How many cans weighing 14 oz are in a case if the case weighs 22 lb 12 oz?
There are cans in the case.

Answer:

Vertex form

( 2 /3 ,  − 10 /3 )

x and y intercepts

 Y intercept ( 2 + √ 10 /3 , 0 ) , ( 2 − √ 10/ 3 , 0 )

X intercept ( 0 , − 2 )

Step-by-step explanation:

The correct statement that describes the solution set of the function f is Two real solutions. So, correct option is C.

To determine the solution set of the function f(x) = 3x² - 4x - 2, we can consider the nature of the solutions by examining the discriminant of the quadratic equation.

The discriminant, denoted as Δ, is calculated as b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.

In this case, the quadratic equation is 3x² - 4x - 2 = 0. Comparing it to the general form, we have a = 3, b = -4, and c = -2.

The discriminant is given by Δ = (-4)² - 4(3)(-2) = 16 + 24 = 40.

Based on the value of the discriminant (Δ = 40), we can determine the nature of the solutions:

If Δ > 0, there are two distinct real solutions.

If Δ = 0, there is one real solution.

If Δ < 0, there are two complex solutions.

Since Δ = 40, which is greater than 0, the correct statement that describes the solution set of the function f is:

C- Two real solutions.

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Complete question is:

Which statement describes the solution set of function f? f(x) = 3x² - 4x - 2

A- One real solution and one complex solution

B- Two complex solutions

C- Two real solutions

D- One real solution

Answer:

Option B, cotangent is the reciprocal of tangent

That option is correct

(a) After t years, the height is 18t² + 3t + 10

(b) The shrubs are847 cm tall when they are sold.

Given growth rate

dh/dt = 1.8t + 3

dh = (18t + 3)dt

Integrating this, we have

h = 18t² + 3t + C

When t = 0, h = 10cm

Then

10 = C

So

(a) h = 18t² + 3t + 10

(b) Because they are sold after every 9 years, then at t = 9

h = 18(9)² + 3(9) + 10

= 810 + 27 + 10

= 847 cm

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Answer:

162 cm

Step-by-step explanation:

Perimeter =35+35+46+46

=162cm

Perimeter is basically adding up all the sides of the length

Answer:

(-2,2)

Step-by-step explanation:

If you graph the equations (I recommend using desmos) you can see that the points intersect at that point.

Saving for a down payment was worth it for Isabel. It reduces the total amount paid for the car by lowering the loan amount, resulting in less interest paid over time.

When evaluating whether saving for a down payment on a car was worth it for Isabel, we need to consider the difference in the total amount paid for the car in two scenarios: with a down payment and without a down payment. Let's analyze the two scenarios to make a judgment.

Scenario 1: With a down payment

In this scenario, Isabel saved up and made a down payment on the car. As a result, her monthly loan payment fits within her budget. By making a down payment, she reduces the principal amount borrowed and, subsequently, the interest charged on the loan.

The benefits of saving for a down payment include:

Lower loan amount: By making a down payment, Isabel reduces the total amount borrowed from the lender.

Reduced interest: With a lower loan amount, the interest charged on the loan is also reduced.

Shorter loan term: A down payment can help Isabel secure a shorter loan term, reducing the overall interest paid over time.

Scenario 2: Without a down payment

In this scenario, Isabel does not make a down payment and finances the entire purchase price of the car. As a result, her monthly loan payment may be higher, as she is borrowing a larger sum and potentially paying more interest over the loan term.

The drawbacks of not saving for a down payment include:

Higher loan amount: Without a down payment, the entire purchase price is financed, leading to a higher loan amount.

Increased interest: With a higher loan amount, more interest may accumulate over the loan term, resulting in a higher total cost of the car.

By comparing the two scenarios, we can assess the impact on the total amount paid for the car. Generally, having a down payment reduces the loan amount, decreases interest charges, and may result in a shorter loan term. This, in turn, can lead to substantial savings in the long run.

To determine the exact difference in the total amount paid for the car in each scenario, we would need specific details such as the purchase price of the car, the interest rate, and the loan term. With these figures, we could calculate the total cost of the car, including interest, in both scenarios and compare the results. Based on this analysis, we can then determine if saving for a down payment was worth it for Isabel.

In conclusion, saving for a down payment on a car can offer financial benefits such as lower loan amounts, reduced interest charges, and potentially shorter loan terms. Considering the potential cost savings and improved financial stability, it is generally advisable for Isabel to save for a down payment, making it worth the effort and consideration.

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Question

The down payment makes the monthly loan payment fit into Isabel's budget. Besides this benefit, do you think saving for a down payment on the car was worth it for Isabel? Use each monthly payment with and without a down payment) to find the difference of the total amount paid for the car in each scenario to justify your answer.

When x = 13, the equation that is true is option D) 5(x - 9) = 20.

To determine which equation is true when x = 13, we can substitute the value of x into each equation and see which equation holds true. Let's go through each option:

A) 3(18 - x) = 67

Substituting x = 13:

3(18 - 13) = 67

3(5) = 67

15 = 67

The equation is not true when x = 13. Therefore, option A is false.

