Use factoring to find the x-intercept(s)
of the function below.
Enter the smaller value first.
0 = 2x² + 5x - 3

Answer: If there is a proportional relationship between the number of pitchers of lemonade Karen wants to make, x, and the number of lemons she needs, y, and the equation modeling this relationship is y = 5x, then we can find the number of pitchers Karen can make with 15 lemons by solving for x:

15 = 5x

Dividing both sides by 5:

3 = x

So Karen can make 3 pitchers of lemonade with 15 lemons.

Step-by-step explanation:

The possible values of the length of the rectangle is x > 34, the correct option is A.

For a rectangle with length and width L and W units, we get:

Area of the rectangle = [tex]L \times W \: \rm unit^2[/tex]

Perimeter of the rectangle = [tex]2(L + W) \: \rm unit[/tex]

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Given that width is 8 inches less than the length x

Sum of length and width more than 60

Now, the length is x

Width is x-8

x-8+x>60

2x>60

x>30

Therefore, the length of rectangle will be  x > 34

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Answer:

The length is [tex]9[/tex] inches and the width is [tex]30[/tex] inches.

Step-by-step explanation:

The perimeter of the rectangle is [tex]2x + \frac{4x}{3} = 30[/tex]. We multiply [tex]3[/tex] by both sides which will give us [tex]6x + 4x = 90[/tex]. Adding, we have [tex]10x = 90[/tex]. Dividing [tex]10[/tex] by both sides will give us [tex]x = 9[/tex]. The length of the rectangle is [tex]9[/tex], and the width is [tex]\frac23 \cdot 9 = 6.[/tex] Checking our answer, we have [tex]6 + 6 + 9 + 9 = 30.[/tex] Therefore, the length of the rectangle is [tex]\boxed{9 \text{ inches}}[/tex] and the width of the rectangle is [tex]\boxed{30 \text{ inches}}[/tex].

Hope that helps!

Answer:

Not Possible

Step-by-step explanation:

No answer choices are shown however, we can solve for some that are equivalent so we know which ones are not.

Here are some that are equivalent:

20(2+1)

2(20+10)

40+20

60

Answer:

Step-by-step explanation:

Since the side lengths are proportional, the ratio of the width to length in the old phone will be equal to the ratio of the width to length in the new phone. That is:

(width of old phone) / (length of old phone) = (width of new phone) / (length of new phone)

We know the length of the old phone is 1.41.4 inches, and the width is 2.82.8 inches, so we can use that information to solve for the width of the new phone:

(2.82.8 inches) / (1.41.4 inches) = (width of new phone) / (1.611.61 inches)

Cross multiplying, we get:

(width of new phone) = (2.82.8 inches) * (1.611.61 inches) / (1.41.4 inches)

Using a calculator, we can find that the width of the new phone is approximately 3.23.2 inches.

I'm sorry, but I'm not sure what you mean by "Imagine math - item 92070." Can you please provide more context or clarification so I can assist you better?

Answer:

-19 > k

Step-by-step explanation:

-4 > k + 15

Subtract 15 from each side.

-4-15 > k + 15-15

-19 > k

Any value less than -19 would make this statement true

Answer:

- 19 > k

Step-by-step explanation:

- 4 > k + 15

Subtract 15 from both sides.

- 4 - 15 > k

- 19 > k

Answer:

32 markers

Step-by-step explanation:

Ty has 8 x 3 = 24 markers.

Together, they have 8 + 24 = 32 markers.

Answer:

Let the number of $2 notes be x, while that of $10 notes be y.

Set two equations

x + y = 21     y = 21 - x ------- 1

2x + 10y < 110  ------ 2

Sub 1 into 2

2x + 10(21-x) < 110

2x + 210 - 10x < 110

-8x < -100

x > 12.5

Minimum number of $2 notes in the envelope = 13

With an area of 11,224 square feet and the dimensions of the screen if it is 30 feet longer than it is wide, the width of the screen is 91.5 feet, and the length of the screen is 121.5 feet.

