Answer:
x=3
y=3
Step-by-step explanation
Here we have been given with two equations and we will solve them by substitution by elimination method.
2x + 3y = 15 (Equation No 1)x + y = 6 (Equation No 2)Transposing y in 1st equation from L.H.S. to R.H.S. it would be negative,
[tex] \implies \: \displaystyle\sf{x \: = \: 6 - y}[/tex]
Now, we would substitute this value of x in Equation No 1.
[tex] \implies \: \displaystyle\sf{2 \: (6 - y) \: = \:15 }[/tex]
[tex] \implies \: \displaystyle\sf{2 \: \times (6 - y) \: = \:15 }[/tex]
[tex]\implies \: \displaystyle\sf{12 - 2y \: = \:15 }[/tex]
Transposing 12 to R.H.S.,
[tex] \implies \: \displaystyle\sf{ - 2y \: = \:15 - 12 }[/tex]
[tex]\implies \: \displaystyle\sf{ - 2y \: = \:3}[/tex]
[tex]\implies \: \displaystyle\bf{ y \: = \: - \dfrac{3}{2} }[/tex]
Therefore, value of y is - 3/2.
★ Finding out value of x:-
[tex] \implies \: \displaystyle\sf{x \: = \: 6 - y }[/tex]
[tex]\implies \: \displaystyle\sf{x \: = \: 6 - ( \dfrac{ - 3}{ 2} )}[/tex]
[tex]\implies \: \displaystyle\sf{x \: = \: \frac{12 + 3}{2} }[/tex]
[tex]\implies \: \displaystyle\bf{x \: = \: \frac{15}{2} }[/tex]
Henceforth,
Value of x is 15/2.Rowan has 3 pieces of yarn, as described below. *a red piece of yarn that is 3/4 foot long *a yellow piece of yarn that is 6/8 foot long * a blue piece of yarn that is 4/12 foot long Wich number sentence correctly compares the lengths of 2 of these pieces of yarn. A 3/4 < 3/6 B 4/12 < 3/4 C 3/4 > 6/8 D 4/12 > 6/8
Answer:
b
Step-by-step explanation:
because all the orher ones are wrong and not correct.
An angle measuring (870n)° is in standard position. for which value of n will the terminal side fall on the y-axis? n = 3 n = 4 n = 5 n = 6
The value of n will the terminal side fall on the y-axis at n=3
The terminal side of an angle fall along the positive portion of the y-axis,
If it can written in the form of [tex](90^0)a[/tex]
Where a = positive odd integer,
We hyave given the given angle is,
[tex](870n)^0,[/tex]
What is terminal side?The terminal side of an angle theta drawn in angle standard position is the side which isn't the initial side
Now for n=3
[tex](870(3))^0=2610^0[/tex]
The angle will be 2610°
Its terminal side fall along the positive portion of the y-axis,
[tex]2610^0 = (90^0)a \implies a = 29[/tex]......( Positive odd integer )
Therefore for n = 3, the terminal side of the angle (870n)° falls along the positive portion of the y-axis,
For n = 4,
Our angle will be 3480°
Its terminal side fall along the positive portion of the y-axis,
[tex]3480^0 = (90^0)a \implies a = 38.6667 ( Not possible )[/tex]
Therefore for n = 4, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis
Next is for n = 5,
Our angle will be 4350°
Its terminal side fall along the positive portion of the y-axis,
[tex]4350^0 = (90^0)a \implies a = 48.333.. ( Not possible )[/tex]
Thus, for n = 5, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis,
For n = 6,
Our angle will be 5220°
Its terminal side fall along the positive portion of the y-axis,
[tex]5220^0 = (90^0)a \implies a = 58..... ( Not possible )[/tex]
Thus, for n = 6, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis.
Therefore,the value of n will the terminal side fall on the y-axis at n=3.
To learn more about the terminal side visit:
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Answer:
a
Step-by-step explanation:
x=3 on edge
These triangles are similar. Solve for the scale factor.
Answer:
Scale factor = 3
Step-by-step explanation:
A - B = 1-3
3 - 1 = 2
A' - B' = 3-9
9 - 3 = 6
6 / 2 = 3
Will give BRAINLIEST!! Write a polynomial and show all the steps you would take to factor this polynomial completely. Please explain each step thoroughly.
