Determine the type of triangle that is drawn below.

By subtraction we get that, Isabel has to pour 35.25 grams of salt into the container.

The operation or process of finding the difference between two numbers or quantities is known as subtraction. To subtract a number from another number is also referred to as 'taking away one number from another'.

According to the information in question:

Total salt = 90.45 grams

Amount of salt poured = 55.2 grams

Thus, the total amount of salt left with her which has to be poured will be calculated by subtraction:

Amount of salt left = 90.45 - 55.2

                               = 35.25 grams

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The expression which is equivalent to the expression 14x+3−13x+(−2) is:

x +1

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression,

14x+3−13x+(−2)

Now it can be simplify in the following way:

⇒ 14x - 13x + 3 - 2

the variable and constant terms can be clubbed together,

⇒ x + 1

Hence, the equivalent expression is x + 1

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The interquartile range is 4 and the median is 27.

The interquartile range is the difference between the third quartile and the first quartile. On a box plot, the interquartile range is the difference between the first line and the third line on the box.

Interquartile range = 28 - 24 =4

Median is the central value of a data set. On a box plot, the median is the second line on the box.

The median is 27.

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The vertical intercept of the graph is 100,000

A function whose value is a constant raised to the power of the argument, especially the function where the constant is e, is called an exponential function.

Given that, the population p of migrating butterflies satisfies the exponential function p = 100,000 (4/5)ⁿ, where n is the number of weeks,

So, we need to find the vertical intercept of the graph,

We know that, vertical intercept = intercept

To find the y-intercept of a line, we will put x = 0,

here x is n,

So, the y-intercept of the graph is = 100,000 (4/5)⁰ = 100,000×1 = 100,000

Therefore, the vertical intercept of the graph is 100,000

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If sentence be "Seven subtracted from b is less or equal to -18" then the inequality be b – 7 ≤ -18

A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. Thus inequality emerges from an imbalance.

Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >, <, ≤ or ≥.

An inequality symbol represents that the expressions on each side are not equal. It indicates that the expressions on the left and right should be bigger or less than one another, or vice versa.

Let the given sentence be "Seven subtracted from b is less or equal to -18" then the inequality be b – 7 ≤ -18

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Answer:

Step-by-step explanation:

Straight line= 180 degrees

|_= 90 degrees

180-90=90

3s-2=52

2s+2=38

52+38=90

s=18

The trigonometric identities can be proved as follows;

32. Using the substitution, tan(x) = sin(x)/cos(x), and cot(x) = cos(x)/sin(x), we get;

cot(x) - tan(x) = (1 - 2·sin²(x))/(sin(x)·cos(x)) = sec(x)·(csc(x) - 2·sin(x))

36. tan(θ)/(1 + sec(θ)) = sin(θ)/(1 + cos(θ)) = (1 - cos(θ))/(sin(θ)) = -cot(θ) + csc(θ)

Trigonometric identities are equations involving trigonometric functions which are valid for the values of the input variable.

as follows;

cot(x) - tan(x) = sec(x)·(csc(x) - 2·sin(x))

The left hand side of the equation can be expressed using sin(x) and cos(x) as follows;

cot(x) = cos(x)/sin(x)

tan(x) = sin(x)/cos(x)

Therefore;

cot(x) - tan(x) = cos(x)/sin(x) - sin(x)/cos(x) = (cos²(x) - sin²(x))/(sin(x)·cos(x))

cos²(x) = 1 - sin²(x), therefore

(cos²(x) - sin²(x))/(sin(x)·cos(x)) = (1 - sin²(x) - sin²(x))/(sin(x)·cos(x))

(1 - sin²(x) - sin²(x))/(sin(x)·cos(x)) = (1 - 2·sin²(x))/(sin(x)·cos(x))

(1 - 2·sin²(x))/(sin(x)·cos(x)) = csc(x)·sec(x)·(1 - 2·sin²(x))

csc(x)·sec(x)·(1 - 2·sin²(x)) = sec(x)·(csc(x) - 2·sin(x))

Therefore;

cot(x) - tan(x) = csc(x)·sec(x)·(1 - 2·sin²(x)) = sec(x)·(csc(x) - 2·sin(x))

36. tan(θ)/(1 + sec(θ)) = -cot(θ) + csc(θ)

The left hand side can be manipulated as follows;

tan(θ) = sin(θ)/cos(θ)

sec(θ) = 1/cos(θ)

Therefore; tan(θ)/(1 + sec(θ)) = (sin(θ)/cos(θ))/(1 + (1/cos(θ)))

(sin(θ)/cos(θ))/(1 + (1/cos(θ))) = (sin(θ)/cos(θ))/((cos(θ) + 1)/(cos(θ)))

