Answers
80+(4x-y)=180
4x-y=100
(4x-y) and (x+2y+10) also form a straight angle, but we know that 4x-y=100
100+x+2y+10=180
x+2y+110=180
x+2y=70
Now we have a system of equation
4x-y=100
x+2y=70
Solve the first equation for y
-y=-4x+100
y=4x-100
Substitute y
x+2(4x-100)=70
x+8x-200=70
9x=270
x=30
Now plug in the known x value
30+2y=70
2y=40
y=20
Final answer: x=30, y=20
Answer:
The values of [tex]x=30^{\circ}[/tex] and [tex]y=20^{\circ}[/tex].
Step-by-step explanation:
A Linear pair is a pair of adjacent angles formed when two lines intersect.
In the given figure, [tex]80^{\circ}[/tex] and [tex]4x-y[/tex] , [tex]4x-y[/tex] and [tex]x+2y+10^{\circ}[/tex] form a linear pair.
By linear pairs theorem, we have
[tex]80^{\circ}+4x-y=180^{\circ}[/tex]
[tex]4x-y+x+2y+10^{\circ}=180^{\circ}[/tex]
On solving we get,
[tex]4x-y=100^{\circ}[/tex] ....(1)
[tex]5x+y=170^{\circ}[/tex] .....(2)
Now, to solve equation (1) and (2) by simultaneously; we get [tex]x=30^{\circ}[/tex]
putting the value of x in equation 1 we get,
[tex]4x-y=100^{\circ}[/tex]
[tex]4\cdot 30^{\circ}-y=100^{\circ}[/tex]
[tex]120^{\circ}-y=100^{\circ}[/tex]
On simplify we have, [tex]y=20^{\circ}[/tex]
Therefore, the values of x and y are: [tex]30^{\circ}[/tex] and [tex]20^{\circ}[/tex]
Related Questions
I don’t 100% remember how to turn this into a standard problem.. could someone help me really quick?
Answers
First evaluate the exponent and expand (foil).
y= 3(x^2-4x+4)+1
Then distribute the 3
y= 3x^2-12x+12+1
Combine like terms
y=3x^2-12x+13
Final answer: 3x^2-12x+13=0
The volume of a cone varies jointly as the square of its radius and its height. if the volume of a cone is 99piπ cubic inches when the radius is 3 inchesinches and the height is 3 inches, find the volume of a cone when the radius is 4 inchesinches and the height is 9 inches.
Answers
At 12 noon in anchorage Alaska Janice noticed that the temperature outside was 12
f. The temperature dropped at a steady rate of 2 F per hour.
Answers
Well, you know that at 12:00 pm, the temperature was 12 F and that it decreases by a steady rate of 2 F each hour.
This means that at 1:00 pm, the temperature was 12-2 = 10 F
At 2:00 pm, the temperature was 10-2 = 8 F
At 3:00 pm, it was 8-2 = 6 F
.......and so on
You can follow this sequence to the timing you are looking for.
Alex wants to put a fence around his garden. It is square and has an area of 196 square feet. He wants to put a post in each corner, and every 7 feet. How may posts and how may feet of fencing does he need?
Answers
So each side is 14 feet
There are 4 posts in the corners and if each side is 14 feet and you put a post every 7 feet there would be an additional post on each side. That means he needs 8 posts.
The perimeter is 14×4=56
This means he needs 56 feet of fencing.
Ivan can type 54 words in 3 minutes. At this rate, how many words can he type in 10 minutes?
Answers
Do even numbers have more factors in odd numbers or do i numbers have more factors than even numbers
Answers
Final answer:
Whether even or odd numbers have more factors depends on the specific properties of each number, such as its prime factor composition, rather than on the binary classification of being even or odd.
Explanation:
The question of whether even numbers have more factors than odd numbers or vice versa does not have a straightforward answer, as it varies from number to number. In general, the quantity of factors a number has depends more on the specific properties of that number, such as its composition of prime factors, rather than simply on whether it is odd or even. For example, a number like 2 (which is even) has only two factors (1 and itself), while an odd number like 9 has three factors (1, 3, and 9). Similarly, an even number such as 12 has more factors (1, 2, 3, 4, 6, and 12) than many other even and odd numbers. Therefore, the distinction between even and odd in terms of number of factors is not particularly meaningful without considering the specific characteristics of individual numbers.
