Answer:
405 gallons
Step-by-step explanation:
Let it be that the amount of gallons of a 70% antifreeze solution is x, when a mixture that is 60 percents of antifreeze is placed in y gallons
x+90=y - the equation of dependence between solutions
The amount of antifreeze in the first one is x/100*70= 0.7x (in gallons), in the second solution (15percents) antifreeze is 90/100*15=13.5 (in gallons).
In the mixture we should get there will be y/100*60=0.6y - gallons of antifreeze
0,7x+13.5=0.6y
We have two equations x+90=y and 0,7x+13.5= 0.6y
0.6x+54=0.6y
0.7x+13.5=0.6y
0.7x+13.5-0.6x-54= 0.6y-0.6y
0.1x-40.5=0
x=405- the answer
p.s. sorry, I don't know what the six-step method is. But the answer is right.
The inequality - 15<-6 is given. Write the inequality you get when you perform the
following operation.
Divide both sides of the inequality by 3.
Answer:
-5
Step-by-step explanation:
-15<-6=-15
-15÷3
=-5
Inequalities are used to show unequal expressions. There are five inequalities, and they are: not equal to, greater than, less than, greater than or equal to and less than or equal to.
The inequality when both sides of [tex]-15 < -6[/tex] is divided by 3 is [tex]-5< -2[/tex]
Given that:
[tex]-15 < -6[/tex]
Divide both sides by 3
[tex]-15 \div 3< -6 \div 3[/tex]
Evaluate the division
[tex]-5< -2[/tex]
Hence, the inequality when both sides of [tex]-15 < -6[/tex] is divided by 3 is [tex]-5< -2[/tex]
Read more about inequalities at:
https://brainly.com/question/17194874
. What is the total cost of 6 books at N8.50k each?
Answer:
51
Step-by-step explanation:
1 book= N8.50
therefore 6 books= N8.50 × 6 = N51
Find the root(s) or zero(s) of the function.
Answer:
-1/2 , 3
Step-by-step explanation:
In order to find the roots of the function 2x² - 5x - 3
We have to solve the quadratic equation :
2x² - 5x - 3 = 0
Calculating the discriminant Δ :
Δ = b² - 4ac
= (-5)² - 4(2)(-3)
= 25 + 24
= 49
Then
√Δ = √49 = 7
Determining the Zeros :
[tex]x=\frac{-b+\sqrt{b^{2}-4ac} }{2a} = \frac{5+7} {2 \times (2)} =\frac{12}{4} =3[/tex]
or
[tex]x=\frac{-b-\sqrt{b^{2}-4ac} }{2a} = \frac{5-7} {2 \times (2)} =\frac{-2}{4} =\frac{-1}{2}[/tex]
if p(x) = 6x³ + 5x² + 7x - 5, find the coefficient of x³
Answer:
6x
Step-by-step explanation:
because in front of x^3 there is 6x and also the qn has asked to find the coefficient of x^3
Answer:
It is 6
Step-by-step explanation:
take an example:
[tex]a {x}^{3} + {bx}^{2} + cx + d[/tex]
a, b, and c are coefficients of x³, x², and x respectively.
d is a constant.
please solve this question i need help
Answer:
4c/2a 60 degrees 3bf 2ad
Answer:
f=120
b=40
d=140
e=120
c=30
a=30
Which of the following is a basic equation?
A.b + 3 = 5
B.O (2, 3)
C .O y-axis
D .3+6
Answer:
A. b + 3 = 5[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Simplify -4+8-2 and 8-(-3)-5
Answer:
-2 and 6
Step-by-step explanation:
[tex] - 4 + 8 - 2[/tex]
[tex] - 6 + 8[/tex]
[tex] = - 2[/tex]
○●○●○●○●○●○●○●○●○●○●○●○●○●○
[tex]8 - ( - 3) - 5[/tex]
[tex]8 + 3 - 5[/tex]
[tex] = 6[/tex]
In △PQR, sinQ=25, sinR=13, and q=6. Find the side length r.
Can someone please help
Answer:
r = 5
Step-by-step explanation:
the sine rules formula :
sin Q/q = sin R/r
=> r = q× sin R / sin Q
= 6× ⅓ / (2/5)
= 2 /(2/5)
= 2× 5/2
= 5
The measure of side length "r" if sinQ=2/5, sinR=1/3, and q=6 is 5
Application of sine rule.According to the rule, the ratio of the sides to the opposite angles is a constant. Mathematically:
p/sinP = q/sinQ = r/sinR
Given the following parameters
sinQ=2/5, sinR=1/3, and q=6.
