A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 35% salt and Solution B is 60% salt. She wants to obtain 50 ounces of a mixture that is 55% salt. How many ounces of each solution should she use?

The degree of the given polynomial 7x³ + 5x + 4x³ + 2x² is 3.

The degree of a polynomial is the highest power of the variable present in the polynomial.

Now the given polynomial is 7x³ 5x 4x³ 2x², and the highest power of x is x³. This indicates that the degree of this polynomial is 3.

It's important to note that when working with polynomials, it's important to pay attention to the signs of the coefficients. In this case, we have 7x³, 5x, 4x³, and 2x². The x³ term has the highest degree, and its coefficient is 7; the x term has the second highest degree, and its coefficient is 5; the x³ term has the same degree as the 7x³ term, but the coefficient is different, and the x² term has the fourth highest degree, and its coefficient is 2.

--The given question is incomplete; the complete question is

"What is the degree of the polynomial 7x³ + 5x + 4x³ + 2x²?"--

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Answer: 2:7

Step-by-step explanation:

Vanilla icecream = 4

Chocolate icecream = 14

4:14=2:7

2X2=4

7X2=14

Step-by-step explanation:

a ratio is simply relating 2 (or more) groups and their sizes.

in our case here the ratio is

4/14 = 2/7

this is often written as

4:14 = 2:7

it means that for every 2 people liking (I assume "preferring") vanilla ice cream there are 7 people liking (preferring) chocolate ice cream.

FYI

in total, a ratio also tells us about the size of the sample for the observation or analysis. 4/14 tells us there are 18 (4+14) people in the survey. and the simplified form 2/7 tells us that we can split the whole survey group into units of 9 (2+7) people with the same behavior as the total group.

a ratio is a fraction (incl. all the calculation and comparison rules) with a special meaning.

so, don't mix the ratio up with e.g. the fractions of the different behaviors in the group :

4/18 = 2/9 of the whole group prefer vanilla.

14/18 = 7/9 of the whole group prefer chocolate.

the ratio is now the relative size relationship between both : 2/9 / 7/9 = 2/7

Answer:

X = 20

Step-by-step explanation:

The two quadrilaterals are similar to each other. So the ratio of  each side of the larger quadrilateral to the corresponding side of the smaller quadrilateral must be the same.

Examining the two figures we see the side which has  68° and 128° pf the smaller quadrilateral has length 2

The corresponding side of the larger quadrilateral on the right is 6

So each side of the larger quadrilateral =6/2 = 3 times each side of the smaller one

Side which has length 10 pf the smaller quadrilateral corresponds to the side with length x+10 of the larger one. This ratio must also be 1:3

So

[tex]\dfrac{10 + x}{10}= 3\\\\[/tex]

Cross-multiplying we get
10 + x = 10 x 3

10 + x = 30

x = 30-10

x =20

ANSWER

The amount of peanuts Maggie puts in each container is 1/9 pounds per container.

Number of pounds of peanut Maggie has = 2/3 pounds

Number of containers = 6

Number of peanuts in each container = Number of pounds of peanut Maggie has / Number of containers

= 2/3 ÷ 6

multiply by the reciprocal of 6

= 2/3 × 1/6

= 2/18

= 1/9 pounds per container

Hence, there are 1/9 pounds of peanuts in each container if Maggie puts an equal amount.

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Answer: 83r^2 - 59 + 60

Step-by-step explanation:

R^2 - 59R - 82r^2 + 60

= 83r^2 - 59 + 60

The required value of the x in a similar triangle by the ratio of proportionality of sides is given as 12.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
In the figure, Similar triangles is shown,
Applying the property of proportional sides in the triangles

30/18 = 20/x
x = 18 / 30 × 20
x = 12

Thus, the required value of the x in a similar triangle by the ratio of proportionality of sides is given as 12.

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The axis of symmetry is the line x=3.

As y  is a linear term and x is quadratic, this means we’re dealing with either an ‘n-shaped’ parabola or a ‘u-shaped’ parabola.

As the coefficients of  x² and y have the same sign they’re both positive, which means we have a ‘u-shaped’ parabola.

