Answer:
[tex]\sf\longrightarrow \boxed{\pink{\sf 3x + 4y -8=0}}[/tex]
Step-by-step explanation:
We need to write the slope intercept form of the equation which passes through (4,-1) and parallel to the line y = -3/4x .
We know that the line parallel to a given line has the same slope . Therefore the slope of the line will be , ( on comparing to Slope Intercept Form ) .
[tex]\sf\longrightarrow Slope =\dfrac{-3}{4}[/tex]
On using point slope form ,
[tex]\sf\longrightarrow y-y_1= m ( x - x_1) [/tex]
Substitute the respective values ,
[tex]\sf\longrightarrow y - (-1) = \dfrac{-3}{4}( x - 4 ) [/tex]
Simplify ,
[tex]\sf\longrightarrow y +1 = \dfrac{-3}{4}x + 3 [/tex]
Multiply both sides by 4 ,
[tex]\sf\longrightarrow 4y + 4 = -3x + 12 [/tex]
Put all terms on same side , i.e. on LHS ,
[tex]\sf\longrightarrow \boxed{\pink{\sf 3x + 4y -8=0}}[/tex]
Hence the equation of the line is 3x + 4y - 8 = 0.
A large container is partially filled with n liters of water. Ito adds 10 liters of water to the container, making it 60% full. If Ignacio adds 6 more liters of water, the container will be 75% full.
What is the value of n?
Answer:
[tex]14\text{ liters}[/tex]
Step-by-step explanation:
Let the total amount of water the container can hold be [tex]t[/tex]. Currently, there are [tex]n[/tex] liters in the container. If Ito adds 10 liters of water, the container will be 60% full. We can express this statement in the following mathematical equation:
[tex]n+10=0.6t[/tex]
Next, we're given that if we add 6 more liters to this, the container will be 75% full.
Therefore, we have:
[tex]n+10+6=0.75t,\\n+16=0.75t[/tex]
This is a system of equations:
[tex]\begin{cases}n+10=0.6t,\\ n+16=0.75t\end{cases}[/tex]
Subtract both equations to conveniently get rid of [tex]n[/tex]:
[tex]10-16=0.6t-0.75t,[/tex]
Combine like terms:
[tex]-6=-0.15t[/tex]
Divide both sides by -0.15:
[tex]t=\frac{-6}{-0.15}=40[/tex]
Now substitute [tex]t=40[/tex] into any equation (I'll choose the first):
[tex]n+10=0.6(40),\\n+10=24[/tex]
Subtract 10 from both sides:
[tex]n=24-10=\boxed{14\text{ liters}}[/tex]
Someone explain this I don’t understand
what is the intrest of rs2160 at the rate of 20% for 4years?in how many years will rs1800earn the same intrest at the rate of 12%
Answer:
considering it was simple interest,
We have the formula:
I = PRT ÷ 100
where,
I = InterestP = principalT = time (in years)R = ratefor the first part of the question,
P = Rs. 2160R = 20T = 4Thus, I = (2160 × 20 × 4)÷ 100
I = Rs. 1728
Now, for the second part,
P = Rs. 1800I = 1728R = 12T = 100×I÷PR
T = 100 × 1728÷(1800 × 12)
T = 8 Years
Pleaseeee help me i have 15 mins to complete I’ll give u a hug
Answer:
1. 39-14a
2. (21*x-5/4) to power of 1/2
3. 2(I9 +10rI+4)
4. 25xsquared -100x+76/4
Step-by-step explanation:
Does anyone know how to do this? IM2 Honors
Which two ratios represent quantities that are proportional?
A. 25/28 and 5/7
B. 22/33 and 14/21
C. 16/13 and 13/16
D. 48/60 and 35/42
Answer:
B
Step-by-step explanation:
22/33 = 0.667
14/21 = 0.667
Since both quantities both have the ratio of 2:3, they are proportional
The other choices are not proportional
25/28 = 0.893
5/7 = 0.714
16/13 = 1.231
13/16 = 0.813
48/60 = .8
35/42 = .833
find the missing side of the triangle
Answer:
x = 40
Step-by-step explanation:
3-4-5 triangle scale factor by 10
Missing side is 4
4*10 = 40 | Multiply by 10 bc of scale factor
x = 40
Help please, thanks :)
Answer:
х=6
Step-by-step explanation:
[tex]7 + 5(x -3 ) = 22 \\ 7 + 5x - 15 = 22 \\ 5x = 22 - 7 + 15 \\ 5x = 30 \\ x = 6[/tex]
Answer:
C
x=6
Step-by-step explanation:
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
A sample of 500 U.S. teachers are asked to express their opinions on standardized testing for their students. The population in this study is _______________.
