Answer:x=8 Y=-6
Step-by-step explanation:
14-2.5x=1.5x-18
+18. +18
32-2.5x=1.5x
+2.5x =2.5x
32= 4x
Divide 4 to both sides you get
8=x
Y=14-2.5(8)
Y=14-20
Y=-6
Coach kunal stacks all of the tennis balls in a square pyramid. The number of tennis balls, P(n), in n layers of the square pyramid is given by P(n) = P(n - 1) + n^2. Which could not be the number of tennis balls Coach Kunal has? A. 30 B. 5 C. 14 D. 9
Answer:
Answer is D.9Step-by-step explanation:
The number of tennis balls, P(n) , in n layers of the square pyramid is given. by: P(n) = P(n - 1) + n ^ 2As the stack of the tennis balls is in shape of a square pyramid, that means in the top layer, there will be one ball. So, P(1) = 1Now, if n = 2 , then P(2)=P(2 - 1)+ (2) ^ 2 = P(1) + 4 = 1 + 4 = 5If n = 3 , then P(3)=P(3 - 1)+ (3) ^ 2 = P(2) + 9 = 5 + 9 = 1414If n = 4 then P(4)=P(4 - 1)+ (4) ^ 2 = P(3) + 16 = 14 + 16 = 3014If n = 4 then P(4)=P(4 - 1)+ (4) ^ 2 = P(3) + 16 = 14 + 16 = 30That means, the number of tennis balls from the top layer will be: 1, 5, 14, 30,14If n = 4 then P(4)=P(4 - 1)+ (4) ^ 2 = P(3) + 16 = 14 + 16 = 30That means, the number of tennis balls from the top layer will be: 1, 5, 14, 30,So, the number of tennis balls that Coach Kunal could not have is 9.Which of the following are identities?
Answer:
A. III only
Step-by-step explanation:
In mathematics, an identity is one of the characteristics of algebraic expressions.
Given variable a and b in an algebraic expression, an identity is defined as an equality that remains the same no matter the values that we choose for either variable a or b.
Identity in mathematics makes it very easy to solve algebraic expressions. The two sides of an identity in an algebra can easily be exchanged for each other.
In the above question, we are given 3 Options.
I) 3(5 + 2x) = 15 + 6x
II) y = x + 3
III) (x² - y²) = (x + y) (x - y)
Option I) 3(5 + 2x) = 15 + 6x
Is showing distributive property in mathematics.
Distributive property is :
a(b + c) = ab + ac
Option I is not an identity , therefore it is wrong.
Option II) y = x + 3 is just an algebraic expression.
Only Option III is an identity. This is because it follows the rule of
(a² - b²) = (a + b) (a - b)
We can prove and confirm this be solving the algebraic expression
(x + y) (x - y)
We expand the bracket
x² - xy +xy - y²
x² - y²
Therefore, option A is the correct option.
In a triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= square root 2 .
Answer:
AC=2.06cm
Step-by-step explanation:
AC^2=AD^2+CD^2
AC^2=1.5^2+1.4142^2
AC^2=2.25+2=4.25
....
[tex] \sqrt{ac {}^{2} } [/tex]
=
[tex] \sqrt{4.25 = } 2.06[/tex]
Answer:
AC=2.06 cm
Step-by-step explanation:
Use the tables below to find (p - 9)(2).
Answer:
5
Step-by-step explanation:
p(2) - q(2)
3 - (-2)
3 + 2
= 5
A lottery ticket costs $5. You pick 3 two-digit numbers (anything from 00 to 99) in order. If you match the first number only, you win $200. If you match the first two numbers and not the third, you win $5000. If you match all three numbers, you win $100,000. In two or more complete sentences, explain whether or not the game is fair. In your explanation, include all necessary calculations.
Answer:
00 to 99 are 100 numbers.
If you match the first number only, you win $200. The Probability for this is 1/100.
If you match the first two numbers and not the third, you win $5000. The Probability for this is 1/50.
If you match all three numbers, you win $100,000. The Probability for this is 3/100.
And, If you are a customer, You will think is fair for you.
But if you are the lottery tickets company, you will think is not fair for you.
It depends who you are.
the game isn't fair because 100,000/3=3333 1/3, so each number should be worth $3333.3333...... dollars but you can't really give 1/3 dollars so the game is impossible to be fair. Also, if you match the first two numbers you apparently get $5000. That's also not fair because each number is worth $50 dollars more than if you get the first number matched. So, the game isn't fair but it will be pretty much impossible to be fair.
