Find the equation of the linear function represented by the table below in slope-intercept form.

The total Area the design is 8 square cm.

Area of rectangular design is product of length and breadth of rectangular design.

In the given question we have,

Rectangular design is made up from 6 squares .

there is 2 small squares surrounded by 4 large squares.

Area of each small square = 1 sq.cm

let the length of rectangular design be l cm

and breadth is b cm.

Area of rectangular design= l×b sq.cm

from the given statement, we can see that side of small square is 1 cm and small squares surrounded by 4 large squares i.e side of large square is sum of side of small squares or 2cm .

Also , length of rectangular design is sum of sides of two large squares and breadth is same as side of one large square.

so, length of rectangular design= 4 cm

breadth of rectangular design= 2cm

Area of rectangular design= 4×2 = 8sq. cm

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Equation of line in slope-intercept form is [tex]y = (\frac{1}{3})x + 2[/tex].

Given in graph,

A(0,2) and B(3,3)

Slope-intercept form => y = mx + c

Slope, m = [tex]\frac{y2-y1}{x2-x1}[/tex]

               = [tex]\frac{3-2}{3-0}[/tex]

               = [tex]\frac{1}{3}[/tex]

Therefore, y = (1/3)x + c

Put A(0,2) in above equation

2 = (1/3)*0 + c

2 = c

Hence, y = (1/3)x + 2.

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Answer:

1/3

Step-by-step explanation

We can immediately tell the y-intercept is 1/3.

Slope intercept form:

y = mx + b

m = slope

b = y-intercept.

Answer: the y - intercept is 1/3

Step-by-step explanation: trust

Answer:

An example would be y = -x.

Step-by-step explanation:

Since the y-intercept is 0, we don't have to write it out. The slope has to be negative, so I chose -1 as the slope. We don't have to write 1 when we use it as a coefficient, so that is why I wrote it as -x. Now to put it all together in slope intercept form, we get y = -x.

Hope this helps.

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Answer:

-15, 9

Step-by-step explanation:

Substituting into the distance formula,

[tex]\sqrt{(6-3)^2+(-1-3)^2+(-3-z)^2}=13 \\ \\ \sqrt{25+(3+z)^2}=13 \\ \\ 25+(3+z)^2=169 \\ \\ (3+z)^2=144 \\ \\ 3+z=\pm 12 \\ \\ z=-3 \pm 12 \\ \\ z=-15, 9[/tex]

The argument against the conjecture The area of a rectangle with a perimeter of 40 units must be at least one square unit. A rectangle with dimensions of 19.99 units long and 0.1 units wide has a 40 unit perimeter and an area of 0.1999 square units.

acc to our question-

The goal of the inquiry is to illustrate any potential connections between a rectangle's perimeter and area.

The counterexample presented dimensions that revealed the perimeter, which is 40, but omitted to provide the area, which is 1 square unit.

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Using the properties of conditional statements we can write the inverse of the statement as ": if the 2 smallest sides sum is not larger than the 3rd side, then it is not a triangle."

The statement  is given as if the sum of two sides is greater than the third side then it is a triangle.

Now for the inverse we have to convert the given line into double negative.

Hence we get:

If the 2 smallest sides sum is not larger than the 3rd side, then it is not a triangle

Conditional statements are part of mathematical reasoning, a vital skill that enables students to evaluate a given hypothesis without reference to a particular context or meaning. Simply put, when a scientific research or allegation is studied, the logic isn't truly founded on an individual's perspective. Deductions and evidence must have factual and scientific foundations.

the various types of conditional statements are:

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The equation the function after the transformation is g(x) = x/10

The equation of the function is given as

y = x

Express as a function

f(x) = x

The sequence of transformations is given as follows:

Vertically stretched by a factor of 1/10

When the above transformations are combined, we have:

Vertically stretched by a factor of 4: g(x) = 1/10f(x)

So, we have

g(x) = 1/10f(x)

Substitute x for f(x)

So, we have

g(x) = 1/10 * x

Evaluate

g(x) = x/10

Hence, the function g(x) is g(x) = x/10

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A 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is 0.282 + 0.055.

