Let's take as x and y the age of the man and of his son
We will do a system, so we can satisfy all the request:
1. sum of ages = 2 (difference)
2. product = 675
[tex]\left \{ {x + y = 2 (x-y)} \atop {x*y=675}} \right.[/tex]
semplify the first equation
x + y = 2x -2y
now let's choose one of the incognite (x) and we solve for it
x - 2x = - 2y - y
- x = - 3y
x = 3y
Let's substitute this solution in the second equation
[tex]\left \{ {x=3y} \atop {(3y)*y=675}} \right.[/tex]
note: x = 3y, so in the second equation x * y = 3y * y
Now let's solve the second equation
3y * y = 675
3y² = 675
y² = 675 / 3 =
y² = 225
y = 15
Son's age is 15
Man's age is 15 * 3 = 45 (See the first equation [x = 3y])
Does this graph show a function? Explain how you know.
5
O A. Yes; the graph passes the vertical line test.
O
B. No; there are y-values that have more than one x-value.
C. Yes; there are no y-values that have more than one x-value.
O
D. No; the graph fails the vertical line test.
Answer: D. No; the graph fails the vertical line test.
The vertical line test is a tool used to determine if we have a function. If we can draw a single straight vertical line through more than one point on the red curve, then the graph is said to have failed the vertical line test. Consequently, this leads to the relation not being a function.
For this circle graph, we can draw a vertical line through more than one point, which is why we don't have a function here.
Put another way, there are inputs (x) that produce more than one output (y), so that's why we don't have a function.
The graph shows a function The graph fails the vertical line test.
A vertical line test is a tool used to determine if we have a function.
What is the vertical line test?The vertical line test is a method that is used to determine whether a given relation is a function or not. The approach is rather simple.
If we can draw a single straight vertical line through more than one point on the red curve, then the graph is said to have failed the vertical line test.
Consequently, this leads to the relation not being a function.
For this circle graph, we can draw a vertical line through more than one point, which is why we don't have a function here.
Put another way, there are inputs (x) that produce more than one output (y), so that's why we don't have a function.
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2. Solve for z and express your answer in interval notation: 10 – 4z < 20
Answer:
z > -5/2
Step-by-step explanation:
Since both sides are divided by a negative number, the equality is switched.
10 - 4z < 20
(10 - 4z) - 10 < 20 - 10
-4z < 10
(-4z)/-4 < 10/-4
z > -5/2
The solution for z will be;
⇒ z ∈ (- 2.5 , ∞ )
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ 10 - 4z < 20
Now,
Since, The inequality is,
⇒ 10 - 4z < 20
Solve for z as;
⇒ 10 - 4z < 20
⇒ 10 - 4z + 4z < 20 + 4z
⇒ 10 < 20 + 4z
⇒ 10 - 20 < 4z
⇒ - 10 < 4z
⇒ - 2.5 < z
⇒ z ∈ (- 2.5 , ∞ )
Thus, The interval notation is,
⇒ z ∈ (- 2.5 , ∞ )
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Liar has a red ribbon that is 2 and 1/12 incest long. She has a blue ribbon that is 4 times as many investors long how many investors long is the blue ribbon
Answer:
I think it would be 8 and 1/3 inches long
Step-by-step explanation:
P.S. You spelled inches wrong
How did the first line get to the second line??? (Check Picture)
Step-by-step explanation:
[tex]15( \frac{11\pi}{6} ) \\ 15 \div 3 = 5 \\ 6 \div 3 = 2 \\ = 5( \frac{11\pi}{2} )[/tex]
[tex]11 \times 5 \\ = \frac{55\pi}{2} [/tex]
Find the solution of the system of equations
shown on the graph.
Answer:
(-4, 3)
Step-by-step explanation:
From the graph, it looks like the two lines intersect at pint (-4, 3).
Solve each absolute value equation and match them with the correct solution.
Answer:
Step-by-step explanation:
First we must understand that absolute value of a function returns both positive and negative function.