What is the solution to the system of equations graphed below?
Answer: C. (1, 4)
Step-by-step explanation:
The point where the two lines meet or intersect is the solution to the system of equations graphed. And in this case, the lines intersect at (1, 4).
Pls help me I need the help!
Answer:
1a) 15, 7, x+5
1b) 7
2a) 18, 3r
Step-by-step explanation:
1a) Since Claire is 5 years older, she will always be her cousin's age plus 5
1b) Claire is 5 years older, so Claire's cousin is 5 years younger. So, Claire's cousin is Claire's age minus 5
2a) Diego will have the amount of Han's books times 3
Answer:
Clare Questions:
Cousin: 10, Clare: 15
Cousin: 2, Clare: 7
Cousin: x, Clare: x + 5
Cousin: 7, Clare: 12
Diego Questions:
Han: 6, Diego: 18
Han: can't tell if it is a 0 or n, Diego: 0 or 3n, respectively
Step-by-step explanation:
Since Clare is older than her cousin by 5, they will both age at the same rate, thus she will always be 5 years older.
example: if her cousin is 10, Clare will be 10 + 5 years older, therefore being 15.
Since DIego has 3 times as many books than Hans, it multiplies by 3.
example: if Han has 6 books, multiply 6 by 3 and you get Diegos amount, 18.
The total amount of water a tank can hold is 14 and one-half gallons. Raul wants to find out how many 1 and one-fourth-gallon buckets of water can be used to fill the tank. Which expressions could be used to represent this scenario? Select two options.. StartFraction 29 over 2 EndFraction divided by StartFraction 5 over 4 EndFraction StartFraction 29 over 2 EndFraction times StartFraction 5 over 4 EndFraction StartFraction 29 over 2 EndFraction times StartFraction 4 over 5 EndFraction StartFraction 2 over 29 EndFraction times StartFraction 5 over 4 EndFraction StartFraction 29 over 2 EndFraction divided by StartFraction 4 over 5 EndFraction
Answer:
Water a tank can hold = 14 1/2 = 29/2
Volume of bucket 1 1/4 = 5/4
The expresson can be
29/2 / 5/4
No. of buckets used = 29/2 x 4/5
Answer:
b and e
Step-by-step explanation:
Write the slope-intercept form of the equation that passes through the point (0,-3) and is perpendicular to the line y = 2x - 6 a. y = -2x + 3 b. y = 2x - 3 c. y = -1/2x - 3 d. y = -1/2x + 3
Answer:
y = (-1/2)x - 3
Step-by-step explanation:
The line y = 2x - 6 has a slope of 2 and so any line perpendicular to it has a slope which is the negative reciprocal of 2: -1/2.
If this perpendicular line passes through (0, -3), then the slope-intercept equation y = mx + b becomes -3 = (-1/2)(0) + b, or -3 = b, and the desired
equation is
y = (-1/2)x - 3
One day, a person went to a horse racing area. Instead of counting the number of humans and horses, he counted 74 heads and 196 legs. How many humans and horses were there?
Answer:
Let humans be x and horses be y
Both have one head each,so x+y=74 (1)
Humans have 2 legs each and horses 4 legs each…… so 2x+4y=196 (2)
In first equation x+y=74 then y=74~x (3) ……… .By solving both equations we have as under… x+3y=122 x=122-3y (4)…. Now in equation 4 we put the value of y taken from equation 3 so it will be x=122~3(74-x)…. x=122-222+3x…………. bringing x on one side x-3x=122~222 therefore -2x=~100….. x=50… put the value of x in first equation… x+y=74… 50+y=74… y=74~50…..… y=24… Now it is concluded that Humans are 50 and Horses are 24.. Now you put the values of x & y in 1st and 2nd equation … you will get x+y=74.. 50+24=74………..2x+4y=196…2×50+4×24=196.. it is proved thru equation.
Please help with this
Answer:
5/2
Step-by-step explanation:
We take the ratio of a side of ABC over the same side on DEF
AB/ DE
35/14
Divide top and bottom by 7
5/2
P(2, 2), Q(1, -3), R(-4, 2), S(-3, 7) Using the information above, answer the following questions. Find the length of RS Find the length of SP Find the length of PQ Find the length of RQ Use this information to determine if the quadrilateral a parallelogram.
Answer:
Yes the Quadrilateral is a Parallelogram.
