Answer:
A. (x , y) = ( 1, 4) is the SOLUTION of the given system of equations.
Step-by-step explanation:
Here, the given set of equations is:
2 y + 5x = 13 ....... (1)
2y - 3x = 5 ...... (2)
Now, to solve this question by SUBSTITUTION:
From (1), we get:
2 y + 5x = 13 ⇒ 2 y = 13 - 5 x
or, [tex]y = \frac{13 - 5x}{2}[/tex]
Put this value of y in (2) . We get
[tex]2y - 3x = 5 \implies 2\times\frac{(13-5x)}{2} - 3x = 5\\\implies 13 - 5 x - 3x = 5\\\implies- 8x = -8\\\implies x = 1[/tex]
Now, x = 1, put this value of x in (1),
2 y + 5x = 13 ⇒ 2y + 5(1) = 13
or, 2 y = 13- 5 = 8
or, y = 8 / 2 = 4, ⇒ y = 4
Hence, x = 1, y = 4 is the SOLUTION of the given system of equations.
15. Which of the following equations was
used to graph the line shown?
A. y=6 + x
B. y=6 - x
C. y=x- 6
D. y=6x
Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c (m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (6, 0)
m = [tex]\frac{0-6}{6-0}[/tex] = [tex]\frac{-6}{6}[/tex] = - 1
Note the line crosses the y- axis at (0, 6 ) ⇒ c = 6
y = - x + 6 or y = 6 - x ⇒ B
is abc = dce? justify your answer below, please explain why! please help :)
Answer:
Step-by-step explanation:
∡ECD = 90°
∡DCA= 90°
∡BCA=90°
∡BCE =90°
⇔ ABC=DCE
Solve the inequality. Graph the solution.
6n < 90
Answer:
[tex]\displaystyle 15 > n[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{6n}{6} < \frac{90}{6} → n < 15[/tex]
Whenever you divide\multiply by a negative, you reverse the inequality symbol.
** The above answer is written in reverse, which is the exact same result.
≥, ≤ → Solid Circle [●]
>, < → Blank Circle [○]
I am joyous to assist you anytime.
What is the answer:
19 7/5-6 1/3- 5 5/6
Answer:
247/30
Step-by-step explanation:
19 7/5-6 1/3-5 5/6
19 7/5=102/5
6 1/3=19/3
5 5/6=35/6
----------------------
102/5-19/3-35/6
612/30-190/30-175/30=247/30
Answer:
8 7/30
Step-by-step explanation:
5 divide 3/4 in simplest
Answer:
20/3
Step-by-step explanation:
5/(3/4)=(5/1)(4/3)=20/3
62 is 50% of what number?
Answer:
62 is 50% of 31
Step-by-step explanation:
For example: 50% of 62 = 31; Example 2: Calculate a percentage based on 2 numbers. For example: 31/62 = 50%
Answer:
31
To calculate a percentage of some number, change the percentage into a decimal, and the word "of" into multiplication
Eli took out a 20-year loan for $135,000 at 4.8% interest, compounded
monthly. If his monthly payment on the loan is $876.09, how much of his first
payment went toward note reduction?
O A. $876.09
B. $336.09
O
c. $540.00
D. $420.48
Answer:
B. $336.09
Step-by-step explanation:
Monthly payment = $876.09
Interest rate = 4.8%
Convert the annual interest rate to monthly rate = 4.8% / 12
Monthly rate = 0.4% or 0.004
Amount going towards interest payment = 0.004* loan amount
Interest = 0.004 * 135,000
Interest = $540
Therefore, from the monthly payment of $876.09 , $540 goes towards paying interest and the balance is the note reduction;
Note reduction = $876.09 - $540 = $336.09
Answer:
336.09
Step-by-step explanation:
this is the right anwser
A long-distance telephone company charges a rate of 8 cents per minute or a 50-cent minimum charge per completed call, whichever is greater. Find the cost, in cents per minute, for a 3-minute call.
Answer:
Cost of a 3 minute call is 50 cents at a rate of 16.67 cents per minute.
Step-by-step explanation:
We are given the following in the question:
Plan A
A rate of 8 cents per minute.
Plan B
A 50-cent minimum charge per completed call.
We have to find the cost, in cents per minute, for a 3-minute call.
Cost according to plan A:
[tex]\text{Cost per minute}\times \text{Call length in minutes}\\= 8 \times 3\\=24 \text{cents}[/tex]
Cost according to plan B:
50 cents for a 3 minute call
Rate =
[tex]\displaystyle\frac{\text{Total cost}}{\text{Duration of call}} = \frac{50}{3} = 16.67 \text{ cents per minute}[/tex]
The company chooses the plan with greater cost, thus, it chooses plan B.
