Solve the system of linear equations by graphing y=-1/2x+6 and y=1/2x+6

The Triangle ABC having perimeter 22cm and AB = 8cm and BC =5cm is not a right angled triangle.

A triangle to have a right angle triangle it should follow the basic theorem of Pythagoras,

If perimeter of ΔABC is 22cm

P = AB + BC + AC

22 = 8 + 5 + AC

AC = 9

By using Pythagoras theorem ,

AC² = AB² + BC²

9² = 8² + 5²

81 ≠ 89

Therefore its not a right angle triangle.

A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle. The right triangle or 90-degree triangle is another name for this triangle. In trigonometry, the right triangle is significant.

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The  temperature when the plane reaches an altitude of ​3000ft is 51.8 F

Temperature is the degree of hotness or coldness of an object.

Given here: the temperature drops every 1.2 F for every thousand feet ascend.

Thus if the temperature on the ground is 55.4 F

When the plane ascends to 3000 feet the number of temperature drops would be 3 .

Thus drop in temperature is 1.2×3=3.6 F

Therefore the temperature at an altitude at an altitude of 3000 ft. is

55.4-3.6=51.8 F

Hence, The  temperature when the plane reaches an altitude of ​3000ft is 51.8 F

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The inequality graph is interpreted to have the equation as;

y  > ⁻³/₄x - 3

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

From the given graph, the y-intercept is seen to be -3.

The slope is gotten by using two coordinates from the formula;

m = (y₂ - y₁)/(x₂ - x₁)

(0, -3) and (-4,0)

m = (0 - (-3))/(-4 - 0)

m = -3/4

Thus, equation of line is;

y = ⁻³/₄x - 3

Since the upper part of the inequality is shaded and the line is a dashed line, then the symbol is greater than and it is expressed as;

y  > ⁻³/₄x - 3

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Answer:

Step-by-step explanation:

answer 10857.3

mean score of the students who failed the test is 4

Let's assume there were X students who took the test.

Here given that:

The mean score of the students who took a mathematics test was 6.

60% of the students passed the test.

The sum of all their scores was 6× X

X×0.6 of them had a mean score of 8

The sum of the scores of the students who passed the test is 8 ×X×0.6.

The sum of the scores of the students who failed was the total sum minus the sum of the scores of the students who passed, which is

6 × X - 8 × X ×0.6

students who failed the test is, divide by the sum of their scores by the number of students who failed, which is

X - X ×0.6.

The mean score of the students who failed is

(6 ×X - 8 × N ×0.6) / (X - X×0.6)

= (6 × X - 8× X × 0.6) / (X * 0.4)

= 4.

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When determining sample size for the first test, it is most important to Weigh the potential consequences of a test that does not lead to improvement against the belief in success.

When evaluating a patient, a patient assessment form is used to evaluate the patient's potential diagnosis and the appropriate course of therapy. To prevent misdiagnosis and ensure that the right therapy is given, it is crucial to gather relevant data. In order to register patients for operations provided by medical institutions, patient registration forms are utilised. Our free patient registration forms will efficiently capture patient information online, streamlining the registration and onboarding process whether you need to register new patients for your hospital, clinic, health centre, or private practise. Usability testing may find and support data-driven design decisions that have been drawn from practitioner usage of the system in a hectic office setting. Health care safety may be improved by using human factors understanding of HCI design and its effects on human performance.

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Answer: It will take 63 minutes for the group to make a wood pile of 45 sticks

Step-by-step explanation:

i hope this helps if so pls mark brainliest !!

Answer:

Below

Step-by-step explanation:

Domain is the 'x' values a function can have   for this one  {1,3,4,5}

Range is the 'y' values a function has   {6,8,10}

The equation of the line that passes through (4,2) and is parallel to the line shown is 3x + y = -10

An equation is an expression that shows the relationship between two or more numbers and variables.

The slope intercept form of a line is:

y = mx + b

where m is the slope and b is the y intercept

Two lines are said to be parallel if they have the same slope.

