Step-by-step explanation:
If x = 3 :
x³ ÷ 3 = y
3³ ÷ 3 = y
27 ÷ 3 = y
y = 27 ÷ 3 = 9
Does the line for y = 6 have a negative slope ?
No, the slope of a horizontal line y=6 is, zero not negative.
What is a Slope?
In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.
The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.
Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,
m = change in y/change in x = Δy/Δx
Where “m” is the slope of a line.
Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter ‘m’.
Slope Formula
If P(x1,y1) and Q(x2,y2) are the two points on a straight line, then the slope formula is given by:
Slope, m = Change in y-coordinates/Change in x-coordinates = Δy/Δx
m = (y2 – y1)/(x2 – x1)
In the given equation of line y=6 .
The line crosses the y-axis at 6, as the line is always at that value. As it is a horizontal line, the slope is zero.
The equation y = 6 means for each and every value of x, y will be equal to 6.
This is the definition of a horizontal line.
By definition, the slope of a horizontal line is m = 0
When x = 0 then y = 6
Therefore, the y-intercept is: (0, 6).
Hence , the the slope of a horizontal line , m = 0.
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7. How can you use square roots to write the solution to x² = 25?
Answer:
Step-by-step explanation:
Take the square root of both sides
[tex]\sqrt{x^2}[/tex]=[tex]\sqrt{25}[/tex]
x=±5
identify the slope. pls help asap
Answer:
Step-by-step explanation:
Slope: 6/3 = -2
since the line is going from left to right, it is a negative slope
Answer:
-7/3 or 2.3333333333333
Step-by-step explanation:
X= -1 – -4 = 3
Y= -4 – 3 = -7
y = -2.3333333333333x – 6.3333333333333
or
y = -7/3 x - 19/3
So when y= -6.33 that will mean x= -2.71
Now that you have converted a terminating decimal number into a fraction, try converting a repeating decimal number into a fraction. Repeating decimal numbers are more difficult to convert into fractions. The first step is to assign the given decimal number to be equal to a variable x, For the decimal number 0.3 that means x=0.3 if x=0.3 what does 10x equal?
If a decimal number, x = 0.3 then 10x is 10 multiplying 0.3 the result is 3
What is a decimal ?A decimal is a number that is divided into two parts: a whole and a fraction.
Between integers and fractions, decimal numbers reflect the numerical value of whole
How to find 10x0.3 is x which is a decimal
10 multiplies 0.3 the result is 3
The process involve converting a fraction to a whole number as the result of multiplication changed the number system from decimal to a whole number
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What is -5 (x-2) + 6x = -7 +4
Answer:
Step-by-step explanation:
x=7/11
A Mazda traveled 326 miles in 7 hours and a Ford Explorer traveled 230 miles in 5
hours. Which car was traveling faster? Justify your work.
Mazda was traveling faster than Ford Explorer by 0.57 miles per hour.
We know that the relation between distance, speed, and time is given by:
distance = speed * time
speed = distance / time
We are given;
A Mazda traveled 326 miles in 7 hours.
A Ford Explorer traveled 230 miles in 5 hours.
Let us find the rate or speed one by one:
For Mazda;
Distance = 326 miles
Time = 7 hours
Rate = distance / time = 326 / 7 mile per hour = 46.57 mile per hour
For Ford Explorer;
Distance = 230 miles
Time = 5 hours
Rate = distance / time = 230 / 5 mile per hour = 46 mile per hour
We can analyze that Mazda was traveling faster than Ford Explorer.
Thus, Mazda was traveling faster than Ford Explorer by 0.57 miles per hour.
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What is the
relationship among the unit rate, slope, and constant
rate of change of a proportional linear relationship?
The relation among unit rate, slope and constant rate of change of a proportional linear relationship is y = kx.
What is unit rate?
The rate of change is the ratio between the x and y (or input and output) values in a relationship. Another term for the rate of change for proportional relationships is the constant of proportionality. If the rate of change is yx, then so is the constant of proportionality.
A unit rate means a rate for one of something. We write this as a ratio with a denominator of one.
The slope is defined as y = mx +b
b =1, m=k
y =k x.
Here, k is constant rate of change.