Thus, cost of a 3 minute call is 50 cents at a rate of 16.67 cents per minute.
Sandria earned $24 babysitting. She owes her friend $7 for dinner, and she owes her mom $4. She will make $15 later this week for mowing the yard.
How much money will she have at the end of the week?
Answer:
28
Step-by-step explanation:
24-7-4=13
13+15=28
A jacket that originally cost 20 is on sale for 75% off what is the sale price of the jacket? What was the amount of the discount?
Thus, a product that normally costs $20 with a 75 percent discount will cost you $5.00, and you saved $15.00. You can also calculate how much you save by simply moving the period in 75.00 percent two spaces to the left, and then multiply the result by $20 as follows: $20 x .75 = $15.00 savings.
Answer: $35
Step-by-step explanation:
20(75%)=15+20= $35
Solve for x in the following situation. Show your work.
11x-4/50=70/60
Answer:
x=17/150
Step-by-step explanation:
11x-4/50=70/60
11x-2/25=7/6
11x=7/6+2/25
11x=187/150
x=(187/150)/11
x=(187/150)(1/11)
x=187/1650
simplify,
x=17/150
Answer:
x=17/150
Step-by-step explanation:
Is 312 evenly divisible by 3?
Answer:
Yes
Step-by-step explanation:
312/3=104
need help solving with working much appreciated
Answer:
i. g = 70°
ii. x = 85°
Step-by-step explanation:
Given:
Let first we name the triangle
i. ) Δ PQR , m∠ PRQ = 40°
ii. ) Δ ABC is a right angle at B and a line B- D-C
m∠ DAC = 25°
m∠ ACD = 60°
m∠ BDA = x°
To Find:
i. g = ?
ii. x = ?
Solution:
i.
In Δ PQR , PR ≅ QR ...........{Given]
∴ Δ PQR is an Isosceles Triangle.
c.........{ Base angles of Isosceles triangle are equal }
∴ m∠ PQR = m∠ RPQ = g
Now sum of all the angles in a triangle is 180°
∴ m∠ PQR + m∠ RPQ + m∠ PRQ = 180°....{Angle sum property of Triangle}
[tex]g + g + 40 = 180\\2g=180-40\\2g=140\\g=\frac{140}{2} \\g=70\°[/tex]
∴ g = 70°
ii.
We know sum of all the angles in a triangle is 180°
In Δ DAC
m∠ DAC + m∠ ACD + m∠ ADC = 180°.....{Angle sum property of Triangle}
[tex]25+60+ \angle ADC = 180\\[/tex]
[tex]\angle ADC = 180-85\\\angle ADC =95\\[/tex]
Now By Linear Pair Angle Property
m∠ ADB + m∠ ADC = 180° ........{Linear Pair Angle Property}
[tex]x+95=180\\x=180-95\\x=85[/tex]
∴ x = 85°
Evaluate the expression. 8 x 7 - 12 ÷ 6 please anwser fast
Answer:
54
Step-by-step explanation:
8*7-12/6=56-2=54
Answer:
56-2=54
Step-by-step explanation:
8×7 - 12÷6 =56 - 2= 54
Graph the solutions of the inequality
Answer:
The graph in the attached figure
Step-by-step explanation:
Graph the solution of the inequality
[tex]t\leq -4[/tex]
we know that
The solution is the interval ---> (-∞,-4]
All real numbers less than or equal to -4
In a number line the solution is the shaded area at left of t=-4 (closed circle, because the number -4 is included in the solution))
using a graphing tool
The graph in the attached figure
Last Monday, two law students met up at café Literatura after school to read the pages they were assigned in the legal methods class. Alejandro can read 1 page per minute, and he has read 28 pages so far. Carly, who has a reading speed of 2 pages per minute has read 12 pages so far.
Part A: Define the variables and write two equations to represent the number of pages that each student read.
Variables:
Alejandro:
Carly:
Answer:
Step-by-step explanation:
Variables:
let x be the number of minutes
let y be the total number of pages read
Use the form y = mx + b
"b" is irrelevant in this context because the initial value is 0 (they have not read it before or it is not given)
m is the rate, how fast they can read, how many pages each minute
Alejandro:
28 = 1x <=Simplify because any number multiplied by 1 is itself.
28 = x
Carly:
12 = 2x
Suppose the x-axis of a density graph represents someone's height in inches.
If the area under the density curve from 60 inches to 70 inches is 0.55, what
is the probability of someone's height being anywhere from 60 inches to 70
inches?
A.70%
B.55%
C.65%
D.60%
Name the only type of polygon that must be regular if it is equiangular?
an equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon
The only type of polygon that must be regular if it is equiangular is a regular polygon.
