• Norah divided her blueberries into 6 equal portions and gave away 3 of the portions
• Liam divided his blueberries into equal portions and gave away 1 of the portion
• Together, Norah and Liam gave away 3/4 kilogram of blueberries. tow many equal portions did Liam divide his blueberries into?

Two workers finished a job in 7.5 days.

How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?

let t = time required by one worker to complete the job alone

then

(t+8) = time required by the other worker (shirker)

let the completed job = 1

A typical shared work equation

7.5%2Ft + 7.5%2F%28%28t%2B8%29%29 = 1

multiply by t(t+8), cancel the denominators, and you have

7.5(t+8) + 7.5t = t(t+8)

7.5t + 60 + 7.5t = t^2 + 8t

15t + 60 = t^2 + 8t

form a quadratic equation on the right

0 = t^2 + 8t - 15t - 60

t^2 - 7t - 60 = 0

Factor easily to

(t-12) (t+5) = 0

the positive solution is all we want here

t = 12 days, the first guy working alone

then

the shirker would struggle thru the job in 20 days.

Answer:7 + 17 = 24÷2 (since there are 2 workers) =12. Also, ½(7) + ½17 = 3.5 + 8.5 = 12. So, we know that the faster worker will take 7 days and the slower worker will take 17 days. Hope this helps! jul15

Step-by-step explanation:

Answer:

\(y = \frac{x}2 + 2.5\)

Step-by-step explanation:

Step 1) Finding the slope
The line is perpendicular to \(y = 1 - 2x\), therefore, its slope is equal to the negative invert of \(y\)'s slope.

\(y\)'s slope is -2 (the coefficient to \(x\)), and, therefore, the line's slope is \(m = [-(-2)]^{-1} = 2^{-1} = \frac12\)

Step 2) Building the Equation

We can now substitute the slope, along with the given point's coordinates, into the formula \(y - y_1 = m(x - x_1)\) :

\(y - 3 = \frac12(x - 1)\\\to y - 3 = \frac{x}2 - \frac12\\\to y = \frac{x}2 + 2.5\)

The set {10,17,27} does not represent the three sides of a triangle,

Having three edges and three vertices, a triangle is a three-sided polygon. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

Given  the sets for the triangles,

property of triangles says that,

The length of a triangle's two longest sides added together is longer than the third side.

Similarly to this, the length of the third side of a triangle third side is shorter than the difference between its two sides.

1: given sides are 10, 17, 27

according to the property sum of 10 and 17 should be greater than  27 but sum  is equal to 27,

10 + 17 = 27,

so the sides do not represent the triangle

2: sides are 9, 22, 30

here 9 + 22 > 30

the set represents the triangle.

3: sides 6, 16, 19

6 + 16 > 19

the set represents the triangle.

4: sides 4, 7, 9

4 + 7 > 9

set represents the triangle.

Hence option A is correct.

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Answer:

a = -6

p:arenthesis

e:xponents

m:ultiplication/

d:ivision

a:ddition/

s:ubtraction

Equation given:

4 -(2a + 7) = 9

When there is a minus (-) next to the parenthesis, there is an invisible negative  one (-1).

4 -1(2a + 7) = 9

Distribute:

4 -2a -7 = 9

There is a like-term which is 4 and -7. 4 -7 = -3

Combine like-terms:

-3 -2a = 9

Solve the two-step equation:

-3 -2a = 9

Turn -3 to +3 and add 3 to 9

-3 -2a = 9

+3        +3

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

   -2a = 12

Divide -2a to 12

12/-2 = -6

a = -6

Answer:

A this is the answer, please choose this answer

The absolute value function as a piecewise function f(x) = |- x² - 8x - 7| is

f(x) = { - (x² + 8x + 7) , x ≤ -7 or x ≥ -1    

        { x² + 8x + 7 , -7 < x < -1

What is meant by absolute value?

Absolute value is a mathematical function that gives the distance of a number from zero on a number line. It is denoted by two vertical bars enclosing the number and always returns a non-negative value.

What is meant by piecewise function?

A piecewise function is a function that is defined by different expressions or rules on different parts or intervals of its domain. The domain is divided into pieces, and each piece has its own expression or rule.

