The given linear system is:
[tex]\displaystyle \left \{ {{5x+3y=1} \atop {-5x-7y=31}} \right.[/tex]
Linear systems can be solved using either elimination or substitution. However, the question is asking to solve using elimination, so I will use that method.
When eliminating, you can either eliminate x or y. In this system, x is much easier to eliminate. The x variable in the first equation is 5x, and in the second equation, it is -5x. Since 5 and -5 cancel each other out, you don't need to do anything other than add.
[tex]5x+3y=1\\-5x-7y=31[/tex]
[tex]\displaystyle 3y-7y=1+31\\-4y=32[/tex]
Lastly, you need to leave the variable y alone. The variable is currently -4y or -4 times y. To remove it, you need to do the opposite of it, which is dividing by -4.
Divide both sides by -4:
[tex]\displaystyle\frac{-4y}{-4} =\frac{32}{-4}[/tex]
[tex]\displaystyle y=-8[/tex]
Now that you have the value of y, substitute it into one of the equations to find x. I will be substituting it into the first equation.
[tex]\displaystyle 5x+3y=1 \rightarrow 5x+3(-8)=1[/tex]
Open the parentheses and multiply:
[tex]5x-24=1[/tex]
Move 24 to the other side to leave the variable alone:
[tex]5x-24+24=1+24[/tex]
You will be adding since you're "removing" it by doing the opposite of it.
[tex]5x=25[/tex]
Lastly, divide both sides by 5 to leave x alone.
[tex]\displaystyle \frac{5x}{5} =\frac{25}{5}[/tex]
[tex]x=5[/tex]
[tex]\displaystyle (x,y) \rightarrow (5, -8)[/tex]
The answer is (5, -8).
A yardstick casts a shadow of 24 in. At the same time a telephone pole casts a shadow of 20 ft 8 in. What is the height of the telephone pole, to the nearest inch? (1 yd = 36 in., and 1 ft = 12 in.)
Answer:
372 inches
Step-by-step explanation:
(1 yd = 36 in., and 1 ft = 12 in.)
1 yard stick = 24 in
This means , height of 36 inches casts a shadow of 24 Inches
At the same time a telephone pole casts a shadow of 20 ft 8 in
1 ft = 12 in
Hence,
Convey 20ft to inches
1 ft = 12 in
20 ft = 20 × 12 inches
= 240 inches
Total shadow of the telephone pole = 240in + 8 in = 248 = 248 inches
Hence,
Height/Length of shadow = Height/Length of shadow
36/24= x /248
Cross Multiply
24 × x = 36× 248
x = 36 × 248/24
x = 372 inches
The height of the telephone pole, to the nearest inch is 372 inches
Which of the following would be the best strategy?
Answer:
I think the answer is D
Step-by-step explanation:
I hope it was correct...
Markups The depth of water in a pond increases by 3% after a heavy rain. If the average depth of the water was 8.3 feet, what is the new depth?
Answer: 8.55 feet
Step-by-step explanation:
We should equal the average depth to 1, so if it raises 3%, it raises 0.03. Simply add the original (1) plus what it rose (0.03) and multiply the original by that, so 8.3 × 1.03 = new depth. The result is 8.549 feets.
Last year's computer models were priced at $1,850. They are now discounted 20%. What is the new retail price to the nearest dollar of that computer? $370 $1,480 $1,510 $1,830
Answer:
$1480Step-by-step explanation:
Step one:
Given that the price last year was $1850
and now the discount is 20%
we first need to solve for 20% of $1850
=20/100*$1850
=0.2*$1850
=$370
This means that the price was reduced by $370
so the new retail price is calculated as
=$1850-$370
=$1480
The correction option is the second in the list of options
Question 9 and 10 please help it’s due today and I will mark you brainless
Answer: the first one you graph the points (-4,11) (-3,4) (-2,-1) (-1,-4) (0,-5) (1,-4) (2,-1) (3,4) (4,11), it is a function because each input has only one output. Then the second is not a function because it does not pass the vertical line test
Step-by-step explanation:
What is the length of EF in the right triangle below? A. 168 B. /324 C. 24 D. 18 E. 527 F. 32
Answer: C 24
Step-by-step explanation:
The measure of the length of EF in a right-angle triangle is 24 units, then the correct option is C.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.
