Find the gradient of the line 2y = 8x + 1

Find the y-intercept of the line 4y + 8x = -8

Bonus = Does the point (1 ,12) lie on the line y = 3x + 8 ? =

Does the point (-2 ,10) lie on the line y = 14 + 2x

Answer:

Discriminant=8

Step-by-step explanation:

-x²+4x-2=0

here a=-1,b=4 and c=-2

Discriminant=b²-4ac

Discriminant=(4)²-4(-1)(-2)

Discriminant=16-8

Discriminant=8

i hope this will help you :)

I'm pretty sure that ' HL ' stands for "hypotenuse and leg". That's the one.

-- We see the little boxes in the lower left corners, so we know that these are right triangles, and we can use the rules we know about for right triangles.

-- The hypotenuses of both triangles are marked with the same length.

-- The base legs of both triangles are marked with the same length.

-- So we have (the hypotenuse and one leg of one right triangle) equal to (the hypotenuse and corresponding leg of another right triangle). That's exactly the description of the HL conguence theorem, so we know that these two triangles are congruent.

Answer:

7/ (3a-1)

Step-by-step explanation:

3a^2 -13a +4        28+7a

------------------ * --------------------

9a^2 -6a+1         a^2 -16

Factor

(3a-1)(a-4)           7(4+a)

------------------ * --------------------

(3a-1) (3a-1)        (a-4)(a+4)

Cancel like terms

1                    7

------------------ * --------------------

(3a-1)                  1

Leaving

7/ (3a-1)

Answer:

  x = 17.349

Step-by-step explanation:

The right-most x-intercept is 17.349, where the curve continues upward to the right.

Answer:

Rebekah, the height of a hemisphere is its radius. The volume of a sphere is 4/3 π r3. So the volume of a hemisphere is half of that: V = (2 / 3) π r3.

Answer:

V = (2 / 3) π r3.

Step-by-step explanation:

1/2 x 4/3 x π r3 = 2/3π r3

i think it is ur required ans..

Answer:

d

Step-by-step explanation:

Answer:

357 mi²

Step-by-step explanation:

The shape is made of a triangle and a half-square

we will calculate the area of each one

let A1 be the area of the half-circle:

A1= (10²*π)/2 = 50π mi²

Let A2 be the area of the triangle:

A2= 10*20=200 mi²

let At be the total area:

At =A1+A2= 200+50π =357.07≈ 357 mi²

Answer:

a) 135 seconds

b) 3.71 standard deviations below the mean

c) Z = -3.71

d) Unusual

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]\mu = 245, \sigma = 36.4[/tex]

a. What is the difference between a duration time of 110 sec and the mean?

Duration of 110 seconds.

Mean of 245

245 - 110 = 135 seconds

b. How many standard deviations is that (the difference found in part (a))?

This is |Z|

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{110 - 245}{36.4}[/tex]

[tex]Z = -3.71[/tex]

[tex]|Z| = 3.71[/tex]

3.71 standard deviations below the mean

c. Convert the duration time of 110 sec to a z score

From b, Z = -3.71

d. If we consider "usual" duration times to be those that convert to z scores between -2 and 2, is a duration time of 110 sec usual or unusual?

Z is not in the interval of -2 and 2, so a duration time of 110 sec is unusual

Answer:

(B)24 Units

Step-by-step explanation:

Triangle MNO is an equilateral triangle with sides  measuring [tex]16\sqrt{3}[/tex] units.

The height divides the base into two equal parts of lengths [tex]8\sqrt{3}[/tex] units.

As seen in the diagram, we have a right triangle where the:

Using Pythagoras Theorem

[tex](16\sqrt{3})^2=(8\sqrt{3})^2+h^2\\16^2*3-8^2*3=h^2\\h^2=576\\h=\sqrt{576}\\ h=24$ units[/tex]

The height of the triangle is 24 Units.

The height of the given equilateral triangle is gotten as;

B: 24 units

Equilateral Triangles

The height of an equilateral triangle starts from the mid - point of the base to the ap ex.

Now, if the sides of the equilateral triangle are 16√3 units, then it means we can use pythagorean theorem to find the height h.