Confidence intervals, which describe how closely study results match reality or how dependable they are based on statistical theory, are regularly mentioned in scientific publications. The sample is used to calculate the confidence interval, which represents the range of likely population parameters. In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.

Given,

Number of credit card holders

n = 450

x = 127

p = 127/450

Proportion:

p = 0.2822

99% confidence interval:

C I = 0.2822 ± 2.576 × 0.2122

CI = 0.2822 ± 0.05465

CI = 0.282 + 0.055

A 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is 0.282 + 0.055.

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The price of a pack of balloons is 4. 39

The price of a pack of party favors is 0. 36

We have that;

Let the cost of balloons be x

Let the cost of party favors by y

From the information given, we have that;

3x + 4y = 14. 63   (1)

2x + 4y = 16. 03  (2)

Now, let's make 'x' the subject from equation (1)

x = 14. 63 - 4y/ 3  (3)

Substitute in equation (2)

3( 14. 63 - 4y/ 3) = 16. 03

expand the bracket

43. 69 - 12y /3 = 16. 03

cross multiply

43. 69 - 12y = 48. 09

collect like terms

- 12y =  - 4. 4

make 'y' the subject

y = 0. 36

substitute in equation (3)

x = 14. 63 - 4(0. 36)/ 3

x = 13. 1/ 3

x = 4. 39

Hence, the prices are 4. 39 and 0. 36 respectively.

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Answer:

that's biology but

Step-by-step explanation:

autotrophs make their owner food

heterotrophs can't make their own food

photosynthesis is the 3rd one

photosynthesis happens in the chloroplast

photosynthesis makes glucose

I can go in depth about any of these, ask me if needed

Answer:34?

Step-by-step explanation: not too sure but yeah

Answer:

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

The angle L is congruent to angle T ∠L ≅ ∠T and the reason is that  opposite angles of a parallelogram are congruent.

We are given the parallelograms GHLJ and GSTU in such a manner that the parallelogram GSTU is inscribed right inside parallelogram GHLJ with angle G coinciding on the two parallelograms.

Now, we can remember that property of parallelogram states that the opposite angles of a parallelogram are congruent.

Thus, angle G is congruent to angle T and angle L .

Therefore, ∠L ≅ ∠T

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Answer:

By the parallelogram angle theorem, opposite angles of a parallelogram are congruent. Therefore, angle T must be congruent to angle G, and angle G must be congruent to angle L. By the transitive property of congruence, angle T is congruent to angle L.

Step-by-step explanation:

got it right on edge2

Answer: -62.5

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Step-by-step explanation:

Answer:

slope = - [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 10 ) and (x₂, y₂ ) = (24, 6 )

m = [tex]\frac{6-10}{24-0}[/tex] = [tex]\frac{-4}{24}[/tex] = - [tex]\frac{1}{6}[/tex]

The product of (4i-5)(4i+5) is -41.

What are complex numbers?

Every complex number can be expressed in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted i, also known as the imaginary unit, and satisfies the equation i² = - 1.

Here, we have

Given function

= (4i-5) (4i+5)

After applying the product rule, we get

=  16i² + 20i - 20i - 25

= 16i² - 25

after putting i² value, we get

= 16(-1) - 25

= -41

Hence, the product of (4i-5)(4i+5) is -41.

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Answer:

Step-by-step explanation:

663.98

Answer: 663.98

Step-by-step explanation:

(8.42*109)=917.78

(2.35*108)=253.8

917.78-253.8=663.98

The values of x after applying congruency to solve the complete shape is 3.5.

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. The symbol to represent two congruent shapes is ≅.

To calculate the values of x in the diagram, we need to first join point Q to point H and point G to form ΔQHG also, we join point Q to point E and point F to form ΔQFE.

Comparing ΔQHG and  ΔQFE, we can deduce that

Therefore,

Hence, the values of x in is 3.5.

