Subtract the sum of(8a-6a^2+9) and-10a-8+8a^2 from-3

Answer:

Step-by-step explanation:

I assume that the amount of peanut butter chips in original recipe is [tex]1\frac{1}{2}[/tex] c (the picture isn't clear!)

2( [tex]1\frac{1}{2}[/tex] + x ) = [tex]4\frac{1}{2}[/tex]

[tex]1\frac{1}{2}[/tex] + x = [tex]4\frac{1}{2}[/tex] ÷ 2

[tex]1\frac{1}{2}[/tex] + x = [tex]2\frac{1}{4}[/tex]

x = [tex]2\frac{1}{4}[/tex] - [tex]1\frac{1}{2}[/tex] = [tex]1\frac{5}{4}[/tex] - [tex]1\frac{2}{4}[/tex] = [tex]\frac{3}{4}[/tex]

There is [tex]\frac{3}{4}[/tex] of a cup of nuts in original recipe.

In order to be in the 85th percentile Eli would need to score 26.62.

In statistics, a score below which a certain percentage of scores (k) in a frequency distribution falls is known as a k-th percentile, whereas a score at or below which a given percentage falls is known as a k-th centile.

Given that act math scores are approximately normally distributed,

mean (μ) = 21 and a standard deviation (σ) = 5.4

percentile P(X>x) = 85 =0.85

P(z<x) = 0.85

z = 1.04

y the formula

z = (x - μ)/ σ

⇒ 1.04 = (x - 21)/5.4

⇒ 1.04*5.4 = x - 21

⇒ 5.616 = x - 21

⇒ x = 5.616 + 21

⇒ x = 26.62

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Answer: The average rate of change over the interval 12 < x < 30 is -4/3

Step-by-step explanation:

The average rate of change over an interval is defined as the change in the output (f(x)) divided by the change in the input (x) over that interval. In this case, the interval is 12 < x < 30. To find the average rate of change, we need to evaluate the function at the endpoints of the interval and subtract the value at the start point from the value at the end point, and divide that by the change in x.

Given the table:

f(30) = 16 and f(12) = 40

The average rate of change over the interval 12 < x < 30 is:

(f(30) - f(12)) / (30 - 12) = (16 - 40) / 18 = -24/18 = -4/3

So the average rate of change over the interval 12 < x < 30 is -4/3

It's worth noting that this is only the average rate of change, and the function may have different rates of change at different points within the interval 12 < x < 30.

Answer:

To find the volume of the cereal box, we multiply the length, width, and height:

12 inches * 7 and 3/4 inches * 2 inches = 96 inches * 7.75 inches * 2 inches = 1458 cubic inches

To find the volume of the pastry box, we multiply the length, width, and height:

3 and 2/3 inches * 3 and 1/2 inches * 2 and 1/3 inches = 3.666 inches * 3.5 inches * 2.333 inches = 25.158 cubic inches

To find the difference in volume between the two boxes, we subtract the volume of the pastry box from the volume of the cereal box:

1458 cubic inches - 25.158 cubic inches = 1432.842 cubic inches

So the difference in volume between the two boxes is 1432.842 cubic inches.

Answer:1432.842 cubic inches

Step-by-step explanation:

The area of the resulting two-dimensional cross-section of the pyramid geometry will be 5 square inches.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

What is an area in math definition

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area. Now, imagine your square is made up of smaller unit squares

A slice is made parallel to the base of a right rectangular pyramid, as shown.

Then the area of the resulting two-dimensional cross-section will be

Area = 2 in × 2.5 in

Area = 5 in²

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The correct option is A, the linear equation has no solutions.

Here we want to see how many solutions do the equation below has:

(1/4)*(8 - 24x) = 12 - 6x

Now let's try to solve that linear equation, we can start by simplifying the left side:

(1/4)*(8 - 24x) = 12 - 6x

8/4 - 24x/4 = 12 - 6x

2 - 6x = 12 - 6x

Now we can add 6x in both sides, so we will get:

2 - 6x + 6x = 12 - 6x + 6x

2 = 12

That is a false equation, thus, the equation has no solutions.