Let's call the width of the screen "w". Then, the length of the screen would be "w + 30". The area of the screen is 11,224 square feet, so we can set up an equation:

w * (w + 30) = 11,224

Expanding the right side of the equation, we get:

w^2 + 30w - 11,224 = 0

We can use the quadratic formula to solve for w:

w = (-b ± √(b^2 - 4ac)) / 2a

Where a = 1, b = 30, and c = -11,224.

Plugging in the values, we get:

w = (-30 ± √(30^2 - 4 * 1 * -11,224)) / 2 * 1

= (-30 ± √(900 + 44,896)) / 2

= (-30 ± √(45,796)) / 2

= (-30 ± 213) / 2

Taking the positive solution, we get:

w = (183 / 2) = 91.5 feet

So the width of the screen is 91.5 feet, and the length of the screen is 91.5 + 30 = 121.5 feet.

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To calculate the probability that the first heart it detects with muscle damage is the 8th image geometric distribution should be used.

According to the question medbiz develops and sells medical imaging devices. they are developing a computer program that reads heart images and detects heart muscle damage.

Machine has success rate of 90%

Number of images of hearts with muscle damage = 100

To calculate the probability that the first heart it detects with muscle damage is the 8th image, geometric distribution should be used because  

Geometric distribution is a type of discrete probability distribution that represents the probability of the number of successive failures before a success is obtained in a Bernoulli trial. A Bernoulli trial is an experiment that can have only two possible outcomes, ie., success or failure

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The question is incomplete, the following question is complete:

MedBiz develops and sells medical imaging devices. They are developing a computer program that reads heart images and detects heart muscle damage. Early studies show the machine has a 90% success rate. The programs is shown 100 images of hearts with muscle damage. What distribution should be used to calculate the probability that the first heart it detects with muscle damage is the 8th image?

binomial distribution

geometric distribution

hypergeometric distribution

none of the other choices

Answer:

0.75

Step-by-step explanation:

The slope-intercept form is one way to write a linear equation (the equation of a line). The slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).

The length of town from the base of the cliff is 848.25 feet

Concept of height and distance

You can use trigonometry formulas to find height and distance from anything. If you know the distance from the Qutub Minar to your current location and the angle at which you can see the top of the Minar, you can find the altitude of the Qutub Minar. Use trigonometry to find the elevation. This is because the ground, minaret elevation, and contour lines all combine to form a 90 degree right triangle between the minaret and the ground.

The distance is usually the "base" of the right triangle formed by the minar's elevation and line of sight. The length of the horizontal plane also forms the base of a triangle parallel to the ground at a given height, so we know the distance. The line of sight forms the "hypotenuse" of a right triangle. Lines perpendicular to the ground form the "height" of the triangle.

To calculate elevation or depression you can use the following formulas:

sinθ = hypotenuse /height.

cosθ = hypotenuse /base,

tanθ = base /height

where θ is the elevation or depression angle.

and in this question the angle of depression is 23 degree and height is 360 feet and we have to calculate the base

tan 23 degree = 360/base

base  = 360/tan 23

=360/0.4244

= 848.25 feet.

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Each week, Desiree earns $925 and pays $149 in payroll tax it will take Desiree at least 4 weeks to earn at least $3000 after taxes.

What is Gross earning ?

Gross earnings refer to the total amount of money that an individual earns before any deductions are taken out. These earnings can include regular salary or wages, as well as any bonuses, tips, or commissions that are earned. Gross earnings are usually reported on a paycheck or pay stub, and may be subject to various taxes and other deductions.

Desiree's net earnings after payroll tax can be calculated by subtracting the tax amount from her gross earnings:

Net Earnings = Gross Earnings - Payroll Tax

Net Earnings = $925 - $149

Net Earnings = $776

To earn at least $3000 after taxes, Desiree needs to earn a total of:

Total Earnings = $3000 + Payroll Tax

Total Earnings = $3000 + $149

Total Earnings = $3149

We can now set up an equation to solve for the number of weeks, x, it will take for Desiree to earn at least $3149:

Net Earnings per week * Number of Weeks = Total Earnings

$776 * x = $3149

Solving for x:

x = $3149 / $776

x = 4.05

Therefore, it will take Desiree approximately 4.05 weeks to earn at least $3000 after payroll tax. Since you can't earn partial weeks, we can round up to 5 weeks to ensure that Desiree has earned at least $3000.