One can express a parabola in the vertex form,  y=a(x−p)²+q, which tells us that the vertex is the point  (p,q)  and the axis of symmetry is the line x=p.

So, let’s apply this format to your parabola.

y=(x−3)²=(x−3)²+0

From this, it’s clear that:

The vertex is the point (3,0)

The axis of symmetry is the line x=3

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To calculate the composition of two functions, "F" and "G", represented by the notation "FG", you first need to have a specific input value, usually represented as "x".The first step is to apply the function "G" to the input "x", resulting in G(x).

The next step is to take the output of the function G, which is G(x), and use it as the input for the function F.

The final step is to apply the function F to the output of G(x) resulting in F(G(x)), which is the composition of the two functions F and G.

In other words, you apply the function G to the input x, and then you apply the function F to the result of G(x). The final result is the function F(G(x)), which is the composition of the functions F and G.

It's important to note that the order of the functions in composition matters and can change the result of composition. The notation "FG)(x)" is different from "GF)(x)" which means that the order of the functions matter in composition.

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Answer:

125

Step-by-step explanation:

5x + 20 + 3x - 8 = 180

8x + 12 = 180

8x = 168

x = 21

5(21) + 20

= 105 + 20

= 125

3/4 fraction of cupcake have vanilla fronting.

A fraction is a mathematical concept that represents a part of a whole or a ratio of two numbers. It is typically represented as two numbers separated by a line or a slash, with the top number representing the numerator and the bottom number representing the denominator. The numerator represents the number of parts being considered, and the denominator represents the total number of parts in the whole.

we have in total 9 cupcakes having vanilla froting and there are total 12 cupcakes.

so the fraction is given as :

9/12

since the HCF of (9,12) is 3

so the fraction in lowest form is 3/4

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The equation of the line is y = 3x-9(slope-intercept form).

The graph of the linear equation y = mx + c is a line with slope m and y-intercept m and c. This is known as the slope-intercept form of the linear equation, and the values of m and c are real numbers.

The slope, m, of a line represents its steepness. Sometimes the slope of a line is referred to as the gradient. A line's y-intercept, b, represents the y-coordinate of the point where the line's graph intersects the y-axis.

Given that,

m = 3

y = 9

Thus, The equation of the line is y = 3x-9(slope-intercept form).

Complete question: A linear function has a slope of 3 and crosses the y- axis at 9. What is the equation of the line?

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Answer:

To solve for g in terms of T, L, we can manipulate the formula T = 2π √(L/g) as follows:

First, we divide both sides by 2π:

T/2π = √(L/g)

Then, we square both sides:

(T/2π)² = (L/g)

Then, we multiply both sides by g^2 :

(T^2/4π^2) = L

Finally, we divide both sides by L:

(T^2/4π^2 * L) = g

So the formula for g in terms of T, L is g = (T^2/4π^2 * L)

Please note that this formula is only valid for simple pendulum and not for any complex pendulum, and also the result is in terms of acceleration due to gravity g.

D) The quadratic equation's roots, 2x2 4x + 3 = 0, are imaginary in nature.

The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem.

Given a quadratic equation, it is 2x 2 + 4x + 3= 0.

∴ a=2,b=4,c=3

As a result, the discriminant of this equation is given by D=b 2 4ac.

∴D=(4) \s2 \s −4(2)(3) (3)

∴D=16−24

∴D=−8<0

The equation's roots are therefore fictitious.

The quadratic equation has the general form ax2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable. An example of a quadratic equation is x2 + 2x + 1.

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Full Question = The nature of the roots of the quadratic equation 2x ^2 + 4x + 3= 0 are

A. Real & Distinct

B. Real & Equal

C. No Real Roots

D. Imaginary

The matched solution for given linear inequalities is given in image attached.

What are linear inequalities?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

e.g. y>x+2

The solution for linear inequalities  is provided in image.

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Answer: 11

Step-by-step explanation: (8/2.56) x 3.52 = 11 ounces

angle RQS = 101 degrees

angle TQS = 79 degrees

===================================================

Explanation:

A straight angle has a measure of 180 degrees. It's another way of saying "straight line".