6/(2/5) = r/(1/3)
30/2 = 3r
15 = 3r
r = 5
Hence the measure of side length "r" if sinQ=2/5, sinR=1/3, and q=6 is 5
Learn more on sine rule here: https://brainly.com/question/27174058
Please help me on this homework assignment, 20 points to whoever can help me and give me a good answer. it is asking for the height and the bottom number under the 90 degree angle is 6.
Answer:
h = 3 sqrt(21)
or
h = 13.75
Step-by-step explanation:
The perimeter of the rhombus is 60 feet. Like a square, all the sides of a rhombus are equal. Therefore your first step is to find FK which is a side.
FK = 60/4 = 15 feet.
Now you can use the Pythagorean Theorem.
a^2 + b^2 = c^2
a = 6
b = height or = h
c = 15
6^2 + b^2 = 15^2
36 + b^2 = 225
b^2 = 225 - 36
b^2 = 189
sqrt(b^2)= sqrt(189)
b = sqrt(3 * 3 * 3 * 7) You can take out the square of 3 * 3 and make it 3.
b = 3 * sqrt(3*7)
b = 3 * sqrt(21)
Assume that an investment of $3000 earns an APR of 6% compounded monthly for 18 months.
How much money is in your account after 18 months?
9514 1404 393
Answer:
$3281.79
Step-by-step explanation:
The compound interest formula is ...
A = P(1 +r/n)^(nt)
where A is the balance resulting from investment of P at annual rate r compounded n times per year for t years.
We have P=$3000, r=0.06, n=12, t=1.5, so the account balance is ...
A = $3000(1 +0.06/12)^(12·1.5) = $3000(1.005^18) ≈ $3281.79
There will be $3281.79 in the account after 18 months.
evaluate the expression when x=3
Answer:
3. 15
6. 4
Step-by-step explanation:
Put 3 instead of x
3. 5x
= 5 × 3
= 15
6. 12 ÷ x
= 12 ÷ 3
= 4
Answer:
When X is 3 it will be
5(3)=15
Then for the second one it will be 12/3
The answer is 4
Hope I helped
18. Solve x^2+ 6x - 16 = 0 by completing the square.
Please give detailed steps!!
Answer:
x1 = -8, x2= 2
Step-by-step explanation:
1. Write 6x as a difference
= x^2 + 8x - 2x - 16 = 0
2. Factor the expressions
= x ( x + 8 ) - 2x - 16 = 0
= x ( x + 8 ) - 2 ( x + 8 ) = 0
Factor out x + 8 from the expression
= ( x + 8 ) ( x - 2 ) = 0
3. When the product of factors = 0, at least one factor is 0
x + 8 = 0
x - 2 = 0
4. Solve the equation for x
x = - 8
x = 2
Therefore, the equation has 2 solutions :
x1 = -8, x2 = 2
A=1/2pie r squared solve for pie
Answer:
[tex]A = \frac{1}{2} \pi r [/tex]
multiply all sides by 2:
[tex]2 \times A = ( \frac{1}{2} \pi r) \times 2 \\ \\ 2A = \pi r[/tex]
divide all sides by r:
[tex] \frac{2A}{r} = \frac{\pi r}{r} \\ \\ \frac{2A}{r} = \pi[/tex]
therefore:
[tex]{ \boxed{ \sf{\pi = \frac{2A}{r} }}}[/tex]
The sum of 7/4 and pi i
Hi! I'm happy to help!
To first of all write this expression, we need to know what sum means. Sum means addition, so we are adding. From there, we write it like this:
[tex]\frac{7}{4}[/tex]+[tex]\pi[/tex]
This is how you write it.
If you want to solve it, you need to know what pi is. pi is 3.14159...
It goes on forever, but we cane round to the nearest ten thousandth.
From here, you need to turn [tex]\frac{7}{4}[/tex] into a decimal. 4/4 is equal to 1, and 3/4 is equal to 0.75. Together, equal 1.75, or 7/4
Now, we solve our equation:
[tex]\frac{7}{4}[/tex]+[tex]\pi[/tex]
[tex]\frac{7}{4}[/tex]+3.14159
1.75+3.14159
4.89159
This is what the answer to the expression is.
I hope this was helpful, keep learning! :D
Write a function rulle
Hey, there! Based on the table from the picture, every hour increased is $6 increased for the cost of the rental.