An expression to convert 50 miles per hour to miles per minute is shown.
What value can be entered in the box to correctly make this conversion?
Answers
Answer:
x = 60
Step-by-step explanation:
We have to convert 50 miles per hour to miles per minute.
1 hour = 60 minutes
Comparing with the given expression, we get
x = 60
Why is the completely factored form X^4+8x^2-9
Answers
This is still factor-able:
[tex]x^4+8x^2-9[/tex]
[tex]x^4+9x^2-x^2-9[/tex]
Factor by grouping.
[tex]x^2(x^2+9)-1(x^2+9)[/tex]
[tex](x^2+9)(x^2-1)[/tex]
Factor by difference in squares.
[tex](x^2+9)(x-1)(x+1)[/tex]
Hope this helps.
-Benjamin
Which is the best simplification of (24 x 32) / (2 x 3)?
Answers
(768)/(6)
=128
I hope this helped you!!
To simplify (24 x 32) / (2 x 3), perform the multiplication operations first. Then perform the division operation. This results in the simplification of the given expression to 128.
Explanation:To simplify the expression (24 x 32) / (2 x 3), we'll first carry out the multiplication operations because of the BIDMAS or PEMDAS rule that gives the order of operations in maths. B or P stands for brackets, I or E stands for Indices or Exponents, D/M for Division/Multiplication and A/S for Addition/Subtraction. According to this rule, Division or Multiplication is performed from left to right. Therefore, we first multiply 24 x 32 which gives 768, and secondly multiply 2 x 3 which gives 6. Thus, the expression now becomes 768 / 6. This division gives us the final answer of 128.
Learn more about Mathematical Simplification here:https://brainly.com/question/33857870
#SPJ2
Diana received $35 worth in Starbucks gift cards for Christmas her favorite drink caramel macchiato costs about $4:00 help diana keep track of the balance left in her gift cards each time she buys a drink how many caramel macchiato will she be able to buy with her gift cards?
Answers
So she will be able to buy 8 caramel macchiatos.
:)
Diana can buy a total of 8 caramel macchiatos with her $35 Starbucks gift cards, and she will have a remaining balance of $3.
To help Diana keep track of the balance on her Starbucks gift cards after purchasing her favorite drink, the caramel macchiato, we need to perform a series of simple subtractions. She starts with a $35 balance, and each caramel macchiato costs $4.00.
After buying the first caramel macchiato, the new balance is $35 - $4.00 = $31.
After the second purchase, $31 - $4.00 = $27.
This process continues until the balance is less than the cost of a caramel macchiato.
To find out how many drinks she can purchase in total, we divide the initial balance by the cost of one caramel macchiato:
$35 / $4.00 = 8.75
Since she cannot buy a fraction of a drink, Diana can buy a total of 8 caramel macchiatos with her gift cards and will have a remaining balance of $3, which is not enough for another drink.
Varia is studying abroad in Europe. She is required pay $3,500 (in US dollars) per year to the university, however, she must pay in euros. How many euros can Varia expect to pay per month to the university? (Round to the nearest whole euro.)
Answers
I cant seem to figure out this question? someone please help me please
Answers
h is measured in miles so you need to convert 1135ft to miles
1 mile = 5280 feet
so 1135/5280 = 0.21496 miles
D = sqrt(2(3960)(0.21496) + 0.21496^2)
D = sqrt(1702.4832 + 0.046207801)
D = sqrt(1702.529408
D = 41.2617 miles round answer as needed
Sammie bought just enough fencing to border either a rectangular plot or a square plot, as shown. The perimeters of the plots are the same.How many meters of fencing did she buy?
