Answer:
x = 8Step-by-step explanation:
[tex]\sqrt{\dfrac{896z^{15}}{225z^6}}=\dfrac{xz^4}{15}\sqrt{14z}\\\\\sqrt{\dfrac{896z^{15}}{225z^6}}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=\sqrt{\dfrac{(64)(14)z^{15-6}}{225}}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b},\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\=\dfrac{\sqrt{64}\cdot\sqrt{14}\cdot\sqrt{z^9}}{\sqrt{225}}=\dfrac{8\cdot\sqrt{14}\cdot\sqrt{z^{8+1}}}{15}\qquad\text{use}\ a^na^m=a^{n+m}\\\\=\dfrac{8\sqrt{14}\cdot\sqrt{z^8z}}{15}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}[/tex]
[tex]=\dfrac{8\sqrt{14}\cdot\sqrt{z^8}\cdot\sqrt{z}}{15}=\dfrac{8\sqrt{14}\cdot\sqrt{z^{4\cdot2}}\cdot\sqrt{z}}{15}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\dfrac{8\sqrt{14}\cdot\sqrt{(z^4)^2}\cdot\sqrt{z}}{15}\qquad\text{use}\ (\sqrt{a})^2=a\\\\=\dfrac{8\sqrt{14}\cdot z^4\cdot\sqrt{z}}{15}=\dfrac{8z^4\sqrt{14}\cdot\sqrt{z}}{15}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{8z^4\sqrt{14z}}{15}[/tex]
[tex]\dfrac{8z^4\sqrt{14z}}{15}=\dfrac{xz^4\sqrt{14z}}{15}\iff x=8[/tex]
There are 32 more apple than oranges in a box. 3/5 of the oranges and 1/3 of the apples are overripe. If the number of overripe apples and the number of oranges is the same, how many pieces of overripe fruit are there?
The answer is:
There is a total of 48 overripe fruit.
Why?To calculate the number of pieces of overripe fruit we have, we need to write two equations to create a relationship between the number of apples and oranges.
Let be "x" the number of oranges, so:
[tex]Oranges=x\\Apples=x+32[/tex]
Now, we know that 3/5 of the oranges and 1/3 of the apples are overripe, so:
[tex]OverripeApples=\frac{1}{3}(x+32)\\\\OverripeOranges=\frac{3}{5}(x)[/tex]
Then, we have a condition that states that the number of overripe apples and overripe oranges is the same, so:
[tex]\frac{1}{3}(x+32)=\frac{3}{5}(x)[/tex]
[tex]\frac{1}{3}(x)+\frac{1}{3}(32)=\frac{3}{5}(x)[/tex]
[tex]\frac{1}{3}(32)=\frac{3}{5}(x)-\frac{1}{3}(x)[/tex]
[tex]\frac{1}{3}(32)=\frac{3x*3-1*x}{15}=\frac{9x-5*x}{15}=\frac{4x}{15}[/tex]
[tex]\frac{32}{3}=\frac{4x}{15}[/tex]
[tex]\frac{32*15}{3}=4x[/tex]
[tex]\frac{480}{3}=4x[/tex]
[tex]160=4x[/tex]
[tex]\frac{160}{4}=x[/tex]
[tex]40=x[/tex]
Therefore, we have that there are 40 oranges and 72 apples (40+32).
Now, calculating the number of overripe oranges and apples, we have:
[tex]OverripeApples=\frac{1}{3}(72)=24\\\\OverripeOranges=\frac{3}{5}(40)=24[/tex]
Hence, we have that there are 24 pieces of overripe oranges and 24 pieces of overripe apples. It means that there is a total of 48 overripe fruit.
Have a nice day!
The function below represents the annual interest Victoria earns on a savings account. Identify the term that represents the amount of money originally deposited in the account.
f(x) = 300(1 + 0.03)x
300
1
0.03
x
Answer:
[tex]\$300[/tex]
Step-by-step explanation:
In this problem we have a exponential function of the form
[tex]f(x)=a(b)^{x}[/tex]
where
a is the initial value ( value of the function when the value of x is equal to zero)
b is the base
r is the rate
b=1+r
we have
[tex]f(x)=300(1+0.03)^{x}[/tex]
therefore
The term that represents the amount of money originally deposited in the account is the initial value
For x=0
substitute
[tex]f(0)=300(1+0.03)^{0}[/tex]
[tex]f(0)=\$300[/tex]
Answer:
The correct option is 1.
