Two angles are complementary. The measurement of ∠GHI is (5x+6)∘ and ∠JKL measures (3x+4)∘. What are the measures of the two angles?

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Answer:

(8,-43)

(4,-22)

Step-by-step explanation:

In order for the ordered pair to be a solution of the inequality, you must be able to plug in the y-value of the ordered pair and it must be less than or equal to 0.

For example:

(4,-22)

x=4 ; y=-22

Plug y into the inequality

y≤0

-22≤0

Since the statement is true, I know that (4,-22) must be a solution to the inequality.

Another way to solve this problem is by graphing. If an ordered pair is in the shaded region, it is a solution to the inequality. Attached is a graph of both the inequality and ordered pairs plotted.

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Answer:

Step-by-step explanation:

To determine whether each ordered pair is a solution to the inequality y ≤ 0, we need to check if the y-coordinate of each pair is less than or equal to zero.

Let's check each ordered pair:

(8, -43):

The y-coordinate is -43. Since -43 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(4, -22):

The y-coordinate is -22. Since -22 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(-3, 25):

The y-coordinate is 25. Since 25 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

(-7, 45):

The y-coordinate is 45. Since 45 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

So, the solutions to the inequality y ≤ 0 are:

(8, -43) and (4, -22).

Answer:

72

Step-by-step explanation:

Answer:

Triangles are equal to 180° so 56+16 is 72 and 180-72 is 108 and every straight line is 180° so 180-108 is 72 and that angle would be 72°

The equation of the line would be y = (4/5)x + 4 which in slope-intercept form represents the graph.

The graph is given in the question.

As per the given line, we take two points (0, 4) and (5, 8)

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = 0, y₁ = 4

x₂ = 5, y₂ = 8

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute values in the equation, we get

⇒ y - 4 = (8 - 4)/(5-0 )[x -0]

⇒ y - 4 = (4/5)x

⇒ y = (4/5)x + 4

The given equation of the line y = 4x + 5 is incorrect because its slope is not correct.

So, the equation of the line would be y = (4/5)x + 4.

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Answer:

768

Step-by-step explanation:

64*12

Answer:

768

Step-by-step explanation:

12x64=768

Answer:

i) pi×4500 cm³

ii) pi×600 cm²

iii) 14 liters

Step-by-step explanation:

in general : the diameter is 30 cm, the radius is half of that (15 cm)

i)

the volume of a cylinder is base area times height.

Vc = pi×r²×h = pi×15²×20 = pi×225×20 = pi×4500 cm³

ii)

similar to volume, the side "mantle" area of the cylinder is the circumference of the base area times height.

surface area of the cylinder mantle is

Scm = 2×pi×r×h = 2×pi×15×20 = pi×30×20 = pi×600 cm²

iii)

for this we need now to do the multiplication with pi and then convert the cm³ to liters.

1 liter = a cube of 10 cm side length = 10×10×10 = 1000 cm³

pi×4500 = 14137.17 cm³ = 14.13717 liters or rounded 14 liters

The reflection of the point (–4, 6) across both axes is (b) (4, -6)

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

Point = (-4, 6)

The rule of reflections across both axes is

(x, y) = (-x, -y)

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

Image = (4, -6)

Hence, the reflection of the point (–4, 6) across both axes is (b) (4, -6)

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Answer:

The slope of the perpendicular line is \(-\frac{5}{3}\)

Step-by-step explanation:

Let us solve the question

∵ The equation of a line is y = \(\frac{3}{5}\) x - 8

→ The form of the equation is y = m x + b, where m is the slope

∴ The slope of the line is  \(\frac{3}{5}\)

→ To find the slope of the line perpendicular to it reciprocal it and

   reverse its sign

∵ The reciprocal of  \(\frac{3}{5}\)  is  \(\frac{5}{3}\)

→ Change its sign from positive to negative

∴ The slope of the perpendicular line is \(-\frac{5}{3}\)

Answer:

Can't be possible.

Step-by-step explanation:

Given:

6+7(x+75)=1

So according to given equation it can't be possible because when we add some value in 6 their result will be always greater than 1.

The length of DP in the diagram, where P is the triangle's circumcenter, is 15 units.

