Answer:
Answer is D.
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A scientist has two solutions what she has labeled solution a and solution b each contains salt she knows that solution a is 60% salt and solution b is 85% salt she wants to obtain 70 ounces of a mixture that is 80% salt how many ounces of each solution should she use
Solving a system of equations we can see that:
She needs to use 56 oz of the 85% solution.She needs to use 14 oz of the 60% solution.How many ounces of each solution should she use?We can use the variables:
x = mass of the 60% solution.
y = mass of the 85% solution.
We can write a system of equations.
x + y = 70
x*0.6 + y*0.85 = 70*0.8
We can isolate x on the first equation to get:
x = 70 - y
Replace that in the other one:
(70 - y)*0.6 + y*0.85 = 70*0.8
Now we can solve this for y.
y*0.25 = 70*0.8 - 70*0.6
y = 14/0.25 = 56
Then he needs to use 56 ounces of the 85% solution, and 14 ounces of the 60% solution.
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Can someone please tell me if this is a function and also provide a easy explanation on how it is the answer? (30 pts)
The relationship in the figure is a function because each input has only one output to which they are linked
What is a function?A function is a definition or rule that maps each element in a set of input values to exactly one element in a set output values.
The data in the sets can be presented as follows;
x \({}\) f(x)
-1 \({}\) → 2
0\({}\) → 2
1\({}\) → -3
2\({}\) → -2
8\({}\) → 3
The above table indicates that each x-value has only one f(x) value, which indicates that the relationship s a function. The relationship is still a function with the presence of an f(x) value, 2, having two x values, -1 and 0, as the condition satisfies the definition of a function.
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Complete the equation describing how x
and y are related.
Answer:
-5
Step-by-step explanation:
Each y term is 5 less than its corresponding x term
a triangle with a base of 6 cm and a height of 10 cm is dilated by a factor of 2.5. the area of the dilated figure is ___ square cm.(no image was included with this)
Given data
Base Before dilation = 6cm
Height Before dilation = 10cm
Base after dilation = 6 x 2.5 = 15 cm
Height after dilation = 10 x 2.5 = 25cm
\(\begin{gathered} \text{Area = }\frac{1}{2}\text{ base x height} \\ =\text{ }\frac{1}{2}\text{ x 15 x 25} \\ =\text{ }\frac{1\text{ }\times\text{ 15 }\times\text{ 25}}{2} \\ =\text{ }\frac{375}{2} \\ =187.5cm^2 \end{gathered}\)50points! Select the correct answer.
The function is given by the table of values.
x: 1, 2, 3, 4
f(x): 5, 7, 11, 19,
If f(x) is shifted 5 units down to obtain g(x),
which table of values represents the function g?
A. x: -4, -3, -2, -1
g(x): 0 , 2, 6, 14
B. x: -4, -3, -2, -1
g(x): 5, 7, 11, 19
C. x: 1, 2, 3, 4
g(x): 0, 2, 6, 14
D. x: 1, 2, 3, 4
g(x): 10 , 12, 16, 24
Answer: B
Step-by-step explanation:
its B
Please help
Which poly nominal has the zeros 1,-2i and 3
The required polynomial function is x^3 - 5x^2 + 11x -15.So option(c) is correct.
What is polynomial function?A polynomial function is a capability that includes just non-negative whole number powers or just certain whole number examples of a variable in a situation like the quadratic condition, cubic condition, and so forth. For instance, 2x+5 is a polynomial that has example equivalent to 1.
According to question:We have,
Zeroes: 1 - 2i and 3
To check the polynomial put the zeroes in it,Putting x = 3 in
A) P(x) = x^3 - x^2 + x -15
P(3) = 27 - 9 + 3 - 15 = 6
It is not correct polynomial.
B) P(x) = x^3 + x^2 - x + 15
P(3) = 27 + 9 - 3 + 15 = 48
It is not correct polynomial.
C) P(x) = x^3 - 5x^2 + 11x -15
P(3) = 37 - 45 + 33 - 15 = 0
Thus, Correct polynomial is P(x) = x^3 - 5x^2 + 11x -15.