The two angles shown add to 180.

We'll use this fact to solve for x.

(angleRQS) + (angleTQS) = angle RQT

(9x+2) + (7x+2) = 180

16x+4 = 180

16x = 180-4

16x = 176

x = 176/16

x = 11

Use this x value to determine the angles we're after.

Check:

(angleRQS) + (angleTQS) = 101+79 = 180 which confirms the answer is correct.

The height of a triangle in Class 7, Height =  (2×Area)/ Base

​

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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The tallest lighthouse in the world is the Jeddah Light. It is 133 m tall. A dhow is sailing away from this lighthouse. From the top of the lighthouse, the angle of depression to the dhow is 65° Later, the angle of depression has changed to 40°.

How far did the dhow travel during that time?

To solve this problem, we can use trigonometry and the fact that the angles in a triangle add up to 180°.

Let's call the distance between the lighthouse and the dhow "d".

We know that the angle of depression from the top of the lighthouse to the dhow is 65°, and the angle of depression later changed to 40°.

Let's call the angle between the horizontal and the line of sight from the lighthouse to the dhow, "x"

Since the angles in a triangle add up to 180°, we can say that:

x + 65 + 40 = 180

x = 75

Now, we can use the tangent function to find the distance d. We know that:

tan(x) = d / h

tan(75) = d / 133

d = 133 * tan(75)

Therefore, the dhow traveled 133 * tan(75) distance during that time.

Hey there,

We have,

f(x) = x² + 11x + 30g(x) = x + 6

Now,

(f.g)(x) = f(g(x))

Substituting...

g(x) = x + 6f(g(x)) = f(x + 6)

Now,

f(x + 6)= (x + 6)² + 11(x + 6) + 30= x² + 12x + 36 + 11x + 66 + 30= x² + 23x + 132

So,The value is x² + 23x + 132

Answer:

x = 7 , VS = 6

Step-by-step explanation:

• If two chords of a circle are equidistant from the centre of the circle then they are congruent.

given ZU and ZV = 5

then the chords QR and ST are equidistant from the centre and are congruent , that is

QR = ST

2x - 2 = 12 ( add 2 to both sides )

2x = 14 ( divide both sides by 2 )

x = 7

---------------------------------------------------

• If a radius is perpendicular to a chord then it bisects it.

radius ZY is perpendicular to chord ST and bisects it, so

VS = [tex]\frac{1}{2}[/tex] × ST = [tex]\frac{1}{2}[/tex] × 12 = 6

To the nearest tenth of a kilogram, m = 0.6 kg.

What is ttemperature rate ?

With increase in temperature, the rate of the reaction and the rate constant increases. As a generalization, the rate of the reaction (and the rate constant) becomes almost double for every ten degree rise in temperature. This is also called temperature coefficient.

the heat Q required to raise the temperature of water varies jointly as the mass m of the water and the amount of temperature change T, and Q = 20,930 J when m = 1 kg and T = 5°C.

So, write an equation for Q as:

Q = k * m * T

where k is a constant of proportionality.

Substituting the known values, we can find k:

20930 = k * 1 * 5

k = 20930 / (1 * 5) = 4186

Now that we have k, use it to find m when Q = 8349 J and T = 3°C:

8349 = 4186 * m * 3

m = 8349 / (4186 * 3)

To the nearest tenth of a kilogram, m = 0.6 kg.

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The mass of the water m is 0.7 kg.

Since Q varies jointly as m and T, we know that Q = k * m * T where k is a constant of proportionality. Using the given information, we can find the value of k:

Q = 20,930 J when m = 1 kg and T = 5° C

k = Q / (m * T) = 20,930 / (1 * 5) = 4186

Now that we have found k, we can use it to find m when Q = 8,349 J and T = 3°C:

Q = k * m * T

8,349 = 4186 * m * 3

m = 8,349 / (4186 * 3) = 8,349 / 12,558

m = 0.67 kg

To the nearest tenth of a kilogram, m = 0.7 kg.