B) 4(9x) = 23

Substituting x = 13:

4(9*13) = 23

4(117) = 23

468 = 23

Again, the equation is not true when x = 13. Therefore, option B is also false.

C) 2(x - 3) = 7

Substituting x = 13:

2(13 - 3) = 7

2(10) = 7

20 = 7

Once again, the equation is not true when x = 13. Therefore, option C is false as well.

D) 5(x - 9) = 20

Substituting x = 13:

5(13 - 9) = 20

5(4) = 20

20 = 20

Finally, the equation is true when x = 13. Therefore, option D is true.

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Note: the translated questions is

X = 13, which equation is true?

Answer:

A’ = (-2, 1.5)

B’ - (2, 1.5)

C’ - (-2, -2)

D- (2, -2)

Step-by-step explanation:

A - (-4, 3)

B- (4, 3)

C - (-4, -4)

D- (4, -4)

A’ = (-2, 1.5)

B’ - (2, 1.5)

C’ - (-2, -2)

D- (2, -2)

Answer:

have a look at the attachment image......

if dilatation center is A, connect all of the the alphabet (B, C, D)to A and the scale factor is 1 by 2. so make a dot in the middle of line that is connected to dilatation center....

if the line is D to A then the dot on the line D will be D prime.... same like that find C and B prime

if you don't understand let me know in the comments

Answer:

B

Step-by-step explanation:

15a + 6

= 5.3.a + 2.3

= 3(5a+2)

Answer:

Step-by-step explanation:

I added a screenshot of the graph hope it helps

Using the pοlygοn tοοl a rectangle with length 5 unit and width 3 units has been drawn

A rectangle is a type οf quadrilateral that has its parallel sides equal tο each οther and all the fοur vertices are equal tο 90 degrees. Hence, it is alsο called an equiangular quadrilateral. Since, the οppοsite sides are equal and parallel, in rectangle, therefοre, it can alsο be termed as a parallelοgram.

Using the pοlygοn tοοl a rectangle with length 5 unit and width 3 units has been drawn

check the attachment given belοw tο understand.

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Answer:

Incomplete question, but I gave a guide to solve using the Empirical Rule.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

It is also important to note that the normal distribution is symmetric. This means of the 68% of the measures are within 1 standard deviation of the mean, for example, 68/2 = 34% are between 1 standard deviation below the mean and the mean, and 34% are between the mean and 1 standard deviation above the mean.

In this question:

You take the mean and the standard deviation. Then you take both bounds that the percentage asks, and see how many standard deviations each are from the mean, and you then use the empirical rule to solve.

Answer:

Step-by-step explanation:

52

Answer:  The correct answer is 52

Step-by-step explanation:

4² + 6²

4*4 + 6*6

16 + 36 = 52

Answer:

she should use 2 cups of peanut butter

Step-by-step explanation:

to know the answer to that

use this equation (pb is peanut butter &o is oil)

1cup of pb=1/2 cup of o

?=1 cup of o

1×1÷1/2= 1×1×2/1=2co cups of pb

The missing vertex in the enlarged shape is the letter C.

In an enlargement, each side of the original shape is multiplied by the scale factor to get the corresponding side in the enlarged shape. Since the scale factor is 3, each side in the original shape is multiplied by 3 to find the corresponding side in the enlarged shape.
Looking at the three sides that are shown in the enlarged shape, we can see that they are 3 times longer than the corresponding sides in the original shape. To find the missing vertex, we need to extend the fourth side of the original shape by 3 times its length. This extension leads to point C, which marks the position of the missing vertex in the enlarged shape.
To summarize, the missing vertex in the enlarged shape is marked by the letter C because it is the result of extending the fourth side of the original shape by 3 times its length, in accordance with the scale factor of 3.

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Answer:

9000

Step-by-step explanation:

Answer: 40 pupils

Step-by-step explanation:

 35           14

-------   =   --------

100             ?

find the denominator.

multiply 14 and 100:

14 x 100 = 1400

divide 1400 by 35

1400/35 = 40

Therefore there are 40 students

The given exponential expression, (2xy³)⁻², on simplifying becomes 1/2²x²y⁶.

In the question, we are asked to simplify the given expression, (2xy³)⁻².

The given expression is an exponential expression.

Some of the exponential laws that are used to simplify exponential expressions are as follows:

The Product of Powers Rule: \(x^m * x^n = x^{m+n\)

The quotient of Powers Rule: \(x^m \div x^n = x^{m-n\)

The Power of a Power Rule: \((x^m)^n = x^{mn\)

The Power of Product Rule: \((xy)^n = x^n*y^n\)

The Power of Quotient Rule: \((x / y)^n = x^n / y^n\)

The Zero Power Rule: \(x^0 =1\)

The Negative Exponent Rule: \(x^{-n} = (1/x^n)\).

Using these laws of exponents, we can simplify the given expression, (2xy³)⁻², as follows:

(2xy³)⁻²

= 2⁻²x⁻²y⁻⁶ {Using The Power of a Power Rule: \((x^m)^n = x^{mn\)}

= 1/2²x²y⁶ {Using The Negative Exponent Rule: \(x^{-n} = (1/x^n)\)}

Thus, the given exponential expression, (2xy³)⁻², on simplifying becomes 1/2²x²y⁶.