A. all U.S. students
B. standardized tests
C. all U.S. teachers
D. the 500 U.S. teachers
Answer:
Option A
Step-by-step explanation:
Dont let the sample of 500 teachers fool you the 500 teachers opinion is on their students standardized testing experience. In this case the students are the test subjects(population).
how many degrees are between 50 and 85
Answer:
35 degrees
Step-by-step explanation:
50+35=85
Can you check if this text is well written?
It's easy but I'm learning French. I appreciate your help.
Bonjour à tous, aujourd'hui je vais répondre à la question "Qui sont vos sportifs préférés ?
Je vais vous décrire ma athlète préféré et vous devriez y prêter attention. À la fin, vous me direz de qui je parle, d'accord ?
Commençons
Question 1 : Quel sport pratique l'athlète ?
Football, basketball o volleyball.
Elle joue au volley-ball
Ma sportive préférée, c'est une joueuse de volley-ball.
Elle est péruvienne et fait partie de l'équipe féminine péruvienne de volley-ball.
Question 2 : Comment est-elle?
Moche, musclée o petite?
Elle est musclée
Elle est brune et musclée.
Elle est grande et mince aussi.
Elle est très belle.
Question 3 : Comment sont ses cheveux
et ses yeux ?
Ses cheveux et ses yeux sont brunes.
Elle a les cheveux brunes et courtes. Elle a les cheveux frisées aussi.
Ses yeux sont brunes comme ses cheveux.
Question 4 : Quel âge a-t-elle ?
Elle a vingt-quatre ans.
Question 5 : Est-elle de petite taille?
Non, elle est grande.
Elle fait 1 mètre 85!
Elle est très grande
Bonsoir,
"Qui sont vos sportifs préférés ?
Je vais vous décrire mon athlète préférée et vous devrez prêter attention. À la fin, vous me direz de qui je parle, d'accord ?
Commençons
Question 1 : Quel sport pratique l'athlète ?
Football, basketball ou volleyball.
Elle joue au volley-ball
Ma sportive préférée, c'est une joueuse de volley-ball.
Elle est péruvienne et fait partie de l'équipe féminine du Pérou de volley-ball.
Question 2 : Comment est-elle?
Moche, musclée ou petite?
Elle est musclée
Elle est brune et musclée.
Elle est grande et mince aussi.
Elle est très belle.
Question 3 : Comment sont ses cheveux
et ses yeux ?
Ses cheveux et ses yeux sont bruns.
Elle a les cheveux bruns , courts et frisés .
Ses yeux sont bruns( on dirait plutôt marron) comme ses cheveux.
Question 4 : Quel âge a-t-elle ?
Elle a vingt-quatre ans.
Question 5 : Est-elle de petite taille?
Non, elle est grande.
Elle fait 1, 85m!
Can some one help please
Answer: [tex]\fbox{C} \: \: \: \dfrac{4 \times 10^{4} }{3 \times 10^{4} }[/tex]
Step-by-step explanation:
36,070 = 3.607 · 10⁴ ≈ 4 · 10⁴
29,029 = 2.9029 · 10⁴ ≈ 3 · 10⁴
Let's how manytimes greater the distance to the bottom of Challenger Deep is than the distance to the top of Mount Everest:
[tex]\dfrac{4 \times 10^{4} }{3 \times 10^{4} }[/tex]
Answer:
C
Step-by-step explanation:
First, the question is asking how many times greater the distance to the Challenger Deep is compared to Mount Everest. This means that the Challenger Deep will be on top, with the distance to Mount Everest on the bottom.