((sin(θ)/cos(θ))×cos(θ))/((cos(θ) + 1)/(cos(θ)) × cos(θ))) = sin(θ)/(cos(θ) + 1)

tan(θ)/(1 + sec(θ)) = sin(θ)/(cos(θ) + 1)

sin(θ)/(cos(θ) + 1) = sin(θ)/(1 + cos(θ)) × ((1 - cos(θ))/(1 - cos(θ)))

sin(θ)/(1 + cos(θ)) × ((1 - cos(θ))/(1 - cos(θ))) = ((sin(θ)·(1 - cos(θ))/(1 - cos²(θ)))

((sin(θ)·(1 - cos(θ))/(1 - cos²(θ))) = ((sin(θ)·(1 - cos(θ))/(sin²(θ)) = (1 - cos(θ))/(sin(θ))

sin(θ)/(cos(θ) + 1) =  (1 - cos(θ))/(sin(θ)) = csc(θ) - cot(θ) = -cot(θ) + csc(θ)

tan(θ)/(1 + sec(θ)) = sin(θ)/(cos(θ) + 1) = -cot(θ) + csc(θ)

Therefore;

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According to the diagram, angle JKL is

Adjacent angles are angles that share a common vertex and a common side, but do not overlap. In a trapezoid, adjacent angles can be any pair of angles that share a common vertex and a common side.

angle JKL and angle MKL are adjacent angels having same vertex at k

angle JKM = angle JKL  angle MKL

94 = angle JKL + 47

angle JKL = 94 - 47

angle JKL = 47

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Answer:

The height of the triangle is 14 m,

Step-by-step explanation:

Let the base be x, then the height is:

The area is half the product of base and height.

Set up equation and solve for x:

The first root is discarded as negative. The second root is the answer.

The base is 3 m, so the height is:

Answer:

The height of the triangle is 14 m.

Step-by-step explanation:

The area of a triangle can be found by using the following formula:

[tex]\boxed{A=\dfrac{1}{2}bh}[/tex]

where:

If the height of a triangle is 8 m more than twice the length of the base, then an expression for h in terms of b is:

[tex]h = 2b + 8[/tex]

Rewrite this equation to make b the subject:

[tex]\implies 2b=h-8[/tex]

[tex]\implies b=\dfrac{1}{2}h-4[/tex]

Given the area of the triangle is 21 m², substitute this value along with the found expression for b into the formula for area of a triangle:

[tex]\implies \dfrac{1}{2}\left(\dfrac{1}{2}h-4\right)h=21[/tex]

To find the height of the triangle, solve the equation for h.

[tex]\implies \dfrac{1}{4}h^2-2h=21[/tex]

[tex]\implies h^2-8h=84[/tex]

[tex]\implies h^2-8h-84=0[/tex]

[tex]\implies h^2-14h+6h-84=0[/tex]

[tex]\implies h(h-14)+6(h-14)=0[/tex]

[tex]\implies (h+6)(h-14)=0[/tex]

Apply the zero-product property:

[tex]h+6=0 \implies h=-6[/tex]

[tex]h-14=0 \implies h=14[/tex]

As length cannot be negative, the height of the triangle is 14 m.

Using the equation of the arithmetic sequence given, the first four terms are 59, 52, 45 and 38 respectively

In the sequence given, the progression is an arithmetic progression since it increases by a common difference.

The first term of the sequence is 59 while the common difference is -7.

A = 59 - 7(n - 1)

n = 1

a = 59 - 7(1 - 1)

a = 59

n = 2

a = 59 - 7(2 - 1)

a = 52

n = 3

a = 59 - 7(3 - 1)

a = 45

n = 4

a = 59 - 7(4 - 1)

a = 38

The terms are 59, 52, 45 and 38

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Translation:  Find the first four terms of the sequence given the following

Answer:

D

Step-by-step explanation:

It's the most random and produces no bias.

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

A) In a geometric sequence, t_(1)=625 and the common ratio is r=(1)/(5). For what value of n is t_(n)=(1)/(25)?

Step 1: Write the formula for the nth term

The formula for the nth term of a geometric sequence is t_n = t_1 * r^(n-1), where t_1 is the first term and r is the common ratio.

Step 2: Substitute the given values into the formula

t_n = 625 * (1/5)^(n-1)

Step 3: Solve for n when t_n = (1/25)

(1/25) = 625 * (1/5)^(n-1)

(1/25) / 625 = (1/5)^(n-1)

(1/5)^(n-1) = (1/25) / 625

(n-1) = log base (1/5) of ((1/25) / 625)

Step 4: Solve for n

n = 1 + log base (1/5) of ((1/25) / 625)

The value of n is the number of terms that have passed when t_n = (1/25).

B) (2)/(5),(3)/(6),(4)/(7),(5)/(8),...

Step 1: Determine the type of sequence

A sequence is an arithmetic sequence if the difference between any two consecutive terms is constant. Since this sequence does not have a constant difference, it is not an arithmetic sequence.

