The system of equations which is represented the equivalent single equation without the y variable in it is x-1=0.
What is a system of equation?A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.
The system of equations as an equivalent single equation without the y variable has to be found out for the given equation.
The first equation given in the problem is,
[tex]x + y = 10[/tex]
Subtract x from both sides and solve it for y,
[tex]x + y -x= 10-x\\y=10-x[/tex] .........1
The second equation given in the problem is,
[tex]y = 4x + 5[/tex]
Put the value of y in this equation from equation 1 as,
[tex]y = 4x + 5\\10-x = 4x + 5\\10-5=4x+x\\5=5x\\5x-5=0[/tex]
Divide both side with number 5,
[tex]x-1=0[/tex]
Thus, the system of equations which is represented the equivalent single equation without the y variable in it is x-1=0.
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Which expresses this solution?
The equation that expresses the solution to the quadratic equation x² - 10x + 13 = 0 is [tex]x =5 \pm 2\sqrt{3}[/tex]
How to express the solution?The equation is given as:
x² - 10x + 13 = 0
The solution to a quadratic equation is represented by:
[tex]x =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
So, we have:
[tex]x =\frac{10 \pm \sqrt{(-10)^2 -4 * 1 * 13}}{2 * 1}[/tex]
Evaluate the radicand
[tex]x =\frac{10 \pm \sqrt{48}}{2}[/tex]
Take the square root of 48
[tex]x =\frac{10 \pm 4\sqrt{3}}{2}[/tex]
Divide
[tex]x =5 \pm 2\sqrt{3}[/tex]
Hence, the equation that expresses the solution to the quadratic equation x² - 10x + 13 = 0 is [tex]x =5 \pm 2\sqrt{3}[/tex]
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There are three containers filled with different gases as shown.
Container Gas Density Container Dimensions
A Hydrogen - 0.09 mg/cm3 a cube with sides of 15 cm
B Helium - 0.175 mg/cm3 a rectangular prism with sides of 14 cm, 12 cm, 10 cm
C Nitrogen - 1.251 mg/cm3 a sphere with a diameter of 8 cm
What is the correct order of mass from least to greatest?
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
As we know,
[tex] \sf \qquad density = \dfrac{mass}{volume} [/tex]
So, we can infer that :
[tex] \sf \qquad mass= {density} \cdot{volume} [/tex]
Now, let's calculate the mass of gases in each case :
Case A : Hydrogen ~[tex]\qquad \sf \dashrightarrow \:mass = 0.09 \times (15) {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \:mass = 0.09 \times 3375 {}^{} [/tex]
[tex]\qquad \sf \dashrightarrow \:mass = 303.75 \: \: mg {}^{} [/tex]
or
[tex]\qquad \sf \dashrightarrow \:mass =0. 30375 \: \: g {}^{} [/tex]
Case B : Helium ~[tex]\qquad \sf \dashrightarrow \:mass =0. 175 \: \cdot \: (14 \sdot 12 \sdot10)[/tex]
[tex]\qquad \sf \dashrightarrow \:mass =0. 175 \: \cdot \: 1680[/tex]
[tex]\qquad \sf \dashrightarrow \:mass =0. 175 \: \cdot \: 294 \: \: mg[/tex]
or
[tex]\qquad \sf \dashrightarrow \:mass = 0.294 \: \: g[/tex]
Case C : Nitrogen ~[tex]\qquad \sf \dashrightarrow \:mass = 1.251\: \cdot \: \dfrac{4}{3} \cdot3.14 \cdot(4) {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \:mass = 0.417\: \cdot \: 803.84[/tex]
[tex]\qquad \sf \dashrightarrow \:mass = 335.201 \: \: mg[/tex]
or
[tex]\qquad \sf \dashrightarrow \:mass = 0.335 \: \: g[/tex]
So, the arrangement of masses from least to greatest is :
(1.) Hydrogen < (2.) Helium < (3.) NitrogenAnswer:
Helium<Hydrogen<Nitrogen
Step-by-step explanation:
Xavier Brown works on a 40-hour week basis with time-and-a-half paid for overtime
work. Her regular-time hourly rate is $17.50. Last week she worked 43.5 hours from
Monday through Thursday and 8.5 hours on Friday. Complete all steps to find Xavier's
gross wages for last week.
With solution.
The gross wages of Xavier Brown when worked 43.5 hours in the week will be Gross pay=$730.625
What is gross pay?The total amount earned by any worker with his basic pay like incentives allowances etc.
