Answer:
A= 24 ounces and B= 36 ounces.
Step-by-step explanation:
Given: Solution A contain 30% salt= 0.30 salt.
Solution B contain 55% salt= 0.55 salt.
New mixture should be of 60 ounces with 45% salt.
Let x be the amount of mixture for solution A. Let y be the amount of mixture of solution B.
Scientist need to to obtain 60 ounce of mixture from solution A and B.
∴ [tex]x+y= 60\ ounces[/tex]
y= [tex]60-x[/tex] equation 1
Now, solving to get final solution.
∴ [tex]0.3x+0.55y=0.45\times 60\ ounces[/tex]
Substituting the value of y from equation 1
⇒ [tex]0.3x+ 0.55\times (60-x)= 27[/tex]
⇒ [tex]0.3x+33-0.55x= 27[/tex]
⇒ [tex]-0.25x= -6[/tex]
∴ x= 24 ounces
Next, finding y
y= 60-x
∴ y= [tex]60-24= 36\ ounces.[/tex]
y= 36 ounces.
Now, we can say scientist would require 24 ounces of solution A and 36 ounces of solution B to obtain mixture of 60 ounces with 45% salt.
Help with geometry, Find the value of x. Round the length to the nearest tenth.
Answer:
it is 9.8 yards wide or 1.8 which is 9.8Solve the following
2.87 x 7.8 =
Answer:
22.386
Step-by-step explanation:
If the graph of function g is 6 units below the graph of function f, which could be function g? f(x) = -2x + 7 A. g(x) = -2x + 1 B. g(x) = -2x − 6 C. g(x) = -6x + 7 D. g(x) = -2x + 20
Answer:
A. [tex]g(x)=-2x+1[/tex]
Step-by-step explanation:
Given:
[tex]f(x)=-2x+7[/tex]
The function [tex]f(x)[/tex] is shifted 6 units below which forms the function [tex]g(x)[/tex]
To find the function [tex]g(x)[/tex], we apply the following translation rules:
[tex]f(x)\rightarrow f(x)+c[/tex]
If [tex]c>0[/tex] the function [tex]f(x)[/tex] shifts [tex]c[/tex] units up.
If [tex]c<0[/tex] the function [tex]f(x)[/tex] shifts [tex]c[/tex] units down.
Since the function [tex]f(x)[/tex] is shifting 6 units below, thus value of [tex]c<0[/tex] which is taken as -6.
The translation occurring here is given by:
[tex]f(x)\rightarrow f(x)-6[/tex]
Thus,
[tex]g(x)=f(x)-6[/tex]
Substituting [tex]f(x)=-2x+7[/tex]
[tex]g(x)=-2x+7-6[/tex]
∴ [tex]g(x)=-2x+1[/tex]
Which of the following numbers would you subtract from each side of the equation x + 12 = 17 + 3 to get the variable by itself?
17
12
3
1/12
Answer:
you will subtract 17 from both sides to get the variable by itself.
Step-by-step explanation:
x+12=17+3.
subtract 12 from both sides
If x+3=5, what is the value of 2(x+4)?
x equals 2, and substituting x=2 into the equation 2(x+4) gives us the result 12.
Explanation:To determine the value of 2(x+4), we begin by solving the equation x+3=5. Subtracting 3 from both sides yields x=2. Substituting this into 2(x+4), we get 2(2+4), which simplifies to 2(6). Multiplying, we find the result to be 12. The process involves solving for x by isolating it in the initial equation, then substituting this value into the expression we seek to evaluate. In this case, x=2, making 2(x+4) equal to 2 times the sum of 2 and 4, resulting in 12. This algebraic approach allows us to systematically find the desired value based on the given information.
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In which type of triangle is the orthocenter on the perimeter of the triangle?
a right triangle
an acute triangle
an obtuse triangle
an equilateral triangle
Answer:
its a right triangle
Step-by-step explanation:
i just took the test
Answer: Yes, I can confirm it is right triangle!
Which expression is equivalent to (x^6×x^10/×^-3)^2 and why?
