The ordered pairs (294.5, 61), (364, 70), and (605.5, 88.5) are on the line given by the equation 5x - 2y = 6.
Explanation:The equation given is 5x - 2y = 6. To determine which group of ordered pairs lies on this line, we can substitute the x and y values of each ordered pair into the equation and check if the equation holds true:
For the ordered pair (294.5, 61), substituting x = 294.5 and y = 61 gives: 5(294.5) - 2(61) = 6, which is true.For the ordered pair (364, 70), substituting x = 364 and y = 70 gives: 5(364) - 2(70) = 6, which is true.For the ordered pair (605.5, 88.5), substituting x = 605.5 and y = 88.5 gives: 5(605.5) - 2(88.5) = 6, which is true.Therefore, all three ordered pairs (294.5, 61), (364, 70), and (605.5, 88.5) lie on the line given by the equation 5x - 2y = 6.
Learn more about Ordered pairs here:https://brainly.com/question/30805001
#SPJ12
If 8 tablespoons of extract are mixed with distilled water to total 300 mL, what is the final concentration?
Answer:
28.2 US tablespoons
Step-by-step explanation:
If 8 tablespoons of extract are mixed with distilled water to total 300 mL, the final concentration is 28.2 US tablespoons.
8 tablespoons + 300 mL = 28.2 US tablespoons
Answer:
418.294 milliliters or 28.28 tablespoons.
Step-by-step explanation:
As we know 1 tablespoon = 14.7868 ml.
8 tablespoons = 14.7868 × 8
= 118.294 ml.
Final concentration = 300 ml + 118.294 ml
= 418.294 ml.
If you want to convert the final concentration to tablespoon
418.294 ÷ 14.7868 = 28.28 tablespoons.
The final concentration would be 418.294 milliliters or 28.28 tablespoons.
What is the value of 5 in 3590
Answer:
Hundreds
Step-by-step explanation:
The value of 5 is given based on the place value in which it is located.
The 5 is located in the "hundreds" place value, and so Hundreds is your answer.
Place value:
3: Thousands
5: Hundreds
9: Tens
0: Ones
Given the equation 10x + 20y + 40 = 0, Find it’s gradient and intercept
Answer:
see explanation
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 )
Rearrange the given equation into this form
10x + 20y + 40 = 0 ( divide all terms by 10 to simplify )
x + 2y + 4 = 0 ( subtract x + 4 from both sides )
2y = - x - 4 ( divide all terms by 2 )
y = - [tex]\frac{1}{2}[/tex] x - 2 ← in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex] and y- intercept c = - 2
What is the solution to this system of equations?
4x + 5y = 7
3x – 2y = –12
Answer:
x = -2 and y = 3
Step-by-step explanation:
It is given that,
4x + 5y = 7 ----(1)
3x – 2y = –12 ---(2)
To find the solution of given equations
eq(1) * 3 ⇒
12x + 15y = 21 ----(3)
eq(2) * 4 ⇒
12x - 8y = -48 ---(4)
eq(3) - eq(4) ⇒
12x + 15y = 21 ----(3)
12x - 8y = -48 ---(4)
0 + 23y = 69
y = 69/23 = 3
Substitute the value of y in eq(1)
4x + 5y = 7 ----(1)
4x + 5*3 = 7
4x = 7 - 15 = -8
x = -8/4 = -2
Therefore x = -2 and y = 3
Jonathan's piggy bank contains 20 nickels, 30 quarters, and 50 one-dollar coins. He picks 20 coins from the bank at random; 12 of these coins are one-dollar coins. The theoretical probability of picking a one-dollar coin from the piggy bank before the draw is %, but the experimental probability, based on the draw, is %.
Answer:
Theoretical probability: 50/100 or 50%
Experimental probability: 12/20 or 60%
Step-by-step explanation:
Let's find out both probabilities asked.
Theoretical probability:
In the whole bank, here are 100 coins (20 nickels + 30 quarters + 50 one-dollars), among which there are 50 one-dollar coins. So the probability to pick up a one-dollar coin is 50 out 100, so...
TP = 50/100 or 50%
Experimental probability:
For the experimental probability, we know Jonathan picked out 20 coins, out of which 12 were one-dollar coins, so the probability is 12 out of 20...
EP = 12 / 20 = 60%
if x does not equal 0, then u/x+5u/x-u/5x=
Answer:
[tex]\frac{29u}{5x}[/tex]
Step-by-step explanation:
If 'x' does not equal 0 then:
[tex]\frac{u}{x}+\frac{5u}{x}-\frac{u}{5x}[/tex] ⇒ [tex]\frac{6u}{x}-\frac{u}{5x}[/tex]
⇒ [tex]\frac{29u}{5x}[/tex]
Then, the solution is: [tex]\frac{29u}{5x}[/tex]
How and why does 2x – 3 = -(3 – 2x )?