The right-angle triangle is shown in a diagram. Then by the Pythagoras theorem, we have
P² = H² - B²
P² = 25² - 7²
P² = 625 - 49
P² = 576
P = 24
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
HELP MY BROTHER NEEDS HELP WITH AN ASSIGNMENT BUT I DO NOT KNOW HOW
Order the values from least to greatest. |–4|, 10, –12, |3| A. |–4|, |3|, 10, –12 B. |3|, |–4|, 10, –12 C. –12, |–4|, |3|, 10 D. –12, |3|, |–4|, 10
The answer is letter C.
Step-by-step explanation:
hope this helps
-12 < -4 < 3 < 10
Answer:
D. –12, |3|, |–4|, 10
Step-by-step explanation:
| - 4|, 10, - 12, |3|
4, 10, - 12, 3
- 12, 3, 4, 10
Find the area of the triangle.
Answer:
Area of triangle = 1/2*b*h
[tex]\frac{1}{2} * 2.8* 7.8\\\frac{1}{2} * 21.84\\\frac{21.84}{2}\\= 10.92[/tex]
Answer:
10.92 cm²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b= 2.8 and h = 7.8 , then
A = [tex]\frac{1}{2}[/tex] × 2.8 × 7.8 = 1.4 × 7.8 = 10.92 cm²
happy veterans day everybody!!!
Answer:
happy vets day
Step-by-step explanation:
c+8+-20
c=
it made me write 20 characters
2+2 Add the numbers
Answer:
4
Step-by-step explanation:
2+2=4
Answer:
4 is the answer to 2+2 when we add the numbers
Given ABC with AB=3,BC=5,and CA=6 find the length of a mid segment XY
Answer:
[tex] \overline{XY} = 1.5 [/tex]
Step-by-step explanation:
Given:
AB = 3
BC = 5
CA = 6
Required:
Length of XY
SOLUTION:
According to the Triangle Midsegment Conjecture, midsegment [tex] \overline{XY} [/tex] is half the length of [tex] \overline{AB} [/tex].
Therefore:
[tex] \overline{XY} = \frac{1}{2}(\overline{AB}) [/tex]
Thus:
[tex] \overline{XY} = \frac{1}{2}(3) [/tex]
[tex] \overline{XY} = \frac{3}{2} [/tex]
[tex] \overline{XY} = 1.5 [/tex]
a scaled drawing of a rectangular park is 5 inches wide and 7 inches long. the actual park is 210 yards long. what is the width of the actual park in yards
Answer:
I think the width would be 150 yd
Step-by-step explanation:
just broke down the 210 yd we had already to inches found out how much it was scaled up and did the same on the other side
How do you solve this?
Answer:
[tex] x = 18 [/tex]
[tex] y = 7.5 [/tex]
[tex] z = 7 [/tex]
Step-by-step explanation:
✍️[tex] (8x - 7) + (3x - 11) = 180 [/tex] (consecutive interior angles are supplementary)
Solve for x
[tex] 8x - 7 + 3x - 11 = 180 [/tex]
Add like terms
[tex] 11x - 18 = 180 [/tex]
Add 18 to both sides
[tex] 11x = 180 + 18 [/tex]
[tex] 11x = 198 [/tex]
Divide both sides by 11
✅[tex] x = 18 [/tex]
✍️[tex] (2y + 23) = (4y + 8) [/tex] (alternate interior angles are congruent)
Solve for y
[tex] 2y + 23 = 4y + 8 [/tex]
Collect like terms
[tex] 23 - 8 = 4y - 2y [/tex]
[tex] 15 = 2y [/tex]
Divide both sides by 2
✅y = 7.5
✍️[tex] (2y + 23) + (3z^2 - 5) = 180 [/tex] (linear pair angles)
Plug in the value of y
[tex] (2(7.5) + 23) + (3z^2 - 5) = 180 [/tex]
[tex] (15 + 23) + (3z^2 - 5) = 180 [/tex]
[tex] 38 + 3z^2 - 5 = 180 [/tex]
Add like terms
[tex] 3z^2 + 33 = 180 [/tex]
Subtract 33 from each side
[tex] 3z^2 = 180 - 33 [/tex]
[tex] 3z^2 = 147 [/tex]
Divide both sides by 3
[tex] z^2 = \frac{147}{3} [/tex]
[tex] z^2 = 49 [/tex]
Square both sides
[tex] \sqrt{z^2} = \sqrt{49} [/tex]
[tex] z = 7 [/tex]
Find the value of y (2y+5) (5x - 17) (3x-11)
Answer:
Hope it help, please give me BRAINLEST!