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In an economy, the price index in 2006 was 100 and the real gross domestic product (GDP) was $1,000. In 2010, the price index was 110 and the nominal GDP was $2,200. Based on that information, which of the
following can be inferred about the economy's nominal GDP in 2006 and real GDP in 2010?
A. Nominal GDP in 2006 = $2,000; Real GDP in 2010 = $1,000
B. Nominal GDP in 2006 $1,000, Real GDP in 2010 = $2,000
C. Nominal GDP in 2006= $1,100, Real GDP in 2010 = $2,420
D. Nominal GDP in 2006 $1,000, Real GDP in 2010 = $2,420
E. Nominal GDP in 2006 = $1,100; Real GDP in 2010 = $2,200
Please show your work.
The economy's nominal GDP in 2006 and real GDP in 2010 is option B) Nominal GDP in 2006 $1,000, Real GDP in 2010 = $2,000.
What does GDP Price Index mean?
A metric for gauging price inflation for American-made goods and services. The prices of American goods and services exported to other nations are included in the gross domestic product price index. This index excludes the costs Americans pay for imports.A country's gross domestic product that has been accounted for inflation is known as real GDP. Compare this to nominal GDP, which calculates GDP using today's prices without taking inflation into account.Nominal GDP in 2006=$1,000;
Real GDP in 2010=$2,000
Price index = (nominal GDP/real GDP) ×100
thus, nominal GDP in 2006=(price index × real GDP)/100
= (100×$1,000)/100
=$1,000
Real GDP in 2010= (nominal GDP/price index) ×100
= ($2,200/110) ×100
=$2,000.
Hence, the economy's nominal GDP in 2006 and real GDP in 2010 is option B) Nominal GDP in 2006 $1,000, Real GDP in 2010 = $2,000.
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The sum of three numbers is -3. If the second number is subtracted from the sum of the first and third numbers, the result is -3. If the third number is subtracted from the sum of the first and second numbers, the result is -5. Find the three numbers.
Answer:
The three numbers are -4, 0, and 1.
The sum of three numbers is -3: -4 + 0 + 1 = -3
If the second number is subtracted from the sum of the first and third numbers, the result is -3: (-4 + 1) - 0 = -3
If the third number is subtracted from the sum of the first and second numbers, the result is -5: (-4 + 0) - 1 = -5
Step-by-step explanation:
x --> first number
y --> second number
z --> third number
x + y + z = -3
(x + z) - y = -3
(x + y) - z = -5
x = -3 - y - z
(-3 - y - z + z) - y = -3
-3 - y - y = -3
-2y = 0
y = 0
(-3 - y - z + y) - z = -5
-3 - z - z = -5
-3 - 2z = -5
-2z = -2
z = 1
x = -3 - 0 - 1
x = -4
NO LINKS!! Use the diagram below, classify the angle pairs as corresponding, alternate interior, consecutive interior, or none
Answer:
a) Consecutive interior angles.
b) Alternate exterior angles.
c) Corresponding angles.
d) Alternate interior angles.
e) Corresponding angles.
f) None.
g) Alternate exterior angles.
h) Consecutive interior angles.
i) None.
j) Corresponding angles.
k) Corresponding angles.
l) Alternate exterior angles.
m) Alternate interior angles.
n) Consecutive interior angles.
Step-by-step explanation:
Transversal
A line that crosses two other lines in the same plane at two distinct points.
Corresponding angles
A pair of angles that are in the same position relative to both lines crossed by the transversal.
Alternate interior angles
A pair of angles on the inner side of the two lines that the transversal crosses, but on opposite sides of the transversal.
Alternate exterior angles
A pair of angles on the outer side of the two lines that the transversal crosses, but on opposite sides of the transversal.
Consecutive interior angles
A pair of angles on the inner side of the two lines that the transversal crosses, and are on the same side of the transversal.
a) Lines p and q are crossed by transversal line s.
Therefore, ∠4 and ∠7 are consecutive interior angles as they are on the inner side of lines p and q, and are on the same side of the transversal s.
b) Lines r and s are crossed by transversal line p.
Therefore, ∠2 and ∠11 are alternate exterior angles as they are on the outer side of lines r and s, but on opposite sides of the transversal p.
c) Lines p and q are crossed by transversal line s.