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9 11 13 15 17

first term (a) = 9

diffrence (d) = 11-9 = 13-11 = 2

we know

a + (n-1)d

9+(n-1)2

9+2n-2

7+2n

2n + 7

2n + 7 is the sequences of 9 11 13 15 17 for nth term

Kweku age is 21 years and his brother kofi is 14 years

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

To solve this problem, we have to state the equation using the information of the problem:

Lets call Kweku's age as (x)

Sofi's age will be 2/3x

If both are 35 then the equation is as follow:

x + 2/3x = 35

Clearing the variable we have:

(3x+2x) /3 = 35

5x = 35*3

5x = 105

x = 105/5

x = 21

Kweku's age is 21 years

Sofi's age is 2/3x = 2/3*21 = 14 years

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If there were 18 students in each group and they were asked to form six equal groups, then there would be a total of 108 students.

i.e. (18 students x 6 groups = 108 students)

When a group of students are asked to form a certain number of equal groups, the total number of students can be determined by multiplying the number of students in each group by the number of groups.

In this case, the students were asked to form six equal groups and there were 18 students in each group.

To find the total number of students, we simply multiply 18 by 6.

Therefore, there were 108 students in total.

This is because when you have x number of groups and y number of students in each group, the total number of students is xy.

In this case x=6 and y=18, so the total number of students is 6*18 = 108.

Question:

"In gym class, students were asked to form ix equal group. If there were 18 students in each group, then how many total students were there?"

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Answer:

6xˆ2 - x - 2 = 0

D = 1 + 1*2*6*4=49=7ˆ2;

using formula of discriminant you get

x1= -1/2

x2= 2/3

answer = x1, x2

The relation's graph can be seen in the graphic at the bottom, where it is clear that it is   function.

The actual function can be specified using this "mapping" notation. Writing f:(x,y)x+y would allow us to define the above f(x, y). Real numbers are referred to as scalars to distinguish them from vectors. Each input is translated into a single output in a relation known as a function (input, output).

The horizontal axis is used for inputs, and the vertical axis is used for outputs. Here, we have the relationship shown below:

(-5,-1), (-4,1), (-3,3), (-1,5), (1,7) (1,7)

The figure below shows the graph of these points. Since there are no two points on the same vertical line, the relation is a function, as you can see.

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Answer:

cp=(SP * 100 ) / ( 100 – percentage loss)

6786*100/100-13

7800

Answer:

I believe the answer is Graph A

The polynomial function with zeroes at -2, 0, and 3√2 is (x+2)(x-0)(x-3√2) = [tex](x+2)*(x-3\sqrt{2}) = x^3 - 3x\sqrt{2x} - 2x^2.[/tex]

The polynomial function with zeroes at -1, 3, and 2i is (x+1)(x-3)(x-2i) = [tex](x+1)(x-3)(x^2+4) = x^3 +x^2 - 11x -12[/tex]

A polynomial function is a function of the form f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where n is the degree of the polynomial and the a_i are constants. To find a polynomial function with zeroes at -2, 0, and 3√2, we can use the fact that if a polynomial function has a zero at x=c, then (x-c) is a factor of the polynomial. Therefore, we can write the polynomial function as [tex](x+2)(x-0)(x-3\sqrt{2}) = (x+2)x(x-3√2) = x^3 - 3x\sqrt{2x} - 2x^2[/tex].

In this case, we can see that x = -2, x = 0, x = 3√2 are the zeroes, so we know that (x+2), x and (x-3√2) are the factors of the polynomial.

Similarly, to find a polynomial function with zeroes at -1, 3, and 2i, we can use the fact that if a polynomial function has a zero at x=c, then (x-c) is a factor of the polynomial. Therefore, we can write the polynomial function as [tex](x+1)(x-3)(x-2i) = (x+1)(x-3)(x^2+4) = x^3 +x^2 - 11x -12[/tex]

In this case, we can see that x = -1, x = 3, x = 2i are the zeroes, so we know that [tex](x+1), (x-3), (x^2+4)[/tex]are the factors of the polynomial.

It is worth noting that (x-2i) is a zero of the polynomial, so (x-2i)(x+2i) = [tex]x^2[/tex]+4 is a factor of the polynomial and it is included in the polynomial..

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