A sequence is a geometric sequence if the ratio between any two consecutive terms is constant. We can see that the ratio between any two consecutive terms is constant, so this sequence is a geometric sequence.

Step 2: Find the common ratio

To find the common ratio, we can divide any two consecutive terms. For example, the common ratio is (3/6) / (2/5) = (3/2) / (6/5) = 5/6.

Step 3: Write the formula for the nth term

The formula for the nth term of a geometric sequence is t_n = t_1 * r^(n-1), where t_1 is the first term and r is the common ratio.

Step 4: Substitute the given values into the formula

To use this formula, we need to know the value of t_1. We are given t_1 = (2/5), so:

t_n = (2/5) * (5/6)^(n-1)

This is the formula for the nth term of the sequence (2)/(5),(3)/(6),(4)/(7),(5)/(8),...

The given graph is represented by the function ( x + 2 )(x - 1 )³(x - 3 ). The correct option is A.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

Graphing functions involve drawing a curve on the coordinate plane that represents the function. Every point on a curve (graph) that represents a function satisfies the function equation.

The graph is represented by the function,

( x + 2 )(x - 1 )³(x - 3 )

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Gaining instructional control is an important aspect of teaching and behavior management.

Instructional control is a term used in behavior analysis to describe a situation in which a teacher or other instructional agent has established the conditions necessary for effective teaching to occur.

Here are some strategies that can help you gain instructional control:

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The graph of the exponential function y = 0.5(2)^x on the domain -1 ≤ x ≤ 4 is given by the image presented at the end of the answer.

The range is given as follows:

0.25 ≤ y ≤ 8.

The standard definition of an exponential function is given as follows:

y = a(b)^x.

In which the parameters are given as follows:

The parameters for the function in this problem are given as follows:

a = 0.5, b = 2.

The numeric values are given as follows:

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The approximate margin of error for a survey based on 2,700 adults, when rounded to nearest thousand is 0.021.

In statistical surveys, the margin of error is a measure of the expected amount of random sampling error that is present in a survey's results. It is a range of values that is likely to contain the true value of the population parameter being estimated, with a certain degree of confidence.

In other words, the margin of error is the amount by which the sample estimate may differ from the true value of the population parameter.

The margin of error is affected by several factors, such as the size of the sample and the level of confidence. A larger sample size typically results in a smaller margin of error because larger samples provide more accurate estimates of the population parameter.

Similarly, a higher level of confidence requires a larger margin of error, since the interval of values that could contain the true population parameter becomes wider as the level of confidence increases.

Assuming a 95% level of confidence, the formula for calculating the margin of error is:

Margin of error = z * sqrt(p * (1 - p) / n)

where:

z is the z-score for the desired level of confidence (1.96 for 95%)

p is the sample proportion, which is the proportion of the sample that exhibits a particular characteristic of interest (e.g., the proportion of respondents who support a certain political candidate)

n is the sample size, which is the number of observations in the sample.

If the sample proportion is not known, it is common to use a value of 0.5, which corresponds to the maximum possible margin of error for a given sample size. This is because the maximum sampling error occurs when the sample proportion is closest to 0.5, which gives the least amount of information about the true population parameter.

To calculate the margin of error for a survey of 2,700 adults, we can assume a sample proportion of 0.5 and a 95% level of confidence. Plugging these values into the formula, we get:

Margin of error = 1.96 * sqrt(0.5 * (1 - 0.5) / 2700)

= 1.96 * sqrt(0.25 / 2700)

= 1.96 * 0.008

= 0.016

Rounding to the nearest thousandth, the approximate margin of error is 0.021. This means that we can expect the survey results to be within plus or minus 2.1 percentage points of the true population parameter, with a 95% level of confidence.

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Answer:

200 lb

Step-by-step explanation:

Let her original weight be [tex]x[/tex].

[tex]0.12x=24 \implies x=200[/tex]

The slope of the line containing (-1, 5) and (2, -4) will be negative 3.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

The points are (-1, 5) and (2, -4). Then the slope of the line is given as,

m = (5 + 4) / (- 1 - 2)

m = 9 / (-3)

m = - 3

The slope of the line containing (-1, 5) and (2, -4) will be negative 3.

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The answers include the following:

This is referred to as a system of government where the citizens of a state exercise power to rule the state, either directly or through electing representatives.

Decisions take much longer because the people have a say in them through the process of voting and is therefore the reason why it was chosen as the correct  choice.

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Answer:

Step-by-step explanation:The form or system of government which gives the most power to the people of the nation is Democracy.

The new prime minister is part of the lawmaking branch and answers to it which means that the system of government is parliamentary.

When they wrote the Constitution, they gave more power to the central government. The states still have authority within their borders but must follow the Constitution and its laws which depicts Confederation.

