The lines are neither parallel nor perpendicular
How to determine the relationship between the lines?The equations of the lines are given as
3 x minus y equals 5
3 y equals x minus 15
Rewrite the equations properly
3x - y = 5
3y = x - 15
Make y the subject in both equations
In 3x - y = 5, we have
y = 3x + 5
In 3y = x - 15, we have
y = 1/3x - 5
The slopes of the two lines are
m1 = 3
m2 = 1/3
The above values are not equal, and they are not opposite reciprocal
This means that the lines are neither parallel nor perpendicular
Read more about linear equations at:
https://brainly.com/question/14323743
#SPJ1
After a gas-filled balloon is released, it rises 90 feet by the end of the first minute. by the end of the second minute, the balloon rises 120 feet, and by the end of the third minute, it rises 150 feet. how many feet would the balloon rise in 8 minutes? a. 300 c. 390 b. 330 d. 660 please select the best answer from the choices provided a b c d
Answer:
330
Step-by-step explanation:
the change in hirght = 120 - 90 = 30
so 90 + (30 x 8)
= 90+240
= 330//
the x and y intercept
Which function in vertex form is equivalent to f(x) = 4 + x² - 2x?
O f(x) = (x - 1)² + 3
O f(x) = (x-1)² + 5
O f(x) = (x + 1)² + 3
O f(x) = (x + 1)² +5
Answer:
f(x)=(x-1)^2+3
Step-by-step explanation:
Both equations vertexes equal (1, 3) while the rest do not match.
f(x) = (x - 1)² + 3 function in vertex form is equivalent to f(x) = 4 + x² - 2x.
We can use the technique of completing the square to rewrite the given function f(x) in vertex form.
f(x) = 4 + x² - 2x
f(x) = (x² - 2x) + 4
Adding and subtracting (1) inside the parentheses
f(x) = (x² - 2x + 1) + 4 - 1
f(x) = (x - 1)² + 3
So, the equivalent function in vertex form is f(x) = (x - 1)² + 3.
Therefore, the correct option is f(x) = (x - 1)² + 3.
To learn more on Functions click:
https://brainly.com/question/30721594
#SPJ5
The following are the distances (in miles) to the nearest airport for 11 families. 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45 Notice that the numbers are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
Answer:
11, 11, 24, 34, 45 and 23===========================
Given data9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45Five-number summaryMinimum:
The smallest number of data ⇒ 11Maximum:
The largest number of data ⇒ 45Median:
The middle number of the data if data consists of odd number of elements ⇒ 24Lower quartile:
The median of the lower half of data, 9, 11, 11, 16, 16 ⇒ 11Upper quartile:
The median of the upper half of data, 28, 30, 34, 42, 45 ⇒ 34Interquartile rangeThe difference of upper and lower quartiles, 34 - 11 = 23If 2 pounds is equal to 3 dollars, which of the following is incorrect?
A. 28 pounds is 44 dollars
B. 23 pounds is 34.50 dollars
C. 11 pounds is 16.50 dollars
D. 10 pounds is 15 dollars
Answer:
A
Step-by-step explanation:
Find the ratio of pounds to dollars, [tex]\frac{3}{2}[/tex] or 1.5.
Next test each option by multiply the pounds by that ratio.
A: 28*1.5=42
B: 23*1.5=34.5
C: 11*1.5=16.5
D: 10*1.5=15
You can see A is the incorrect answer as 28 pounds would be 42 dollars, not 44.
What's the circumference of a
circle with a diameter of 31 inches?
Use 3.14 for I.
C = [?] inches
Enter the number that belongs in the green
box. Do not round your answer.
Hint: C = nd
Answer: C = 97.34 inches
Step-by-step explanation:
C = πd
= 3.14(31)
= 97.34
2t - 9 - 6t + 2 i really need help
Answer:
-4t-11
Step-by-step explanation:
rearrange the numbers
2t-6t-9+2
Add negative 2
2t-6t-11
2-6
-4t-11
Consider the incomplete paragraph proof.
