An equation that represents a line that is perpendicular to the given line is [tex]2y=3x+1[/tex].
Given the following data:
[tex]y=\frac{2}{3} x+1[/tex]
To determine an equation that represents a line that is perpendicular to the given line:
The perpendicularity of a straight line.In Mathematics, the slopes of two lines are said to be perpendicular when the product of these slopes is equal to negative one (-1).
Mathematically, this is given by the formula:
[tex]m_1 \times m_2 = -1[/tex]
Note: Slope, [tex]m_1[/tex] = [tex]\frac{2}{3}[/tex]
Substituting the given parameters into the formula, we have;
[tex]\frac{2}{3} \times m_2=-1\\\\2m_2=-3\\\\m_2=\frac{3}{2}[/tex]
For the perpendicular line:
[tex]y=mx+b\\\\y=\frac{3}{2}x +1\\\\2y=3x+1[/tex]
Read more on perpendicular line here: https://brainly.com/question/20475360
Find the equation of the line that passes through (−4, 8) with slope −3. Write in slope-intercept form. F y = – 3x – 4 G y = – 4x + 3 H y = 3x + 4 J y = 4x – 3
Answer: y=-3x-4
Step-by-step explanation:
Since we know slope, we can plug it into slope-intercept form to find the y-intercept by using the given points,
y=-3x+b
8=-3(-4)+b
8=12+b
b=-4
Now that we know the y-intercept, we can complete the slope-intercept form.
y=-3x-4
There are 25 students in a class. Sixteen of those students are boys. What percent of the class are girls?
Answer:
36% of the students are girls
Step-by-step explanation:
(Boys) 16/25 = 64%
(Girls) 9/25 = 36%
Answer:
36%
Step-by-step explanation:
you first do 25 minus 16 to find out how many girls are in the class which is 9
now u do 9/25 = ?/100 to find out the percent of girls
9 times 100 divided by 25 which gives u 36%
hope this helps
How do I find x to the nearest tenth?
Answer:
x=18.9
Step-by-step explanation:
what does a shape need to be a prallelogram?
Answer: Needs to be flat with opposite sides that are parallel and are the same in length
The Interplanet Space Centre is planning to launch a probe which will travel from Earth to Mars, on to Jupiter and then to Saturn. Distance from Earth to Mars 78 300 000 km Distance from Mars to Jupiter 550 400 000 km Distance from Jupiter to Saturn 648 700 000 km million km
Estimate to the nearest million how far it will travel on its journey.
Answer:
1,300,000,000
Step-by-step explanation:
78 300 000
550 400 000
648 700 000
1 277 400 000
To the nearest million
1,2 | 77 400 000 more than 4, so +1
1,300,000,000
Graded Problem Set Jenna needs to make some house repairs in three years that will cost $9,000. She has some money in an account earning 9% annual interest. How much money needs to be in the account today so she will have enough to pay for the repairs
Answer:
She needs $6,949.65 in the account today.
Step-by-step explanation:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
In this question:
She needs $9,000 in 3 years, so [tex]t = 3, A(t) = A(3) = 9000[/tex]
9% annual interest, so [tex]r = 0.09[/tex]
1 compounding, so [tex]n = 1[/tex]
How much money needs to be in the account today so she will have enough to pay for the repairs
We need to find P.
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]9000 = P(1 + \frac{0.09}{1})^{1*3}[/tex]
[tex]P(1.09)^{3} = 9000[/tex]
[tex]P = \frac{9000}{(1.09)^{3}}[/tex]
[tex]P = 6949.65[/tex]
She needs $6,949.65 in the account today.
solve system by substitutition or elimination.
9x-8x=9
-18x+16y=-18
Answer:
1. 9x-8y=9
2. -18x+16y= -18 ⇒ -9x+8y= -9 ⇒ 9x-8y=9
as we see both equations are same, it means the lines overlap and there is infinite number of solutions
11. In your own words, describe how to view the
hean of a set of numerical data in two different
ways: in terms of leveling out and as a balance
point. In each case, give an example to illustrate.