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Answer:x=251

Step-by-step explanation:

Step 1: Subtract 8 from both sides of the equation.

Explanation: Subtracting 8 from both sides of the equation keeps the equality balanced.

Step 2: x = 251

Explanation: Subtracting 8 from both sides of the equation gives us

x = 259 - 8 = 251.

Answer:

Step-by-step explanation:

x = -251

Answer: 4x2

Step-by-step explanation:

Answer:

[tex]4x^2[/tex]

Step-by-step explanation:

[tex](2x)(2x)=(2*2)(x*x)=4x^2[/tex]

Five packets of marshmallows cost £4. 80. Then, eight packets of marshmallows cost £7.68.

The problem states that five packets of marshmallows cost £4.80. We need to find out how much eight packets of marshmallows will cost.

To solve the problem, we can use the concept of proportionality. If we assume that the cost of marshmallows is directly proportional to the number of packets, then we can set up a proportion between the cost of five packets and the cost of eight packets.

The proportion can be written as follows:

5 packets / £4.80 = 8 packets / x

where x is the cost of eight packets.

To solve for x, we can cross-multiply the proportion and simplify:

5 packets x = £4.80 x 8 packets

5x = £38.40

x = £38.40 / 5

x = £7.68

Therefore, eight packets of marshmallows will cost £7.68.

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Hexagonal prism A has a surface area of 43 cm2.

A three-dimensional shape's surface area is the total area on its surface. A cuboid's surface area is calculated by adding the areas of each of its six rectangular sides. The cuboid's length, width, and height may all be identified, and the formula SA=2lw+2lh+2hw can be used to determine its surface area (SA).

The surface area of a hexagonal prism is given by the formula:

SA = 2B + PH

where B is the base's surface area, P is its perimeter, and H is the prism's height.

Since prism B is a dilation of prism A with a scale factor of 2, its surface area is four times the surface area of prism A. So we can write:

SA_B = 4×SA_A

where SA_B is the surface area of prism B and SA_A is the surface area of prism A

We are given that SA_B = 172 cm², so we can substitute this value into the equation above to find SA_A:

172 = 4×SA_A

SA_A = 43 cm²

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The area and perimeters of the shapes are: (1) Area = 702 ft², perimeter = 96 ft (2): Area = 20 in² Perimeter = 21 in

Perimeter is the distance round the object while the area is the floor space the object occupies

1) Area =  (l*w) + (L*W)

Area = (6*9)  + (24*27)

Area = 54 + 648

Area = 702 ft²

ii) perimeter = 24+27+30+9+6= 96 ft

2)  Area =  (l*w) + (L*W)

Area = (2*3) +( 7*2)

Area = 6+14 = 20 in²

ii) perimeter =2+7+2+2+3+2+3 = 21 in

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Answer:

the slope is -6/-5

The properties justify the steps are taken to solve the system 2a+7b=0 3a-5b=31 as Multiplication, Substraction, Division,  Simplify, etc.,

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

'The properties that justify the steps taken to solve the system 2a + 7b = 0, 3a - 5b = 31 are:

2a + 7b = 0, 3a - 5b = 31

10a + 35b = 0, 21a - 35b = 217   <-------> Multiplication property of equality.

31a = 217                                      <-------> Substraction property of equality.

a = 7                                            <-------> Division property of equality.

2(7) + 7b = 0,                             <-------> Substitution property of equality.

14 + 7b = 0,                              <-------> Simplify  

7b = -14,                                   <-------> Simplify  

b = -14/7,                                  <-------> Division property of equality.

b = -2

Therefore, the properties justify the steps are taken to solve the system 2a+7b=0 3a-5b=31 as Multiplication, Substraction, Division,  Simplify, etc.,

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Answer: Demographic republic of Congo, Uganda and Gabon

The term "difference" os the result of subtracting one number from another.