Therefore, ∠12 and ∠16 are corresponding angles as they are in the same position relative to lines p and q crossed by the transversal s.
d) Lines r and s are crossed by transversal line q.
Therefore, ∠8 and ∠13 are alternate interior angles as they are on the inner side of lines r and s, but on opposite sides of the transversal q.
e) Lines p and q are crossed by transversal line s.
Therefore, ∠11 and ∠15 are corresponding angles as they are in the same position relative to lines p and q crossed by the transversal s.
f) ∠7 and ∠10 have no relationship.
g) Lines p and q are crossed by transversal line r.
Therefore, ∠1 and ∠14 are alternate exterior angles as they are on the outer side of lines p and q, but on opposite sides of the transversal r.
h) Lines p and q are crossed by transversal line s.
Therefore, ∠12 and ∠15 are consecutive interior angles as they are on the inner side of lines p and q, and are on the same side of the transversal s.
i) ∠6 and ∠7 have no relationship
j) Lines r and s are crossed by transversal line p.
Therefore, ∠1 and ∠3 are corresponding angles as they are in the same position relative to lines r and s crossed by the transversal p.
k) Lines r and s are crossed by transversal line q.
Therefore, ∠14 and ∠16 are corresponding angles as they are in the same position relative to lines r and s crossed by the transversal q.
l) Lines r and s are crossed by transversal line q.
Therefore, ∠6 and ∠15 are alternate exterior angles as they are on the outer side of lines r and s, but on opposite sides of the transversal q.
m) Lines p and q are crossed by transversal line r
Therefore, ∠5 and ∠10 are alternate interior angles as they are on the inner side of lines p and q, but on opposite sides of the transversal r.
n) Lines r and s are crossed by transversal line q.
Therefore, ∠8 and ∠14 are consecutive interior angles as they are on the inner side of lines r and s, and are on the same side of the transversal q.
Write equations for the horizontal and vertical lines passing through the point (2, -6).
horizontal line: 0
vertical line:
Continue
0
00
X
0=0
3
The equation of the horizontal line passing through the point (2, -6) is :
y = -6
and the equation of the vertical line passing through the point (2, -6):
x = 2
We need to write equations for the horizontal and vertical lines passing through the point (2, -6)
For a vertical line the value of x will never change. This will be true for any value of y.
So, the equation for a vertical line passing through this point is:
x = 2
Similarly, for a horizontal line the value of y will never change. This is true for any value of x.
So, the equation for a horizontal line passing through this point is:
y = -6
Therefore, the equation of the horizontal line passing through the point (2, -6) is y = -6
and the equation of the vertical line passing through the point (2, -6) is x = 2
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what is the answer to b
B.
The age of a person's systolic pressure is 130 mm Hg is 45.98 years.
P = 0.004[tex]y^{2}[/tex] - 0.01y + 122
substitute p = 130 mm
130 = 4/1000 [tex]y^{2}[/tex] - 1/100 y + 122
8 = 4[tex]y^{2}[/tex] - 10y / 1000
8000 = 4[tex]y^{2}[/tex] - 10 y
[tex]2y^{2} -5y -4000=0[/tex]
y = 45.98 years
Therefore the age of a person's systolic pressure is 130 mm Hg is 45.98 years.
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To qualify to compete in the high jump finals, athletes must jump a certain height in the
semi-finals. Jon jumped 1 inches below the qualifying height, but his friend Anthony
made it to 2 inches above the qualifying height. How much lower was Jon's semi-final
jump compared with Anthony's?
Jon's semi-final jump compared with Anthony's was 3 inches lower. This was based on the heights given.
How to find the value?Given that Jon jumped 1 inches below the qualifying height, but his friend Anthony
made it to 2 inches above the qualifying height.
In this case, the difference in the jump will be gotten by subtracting the values. This will be illustrated as:
= Anthony's jump - Jon's jump
= 2 - (-1)
= 2 + 1
= 3
Therefore, Jon was 3 inches lower.
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This is a safe space please answer how you are feeling today and why!!