Next, we can see that in our answers, we are only given one significant digit. This means that we have to round our original numbers to the nearest significant digit and work from there. For Challenger Deep, 36,070 must be rounded to the nearest ten thousandth as it is in the ten thousands. Therefore, it must be rounded to 40,000 or 30,000. As 36,070 is closer to 40,000 than 30,000 (we can tell this because the second number, 6, is greater than 5, so we round up), we can represent this as 40,000. For Mount Everest, we can round 29,029 to either 20,000 or 30,000. 30,000 is the appropriate choice here because 9, the second number, is greater than 5.
Therefore, our ratio is now 40,000 / 30,000 . Our answers are written in scientific notation, so we must convert our numbers to those values.
Let's start with 40,000 . Our one significant digit is 4, so we can write this as 4 * something. For each number in 10 to the power of x (x is a placeholder value), we add x amount of zeros. For example, for 4 * 10², we add 2 zeros, making it 400. There are 4 zeros here, so to write this in scientific notation, we have 4 * 10^4
Similarly, for 30,000 , we can write this as 3 * 10^4 as there are 4 zeros.
Our ratio is thus 40,000 = 4*10^4 , which is the Challenger Deep value rounded, over 30,000 = 3 * 10^4, which is the Mount Everest value rounded. We can write this as [tex]\frac{4*10^{4}}{3*10^{4}}[/tex], or C
HELP !!! find the surface area of each figure. Round it to the nearest tenth.
Answer:
556
Step-by-step explanation:
Surface area=2*(lb+bh+lh)=2*(110+80+88)=556
In Exercises 1-4, determine whether the dilated figure or the original figure is closer to the center of dilation. Use the given location of the center of dilation and scale factor k.
1. Center of dilation inside the figure; k = 3
Center of ditation inside the figure, k = 1/2
3. Center of dilation outside the figure: = 120%
4. Center of dilation outside the figure; k = 0.1
When the Center of dilation is inside the figure
The original figure is closer to the center of dilationThe dilated figure is closer to the the center of dilationWhen the Center of dilation is outside the figure
3. The original figure is closer to the the center of dilation
4. The dilated figure is closer to the center of dilation
The center of dilation is the fixed point from which the distances in a dilation are measured
The scale factor is ratio of the side lengths of an original figure or preimage to the side lengths of the newly formed image
Center of dilation is inside the figure
Where the center of dilation is inside the figure, and the scale factor is larger than 1, k = 3 > 1, we have;The distance of a point on the dilated figure, including the distances from the center of dilation is 3 times the distances of points on the original image from the center of dilation
Therefore, the original figure has a shorter distance to and is therefore closer to the the center of dilation than the dilated figure
2. Where the center of dilation is inside the figure, and the scale factor is a fraction between 0 and 1 k = 1/2, we have;
The distance of a point on the dilated figure, including the distances from the center of dilation is 1/2 times the distances of points on the original image from the center of dilation
Therefore, the dilated figure has a shorter distance to and is therefore closer to the the center of dilation than the original figure
Center of dilation outside the figure
3. Given that the center of dilation is outside the figure and the scale factor is larger than 1, k = 120% = 120/100 = 1.2 > 1, we have;
The distance of the dilated figure from the center of dilation is 120% of the distance of the original figure from the center of dilation, therefore, the original figure is closer to the the center of dilation than the dilated figure
4. Where the center of dilation is outside the figure and the scale factor is a fraction between 0 and 1, k = 0.1 < 1
The distance of the dilated figure from the center of dilation is only 0.1 times the distance of the original figure from the center of dilation, and therefore, the dilated figure is closer to the center of dilation
Learn more about scale factors and center of dilation here;
https://brainly.com/question/12162455
5. Which pair of equations represents parallel lines?
A. y =2x+7
Y=2x-7
B. Y=7
X=7
C. Y=2x-7
Y=-1/2-7
D. Y=2x+7
Y=x+7
Answer:
C
Step-by-step explanation:
What is the factored form of 1,458,43 – 2?
Answer:
Factors of 1458 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486, 729, 1458. There are 14 integers that are factors of 1458. The biggest factor of 1458 is 1458. Positive integers that divides 1458 without a remainder are listed below.