So in other terms you want to know what would be the result of subtracting -4.6 from 13.5 :

13.5 - -4.6 = Difference between the two temperatures

Two minus signs turn into a positive sign so :

13.5 - -4.6 =

13.5 + 4.6 =

18.1 = Difference between the two temperatures

Your answer is : The difference between the two temperatures is 18.1

The length of PC and GC is 4.4 and 6.6 respectively.

What is centroid of a triangle?

A centroid of a triangle is defined as a equidistant from all the point present on the triangle. It is always lies on the interior of the triangle. The centroid divided the median in the ratio 2:1

Given ABC is the triangle.

In which G, H, J are the midpoints on AB, BC, AC sides respectively.

Then, AH, CG, BJ are the medians and they are intersect at the point P.

P is the centroid of the triangle.

Given, GP =2.2 we have  to find the PC and GC.

We know that the centroid divided the median in 2:1 ratios.

i.e., AP:PH = CP:PG = BP:PJ = 2:1

We know , GP = 2.2, then, [tex]\frac{CP}{PG} = \frac{2}{1}[/tex]

⇒CP= 2(2.2)= 4.4then, GC = GP+PC= 2.2 + 4.4= 6.6.

Hence, the length of PC and GC is 4.4 and 6.6 respectively.

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Answer: The equation of a line in the form y = mx + b can be found using the slope-intercept form, where m is the slope of the line and b is the y-intercept. To find the equation of BC, we need to find the slope of the line and one point on the line.

The slope of the line can be found using the two points A and B. The slope of the line can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively. Plugging in the values, we get:

m = (4 - (-1)) / (4 - (-3)) = 5 / 7

So the slope of the line BC is 5/7.

One point on the line BC is B = (4, 4), so we can use this point and the slope to find the y-intercept:

b = y - mx

where y and x are the y and x coordinates of point B, respectively. Plugging in the values, we get:

b = 4 - (5/7) * 4 = 4 - 20/7 = -16/7

So the equation of line BC in the slope-intercept form is:

y = (5/7)x - 16/7

Step-by-step explanation:

The equivalent to the ratio 1:2 is 2 : 4

From the question, we have the following parameters that can be used in our computation:

Ratio = 1 : 2

To determine the equivalent expression, we multiply each proportion of the ratio by the same number (say 2)

Using the above as a guide, we have the following:

Ratio = 2 * 1 : 2 * 2

Evaluate

Ratio = 2 : 4

Hence, the ratio is 2 : 4

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The expression for f(x) - g(x) - h(x) is 6x - 5x² + 6.

Option C is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 3x + 5

g(x) = 4x² - 2

h(x) = x² - 3x + 1

Now,

f(x) - g(x) - h(x)

= 3x + 5 - (4x² - 2) - (x² - 3x + 1)

= 3x + 5 - 4x² + 2 - x² + 3x - 1

= 6x - 5x² + 6

Thus,

6x - 5x² + 6 is the expression.

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Range, interquartile range, standard deviation, and variance are four measures of variability that can be used to compare two data sets.

area:

Difference between highest and lowest values.

Range is the straightforward allowance to calculate variability. To asset the area, follow these steps:

Sort all the values ​​in the dataset from lowest to highest.

Subtract the lowest value from the highest value. Interquartile range:

area of ​​the middle half of the distribution

standard deviation:

mean distance from mean

Standard deviation is a useful measure of the variance of a normal distribution.

A normal distribution distributes data symmetrically without skew. Most of the values ​​are clustered around the central region, with values ​​tapering away from the center. Standard deviation indicates how far the data are, on average, from the center of the distribution.

deviation:

mean squared distance from mean 

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The probability the math majors are seated together is 0.028 and all seated togeather with their group is 0.0047.

Probability is the probability that something will happen. Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome. Analyzing events according to their probabilities is called statistics.

Probability determines the likelihood of an event occurring.

P(A) = f / N. Odds and probabilities are related, but odds depend on probabilities. Before we can determine the probability that an event will occur, we first need the probability.  

total number of teacher is 10

so number of ways total 10 teacher seat = 10!/(6!*4!)

= 210

and

the number of ways  the math majors are seated together

= 6

probability = 6/210 = 0.028

the number of ways the math majors are seated together and the computer science majors are seated together

= 1

probability = 1/210

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