Because triangle XYZ is a right triangle, the side lengths
Given: Isosceles right triangle XYZ (45°-45°-90°
must satisfy the Pythagorean theorem, a? + b2 c2
triangle)
which in this isosceles triangle becomes a2 + a? = c?. By
Prove: In a 45°-45°-90° triangle, the hypotenuse is V2
combining like terms, 2a? c2.
times the length of each leg.
Which final step will prove that the length of the
hypotenuse, c, is /2 times the length of each leg?
• Substitute values for and c into the original
Pythagorean theorem equation.
O Divide both sides of the equation by two, then
determine the principal square root of both sides of the
equation.
Determine the principal square root of both sides of
the equation.
O Divide both sides of the equation by 2.
The hypotenuse is [tex]c = a\sqrt{2}[/tex] times the length of each leg 'a'. Triangle XYZ is a isosceles right triangle, therefore the Pythagoras theorem becomes and this can be evaluated by using properties of isosceles triangle.
According to the statement
we have given that a theorem and we have to prove it.
So, For this purpose,
The given information is :
Isosceles triangle XYZ where [tex]Angle X = 45^{0}[/tex] [tex]Angle Y = 45^{0}[/tex] [tex]Angle Z = 90^{0}[/tex]
Let the sides of triangle XYZ be a, b, and c. Then side XY = c, YZ = b and ZX = a.
Now, it is given that triangle XYZ is isosceles triangle therefore, the shorter sides must be equal that is, a = b.
Now use Pythagoras theorem
[tex]a^{2} + b^{2} = c^{2}[/tex]
But here a= b then the equation become
[tex]a^{2} + a^{2} = c^{2}[/tex]
Then after solving it become
[tex]2a^{2} = c^{2}[/tex]
And here we have to find the value of the hypotenuse,
so we solve it for c.
Then
[tex]c = a\sqrt{2}[/tex]
From this it is clear that the
it can be concluded that the hypotenuse is times the length of each leg 'a'.
Learn more about Pythagoras theorem here
https://brainly.com/question/343682
#SPJ1
Carries family broke a package of graham crackers into 32 pieces. carries two brothers each ate 1/8 of the pieces and the rest of the family ate 7/16 of the pieces.
Carries two brothers each ate 4 pieces, the rest of carries family ate 14 pieces and there were 14 pieces remaining given that Carries family broke a package of graham crackers into 32 pieces. carries two brothers each ate 1/8 of the pieces and the rest of the family ate 7/16 of the pieces. This can be obtained by multiplying the fractions given with the total number.
Find the required number of pieces:From the question it is given that,
Carries family broke a package of graham crackers into 32 pieces.
Therefore total number of pieces will be 32 pieces.
First it is said that,carries two brothers each ate 1/8 of the pieces
This means that out of 32, 1/8 of the pieces were ate by the two brothers.
1/8 of 32 = 1/8 × 32 = 4 pieces
⇒ Carries two brothers each ate 4 pieces
Next it is said that,the rest of the family ate 7/16 of the pieces
This means that out of 32, 7/16 of the pieces were ate by the rest of the family
7/16 of 32 = 7/16 × 32 = 14 pieces
⇒ the rest of carries family ate 14 pieces
To find the remaining pieces add the number of pieces ate by both carries brothers and the rest of the family and subtracting from the total number of pieces.remaining pieces = 32 - (4 + 14) = 32 - 18 = 14 pieces
⇒ there were 14 pieces remaining
carries two brothers each ate 4 piecesthe rest of carries family ate 14 piecesthere were 14 pieces remainingHence Carries two brothers each ate 4 pieces, the rest of carries family ate 14 pieces and there were 14 pieces remaining given that Carries family broke a package of graham crackers into 32 pieces.
Learn more about fraction here:
brainly.com/question/10354322
#SPJ1
Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: Carries family broke a package of graham crackers into 32 pieces. carries two brothers each ate 1/8 of the pieces and the rest of the family ate 7/16 of the pieces.
carries two brothers each ate ____ pieces
the rest of carries family ate ____ pieces
there were ____ pieces remaining
Exponential Decay
Find f(3), where f(x) = 2x(1/2)^x
f(x) = 2 * (1/2)^x
f(3) = 2 * (1/2)^3
f(3) = 2 * (1/2 * 1/2 * 1/2)
f(3) = 2 * 1/8
f(3) = 2/8
f(3) = 1/4
Hope this helps!
