions are fraction that are equal in ratio.
1/3 is equivalent to 4/12
4/12 can be simplify to 1/3 because 4 is a highest common factor of 4 and 12
When you divide by numerator ( 4) and denominator (12) by 4, the fraction result to 1/3.
Hence, 1/3 is equivalent to 4/12.
Final answer
[tex]\frac{1}{3}\text{ = }\frac{4}{12}[/tex]
A lab assistant needs to create a 1000 ML mixture that is 5% hydroelectric acid. The assistant has solutions of 3.5% and 6% in supply at the lab. Using the variables x and y to represent the number of milliliters of the 3.5% solution and the number of milliliters of the 6% solution respectively, determine a system of equation that describes the situation the situation.Enter the equations below separated by a comma How many milliliters of the 3.5% solution should be used?How many milliliters of 6% solution should be used?
Answers
Given:
A lab assistant needs to create a 1000 ML mixture that is 5% hydroelectric acid.
The assistant has solutions of 3.5% and 6% in supply at the lab.
let the number of milliliters from the solution of 3.5% = x
And the number of milliliters from the solution of 6% = y
so, we can write the following equations:
The first equation, the sum of the two solutions = 1000 ml
So, x + y = 1000
The second equation, the mixture has a concentration of 5%
so, 3.5x + 6y = 5 * 1000
So, the system of equations will be as follows:
[tex]\begin{gathered} x+y=1000\rightarrow(1) \\ 3.5x+6y=5000\rightarrow(2) \end{gathered}[/tex]Now, we will find the solution to the system using the substitution method:
From equation (1)
[tex]x=1000-y\rightarrow(3)[/tex]substitute with (x) from equation (3) into equation (2):
[tex]3.5\cdot(1000-y)+6y=5000[/tex]Solve the equation to find (y):
[tex]\begin{gathered} 3500-3.5y+6y=5000 \\ -3.5y+6y=5000-3500 \\ 2.5y=1500 \\ y=\frac{1500}{2.5}=600 \end{gathered}[/tex]substitute with (y) into equation (3) to find x:
[tex]x=1000-600=400[/tex]So, the answer will be:
Enter the equations below separated by a comma
[tex]x+y=1000,3.5x+6y=5000[/tex]How many milliliters of the 3.5% solution should be used?
400 milliliters
How many milliliters of 6% solution should be used?
600 milliliters
I have 5 digits in my number. I do not have any tens. My digits add upto the product of 2 and 6. My biggest place has a value of 30,000. Myhundreds and thousands place adds up to three. The value of mythousands place is bigger than my hundreds. I only have one 0 in mynumber. The sum of my ten thousands, thousands, and hundredsequals the value of my ones place.
Answers
Let's begin by listing out the information given to us:
I have 5 digits in my number means the number is XXXXX (10,000 - 99,999)
No tens: the place value of 'tens' is zero
My digits add up to the product of 2 and 6: 2 * 6 = 12
[tex]\begin{gathered} \Sigma X=2\cdot6=12 \\ \Sigma X=12 \end{gathered}[/tex]My biggest place has a value of 30,000: this restricts the number to lie between 10,000 - 30,000
My hundreds and thousands place adds up to three: this can either be 2 + 1 or 1 + 2 or 0 + 3 or 3 + 0
The value of my thousands place is bigger than my hundreds: this implies that it is 2 + 1 or 3 + 0
I only have one 0 in my number: this cannot be in the 'ten thousands' place, it is the 'tens' place value (I do not have any tens)
The sum of my ten thousands, thousands, and hundreds equals the value of my ones place: the value of the 'ones' place is 6, the value of the 'ten thousands' is 2, the value of the 'thousands' is 3, the value of the 'hundreds' is 1
Hence, the number is 23,106 (remember that "My biggest place has a value of 30,000")
60% discount on $500 sweater
Answers
The discount price of the sweater will be, the original price minus the percentage of discount of the original price.
First, express the percentage of discount as a decimal:
60% = 60/100 = 0.6
so:
[tex]\begin{gathered} 500-0.6\cdot500 \\ 500-300=200 \end{gathered}[/tex]The discount price of the sweater is $200
IIIALGEBRA AND GEOMETRY REVIEWUsing distribution and combining like teSimplify.-3(x + 1)- 5
Answers
-3(x + 1) - 5
(-3)(x) + (-3)(1) -5
-3x - 3 -5
-3x - 8
-2(u + 3) + 4u
-2u - 6 + 4u
2u - 6
89, 81,96, 85, 93, 70, 66, 64, 68, 70MeanMedianMode(s)Range
Answers
Okay, here we have this:
Considering the provided data set, we are going to calculate the requested data, so we obtain the following:
Mean:
It corresponds to the result of adding all the data and dividing it by the amount of data, then we have:
Mean=(89+81+96+85+93+70+66+64+68+70)/10
Mean=782/10
Mean=78.2
Median:
First we will order the data from smallest to largest and the value that is in the center will be the median:
Sorted Data Set: 64, 66, 68, 70, 70, 81, 85, 89, 93, 96
Since 70 and 81 are in the middle, the median will be their average.