I am not accepting links. Thank you:)
Step-by-step explanation:
Consider this polynomial,
[tex]8 {x}^{2} + 2x - 3[/tex]
First, I do the AC memethod. To find my two numbers,
That is to find two numbers that multiplied will equal my leading coeffeicent, A times my constant, C
And that will also add to 2, my middle term.
So using that
[tex]8 \times - 3 = - 24[/tex]
So let find factors of-24:
Factors can be positve or negative
The factors of 24 are : 1,2,3,4,6 8,12,24.
So which one of these add up to 2.
[tex]6 + ( - 4) = 2[/tex]
and
[tex]6 \times - 4 = - 24[/tex]
So six and negative four is our numbers.
Now, let set up our binomials
Step 1: Rewrite the orginal equation by using 6x and -4x instead of 2x.
Disclaimer: The placement of these numbers doesn't matter.
So we have
[tex]8 {x}^{2} + 6x - 4x - 3[/tex]
Step 2: Group the first two terms and last two terms
[tex](8 {x}^{2} + 6x) + ( - 4x - 3)[/tex]
Factors the first group by finding the GCF.
x is the greatest common variable, and 2 is the gcf so we have
[tex]2x(4x + 3) + ( - 4x - 3)[/tex]
Next, factor the next group by -1.
[tex]2x(4x + 3) - 1(4x + 3)[/tex]
Combine the outside factors.
[tex](2x - 1)(4x + 3)[/tex]
So those are the factors.
Question 4 of 10
You have $10.00 and want to buy all of the items below. How much change
will you have left after you make your purchase? Do not include $ in your
answer.
COST
ITEM
Pancake Mix
Eggs
Syrup
$2.18
$2.28
$3.98
PLS HELP!’
Answer: 1.56
Step-by-step explanation:
Add all the cost together, the subtract the ten dollars.
2.18 + 2.28+ 3.98 = 8.44
10.00 - 8.44 = 1.56
Answer below
due today at noon
Answer:
x = -3
Step-by-step explanation:
A vertical line has an equation of the form
x = a
where a is the x-coordinate of every point on the line.
Every point on the line has x-coordinate -3, so the equation is
x = -3
A figure is made up of a triangle and a rectangle. The triangle has a height of 8 inches and a base of 9 inches. The rectangle has dimensions of 7 inches×9 inches. What is the area of the figure?
Step-by-step explanation:
area of triangles
1/2*9*8= 36
area of.rectangle
8*9= 72
36+72=108 square inches
Answer 11-12 it’s ok if your don’t no one of them. Please do at least one. Thanks.
[11]
Equation: 180° - 75°
Measure: 105°
A straight line has an angle measurement of 180°. Since we have GFB, 75°, we can find EFB this way.
[12]
Equation: 90° - 40°
Measure: 50°
The little box in the angle shows that it is equal to 90°. Since they give us HGB, 40°, we can solve for EFB using this information.
8. A 140-pound female has three mixed drinks one right after the other.
a. What is her BAC after consuming the three drinks?
BAC =
b. What is her BAC three hours after finishing the last drink?
The BAC of the female is an illustration of proportion
The BAC after consuming the three drinks is 0.029wThe BAC three hours after consuming the drinks is 0.087 wHow to calculate the BAC?BAC is calculated using:
BAC = Alcohol consumed/(Body Weight * R)
The weight is given as:
Body weight = 140 lb
Convert to kg
Body weight = 63.5 kg
For female
R = 0.55
So, we have:
BAC = Alcohol/(63.5 * 0.55)
BAC = Alcohol/34.925
BAC = 0.029Alcohol
The weight or volume of the alcohol consumed is given.
So, we represent it with w.
BAC = 0.029w
Hence, the BAC after consuming the three drinks is 0.029w
How to calculate the BAC after 3 hours?We have:
BAC1 = 0.029w
Time (t) = 3 hours
The BAC after 3 hours is
BAC = BAC1 * (t - 0.015)
So, we have:
BAC = 0.029w * (3 - 0.015)
Evaluate the product
BAC = 0.087w
Hence, the BAC three hours after consuming the drinks is 0.087 w
Read more about BAC at:
https://brainly.com/question/1781657
this question is too hard
Answer:
There are 33 nuts in the bag, to 21 dried fruits.
Total number of dried fruits is 21, while the total number of nuts is 33.