“Decisions take much longer because the people have a say in them therefore the section of the chart which you would place this statement is Democracy.

Answer: Janelle can fill 6 feeders.

Step-by-step explanation:

To find the number of feeders Janelle can fill, we need to divide the total amount of bird food she has by the amount of bird food each feeder can hold.

First, let's convert the total amount of bird food from cups to half-cups:

3 cups / 2 = 6 half-cups

So, Janelle has 6 half-cups of bird food, and each feeder can hold 1 half-cup.

Therefore, she can fill:

6 half-cups / 1 half-cup per feeder = 6 feeders.

So, Janelle can fill 6 feeders.

When the surface area of the cell phone is converted to Cm² it would be. = 59cm²

The surface area of the cell phone screen = 5900mm²

But 10 mm = 1 cm

When squared after calculating the area,

100 mm² = 1 cm²

5900 mm² = X cm²

Make X cm² the subject of formula;

X cm² = 5900/100 = 59cm²

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Answer:

Step-by-step explanation:

To solve the equation c = 3/7(wm + a) for m, we can isolate m on one side of the equation.

Here's the step-by-step process:

Distribute the 3/7:

c = 3/7 * wm + 3/7 * a

Subtract 3/7 * a from both sides:

c - 3/7 * a = 3/7 * wm

Divide both sides by 3/7 * w:

(c - 3/7 * a) / (3/7 * w) = m

And that's it! m is the value you're looking for. Just remember to use the values of c, w, and a that you have in your specific problem when you evaluate the expression.

[tex]m=\frac{7 c-a}{3w}.[/tex]

[tex]c=\frac{3}{7} (wm+a)[/tex]

Remember that dividing by a fraction is the same as multiplying by its multiplicative reciprocate. Hence, we may multiply by [tex]\frac{7}{3}[/tex] on both sides and it'd have the same efect as dividing by [tex]\frac{3}{7}[/tex].

[tex]\frac{7}{3} c=\frac{3}{7} (wm+a)*\frac{7}{3}[/tex]

The two fractions on the right side cancel each other out and we're left with:

[tex]\frac{7}{3} c=(wm+a)[/tex]

[tex]\frac{7}{3} c=wm+a[/tex]

[tex]\frac{7}{3} c-a=wm+a-a\\ \\\frac{7}{3} c-a=wm[/tex]

[tex]\frac{\frac{7}{3} c-a}{w} =\frac{wm}{w} \\ \\\frac{7 c-a}{3w} =m[/tex]

[tex]m=\frac{7 c-a}{3w}.[/tex]

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If you want to verify whether the answer is correct or not, you may take the original equation and plug the calculated value of "m" in the place of said variable. Then, if the equation returns the same value after simplifying completely, the solution is correct!

This step is show on the attached image.

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Answer:

3.4 x 10⁻²  kg · m²/s²

Step-by-step explanation:

[tex]3.4\times \:10^5=340000[/tex]

The numerator is in g.cm² and the denominator is the same s²

So we only need to convert the numerator from g.cm² to kg.m²

1 kg = 1000 grams = 10³ grams
1 gm = 1/10³ kg
1 gm = 10⁻³ kg

1 m = 100 cm = 10² cm

1 m² = 100² cm² = (10²)² = 10⁴ cm²

Or 1 cm² = 1/10⁴ cm² = 10⁻⁴ cm²

Therefore to convert g · cm² to kg · m² we multiply by

(10⁻³)  · (10⁻⁴) = 10⁻⁷

Therefore 3.4 x 10⁵ g · cm² =  3.4 x 10⁵ x 10⁻⁷ kg · m²

= 3.4 x 10⁻² kg · m²/s²

The value of summation of ( x-2)² is 973

A summation, also called a sum, is the result of arithmetically adding numbers or quantities. A summation always contains a whole number of terms. There can be as few as two terms, or as many as a hundred, a thousand, or a million. Some summations contain infinitely many terms.

if

x (x-2) ( x-2)²

15 13 169

13 11 121

13 11 121

4 2 4

19 17 289

12 10 100

6 4 16

5 3 9

14 12 144

Therefore the summation of (x-2)²

= 169+121+121+4+289+100+16+9+144 = 973

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Answer:answer

Step-by-step explanation:

The value of summation of ( x-2)² is 973

The domain of the function for this situation is given as follows:

B. All whole numbers greater than or equal to 0 and less than or equal to 7.

The domain of a function is the set that contains all the values assumed by the input of the function.

Hence, on a graph, the domain is given by the values assumes on the horizontal axis of the graph.

The values that compose the domain of the graph are given as follows:

0, 1, 2, 3, 4, 5, 6 and 7.

Which is best described by option B.

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Answer:

1.02n or 51/50n

Step-by-step explanation:

n + 2% raise = 1.02n and 50/51n