Here, we have,
we know that,
A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges.
an equiangular polygon is a polygon whose vertex angles are equal.
If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon.
Hence, The only type of polygon that must be regular if it is equiangular is a regular polygon.
To learn more on polygon click:
brainly.com/question/24464711
#SPJ2
What is the factored form of 8x^2+ 12x? 4(4x^2+8x) 4x(2x+3) 8x(x+4) 8x(x^2+4)
Answer:
4x(2x+3)
Step-by-step explanation:
The answer is 4x(2x+3)
Kayla is buying fruit for packed lunches. She needs to buy an assortment of at least 15 apples and oranges and spend less than $20.00. Apples (x) cost $0.65 each, an oranges (y) cost $0.78 each. Which system of linear inequalities models this situation?
Final answer:
The system of linear inequalities for Kayla's fruit purchase is x + y ≥ 15 to represent the quantity of fruit, and 0.65x + 0.78y < 20 to represent the budget constraint.
Explanation:
The student's question is asking for a system of linear inequalities that would model the situation in which Kayla wants to buy at least 15 fruits consisting of apples and oranges, without spending more than $20. Given that apples (x) are $0.65 each and oranges (y) are $0.78 each, we can set up the following inequalities:
x + y ≥ 15
0.65x + 0.78y < 20
The first inequality represents the requirement that Kayla needs to buy at least 15 pieces of fruit. The second inequality represents the constraint that she needs to spend less than $20 on her purchase.
Solve 3x - 5 = 16.
9
8
6
7
Answer:
7
Step-by-step explanation:
3(7)=21-5=16
HELP WITH THIS???????????????????Will mark brainliest
Answer:
(1,c) (2,b) (3,A)
Step-by-step explanation:
May be right or worng i just read thought it better.
6[4x(72-36) divided by 3
Simplify the expressions:
2(3a+1)-5a
Answer:
6a+2-5a
ascending
2+a
descending
a+2
What is the minimum cuts
needed to cut a circle into 8
equal parts?
What is the minimum cuts needed to cut a circle into 8 equal parts ?
A : 4 cuts
Answer:
4 cuts.Step-by-step explanation:
When we have a circle, each cut (supposing the curst are in the exact middle) which give use two haves. So, if we cut one time, we'll have two equal parts, if we cut a second time, we'll have 4 equal parts, a third time, we'll get us 6 equal parts, and if we cut a fourth time, we'll have 8 equal parts.
So, whenever we have this kind of problem dividing circles, we just say that each cut in the exact middle equals two equal haves, so if we have 4 cuts, we just multiply them by 2, 4(2)=8. Therefore, we have 8 equal parts.
「14+ (-4) +6+(-16) = _
Answer:
0
Step-by-step explanation:
14+ (-4) +6+(-16) = _
10+6+(-16) =
16+(-16) = 0
Answer:
0
Step-by-step explanation:
14 + (-4) + 6 + (-16) =
10 + 6 + (-16) =
16 + (-16) =
0
Simplify (-8)(-2) + 11
Answer:
27
Step-by-step explanation:
-8 * -2 = 16
16 + 11 = 27
When a window is open, the temperature in a room falls 5°F every 15 minutes. Before the window is opened, the temperature was 70°F . Pls Help Me! Will mark Brainliest
Use the Ray tool to make a graph that shows the temperature of the room, T, after the window has been open for m minutes.
Answer:
See attached graph
Step-by-step explanation:
Let m be the number of minutes passed and T be the temperature (in F°)
Before the window is opened, the temperature was 70°F, then at m = 0 minutes, T = 70°F
When a window is open, the temperature in a room falls 5°F every 15 minutes. This means
at m = 15, T = 70°F - 5°F = 65°F
at m = 30, T = 70°F - 10°F = 60°F
at m = 45, T = 70°F - 15°F = 55°F
and so on.
Plot points (0,70), (15,65), (30, 60), (45, 55) and connect them with a straight line. This is the graph that shows the temperature of the room, T, after the window has been open for m minutes.
How is the number 6.24 x 10^-4 expressed in regular numbers?
Answer:
The scientific notation, 6.24 x 10^-4, means that the 6.24 is multiplied to 10 which is raised to exponent -4. 10^-4 has a regular number value of 0.0001. So, to find the answer you should multiply 6.24 by 0.0001 which gives an answer of 0.000624.20
Step-by-step explanation:
Three consecutive integers have a sum of 132
Answer:
43+44+45
Step-by-step explanation:
X + X + 1 + X + 2 = 132
3X + 3 = 132
3X + 3 - 3 = 132 - 3
3X = 129
3X/3 = 129/3
X = 43
consecutive means numbers after