Step-by-step explanation:
The function is
[tex]f(x)=300(1+0.03)^x[/tex]
We need to find the term that represents the amount of money originally deposited in the account. It means we need to find the initial amount.
Substitute x=0 in the given function, to find the initial value of the function.
[tex]f(0)=300(1+0.03)^(0)[/tex]
[tex]f(0)=300(1)[/tex]
[tex]f(0)=300[/tex]
The term 300 represents the amount of money originally deposited in the account. Therefore the correct option is 1.
Write a numerical expression for each verbal phrase? How many more pencils Chet has than Benito if Benito has ten pencils and Chet has seventeen pencils
Answer:
-10 + 17 [OR 17 - 10]
Step-by-step explanation:
To find out how MANY MORE of something someone has THAN the other, you use the operation of deduction [subtraction].
I am joyous to assist you anytime.
Answer:
Chet has 7 more pencils than Benito.
Step-by-step explanation:
We have to Write a numerical expression for each verbal phrase:
Number of pencils Benito has = 10
Number of pencils Chet has = 17
The number of more pencils Chet has than Benito is = [tex]17-10=7[/tex]
Therefore, Chet has 7 more pencils than Benito.
Write an equation: 1/5 of a shipment of books weights 25 pounds
To find the total weight of the shipment where [tex]\frac{1}{5}[/tex] weighs 25 pounds, we use the equation [tex]\frac{1}{5}[/tex]W = 25 and solve for W, leading to a total weight of 125 pounds.
The question is asking us to write an equation that represents the situation where [tex]\frac{1}{5}[/tex] of a shipment of books weighs 25 pounds.
To find the total weight of the shipment, we should set this up as an equation where the total weight of the shipment is represented by W. Since [tex]\frac{1}{5}[/tex] of the shipment weighs 25 pounds, we can write the equation as [tex]\frac{1}{5}[/tex] W = 25.
To find the weight of the whole shipment, we need to multiply both sides of the equation by 5, which will give us
W = 125 pounds.
When converting units such as pounds to ounces, we use the unit equivalence 1 pound = 16 ounces.
If the weight of the books needed to be in ounces, we could convert 125 pounds by multiplying
125 x 16 = 2000 ounces
What is the equation of the line (in point-slope form) that passes through the point (2,3) and is parallel to the line y−9=2/3(x+7)?
Answer:
[tex]\large\boxed{y-3=\dfrac{2}{3}(x-2)}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================[/tex]
[tex]\text{The point-slope form of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\\\(x_1,\ y_1)-point\ on\ a\ line\\\\===============================[/tex]
[tex]\text{We have the equation of a line:}\ y-9=\dfrac{2}{3}(x+7)\to m_1=\dfrac{2}{3}.\\\\\text{A slope of parallel line:}\ m_2=m_1=\dfrac{2}{3}.\\\\\text{Put the value of the slope and the coordinates of the point (2, 3)}\\\text{to the equation of a line in point-slope form:}\\\\y-3=\dfrac{2}{3}(x-2)[/tex]
Answer:
The answer is y = -3/2x + 6
Step-by-step explanation:
A certain triangle has a 30 angle and a 60 angle.
Answer:
Step-by-step explanation:
It is B, The longest side is sqrt 3 times as long as the shortest side.
Attached is a image showing the side length rules for 30-60-90 triangles.
Hope this helps :)
help please Compute the volume of a sphere with a radius of 6 inches. a. 864π in3 b.72π in3 c. 216π in3 d. 288π in3
Answer:
d. 288π in3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
The radius is 6
V = 4/3 pi 6^3
V = 288 pi in^3
Rational numbers do NOT include:
infinite decimals
repeating decimals
terminating decimals
Answer:
Infinite decimals that do not repeat.
Step-by-step explanation:
Repeating decimals can be as fractions where the top and bottom are integers.
Examples: .3333333333333333333333333333333.... can be written as 1/3.
or .19191919191919191919..... can be written as 19/99.