1) Given |x-6| = 5
For the positive value of the function:
x-6 = 5
Add 6 to both sides
x-6+6 = 5+6
x = 11
For the negative function:
-(x-6) = 5
Open the parentheses
-x+6 = 5
Subtract 6 from both sides
-x+6-6 = 5-6
-x = -1
x = 1
Hence x = 1, x = 11
2 ) Given |3x-7| = 12
For the positive value of the function:
3x-7 = 12
Add 7 to both sides
3x-7+7 = 12+7
3x = 19
x = 19/3
For the negative function:
-(3x-7) = 12
Open the parentheses
-3x+7 = 12
Subtract 7 from both sides
-3x+7-7 = 12-7
-3x = 5
x = -5/3
Hence x = 19/3, x = -5/3
3) Given |2x+9| - 10= 5
For the positive value of the function:
2x+9-10= 5
2x-1 = 5
Add 1 to both sides
2x-1+1 = 5+1
2x = 6
x= 3
For the negative function:
-(2x+9)-10 = 5
Open the parentheses
-2x-9-10 = 5
-2x-19 = 5
Add 19 to both sides
-2x-19+19 = 5+19
-2x= 24
x = -24/2
x= -12
Hence x = 3, x = -12
4) ) Given |5x-3|+12 = 4
For the positive value of the function:
5x-3+12= 4
5x+9 = 4
Subtract 9 from both sides
5x+9-9 = 4-9
5x = -5
x= -1
For the negative function:
-(5x-3)+12= 4
Open the parentheses
-5x+3+12 =4
-5x+15 = 4
Subtract 15 from both sides
-5x+15-15 = 4-15
-5x = -11
x = 11/5
Hence x = -1, x = 11/5
(-2÷3)^-3 ÷ x = (9÷8)^-2
Answer:
- 3⁷/2⁹
Step-by-step explanation:
(-2÷3)⁻³ ÷ x = (9÷8)⁻²-(2⁻³)×3⁽⁻¹⁾ˣ⁽⁻³⁾ ÷ x = (3²)⁻²×(2⁻³)⁻²-2⁻³×3³÷x = 3⁻⁴×2⁶x = -2⁻³×3³ ÷ (3⁻⁴×2⁶)x = - 2⁻³⁻⁶×3³⁻⁽⁻⁴⁾x = -2⁻⁹×3⁷x = - 3⁷/2⁹Solve −2x − 15 = 6x + 9. (1 point) 3 −3 −1 6
Answer:
-2x-15=6x+9
-2x-6x=9+15
-8x=24
x=-24/8
x=-3
You roll a die. If it comes up a 1 or 2, you win $200. If not, you get to roll again. If you get a 1 or 2 the second time, you win $100. If not, you lose. a) Create a probability model for the amount you win. b) Find the expected amount you'll win.
On the first roll, you have a 1/3 probability of rolling a 1 or 2 and thus winning $200.
There's a 2/3 probability of not rolling a 1 or 2 on the first roll. On the second roll, there is again a 1/3 probability of rolling a 1 or 2, and 2/3 probability otherwise, so that there is a 1/3*2/3 = 2/9 probability of getting a 1 or 2 and thus winning $100, and 2/3*2/3 = 4/9 probability of losing.
(a) Let [tex]W[/tex] be a random variable representing the winnings from playing the game. It has the probability mass function
[tex]P(W=w)=\begin{cases}\frac13&\text{for }w=\$200\\\frac29&\text{for }w=\$100\\\frac49&\text{otherwise}\end{cases}[/tex]
(b) Compute the expected value of [tex]W[/tex]:
[tex]E[W]=\displaystyle\sum_w w\,P(W=w)=\$200\cdot\frac13+\$100\cdot\frac29+\$0\cdot\frac49\approx\$88.89[/tex]
Businesses in a country are listed by size: small, medium, and large. Explain why business size is an example of an ordinal-scaled variable. A. The size of a business is ordinal-scaled because it has numerical values that arise from a measuring process. B. The size of a business is ordinal-scaled because it has values that represent quantities. C. The size of a business is ordinal-scaled because it has values that can be used as an order or rank of a categorical variable. D. The size of a business is ordinal-scaled because it has numerical values that arise from a counting process.
Answer: C. The size of a business is ordinal-scaled because it has values that can be used as an order or rank of a categorical variable.
Step-by-step explanation: Ordinal variables are simply categorical in nature just like nominal variables, however, the difference exists in the fact that ordinal labels posses an ordered rank or level unlike nominal variables. Though the extent or width of the difference between these labels cannot be ascertained. In the scenario above, size of businesses are labeled qualitatively with labels such as : small, medium and large. This labels depicts and follow a certain order with small being the least, then medium, then large. Telling us large businesses are superior in size to small and medium and medium is superior to large. Though the extent of the difference cannot be accurately ascertained.
trig: Solve Quadratic Equations by Factoring help with 2b and 2c
Answer:
2b)x=1/3 or x= -4
2c) x= 0 or x= -2/3
Step-by-step explanation:
To factor ax² + bx + c, use the AC method.
Multiply a and cFind factors of ac that add up to bDivide those two factors by a. Reduce the fractions.The numerators are the constants, and the denominators are the coefficients.(b) 3x² + 11x − 4 = 0
a = 3, b = 11, c = -4ac = (3)(-4) = -12Factors of -12 that add up to 11 are 12 and -1.Divide by 3: -1/3 and 12/3 = 4/1The factors are 3x − 1 and x + 4.(3x − 1) (x + 4) = 0
3x − 1 = 0, or x + 4 = 0
x = 1/3, or x = -4
(c) 12x² + 8x = 0
Here, you can simply factor the greatest common factor, 4x.