Answers
p = 4(x + 2)
p = 4x + 8
perimeter of rectangle : p = 2(L + W)
p = 2(3x + 2 + x - 1)
p = 2(4x + 1)
p = 8x + 2
so if the perimeters are te same, lets set them equal to each other and solve for x
4x + 8 = 8x + 2
8 - 2 = 8x - 4x
6 = 4x
6/4 = x
1.5 = x
the square : p = 4x + 8.....p = 4(1.5) + 8.....p = 14 meters
the rectangle : p = 8x + 2....p = 8(1.5) + 2.....p = 14 meters
so she bought 14 meters of fencing <==
The fencing purchased by Sammie corresponds to the perimeter of either a square or rectangular plot. The perimeters of both these shapes are equal. Therefore, the amount of fencing purchased is equivalent to the perimeter calculated using either of these shapes' formulas.
Explanation:This question is about the concept of perimeter in mathematics. Perimeter is the distance around the border of a shape. In this case, the shapes in question are a square and a rectangle. Because the question states that Sammie has enough fencing for either shape and that the perimeters are the same, we can infer that she bought a length of fencing equivalent to the perimeter of either shape.
Let's take a look at how we calculate perimeter:
For a square, the perimeter (P) is calculated by multiplying the length of one side (s) by 4. So, P = 4s.For a rectangle, the perimeter is calculated by adding twice the width (w) and twice the length (l) of the rectangle. So, P = 2l + 2w.In this scenario, even without specific numerical information, because the perimeters for both shapes are equal, it means that the fencing purchased would correspond to the same value obtained using either of these formulas.
Learn more about Perimeter here:https://brainly.com/question/31695951
Which expression is equal 3(5+6) ?
a. 15+6
b. 5+18
c. 15+18
d. 3+11
please explain
Answers
is 70 thousand written in a standard form or a word form? explain
Answers
In which number is the digit 4 one hundred times larger than the value of 4 in the number 41?
A) 435
B) 540
C) 4,350
D) 9,400
Answers
I need major help!!!!
What is the area of a circle with a diameter of 13.2 cm?
Use 3.14 for pi and round your final answer to the nearest hundredth.
Enter your answer in the box.
Which explanation can be used to derive the formula for the circumference of a circle?
A. Find the length of the diameter and double this amount. Subtract it from the length of the circumference. Set an equation to show the difference equaling the ratio between a circumference and radius. Then rearrange the equation to solve for the circumference.
B. Find the length of the radius. Then find the circumference. Use the square of the radius to set up an equation showing the relationship that the square of the radius equals the π times circumference. Then rearrange the equation to equal the circumference.
C. Find the length of the radius and the area of the circle. Divide the area by the radius to get a quotient of π . Write an equation showing the area of a circle equals this quotient times the radius. Then substitute the area for 3 times the circumference and rearrange the equation to equal the circumference.
D. Find the length of the diameter and the length of the circumference of the circle. Divide the length of the circumference by the length of the diameter. Set up an equation showing the ratio of the circumference to the diameter equal to π . Then rearrange the equation by solving it for the circumference. Substitute 2 times the radius for the diameter.
A regular polygon inscribed in a circle can be used to derive the formula for the area of a circle. The polygon area can be expressed in terms of the area of a triangle.
Let s be the side length of the polygon,
let r be the hypotenuse of the right triangle,
let h be the height of the triangle, and
let n be the number of sides of the regular polygon.
polygon area = n(1/2*sh)
Which statement is true?
As h increases, the area of the regular polygon approaches the area of the circle.
As s increases, the area of the regular polygon approaches the area of the circle.
As n increases, the area of the regular polygon approaches the area of the circle.
As r increases, the area of the regular polygon approaches the area of the circle. (has picture)
What is the area of a circle whose radius is 5 ft?
5π ft²
10π ft²
20π ft²
25π ft²
The circumference of a circle is 5π cm.
What is the area of the circle?
25π cm²
10π cm²
6.25π cm²
2.5π cm²
Answers
Radius = 13.2 ÷ 2
= 6.6
Area = (3.14)(6.6)^2
= 136.78cm^2
I hope this helps!
Earl runs 75 meters in 30 seconds. How many meters does Earl run per second?
Answers
divide distance by time
75 /30 = 2.5 meters per second
What is the integer of the square root of 70?
Answers
9*9 = 81
so integer part of sqrt 70 is 8 Answer
You see a used car you wish to buy. The dealer quotes you a price of $11,550. You have a blue book quotation of $8,400 for the same model and year. How much markup on cost is the dealer using?