Terminating decimals can also be written as fractions where the top and bottom are integers.
Examples: .11=11/100 or .161=161/1000
Any number that can be written as a fraction where the top and bottom are integers (bottom integer not 0)
is a rational number.
Repeating decimals are infinite. So what I think they mean by infinite here is numbers like [tex]\pi[/tex] or [tex]\sqrt{2}[/tex]. There are not rational. They cannot be written as a fraction where the top and bottom are integers.
Answer:
Rational numbers do NOT include:
infinite decimals
Step-by-step explanation:
Solve for x -2x + 5 <7
Answer:
[tex]\large\boxed{x>-1}[/tex]
Step-by-step explanation:
In this question, we're trying to solve for x.
In other words, we're going to need to get x by itself in order to get our answer for the inequality.
Solve:
[tex]-2x + 5 <7\\\\\text{Subtract 5 on both sides to get -2x by itself}\\\\-2x<2\\\\\text{Divide both sides by -2}\\\\\text{Since you're dividing by a negative, the} < \text{will flip to} >\\\\x>-1[/tex]
When you're done solving, you should get x > -1
This means that when you solve for x, you should get x > -1
I hope this helped you out.Good luck on your academics.Have a fantastic day!
LOOK AT PICTURE PLEASE ANSWER ASAP parabola directrix focus and vertex
Answer:
[tex]y = - \frac{3}{20} {x}^{2} [/tex]
Step-by-step explanation:
The given parabola has focus at:
[tex](0, - \frac{5}{3} )[/tex]
and directrix at
[tex]y = \frac{5}{3} [/tex]
This is a vertical parabola that opens downwards.
The equation is of the form;
[tex] {x}^{2} = - 4py[/tex]
p is the distance from the vertex to the directrix.
Since the vertex is at the origin, we have
[tex]p = \frac{5}{3} [/tex]
We plug this value into the equation to get:
[tex] {x}^{2} = - 4( \frac{5}{3} )y[/tex]
[tex] {x}^{2} = - \frac{20}{3} y[/tex]
We solve for y to obtain:
[tex]y = - \frac{3}{20} {x}^{2} [/tex]
The 3rd option is correct.
3 integers less than 25 range of 10 mean of 13
Answer:
8, 13, 18
Step-by-step explanation:
If we want the mean to be 13, and there are 3 integers, that means the sum of all 3 integers must be 39. I started at 13 and counted 5 up and 5 down, which already makes sure of the range and the mean is 13 (since it's balanced with 13 being the middle), therefore, 13+5 is 18, 13-5=8.
What is the slope of the line through (-7, -2) and (-6, 7)?
Make sure to explain your answers, please!
{No spam answers, please! Thank you!}
Answer:
[tex]\displaystyle =9[/tex]
Step-by-step explanation:
The slope formula is
[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\displaystyle y_2=7\\\displaystyle y_1=(-2)\\\displaystyle x_2=(-6)\\\displaystyle x_1=(-7)[/tex]
[tex]\frac{7-(-2)}{(-6)-(-7)}=\frac{9}{1}=9[/tex]
Therefore, the slope is 9, and the correct answer is 9.
Hope this helps!
What is the solution set of - x = -8?
[tex]-x=-8\\x=8[/tex]
Answer:
x = 8
Step-by-step explanation:
The solution set of - x = -8 is x=8.
- x = -8 = x = 8
Write the equation that contains the point (3, -9), and in which the graph of the line has a slope of 4 in slope-intercept form.
[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-9})~\hspace{10em} slope = m\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-9)=4(x-3) \\\\\\ y+9=4x-12\implies y=4x-21[/tex]
what is the inverse of the function f(x)=2x+1
Answer:The inverse of the linear function f(x)=2x+1 is f^(-1) (x) = (1/2)x-1/2
Step-by-step explanation:
what are solutions to the quadratic equation 2x^2+6x-10=x^2+6
Answer:
x = -2 or x = 8Step-by-step explanation:
[tex]2x^2+6x-10=x^2+6\qquad\text{subtract}\ x^2\ \text{and 6 from both sides}\\\\x^2+6x-16=0\\\\x^2+2x-8x-16=0\\\\x(x+2)-8(x+2)=0\\\\(x+2)(x-8)=0\iff x+2=0\ \vee\ x-8=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\x=-2\\\\x-8=0\qquad\text{add 8 to both sides}\\x=8[/tex]
Answer:
2 and -8
Explanation is Apex
Hair color. |. Clothing
Brown. I Dress
Black. I Jumpsuit
Blonde. I Pajamas
Red. I Jeans
The table above shows hair colors and clothing available at a doll shop. How many different combinations of hair color ND clothing are there?