Answer:
[tex]f(x) = 2 \times ( { \frac{1}{2} })^{x} \\ \\ f(3) = 2 \times ({ \frac{1}{2}})^{3} \\ \\ = 2 \times \frac{1}{8} \\ \\ f(3) = \frac{1}{4} = 0.25[/tex]
Suppose you live in a country with a proportional tax system. you make $20,000 a year and pay $5,000 in taxes. your friend makes twice as much money as you. what amount can your friend expect to pay in taxes this year? $2,500 $5,000 $10,000 $20,000
Answer:
10,000
Step-by-step explanation:
Tbh this was pretty simple. If he makes twice the money as you, he pays twice as much too. Meaning he makes 40k a year and pays 10k for taxes
BRAINLIEST!
Find the area of the figure below
Answer:
140 in^2
Step-by-step explanation:
Take the outside dimensions of the LARGE rectangle
11 x 17 = 187 in^2
subtract the two corner cutout rectangles
187 - 8x4 - 3 x 5 = 140 in^2
Diagram
What additional information could be used to prove that the triangles are congruent using aas? select two options.
Two angles and a non-included side of one triangle.
The AAS rule states that:
If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.
In the diagrams below, if AC = QP,
∠ A = ∠ Q,
∠ B = ∠ R,
then triangle ABC ≅ QRP.
What is meant by congruence of triangles?Congruence of triangles: Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
There are 5 main rules of congruency for triangles:
SSS Criterion: Side-Side-Side.
SAS Criterion: Side-Angle-Side.
ASA Criterion: Angle-Side- Angle.
AAS Criterion: Angle-Angle-Side.
RHS Criterion: Right angle- Hypotenuse-Side.
To learn more about concurrency of triangles from the given link
https://brainly.com/question/15552454
#SPJ4
what is the range 42,43,44,44,49,40,39
Answer:
range is 10
Step-by-step explanation:
highest number is 49
loweest number is 39
49 - 39 = 10
Answer:
10
Step-by-step explanation:
The range is found by taking the largest number and subtracting the smallest number
The largest number is 49
The smallest number is 39
The range is 49-39 = 10
Please help and explain.
Considering the given graph, we have that:
The slope of the graph of the function is equal to 1 for x between x = -3 and x = -2.The slope of the graph is equal to 0 for x between x = 3 and x = 4.The greatest value of y is y = 4.The smallest value of y is y = -3.How to find the slope of a function?The slope of a function, given two points, is given by the change in y divided by change in x.
When x = -3, y = -3, and while x = -2, y = -2, hence when x changes by 1, y also changes, hence the slope of the graph of the function is equal to 1 for x between x = -3 and x = -2.
When x = 3, y = 4, and when x = 4, y = 4, hence the slope of the graph is equal to 0 for x between x = 3 and x = 4.
Looking at the vertical axis:
The greatest(top) value of y is y = 4.The smallest(bottom) value of y is y = -3.More can be learned about the graph of a function at https://brainly.com/question/19376563
#SPJ1
Determine whether the series is convergent or divergent. [infinity] n = 1 1 n√9 the series is a ---select--- p-series with p =
The series is a convergent p-series with p = 3
How to know it is a divergent or a convergent seriesWe would know that a series is a convergent p series when we have ∑ 1 np. Then you have to be able to tell if the series is a divergent p series or it is a convergent p series.
The way that you are able to tell this is if the terms of the series do not approach towards 0. Now when the value of p is greater than 1 then you would be able to tell that the series is a convergent series.