Answers
Answer:
37.5%
Step-by-step explanation:
We have been given that the dealer quotes you price of a car $11,550. You have a blue book quotation of $8,400 for the same model and year.
First of all, we will subtract the blue book quotation price from the price quoted by dealer to get the amount of markup.
[tex]\text{Mark-up}=\$11,550-\$8,400[/tex]
[tex]\text{Mark-up}=\$3,150[/tex]
Now, we will find $3,150 is what percent of $8,400.
[tex]\text{Mark-up percent}=\frac{\$3150}{\$8400}\times 100[/tex]
[tex]\text{Mark-up percent}=0.375\times 100[/tex]
[tex]\text{Mark-up percent}=37.5\%[/tex]
Therefore, the dealer is using 37.5% of markup on the cost.
Let f(x) = x2 and g(x) = x − 3. Evaluate (g ∘ f)(−2).
Answers
f(-2) = (-2)^2 = 4
g(f(-2)) = 4 -3 = 1
answer
(g ∘ f)(−2) = 1
Answer:
The value of (g ∘ f)(-2) is 1
Step-by-step explanation:
Given two functions
[tex]f(x)=x^2, g(x)=x-3[/tex]
we have to evaluate (g ∘ f)(-2).
As, (g ∘ f)(-2)=g(f(x))
[tex]g(f(x))=g(x^2)[/tex]
As g(x)=x-3
[tex]g(x^2)=x^2-3[/tex]
Therefore,
[tex](g o f)(x)=x^2-3[/tex]
To find the value of (g ∘ f)(-2), we have to substitute x=-2
[tex](g o f)(-2)=(-2)^2-3=4-3=1[/tex]
Hence, the value of (g ∘ f)(-2) is 1
On the first of three tests sally scored 75 points. on the third test her score was one point more than the second test her average on the three test was 82 what were her scores on the second and third test
Answers
Find the principal amount invested if the amount in a monthly compounded account with a 5.1% interest rate is $9,996.32 after 54 months.
Answers
[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\to &\$9996\\ P=\textit{original amount deposited}\\ r=rate\to 5.1\%\to \frac{5.1}{100}\to &0.051\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\to &12\\ t=years\to \frac{54}{12}\to &\frac{9}{2} \end{cases}[/tex]
[tex]\bf 9996=P\left(1+\frac{0.051}{12}\right)^{12\cdot \frac{9}{2}}\implies \cfrac{9996}{\left(1+\frac{0.051}{12}\right)^{12\cdot \frac{9}{2}}}=P[/tex]
The scale of a map is 1 in. :500 mile. City A is 650 miles from City B. How far is it's distance on the map?
Answers
650/500 * 1
1.3 * 1
1.3 in
Hope this helps!
What the simplified form of x- 1 +4+7x-3
Answers
Simplify
Answer: 8x
A scientist measures a substance to be 0.6 grams. Calculate the percent of error in the measurement. Show all work for full credit.
Answers
% Error = ( |accepted value - measured value| / accepted value ) x 100%
During the first day of a heat wave and emergency room had three times as many patients as the day before they were 48 patients seen total over there today. How many patients visited the ER on each day
Answers
In this question, we know that the ER the ratio number of the patient when heat wave compared to yesterday(3 times) and the number of patients today (48 patient).
Since 48 patient of today is 3 times more than yesterday, then the number of patient visit ER each day(without heat wave) is:
Patient when heat wave= 3x normal patient visit
48 patient = 3x Normal patient visit
Normal patient visit = 48/3= 16 patients
Are you smart enough to answer this??
Answers
Find the slope:
(0,-3)(4,0)
0-(-3)/4-0
3/4
Put into slope intercept form
y=3/4x-3
Because it is shaded above with a dashed line, the sign is >
Final answer: y>3/4x-3
Lois and Clark own a company that sells wagons. The amount they pay each of their sales employees (in dollars) is given by the expression 12h+30w where h is the number of hours worked and w is the number of wagons sold. What is the amount paid to an employee that works 6 hours and sells 3 wagons?
Answers
So I get 72 and 90 then add those together your final answer should be 162
Diego says that the product of 0.51 * 2.427 will have have five decimal places. is Diego correct? Explain