Step-by-step explanation:
A parallelogram can be defined as a quadrilateral i.e a geometric shape with four sides that has opposite sides parallel and equal in length.
From the question, we are given the following points
P(2, 2), Q(1, -3), R(-4, 2), S(-3, 7)
Given points: (x1, y1) and (x2, y2)
The formula would be
√(x2 - x1)² +(y2 - y1)²
a) P(2, 2), Q(1, -3)
Length PQ = √(1 - 2)² +(-3 - 2)² = √-1² + -5² = √26
b) R(-4, 2), S(-3, 7)
Length RS = √(-3 - (-4))² + (7 - 2) ² = √ 1² + 5² = √26
c) R(-4, 2), Q(1, -3)
Length RQ = √(1 - (-4))² + (-3 - 2)² = √5² + 5² = √(25 + 25) = √50
d) S(-3, 7), P(2, 2)
Length SP = √(2 - (-3))² + (2 - 7)² = √5² +(-5)² = √(25 + 25) = √50
From the above solution, we can see that
Length PQ = Length RS
Length RQ = Length SP
This means the opposite sides are parallel and equal in length, hence it is a Parallelogram.
Owners of a recreation area are filling a small pond with water. Let y represent the total amount of water in the pond (in liters). Let x represent the total number of minutes that water has been added. Suppose that x and y are related by the equation y=400+32x . Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number. What is the change per minute in the amount of water in the pond? What was the starting amount of water in the pond?
Answer:
32400Step-by-step explanation:
Lets start by defining the numbers in the equation.
This equation is in slope-intercept form meaning that it is y=mx+b or y = b+mx they are both the same
In slope-intercept form,
m = slope or rateand b = y-intercept
Th equation is y=400+32x so now we know
b=400and m=32For the first question the change per minute is the rate so it is 32.
For the second question the starting amount is the same as the y-intercept so it is 400.
You want to design a survey to determine how much money people are willing to spend
on concert tickets. Which of the following methods would be most practical and have
the least bias?
Choose 4 neighborhoods at random and poll every home in those
neighborhoods.
Poll 10% of the homes in the area chosen at random.
Poll the first 100 people who enter the mall.
Poll everyone in the area.
Answer:
The correct option is;
Choosing 4 neighborhoods at random and poll every home in those neighborhoods
Step-by-step explanation:
Given that the survey relate to how much money people are willing to spend on on concert tickets with the goal of being practical and unbiased, we have;
Required sampling = Random Sampling
The preferable type of random sampling is either;
1) Simple random sampling
Sampling a given percentage of the homes in the area randomly
2) Clustered random sampling
Completely polling entire population of randomly selected area
Given the practicability of sampling concert goers, since people may have different interests, a better representative sample will be to perform the clustered random sampling approach by choosing 4 neighborhoods at random and poll every home in those neighborhoods.
A store sells 3 categories of kitchen items: cups, bowls, and spoons. There are 5 types of cups, 4 types of bowls, and 2 types of spoons. How many different combinations can you buy in this store of: A set of a bowl, cup, and spoon
On a coordinate plane, 2 quadrilaterals are shown. Quadrilateral Q R S T has points (negative 1, 0), (5, 0), (3.5, negative 6) and (negative 2.5, negative 6). Quadrilateral Q prime R prime S prime T prime has points (negative 1, 2), (1, 2), (0.5, 0), and (negative 1.5, 0). Quadrilateral QRST is dilated and translated to form similar figure Q'R'S'T'. What is the scale factor for the dilation?
Answer:
[tex]\dfrac{1}{3}[/tex].
Step-by-step explanation:
In quadrilateral QRST, Q(-1,0), R(5,0), S(3.5,-6), T(-2.5,-6).
In quadrilateral Q'R'S'T', Q'(-1,2), R'(1,2), S'(0.5,0), T'(-1.5,0).
Distance formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula , we get
[tex]QR=\sqrt{(5-(-1))^2+(0-0)^2}=\sqrt{6^2}=6[/tex]
[tex]Q'R'=\sqrt{(1-(-1))^2+(2-2)^2}=\sqrt{2^2}=2[/tex]
Now,
[tex]\text{Scale factor}=\dfrac{Q'R'}{QR}[/tex]
[tex]\text{Scale factor}=\dfrac{2}{6}[/tex]
[tex]\text{Scale factor}=\dfrac{1}{3}[/tex]
Therefore the scale factor is [tex]\dfrac{1}{3}[/tex].