Answer:
The solution for the given expression is [tex]x^{38}[/tex] , i.e option C
Step-by-step explanation:
Given expression as :
[tex](\dfrac{x^{6}\times x^{10}}{x^{-3}})^{2}[/tex]
Now, From the common radix method
∵ In multiplication of radix , if the radix is same , then power is added
I.e [tex]x^{6}\times x^{10[/tex] = [tex]x^{6+10}[/tex]
Or , [tex]x^{6}\times x^{10[/tex] = [tex]x^{16}[/tex]
Now, The expression can be written as
[tex](\frac{x^{16}}{x^{-3}})^{2}[/tex]
And In Division of radix , if the radix is same , then power is subtracted
So, [tex]\frac{x^{16}}{x^{-3}}[/tex]
Or, [tex]x^{16 - (-)3}[/tex]
Or, [tex]x^{16 + 3}[/tex]
or, [tex]x^{19}[/tex]
∴ The expression is now
[tex](x^{19})[/tex]²
Now, again this is written as
[tex]x^{19}[/tex] × [tex]x^{19}[/tex]
I.e here again the radix is same and in multiple for, so, power is added
∴ [tex]x^{19}[/tex] × [tex]x^{19}[/tex] = [tex]x^{19+19}[/tex]
I.e [tex]x^{19}[/tex] × [tex]x^{19}[/tex] = [tex]x^{38}[/tex]
Hence The solution for the given expression is [tex]x^{38}[/tex] , i.e option C . Answer
30 points!! Please help me ASAP!! I don't understand this.
ABCD is a trapezoid with midsegment (EF). If AD=5x-11, EF=3x+7, BC=2x+7, how many units in length is (EF)?
Answer:
[tex]EF=61\ units[/tex]
Step-by-step explanation:
we know that
In this problem, the length of the mid-segment EF is the sum of the two bases divided by 2
so
[tex]EF=\frac{1}{2}(BC+AD)[/tex]
substitute the given values
[tex]3x+7=\frac{1}{2}(2x+7+5x-11)[/tex]
Solve for x
[tex]6x+14=(7x-4)[/tex]
[tex]7x-6x=14+4[/tex]
[tex]x=18[/tex]
Find the length of EF
[tex]EF=3x+7[/tex]
substitute the value of x
[tex]EF=3(18)+7[/tex]
[tex]EF=61\ units[/tex]
How does the value of 30,000 x (4 x 3) compare to the value of 300 x (4 x 3)?
Answer:
30,000 x (4 x 3) = 100 times 300 x (4 x 3)
Step-by-step explanation:
Here, the given expressions are:
Expression 1 : 30,000 x (4 x 3)
Expression 2 : 300 x (4 x 3)
Now, simplifying both the expressions, we get
30,000 x (4 x 3) = 30,000 x (12) = 3,60,000
300 x (4 x 3) = 300 x (12) = 3,600
Now, dividing both the expressions, we get:
[tex]\frac{3,60,000}{3,600} = 100[/tex]
or, [tex]\frac{\textrm{Expression 1}}{\textrm{Expression 2}} = 100\\[/tex]
or, {Expression 1} = {Expression 2} x 100
⇒The expression 1 is 100 times the expression 2
Hence, 30,000 x (4 x 3) = 100 times 300 x (4 x 3)
|4*(6-10)| algebra
--------------
Answer:
16
Step-by-step explanation:
6-10=-4
4*-4=-16
abs(-16)=16
Answer:
|4(6-10)|
|4(-4)|
|-16|=16
Step-by-step explanation:
do parentheses firstdo multiplicationthe answer is 16 because the distance of a number from zero is positive not negative.
nd
A farmer has 113 sheep.
47 of them are males. How
many more female sheep
are there than male sheep?
Answer:
19 more female sheep.
Step-by-step explanation:
Answer:
66 more female sheep.
Step-by-step explanation:
What you do is subtract 113 subtract 47 which is 66 and if you want to make sure add,66+47.