The value of [tex]\sqrt{9}= 3[/tex]
The formular for this is
∑[tex]\frac{1}{n^p} \\[/tex]
where n = 1
we know it is convergent because p is greater than 1. 3>1
Read more on convergent series here:
https://brainly.com/question/337693
#SPJ1
The equation h = 7 sine (startfraction pi over 21 endfraction t) 28 can be used to model the height, h, in feet of the end of one blade of a windmill turning on an axis above the ground as a function of time, t, in seconds. how long is the blade? assume that the blade is pointing to the right, parallel to the ground, at t = 0, and that the windmill turns counterclockwise at a constant rate.
The windmill's blade measures 7 feet in length.
What is an equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =.To find the measure of the windmill's blade:
We have the equation: [tex]h=sin(\frac{\pi }{21t} )+28[/tex]At the time 't' = 0, the end of the blade is parallel to the ground and pointing to the right, indicating that it is the same height as the other end. (Ф = 0°)We may calculate the length of the blade by calculating the greatest height of this end at = 90°.We now know that the general model equation of a circular simple harmonic motion is written as follows: y = A sinωt + kWhere A is the maximum displacement from mean to maximum positionThe angular frequency is ω.When eq1 and eq2 are compared:A = 7As a result, the difference in blade end height at = 0° and = 90° is 7 feet.Therefore, the windmill's blade measures 7 feet in length.
Know more about equations here:
https://brainly.com/question/2972832
#SPJ4
The correct question is given below:
The equation h=7sin(pi/21t)+28 can be used to model the height, h, in feet of the end of one blade of a windmill turning on an axis above the ground as a function of time, t, in seconds. How long is the blade? Assume that the blade is pointing to the right, parallel to the ground, at t = 0, and that the windmill turns counterclockwise at a constant rate. 7 feet 14 feet 21 feet 28 feet
please help im stuck its math
Answer:
y = 5x - 6
Step-by-step explanation:
We are given a line, which is parallel to the line y=5x+3.
We also know that this line passes through the point (3,9).
We want to find the equation of this line.
Parallel lines have the same slopes, yet different y intercepts.
So, let's find the slope of the line y=5x+3.
The line is written in slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.
As 5 is in the place of where the slope (m) is, 5 is the slope of the line.
It is also the slope of the line parallel to it (which is the line we are trying to find).
We can write the equation of this new line in slope-intercept form as well, which is also the format your system wants.
Before we write the equation of the line in slope-intercept form, we can write it in point-slope form, then convert it into slope-intercept form.
Point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point.
As we have already found the slope (5), we can immediately plug it into the formula.
[tex]y-y_1=5(x-x_1)[/tex]
Now, remember that we were also given a point, that passes through the line. This point is (3,9).
We can use its values in the formula.
Substitute 3 as [tex]x_1[/tex] and 9 as [tex]y_1[/tex].
y - 9 = 5(x-3)
Now, we have written the line in point-slope form.
However, we're not done yet; remember that we want it in slope-intercept form.
We can solve the equation for y to get slope-intercept form.
So, on the right, open up the parentheses and distribute 5 to both x and -3.
y - 9 = 5x - 15
Now add 9 to both sides.
y = 5x - 6
Izzo's Pizza sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what he found. Type of Crust Number Sold
Thin crust 307
Thick crust 224
Stuffed crust 161
Pan style 191
Based on this information, of the next 2000 pizzas he sells, how many should he expect to be stuffed crust or pan style? Round your answer to the nearest whole number. Do not round any intermediate calculations.
Answer:
797
Step-by-step explanation:
First, we need to find the number of pizzas sold last week by finding the sum of the pizzas sold:
307 + 224 + 161 + 191 = 883
Next, we need to find the proportion of stuffed crust and pan style pizzas sold last week by adding the number of both sold and dividing by the total number of pizzas sold:
(191+161) / 883 = 352 / 883
Now we need to multiply this proportion by 2000 to find the expected number of stuffed crust or pan style pizzas:
(352 / 883) * 2000 = 797.28 = 797
factor (16x^2-8x+1)
Please show your work lol
Answer:
(4x - 1)^2.
Step-by-step explanation:
16x^2 - 8x + 1
Multiplying the first and last coefficients:
16 * 1 = 16
We need 2 numbers whose product is 16 and whose sum is -8.
These are - 4 and -4.