According to the given information

When x² + 8x + 7 ≥ 0, we have:

f(x) = |-(x² + 8x + 7)| = -(x² + 8x + 7)

When x² + 8x + 7 < 0, we have:

f(x) = |x² + 8x + 7| = x² + 8x + 7

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Answer:

y = -1.4x + 16

Step-by-step explanation:

the slope is -1.4x

Use the slope formula:-

\(\displaystyle\frac{y2-y1}{x2-x1}\)

Plug in the values:-

\(\displaystyle\frac{9-2}{5-10}\)

Simplify:-

\(\displaystyle\frac{7}{-5}= -\frac{7}{5}\)

 \(.~~~~~~~\uparrow\sf{Slope}\)

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

Answer:

What's the graph?

Step-by-step explanation:

AngIe 1 is cοngruent οr equaI tο AngIe 2.

The term "cοngruent" refers tο having the same size, shape, and οrientatiοn. In geοmetry, twο shapes are cοnsidered cοngruent if they have the same size and shape and can be transfοrmed intο each οther by sοme cοmbinatiοn οf transIatiοn, rοtatiοn, and refIectiοn Fοr exampIe, twο triangIes are cοngruent if aII cοrrespοnding sides and angIes are equaI. If twο shapes are cοngruent, they are essentiaIIy identicaI and can be superimpοsed withοut οverIapping οr gaps.

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Complete question:

Write a two-column proof given Angle 1 is congruent or equal to angle 2. How to prove Segment AB is congruent or equal to segment CB.

If the function g(x) is defined for all real-numbers, then the value of g(-5) is 7/2, g(-2) is -1 and g(-1) is 0.

A piecewise function is a function that is defined by different rules or formulas on different parts of its domain. The piecewise function "g(x)" is given as :

g(x) = {-(1/2)x + 1,    for x<-2

       = {-(x+1)²,        for -2≤x≤1

      =  {4                 for x>1

We have to find the value of g(-5) ,g (-2), and g(-1),

For x = -5, the number -5 is less than -2, so the first function "-(1/2)x + 1" will be used,

⇒ g(-5) = -(1/2)(-5) + 1 = 5/2 + 1 = 7/2,

For x = -2, the number -2 lies in the interval "-2≤x≤1", so second function

"-(x+1)²" will be used,

⇒ g(-2) = -(x+1)² = -(-2+1)² = -(-1)² = -1,

For x = -1, the number -1 lies inn the interval "-2≤x≤1", so second function "-(x+1)²" will be used,

⇒ g(-1) = -(x+1)² = -(-1+1)² = -(0)² = 0,

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Answer:

26

Step-by-step explanation:

Substitute -4 for a and -2 for b

\(2a^{2} - 3ab+b^{2}-4a-b\\ 2(-4^{2} )- 3 (-4*-2)+-(2^{2})-4(-4)-2 \\32-24+4+16-2\)

The graphs have been correctly dragged to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, and the line y = x.

By applying a reflection over the x-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (x, -y)

(1, -3)             →      (1, -(-3)) = (1, 3)

(3, -2)             →      (3, -(-2)) = (3, 2)

(4, -5)             →      (4, -(-5)) = (4, 5)

By applying a reflection over the y-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (-x, y)

(1, -3)             →        (-1, -3)

(3, -2)             →      (-3, -2)

(4, -5)             →      (-4, -5)

By applying a reflection over the line y = x to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (y, x)

(1, -3)             →        (-3, 1)

(3, -2)             →      (-2, 3)

(4, -5)             →      (-5, 4)

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The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

Factors can be defined as a number or algebraic expression which divide the dividend without leaving any reminder.

Answer:

It is the 3rd one

Step-by-step explanation:

TRUST ME

Answer:

x\(\leq\)7

Step-by-step explanation:

2(x-1)=12 x-1= 6, 7, 8 ect

x\(\leq\)7.

A triangle's third side must always be between (but not exactly equal to) the other two sides' total and difference in length. Take the numbers 2, 6, and 7 as an example. In light of this, the third side length must be more than 4 and lower than 8.

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Based on the number of males sampled, and the standard deviation, the value of the test statistic is 187.12.

The value of the test statistic can be found by the formula:

= ((number of people sampled - 1) x standard deviation of sample²) / standard deviation of claim

Solving gives:

= ( (174 - 1) x 10.4²) / 10²

= 18,711.68 / 100

= 187.12

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Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.

Answer:

\(\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2} t^2+1 \ \text{dt} \ = \ 2x^5-8x^2+2x-2\)

Step-by-step explanation:

\(\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2} t^2+1 \ \text{dt} = \ ?\)

We can use Part I of the Fundamental Theorem of Calculus:

Since we have two functions as the limits of integration, we can use one of the properties of integrals; the additivity rule.