Step-by-step explanation:
The two-way table shows the number of sport utility vehicles with certain features for sale at the car lot. a 4-column table has 3 rows. the first column has entries third-row seats, no third-row seats, total. the second column is labeled 4-wheel drive with entries 18, 7, 25. the third column is labeled no 4-wheel drive with entries 12, 28, 40. the fourth column is labeled total with entries 30, 35, 65. what is the probability that a randomly selected car with no 4-wheel drive has third-row seats? 0.3 0.4 0.7 0.8
The probability that a randomly selected car with no 4-wheel drive has third-row seats is given by: Option B: 0.4
How to calculate the probability of an event?Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
What is chain rule in probability?For two events A and B, by chain rule, we have:
[tex]P(A \cap B) = P(B)P(A|B) = P(A)P(B|A)[/tex]
where P(A|B) is probability of occurrence of A given that B already occurred.
For this case, the table given is:
Entries 4-wheel drive No 4-wheel drive Total
Third Row Seats 18 12 30
No Third Row Seats 7 28 35
Total 25 40 65
Let we take
A = event that a randomly selected car has no-4 wheel drive
B = event that a randomly selected car has third row seats
The total ways a car can be selected = 65 = n(S)
Total ways A can happen = n(A) = 40 (from the table).
Similarly, n(B) = 30
P(A) = n(A)/n(S) = 40/65
P(B) = n(B)/n(S) = 30/65
P(A∩B) = n(A∩B)/n(S) = 12/65
As by chain rule, we have:
P(A∩B) = P(A)P(B|A) = P(B)P(A|B)
We need P( A randomly selected car has three seats given that the selected car is with no 4-wheel drive)
which is symbolically P( B | A)
Thus, we use: P(A∩B) = P(A)P(B|A)
or
[tex]12/65 = (30/65)(P(B|A))\\\dfrac{12/65}{30/65} = P(B|A)\\\\P(B|A) = \dfrac{12}{30} = \dfrac{2}{5} = 0.4[/tex]
Thus, the probability that a randomly selected car with no 4-wheel drive has third-row seats is given by: Option B: 0.4
Learn more about probability here:
brainly.com/question/1210781
Answer:
b. 0.4
Step-by-step explanation:
took the test
The rate at which people learn about a secret is directly proportional to the number of people who know the secret. If two people know the secret on day 0, and 20 people know it on day 2, how long will it take for the whole school (4000 people) to know?
Answer:
between 222 and 223 days
Step-by-step explanation:
This relation includes the point (0, 2).
A proportional relation must include the point (0, 0).
This is not proportional, but it may be linear.
Points: (0, 2), (2, 20)
y = mx + b
20 = (20 - 2)/(2 - 0) × 2 + b
20 = 18/2 × 2 + b
b = 2
y = 18x + 2
When 4000 people know, y = 4000.
y = 18x + 2
4000 = 18x + 2
3998 = 18x
x = 3998/18
x = 222.111...
Answer: between 222 and 223 days
You are starting a savings account for college. You put $1,000 in as your starting balance. You earn simple interest at 10% every year. You also must pay 30% income tax on the interest earned annually. Calculate the balance for the account after 5 years
Answer:
$1,350
Step-by-step explanation:
Simple interest formula
I = Prt
where:
I = interestP = principalr = interest rate (in decimal form)t = time (in years)Given:
P = $1,000r = 10% = 0.1t = 5 years⇒ Total interest earned = 1000 × 0.1 × 5 = $500
If you have to pay 30% income tax on the interest earned annually, then you will keep 70% of your earned interest.
⇒ 70% of $500 = 0.7 × $500 = $350
Account balance = principal + interest earned after tax
= $1,000 + $350
= $1,350
a fast food chain surveyed a random sample of students to determine what pizza they prefer.cheese pizza was preferred by 40 students.pepperoni pizza was preferred by 28 students.based on the results,how many of 340 student can be expected to prefer cheese pizza
Answer:
12%, 0.12, 5/17, or as a ratio: 5:17
Step-by-step explanation:
To find the percentage:
Take the 40 students who prefer cheese and divide it by 340:
0.11764705882 rounded would be 0.12.
Convert 0.12 into 12% of students prefer cheese pizza.
To find the decimal, to the same exact thing I did up there, but, don't turn it into a percent, just leave it as 0.12.
To find the fraction, turn it into:
40/340
Then simplify it:
5/17 prefer cheese pizza.