Answer:
16 possible hair/clothing combinations
Step-by-step explanation:
1) Brown-dress; 2)Brown-jumpsuit; 3)Brown-pajamas ; 4)Brown-Jeans; 5)Black-Dress; 6)black jumpsuit; 7)black pajamas; 8)black jeans; 9)blonde dress; 10)blond jumpsuit; 11)blonde pajamas; 12)blond jeans; 13)red dress; 14)red jumpsuit; 15)red pajamas; 16)red jeans
Or just multiply 4x4 because there were four of each.
Find the equation for the linear function that passes through the points ( see photo )
Answer:
[tex]f(x)=\frac{3}{2}x-2[/tex]
Step-by-step explanation:
step 1
Find the slope m
we have
(-2,-5) and (4,4)
The slope is equal to
[tex]m=\frac{4+5}{4+2}[/tex]
[tex]m=\frac{9}{6}[/tex]
simplify
[tex]m=\frac{3}{2}[/tex]
step 2
Find the equation of the line into slope point form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{3}{2}[/tex]
[tex](4,4)[/tex]
substitute
[tex]y-4=\frac{3}{2}(x-4)[/tex]
step 3
Convert to slope intercept form
[tex]y-4=\frac{3}{2}(x-4)[/tex]
[tex]y=\frac{3}{2}x-6+4[/tex]
[tex]y=\frac{3}{2}x-2[/tex]
Convert to function notation
[tex]f(x)=\frac{3}{2}x-2[/tex]
40 pts!! please help T^T
A football quarterback enjoys practicing his long passes over 40 yards. He misses the first pass 40% of the time. When he misses on the first pass, he misses the second pass 20% of the time. What is the probability of missing two passes in a row?
A football quarterback enjoys practicing his long passes over 40 yards. He misses the first pass 40% of the time. When he misses on the first pass, he misses the second pass 20% of the time. What is the probability of missing two passes in a row?
30%
Probability of missing two passes in a row is 0.08.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given
Event E = A football player misses twice in a row.
P(E) = ?
Event X = Football player misses the first pass
P(X) = 0.4
Event Y = Football player misses just after he first miss
P(Y) = 0.2
Both the events are exclusive so the probability of occurring of these two events can be calculated by the formula:
P(E) = P(X).P(Y)
P(E) = 0.4*0.2
P(E) = 0.08
To know more about probability refer to :
https://brainly.com/question/13604758
#SPJ2
- (1-7x) -6 (-7-x) = 36
Solving for x:
Start by distributing the numbers outside the parentheses to inside the parentheses:
-1 + 7x + 42 + 6x = 36
Now combine like (similar) terms:
13x + 41 = 36
Subtract 41 from both sides:
13x = -5
Divide both sides by 13:
x = [tex]-\frac{5}{13}[/tex]
Therefore, x = [tex]-\frac{5}{13}[/tex].
Hope this helps! :)
Max saved some money by buying a book of 10 movie passes rather than individual tickets.Howcan he figure out how much money he saved?
What is true about triangle ABC. Select three options
Answer: The answer is sin A = cos C
Step-by-step explanation: sin A = cos C
Answer:
It should be A, B, C
Step-by-step explanation:
anyone willing to help out really quick?^^
Answer:
15.86 inches
Step-by-step explanation:
Area of rectangle = length times width
l = ∛81 inches
w = 3 2/3 inches
= l x w
= ∛81 x 3 2/3
= 15.86 inches
Which of the following values is a solution for the inequality statement? Select all that apply. 11 > a/4 -16 55 -150 210 -78 108
Answer:
55, -150, -78
Step-by-step explanation:
The given inequality is:
[tex]11>\frac{a}{4}-16[/tex]
Adding 16 to both sides, we get:
[tex]11+16>\frac{a}{4}-16+16\\\\ 27>\frac{a}{4}[/tex]
Multiplying both sides by 4, we get:
[tex]27 \times {4}>\frac{a}{4} \times 4\\\\ 108>a[/tex]
Hence, the solution to the inequality is 108 > a or this can be written as a < 108
This means, the values less than 108 are a solution of the given inequality. 108 is not a part of the solution as the inequality symbol says less than 108.