It is given that Xavier Brown works on a 40-hour week basis and-a-half paid for overtime work.
Last week she worked 43.5
The distribution of the work is given as:-
Monday Tuesday Wed Thursday Friday Total
9 Hours 9 Hours 8.5 8.5 8.5 43.5
So we have the total working hours = 43.5 hours
Weekly working hours are =40 hours
So for 40 hours she will be paid:-
Pay =40x17.50
Now extra hours or overtime is =43.5-40=3.5 hours
So the extra income will be half of the regular:-
Pay=3.5x({1}÷{2}) x17.5=$30.625
So total gross pay will be = $700+$30.625=$730.625
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Guys, I need the answer, please
The radius of a circle is 1 centimeter. What is the circle's area?
Answer:
6.28
Step-by-step explanation:
Find the diameter by multiplying the radius by 2, then multiply the diameter by Pi, which in your case is 3.14
R times 2= diameter
D time Pi= area
Area = 6.28
Please mark Brainliest
determine the value of sin theta + cos theta whole square is equal to 2 sin theta cos theta.
Answer:
That will be 1.
Step-by-step explanation:
y = 6 - x; (-3,3)
is it a solution?
Need help,added picture .Use the rectangle to find the lengths of the following sides if AC=26 and BC=10
1) Diagonals of a rectangle bisect each other, so AW=13.
2) Since diagonals of a rectangle are congruent, AC=BD. Then, since diagonals of a rectangle bisect each other, DW=13.
3) Diagonals of a rectangle are congruent, so BD=26.
4) Opposite sides of a rectangle are congruent, so AD=10.
5) Using the Pythagorean theorem, BA=24.
an airplane files 867 miles with a constant speed of 612 mph and then another 1984 miles with a constant speed of 744 mph what is its average speed for the total trip?
The average speed is the ratio of the total distance to the total time. Then the average speed of the airplane will be 698.19 miles per hour.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
An airplane files 867 miles with a constant speed of 612 mph and then another 1984 miles with a constant speed of 744 mph.
Then time taken for the first trip will be
t₁ = 867 / 612
t₁ = 1.4167 hours
Then time taken for the second trip will be
t₂ = 1984 / 744
t₂ = 2.6667 hours
Then the average speed is the ratio of the total distance to the total time.
The total distance will be
Total distance = 867 + 1984
Total distance = 2851 miles
The total time will be
Total distance = 1.4167 + 2.6667
Total distance = 4.0834 hours
Then the average speed will be
Average speed = 2851 / 4.0834
Average speed = 698.19 mi/h
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What is the equation of the quadratic function with a vertex at (2,–25) and an x-intercept at (7,0)? f(x) = (x – 2)(x – 7) f(x) = (x 2)(x 7) f(x) = (x – 3)(x 7) f(x) = (x 3)(x – 7)
The quadratic equation with the given characteristics is:
f(x) = (x + 3)*(x - 7).
How to get the quadratic equation?We know that the vertex must be (2, -25) and it passes through (7, 0).
For a quadratic equation:
y = a*x^2 + b*x +c
The x-value of the vertex is:
x = -b/2a
Then we have:
2 = -b/2a
We also have:
-25 = a*4 + b*2 + c
And because the function passes through (7, 0) we know that 7 is one of the roots, then:
0 = a*49 + b*7 + c
Then we have 3 equations to work with:
2 = -b/2a
-25 = a*4 + b*2 + c
0 = a*49 + b*7 + c
If we subtract the third and second equations we get:
25 = a*45 + b*5
Now, with the first equation we can rewrite:
a = -b/4
Replacing that in the other equation:
25 = a*45 + b*5
25 = (-b/4)*45 + b*5 = b*(-25/4)
25*(-4/25) =b = -4
Now we know the value of b.
2 = -(-4)/2a
a = 1
Now we need to find the value of c, we have that:
0 = 1*49 + -4*7 + c
0 = 49 - 28 + c
0 = 21 + c
Then c = -21
The equation is:
[tex]y = x^2 - 4x - 21[/tex]
It can be factorized to:
f(x) = (x + 3)*(x - 7).
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What kind of triangle appears to be formed
if one of two circles has a radius twice as long as the other how do the circumference compare.