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Answer:

(a) Refer below for the Probability tree diagram

(b) [tex]\frac{7}{33}[/tex]

Step-by-step explanation:

(a) Probability tree diagram:

First bag:                                         Second bag

                                                       Red: [tex]\frac{7}{7 + 4}[/tex] = [tex]\frac{7}{11}[/tex]

Red: [tex]\frac{5}{12}[/tex]                                

                                                      Green:[tex]\frac{4}{7 + 4}[/tex] = [tex]\frac{4}{11}[/tex]

                                                        Red: [tex]\frac{7}{11}[/tex]

Green [tex]\frac{7}{12}[/tex]      

                                                        Green: [tex]\frac{4}{11}[/tex]      

(b) Probability that Hannah takes two green sweets:

Green sweet from first bag AND green sweet from second bag

= [tex](\frac{7}{12}).(\frac{4}{11} )[/tex]

= [tex](\frac{28}{132})[/tex]

Divide the numerator and denominator by the highest common factor (i.e  4)

= [tex]\frac{7}{33}[/tex]                                                    

If the expression [tex]r(x) = 3x - 1[/tex] and the expression [tex]s(x) = 2x + 1[/tex] , then the expression equivalent to [tex]\frac{r}{s} (6)[/tex] is (a) [tex]\frac{3(6)-1}{2(6) +1}[/tex] .

What are Algebraic Expression ?

The algebraic Expression are defined as the expressions that are written with the combination of variables and constants joined by mathematical operators , For Example : [tex]3x+7[/tex] .

Here the two expressions are given as [tex]r(x) = 3x - 1[/tex] and [tex]s(x) = 2x + 1[/tex] ;

we have to find equivalent expression for [tex]\frac{r}{s} (6)[/tex] ;

By the Division Property of Algebraic Expression ;

it can be written as : [tex]\frac{r(6)}{s(6)}[/tex] ;

So , Substituting [tex]x=6[/tex] , in r(x) ,

we get ; [tex]r(6) = 3(6) - 1[/tex] , ......equation(1)

On Substituting [tex]x=6[/tex] , in s(x) ,

we get ; [tex]s(6) = 2(6)+1[/tex] ,  ....equation(2) ;

Substituting the values of r(6) and s(6) from equation(1) and equation(2) in [tex]\frac{r(6)}{s(6)}[/tex] ;

we get ;

⇒ [tex]\frac{r(6)}{s(6)} = \frac{3(6)-1}{2(6) +1}[/tex] ;

Therefore , the expression equivalent to [tex]\frac{r}{s} (6)[/tex] is [tex]\frac{3(6)-1}{2(6) +1}[/tex] .

The given question is incomplete , the complete question is

If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to r/s(6) ?

(a) [tex]\frac{3(6)-1}{2(6) +1}[/tex]

(b) [tex]\frac{(6)}{2(6)+1}[/tex]

(c) [tex]\frac{36-1}{26+1}[/tex]

(d) [tex]\frac{(6)-1}{(6)+1}[/tex]

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The ratios are 80 : 2/3, 10 : 1/12 and 90 : 3/4 for the equivalent ratio 20 : 1/6.

By dividing both the antecedent and consequent values by a similar fraction, equivalent ratios can be reduced to the same value. In other words, two ratios are deemed equivalent if the bigger one in value can be expressed as a multiple of the other.

Therefore, we only need to multiply the two amounts by the same number to obtain the equivalent ratio of another ratio. Equivalent ratios and equivalent fractions both have similar ideas. Examples of equivalent ratios include 1:2 and 4:8, 3:5 and 12:20, 9:4 and 18:8, etc.

20 : 1/6

Multiply both by 6

120  : 1

Thus, 120 × 2/3  : 1 × 2/3

80 : 2/3

multiply by 3

80 × 3 : 2/3 × 3

240 : 2

120 : 2

When ratio is 120  : 1

divide both by 120

120/120  : 1/120

1 : 1/120

1 × 10 : 1/120 × 10

10 : 1/12

multiply by 12

120 : 1

1 × 90 : 1/120 × 90

90 : 3/4

multiply by 4

90 × 4 : 3/4 × 4

360 : 3

120 : 1

Thus, the ratios are 80 : 2/3, 10 : 1/12 and 90 : 3/4 for the proportion 20 : 1/6.

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​

At 2.57 hours distance between them is 35 miles

(2t)2 + (2.5(t - 2))2 = 302

4t2 + (2.5t - 5)2 = 900

4t2 + 6.25t2 - 25t + 25 = 900

2.25t2 - 25t - 875 = 0

Let t (hours) be the amount of time Elsie needs to travel in order to reach a distance of 35 miles. Steve travels t + 2 miles to the north in the time it takes him since he is 2 hours early.

Solve for t, then add to 7:00 for your time.

which will give you 2.57 hours.