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Answer:

A

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then

[tex]\sqrt{12}[/tex]

= [tex]\sqrt{4(3)}[/tex]

= [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex]

= 2[tex]\sqrt{3}[/tex]

Then

[tex]\sqrt{144}[/tex] + 18[tex]\sqrt{12}[/tex] - 5[tex]\sqrt{64}[/tex]

= 12 + 18(2[tex]\sqrt{3}[/tex] ) - 5(8)

= 12 + 36[tex]\sqrt{3}[/tex] - 40

= - 28 + 36[tex]\sqrt{3}[/tex]

Answer:

23 and 24

Step-by-step explanation:

let the 2 consecutive numbers be n and n + 1 , then

n² + (n + 1)² = 1105

n² + n² + 2n + 1 = 1105 ( subtract 1105 from both sides )

2n² + 2n - 1104 = 0 ( divide through by 2 )

n² + n - 552 = 0 ← in standard form

(n + 24)(n - 23) = 0 ← in factored form

equate each factor to zero and solve for n

n + 24 = 0 ⇒ n = - 24

n - 23 = 0 ⇒ n = 23

However, n > 0 , then n = 23 and n+ 1 = 23 + 1 = 24

the numbers are 23 and 24

Answer:

x< -1

Step-by-step explanation:

x^3 < 9 - 10

x^3 < -1

x< -1

Answer:

x < -1

Step-by-step explanation:

x³<9-10

x³<-1

x < -1

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The equation of a line in the point-slope form that has a slope of 1/3 and passes through the point (6,-2) is [tex]y+2 =\frac{1}{3} (x-6 )[/tex].

Calculation

[tex]y-y_{1} =m(x-x_{1} )[/tex]

[tex]y-(-2) =\frac{1}{3} (x-6 )[/tex]

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

Therefore, the equation of a line in the point-slope form that has a slope of 1/3 and passes through the point(6, -2) is [tex]y+2 =\frac{1}{3} (x-6 )[/tex]

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Answer:

a. its a prime number cuz as far as ik 67 has one factor 67x1

Answer:

Number 67 is prime because it doesn't have proper factors. In other words, the only factors of 67 are 1 and itself

So, approximately 59 fish in the school would be longer than 92 cm.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). The expressions on both sides of the equal sign can contain variables, constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, logarithms, etc.

Here,

We can solve this problem using the normal distribution formula, which states:

z = (x - mu) / sigma

where z is the standard score, x is the raw score, mu is the mean, and sigma is the standard deviation.

To find the number of fish longer than 92 cm, we need to find the proportion of fish in the population with lengths greater than 92 cm. We can then multiply this proportion by the total number of fish in the school to get the number of fish longer than 92 cm.

First, we calculate the standard score for 92 cm:

z = (92 - 78) / 14

z = 1

Next, we look up the proportion of the standard normal distribution that corresponds to a z-score of 1. We can use a standard normal distribution table or calculator to find this value. The proportion of the distribution that is greater than z = 1 is approximately 0.1587.

Therefore, the proportion of fish in the population with lengths greater than 92 cm is 0.1587. To find the number of fish longer than 92 cm, we multiply this proportion by the total number of fish in the school:

370 * 0.1587 = 58.8

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Answer:

0.86 pounds of fruit is left.

Step-by-step explanation:

If Stacey bought 8.3 pounds and the class ate 7.44 pounds, the amount of fruit that's left is 8.3-7.44=0.86      

Answer:

x = 0.3

Step-by-step explanation:

[tex] \sf1.9x + 0.1x = 0.6[/tex]

Combine like terms.

[tex] \sf2x = 0.6[/tex]

Divide both sides by 2.

[tex] \sf \: x = 0.3[/tex]

Answer:

Common side: UV

Step-by-step explanation:

There should be 12 emails total.

7.200 and 2.683 are the variance and standard deviation, respectively.

Calculation of expected number of emails, variance and standard deviation:

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