It also illustrates a situation where different methods can lead to what appear to be entirely different answers, yet they may be identical. A circle O is circumscribed around a triangle ABC, and its radius is r. The angles of the triangle are CAB = a, ABC = b, BCA = c.
PLEASE I AM HAVING A PANIC ATTACK OVER THIS PLEASE!!!!!!!!!!
Answer:
the answer is c
Step-by-step explanation:
I already did that
Answer:
C that's the answer
no explanation I'm jus saying
Which term best describes the expression 5x2 + 6x + 4 ?
O Linear
O Quadratic
O Quartic
O Cubic
Use the interactive ruler to measure the distance from the
center of dilation, C, to the image and pre-image.
The distance from point to point Ais units.
The distance from point to point A'is units.
The distance from point to point A'is
distance from point to point A.
the
Å
8
I need help!!!!!
Answer:
4
2
one-half
Step-by-step explanation:
Hope this helps!! :)
Using the interactive ruler, we can determine that it is 4 Units from the dilation's center to the image and pre-image.
What is a ruler that is interactive?This virtual instrument, which appears on the computer screen and is also known as an Interactive Teaching Program (ITP) ruler, is used to measure a shape's lines and sides.
Given, we need to find the distance in units between points C and A
Using the interactive ruler, we can determine that the separation between points C and A is 2 units.
Therefore, it takes 1.5 units to get from point C to point A'.
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pls answer im so desperate ill mark brainliest!! pls answer all three questions
Answer:
For the Third Question The answer would be D
Step-by-step explanation:
When u multiply 5×3=15
so 18^15/8 would be the correct answer
6. A company ordering parts
$20 per part. Which equation represents the cost c(in dollars) of ordering p parts?
F. c= 25 + 20p
G. c= 20 + 25p
1. p= 20 + 25c
H. p= 25+ 200
8. Which property is illustrated by the statement?
p=20+25c because it i did this on paper so i got what it equals to
Joel stands 15 meters away from the base of a
flagpole that is 11 meters tall. Joel's shadow is
2.7 meters long, and his shadow ends in the
same place as the flagpole's shadow (as shown).
How tall is Joel?
SHOW WORK. Round to two decimal places if necessary.
+
Answer: Its 28.7
Step-by-step explanation:
Answer:use camera math!
Step-by-step explanation:it helped me!it only works
On math though so you cant use it on any
Other subject hope this helped sorry
If it didn’t!
Plxx help mee giving brainlyist to the first to answer correctly
Answer:
0.9/3=0.3 First one
Step-by-step explanation:
0.9/3=0.3
The boxes are being divided into 3 equal parts and each section has 0.30 squares
Answer:
The answer is A: 0.9÷3=0.3
Step-by-step explanation:
The boxes are equally divided into thirds
Can someone help me with this question
Answer:
∠A≅∠Y AB≅YZ
∠B≅∠Z AC≅YX
∠C≅∠X BC≅ZX
ΔABC≅ΔYZX
Step-by-step explanation:
congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle
The tank for a car holds 20 gallons. the gpsoline suze shows
1
the tank is full. how much gas is still in the tank. give
4
your answer as a whole number or as a mived fraction
reduced to lowest terms.
Answer:
20 gallons
Step-by-step explanation:
The tank is at its full capacity, and its full capacity is 20 gallons. This means there is 20 gallons of gas in the tank.
3 lines Line 1: cap A tree standing vertically on level ground casts a. 72 foot long shadow period Line 2: If the angle of elevation from the end of the shadow to the top of the tree is Line 3: 34.6 degrees comma find the height of the tree to the nearest foot period
The height of the tree is 50 feet.
We have given,
cap A tree standing vertically on level ground casts a. 72feet.
We solve this by using trigonometry, the height of the tree to the nearest foot is 50 feets
What is the tan ratio?[tex]tan\theta = opposite / Adjacent[/tex]
Opposite = height, h
Adjacent, = 140 feets
Angle, θ = 19.8°
[tex]tan(19.8) = h / 140[/tex]
Cross multiply
[tex]h = 140 \times tan(19.8)[/tex]
h = 50.403 feets
Height, h = 50 feets (nearest foot)
Therefore, the height of the tree is 50 feets
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don’t mind this my question has to be at least 20 characters long
Answer:
B. The equation of the linear function is y = 3x + 2
D. The rate of change of the linear function is 3.
Step-by-step explanation:
First find the slope by choosing two ordered pairs and using the slope formula:
[tex]\textsf{let}\:(x_1,y_1)=(2,8)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(3,11)[/tex]
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{11-8}{3-2}=3[/tex]
Now use the Point-slope form of linear equation with the found slope and one of the points to create the equation of the linear function:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]\implies y-8=3(x-2)[/tex]
[tex]\implies y=3x + 2[/tex]
The rate of change of a linear function is its slope.