Answer:
feeling good
Step-by-step explanation:
I am just happy
Mary borrowed $12,000.00 for starting a bakery shop at $11.5% per year at simple interest. What is the amount of money that she yas to pay at the end of 3 yesrs to clear her debt ?
The amount of money that she yas to pay at the end of 3 yesrs to clear her debt is: $16,140.
How to find the interest rate?First step is to find the interest
Interest = ( Principal × Interest rate × time)
Interest = $12,000 × 11.5% × 3
Interest = $4,140
Now let find the amount she use to clear the debt
Amount = Principal + Interest
Amount = $12,000 + $4,140
Amount = $16,140
Therefore she will use $16,140 to clear the debt.
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Kyle starts a fundraiser with 43 pennies. He recruits all of the players on his baseball team to participate. His goal is to triple the number of pennies each day. Assume Kyle meets his daily goal.
Use x to represent the number of days and y to represent the total number of pennies.
Enter an equation in the box that represents this scenario.
The equation to represent this scenario is y = 43*(3)ˣ , the correct option is (a) .
In the question ,
it is given that ,
Number of pennies that Kyle starts the fundraiser = 43 pennies
goal is to triple the number of pennies each day .
let "x" to represent the number of days .
let the total number of pennies be "y" .
this situation is represented by an exponential increase ,
that can be represented as
y = 3ˣ * 43
y = 43*3ˣ
Therefore , The equation to represent this scenario is y = y = 43*3ˣ .
The given question is incomplete , the complete question is
Kyle starts a fundraiser with 43 pennies. He recruits all of the players on his baseball team to participate. His goal is to triple the number of pennies each day. Assume Kyle meets his daily goal. Use x to represent the number of days and y to represent the total number of pennies .
Select the Equation that represents the this scenario ?
(a) y = 43(3)ˣ
(b) y = 3(43)ˣ
(c) y = [(43)(3)]ˣ
(d) y = 43(x)³
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A motorboat travels 74 kilometers in 2 hours going upstream. It travels 110 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
The rate of the boat in still water is 45.5 km/hr and the rate of the current is 100.5 km/hr.
How to find speed?A motorboat travels 74 km in 2 hours going upstream.
Rate = Distance/time
Rate = 74 /2
Rate = 36 km/hr
It travels 110 km going downstream
Rate = Distance/time = 110/2
Rate = 55 km/hr
Equations:
Upstream: b-c = 36 km/hr
Downstrm: b+c = 55 km/hr
Add and solve for b
2b = 36 km/hr + 55 km/hr
2b = 91 km/hr
Divide both side by 2b
b = 91 km/hr /2
b = 45.5 km/hr (speed of the boat)
Solve for c
b+c = 55
45.5+ c = 55
c = 55 + 45.5
c = 100.5 km/hr (speed of the current)
Therefore 45.5 km/hr and 100.5 km/hr are the speed.
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[tex]\sqrt{3p^{9}q^{7} r^{6}\\/ 16x^{6}y^{12}[/tex]
Using Laws of exponents, the solution to the expression √(3p⁹q⁷r⁶)/(16x⁶y¹²) is; (p⁴q³r³/(x³y⁶))√(3pq/16)
How to use laws of exponents?The different laws of exponents are;
1) Product With the Same Bases; a^m × a^n = a^(m+n)
where;
m and n are real numbers.
2) Quotient with Same Bases;
a^m/a^n = a^(m-n)
where;
a is a non-zero term and m and n are integers.
3) Power Raised to a Power; (a^m)^n = a^(mn)
where;
a is a non-zero term and m and n are integers.
4) Product to a Power; a^n * b^n = (ab)^(n)
where;
a is a non-zero term and n is the integer.
5) Quotient to a Power; It states that the fraction of two different bases with the same power is represented as; a^n/b^n = (a/b)^n
where;
a and b are non-zero terms and n is an integer.
6) Zero Power; When the power of any integer is zero, then it means that its' value is equal to 1, such that;
a⁰ = 1
where;
a is any non-zero term.
7) Negative Exponent Rule; a^(-m) = 1/(a^m)
We are given the expression as;
√(3p⁹q⁷r⁶)/(16x⁶y¹²)
Applying the laws of exponents, we will have;
√(3p⁹q⁷r⁶)/(16x⁶y¹²) = (p⁴q³r³/(x³y⁶))√(3pq/16)
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The area of a children's rectangular playground is 1189 square meters. The length
is 12 meters longer than the width. Determine the length and width of the
playground.