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Answer:

24×20×30=14,400 minutes

Answer:

Area of the given figure is 51.5 square units.

Step-by-step explanation:

Area of rectangle OCBH = Length × width

                                         = 11 × 8

                                         = 88 square units

Area of trapezoid OGEF = \(\frac{1}{2}(b_1+b_2)\times h\)

                                         = \(\frac{1}{2}(\text{GE+OF)}\times (\text{OG})\)

                                         = \(\frac{1}{2}(3+6)\times 4\)

                                         = 18 units²

Area of trapezoid GCDE = \(\frac{1}{2}(\text{GC+DE)}\times (\text{GE})\)

                                         = \(\frac{1}{2}(7+2)\times 3\)

                                         = 13.5 units²

Area of triangle AFH = \(\frac{1}{2}(\text{Base})\times (\text{Height})\)

                                  = \(\frac{1}{2}(5)(2)\)

                                  = 5 units²

Area of polygon ABCDEF = Area of rectangle CBHO - (Area of trapezoid OGEF + Area of trapezoid GCDE + Area of triangle AFH)

                                           = 88 - (18 + 13.5 + 5)

                                           = 88 - 36.5

                                           = 51.5 units²

Therefore, area of the given polygon is 51.5 units²

The required distance between the two given cities using the distance formula is 93 miles.

Distance is the sum of an object's movements, regardless of direction.

The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula.

The Pythagorean theorem can be rewritten as d=(((x 2-x 1)2+(y 2-y 1)2) to calculate the separation between any two locations.

So, we have the points:

(53, 17) and (123, 78)

Distance formula:

d = √(x2-x1)² + (y2-y1)²

Now, calculate as follows:

d = √(x2-x1)² + (y2-y1)²

d = √(123-53)² + (78-17)²

d = √(70)² + (61)²

d = √(4,900) + (3,721)

d = √8,621

d = 92.84

Rounding off: 93 miles

Therefore, the required distance between the two given cities using the distance formula is 93 miles.

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The percentage is: 0.480887793%

If you want to round it up: 0.48%

The exact value of sin(5π/12) is (√6 + √2)/4

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

sin 5pi/12

Express properly

So, we have

sin(5π/12)

Convert the angle to degrees

This gives

sin(5π/12) = sin(5/12 * 180)

Evaluate

sin(5π/12) = sin(75)

The actual value of sin(75) is (√6 + √2)/4

This means that

sin(5π/12) = (√6 + √2)/4

Hence, the exact value of sin(5π/12) is (√6 + √2)/4

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The exact value of sin 5π/12 is (√6 + √2)/4

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Angle in trigonometry can be measured in either degree or radian.

π is a measurement in radian which is equivalent to 180° in degrees.

Therefore:

5π/12 = 5 × 180/12

= 75°

Therefore sin5π/12 = sin75°

sin75 = sin( 45+30) = sin45cos30+ cos 45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= √3/2√2 + 1/2√2

= (√3+1)/2√2

rationalizing;

(2√6 + 2√2)/8

dividing through by 2

=(√6 + √2)/4

therefore tan75 =(√6 + √2)/4

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Answer:

$2384.87

Step-by-step explanation:

Given data

P=2300

t= 2 years

r= 1.23%

Required

The amount in their account

Let us apply the simple interest formula

A=P(1+rt)

Substitute

A= 2300(1+0.0123*3)

A= 2300(1+0.0369)

A= 2300*1.0369

A=$2384.87

Hence the amount in the account is $2384.87

Answer:

The answer is −6(10a−7)(a−10)

Step-by-step explanation:

1) Factor out the common term 6.

\( - 6( {10a}^{2} - 107a + 70)\)

2) Split the second term in 10a² - 107a + 70 into two terms.

\( - 6( {10a}^{2} - 7a - 100a + 70)\)

3) Factor out common terms in the first two terms, then in the last two terms.

\( - 6(a(10a - 7) - 10(10a - 7))\)

4) Factor out the common term 10a - 7.

\( - 6( 10a - 7)(a - 10\)

Therefor, the answer is -6 ( 10a - 7) (a - 10).

Answer:

\(x = \frac{20}{91}\)

Step-by-step explanation:

Since this is a proportion, first you need to cross multiply.

\(\frac{20}{7}\) × \(\frac{2}{25}\) = \(\frac{40}{175}\)

\(\frac{26}{25} x = \frac{40}{175}\)

Now multiply both sides by the reciprocal of 26/25 which is 25/26.

\(\frac{25}{26} (\frac{26}{25} )x=\frac{40}{175} (\frac{25}{26} )\\\)

Cancel on the right side, 25 and 175, by 25.  Then cancel 40 and 26 by 2.

\(x = \frac{20}{7} (\frac{1}{13} )\)

\(x = \frac{20}{91}\)

6/15

you add everything she sells together. ( 3+1+6+5=15) Then you put the amount of ovens she sells above taht number, making it a fraction.

Answer:

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