Among the given options following are the values that are less than 108 and thus will satisfy the inequality:
55, -150, -78
A patient’s weight is recorded as 75 kilograms. How many pounds does the patient weigh?
Answer:
165.347 pounds ..
Step-by-step explanation:
The weight of patient is given in kilograms which is
W = 75 kilo grams.
In order to convert the weight into pounds we have to multiply or divide 75 with some number.
There are 2.20462 pounds approximately in one kilogram.
So the weight in pounds will be:
Weight in pounds = 75 * 2.20462
= 165.3465 pounds
= 165.347 pounds ..
The domain of r:(3,-2)(1,2)(-1,-4)(-1,2)
Answer:
domain {-1,1.3}
Step-by-step explanation:
The domain is the input values, or in this case the first or x values
domain {3,1,-1,-1}
We do not put the same value twice
domain {3,1,-1}
We like to put them in numerical order
domain {-1,1.3}
Find the area of the rhombus. (4)
Answer:
24 cm2 is the answer or option d
Step-by-step explanation:
a keycode must contain 4 letters followed by 3 numbers. The letters may be any letters of the alphabet. The numbers should be any number from 0 to 5. How many different keycode combinations are there?
Answer:
98,706,816 combinations
Step-by-step explanation:
Let's make a little graphic of it:
Letters (4): ___ ___ ___ ___
Numbers (3): ___ ___ ___
In the 4 lines/placeholders of the letters, it can be ANY letter of the alphabet, it can be any 26 of them.
In the 3 lines of the numbers, it can be any number from 0 - 5, which is 6 numbers.
Thus we can say:
Letters = 26 * 26 * 26 * 26 = 456,976
Numbers = 6 * 6 * 6 = 216
Their PRODUCT is the number of combinations possible.
456,976 * 216 = 98,706,816 combinations
A 279-foot rope is cut into three pieces. The second piece is twice as long as the first. The third piece is as long as the second. How long is each piece of rope?
Step-by-step explanation:
Let's say x is the length of the first piece.
The second piece is 2x.
The third piece is 2x.
So the total length is:
x + 2x + 2x = 279
5x = 279
x = 55.8
That means 2x = 111.6.
So the first piece is 55.8 feet, the second piece is 111.6 feet, and the third piece is also 111.6 feet.
Answer:
Piece 1 : 55.8 ft
Piece 2: 111.6 ft
piece 3: 111.6 ft
Step-by-step explanation:
From the question we can see that the total length of the rope is 279 ft and as mentioned it is cut into three pieces. Since the first piece has no length we can give it a variable of x . Piece two is twice as long as piece one, so we can give it a value of 2x . Lastly, piece three is the same as piece two, so it would also be 2x.
So we can now say the following:
[tex]x + 2x + 2x = 279ft[/tex] .... now we can solve for x.
[tex]5x = 279[/tex]
[tex]x = 55.8 ft[/tex]
So we can see that piece one is 55.8 ft long . Now we can use this value to find pieces two and three.
[tex]2x = P2[/tex]
[tex]2(55.8) = P2[/tex]
[tex]111.6 = P2[/tex]
So pieces two and three are 111.6 ft long
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
I Need Help!! Answer Please!!
Answer:
50 degrees
Step-by-step explanation:
all inside angles in every triangle can be added up to equal 180 degrees.
this is a right angle, so one has to be 90 degrees
on the bottom right it's marked 140 degrees on the outside, in order to find the inside angle, you need to subtract 140 from 180, which gives you 40 degrees
180-90=90
90-40=50
so the answer is 50
if that's not clear enough leave a comment, hope this helps!
Answer:
50°
Step-by-step explanation:
Inside angles of a triangle = 180°
The triangle shown is a right triangle.
Therefore, it is 90°
180 - 90 = 90
90 - 40 = 50
Answer = 50°