So we now write:
16x^2 - 4x - 4x + 1
Now factor by grouping :
= 4x(4x - 1) - 1(4x - 1)
= (4x - 1)(4x - 1)
= (4x - 1)^2
This method of factoring quadratics is called the 'ac' method - you split the middle term ( in this case the -8x) into 2 parts.
Answer:
[tex](4x-1)^2[/tex]
Step-by-step explanation:
Given quadratic expression:
[tex]16x^2-8x+1[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b:
[tex]ac = 16 \times 1 = 16[/tex][tex]b = -8[/tex]Therefore, two numbers are: -4 and -4
Rewrite the middle term as the sum of these two numbers:
[tex]\implies 16x^2-4x-4x+1[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 4x(4x-1)-1(4x-1)[/tex]
Factor out the common term (4x - 1):
[tex]\implies (4x-1)(4x-1)[/tex]
Apply the exponent rule: aa = a²
[tex]\implies (4x-1)^2[/tex]
Learn more about factoring quadratics here:
https://brainly.com/question/27956741
https://brainly.com/question/27947331
determine the rate of change of the function.
decreasing at increasing rate
increasing at a decreasing rate
decreasing at a decreasing rate
increasing at an increasing rate
The graph of a linear relation passes through the point (-3,-5) and has a slope of 3.
Determine an equation for this linear relation in slope intercept form.
Answer:
y = 3x + 4
Step-by-step explanation:
Substituting into point-slope form and converting to slope-intercept form,
[tex]y+5=3(x+3) \\ \\ y+5=3x+9 \\ \\ \boxed{y=3x+4}[/tex]
Use distributive properties for 5(8+r)
Answer:
40 + 5r
usually you put the one with the variable infront
so 5r+40
Step-by-step explanation:
5(8+r)
5*8 + 5*r
40 + 5r
-5/12 - (-9/3) what is the answer for this equation
Answer:
2 7/12
Step-by-step explanation:
Simple fraction problem
q=mc(T₂-T₁)
Solve for T₂
1. There are only two numbers that are twice the sum of their
individual digits. One of them 0 and I am the other one. I am a
multiple of 9. Which number am I
Answer: 18
Step-by-step explanation: 18=1+8=9
its complicated but when you check something like
23= 2+3 =5
10 = 1+0=1
the individual digits of 18 are 1 and 8
Sum = 1+8=9
multiply 9 by 2 we get 18
18 is also a multiple of 9.
I hope this helps
If amy cuddy and her research team originally established a sample size of n=200 (100 in each group) and then discovered that 86% of the high-power group (86 of 100) took a gambling risk while 60% of the low-power group (60 of 100) took the risk, then the p-value would have been much lower than that originally found in question 1. this p-value would have been less sensitive and would have provided stronger evidence for the researcher's hypothesis. state the p-value, rounding to 5 decimal places.
The p-value that would be given as the evidence would be given as p-value = 0.00002 and also P value = 0.00003
How to solve for the p valueThe sample size of the first sample = 100
x1 = success 0f 86%
We have to find the proportion of this = 0.86
The sample size of the second sample n2 = 100
x12 = success 0f 60%
We have to find the proportion of this = 60/100
= 0.6
The difference = 0.86-0.6= 0.26
Next we have to find the pooled proportion. This is taken given as p = (x1+x2)/(n1+n2) this gives us 0.73
Next we have to find the standard error
= √(p*(1-p)*(1/n1+ 1/n2)= 0.06279
Z stat = (0.26-0)/0.0628= 4.1411
From here the p value would have to be
p-value = 0.00002 and also
P value = 0.00003
Read more on p value here:
https://brainly.com/question/4621112
The daily high temperature of Elk Creek drops by 1.2°C every day. What is the net change in the daily high temperature after two calendar weeks?
Answer:
Step-by-step explanation:
Answer: 16.8°C
the function F(x)=log0.5^x is decreasing
true or false
Answer: True
Step-by-step explanation:
The base is less than 1.
Rod waxes two thirds of his car with one fourth bottle of car wax. What fraction of the bottle of car wax will Rod need to wax his entire car?