Answer:
Because the negative in the front cancels out the other neg.
Step-by-step explanation:
Answer:
-(3 - 2x ) = -3 + 2x = 2x - 3
Step-by-step explanation:
If you expand the brackets in -(3 - 2x) by multiplying all numbers by -1 (the negative symbol in front of the brackets represents negative 1 just without the 1)
Thus you get -3 + 2x.
Then rearranging the equation by swapping the 2x with the -3 you get 2x - 3.
What is the equation of the line written in general form?
-x + y - 2 = 0
x+y - 2 = 0
2x+y - 2 = 0
Answer:
x + y - 2 = 0
Step-by-step explanation:
First, set the equation equal to 2 by moving 2 to the other side of the equation to get x + y = 2, then move -x over to the other side to end up with y = -x + 2. The reason being is because the rate of change [slope] is -1. Simply do rise\run until you hit another endpoint, starting from your y-intercept. As you can see, you go two blocks south, then go two blocks over east. Now, if when you look carefully, you will see that -2\2 = -1. This is the simplification of the slope. Do you understand?
The histogram shows the number of gallons of gasoline purchased weekly by some drivers. According to the histogram, what is the greatest number of gallons the drivers purchase during the week?
A) 25 gallons
B) 29 gallons
C) 30 gallons
D) 31 gallons
Answer:
31
Step-by-step explanation:
I beleve
Answer:
It is actually C) 30 gallons
a cone has a diameter of 12 and a height of 7 what is the area
[tex]\bf \textit{surface area of a cone}\\\\ SA=\pi r\sqrt{r^2+h^2}+\pi r^2~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} \stackrel{\textit{half of diameter}}{r=6~\hfill }\\ h=7 \end{cases}\implies SA=\pi (6)\sqrt{6^2+7^2}+\pi 6^2 \\\\\\ SA=6\pi \sqrt{85}+36\pi \implies SA=6\pi (\sqrt{85}+6)\implies SA\approx 286.88[/tex]
A barrel in Jim's yard contains 60 gallons of water. Water leaks out of the barrel at a rate of 1 gallon every 10 minutes. Create and graph the solution set of the equation for the gallons of water, y, remaining in the barrel in terms of the number of minutes elapsed, x.
The equation that shows the water remaining in the barrel is given by y = -(1/10)x + 60
What is a linear equation?A linear equation is in the form:
y = mx + b
Where y,x are variables, m is the rate of change and b is the initial value of y.
Let y represent the amount of water remaining after x minutes.
Jim's yard contains 60 gallons of water. Hence b = 60.
The water leaks out of the barrel at a rate of 1 gallon every 10 minutes. Hence m = -1/10. The equation is:
y = -(1/10)x + 60
The equation that shows the water remaining in the barrel is given by y = -(1/10)x + 60
Find out more on linear equation at: https://brainly.com/question/14323743
Which expression is equivalent to sec2x − 1?
Answer:
tan²x
Step-by-step explanation:
Using the Pythagorean identity
sin²x + cos²x = 1
Divide all terms by cos²x
[tex]\frac{sin^2x}{cos^2x}[/tex] + [tex]\frac{cos^2x}{cos^2x}[/tex] = [tex]\frac{1}{cos^2x}[/tex], that is
tan²x + 1 = sec²x ( subtract 1 from both sides )
tan²x = sec²x - 1
Solve 2x - 1 < 7 and 5x + 3 < 3.
Step-by-step explanation:
2x-1 <7
2x <7+1
2x/2 <8/2
x <4
5x+3 <3
5x <3-3
5x <0
x <0
The solution of the given inequalities is x < 0.
What is inequality ?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
We have,
2x - 1 < 7
And
5x + 3 < 3.
Now,
Take 2x - 1 < 7 ,
Now,
Rearrange variable terms to the left side of the equation,
i.e.
2x < 7 + 1
2x < 8
We get,
x < 4
Now,
Take 5x + 3 < 3,
Now,
Rearrange variable terms to the left side of the equation,
i.e.
5x < 3 - 3
5x < 0
We get,
x < 0
So,
The intersection of the two solution will give us the solution to the system of inequalities, i.e.
x < 0 is the solution to the inequalities.
Hence, we can say that the solution of the given inequalities is x < 0.
To know more about inequality click here
https://brainly.com/question/20383699
#SPJ2
Solve this quadratic equation using the quadratic formula. x^2 - 6x + 6 = 0
Answer:
Step-by-step explanation:
x= 6± √(6)^2-4(1)(6) /2(1)
=6± √12 /2
=6± 2√3 /2
=3± √3
Answer: The required solution of the given quadratic equation is
x = 3 + √3 and x = 3 - √3.