Therefore,
B. The equation of the linear function is y = 3x + 2
D. The rate of change of the linear function is 3.
-How many real-number solutions does the equation have? 0=3x2-5x-5
a. one solution
b. two solutions
c. no solutions
d. infinitely many solutions
The equation 3x²-5x-5 will have two solutions.
What are real roots?If the value of x in the given quadratic equation is a real number then the roots of the equation are real.
The discriminant of the equation will be calculated as:-
= 3x ²- 5x - 5
D = b² - 4ac
D = ( 5 )² - 4 x 3 x -5
D = 25 - ( -60 )
D = 85
Since the discriminant is positive then the equation will have real roots and the degree of the equation is 2 so it will have two solutions.
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The equation of a line is y = –4x + 1. What is the equation of the line that is parallel to the first line and passes through (–2, –1)?
y = -4x - 1
the gradient of the parallel line will be the same as the given line so you just need to change the y intercept
The process of completing the square
The method of completing the square can be used to determine the vertex of a function. he unknown value is -162
Completing the square of a functionThe method of completing the square can be used to determine the vertex of a function.
Given the quadratic function
-2x² + 36x
-2(x²-18)
Complete the square
-2(x² - 18x + ( -9)²+ 9²)
-2(x-9)² + -2(81)
-2(x-9)² - 162
Compare
On comparing with the expression, you can see that the unknown value is -162
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Jenn's carpool ride has been late 4 days out of the 20 days. what is the estimated probability, based on relative frequency, that her ride will be late tomorrow? a. 60% b. 20% c. 80% d. 40%
Answer:B 20 percent
Step-by-step explanation:
Find f(-2) for the function f(x) = 3x2 - 2x + 7.
-13
1
-1
23
Answer:
23
Step-by-step explanation:
3(-2)^2-2(-2)+7
=23
The spinner below is spun once, then a coin is tossed. find the probability of getting a shape with at least four sides, then tails
The probability of getting a shape with at least four sides, then tails will be 1/12.
What is probability?Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of occurrences.
The spinner below is spun once, then a coin is tossed.
Then the probability of getting a shape with at least four sides, then tails will be
For spinner
Favorable event = 5
Total event = 6
For a coin
Favorable event = 1
Total event = 2
P = 5/6 x 1/2
P = 5/12
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3 calculators and 4 books cost £23
2 calculators and 3 books cost £16
Work out the price of a single calculator and a single book.
Price of a calculator =
Price of a book =
Answer:
Step-by-step explanation:
Let the calculators be C and the books be B.
3C + 4B = 23 and 2C + 3B = 16
3C = 23 - 4B 2(23 - [tex]\frac{4B}{3}[/tex]) + 3B = 16
C = 23 - 4B 46 - [tex]\frac{8B}{3}[/tex] + 3B = 16
3 46 - [tex]\frac{-8B + 3B }{3}[/tex]
A box is shaped like a cube. The box has a length of 1 foot, a width of 1 foot, and a height of 1 foot. What is the volume of the box?
Answer:
1 cubic foot.
Step-by-step explanation:
A survey was given asking about preferred shopping methods.
. Of the 88 people surveyed without children. 73 prefer using a smart phone.
• of the 98 people surveyed with children. 67 prefer using a tablet
.
Complete the table for this situation
Device
Tablet
Phone
Total
Number of Children
Without Children 73
With Children
67
Total
104
82
186
Please help me
Answer:
Step-by-step explanation:
Without Children - 73 - 15 - 88
With Children - 31 - 67 - 98
Total - 104 - 82- 186
The required table for given situation as:
Without Children : 73 Phone + 15 Tablet = 88 Total Device
With Children : 31 Phone + 67 Tablet = 98 Total Device
Total : 104 Total Phone + 82 Total Tablet = 186 Total
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
The operator that perform arithmetic operation are called arithmetic operators.
Without Children : 73 Phone + 15 Tablet = 88 Total Device
With Children : 31 Phone + 67 Tablet = 98 Total Device
Total : 104 Total Phone + 82 Total Tablet = 186 Total
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