A circle has a diameter of 10 feet. What is the area of the circle? Leave answers in terms of π.
Answer:
25pi
Step-by-step explanation:
If the circle has a diameter of 10, it has an radius of 5. The area of a circle is pi*r^2. If r=5, then it is 25pi.
Answer:
25π feet^2
Step-by-step explanation:
The area of a circle can be found using the following formula.
a=πr^2
We are given the diameter, but we need to find the radius. The radius is half of the diameter, or
r=d/2
We know the diameter is 10 feet. Therefore, we can substitute 10 in for d.
r=10/2
Divide 10 by 2
r=5
The radius is 5 feet.
Now we know the radius, and can substitute it into the area formula.
a=πr^2
r=5
a=π*5^2
Evaluate the exponent.
5^2 is equal to 5*5, which is 25.
a=π*25
a=25π
Add appropriate units. Area always uses units^2, and the units in this problem are feet.
a=25π feet^2
The area of the circle is 25π square feet
What’s the correct answer for this? Select two answer choices
Answer:
D and F
Step-by-step explanation:
In the attached file
Find the Ratio of 250m to 1.5km
Answer:
Step-by-step explanation:
1 km= 1000m
1.5 km = 1 x 1000 + 500
1000 + 500
1500m
1500 m : 250 m
750 m : 125 m
150 m : 25 m
30 m : 5 m
6 m : 1m
0.0
What is x X/5=15. ⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️
Answer:
x=3
Step-by-step explanation:
15/5=3 now I gotta get 20 chatacters
Answer:
[tex]x=75[/tex]
Step-by-step explanation:
[tex]\frac{x}{5} =15[/tex]
[tex]x=15 \times 5[/tex]
[tex]x=75[/tex]
Solve the equation.
C +9 = 3.7
Answer:
C= -5.3
Hope this helps!
Brainliest?
Answer:
C = -5.3
Step-by-step explanation:
C+9=3.7
Subtract 9 from both sides
C+9-9=3.7-9
Simplify
C = -5.3
A fish tank has a base, B, with an area, in square inches, modeled by B(x) = 2x^2 + 6x + 4. The height, H, in inches, is modeled by H(x) = x + 3. Find the equation that models the fish tank’s volume, V, in cubic inches.
A. V(x) = 2x^2 + 7x + 7
B. V(x) = 2x^2 + 5x + 1
C. V(x) = 2x^3 + 12x^2 + 22x + 12
D. V(x) = 2x^3 + 8x^2 + 10x + 4
Answer:
C. V(x) = 2x^3 + 12x^2 + 22x + 12
Step-by-step explanation:
The volume of a fish tank is the multiplication of the area of the base by the height.
In this question:
Area of the base: [tex]B(x) = 2x^{2} + 6x + 4[/tex]
Height: [tex]H(x) = x + 3[/tex]
Volume:
[tex]V(x) = B(X)*H(x) = (2x^{2} + 6x + 4)(x + 3) = 2x^{3} + 6x^{2} + 4x + 6x^{2} + 18x + 12 = 2x^{3} + 12x^{2} + 22x + 12[/tex]
So the correct answer is:
C. V(x) = 2x^3 + 12x^2 + 22x + 12
Solve for x.
6(x - 1) = 9(x + 2)
X = -8
X = -3
X = 3
x = 8
Answer:x=-8
Step-by-step explanation:
ssume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between -1.94°C and -1.5°C.