The given transformation of quadrilateral QRST to quadrilateral Q'R'S'T'
are a dilation and a translation, therefore, QRST is similar to Q'R'S'T'.
[tex]\mathrm{The \ scale \ factor \ of \ the \ dilation\ between \ QRST \ and \ Q'R'S'T' \ is} \ \dfrac{1}{3}[/tex]
Reasons:
The vertices of the quadrilateral are;
Quadrilateral QRST
Q(-1, 0)
R(5, 0)
S(3.5, -6)
T(-1, 2)
Quadrilateral Q'R'S'T'
Q'(-1, 2)
R'(1, 2)
S'(0.5, 0)
T'(-1.5, 0)
The given transformation that gives quadrilateral Q'R'S'T' from quadrilateral QRST are a dilation and a translation.
Required:
The scale factor of the dilation
Solution:
[tex]\mathrm{The \ scale \ factor \ of \ the \ dilation} = \dfrac{\mathrm{Length \ of \ \overline{Q'R'} }}{\mathrm{Length \ of \ \overline{QR}} }[/tex]
Length of [tex]\overline{Q'R'}} }[/tex] = 1 - (-1) = 2
Length of [tex]\overline{QR}} }[/tex] = 5 - (-1) = 6
Therefore;
[tex]\mathrm{The \ scale \ factor \ of \ the \ dilation} = \dfrac{2}{6} = \dfrac{1}{3}[/tex]
Learn more here:
https://brainly.com/question/12077721
3x-2=16 pls help!!!!!!!
Answer:
x = 6
Step-by-step explanation:
3x - 2 = 16
3x = 16 + 2
3x = 18
x = 18/3
x = 6
Answer:
x=6
Step-by-step explanation:
3x-2=16
+2 +2
3x = 18
÷3 ÷3
x=6
The angles of a quadrilateral are in the ratio of 2:6:9:13
Find all the angles of the quadrilateral
Answer:
24° , 72° , 108° , 156°Step-by-step explanation:
Let the angles be 2x , 6x , 9x , 13x
We know that the sum of quadrilateral is 360°
Now,
[tex]2x + 6x + 9x + 13x = 360[/tex]
Calculate the sum
[tex]30x = 360[/tex]
Divide both sides of the equation by 30
[tex] \frac{30x}{30} = \frac{360}{30} [/tex]
Calculate
[tex]x = 12[/tex]
Replacing the value,
2x = 2 * 12 = 24°
6x = 6 * 12 = 72°
9x = 9 * 12 = 108°
13x = 13 * 12 = 156°
So, the angles are 24° , 72° , 108° , 156°
Hope this helps...
Good luck on your assignment...
Answer:
Below in bold.
Step-by-step explanation:
2+6+9+13 = 30.
Now there are 360 degrees in a a quadrilateral.
So the value of the shortest angle = 2/30 * 360
= 1/15 * 360
= 24 degrees.
In the same way the value of the other 3 angles is:
6/30 * 360, 9/30 * 360 and 13/30 * 360
= 72, 108 and 156 degrees.
Find an equivalent function to f(x) = 5(3)^3x. (5 points)
Answer:
[tex]B. f(x) = 5(27)^x[/tex]
Step-by-step explanation:
Well lets graph it first,
Look at the image below ↓
By looking at the image we can tell that answer choice [tex]B. f(x) = 5(27)^x[/tex].
Thus,
answer choice B is correct.
Hope this helps :)
Answer:
The correct result would be f(x) = 5(27)x.
Step-by-step explanation:
If you would like to find an equivalent function to f(x) = 5(3)^(3x), you can do this using the following steps:
f(x) = 5(3)^(3x) = 5(3^(3x)) = 5(27)^x = 5(27)x
hope this helped :)
help please heeeeeeeeeeeeeeeeeeeeeeeeeeelp
Answer:
8.29166
Step-by-step explanation:
3.5_0.375+5.166666
Answer:
[tex]8 \frac{7}{24} [/tex]
Step-by-step explanation:
Please see attached picture for full solution.
Solve 3n - 5p + 2n = 10p for n
Answers above
Answer:
D
Step-by-step explanation:
3n - 5p + 2n = 10p
Add like terms.
5n - 5p = 10p
Add 5p to both sides.