The point in the triangle where the perpendicular bisectors of its sides cross is known as the circumcenter.

The intersection of the perpendicular bisectors of a triangle's sides is referred to as the triangle's circumcenter. In other terms, the circumcenter is the point at where a triangle's sides intersect to form a bisector.

In the triangle given where P exists the circumcenter, we have:

AD = DB

Substitute the values in the above equation, we get

2x + 14 = 8x - 52

simplifying the above equation, we get

2x - 8x = -14 - 52

-6x = -66

x = 11

AD = 2x + 14

Plug in the value of x

AD = 2(11) + 14

simplifying the above equation, we get

AD = 36

Also, AP = BP = CP = 39

AP = 39

Considering right triangle, ADP, to find DP, apply the Pythagorean theorem:

DP = √(AP² - AD²)

substitute the values in the above equation, we get

DP = √(39² - 36²)

DP = 15 units.

Therefore, the length of DP in the diagram, where P is the triangle's circumcenter, is 15 units.

The complete question is:

If P is the circumcenter of triangle ABC, find each measure.

Find DP.

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Answer: The length is 14cm

Step-by-step explanation:

52=2(2x-2)

26=2x-2

28=2x

x=28/2=14

Answer:

\(\huge \boxed{{m=6}}\)

Step-by-step explanation:

Let's take two points,

(12, -4) and (13, 2).

slope = (difference of y) / (difference of x)

m = (2 - - 4) / (13 - 12)

m = (2 + 4) / 1

m = 6 / 1 = 6

The slope of the line is 6.

Answer:

6

Step-by-step explanation:

The slope is the change in y over the change in x

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

    = (14-8)/(15-14)

   = 6/1

Answer:

False

Step-by-step explanation:

Answer:

go Amoeba and Paramecium.

Step-by-step explanation:

1) If the Midpoint of AB is (4,2) let's find the endpoint, given that the coordinates of A are (6,-4).

Let's find the coordinates of B:

6 + x_2 =2 x 4

6+ x_2=8

x_2=8-6

x_2 =2

-4+y_2= 2 x 2

-4 +y_2=4

y_2=4+4

y_2=8

So the coordinates of B is (2, 8)

The third side of the triangle 12.5

A triangle is a polygon with three edges and three vertices. The important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

we the measurements of given two sides of the triangle 16.5 and 29

In a triangle, the sum of any two sides should be greater than the third side and the difference between any two sides should be lesser than that of the third side.

The sum of two sides rule

\(x + 16.5 > 29\\ x > 29 - 16.5\\ x > 12.5\\\)

The difference between the two sides rule

\(29 - 16.5 < x \\ 12.5 < x\)

Therefore, the value of x is 12.5

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Answer:

1/15

Step-by-step explanation:

\(7/24 * 8/35\)

\(1/3*1/5=1/15\)

Step-by-step explanation:

\( \frac{7}{24} \times \frac{8}{35} \\ \\ = \frac{1}{3} \times \frac{1}{5} \\ \\ = \frac{1}{15} \)

Answer:

Step-by-step explanation:

\(h(x) = - 49x - 125\)

To find h(-67) , substitute the value of x that's - 67 into h(x). That is for every x in h(x) , replace it with - 67

We have

\(h( - 67) = - 49( - 67) + 125 \\ = 3283 - 125\)

We have the final answer as

Hope this helps you

Answer: 3 then 0

Step-by-step explanation:

Answer:

the whole thing is 174

Step-by-step explanation:

Answer:

C. (9, 26)

Step-by-step explanation:

By Substitution:

y = 2x + 8

y = 3x - 1

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

2x + 8 = 3x - 1

-x + 8 = -1

-x = -9

x = 9

Now we can choose either of the two equations given to solve for y:

y = 2x + 8

y = 2(9) + 8

y = 18 + 8

y = 26

(9, 26)

By Elimination:

For this process, I am going to rewrite the equation in "x + y" for as it will make it easier to eliminate the variables

y = 2x + 8

2x - y = -8

y = 3x - 1

-3x + y = -1

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

2x - y = -8

-3x + y = -1

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

-x = -9

x = 9

2x - y = -8

2(9) - y = -8

18 - y = -8

-y = -26

y = 26

(9, 26)

Answer: x < 2

Step-by-step explanation:

First subtract 1 on both sides

2x < 4

Then divide both sides by 2

x < 2

Hey there!