Answer:
[tex]P(-1.94<X<-1.5)=P(\frac{-1.94-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{-1.5-\mu}{\sigma})=P(\frac{-1.94-0}{1}<Z<\frac{-1.5-0}{1})=P(-1.94<z<-1.5)[/tex]
And we can find this probability with this difference:
[tex]P(-1.94<z<-1.5)=P(z<-1.5)-P(z<-1.94)=0.0668-0.026= 0.0408[/tex]
Step-by-step explanation:
Let X the random variable that represent the temperatures of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(0,1)[/tex]
Where [tex]\mu=0[/tex] and [tex]\sigma=1[/tex]
We are interested on this probability
[tex]P(-1.94<X<-1.5)[/tex]
And using the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
And using this formula we got:
[tex]P(-1.94<X<-1.5)=P(\frac{-1.94-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{-1.5-\mu}{\sigma})=P(\frac{-1.94-0}{1}<Z<\frac{-1.5-0}{1})=P(-1.94<z<-1.5)[/tex]
And we can find this probability with this difference:
[tex]P(-1.94<z<-1.5)=P(z<-1.5)-P(z<-1.94)=0.0668-0.026= 0.0408[/tex]
Which is the graph of the equation ? y-1=2/3(x-3)?
A function assigns values. The graph of the equation y-1=2/3(x-3) is the second graph.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
As the function is given to us that y-1=2/3(x-3), now substitute the value of x as 0 and y as 0 to get the intercept of the function. Therefore,
x-intercept
[tex]y-1=\dfrac23(x-3)\\0-1= \dfrac23x-\dfrac23(3)\\\\-1 = \dfrac23x - 2\\\\-1+2 = \dfrac23x\\\\x = \dfrac32[/tex]
y-intercept
[tex]y-1=\dfrac23(x-3)\\\\y-1=\dfrac23(0-3)\\\\y-1=\dfrac23(-3)\\\\y= -2+1\\\\y=-1[/tex]
Thus, we need to look for the graph which intersects the x-axis at 3/2 while the y-axis at -1. Therefore, as shown the below graph.
Hence, the graph of the equation y-1=2/3(x-3) is the second graph.
Learn more about Function:
https://brainly.com/question/5245372
Would you rather 36 spherical bottles with radi = 4.57 or three 12-packs of cans if each box is 15inx5inx4.4in
Answer:
36 bottles
Step-by-step explanation:
Each spherical bottle will have a volume of ...
V = (4/3)πr³ = (4/3)π(4.57³) = 399.8 . . . . cubic inches
Each box (12-pack?) will have a volume of ...
V = LWH = (15 in)(5 in)(4.4 in) = 330 in³
This is a smaller volume than even one spherical bottle, so 36 bottles will have the larger volume.
Sloane kicked a soccer ball at a speed of 48 feet per second. If the ball never leaves the ground, then it can be represented by the function H(t) = −16t2 + 48t. Determine the time the ball traveled. t = 0.33 seconds t = 3 seconds t = 16 seconds t = 48 seconds
Answer:
t = 3 seconds
Step-by-step explanation:
I took the test and i got it right.
The time the given ball traveled for is required.
The time the ball traveled was t = 3 seconds
Equation of motionThe given equation is [tex]H(t)=-16t^2+48t[/tex]
The ball never leaves the ground so the height of the ball is 0.
[tex]0=-16t^2+48t[/tex]
Solving the equation we get
[tex]-48t=-16t^2[/tex]
Dividing the equation by [tex]t[/tex] on both sides
[tex]\Rightarrow 48=16t[/tex]
Dividing the equation by 16 on both sides
[tex]\Rightarrow t=\dfrac{48}{16}\\\Rightarrow t=3\ \text{s}[/tex]
Learn more about equation of motion:
https://brainly.com/question/25951773
What is the minimum and maximum whole number side length for △ABC with given side lengths of 9 cm and 11 cm? Please explain why
Answer:
Step-by-step explanation:
We would assume that triangle ABC is a right angled triangle. This means that we can apply Pythagoras theorem in determining the unknown side length.