Step-by-step explanation: We are given to solve the following quadratic equation using quadratic formula :
[tex]x^2-6x+6=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Quadratic formula : The solution of a quadratic equation of the form [tex]ax^2+bx+c=0,~a\neq 0[/tex] is given by
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
For the given quadratic equation (i), we have
a = 1, b = -6 and c = 6.
Therefore, the solution of equation (i) is given by
[tex]x\\\\\\=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\=\dfrac{-(-6)\pm\sqrt{(-6)^2-4\times 1\times6}}{2\times1}\\\\\\=\dfrac{6\pm\sqrt{36-24}}{2}\\\\\\=\dfrac{6\pm\sqrt{12}}{2}\\\\\\=\dfrac{6\pm2\sqrt{3}}{2}\\\\=3\pm\sqrt3.[/tex].
Thus, the required solution of the given quadratic equation is
x = 3 + √3 and x = 3 - √3.
What is the total surface area of the square pyramid
Answer:
The formula is a^2+2a+ sqrt a^2+h^2
Step-by-step explanation:
a=base edge
h=height
Answer:
The formula is A=a²+2a(√a^2 )/4+h²
Step-by-step explanation:
Expand and Simplify (x+3)(x+5)
[tex](x+3)(x+5) =x^2+5x+3x+15=x^2+8x+15[/tex]
[tex]x^2+8x+15[/tex]
Explanation:Use the FOIL method of multiplying binomials.
First term in each binomial: [tex]x*x=x^2[/tex]
Outside terms: [tex]x*5=5x[/tex]
Inside terms: [tex]3*x=3x[/tex]
Last term in each binomial: [tex]3*5=15[/tex]
Add them all together. [tex]x^2+5x+3x+15[/tex]
Simplify. [tex]x^2+8x+15[/tex]
The height, h, in feet of a golf ball above the ground after being hit into the air is given by the equation, h = -16t 2 + 64t, where t is the number of seconds elapsed since the ball was hit. How many seconds does it take for the golf ball to hit the ground?
Answer: 4 seconds
Step-by-step explanation:
We have the equation that models the height of the golf ball in feet after being hit.
When the ball reaches the ground its height is equal to zero.
Then to solve this problem you must equal h to zero and solve the equation for the variable t
[tex]h = -16t^2 + 64t=0[/tex]
[tex]-16t^2 + 64t=0[/tex]
Take 16t as a common factor
[tex]-16t(t - 4)=0[/tex]
The equation is equal to zero when t = 0 and when t = 4
t = 0 is at the instant in which the ball has just been hit and t = 4 seconds is the instant in which the ball touches the ground.
Then the answer is t=4 seconds
Given the function f(x) = x + 3 and g(x) = a + bx2. If gf(x) = 6x2 + 36x + 56,
find the value of a and of b.
Answer:
a = 2, b = 6
Step-by-step explanation:
To obtain g(f(x)) substitute x = f(x) into g(x), that is
g(x + 3) = a + b(x + 3)²
= a + b(x² + 6x + 9) = a + bx² + 6bx + 9b
For a + bx² + 6bx + 9b = 6x² + 36x + 56
Then coefficients of like terms must be equal
Comparing like terms
x² term ⇒ b = 6
constant term ⇒ a + 9b = 56 ⇒ a + 54 = 56 ⇒ a = 56 - 54 = 2
[tex]g(f(x))=a+b\cdot(x+3)^2=a+b(x^2+6x+9)=a+bx^2+6bx+9b=\\=bx^2+6bx+9b+a\\\\6x^2+36x+56=bx^2+6bx+9b+a\\b=6\\9b+a=56\\9\cdot6+a=56\\a=2\\\\\\\boxed{a=2,b=6}[/tex]
What is the factored form of 8x^2+12x
Answer:
4x(2x+3)
Step-by-step explanation:
Since the common factor of 8x^2 and 12x is 4x, put that out and separate the distributed remaining factors.
Marking Brainliest!
Look at polygon ABCD and its translation
If B is 120°, what is the measure of B?
What is the slope-intercept equation of the line going through (-2,5) and (1,-1)?
Answer:
y = -2x+1
Step-by-step explanation:
The slope is found by
m = (y2-y1)/(x2-x1)
= (-1-5)/(1--2)
= -6/(1+2)
= -6/3
= -2
Then we can use point slope form to make an equation
y-y1 = m(x-x1)
y-5 = -2(x--2)
y-5 = -2(x+2)
Distribute
y-5 = -2x -4
Add 5 to each side
y-5+5 = -2x-4+5
y = -2x+1
This is in point slope form
The graph of y = ax 2 + bx + c is a parabola that opens up and has a vertex at (-2, 5). What is the solution set of the related equation 0 = ax 2 + bx + c?
Answer:
The solution set is ∅
Step-by-step explanation:
The expression
y = ax^2 + bx + c
is a quadratic equation.
The vertex is located at (-2, 5) and the graph opens up, this means that it never intercepts the x-axis.