4x (3x + 2) = 0
4x = 0, or 3x + 2 = 0
x = 0, or x = -2/3
Janice correctly answered 21 of the 24 question. What percent of the questions did she answer correctly?
Tell whether x and y show direct variation. Explain your reasoning. x=y+2
Answer:
x and y do not show direct variation
Step-by-step explanation:
Two quantities x and y show direct variation when
y = kx
and k ≠ 0
Given x = y + 2
Making y the subject of the formula:
y = x - 2
The equation above cannot be written in the form y = kx
This means that x and y are not in a proportional relationship
For instance, let's say when x = 4
y = (4) - 2 = 2
Now, if x is doubled, x = 8
y = (8) - 2 = 6
Therefore, doubling x does not necessarily double y, hence they are not in a direct variation.
In a triangle, the measure of the first angle is three times the measure of the second angle. The measure of the third angle is 75º more than the measure of the second
angle. Use the fact that the sum of the measures of the three angles of a triangle is 180° to find the measure of each angle.
The measure of the first angle is°?
The measure of the second angle is º?
The measure of the third angle is °?
Answer:
Angle 1= 63°
Angle 2 = 21°
Angle 3 = 96°
what is formula for circumfrences
The circumference of a circle, which is another way of saying the perimeter of a circle, can be found using the formula 2πr.
Note that π represents the irrational number 3.14159... which
rounds to 3.14 and r represents the radius of the circle.
Therefore, since π = 3.14, another way of writing the formula
for the circumference of a circle is 2 · 3.14r or 6.28r.
Answer:
circumference = 2 π r
or
circumference = π d
Step-by-step explanation:
r = radius of a circle
d = diameter
therefore
circumference = 2 π r
or
circumference = π d
Round 141.999 to the next tenth
Answer:
142
Step-by-step explanation
A candy factory wants to compare a new machine to their current machine. Both machines produce y boxes of candy for every hour x. The current machine is represented by the equation f(x). The new machine is represented by the equation g(x). f(x) = 15x + 90 g(x) = 30x + 30 After what number of hours will the amount of candy produced be the same for both machines?
Answer:
In 4 hours.
Step-by-step explanation:
Just equate f(x) = g(x). So:
15x + 90 = 30x + 30
60 = 15x
x = 4 hours.
In 4 hours the amount of candy produced be the same for both machines.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
It is given that A candy factory wants to compare a new machine to their current machine. Both machines produce y boxes of candy for every hour x. The current machine is represented by the equation f(x). The new machine is represented by the equation g(x). f(x) = 15x + 90 g(x) = 30x + 30.
The value of time will be calculated below:-
Just equate f(x) = g(x).
15x + 90 = 30x + 30
60 = 15x
x = 4 hours.
Therefore, In 4 hours the amount of candy produced is the same for both machines.
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I NEED HELP PLEASE
Answer:
m= 0
y^m = x ^8m over z ^5m
x^ 8m = y^m z5^m
z^ 5m = x^8m over y^m
Step-by-step explanation:
A retailer is having a promotional sale for 35% off all items. There is a 7% sales tax added to the price. Which
represents the situation, where x is the original cost of the item(s)?
Answer:
0.6955x
Step-by-step explanation:
Given the following :
Promotional discount on items = 35%
Sales tax on items = 7%
Original cost of items = x
First we obtain the cost of item after the promotional discount is applied
Cost of item :
Original price - (original price * promotional discount)
x - (x * 0.35) = x - 0.35x
Cost of item = 0.65x
Then the sales tax is added :
Total amount after tax:
Cost of item + (cost of item × sales tax rate)
0.65x + (0.65x * 0.07)
0.65x + 0.0455x
= 0.6955x
Answer:
0.6955x
edge 2020 .
Help meeeee time card. Weekly time card $11hr
Answer: it would be $96.25
Step-by-step explanation:
In the am, it’s 4 hours. 4x11= $44
In the pm it’s 4 hours and 45mins. 4x11=44
The for the 45 mins. Multiply 45x11= 495 then divide by 60. That gives you $8.25. When you add them all together, you get 96.25
Which could describr the motion of an object in distance and displacement
Answer:
Hope this will help you :)
Step-by-step explanation:
In the diagram above <1=135 find the measure of <2
Answer:
∠ 2 = 45°
Step-by-step explanation:
∠ 1 and ∠ 2 are same- side interior angles and are supplementary, thus
∠ 2 = 180° - ∠ 1 = 180° - 135° = 45°
Answer: 45
Step-by-step explanation:
7. x – a is the factor of a polynomial P(x) if P(a) is equal to
options:
A) 2
B) 1
C) 3
D) 0
Answer:
[tex]\huge \boxed{\mathrm{D) \ 0}}[/tex]
Step-by-step explanation:
x - a is a factor of the polynomial P(x).