The line shown passes through point (0, 1) and (-1, -2). Hence:

Slope = (-2 - 1) / (-1 - 0) = 3

The line parallel will also have a slope of 3. It then passes through (4, 2). Hence:

y - y₁ = m(x - x₁)

y - 2 = 3(x - 4)

y = -3x - 10

3x + y = -10

The equation of the line is 3x + y = -10

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Answer:

To figure out how many adults and children bought tickets, we can set up a system of equations using the information provided. Let x be the number of adults and y be the number of children. We know that:

x + y = 500 (because a total of 500 people bought tickets)

17.95x + 12.95y = 7355 (because the total revenue from ticket sales is $7355)

We can use the first equation to solve for one of the variables in terms of the other variable. For example, we can substitute y = 500 - x into the second equation:

17.95x + 12.95(500 - x) = 7355

This simplifies to:

17.95x + 6475 - 12.95x = 7355

5x = 1880

x = 376

so there are 376 adults bought tickets and 500-376=124 children bought tickets.

Step-by-step explanation:

Answer:

he would only be able to bring 2 friends

Step-by-step explanation:

250- 100= 150    cost of table

150/ 40=3.75   cost of friends

He was would not be able to bring a .75 of a friend so you would have to round down.

We can substitute the first equation into the second to eliminate [tex]y[/tex] and solve for [tex]x[/tex]

[tex]$$\begin{gathered}-x+4\left(\frac{1}{4} x-3\right)=-4 \\\Rightarrow \\-x+x-12=-4 \\\Rightarrow \\-12=-4 \\\Rightarrow \\x=3\end{gathered}$$[/tex]

An infinite solution has both sides equal. For example, 6x + 2y - 8 = 12x +4y - 16. If you simplify the equation using an infinite solutions formula or method, you'll get both sides equal, hence, it is an infinite solution. Infinite represents limitless or unboundedness. It is usually represented by the symbol ” ∞ “.

Some equations have infinitely many solutions. In these equations, any value for the variable makes the equation true. You can tell that an equation has infinitely many solutions if you try to solve the equation and get a variable or a number equal to itself.

This system of linear equations can be graphed on a [tex]$x-y$[/tex] plane. The first equation represents a line with slope [tex]\frac{1}{4}[/tex] and [tex]$y$[/tex]-intercept [tex]-3[/tex]. The second equation represents another line with slope [tex]-1[/tex] and [tex]$y$[/tex]-intercept [tex]-4[/tex]. The intersection point of the two lines is the solution to the system of linear equations.

To find the solution, we can substitute the first equation into the second to eliminate [tex]y[/tex] and solve for [tex]x[/tex]

[tex]$$\begin{gathered}-x+4\left(\frac{1}{4} x-3\right)=-4 \\\Rightarrow \\-x+x-12=-4 \\\Rightarrow \\-12=-4 \\\Rightarrow \\x=3\end{gathered}$$[/tex]

We can then use either equation to find the value of [tex]y[/tex]

[tex]$$\begin{gathered}y=\frac{1}{4} x-3 \\\Rightarrow \\y=\frac{1}{4} \cdot 3-3 \\= \\y=-2\end{gathered}$$[/tex]

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The function f(x) and the number [tex]a[/tex] that satisfies the given equation is:[tex]$$f(x)=x^{3 / 2} \quad \text { and } \quad a=\frac{49}{4} .$$[/tex]

Let's differentiate both sides of the given equation with respect to [tex]x[/tex] obtain

[tex]\frac{d}{d x}\left[5+\int_a^x \frac{f(t)}{t^2} d t\right]=\frac{d}{d x}[2 \sqrt{x}] .[/tex]

The Fundamental Theorem of Calculus combines the concepts of differentiating a function (calculating the slope or rate of change at any point in time) and integrating a function (calculating the area under a graph, or calculating the cumulative effect ) is a combination of of small contributions). 

Using the Fundamental Theorem of Calculus and the Power Rule, we have

[tex]\frac{d}{d x}\left[\int_a^x \frac{f(t)}{t^2} d t\right]=\frac{d}{d x}\left[2 x^{1 / 2}\right][/tex]

Applying the Chain Rule and simplifying, we get

[tex]\frac{f(x)}{x^2}=x^{-1 / 2}[/tex]

Solving for [tex]f(x) \$$, we get $\$ f(x)=x^{\wedge}(3 / 2\}[/tex].