How do I do this whole equation
Answer:
x = - g - c + y or g+c-y=x
Step-by-step explanation:
Answer:
x = g + c - yStep-by-step explanation:
[tex]g=x-c+y\qquad\text{add}\ c\ \text{to both sides}\\\\g+c=x-c+c+y\\\\g+c=x+y\qquad\text{subtract}\ y\ \text{from both sides}\\\\g+c-y=x+y-y\\\\g+c-y=x\to x=g+c-y[/tex]
A simple question:
Is a vector made like or ?
Answer:
A vector is a quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another.
The equation SA = 2B + Ph represents the surface area of a triangular prism. Which of the following describes the meaning of Ph?
Answer:
The product of the perimeter of the triangle and the height of the prism
Step-by-step explanation:
The options of the question are
The product of the perimeter of the triangle and the height of the prism
The product of the perimeter of the side times the height of the triangle
The product of the perimeter of the triangle and the height of the triangle
The product of the perimeter of the side times the height of the prism
we know that
The surface area of a triangular prism is
[tex]SA=2B+Ph[/tex]
where
B is the area of the triangular base
P is the perimeter of the triangular base
h is the height of the triangular prism
The term 2B represent the area of the top and the bottom of the triangular prism
The term Ph represent the lateral area of the triangular prism (The product of the perimeter of the triangle and the height of the prism)
Answer:
B is the volume of the base
Step-by-step explanation:
simplify numeric expression 4x(1.5+1.5)+5.75
Answer:
17.75
Step-by-step explanation:
4(1.5+1.5)+5.75
4(3)+5.75=12+5.75=17.75
Gary’s pet gorilla eats all the time. He eats 5/6 pound of food in 1/4 of an hour. How much food does he eat in an hour
Answer:
5/16
Step-by-step explanation:
1/4 x 5/4= 5/16
(just multiply it, straight across.)
f ∠A is 95° and ∠B is 105°, what is ∠C?
A) 75°
B) 85°
C) 95°
D) 105°
The question is missing important data. The quadrilateral having vertices A, B, C and D is a cyclic quadrilateral.
Answer:
B) 85°
Step-by-step explanation:
Given:
A cyclic quadrilateral with ∠A is 95° and ∠B is 105°.
For a cyclic quadrilateral, the sum of the opposite interior angles is equal to 180°
Therefore, sum of angles A and C is 180°.
[tex]\angle A + \angle C=180\°\\95\°+\angle C=180\°\\\angle C=180-95\\\angle C =85\°[/tex]
Therefore, the correct option is option B) 85°
Answer:
A)75
Step-by-step explanation:
Opposite angles in an inscribed quadrilateral are supplementary.
∠B + ∠D = 180°
105° + ∠D = 180°
∠D = 75°
STATE THE DOMAIN OF EACH OF THE FOLLOWING RELATIONS.
1.7) {(x, y): x = root y}
Domain ………
1.8) {(r, s): s = (2r -5)/13r }
Domain ………
1.9) {(a, b): ab = 12}
Domain ………
Step-by-step explanation:
1.7) x = √y
The square root must be non-negative, so the domain is x ≥ 0, or in interval notation, [0, ∞).
1.8) s = (2r − 5) / (3r)
The denominator can't be 0, so r can't be 0. So the domain is r ≠ 0, or in interval notation, (-∞, 0) (0, ∞).
1.9) ab = 12
Solve for b: b = 12/a
The denominator can't be 0, so a can't be 0. So the domain is a ≠ 0, or in interval notation, (-∞, 0) (0, ∞).
what is 2x + 1 = 15 if x =8
Answer:
17
Step-by-step explanation:
17=15
so this is not equal
The figure below is a rhombus.
z = [ ? 10
Answer:
27
Step-by-step explanation:
x=90 because it's a rhombus
Answer:
27 degrees
Step-by-step explanation:
one property of a rhombus is that the diagonals makes an 90 degree angle. so x= 90 degrees. the angle above x is also 90 degrees as well and since angles in a triangle add up to 180, we do 180-63-90, to get z which is 27 degrees
10 5/12- 12 7/12 = in simplest form
Answer:
-13/6 or (in mixed number form) -2 1/6
Step-by-step explanation:
Rewriting our equation with parts separated
=10+512−12−712
Solving the whole number parts
10−12=−2
Solving the fraction parts
512−712=−212
Reducing the fraction part, 2/12,
−212=−16
Combining the whole and fraction parts
−2−16=−216
Another way to do it:
Convert any mixed numbers to fractions.