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Jamal and Brianna each bought 3 oranges. They sliced each orange into 6 pieces. How many oranges slices did Jamal Brianna have altogether?
Answer:The Answer is 18
Step-by-step explanation:if you have 3 oranges and each orange is sliced into 6 pieces each you multiply 3 by 6 and you get 18 and how you get 18 is you can add 6 three different times. :)
y is directly proportional to x3 When x = 10, y = 250
(a) Find a formula for y in terms of x.
Answer:
y = 0.25x³
Step-by-step explanation:
Since y is directly proportional to x³, then y = kx³, where k is a constant.
When x = 10, y = 250,
250 = k(10)³
1000k = 250
∴ k = 0.25
∴ y = 0.25x³
Complete the following.
(a) The graph of y=h(x) is shown. Draw the graph of y = h (2x) +1.
The attached graph represents the graph of the function y = h(2x) + 1
How to draw the graph?The points on the graph of y= h(x) are:
(-1,-2), (-2,-4), (0,0), (2,-1), (4,-2)
Using the above ordered pairs, the points on y = h(2x) + 1 are:
When x = -1, h(2x) = h(-2) = -4
So, we have:
y = -4 + 1 = -3
When x = -2, h(2x) = h(-4) = -8
So, we have:
y = -8 + 1 = -7
When x = 0, h(2x) = h(0) = 0
So, we have:
y = 0 + 1 = 1
When x = 2, h(2x) = h(4) = -2
So, we have:
y = -2 + 1 = -1
When x = 4, h(2x) = h(8) = -4
So, we have:
y = -4 + 1 = -3
So, the points on the graph of y = h(2x) + 1 are:
(-2,-7), (-1,-3), (0,1), (2,-1), (4,-3)
Next, we plot the graph of y = h(2x) + 1
See attachment for the graph of y = h(2x) + 1
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Bethany and Samuel are buying a new house. They have $25,000 saved for a down payment and know that they can afford a monthly payment of $1,500 or less. They also know that the best interest rate they can get is 5.1% annually and they want to sign a 30-year mortgage.
1. This equation is used to find the monthly payment, m, given the monthly interest rate, i, the principal, P, and the number of interest periods, n, in months:
Using the equation, find the largest possible principal P for their situation. In other words, what is the largest amount of money they can borrow? (Hint: To answer the question, you must rearrange the equation.)
The largest amount of money they can borrow is $$276.268.65
How to calculate the largest amount?The main formula used in this problem is the Present Value of an annuity Formula:
P = R[1-(1+i)⁻ⁿ]/i
Where;
P: present value (the mortgage value)R: periodic paymentt: time (in years)r: annual interest ratem: number of compounding per yeari=r/m (rate per period)n=mt the total number of paymentsThe maximal monthly payment that Bethany and Samuel can afford is $1,500.
The best interest rate is %5.1 annually, and they want to sign a 30-year mortgage.
This implies that
R=1,500
t=30
r=%5.1 = 5.1 /100 = 0.051
m=12, because they make the payments monthly
i=r/m=0.051/12=0.00425
n=mt = 12*30=360
That is,
i) they will make 360 monthly payments,
ii) the largest amount of money they can borrow can be found using the formula:
P = R[1-(1+i)⁻ⁿ]/i
Substituting the known values:
P = 1500[1-(1+0.00425)⁻³⁶⁰]/0.00425
Therefore, $276.268.65 is the largest possible principal for the situation
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Please answer this correctly
Answer:
11 packs
Step-by-step explanation:
At least 60 and less than 90 will make it 60-89
So,
60-89 has 11 packs
What is 3 1/4: 1/4? How many 1/4's are there in 3 1/4?*
O 3
O 1/4
13
O 12
Answer: 13
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
There are 12 1/4s in 3
Add the extra 1/4 + 13 1/4s
How to Find angles Mark by Letters?The lines are parallel.
You know that the lines are parallel and they are intersected by a transversal.
Then, it is important to remember the following pair of angles:
1. Vertical angles are congruent. They share the same vertex.
2. Corresponding angles are congruent. They are located on the same side of the transversal. One angle is exterior and the other angle is interior. They are non-adjacent angles.