2x + 1 < 5

SUBTRACT 1 to BOTH SIDES

2x + 1 - 1 < 5 - 1

SIMPLIFY IT!
2x < 5 - 1

2x < 4

DIVIDE 2 to BOTH SIDES

2x/2 < 4/2

SIMPLIFY IT!
x < 4/2

x < 2

Therefore, your answer is: x < 2

(The graph is down below)

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

More than 65% of people are right-handed, hence the assertion is true.

People who are right-handed: Since A hypothesis test is performed with a 5% level of significance. According to the alternate theory, more than 65% of people are right-handed. The test's p-value is calculated to be 0.03

Therefore, based on this, we may estimate that more than 65% of the population is right-handed.

As a result, choice c is the right one.

The complete question is:

A hypothesis test is conducted with a significance level of 5%. The alternative hypothesis states that more than 65% of a population is right-handed. The p-value for the test is calculated to be 0.03. Which of the following statements is correct?

a .We can conclude that more than 3% of the population is right-handed.

b .We cannot conclude that more than 65% of the population is right-handed.

c .We can conclude that more than 65% of the population is right-handed.

d .We can conclude that exactly 3% of the population is right-handed.

e .There is not enough information given to make a conclusion.

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Answer:

5.8%

Step-by-step explanation:

To find the average growth on Alexandra's total investment, we need to calculate the weighted average of the growth in each of the three investments. The weighted average is calculated by multiplying the growth of each investment by its proportion of the total investment and then adding them together.

First, we need to calculate the total amount of money that Alexandra invested. Since he invested 40% in mutual funds, 40% in real estate, and 20% in stocks, we can assume he invested $100.

So the amount invested in mutual funds is 40/100 * $100 = $40

The amount invested in real estate is 40/100 * $100 = $40

The amount invested in stocks is 20/100 * $100 = $20

Then we can calculate the growth of each investment using the percentages provided:

The growth of mutual funds is 2/100 * $40 = $0.80

The growth of real estate is 7/100 * $40 = $2.80

The growth of stocks is 11/100 * $20 = $2.20

Now we can add up the growth of each investment and divide it by the total investment to find the average growth:

($0.80 + $2.80 + $2.20) / $100 = $5.80 / $100 = 0.058 or 5.8%

So the average growth on Alexandra's total investment is 5.8%.

The probability that the mean amount of cereal in 5 randomly selected boxes is at most 9.65 ounces is 0.4808.

The Central limit theorem is used to find the probability

Data given:

sample size = 5.

mean, μ = 9.70 ounces

standard deviation, σ = 0.03 ounce.

To calculate the probability, we determine the z-score corresponding to the sample mean of 9.65 ounces using the z-score formula.

x is the sample mean,

μ is the population mean,

σ is the population standard deviation, and

n is the sample size.

For the sample mean of 9.65 ounces in 5 boxes:

z = (9.65 - 9.70) / (0.03 / √5)

z ≈ -0.05 / (0.03 / √5)

Using a calculator, we find that the probability is approximately 0.4801.

Therefore, the probability that the mean amount of cereal in 5 randomly selected boxes is less than 9.65 ounces is approximately 0.4801.

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Answer: $36

Explanation: Find the unit rate and then multiply by 9. Unit rate is 4.

Answer:

Answer is E hope this helps :)

Step-by-step explanation:

Answer:

17x+7y+10

Step-by-step explanation:

y+4+3(y+2)

you have to multiply 3 by the numbers/variables in the parenthesis

y+4+3y+5

Do the same to the other equation

5x+3(y+4x)

5x+3y+12x

Set an equation that will let you add their like terms.

y+4+3y+5+5x+3y+12x

I'm going to add like terms with the y

y+3y+3y = 7y

Now like terms with x

5x+12x = 17x

Now put them all as a single equation

17x+7y+10

Answer:

1050

Step-by-step explanation:

Multiply 150 by 7