First hour: $10
Second hour: $16
Third hour: $22
Fourth hour: $28
So, final answer is:
+1 hour=+$6.
Anyways, I hope this helps! Enjoy your day! Take care!
Find two given numbers in a given ratio such that the sum of their squares is to their difference in a given ratio. Ratios being 3 : 1 and 10 : 1.
Answer: a=6 and b=2
Step-by-step explanation:
Let say A and b the 2 numbers.
[tex]\dfrac{a}{b} =\dfrac{3}{1} \Longrightarrow\ a=3b\\\\\dfrac{a^2+b^2}{a-b} =\dfrac{10}{1} \Longrightarrow\ (3b)^2+b^2=10*(3b-b)\\\\\Longrightarrow\ 10*b^2=10*2b\\\\\Longrightarrow\ b=2\\\\\Longrightarrow\ a=6\\\\[/tex]
The formula for determining the pressure, p, exerted on an object at a depth, h, below the surface of a liquid is p = s + dgh, where s is the atmospheric pressure, d is the density of the liquid, and g is the acceleration due to gravity.
(Pls Explain in Simple terms)
Answer:
The formula for determining the pressure, p, exerted on an object at a depth, h, below the surface of a liquid is p = s + dgh,
Which expression represents -8x^2+54x+140 in factored form?
A. (x-70)(-8x+2)
B. (x+1)(8x- 140
C. (x-8)(2x+70)
D. (x+2)(-8x+70)
Answer:
D. (x+2)(-8x+70)
Step-by-step explanation:
-8x^2+54x+140
Factor out -2
-2(4x^2+27x+70)
Factor
-2(x+2)(4x-35)
Option D is the same answer if we multiply -2 in the second term
(x+2) (-8x+70)
solve for Y: Y=6b+12ab^2 a= 4, b=6
Answer:
1764
Step-by-step explanation:
Y=6b+12ab^2
Let a = 4
b = 6
Y = 6(6) +12 (4)(6)^2
= 36 + 12 (4) (36)
= 36+1728
=1764
Answer:
[tex]\huge\boxed{\sf Y = 1764}[/tex]
Step-by-step explanation:
[tex]Y = 6b+12ab^2\\\\Given \ that \ a = 4 , \ b = 6\\\\Putting \ values\ in \ given \ equation\\\\Y = 6(6) +12(4)(6)^2\\\\Y = 36 + 48(36)\\\\Y = 36 + 1728\\\\Y = 1764\\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Peace!मच्ने costing Rs 10,000 is depreciated at 15% per annum find the value of maths in after 1 year?
Answer:
8500
Step-by-step explanation:
depreciation=10000×15%=1500
initial cost = 10000
final cost = initial cost- depreciation
=10000-1500
=8500
I need help as soon as possible pleaseeeeeee!!!!!!!
(1.) Find the equation of the line passing through the points (-4,-6 ) and (-5,5).
(2.) Find the equation of the line with slope -8 that passes through the point (3, -8).
Answer:
1) y=-11x-50 2)y=-8x+16
Step-by-step explanation:
1. y=mx+b- it is the main equation for a line'
If we take the first point and use its coordinates we have -6=-4m+b
If we take the second point and use its coordinates we have 5=5m+b
These equations are simultaneous for our line because the line passes through both points
-6=-4m+b
5=-5m+b
If subtract the second one from the first equation
-6-5= -4m+b- (-5m+b)
-11= m
b= -6-44=-50
y=-11x-50
2) y=mx+b
-8=-8*3+b
b=16
y=-8x+16
solve 4x+y=24 and y=-4x+24 using substitution
Answer:
no solutions
Step-by-step explanation:
[tex]4x + y = 24 - - - (a) \\ y = - 4x + 24 - - - (b)[/tex]
substitute for y in (a) with (b):
[tex]4x + ( - 4x + 24) = 24 \\ 0x = 0[/tex]
Answer:
infinite solutions
Step-by-step explanation:
substitute y in the first equation
4x+(-4x+24)=24
4x and -4x cancel out
24/24=1
or solve for x, you should also get 1
Find the value of x.
95
38°
X
Answer:
47
Step-by-step explanation:
x is one of the three angles of a triangle. The other two are given as 95 and 38.