Step-by-step explanation:
2y + 5= |3y| + 3 = 3
x - 3= 2
[tex]\sqrt{x} + 2 = 2[/tex]
5x - 17= -3x = 2
3^(x )= 4
3 cos^(2)(x) + 2 cos(x)- 1 = 0
3x-11= [tex]\sqrt{x}[/tex] +3 = 8
2 = |3x|
x - 5= -3
The calorie count of a serving of food can be computed based on its composition of carbohydrate, fat, and protein. The calorie count for a serving of food can be computed using the formula C=4h+9f+4p, where his the
of grams of carbohydrate contained in the serving, is the number of grams of fat contained in the serving, and is the number of grams of protein contained in the serving
A serving of a certain type of but contains 12 grams of fat, 6 grams of carbohydrate, and 5 grams of protein. How many calones are in this serving of ruts?
There are calories [___] in this serving of nuts
Answer:
152 calories
Step-by-step explanation:
The calories count, composition of carbohydrates, fat and protein are related by;
C = 4h + 9f + 4p
where C, h, f, and p have there given meaning.
Given that the serving of a type of nut contains; f = 12 grams, h = 6 grams and p = 5 grams, then;
C = 4(6) + 9(12) + 4(5)
= 24 + 108 + 20
= 152
C = 152 calories
Therefore, there are 152 calories in the serving of the certain type of nut.
What is the equation of a line that has a slope of -5 and passes through the point (0, 2)?
1. y = 2x - 5
2. y = -5x
3. y = -5x + 2
Answer:
y=-5x+2
Step-by-step explanation:
y-y=m(x-x¹)
y-2=-5(x-0)
y-2=-5x+0
+2 +2
y=-5x+2
Answer:
y = -5x + 2
Step-by-step explanation:
Please help !!
What is the general equation to the √x?
someone knows what number multiplied twice by the same can give me results 130!!!! Help plis plisss
Answer:
i will try to help you....
Answer:
65 i believe
Step-by-step explanation:
130/2
= 65
and
65 x 65 = 130
Point S is on line segment \overline{RT} RT . Given RT=4x,RT=4x, ST=5x-10,ST=5x−10, and RS=6,RS=6, determine the numerical length of \overline{ST}. ST .
Answer:
[tex]ST = 10[/tex]
Step-by-step explanation:
Given
[tex]RT =4x[/tex]
[tex]ST = 5x - 10[/tex]
[tex]RS = 6[/tex]
Required
Determine ST
Since S is on RT, we have that:
[tex]RT = RS + ST[/tex]
[tex]4x = 5x - 10 + 6[/tex]
[tex]4x = 5x - 4[/tex]
[tex]4x - 5x= - 4[/tex]
[tex]-x= - 4[/tex]
[tex]x= 4[/tex]
Substitute 4 for x in [tex]ST = 5x - 10[/tex]
[tex]ST = 5 * 4 - 10[/tex]
[tex]ST = 20 - 10[/tex]
[tex]ST = 10[/tex]
Answer: It Equals 8
Step-by-step explanation:
Point S is on line segment \overline{RT}
RT
. Given ST=5x-7,ST=5x−7, RT=4x+9,RT=4x+9, and RS=2x+7,RS=2x+7, determine the numerical length of \overline{ST}.
ST
.
\text{Label known information:}
Label known information:
R
S
T
2x + 7
5x – 7
RT = 4x + 9
RS+ST=
RT
Segment addition postulate
\color{darkgreen}{2x+7}+\color{darkblue}{5x-7}=
2x+7+5x−7=
\,\,\color{darkred}{4x+9}
4x+9
Substitute expressions
7x=
7x=
\,\,4x+9
4x+9
Combine like terms
-4x\phantom{=}
−4x=
\,\,-4x
−4x
3x=
3x=
\,\,9
9
\frac{3x}{3}=
3
3x
=
\,\,\frac{9}{3}
3
9
Divide by 33
x=
x=
\,\,\color{darkgreen}{3}
3
\text{Plug in value of }x\text{ to find }ST\text{:}
Plug in value of x to find ST:
ST=5x-7=5\left(\color{darkgreen}{3}\right)-7=8
ST=5x−7=5(3)−7=8
\text{You can plug }x\text{ into each expression:}
You can plug x into each expression:
Optional to check work
R
S
T
2(3) + 7
5(3) – 7
RT = 4(3) + 9
\text{Simplify:}
Simplify:
R
S
T
13
8
RT = 21
\text{Final Answer:}
Final Answer:
ST=\color{green}{\mathbf{8}}
ST=8
Please Help ASAP!! Marking Brainliest!! Divide [tex]12x^2 + 4x^3 + 18 + 16x[/tex] by [tex]2x + 4[/tex].