To find a, we can use the given equation with x=1 and simplify:

[tex]$$5+\int_a^1 \frac{f(t)}{t^2} d t=2 \sqrt{1} \Rightarrow \int_a^1 \frac{f(t)}{t^2} d t=-3 .$$[/tex]

Substituting [tex]$ f(x)=\mathrm{x}^{\wedge}[3 / 2\}[/tex], we have

[tex]$$\int_a^1 \frac{f(t)}{t^2} d t=\int_a^1 \frac{t^{3 / 2}}{t^2} d t=\int_a^1 t^{-1 / 2} d t=2(\sqrt{1}-\sqrt{a})=-3$$[/tex]

Solving for a, we obtain [tex]a=\backslash f r a c\{49\}\{4\}[/tex]. Therefore, the function f(x) and the number [tex]a[/tex] that satisfy the given equation are

[tex]$$f(x)=x^{3 / 2} \quad \text { and } \quad a=\frac{49}{4} .$$[/tex]

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Answer:

4x-6=-5y+9

4×=-5y+9+6

Answer:2 45833333333/50000000000

The measure of angle R is 16.1°

Law of Sines In trigonometry, an equation relating the lengths of the sides of any triangle to the sines of its angles.

Given that, a triangle RST, with one angle S = 39° and RT = 25, ST = 11

We need to measure the angle R,

Using law of sine,

Sin R / TS = Sin T / RS = Sin S / RT

Sin R / 11 = sin 39° / 25

Sin R = 11 × sin 39° / 25

Sin R = 0.2769

R = sin⁻¹(0.2769)

R = 16.1

Hence, the measure of angle R is 16.1°

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Answer:

[tex]The[/tex] [tex]length[/tex] [tex]of[/tex] [tex]BC[/tex] [tex]is[/tex] [tex]\sqrt{55}[/tex] [tex](units)[/tex].

Step-by-step explanation:

Given ABC is a right triangle.

AC is the hypotenuse and BD is the altitude.

AB and BC are legs of the triangle ABC.

AC = 11 and DC = 5

Leg rule of geometric mean theorem:

[tex]\frac{hypotenuse}{leg}=\frac{leg}{part}[/tex]

[tex]\frac{AC}{BC}=\frac{BC}{DC}[/tex]

[tex]\frac{11}{x}=\frac{x}{5}[/tex]

Do cross multiplication.

[tex]11 * 5= x*x[/tex]

[tex]55=x^{2}[/tex]

Taking square root on both sides.

[tex]\sqrt{55} =\sqrt{x^{2} }[/tex]

[tex]\sqrt{55}=x[/tex], [tex]since[/tex] [tex]\sqrt{55}[/tex] [tex]cannot[/tex] [tex]be[/tex] [tex]reduced.[/tex]

The length of BC is [tex]\sqrt{55}[/tex].

Answer:

138°

Step-by-step explanation:

∠BCD and ∠CDB are equivalent, meaning they both are 48°.  Together, that is 96°.  Subtract 96° from 180° (the measure of all of the inside angles in a triangle added together.) and you get 84°.  Subtract 84° from 360° (the number of degrees in a circle) and you get 276°.  Divide that by two (∠ABD and ∠ABC) to get 138°.

At the point of tangency, a tangent to a circle is perpendicular to the radius.

A tangent is a line that extends from a point on the circle to two points that are eternally close to one another. To put it another way, we can say that tangents are lines that precisely cross a circle at a certain location. Where the tangent touches the circle is known as the point of tangency. An angle is tangent to the radius at the point of tangency. This is a key component of geometric constructions and proofs, and as such, it is related to a number of theorems. One by one, we will examine them.

Theorem: 1

By connecting the center with the point of tangency, a radius is produced. A circle's tangent at a given location is perpendicular to its radius. Simply adhere to the diagram below: Here AB⊥OP

Theorem:2  

According to this theorem, two tangents traced to a circle from a single exterior point have equal numbers of tangent segments. Line connecting the exterior point and the point of tangency is referred to as a tangent segment.

Hence the theorem of the tangent of circle mentioned above.

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Complete question:

At the point of tangency, a tangent to a circle is ______ to the radius.

We can see here that the division expression that is shown in the model is: A. 3 ÷ 2/5

Division is a mathematical operation that involves splitting a number into equal parts. It is the inverse of multiplication, and can be represented as the division symbol "/" or "÷". The result of division is called a quotient.

Division in mathematics is an arithmetic operation that separates a quantity into equal parts or groups. Division can also be expressed as a fraction or ratio, where the numerator represents the dividend and the denominator represents the divisor.

We see here that:

3  ÷ 2/5 = 3/1 x 5/2 = 15/2

∴ 15/2 = 7.5.

We can see here that the shaped boxes in the diagram are 7 that were fully shaded. The last box was shaped half. This actually shows it is 7.5.