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The correct question will be

Steve and Elsie are camping in the desert, but have decided to part ways. Steve heads north, at 7 AM, and walks steadily at 3 miles per hour. Elsie sleeps in and starts walking west at 2.5 miles per hour starting at 9 AM.

When will the distance between them be 35 miles?

Using Elimination method the simultaneous equations is -16/3.

Elimination is a mathematical technique that can be used to solve a system of three equations with three variables.

In standard form, without any fractions or decimals, write all the equations. Decide which one of the three variables you want to eliminate, then pick any two of the equations to do so.

The term "simultaneous equations" refers to two or more algebraic equations that share the same unknown variables and have the same answer. This suggests that the simultaneous equations have a single, solvable problem. For instance, 2x - 4y = 4, 5x + 8y = 3, are instances of simultaneous equations.

    10m-7n=26

  - 7m+7n=42​

    3m = -16

m = -16/3

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Answer:

.5 or 1/2

Step-by-step explanation:

1-.5      .5

------=------- simplify= .5 slope is in fractions 1/2

2-1       1

Answer:

84

Step-by-step explanation:

this is an isosceles triangle so the base angles are equal meaning <BAC= <BCA =48°

48° +48° =96°

180°- 96° = 84°

<ABC = 84°

A graph of the image of the triangle with vertices (4, 7), (3, 4), and (8, 2) after a transformation with the rule (x, y) → (−x, y) is shown in the image attached below.

In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the coordinates of this triangle the image coordinates include the following:

(x, y)                               →              (-x, y)

Coordinate A = (4, 7)   →  Coordinate A' = (-(4), 7) = (-4, 7).

Coordinate B = (3, 4)   →  Coordinate B' = (-(3), 4) = (-3, 4).

Coordinate C = (8, 2)   →  Coordinate C' = (-(8), 2) = (-8, 2).

Next, we would use an online graphing calculator to plot the coordinates of the image as shown in the image attached below.

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Isabelle concluded that the sample maximum is an unbiased estimator of the population maximum.

Value is a term used to describe the worth of something. It can refer to monetary value, but it can also be used to describe the worth of intangible things such as relationships, ideas, and experiences. Value creates an understanding between two parties, as each may have a different opinion on what something is worth. It can be seen as an exchange or trade of something that both parties consider to be of equal or greater value.

This conclusion is supported by the high number of samples that had a maximum value of 999999. The dotplot shows that the sample maximum was 999999 in over 95% of the trials. The other samples had maximum values that were lower, but still close to the true maximum of 999999. This indicates that the sample maximum did not systematically overestimate or underestimate the population maximum.
The sample maximum was also consistent across the different trials, with the majority of the samples having a maximum value near 999999. This consistency indicates that the sample maximum is a reliable estimator of the population maximum. While there is always a chance that the sample maximum may deviate from the population maximum, the results suggest that the sample maximum is unbiased and reliable for estimating the population maximum.

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The volume of a hemisphere with a radius of 44.9 m is approximately 189582.2 cubic meters, rounded to the nearest tenth.

To calculate the volume of a hemisphere, you can use the formula

V = (2/3)πr^3

where V is the volume, π is pi (approximately 3.14), and r is the radius. In this case, r = 44.9 m.

So, (2/3)π(44.9)^3 = 189582.234 cubic meters.

This is the exact volume, but since the question asked for the volume rounded to the nearest tenth, the final answer would be 189582.234 cubic meters. It's worth mentioning that a hemisphere is half of a sphere, thus, the volume of a full sphere with a radius of 44.9 m would be double of this value.

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The answers are  46/35 ,5/4, 5/4, 7/3

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given here: 3/5 + 5/7 = 46/35

6/12 + 9/12=5/4

1/4 + 4/4 = 5/4

2/3 + 5/3 = 7/3

Hence, The answers are  46/35 ,5/4, 5/4, 7/3

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Work Shown:

y - y1 = m(x - x1)

y - (-3) = -3(x - 5)

y + 3 = -3(x - 5)

Explanation:

The variable m refers to the slope. The point (x1,y1) is on the line. We do not distribute the -3 through to the terms in (x-5), nor do we isolate y, since your teacher wants this in point-slope form.