For ratio, do the same as fraction, but, instead of the slash mark, turn it into a colon like this: 5:17.
:)
Form and solve an equation to find x
Perimeter = 42 cm
2x
- 3
Х
Х
2x – 3
-
what is the answer for this also?
Answer:
64 cm^3
Step-by-step explanation:
V = lwh
V = 4 x 4 x 4
V = 64 cm^3
Hope this helps!
[tex] \huge\fbox\orange{ANSWER} [/tex]
[tex] \mathsf \purple{volume \: of \: square = {x}^{3} }[/tex]
[tex] \mathsf \pink{v = {4}^{3} }[/tex]
[tex] \mathsf \purple{v = {64cm}^{3} }[/tex]
solve for x use the trig to find angle
[tex]\qquad\qquad\huge\underline{{\sf Answer}}☂[/tex]
Let's solve, using Trigonometry ~
[tex]\qquad \sf \dashrightarrow \: \tan(x) = \frac{54}{72} [/tex]
[tex]\qquad \sf \dashrightarrow \: \tan(x) = \frac{3}{4} [/tex]
[tex]\qquad \sf \dashrightarrow \:x = \tan { }^{ - 1} ( \frac{3}{4} ) [/tex]
[tex]\qquad \sf \dashrightarrow \:x = 37 \degree[/tex]
Answer:
[tex]\displaystyle 36,9[/tex]
Step-by-step explanation:
[tex]\displaystyle 1\frac{1}{3} = cot\:x \hookrightarrow cot^{-1}\:1\frac{1}{3} = x \hookrightarrow 36,869897646...° = x \\ \\ 36,9° ≈ x[/tex]
OR
[tex]\displaystyle \frac{3}{4} = tan\:x \hookrightarrow tan^{-1}\:\frac{3}{4} = x \hookrightarrow 36,869897646...° = x \\ \\ 36,9° ≈ x[/tex]
Information on trigonometric ratios
[tex]\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOCITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:θ \\ \frac{ADJACENT}{OPPOCITE} = cot\:θ[/tex]
I am joyous to assist you at any time.
What is the slope-intercept equation for this line?
Answer:
y=-2x-1
Step-by-step explanation: This is because of rise/run. This means rise, count up or down until you hit the line that is horizontal to where your line intersects a whole point. Then run, what you count horizontal matches with your rise count. This means we can count 2/1 and since it's going down it's negative. So the slope is -2 and the y-intercept is -1 because it intersects through the y-intercept -1.
What is the area of this figure?
Answer:
234 mm^2
Step-by-step explanation:
These questions are tricky but to make them easier, try to break down the shape into smaller regular shapes and work them out.
I would divide this shape into 2 rectangles and one triangle
Area of small bottom rectangle: 4 x 11 = 44mm^2
Area of rectangle in the middle: 14 x 8 = 112mm^2
Area of triangle: 12 x 13/2 = 78mm^2
Add all the areas together = 44+112+78 = 234mm^2
Let T be the set of things found in a toy store, and V be the set of things that cost more than $50.
Select the words from the drop-down menus to correctly complete the sentences.
The set T∪V is the set of things that
Choose...
.found in a toys store and cost more then 50$
found in a toys store or cost more then 50$
The set T∩V is the set of things that
Choose...
.found in a toys store and cost more then 50$
found in a toys store or cost more then 50$
The set T′ is the set of things that
Choose...
cost under 50$
not found in toy store
not found in toy store and cose more then 50
Answer:
found in a toys store and cost more than 50$
Step-by-step explanation:
it makes the most sense don't you think?
Does anyone know the answer to these?
(5) to the 7 over 3 power
[tex]5^{7/3} = 42.75[/tex] (approximately)
using the formula [tex]x^{a/b}=\sqrt[b]{x^a}[/tex] we can solve the problem
so we rewrite it as [tex]\sqrt[3]{5^7}[/tex] and get ~42.75
Jasmine is trying to replace the flooring in her rectangular bedroom. When she measured the width and length of the floor, she found that the length is 5 ft. longer than the width. If the perimeter of the room is 50 ft., how much flooring will she need to replace the existing flooring in her room?
Answer:
150ft^2
Step-by-step explanation:
FINDING THE LENGTHS
50 = x + 5 + x + x + 5 + x
50 = 4x + 10
50 - 10 = 4x
40 = 4x
40/4 = x
10ft = x
AMOUNT OF FLOORING
area = l x b
= (10 + 5) x 10
= 15 x 10
= 150ft^2
Help me answer this question about congruent triangles. 50 points available.