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The intersection of the graphs of the inequalities is shown by a compound inequality with a "and" in it.

When two inequalities are separated by "and" or "or," the result is a compound inequality. The intersection of the graphs of the inequalities is shown by a compound inequality with a "and" in it. A number is a compound inequality solution if it also solves the underlying inequality.

Divide a compound inequality into two individual inequalities before solving it. The solution should either be a union of sets ("or") or an intersection of sets ("and"). Inequalities and the graph should then be solved.

Compound inequality comes in two flavors. Both conjunction and disjunction issues are present. Sometimes, the two simple inequalities in these compound inequalities will be separated by the words AND or OR. When resolving compound "and/or" inequalities, start by resolving each inequality separately.

Therefore, the correct answer is option D.

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The cafe served 72 regular coffees.

Here are the steps to find the number of regular coffees served:

The method used for this problem is simple arithmetic calculation, specifically percent calculation.

Percent calculation is used to find the proportion of a number in terms of a percent. To perform a percent calculation, you multiply the original number by the percent (expressed as a decimal) and then round the result to the desired number of decimal places. In this case, the original number is 80 and the percent is 90, which we first convert to 0.90 (by dividing by 100).

You could determine that this method was used because the problem statement asked for the proportion of regular coffee in terms of percent (90%) of the total number of coffees served (80). To find this proportion, you needed to multiply 80 by 0.9, which is equivalent to 80 * 90%.

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Answer:

:)

Step-by-step explanation:

Just divide 1,004.7 by 59.1

Step-by-step explanation: To find the values of l and m, we need to solve the equation 15 - 28i = 3l + (4m)i for l and m.

First, we can move all the terms with i to one side of the equation:

15 = 3l + 4mi

-28i = 4mi

To solve for m, we can divide both sides by 4i:

-28i/4i = m

m = -7

Now that we know the value of m, we can substitute it back into the equation to solve for l:

15 = 3l + 4(-7)i

15 = 3l - 28i

3l = 15 + 28i

To solve for l, we can divide both sides by 3:

l = (15 + 28i)/3

So the values of l and m are l = (15 + 28i)/3 and m = -7

Answer:15

Step-by-step explanation:

Aaron should answer 3 open-ended questions and 0 multiple-choice questions to get a maximum of 3 * 20 points/question = 60 points

Aaron has 45 minutes to answer the questions, so he has 45 minutes / 15 minutes/question = 3 open-ended questions that he can answer.

For the remaining questions, he has 45 minutes - (3 * 15 minutes) = 45 minutes - 45 minutes = 0 minutes.

So he cannot answer any more open-ended questions.

He can answer 0 minutes / 1 minute/question = 0 multiple-choice questions.

Therefore, Aaron should answer 3 open-ended questions and 0 multiple-choice questions to get a maximum of 3 * 20 points/question = 60 points.

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Answer:

in 2014=4100 in 2008=6800 last question=2020

Step-by-step explanation:

multiply (-5+i) and 2i with 2i

2i × 2i = 4i^2 ➡-4

2i × (-5+i) = -10i + 2i^2 ➡-10i -2

then do the division

(-10i -2)/-4 = (5i + 1)/2

Answer:

I think its this, anns gym membership: y=$5x+$20
blakes gym membership: y= $3x+$30

i don’t understand the last question, I apologize if this is wrong.

Answer:

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

Step-by-step explanation:

Attached is an image of the function graphed. From the image, you can see that the only zero, or x-intercept, is at about -0.327, or [tex]\sqrt[3]{2}[/tex] to be exact.

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Inverse of v(R) = R/(2Gv^2) where G is the universal gravitational constant and v is the escape velocity.

The equation for the escape velocity from a planet of mass M and radius R is v(R) = √(2GM/R). To find the inverse of v(R), we can start by rearranging the equation to solve for R. We can do this by multiplying both sides of the equation by R, giving us 2GM = Rv(R)^2. Then, we can divide both sides of the equation by 2G, leaving us with R = v(R)^2/2G. Now, we can substitute v for v(R). This gives us R = v^2/2G. To find the inverse of v(R), we can take the reciprocal of both sides, giving us the inverse of v(R) as R/(2Gv^2).

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Answer:

6/11

Step-by-step explanation:

Mammal - yes

Giraffe - no

Seal - no

Mouse - no

Cat - no

Tiger - no

Bat - yes

Can fly - yes

Swan - yes

Lizard - no