Together all three have to make 180 degrees.
x + 95 + 38 = 180
x + 133 = 180
x = 180 - 133
x = 47
Answer:
47
Step-by-step explanation:
as we know that sum of a triangle is always=180°
so x+38°+95°=180
so x+133=180
and x=180-133
so x= 47
Group discounted lift tickets were $14 for those paying with cash and $15 for those
paying with a credit card. The total paid by the group was $177.00. Three times as many
people paid with a credit card as those who paid with cash. How many people paid with
cash?
PLEASE ANSWER WITH AN EXPLANATION
Answer:
3 people
Step-by-step explanation:
Let "x" represent the number of people who payed with cash
Let "y" represent the number of people who payed with credit card
14x +15y = 177 ---------1
3x =y--------- 2
solving simultaneously,
put eqn 2 into eqn 1
14x + 15 (3x) = 177
14x + 45x = 177
59x = 177
x=3
From eqn 2 , y = 3 x
y = 3 (3)
y=9
therefore the number of people who paid with cash were 3.
Lindsay prepared 9 containers of fruit punch for a party. After the party, there were still 4 4/9 containers of fruit punch left. How many containers were consumed in the party?
Turn 9 into [tex]\frac{81}{9}[/tex]. Then, convert 4 [tex]\frac{4}{9}[/tex] into a improper faction ( [tex]\frac{40}{9}[/tex] ). Then, subtract
[tex]\frac{81}{9} - \frac{40}{9} = \frac{41}{9}[/tex]. Lastly, convert [tex]\frac{41}{9}[/tex] to a mixed fraction ( [tex]4\frac{4}{9}[/tex] ).
Your answer is [tex]4\frac{4}{9}[/tex].
pelase asnwer da question
Answer:
D
Step-by-step explanation:
I think its D because you multiple the number that is out of the the bracket with the numerators..
so its
a^4/b^12
What do these have in common??
Answer:
They can all be simplified to 2/3
Tavon has a gift card for $65 that loses $3 for each 30-day period it is not used. He has another gift card for $55 that loses $2.50 for each 30-day period it is not
used
a. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal.
b. What will the value of each card be when they have equal value?
a. If x is the number of 30-day periods, then the equation can be used to find the number of 30-day periods until the values of the gift cards will be equal.
(Type an equation. Use integers or decimals for any numbers in the equation)
Answer:
a. 65 - 3 x = 55 - 2.5 x
ab. 20
b. 5
Step-by-step explanation:
The equations are y = 110 - 2.5x and y = 90 - 2x. Then the value of each card, when they have equal value, will be $10.
What is a linear equation?The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let x be the number of days and y be the value of the card.
Tavon has a gift card for $110 that loses $2.50 for each 30-day period it is not used. He has another gift card for $90 that loses $2 for each 30-day period it is not used. Then the equations will be
y = 110 - 2.5x ...1
y = 90 - 2x ...2
From equations 1 and 2, we have
110 - 2.5x = 90 - 2x
20 = 0.5x
x = 40
And the value of y will be
y = 110 - 2.5(40)
y = 110 - 100
y = $10
The equations are y = 110 - 2.5x and y = 90 - 2x. Then the value of each card, when they have equal value, will be $10.
More about the linear equation link is given below.
brainly.com/question/11897796
#SPJ2
Integrate f(x,y,z) = (x+y+z) / (x^2 +y^2 + z^2) over the path r(t) = 2ti +2tj +t k, 0
The information about the path is incomplete, so I'll just use a domain of a ≤ t ≤ b, where a > 0 and b < ∞.
Differentiating r(t) gives
[tex]\vec r(t) = 2t\,\vec\imath + 2t\,\vec\jmath + t\,\vec k \implies \dfrac{\mathrm d\vec r(t)}{\mathrm dt} = 2\,\vec\imath + 2\,\vec\jmath + \vec k[/tex]
with magnitude √(2² + 2² + 1²) = √5.
Then we have
[tex]\displaystyle \int_C f(x,y,z)\,\mathrm ds = \int_a^b f(2t,2t,t) \left\|\frac{\mathrm d\vec r(t)}{\mathrm dt}\right\| \,\mathrm dt \\\\= \sqrt5 \int_a^b \frac{2t+2t+t}{(2t)^2+(2t)^2+t^2}\,\mathrm dt \\\\ = \sqrt5 \int_a^b \frac{5t}{5t^2} \,\mathrm dt \\\\ = \sqrt5 \int_a^b \frac{\mathrm dt}t \\\\ = \sqrt5 (\ln(b)-\ln(a)) = \boxed{\sqrt5 \ln\left(\frac ba\right)}[/tex]