Answer:
B
Step-by-step explanation:
No these triangles are not congruent.
Left triangle
Shortest side = 6 cm
Longest side = 13 cm
3rd side = unknown but < 13
Right triangle
Shortest side = 6 cm
Longest side = unknown but > 13
3rd side = 13 cm
Although the shortest side of both triangles is 6 cm, the longest side of the left triangle is 13 cm, whereas the longest side of the right triangle is unknown but will be more than 13 cm.
We do not know if any of the angles are congruent. If they were congruent, we would expect to see this marked by the same angle line(s) on each triangle.
Pls help thanks to who ever does and please do NOT put links
Answer:
C
Step-by-step explanation:
Remark
The way to solve the problem is to figure out how many cubic feet would be present if the window was not there and then calculate the volume of the window and subtract it. That is the general method used to obtain the answer to the question you have asked.
Volume Original Shape
Each side of the figure is one side of a square.
So the volume of the square face is 6 by 6 or 6*6 = 36 (no window)
The window is 2*2 which is 4.
The volume of the original shape is 36 - 4 = 32
Volume new shape
Each side of the figure is 12 by 12 = 144 With no window
The size of the window is 4 by 4 = 16 With the window (Subtract)
The size of the modified figure is 128
Answer and discussion
The question is a bit ambiguous. I think the question means that the wall has gone from 32 to 128 cubic feet. So you need Subtract to find the difference..
Answer: 128 - 32 = 96 which is C.
A man invests a sum of money ($8,000) in a bank that offers a rate of 5%. He invests the money for 2 years. Calculate the amount of money in the bank at the end of the 2-year period if invested at:
(a) simple interest
(b) compound interest.
Question 6 (6 marks)
The diameter of a circle is 10 cm (as shown in the diagram). Use π = 3.14 Calculate to 2 decimal places, the:
(a) circumference
(b) area
Answer:
(a) 8000 times 5 times 2 = 800
Simplify −4(x+1)+6x . Write your answer in factored form.
Answer:
2(x - 2)
Step-by-step explanation:
- 4(x + 1) + 6x ← distribute parenthesis by - 4
= - 4x - 4 + 6x ← collect like terms
= 2x - 4 ← factor out 2 from each term
= 2(x - 2)
=================================================
Let's simplify this expression.
The first step is to use the distributive property, which states:-
[tex]\bigstar{\boxed{a(b+c)}[/tex]
Simplify:-
[tex]\bigstar{\boxed{-4(x+1)}[/tex]
[tex]\longmapsto\sf{-4x-4}[/tex]
Add 6x:-
[tex]\longmapsto\sf{-4x+6x-4}[/tex]
Combine Like Terms:-
[tex]\longmapsto\sf{2x-4}[/tex]
Now, we should write our answer in factored form, so we factor 2 out:-
[tex]\longmapsto\sf{2(x-2)}[/tex]
=============================================
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
What is the value of In e^4
a 0
b 1
c 2
d 4
Answer:
[tex]4[/tex]
Step-by-step explanation:
[tex]\ln e^4= 4\ln e = 4 \log_e e = 4 \times 1 = 4[/tex]
I want to know how to find EF and what the answer is.
[tex]\huge\underline\mathtt\colorbox{cyan}{37✅✅✅}[/tex]
Step-by-step explanation:
5x+12=6x+7 (opposite sides of a parallelogram are equal) 12=x+7 (subtract 5x from both sides) x=5 (subtract 7 from both sides) Now put x in any of the equations-- 5(5)+12=37 or 6(5) +7=37To determine the age of fossils, scientists use radiometric dating. This involves measuring quantities of certain radioactive isotopes and using mathematical equations to compare the amounts of each isotope present.
Suppose a scientist dates a piece of petrified wood and calculates that it is approximately 23,881,392.3102 years old. The petrified wood is later displayed in a museum.
What is the most reasonable way for the museum tour guide to describe the age of the wood to museum visitors?
(A): 2.3881×107 years old
(B): 24 million years old
(C): 23.8813923102 mega years old
(D): 23 billion years old
Answer:
B 24 million years old
Step-by-step explanation:
i did this quiz a long time ago tho so it might be B or D