The solution set is ∅
Please see attached image
Answer:
[tex]y=\frac{-5}{4}x^{2} -5b[/tex]
Step-by-step explanation:
Assume c = 0
Using the formula for the x-coordinate of the vertex, b can be calculated in terms of a:
[tex]x=\frac{-b}{2a} \\-2=\frac{-b}{2a} \\b=4a[/tex]
B can then be substituted into the quadratic equation, along with the coordinates of the vertex, to solve a:
[tex]y=ax^{2}+bx\\y=ax^{2}+4ax\\5=a(-2)^{2}+4(-2)a\\5=4a-8a\\5=-4a\\a=\frac{5}{-4}[/tex]
AND
[tex]b=4a\\b=\frac{-5}{4} *4\\b=-5[/tex]
Substituting into the quadratic equation:
[tex]y=\frac{-5}{4}x^{2} -5b[/tex]
Because a is negative, the parabola opens up.
what is 16% of 90 helpppp plssss
Answer:
first off, welcome to brainly, second, your answer is 14.4
Step-by-step explanation:
An electrical tower casts a 120-foot shadow. At the same time, a 10-foot
street sign casts a shadow of 8 feet. What is the height of the tower?
Answer:
The height of the tower is 150 ft
Step-by-step explanation:
Let the height of the tower be H feet.
The corresponding sides will then be in the same proportion.
The ratio of the shadows will be in the same proportion as the ratio of the heights.
[tex]\frac{H}{10}=\frac{120}{8}[/tex]
We multiply both sides by 10 to get:
[tex]\frac{H}{10}\times 10=\frac{120}{8}\times 10[/tex]
[tex]H=150[/tex]
Therefore, the height of the tower is 150 ft
Answer:
Height of the tower = 150 foot
Step-by-step explanation:
We need to find height of the tower with 120-foot shadow.
We have a 10-foot street sign casts a shadow of 8 feet.
[tex]\texttt{Ratio of height to shadow height =}\frac{10}{8}=\frac{5}{4}[/tex]
We have
[tex]\frac{\texttt{Height of tower}}{\texttt{Shadow height of tower}}=\frac{5}{4}\\\\\frac{\texttt{Height of tower}}{120}=\frac{5}{4}\\\\\texttt{Height of tower}=\frac{5}{4}\times 120=150feet[/tex]
Height of the tower = 150 foot
What is the absolute value of -72?
Answer:
72
Step-by-step explanation:
Answer:
72
Step-by-step explanation:
Absolute value is the distance a number is from 0.
For example, look at the following number line.
<-|-------|--------|---------|---------|----------|---------|->
-6 -5 -4 -3 -2 -1 0
The absolute value of -6 is 6 since the number -6 is 6 digits away from 0.
So likewise if:
|-6| = 6
[keep in mind that this symbol ---> | | is the absolute value symbol]
then:
|-72| = 72
Since -72 is 72 digits away from 0.
I hope this helps! :)
1/2x=1/4 what does x =???
Answer:
x=2
Step-by-step explanation:
First of all cross-multiply.
1/2x=1/4
(1) x (4) =1 x 2x
4=2x
After flip the equation.
2x=4
Then divide both sides by 2.
2x/2=4/2
x=2
are and circumfrence of a circle with radius 4 inches
Answer:
area = 50.27 sq inches
circumference = 25.14 in
Step-by-step explanation:
given radius r = 4 in
area = πr² = 3.142 x 4² = 50.27 square inches
circumference = 2πr = 2 x 3.142 x 4 = 25.14 inches
Nosaira solved an equation. Her work is shown below:
3(2x + 1 ) = 2(x + 1) + 1
6x + 3 = 2x + 2 + 1
6x + 3 = 2x + 3
4x = 0
x = 0
She determines the equation has no solution.
Which best describes Nosaira’s work and answer?
Answer:
Making it the answer A
Step-by-step explanation:
Find the equation of the line that passes through the pair of points. (-4,3), (-4,-2)
Answer:
x = -4
Step-by-step explanation:
Using the slope formula,
we would get (3+2)/(0),
which isn't possible. Then, we realize why. A line will not have an equation when going straight up and down. And that's what this line is doing. Both of the x values are the same, so it's only going up. So therefore, the equation is x = a constant.
This constant is -4
Hope this helps!
( NEED ANSWER NOW ) How many possible outcomes exist when Louisa spins the spinner below twice?
A. 8
B. 10
C. 16
D. 64
Answer:
Step-by-step explanation:
64
There are 8 numbers on the spinner.
The first spinner could be 1 of 8 and the second spin could also be 1 of 8.
To find the total outcomes, multiply the number of outcomes of each spin by each other.
Spin 1 : 8 out comes
Spin 2: 8 outcomes
Total outcomes = 8 x 8 = 64
The answer is D. 64