Then your initial equation becomes:
125/12−151/12
Applying the fractions formula for subtraction,
=(125×12)−(151×12) / 12×12
=1500 − 1812/ 144
=−312/144
Simplifying -312/144, the answer is
=−2 1/6
Michael earns
Michael earns $9 per hour. He works 28 hours each week. How much does he earn in 6 weeks
The amount of money he earns in 6 weeks is equal to $1512.
Given the following data:
Salary = $9 per hourNumber of hours worked = 28 hours each week.To find the amount of money he earns in 6 weeks:
First of all, we would determine the amount of money he earns each week:
[tex]Weekly\;salary = Salary \times Number \;of \;hours \;worked\\\\Weekly\;salary =9\times 28[/tex]
Weekly salary = $252
In 6 weeks:
Total salary = [tex]252\times6[/tex]
Total salary = $1512
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Gina recently got an 10% raise on her salary. If Gina used to make $25 per hour, what is her new salary?
Answer:
Her new salary is $27.5.
Step-by-step explanation:
25*0.10=2.5
2.5+25=27.5
How do you simplyfy -x squared + 4/2x
Answer:
The solution for the given expression is 0 , 2
Step-by-step explanation:
Given expression as :
- x² + [tex]\frac{4}{2}[/tex] x = 0
or, - 2 x² + 4 x = 0
or, 2 x ( -x + 2 ) = 0
or, ( - x + 2 ) ( 2 x ) = 0
or, 2 x = 0
∴ x = 0
and ( - x + 2 ) = 0
Or, - x = - 2
∴ x = 2
Hence The solution for the given expression is 0 , 2 Answer
Choose the equation that represents the line passing through the point (2, - 5) with a slope of −3.
y = −3x − 13
y = −3x + 11
y = −3x + 13
y = −3x + 1
Answer:
y = -3x + 1
Step by step (I hope I don't confuse you):
1. First, look for the equation that has a slope of -3. In this case, it's all of them because they all have -3 before the x value.
2. Then look for what's given:
The y of (2, -5) is negative. If the x is 2, that means that the slope has moved down 3 units twice. (-3 is the slope. -3 x 2 is -6.)3. Now see what equation will have -5 when you subtract 6 from it's y intercept.
y = 3x + 11. 11 - 6 is 5, not -5. this one is wrong.y = 3x - 13. -13 - 6 is -19, also incorrect.y = 3x + 1. 1 - 6 is -5, so this is the correct answer.Hope you found this helpful.
The equation of line is y= -3x + 1.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
point (2, - 5) with a slope of −3.
Using slope- intercept form
y = mx + c
-5 = (-3) (2) + c
-5 = -6 + c
c = -5 + 6
c= 1
So, the equation of line is y= -3x + 1
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guys what is the answer 3/8+4/5
Answer:
the answer would be 47/40
Answer:
1 ⁷/40
find lcm of the denominators (the bottom numbers) 8&5
lcm is 40
ask your self how many times can 40 be divided by 8? 5 times good job .
so you multiply top & bottom of 3/8 by 5
3×5=15 8×5=40
we now get a new fraction 15/40
ask your self how many times can 40 be divided by 5? 8 times very good !
so you multiply top & bottom of tht fraction by 8
4×8=32 5×8=40
new fractions are 15/40 & 32/40
we did all of that to get fractions with the same denominator because fractions with like denominators are easy to add you add the top numbers & keep the bottom.
15+32=47
47/40 now this fraction can be simplified to a mixed number
ask yourself how many times can 40 go into 47 ? one time
40×1 =40 & there are 7 remainders & you just keep the denominator the same .