For the case of the minimum side length, we would assume that the unknown length, L is one of the shorter legs of the triangle. By applying Pythagoras theorem, it becomes
11² = 9² + L²
L² = 121 - 81 = 40
L = √40 = 6.32
For the case of the maximum side length, we would assume that the unknown length, L is one of the hypotenuse of the triangle. By applying Pythagoras theorem, it becomes
L² = 9² + 11²
L² = 81 + 121 = 202
L = √202 = 14.21
The minimum side length is 6.32 and the maximum side length is 14.21
A cylindrical metal pipe has a diameter of 8.4 millimeters
and a height of 10 millimeters. Ahole cut out of the center
has a diameter of 6 millimeters,
What is the volume of metal in the pipe? Use 3.14 for
and round the answer to the nearest tenth of a cubic
millimeter
8.4 mm
© 282.6 mm
271.3 mm
553.9 mm
836.5 mm
thand
Next
Submit
Answer:
C. 271.44 [tex]mm^3[/tex]
Step-by-step explanation:
We need to first find the volume of the pipe, then find the volume of the hole and then subtract the volume of the hole from the volume of the pipe.
The diameter of the pipe is 8.4 mm. This means its radius is:
8.4/2 = 4.2 mm
The height of the pipe is 10 mm
The volume of a cylinder is given as:
[tex]V = \pi r^2h[/tex]
where r = radius
h - height
Therefore, the volume of the cylinder without the hole is:
[tex]V = \pi * 4.2^2 * 10\\\\V = 554.18 mm^3[/tex]
The diameter of the hole is 6 mm. Its radius is:
6/2 = 3 mm
The volume of the hole is:
[tex]V = \pi * 3^2 * 10\\\\V = 282.74 mm^3[/tex]
The volume is:
554.18 - 282.74 = 271.44 [tex]mm^3[/tex]
Answer:
B. 271.3 [tex]mm^{3}[/tex]
Step-by-step explanation:
Volume of the outer cylinder minus the volume of the inner cylinder returns the volume of the metal outer ring that surrounds the hole.
What’s the correct answer for this?
Answer:
6
Explanation:
According to secant-secant theorem,
(PB)(PA)=(PD)(PC)
(7)(12)=(PD)(14)
NOW
84/14 = PD
PD = 6
The football team makes a profit of 20% on all sales of jerseys. During one season, the total sales on jerseys were $2625. How much was the profit?
Answer:
2625*0.2= $525 in profit
Pls brainliest!!
Pick 3 cards from a standard 52-card deck. Find the P(of at least 1 red card).
Does this experiment represent a binomial probability situation? Explain why or why not.
Answer:P(BBR) = 1/2 × 25/51 × 26/50 = 13/102 if cards are not replaced.
P(RBB) = 1/2 × 26/51 × 25/50 (simplified 1/2) = 13/102
P(BRB) = 1/2 × 26/51 ×25/50 (simplified 1/2) = 13/102
Step-by-step explanation: P(B) at first step is 26 cards out of a possible 52 therefore 26/52 (or simplified 1/2). We then have 25 black cards left out of a possible 51 therefore 25/51. The final card then has to be red to meet the criteria, we have 26 red cards still out of a possible 50 therefore 26/50.
This would be an example of binomial probability as at each step there are only 2 options R or B.
Write the following statement as a unit rate: 18 laps in 6 minutes
Answer:
3 laps per minute
Step-by-step explanation:
Take the number of laps and divide by the minutes
18/6 = 3 laps per minute
Answer:
3 laps per min
Step-by-step explanation: divide 18 and 6
What’s the correct answer for this?
Answer:
167
Step-by-step explanation:
A cement walkway of uniform width has been built around an in-ground rectangular pool. the area of the walkway is 1344 square feet. the pool itself is 80 feet long by 20 feet wide. what is the width of the walkway?
Answer:
6 feet.
Step-by-step explanation:
Dimensions of the Pool =80 feet long by 20 feet wide
Area of the walkway =1344 square feet.