Answer:
[tex]1+\sqrt{1190}[/tex] and [tex]\sqrt{1190}-11[/tex]
Step-by-step explanation:
Let the length in meters be [tex]l[/tex]. Then, the width is [tex]l-12[/tex].
[tex]l(l-12)=1189 \\ \\ l^2-12l=1189 \\ \\ l^2-2l-1189=0 \\ \\ l=\frac{2 +\sqrt{(-2)^2-4(1)(-1189)}}{2(1)} \text{ } (l>0) \\ \\ l=1+\sqrt{1190} \\ \\ \implies l-12=\sqrt{1190}-11[/tex]
what's the constant of proportionality: the table represent the linear relationship between the number of seconds a paper airplane is in the sky and the total distance it will fly
PLEASE HURRY!!!!!!!!!!!!!!!!!!! i need to complete this it im studying it for my test tomorrow
The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
What is constant of proportionality?When two or more parameters are directly or indirectly proportional to one another, their relationship is expressed as a = kb or a = k/b, where k indicates the nature of the relationship between the two variables. This k is referred to as the proportionality constant.
For example, the number of apples in a crop is proportional to the number of trees in an orchard, with the ratio of proportionality being the average number of apples per tree.
This can be illustrated as:
Let's say y = 4
Let's say x = 2
y = kx
4 = 2k
Divide
k = 4/2
k = 2
The constant is 2.
Note that an overview was given as the information is incomplete.
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BIG IDEAS MATH
# 30 i
A coordinate plane is superimposed on a property map. Each unit in the coordinate plane represents 1 foot. The
location of a wellhead on the property is given by the point (12, 6). How close is the wellhead to a property line
modeled by the line y = x - 14? If necessary, round your answer to the nearest tenth place.
feet
The distance between point (12,6) and the line y = x - 14 is given as follows:
5.6 feet.
How to obtain the distance of a point to a line?The standard equation of a line is given by the rule presented as follows:
ax + by + c = 0.
The coordinates of the point which we want to find the distance from the line are given as follows:
(x0,y0).
The equation that obtains the shortest distance of the point (x0, y0) to the line ax + by + c = 0 is presented as follows:
[tex]D = \frac{|a(x_0) + b(y_0) + c|}{\sqrt{a^2+b^2}}[/tex]
The line for this problem is given by the rule presented as follows:
y = x - 14.
In standard notation, it is defined by the rule presented as follows:
x - y - 14 = 0.
Hence the coefficients are presented as follows:
a = 1, b = -1, c = -14.
The point has the coordinates given as follows:
(12,6).
Hence:
x0 = 12, y0 = 6.
Thus the distance from the point to the line is obtained as follows:
[tex]D = \frac{|a(x_0) + b(y_0) + c|}{\sqrt{a^2+b^2}}[/tex]
D = |1(12) -1(6) - 14|/sqrt(1²+(-1)).
D = 8/sqrt(2)
D = 5.6 feet.
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Dave and LaVontae are saving money. Dave has $10, and LaVontae has $5. Write an
equation expressing the relationship between the amount that LaVontae has, x, and
the amount that Dave has, y.
I need some help with this problem please
Answer:
1st = 2 sin (x)
2nd = cos^2 (x)
3rd = sin^2 (x)
-(4x-5)+16x>-31
I need the work shown please :))
The solutions of the inequality are given by:
x > -3
How to solve the inequality?
Here we have the following inequality:
-(4x - 5) + 16x > -31
To solve this, we need to isolate the variable x in one of the sides of the inequality, so let's do that.
-(4x - 5) + 16x > -31
-4x + 5 + 16x > -31
(-4 + 16)*x + 5 > -31
12x + 5 > -31
12x > -31 - 5
12x> -36
x > -36/12
x > -3
So all the values of x that are larger than -3 are solutions of the inequality.
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Mrs. Gallas is playing with her class. She picks one of the points on the graph and gives three clues. If the class can correctly guess the point, they win.