1 ⁷/40
Can someone help me with this????? The question is attached in the image
Answer:
See explanation
Step-by-step explanation:
Since [tex]\overline{CB}[/tex] is parallel to [tex]\overline {ED},[/tex] then
angles EDF and CBF are congruent as alternate interior angles when parallel lines [tex]\overline{CB}[/tex] is parallel to [tex]\overline {ED}[/tex] intersect by transversal DB;angles DEF and BCF are congruent as alternate interior angles when parallel lines [tex]\overline{CB}[/tex] is parallel to [tex]\overline {ED}[/tex] intersect by transversal CE.Consider triangles CBF and EDF. In these triangles:
[tex]\angle EDF\cong \angle CBF[/tex] (proven);[tex]\angle FED\cong \angle FCB[/tex] (proven);[tex]\overline{CB}\cong \overline {ED}[/tex] (given).Thus, triangles CBF and EDF are congruent by ASA postulate.
III.
a small appliance manufacturer finds that if the firm produces and sells x blenders
monthly, the total monthly profit P (in dollars) is given by
P(x) = 8x + 0.3x2 - 0.0013x3 - 372.
ne owner wants to produce no more than 225 blenders/month in order to maintain quality
(SLO #1, 2, 6)
a. Find the y-intercept and explain what it means in this context.
Answer:
The y-intercept is - 372 and it means that if the manufacturers do not produce and sell any blenders they will have a loss of $ 372.Explanation:
The polynomial that represents the function is:
[tex]P(x)=8x+0.3x^2-0.0013x^3-372[/tex]Where the variable, x, represents the number of blenders produced and sold monthly, and P(x) is the monthly profit in dollars obtained for the sale of x blenders.
As for the question, the y-intercept is the point on the graph where the function crosses the y-axis, i.e. where the input of the function is x = 0.
Therefore, the y-intercept is the value of the function for x = 0, P(0), and it is found by substituting 0 for x in the polynomial function, which is shown next:
[tex]P(0)=8(0)+0.3(0)^2-0.0013(0)^3-372=-372[/tex]The meaning of this value is that the firm loses $372 when it does not produce and sell any blenders.
according to the blueprint, the floor area of the stage in the new auditorium at your college must be rectangular and equal to 1200 square feet. The width of the stagr is key to all of the theatre priductions. therefore, in this situation, the stages depth is a function of its width.
Answer:
[tex]d = \frac{1200}{w}[/tex]
Step-by-step explanation:
According to the blueprint, the floor area of the stage in the new auditorium at my college must be rectangular and equal to 1200 sq. feet.
If the width of the stage is w feet and depth of the stage is equal to d feet, then being a rectangle, we can write
[tex]d \times w = 1200[/tex]
Therefore, the equation that represents the depth d as a function of width w is given by [tex]d = \frac{1200}{w}[/tex] (Answer)
Answer:
the correct answer d=1200[tex]d=1200/w[/tex]
Step-by-step explanation:
Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie crochets at a rate of
of a blanket per day. She has 60 days until when she wants to donate the blankets, but she also wants to
skip crocheting some days so she can volunteer in other ways.
Write an inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal.
How many days can Darcie skip to still meet her goal?
Answer:
I believe it's 15 days
Answer:
The maximum number of days that she can skip crocheting is s = 57
Step-by-step explanation:
Darcie wants to crochet a minimum of 3 blankets.
She can crochet at a rate of a blanket per day, so she makes 1 blanket in one day.
She has a total of 60 days to work.
If X is the number of days that she works, we can write it as:
X ≥ 3
This means that she works at least 3 days, so she makes at least 3 blankets.
X < 60
This means that she not can work 60 days or more, in this way she has at least one day to do another volunteer job.
then
3 ≤ X < 60
then we have:
1 ≤ s ≤ 60 - 3 = 57
where s is the days that she can skip, where the less or equal sign is used because we have a bigger or equal sign previously.
The maximum number of days that she can skip
The maximum number of days that she can skip crocheting is when the right equality is true, so s = 57.