If the width of the walkway=w
Length of the Larger Rectangle =80+2wWidth of the Larger Rectangle =20+2wArea of the Walkway =Area of the Larger Rectangle - Area of the Pool
[tex]1344=(80+2w)(20+2w)-(80*20)\\1344=80*20+160w+40w+4w^2-80*20\\4w^2+200w=1344\\4w^2+200w-1344=0\\We factorize\\4(w^2+50w-336)=0\\4(w^2-6w+56w-336)=0\\w(w-6)+56(w-6)=0\\(w-6)(w+56)=0\\w-6=0$ or $ w+56=0\\w=6$ ft or $ w=-56$ \\Therefore, the width of the walkway , w=6 feet.[/tex]
5 customers buy 10,15,20,25,30 toffees respectively from 1 shop. But the the person who bought 20 toffees forgot to pay .if the shopkeeper makes 20% profit what will be his profit or loss from these five customers of the person who forgot to pay at pay his amount had paid his amount?
50% profit ,60% profit, 40% loss ,20% loss.
Answer:
40% profit
Step by step Explanation:
Profit percentage
=( profit/cost price) * 100
0.2 = profit/cost
10+15+20+25+30= 100
Let's assume the cost price of the items is $1 each
Cost price total= $100
Profit made when buyer of 20 toffe didn't say was
0.2=profit/cost
0.2*100 =$20
If the$ 20 paid.
Total profit = $40
So percentage profit now
40/100 * 100 = 40%
The shopkeeper makes a loss of 40% and this can be determined by using the given data.
Given :
5 customers buy 10,15,20,25,30 toffees respectively from 1 shop. But the person who bought 20 toffees forgot to pay.The shopkeeper makes a 20% profit.The following steps can be used in order to determine the profit or loss the shopkeeper makes:
Step 1 - The total number of toffees can be calculated as:
[tex]\rm Total \; Toffees = 10 +15 + 20+ 25+ 30\\\rm Total \; Toffees = 100\\[/tex]
Step 2 - Now, let the cost of 1 toffee be $1. So, the cost of 80 toffees is $80.
Step 3 - So, the value of 20% profit by selling 80 toffees be 'x'. So, the value of 'x' is:
[tex]x = \dfrac{20}{100}\times 80[/tex]
[tex]x = \$16[/tex]
Step 4 - Now, let the profit or loss be 'y'. So, the value of 'y' is:
[tex]y = \dfrac{20}{80}\times 16[/tex]
[tex]y = \$4[/tex]
Step 5 - So, the loss percentage is 40%.
Therefore, the correct option is C).
For more information, refer to the link given below:
https://brainly.com/question/1494270
Suppose that you had consumer group wanted to test to see if weight of participants in a weight loss program changed (up or down). They computed a 95% confidence interval of the result (-4.977, 2.177). What do we know about the p-value for the test?
Answer:
What we know about the p-value for the test is that it will be less than 0.05
Step-by-step explanation:
The complete question is as follows;
Suppose that you had consumer group wanted to test to see if weight of participants in a weight loss program changed (up or down). They computed a 95% confidence interval of the result (-4.977, -2.177). Suppose that we had a significance test with the following hypothesis:
H0: population mean weight loss = 0
Ha: population mean weight loss does not equal 0
What do we know about the p-value for the test?
solution;
Given the information in the question, we are concerned with saying what we know about the p-value for the test
To answer this question, we shall be looking at it from the angle of the confidence interval
The confidence interval given is 95%.
Now what does this indicate?
It indicates that 95% confidence interval contains only values which are less than 0.
What does this mean for the p-value?
This means that the p-value will be less than 0.05
Please answer this question and thank you !! Will give you brainliest !!
Answer:
D
Step-by-step explanation:
Two lines are parallel if they have the same slope
y= mx+bthose with same m,
It only appears in the last option where m= -5 for both lines, so option d