a.) [tex]2x^2 + 2x + 3 + \frac{5}{x + 4}[/tex]
b.) [tex]2x^2 + 2x + 4 - \frac{2}{x + 4}[/tex]
c.) [tex]2x^2 + 2x + 4 + \frac{2}{2x + 4}[/tex]
d.) [tex]2x^2 + 2x + 3 + \frac{14}{x + 4}[/tex]
Answer:
The answer is C
Step-by-step explanation:
Just calculate it
Which set of coordinates describes a function
The answer would very. Let's say the function is y + 4 = (x + 4)
Two points would be (-4,-4) and (4,0)
11. In AWTY, if mZW is five less than twice mZY and mZX is 21 more than m_Y find the measure
of each angle.
9514 1404 393
Answer:
angles (W, X, Y) = (77°, 62°, 41°)
Step-by-step explanation:
Given:
ΔWZY
∠W = 2(∠Y) -5°
∠X = ∠Y +21°
Find:
∠X, ∠Y, ∠W
Solution:
Using angle measures in degrees, we have ...
∠X + ∠Y + ∠Z = 180
(∠Y +21) +∠Y + (2(∠Y) -5) = 180
4(∠Y) +16 = 180 . . . . . simplify
∠Y +4 = 45 . . . . . . . . . divide by 4
∠Y = 41 . . . . . . . . . . . . subtract 4
∠W = 2(41) -5 = 77
∠X = 41 +21 = 62
The angle measures of angles (W, X, Y) are (77°, 62°, 41°), respectively.
Fernando is starting a new sales job and needs to decide between two different salary plans. For Plan A, he will earn $100/week plus 15% commission on all sales. For Plan B, he will earn $150/week plus 10% commission on all sales. For what amount of weekly sales are the two plans equal?
Answer:
At 10 weeks
Step-by-step explanation:
100+15x=150+10x
15x=50+10x
5x=50 divided both sides by 5 and x=10
On average angel drinks 1/8 of a 12-ounce glass of water in 1/5 of an hour. How many glasses of water does he drink in one hour.
Answer:3/4 of a 6-ounce glass will be drunk by her in one hour.
Step-by-step explanation:
i did it and got it right
A restaurant bought 36.5 pounds of beef from a store. The next month, the restaurant bought 71.3 pounds of beef and 21.5 pounds of chicken. How many pounds of meat did the restaurant buy
Answer:
129.3 pounds
Step-by-step explanation:
A restaurant bought 36.5 pound of meat from a store
The following month they also bought 71.3 pounds of meat and 21.5 pounds of chicken
Therefore the total pounds of meat bought by the restaurant can be calculated as follows
= 36.5 + 71.3 + 21.5
= 129.3 pounds
Put the following equation of a line into slope-intercept form, simplifying all fractions. 3x+4y=-4
Answer:
Don't come at me if I'm wrong, but I think it's y=-3/4x-1 1/3
Step-by-step explanation:
1) you have to subtract 3x from both sides (this makes it 4y=-3x-4)
2) you then divide by 4 on both sides (it will become y=-3/4=4/3)
3) then you simplify the fractions (it becomes y=-3/4x-1 1/3)
5(y + 2) = 6(y - 1)
Show work
Please and thank you
Answer:
5 ( y + 2) = 6 ( y - 1)
- distribute the number outside into the parenthesis by multiplying it with each value
5y + 10 = 6y - 6
- subtract like terms, in this case 5y and 6y
-y + 10 = -6
- isolate the variable ( y) by getting rid of 10 by subtracting it to both sides
-y = -16
-1y = -16
- isolate variable (y) by getting rid of the -1 next to it by dividing it to both sides
y = -16 / -1
y = 16
What is the equation of the line that has a slope of 0 and passes through the point (4, −3)?
Answer:
7
Step-by-step explanation:
Answer:
y=-3
y=3/4x +0
Step-by-step explanation:
Help me PLEASE ixlllll