Write the sum using the summation notation assuming the suggested pattern continues 2, -10, 50, -250, +…
Is this sequence arithmetic or geometric? How do you know?
Answer:
geometric
x=number of terms
∑ 2(-5)^(k-1)
k=1
Step-by-step explanation:
the sequence has a ratio of -5 (2*-5=-10, -10*-5=50)
x=number of terms
∑ 2(-5)^(k-1)
k=1
for this i don't know what the last term is since it doesn't show in the question but just find 2(-5)^x and x will be the top term
.simplify
(2a+5)²-(a+3)(a-3)
Answer:
3a^2 + 20a + 34
Step-by-step explanation:
(2a + 5)^2 = 4a^2 + 20a + 25
(a +3)(a - 3) = a^2 - 9
Put these two partial answers together.
4a^2 + 20a + 25 -(a^2 -9 ) Remove the brackets.
4a^2 + 20a + 25 - a^2 + 9
4a^2 + 20a + 25 - a^2 + 9
3a^2 + 20a + 34
Answer: 3a² + 20a + 34
Concept:
When doing simplifying expressions, following the PEMDAS method would be easier.
ParenthesesExponentsMultiplicationDivisionAdditionSubtractionWhen expanding parentheses, following the FOIL method would be easier.
FirstOuterInner LastSolve:
Given expression
(2a + 5)² - (a + 3) (a - 3)
Simplify exponenets
= (2a + 5) (2a + 5) - (a + 3) (a - 3)
Expand parentheses
= 4a² + 10a + 10a + 25 - (a² - 3a + 3a - 9)
= 4a² + 10a + 10a + 25 - a² + 3a - 3a + 9
Combine like terms
= 4a² - a² + 10a + 10a + 3a - 3a + 25 + 9
= 3a² + 20a + 34
Hope this helps!! :)
Please let me know if you have any questions
A. 4
B. -9/8
C. 8/7
D. -7/2
(it’s not C ik that)
***CAN SOMEONE HELP ME PLEASE!!***
The polygon in each pair are similar. Find the missing side length
Answer:
45 / 27 = 30 / 18 = x / 24
x = 40
Step-by-step explanation:
Hi there!
The question here states that the two polygons are similar
Polygons that are similar have similar side length ratios.
If we want to find a side length we must create a proportional relationship
We are already given a partial proportional relationship.
Which is...
45 / __ = __ / 18 = x / __
First let's fill in the blanks
The side that is corresponding to the side with a length of 45 has a length of 27. So it would be 45/27
The side that is corresponding to the side with a length of 18 has a length of 30. So it would be 30/18
The side corresponding to side labeled "x" has a length of 24. so it would be x/24
So we would have
45 / 27 = 30 / 18 = x / 24
Now let's find x
We only need 2 ratios ( the one including x of course, and the other one can either be 30/18 or 45/27)
30 / 18 = x / 24
Now let's solve for x
Cross multiply
30*24=720
18*x=18x
We now have 18x = 720
Divide both sides by 18
18x / 18 = x
720 / 18 = 40
x = 40
To check our answers we can see if the ratios are similar
If they are then we are correct
45/27 = 1.66
30/18 =1.66
40/24 = 1.66
They are all equivalent meaning that our answers are correct
Solve for b.
-32 + 10b = -22
Answer: b = 1
Step-by-step explanation:
= -32 + 10b = -22
-32 + 10 = -22
b = 1
Check: -32 + 10(1) = -22
= -22
Answer:
b=1
Step-by-step explanation:
Hello,
We would like to solve for b in the equation -32+10b=-22.
When we want to solve for a variable, we want to isolate it on one side (have it on one side by itself. No other numbers.)
So to start, add 32 to both sides to remove it from the left side (-32+32=0).
-32+10b=-22
+32 +32
______________
10b=10
Now, there isn't anything with 10b, but we want the value of b by itself (1b), as 10b is 10 times the value of what b is.
So divide both sides by 10
b=1
Hope this helps!
What is the volume of the rectangular prism?
Answer:
94.5 yd^3
Step-by-step explanation:
The volume of a rectangular prism is given by the formula:
A = lwh
Where:
l = length
w = width
h = height
Volume is how much space a 3d figure occupies.