Median=(70+81)/2=151/2=75.5
Mode:
It is the data that is repeated the most, in this case it is 70 because it is twice
Range:
It is the difference between the smallest and largest value, then:
Range=96-64=32
You and 2
2
friends have a job cleaning houses. You split the total money you make so that you each get the same amount. On the first day, you earn $93
$
93
. The second day, you earn $75
$
75
. The third day, you earn $108
$
108
. How much money do you each get for 3
3
days of work?
Answers
The amount of money that each person would get for the three days of work is $92.
How much would each person get?The first step is to add all the money earned on the three days together. Addition is the process of determining the sum of two or more values.
Total amount earned in the 3 days = amount earned on the first day + amount earned on the second day + amount earned on the third day
= $93 + $75 +$108 =$276
The next step is to divide the total amount of money earned in the three days by the total number of people that would share the money. Division is the process of determining the quotient of a number.
The amount of money gotten by each person = total earnings / total number of people
$276 / 3 = $92
To learn more about division, please check: https://brainly.com/question/194007
#SPJ1
Solve them all pleaseeeeee
Answers
The solution to the inequalities will be,
( 5 ) y ≥ 2
( 6 ) x < 3
( 7 ) No solution.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
The given inequalities will be calculated as:-
-4 ≤ 4( 6y - 12 ) - 2y
-4 ≤ 24y - 48 - 2y
-4 ≤ 22 y - 48
22y ≥ 44
y ≥ 2
4x + 3 < 3x + 6
4x - 3x < 6 - 3
x < 3
-5r + 6 ≤ -5( r + 2 )
-5r + 6 ≤ -5r - 10
No solution
Therefore, the inequalities are solved above.
To know more about inequality follow
https://brainly.com/question/24372553
#SPJ1
If the discriminant is 22, then the roots of the quadratic equation are ________________.irrationalrationalreal and equalcomplex
Answers
Given:
The discriminant is 22.
Required:
To choose the correct option for the roots.
Explanation:
The desciminant is 22 means
[tex]b^2-4ac=22[/tex]We know that if
[tex]b^2-4ac>0[/tex]the equation has two distinct real number roots.
Therefore the roots are irrational or rational.
Final Answer:
The roots are irrational or rational.
5. A baker makes 275 wheat rolls.
He fills 9 boxes with 24 rolls in
each box. How many rolls are
not in boxes?
Answers
275 - 216 = 59
He would have 59 rolls not in boxes
Answer:
59 rolls are not in boxes
Step-by-step explanation:
9×24=216-275=59
10 pts What is x and y intercept for the following equation? 8x + y = 12 A. x intercept = 0 y intercept = 4 B. x intercept = 12 y intercept = 0 C. x intercept = 4 y intercept = 6 D. x intercept = 3/4 y intercept = 12 OB ОА Oc
Answers
To find the x intercept of the equation make y=0 and solve for x.
[tex]\begin{gathered} 8x+y=12 \\ 8x=12 \\ x=\frac{12}{8} \\ x=\frac{6}{4} \\ x=\frac{3}{2} \end{gathered}[/tex]The x intercept is 3/2
To find the y intercept, make x=0 and solve for y
[tex]\begin{gathered} 8x+y=12 \\ 8(0)+y=12 \\ y\text{=}12 \end{gathered}[/tex]The y intercept is 12.
From the given information. Write the recursive and explicit functions for each geometric sequence. Please use these terms. recursive f(1) = first term, f(n) = pattern*f(n-1). what is the 1st term and pattern? explicit is y = pattern^x * 0 term. work backwards to find 0 term
Answers
We know that a geometric sequence is given by:
[tex]f(n)=f(1)r^{n-1}[/tex]where r is the common ratio of the sequence.
For this sequence we have that the common ratio is r=2, this comes from the fact that in the first day we have 6 dots, for the second day we have twelve and for the third day we have 24. We also notice that the first term is:
[tex]f(1)=8[/tex]Therefore the sequence is given by:
[tex]f(n)=8(2)^{n-1}[/tex]Now, to find the zeoth term we plug n=0 in the sequence above, therefore the zeroth term is:
[tex]\begin{gathered} f(0)=8(2)^{0-1} \\ f(0)=8(2)^{-1} \\ f(0)=4 \end{gathered}[/tex]