Answer:

a line

Step-by-step explanation:

y equals one half times x x + 2y = 8 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 5 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 3 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points negative 1 comma 2 and 0 comma 4 and another line that passes through the points 0 comma 0 and 1 comma 2 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 0 and another line that passes through the points 0 comma 0 and 1 comma 2

Answer:

B)  A coordinate plane with one line that passes through the points (0, 4) and (2, 3) and another line that passes through the points (0, 0) and (2, 1)

Step-by-step explanation:

Given system of linear equations:

[tex]\begin{cases}y=\frac{1}{2}x\\x+2y=8\end{cases}[/tex]

Substitute the first equation into the second equation and solve for x:

[tex]\implies x+2\left(\dfrac{1}{2}x\right)=8[/tex]

[tex]\implies x+x=8[/tex]

[tex]\implies 2x=8[/tex]

[tex]\implies x=4[/tex]

Substitute the found value of x into the first equation and solve for y:

[tex]\implies y=\dfrac{1}{2}(4)[/tex]

[tex]\implies y=2[/tex]

Therefore, the solution to the given system of linear equations is:

The point of intersection is the solution to a graphed system of linear equations.  

Therefore, the graph that shows the solution to the given system of linear equations is the graph where the point of intersection of the two lines is (4, 2).

The equation 291 = 359 + 125m represents the given phrase, and the required value of m is 2.33

Algebra is a discipline of mathematics that deals with symbols and the rules that govern their use. These symbols, known as variables in elementary algebra, indicate quantities with no set values. Equations in mathematics express relationships between variables in the same way that sentences indicate relationships between specific words.

The equation 291 = 359 + 125m can be solved for m by subtracting 359 from both sides, resulting in:

291 - 359 = 125m - 359

-68 = 125m - 359

Adding 359 to both sides gives:

-68 + 359 = 125m

291 = 125m

Dividing both sides by 125 gives the solution for m:

291 / 125 = 125m / 125

2.33 = m

So, m is equal to 2.33.

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The question seems incomplete, the completed question would be as:

If 291 is the same as 359 increased by the product of 125 and m. what is the value of f?

Answers : A(-1,0) is a local maximum point, B(-1,2) is saddle point, C(3,0) is also a saddle point, D(3,2) is the minimum point.

saddle point : a point on a curved surface at which the curvatures in two mutually perpendicular planes are of opposite signs

The function :

f(x , y) = x³ = y³ = - 3x² - 3y² - 9x

The first partial derivative with respect to x is:

f' x = 3x²-6x-9

And the partial derivative with respect to y is:

f' y = 3y²-6y

Now equate the above derivatives to zero, to obtain the system of equation:

3x²-6x-9 = 0

3y²-6y = 0

On solving the two equations:

The critical points are : A(-1,0), B(-1,-2), C(3,0) and D(3,2)

Now calculate the discriminant

D = f xx(x , y)f y(x , y)-f xy(x , y)²

Here,

f xx = 6x-6

f yy = 6y-6

f xy = 0

On putting the above values we get:

D = (6x-6)(6y-6)

At, A(-1,0)

D = -18<0

Hence , A(-1,0) is a local maximum point.

At, B(-1,2)

D = -72<0

Hence B(-1,2) is saddle point.

At, C(3,0)

D = -72

Hence C(3,0) is also a saddle point

At, D(3,2)

D = 12>0

Hence , D(3,2) is the minimum point.

Answers : A(-1,0) is a local maximum point, B(-1,2) is saddle point, C(3,0) is also a saddle point, D(3,2) is the minimum point.

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According to the given information the line integral is 8(1+125[tex]\sqrt{110}[/tex]) / 15 .

What distinguishes a line integral from a definite integral?

Line integrals include several integrals across a curve, but definite integrals only entail a single integral over a specified interval. This is the primary distinction between the two types of integrals.

[tex]\int\limits_c {xy} \, ds[/tex],  C : x = t^2 , y = 2t,  0 ≤ t ≤ 3

x' = 2t , y' = 2

ds = [tex]\sqrt{(x')^2 + (y')^2}[/tex]

[tex]\sqrt{4(t)^2 + 4}[/tex]

[tex]\int\limits C {xy} \, ds[/tex] = [tex]\int\limits^3_0 {2.2t.2\sqrt{1+t^2}} \, dt[/tex]

t = tanθ

dt = (1+[tex]tan^{2}[/tex]θ)dθ = ([tex]sec^{2}[/tex]θ)dθ

= [tex]\int\limits^3_0 {4t^3\sqrt{1+t^2} } \, dt[/tex]

= 8(1+125[tex]\sqrt{110}[/tex]) / 15

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Answer:

Pete is 5

Step-by-step explanation:

Let Pete's age be x

Therefore Masha is 3x

since their age difference is 10,

3x - x = 10

2x = 10

x = 5

check:

3x = 15

x = 5

15 - 5 = 10

Answer:

The Sun has 1.0975 x 10^2  times the diameter of Earth

Step-by-step explanation:

Diameter of Sun = 1.4 x 10^9 m

Diameter of Earth = 1.2756 x 10^7 m

ratio between Diameter of Sun and Earth :-

Diameter of Sun/Diameter of Earth = 1.4 x 10^9/ 1.2756 x 10^7

= 1.0975 x 10^2

The value of x is 85°

A circular sector, also known as circle sector or disk sector is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector

A sector is a region bounded by two radii of a circle and the intercepted arc of the circle. The angle formed by the two radii is called a central angle. A sector with a central angle less than 180° is called a minor sector. A sector with a central angle greater than 180° is called a major sector.

The sector where x is the minor sector

The angular distance is x and it is measured in degrees (°)

Therefore the value of x is 85°

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The area of shaded triangle is 20 square feet

What is the area?

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.

Area of triangle = 0.5*base*height

Area of whole triangle = 0.5*8*10 =  40 square feet

Area of unshaded triangle = 0.5*4*10 =  20 square feet

Area of shaded triangle

= Area of whole triangle  - Area of unshaded triangle

=  40 - 20

= 20 square feet

Thus, the area of shaded triangle is 20 square feet

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The z-score for this amount of advertising time will be -5.217.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

A TV slot guarantees how much promotion each hour of transmission time has a normal of 17 minutes and a standard deviation equivalent to 2.3 minutes.

The amount of advertising time is equal to 5 minutes. Then the z-score is calculated as,

z = (5 - 17) / 2.3

z = -12/ 2.3

z = -5.217

The z-score for this amount of advertising time will be -5.217.

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Therefore , the solution of the given problem of linear equation comes out to be  $105 is the total cost

A linear regression model is one that uses the equation y=mx+b. The slope is B, and the y-intercept is m. The preceding sentence is commonly referred to as a "math equation with two variables," despite the fact that both y and x are separate factors. The only variables in bivariate linear equations are two. In all circumstances, the solutions to linear equations' application domains are zero. Y=mx+b is the formula for a single linear equation.

Here,

The first company's equation is y = 10.5x.

Additionally, the second company's equation is y = 7.5x + 30.

Where

number of T-shirts equals x.

y = overall cost

For the overall cost to be the same for both businesses, we have to:

=> 10.5x = 7.5x + 30

=> 10.5 x - 7.5 x = 30

=> 3 x = 30

=> x = 30/3

=> x = 10

To make the T-shirts' prices equal, the volleyball team must purchase 10 from each vendor.

Total for each business:

=> 10.5x = 10.5 (10) = $ 105

OR

Totals for each company are calculated as follows:

=> 7.5x + 30 = 7.5(10) + 30 = 75 + 30

=> $105

Therefore , the solution of the given problem of linear equation comes out to be  $105 is the total cost.

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Orthocenter is the best term to describes point R in the triangle UVW.

What is orthocenter?

" Orthocenter is defined as intersecting point of the altitudes of the sides of the acute angle triangle."

According to the given figure,

In triangle UVW,

Ray VR perpendicular to UW

Ray UR perpendicular to VW

Ray WR perpendicular to UV

Altitudes of side  ( UV , VW, and WU) of triangle UVW intersect at

point R.

As per the definition of orthocenter , point R represents orthocenter.

Hence, orthocenter is the best term to describes point R in the triangle UVW.

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Answer:

To prove that the measure of angle RST is greater than the measure of angle R, we can use the following steps:

By the definition of a triangle, angle RST is supplementary to angles R, S and T.

Since RT > ST, we can conclude that angle R is less than angle S.

Since angle RST is supplementary to angles R and S, the measure of angle RST is greater than the measure of angle R.

This can be written as measure of angle RST = measure of angle R + measure of angle S > measure of angle R

So, we've proven that if RT > ST in triangle RST, then measure of angle RST > measure of angle R.

Proof by contradiction could also be used to prove that if RT > ST in triangle RST, then measure of angle RST > measure of angle R.

Assume that the measure of angle RST <= measure of angle R. By the triangle inequality theorem, we know that RT + ST > R. But we are given that RT > ST, so RT + ST > RT > R which is a contradiction. Therefore, measure of angle RST must be greater than measure of angle R.