P(a) means the input for the polynomial is a.
a - a = 0
Anything multiplied by 0 is 0. If the factor is equal to 0 then the whole polynomial will be equal to 0.
Answer:
D) 0
Step-by-step explanation:
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 404 gram setting. It is believed that the machine is underfilling the bags. A 27 bag sample had a mean of 402 grams with a variance of 676. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?
Answer:
There is no sufficient evidence to support the claim that the bags are underfilled
Step-by-step explanation:
We are given;
n = 27 bags
Sample mean;X = 402 gram
Population mean;μ = 404 gram
Variance = 676
We know that, standard deviation(σ) = √variance
Thus;
σ = √676
σ = 26
The hypotheses are;
Null hypothesis; H0: μ = 404
Alternative hypothesis; HA: μ < 404
Let's find the z-score from the formula;
z = (X - μ)/(√σ/n)
z = (402 - 404)/√(26/27)
z = -2.04
From the z-distribution table attached, we have a p-value of 0.02068
This is less than the significance value of 0.01 and thus we will reject the null hypothesis and conclude that there is no sufficient evidence to support the claim that the bags are underfilled
PLEASE HELP !!! The height of a rectangle is twice the width and the area is 32. Find the dimensions.
Answer:
The rectangle has a width of 4 and a height of 8
Step-by-step explanation:
Let the height of the rectangle be H and the width be W.
We know the height of the rectangle is twice the width, so:
H = 2W
The area of a rectangle, A, is given by A = W * H, so in this case:
32 = W * 2W
32 = 2W²
W² = 16
W = 4
Knowing that the width is 4, the height must be 8. This gives us an area of 32.
how do i solve this absolute value equation |3x-2|+4=7?
Answer:
{3x-2}+4=10
Step-by-step explanation:
Which of the following is the midpoint of a line segment with endpoints -4 and 7?
A. 1.5
B. 0
C. -3
D. 5.5
Answer:
A.1.5 is the correct answer.
Answer:
A. 1.5
Step-by-step explanation:
End points of the line segment:
- 4 and 7Length of line segment:
7 - (-4) = 11Half length of the line segment:
11/2 = 5.5Midpoint is at same distance from either end:
7 - 5.5 = -4 + 5.5 = 1.5Midpoint is 1.5
The dependent variable y is missing in the given differential equation. Proceed as in Example 1 and solve the equation by using the substitution u = y'.
y'' + (y' )^2 + 4 = 0
Answer:
y = In | cos(2x + c ) | + c
Step-by-step explanation:
y" + (y')^2 + 4 = 0
substituting u = y'
u' + u^2 + 4 = 0
hence : u' = - (u^2 + 4 )
[tex]\frac{u'}{-(u^2 + 4)}[/tex] = 1 ------- (1)
integrating both sides of the equation 1
[tex]1/2 \int\limits^1_1 {\frac{2du}{(u^2+4)} } \, = x + c[/tex]
x + c = [tex]- \frac{1}{2} arc tan (\frac{u}{2} )[/tex] hence u = -2 tan(2x + c )
remember u = y'
y' = -2 tan(2x + c) ------ (2)
integrating both sides of the equation 2
y = ∫ [tex]\frac{-sin u}{cos u } du[/tex]
therefore Y = In | cosu | + c
y = In | cos(2x + c ) | + c
i will give you brainliest if you right down the answer and explain it
Answer:
[tex]\sqrt{113\\[/tex]
Step-by-step explanation:
set the problem up like this:
[tex]\sqrt{(x2-x1)^{2} +(y2-y1)^2[/tex]
(x1,y1) (x2,y2)
x1=-3
y1+3
x2=5
y2=-4
The equation should look like this:
[tex]\sqrt{(5-(-3))^2 + (-4-3)^2[/tex]
Then you solve it and 113 is the square root in between.
Hope it helps...
Which statement is true?
A. This scatter plot has no clusters and no outliers.
B. This scatter plot has one cluster and no outliers.
C. This scatter plot has one cluster and three outliers.
D. This scatter plot has one cluster and one outlier.
A cluster is a small group of dots close together. An outlier is a single dot far away from the rest of the dots.
The above graph has a small cluster around y 6&7 and has an outlier at (9,5)
The answer should be D.
Answer:
The correct answer is D. This scatter plot has one cluster and one outlier.
Step-by-step explanation:
From looking at the scatterplot, the majority of the points are collected on the upper left side of the coordinate grid, creating a cluster. This just means that these data points are located close to one another.
If we continue to look at the scatterplot, we can see that there is one data point at approximately (9, 5.25) that is very far from the other data points. This point is considered to be an outlier because it does not follow the general trend of the other data points and changes the data analysis significantly if included in the calculations.
Hope this helped!