USE THE FORMULA WITH THE GIVEN DIMENSIONS:
A = (7)(4.5)(3)
= (31.5)(3)
= 94.5
Volume is measured in cubic yards, in this case.
Therefore your answer is 94.5 yd^3
I hope I helped!
Answer:
Step-by-step explanation:
length = 7 yd
Width = 4.5 yd
height = 3 yd
Volume of rectangular prism = length * width * height
= 7 * 4.5 * 3 = 94.5 yd³
Three is subtracted from a number, and then the difference is divided by eleven. The result is twelve. What is the
number?
Answer:
The number is 135.
Step-by-step explanation:
1) Form an equation
Three is subtracted from a number
⇒ [tex]x-3[/tex] (where x is "the number")
The difference is divided by 11
⇒ [tex]\displaystyle \frac{x-3}{11}[/tex]
The result is 12
⇒ [tex]\displaystyle \frac{x-3}{11}=12[/tex]
2) Solve the equation
[tex]\displaystyle \frac{x-3}{11}=12[/tex]
Multiply both sides by 11
[tex]\displaystyle \frac{x-3}{11}*11=12*11\\\\x-3=132[/tex]
Add 3 to both sides
[tex]x-3+3=132+3\\x=135[/tex]
Therefore, the number is 135.
I hope this helps!
HELP PLEASE ASAP!!!!! Alex can cut a cord into 7 pieces in 36 seconds. How long will it take him to cut the cord into 12 pieces?
Answer:
GIVE ME BRAINLIEST
Step-by-step explanation:
How do I solve this: h + 6/5 = 2
Need help!
.......................
Answer:
[tex]24x^{3} \sqrt{5x} -4x^{3} \sqrt{10x}[/tex]
Step-by-step explanation:
[tex]2\sqrt{8x^{3} } (3\sqrt{10x^{4} } -x\sqrt{5x^{2} } )[/tex]
[tex]=2.2x\sqrt{2x} (3x^{2} \sqrt{10} -x^{2} \sqrt{5} )[/tex]
[tex]=4x\sqrt{2x} (3x^{2} \sqrt{10} -x^{2} \sqrt{5} )[/tex]
[tex]=12x^{3} \sqrt{2xx10} -4x^{3} \sqrt{2xx5}[/tex]
[tex]=24x^{3} \sqrt{5x} -4x^{3} \sqrt{10x}[/tex]
OAmalOHopeO
Let A represent the average value of the function f(x) on the interval [0,6]. Is there a value of c for which the average value of f(x) on the interval [0,c] is greater than A?
Answer:
The average value of the Function f(x) by squeeze theorem states that no extreme or greater value will exist within the designated area for f(x)
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE QUESTION!!
Answer:
(base x height x length)/2 = volume
6x8x8 = 384/2 = 192in^3
hope that answers your question
HURRYYYYYYYYYYYYYY PLZZZZ
Answer:
G
Step-by-step explanation:
you know its G just by the way it is
If Tan A=5/12 then find cot A, cos A and Sin A
Cot A=1/tan A=12/5
cos A= 12/13
sin A=5/13
Draw a right angled triangle
the hypotenuse is the longest side which is 13 using Pythagoras theorem
the side opposite the angle A is 5
the side closest to the angle A which is called the adjacent is 12
sinA =opp/hyp
cos A= adj/hyp
cotA =1/tanA=cos A/sinA
Note: Pythagoras theorem is
hyp²=opp²+adj²
Answer:
Step-by-step explanation:
[tex]tan \ A = \frac{5}{12}=\frac{opposite \ site}{adjacent \ side}[/tex]
hypotenuse² = (opposite side)² + (adjacent side)²
= 5² + 12²
= 25 + 144
= 169
hypotenuse = √169 = √13*13 = 13
[tex]Cot \ A = \frac{adjacent \ side}{opposite \ side}=\frac{12}{5}\\\\Cos \ A = \frac{adjacent \ side}{hypotenuse}=\frac{12}{13}\\\\Sin \ A = \frac{opposite \ side}{hypotenuse}=\frac{5}{13}[/tex]