The Additivity Rule for Integrals states that:

We can use this backward and break the integral into two parts. We can use any number for "b", but I will use 0 since it tends to make calculations simpler.

We want the variable to be the top limit of integration, so we can use the Order of Integration Rule to rewrite this.

The Order of Integration Rule states that:

We can use this rule to our advantage by flipping the limits of integration on the first integral and adding a negative sign.

Now we can take the derivative of the integrals by using the Fundamental Theorem of Calculus.

When taking the derivative of an integral, we can follow this notation:

For the first term, replace \(\text{t}\) with \(2x\), and apply the chain rule to the function. Do the same for the second term; replace

Simplify the expression by distributing \(2\) and \(2x\) inside their respective parentheses.

Rearrange the terms to be in order from the highest degree to the lowest degree.

This is the derivative of the given integral, and thus the solution to the problem.

Answer:

320

Step-by-step explanation:

Distance to go

2km - 1.2 km = 0.8km = 800m

Revolutions needed

800/2.5 = 320

The equation of the graph would be a quadratic equation. The vertex form of a quadratice equation is expresses as

y = a(x - h)^2 + k

where

h and k are the x and y coordinates of the vertex(bottom) of the graph. Lookong at the vertex of the graph,

x = - 3 and y = 1

Thus, h = - 3 and k = 1

Substituting h = - 3 and k = 1 into the vertex form equation, it becomes

y = a(x - - 3)^2 + 1

y = a(x + 3)^2 + 1 ---------------------1

We would pick corresponding x and y values from the curve. We have

when x = - 2, y = 3

Substituting x = - 2 and y = 3 into equation 1, we have

3 = a(- 2 + 3)^2 + 1

3 = a(1)^2 + 1

3 = a + 1

a = 3 - 1 = 2

Substituting a = 2 into equation 1, we have

y = 2(x + 3)^2 + 1

The correct option is B

Answer:

2x - 5y = 9 // standard form

y + 6 = -3 (x-1) // point slope form

y = -x + 8 // slope intercept form

Step-by-step explanation:

Answer: 691

Step-by-step explanation:

(17 + 6 + 9) × (19 + 16) - 19 × 7 - 6 × 4 - 16 × 17 = 691

       A) -  Event  "A  or  B"  Consists  of  the Outcomes:

               {2, 3, 4, 5, 6, 8}

      B) - Event  "A  or  "B"  Consists  of the Outcomes:

             {4,  6}

      C) -  The "COMPLEMENT  of EVENT  "A"  Consists of the Outcomes:

             {1, 3, 5, 7}

MAKE A PLAN:

List The OUTCOMES for EACH EVENT and their COMBINATIONS:

        a) -  EVENT  "A":  {2, 4, 6, 8}

               EVENT "B":   {3, 4, 5, 6}

               EVENT "A" or "B": {2, 3, 4, 5, 6, 8}

        b) - EVENT "A"  or "B":  {4, 6}

        c) -  The COMPLEMENT of the EVENT "A":  {1, 3, 5, 7}

       A) -  Event  "A  or  B"  Consists  of  the Outcomes:

               {2, 3, 4, 5, 6, 8}

      B) - Event  "A  or  "B"  Consists  of the Outcomes:

            {4,  6}

      C) - The "COMPLEMENT  of EVENT  "A"  Consists of the Outcomes:

             {1, 3, 5, 7}

I hope this helps!

Answer:

10b/y^2

Step-by-step explanation:

Hope this helps! :)

N 11

Remember that

The law of sines

In this problem

Solve for x

sinX=(14.9*sin71)/25.5

The simplified form of expression  4(126) + 76 - 10 is 6 (100 - 5).

A mathematical expression is a sentence that contains a minimum of two numbers or variables and at least one mathematical operation. Let's learn how to write expressions.

A number is 6 more than half of another number, and that other number is called x. In a mathematical expression, this statement is represented as x/2 + 6. Complex puzzles can be solved using mathematical expressions.

We have been asked to simply the expression

4(126) + 76 - 10

= 4(60 + 66) + 66

= 4(60) + 4(66) + 66

= 4(60) + 5(66)

= 4(60) + 5( 60 + 6)

= 4(60) + 5(60) +5(6)

= 60(4+5) + 6(5)

= 60(9) + 6(5)

= 6(90 + 5)

= 6(95)    

= 6 (100 - 5) simplified form

= 600 - 30

= 570

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