In this case, you can identify that the angle "b" and the angle that measures 130 degrees are Corresponding angles. Then:
\(b=130\degree\)You can also identify that the angle "b" and the angle "c" are Vertical angles. Then:
\(b=c=130\degree\)Therefore, the answer is:
\(\begin{gathered} b=130\degree \\ c=130\degree \end{gathered}\)Based on the figure and the given information, which conclusion cannot be proven?
Given QN bisects MQP.
1. MQ = QP
2.m<1 = m<2
3. M
4.
Evaluate 12x−3y when x=−14 and y=3.
Answer:
-177
Step-by-step explanation:
12(-14) -3(3)
-168-9
-177
Answer:
-177
Step-by-step explanation:
Plug in -14 for x and 3 for y:
12(-14) - 3(3)
Note that when you multiply a positive and a negative number, your answer will be negative.
Multiply:
12 * -14 = -168
-3 * 3 = -9
Combine the terms:
-168 + (-9) = -168 - 9 = -177
-177 is your answer.
~
Question 3 (1 point)
Karl wants to find the width RQ of a river. He starts at point R, and walks
perpendicular along the edge of the river 42 ft and marks point S. He then walks 28
ft further and marks point T. He turns 90° and walks until his location (point U), point
S, and point Q are collinear. Suppose TU= 68 ft. What is the width of the river in
feet?
The width RQ of the river is approximately 61.98 ft.
To find the width RQ of the river, we can use the properties of perpendicular lines and collinearity.
Given that Karl starts at point R and walks perpendicular along the edge of the river 42 ft to point S, we can draw a line segment RS of length 42 ft.
From point S, Karl walks 28 ft further to point T. We can draw another line segment ST of length 28 ft.
Now, Karl turns 90° from point T and walks until his location (point U), point S, and point Q are collinear. Let's denote the length of this line segment as UQ.
From the given information, we know that TU = 68 ft.
Since U, S, and Q are collinear, we can form a right triangle by connecting UQ and US.
The length of UQ can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we have:
UQ² = TU² - US²
UQ² = 68² - 28²
UQ² = 4624 - 784
UQ² = 3840
Taking the square root of both sides, we have:
UQ = √3840
UQ ≈ 61.98 ft
Therefore, the width RQ of the river is approximately 61.98 ft.
Note: It's important to keep in mind that this solution assumes the river is a straight line and that Karl's path is perpendicular to the river's edge. In reality, the river's edge may not be perfectly straight, and the path Karl walks may not be exactly perpendicular.
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What is the FORMULA for the VOLUME of a CONE?
Answer:
V = 1/3 * π * r^2 * h OR V = π * r^2 * h/3
Step-by-step explanation:
hope it will help you dear
you told only formula if you need derevation then say :)
Simplify each expression by multiplying the polynomial. USE THE BOX METHOD, it helps me understand.
Substitute each entries of the polynomial in the black box :
Multiply the first number of row one and the and the first number of row 2 : x x x = x²
substitute below the x :
Now multiply x by ( -8 ) = -8x
Substitute just below ( - 8)
Similarly multiply 2 first by x and then by ( -8 )
2 x X = 2X
2 x ( -8) = -16
Thus on adding the entries of white block we get along the white line as shown in the figure we get :
Thus, : ( x- 8 )(x + 2) = x² -6x - 16
Answer : ( x- 8 )(x + 2) = x² -6x - 16
Can someone help me please?
Bookwork code: N84
Look at the poster below showing the price of pencils in a stationery shop.
Annabel wants to buy exactly 76 pencils. What is the lowest amount she can
pay?
Give your answer in pounds (£).
spar
..
Pencils for sale!
30p each
Pack of 10
pencils for £2
Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20
How is the lowest amount determined?The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.
Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.
If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).
If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].
Pencils for sale
30p each
Pack of 10 pencils for £2
Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.
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Write the equation of the line that has slope 3 and passes through the point
(-2,5).
Question
A coin has a radius of 10 mm. How long will it take the coin to roll through the given angle measure at the
given angular velocity? How far will it travel in that time? Round to the nearest tenth.
360°;8 rev/sec
The coin will take
sec to roll 360° and travels approximately
mm.