5n = 10p + 5p
5n = 15p
Divide both sides by 5.
n = 15/5p
n = 3p
The solution of expression for n is,
⇒ n = 3p
We have to given that,
An expression to solve,
⇒ 3n - 5p + 2n = 10p
Now, We can solve the expression for n as,
⇒ 3n - 5p + 2n = 10p
Combine like terms,
⇒ 3n + 2n = 10p + 5p
⇒ 5n = 15p
Divide by 5 both side,
⇒ n = 15p/5
⇒ n = 3p
Therefore, The correct option is,
D. n = 3p
Learn more about the equation visit:
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#SPJ2
a. 1620
b. 180
c. 38
d. 29
Answer:
V =1620 pi cm^2
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
V = pi ( 9)^2 * 20
V =1620 pi cm^2
Which choice shows the image of quadrilateral WXYZ after a reflection over the y-axis followed by a translation down 2 units?
Answer:
Choices are not provided, but you can answer the question as follows: take the coordinates of quadrilateral WXYZ and apply:
W(xW, yW) -> W'(-xW, yW-2)
X(xX, yX) -> X'(-xX, yX-2)
Y(xY, yY) -> Y'(-xY, yY-2)
Z(xZ, yZ) -> Z'(-xZ, yZ-2)
For example, if point W is located at (1, 1), W' would be located at (-1, -1)
Step-by-step explanation:
Reflection over the y-axis transforms point (x, y) into (-x, y)
Translation down 2 units transforms point (x, y) into (x, y-2)
Answer:
The first choice hope this helps :)
Step-by-step explanation:
by what rational no. should -7/85 be multiplied to obtain 1/17?
Answer:
-1/10115
Step-by-step explanation:
Let x be the rational number.
-7/85 × x = 1/17
x = 1/17 ÷ -7/85
x = 1/(17 × -7 × 85)
x = 1/(-10115)
x = -1/10115
The rational number is -1/10115.
Answer:
- 5/7
Step-by-step explanation:
-7/85*x= 1/17
x= 1/17 ÷ (-7/85)
x= - 1/17 × 85/7
x= - 5/7
HELPPPPP NEEDED FIRST GETS BRAINLLEST !!!! Kobe, Amari, and DJ raised $125.45 for their football team. Kobe collected $24.55 more than Amari, and DJ collected $15.60 less than Kobe. If x = the amount raised by Amari, choose the expressions that represent the amount each other player raised. x + 24.55 x + 8.95 2x – 15.60 3x + 24.55
Answer:
Kobe raised x + 24.55
Amari raised x
DJ raised 2x – 15.60
Lines L and M are parallel.
3/4
2 5
16
38° 7
-L
<-M
:
Find : m_1
Enter the number that
belongs in the green box.
[? ? ]
Enter
How do you know if x is on the rhs or the lhs?
Answer:
Step-by-step explanation:
RHS means on the right hand side
And LHS means on the left hand side
So if x is one the right side of the expression ,it is on the RHS and if it is on the left side of the expression , it is on the LHS
Find the value of x in this figure
A. 120
B. 105
C. 115
D. 110
Answer:
A. 120
Step-by-step explanation:
To find the measure of x, you would need to subtract the major arc minus the minor arc. A circle is 360 degrees so, 360-60=300. That is the major arc. Now, we use the formula, x=1/2(major-minor). When we plug the information in, we get 1/2(300-60)...1/2(240)...x=120.
Hence,
the correct option would be 120.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
(NEED HELP ASAP)Determine whether the situation calls for a survey, an observational study, or an experiment. You want to find new car buyers' opinions on the most important options. Question 7 options: survey observational study experiment
Answer: The answer is "experiment."
Step-by-step explanation:
This procedure is being used in order to validate a hypothesis, particularly in a research study. In the situation above, you have to validate whether a new reading program can increase reading comprehension or not.
The experiment consists of independent, dependent, and controlled variables. The independent variables are the ones being changed by the researcher, while the dependent variables tell whether the changes in the independent variable is significant. The controlled variables are the ones that are constant.
The dependent variable above is reading comprehension, while the new reading program is the independent variable. Examples of controlled variables are the ages of the participants. The age directly affects the reading comprehension, thus it has to be considered.
Which of the following list of ordered pairs is a function?
Answer:
C
Step-by-step explanation:
A. (4, 0) and (4, 3) have the same x coordinate (Can't happen in a function).
B. (2, 5) and (2, 1) have the same x coordinate.
C. It passes the vertical line test on a graph and no x is repeated.
D. (2, 3) and (2, 5) share the same x coordinate.
Answer:
c is correct answer.
a function from set A (x coordinate) to set B (y coordinate) a special type of relation defined from set A to set B if every element of set A is mapped with unique element of set B.