Clue #1: y = 0
Clue #2: The distance from the origin is greater than 3 units.
Clue #3: The distance from the origin is greater than 3 units.
Which point did Mrs. Gallas choose?
Answer: It could be (3, -3) (3,3) or (-3,-3)
Step-by-step explanation:
they are all 3 away.
-9x+2y =24
x = 10-4y
Answer: x = -2, y = 3
Step-by-step explanation:
Given that,
-9x+2y = 24..................................(i)
x = 10-4y.......................................(ii)
From equation (i)
-9(10-4y) + 2y = 24 [as x = 10-4y]
=> -90 +36y + 2y = 24
=> 38y = 90 + 24
=> 38y = 114
=> y = 114/38
Therefore, y = 3
Again,
x = 10 - 4(3) [as y = 3]
=> x = 10-12
Therefore, x = -2
Here, x = -2 and y = 3
Robert bought a used car for $10,332 with an added sales tax of 2.5%. What was the
original price of the car?
A $11,080
B. $10,080
C. $20,800
D. $15,416
If Robert bought a used car for $10,332 with an added sales tax of 2.5%. Then the original price of the car would be around $10,080.
Option (B) is correct.
What is a percentage?
A percentage is a relative value that represents the hundredth part of any quantity. One percent (symbolized 1%) is the one-hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice the given amount.
Robert bought a used car for $10,332 with an added sales tax of 2.5%.
so the additional amount would be = 10,332 * 2.5%
= 10332 * 0.025
= $258.3
So the original price of the car would be = 10332 - 258.3
≈ $10,080.
Hence, If Robert bought a used car for $10,332 with an added sales tax of 2.5%. Then the original price of the car would be around $10,080.
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Macmillan Learning
Holly is deciding between 2 yoga studios. If she chooses Life Studio, she will pay a $60 initial sign-up fee and $30 each
month. If she chooses Yoga Mind, she will pay $40 each month and no initial sign-up fee. If Holly thinks she will do yoga
for 6 months, which studio should she join to pay less money?
She will pay the same amount at both.
Life Studio
Yoga Mind
Answer:
She will pay the same amount at both
Step-by-step explanation:
For Life Studio,
the initial sign up fee + $30 each month
= $30 = 30 × 6 = $180
Hence, $60 + $180 = $240
For Yoga Mind,
$40 each month for 6 months
= $40 × 6
$40 × 6= $240
Therefore, she will pay the same amount at both
E
Solving a word problem using a system of linear equations of th...
QUESTION
ODD 03
Zachary
A store is having a sale on walnuts and chocolate chips. For 4 pounds of walnuts and 8 pounds of chocolate chips, the total cost is $25. For 2 pounds of walnuts
and 3 pounds of chocolate chips, the total cost is $11. Find the cost for each pound of walnuts and each pound of chocolate chips.
As per the given cost of pounds of walnuts and chocolate chips , the cost of each pound of walnuts and chocolate chips is equal to $(13/4) and $(3/2) respectively.
As given in the question,
Let us consider the cost of each pound of walnuts is equal to $x.
And cost of each pound of chocolate chips is equal to $y.
Now as per the given condition system of equation is given by,
4x + 8y = 25 __(1)
2x + 3y = 11 __-(2)
Multiply (2) by 2 and subtract it from (1) we get,
4x + 8y = 25
4x + 6y = 22
0x + 2y = 3
⇒y = $(3/2)
Substitute value of y in (1) to get the value of x,
4x + 8(3/2) = 25
⇒4x = 25-12
⇒x = $(13/4)
Therefore, for the given cost of pounds of walnuts and chocolate chips , the cost of each pound of walnuts and chocolate chips is equal to $(13/4) and $(3/2) respectively.
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7. Select all of the numbers that are multiples of 12.
22
26
36
42
48
60
Answer:
36
48
60
Reason:
Since it is multiples of twelve, we can find out and multiply
12*3= 36
12*4= 48
12*5= 60
I hope this helps!
Answer: 36, 48, and 60.
Step-by-step explanation:
36, 48, and 60 are the only numbers that can be divided by 12 into a whole number.
36/12 = 3
48/12 = 4
60/12 = 5