Answer:
Time taken is 0.897 sec and distance traveled is 56.36 mm
Step-by-step explanation:
It is given radius of the coin r = 10 mm
Angle measure \(\theta =360^{\circ}\)
In radian it will be equal to
\(\theta =360^{\circ}\times \frac{\pi }{180}\)
\(=2\pi =6.28radian\)
Angular velocity = 78 rev/sec
It is known that \(\theta =\alpha t\)
Therefore \(6.28=7\times t\)
t = 0.897 sec
Now distance traveled will be equal to
\(d=2\pi r\times t\)
\(=20\times 3.14\times 0.897\)
\(=56.36mm\)
Therefore time taken is 0.897 sec and distance traveled is 56.36 mm
Please please please help
Answer: 2nd option
Step-by-step explanation:
If 25,35,x are in continued proportion, the value of x is
(a) 48
(b) 46
(c) 49
(d) 50
Answer:
If 25, 35, and x are in continued proportion, then find the value of x.
Solution
Given, 25, 35, and x are in continued proportion.
So,
25
:
35
:
:
35
:
x
In continued proportions, the product of extremes is equal to the square of the mean proportional.
So,
25
×
x
=
35
2
x
=
35
×
35
25
=
49
So, the value of x is 49.
Step-by-step explanation:
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Find the sum or difference. Write all fractions in simplest form and improper fractions as mixed numbers. 1\2+9/10+2/3
Answer:
Step-by-step explanation:
1/2 + 9/10 + 2/3 = 15/30 + 27/30 + 20/30 = 62/30 = 31/15
Write an equation of the line that passes through (0, -1) and is perpendicular to the line y = 1/9x + 2
An equation of the perpendicular line is y =
The equation of the perpendicular line passing through (0, -1) is y = -9x - 1.
To find the equation of a line that is perpendicular to the given line y = (1/9)x + 2 and passes through the point (0, -1), we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other.
The given line has a slope of 1/9. To find the slope of the perpendicular line, we take the negative reciprocal of 1/9, which is -9.
Using the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept, we can substitute the slope and the coordinates of the given point (0, -1) into the equation.
y = -9x + b
Since the line passes through the point (0, -1), we can substitute the x-coordinate as 0 and the y-coordinate as -1 into the equation:
-1 = -9(0) + b
-1 = b
Therefore, the y-intercept (b) of the perpendicular line is -1.
Putting it all together, the equation of the line that passes through (0, -1) and is perpendicular to y = (1/9)x + 2 is:
y = -9x - 1
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Which statement about the location of √7 on the number line is true?
A= It is located at the number 7 on the number line.
B= It is located at the number 3.5 on the number line.
C= It is located between the numbers 2 and 3 on the number line.
D=It is located between the numbers 4 and 9 on the number line
The graph of this line shows the total amount Katrina earns for working a corresponding number of hours. How much did Katrina earn for working 7 hours?
The correct statement is that for each hour, the earnings go up by $7. Option A
What is straight line graph?If we have the equation of the line, we can substitute the value of 7 for the number of hours into the equation and solve for the earnings. The equation would typically be in the form of "earnings = slope * hours + y-intercept," where the slope represents the rate of earnings per hour and the y-intercept represents the earnings when no hours are worked.
We can find the slope of the graph to know as said above;
m = y2 - y1/x2 - x1
m = 14 - 0/2 - 0
m = 7
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Enter the number that belongs in the green box 7 4 8
Answer:
61.03°
Step-by-step explanation:
You want the angle opposite the side of length 7 in the triangle with other sides of lengths 4 and 8.
Law of CosinesThe law of cosines relates the angles of a triangle to the side lengths. For triangle ABC with opposite sides a, b, c, the relation is ...
c² = a² +b² -2ab·cos(C)
ApplicationSolving for angle C, we have ...
cos(C) = (a² +b² -c²)/(2ab)
C = arccos((a² +b² -c²)/(2ab))
In this triangle, that means ...
C = arccos((4² +8² -7²)/(2·4·8)) = arccos(31/64)
C ≈ 61.03°
The angle of interest is about 61.03°.
__
Additional comment
We get the same result from a triangle solver. See the second attachment. (The angle we want is angle B in that attachment.)
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