Half of the base will be; ¹/₂ * 16√3 = 8√3

Thus, the height h can be calculated from;

h²= ((16√3)² - (8√3)²)

h² = 3(256 - 64)

h² = 576

h = √576

h = 24 units

Read more about equilateral triangles at; https://brainly.com/question/4293152

Answer:

Step-by-step explanation:

To solve for c we use the formula for Pythagoras theorem

That's

a² = b² + c²

Where a is the hypotenuse

From the question above

c is the hypotenuse

So we have

c² = 9² + 7²

c ² = 81 + 49

c² = 130

Find the square root of both sides

Hope this helps you

Answer:

c=√130

Step-by-step explanation:

In order to solve this question, you have to know the Pythagorean Theorem. The Pythagorean Theorem uses this equation: a^2 + b^2 = c^2. The letters indicate one side of the triangle, but c is always the longest side of the triangle, or the hypotenuse. In the image, both of the triangles are the same size so we basically just have to solve for one. We plug in 9 for a and 7 for b in our equation we just learned.

a^2 + b^2 = c^2

9^2 + 7^2 = c^2

We have to square the 9 and 7. In order to do that, we just multiply 9 by itself, and 7 by itself (9*9, 7*7), because the small number on the right corner tells you how many times you have to multiply that number.

81 + 49 = c^2

Now we add them together and we get:

81 + 49 = 130

130 is our c^2, and that number goes into the green box in the image. The actual number is very long so we just use this number for your answer! Hope this helps :)

Answer:

don't know

Step-by-step explanation:

sorry buddy

Answer:

(D)Jaleel's method is correct because 2(x-2)=2x-4.

Step-by-step explanation:

Jaleel and Lisa are simplifying the expression 2(x-2)+2 as shown.

[tex]J$aleel's Method: \left\{\begin{array}{ccc}2 (x -2) + 2 \\= 2 x - 4 + 2 \\= 2 x - 2\end{array}\right[/tex]

[tex]L$isa's Method: \left\{\begin{array}{ccc}2 (x-2) + 2 \\= 2 x -2 + 2 \\= 2 x\end{array}\right[/tex]

We can see that Jaleel's method is correct because:

2(x-2)=2x-4.

When you expand, you must multiply the term outside by all the terms inside the bracket.

The correct option is D.

Answer:

Jaleel is correct because 2 (x minus 2) equals 2 x minus 4.

D is correct

Step-by-step explanation:

i just took the quiz.

Answer:

42 m

Step-by-step explanation:

First, find <S

<S = 180 - (41+113) [ sum of angles in a triangle)

<S = 180 - 154 = 26°

Next is to find length of ST, using the law of sines: a/sin A = b/sinc B = c/sin C

Let a = RT = 28m

A = <S = 26°

b = ST

B = <R = 41°

Thus, we have:

28/sin(26°) = b/sin(41°)

Cross multiply

28*sin(41°) = b*sin(26°)

28*0.6561 = b*0.4384

18.3708 = b*0.4384

Divide both sides by 0.4384 to make b the subject of formula

18.3708/0.4384 = b

41.9041971 = b

b ≈ 42m (rounded to nearest meter)

Length of ST to nearest meter = 42 meters

Answer:

m = 0.5

Step-by-step explanation:

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

= (0.25 - 0) / (0.5 - 0)

= 0.25/0.5

= 0.5

Answer:

[tex]L$ength of \overline{BC} \rightarrow 4$ units\\Value of y\rightarrow44^\circ\\m\angle DAB\rightarrow56^\circ\\$Value of x \rightarrow 2$ units[/tex]

Step-by-step explanation:

In parallelogram ABCD, BC=AD

Given:

BC=(6-x) units

AD =(x+2) units

Therefore:

6-x=x+2

x+x=6-2

2x=4

x=2

BC=(6-x) units

=(6-2) units

BC=4 units

The opposite angles of a parallelogram are equal. Therefore:

[tex]m\angle BCD=m\angle BAD\\12^\circ+y^\circ=100^\circ-y^\circ\\y^\circ+y^\circ=100^\circ-12^\circ\\2y^\circ=88^\circ\\y=44^\circ[/tex]

[tex]m\angle DAB=100^\circ-y^\circ\\=100^\circ-44^\circ\\m\angle DAB=56^\circ[/tex]

Therefore, the match is:

[tex]L$ength of \overline{BC} \rightarrow 4$ units\\Value of y\rightarrow44^\circ\\m\angle DAB\rightarrow56^\circ\\$Value of x \rightarrow 2$ units[/tex]

Answer:

Step-by-step explanation:

plato i guess

Answer:

8, 8, 13

Step-by-step explanation:

The three numbers 8, 8, 13 have a range of 5.

13 - 8 = 5

The mode is 8, the repeated number.

Answer:

need pls

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

36= 2 × 2 × 3 × 3

60= 2 × 2 × 3 × 5

HCF(36, 60)= 2 × 2 × 3 = 12

12 is the greatest number that divides 36 and 60 without leaving a remainder​

Answer:

5249 years

Step-by-step explanation:

Half-Life of Carbon-14 is approximately 5730 years.

When we want to determine the age of a fossil using carbon dating, we use the formula:

[tex]t=\dfrac{\ln(N/N_0)}{-0.693} \cdot t_{1/2}[/tex]

Where:

In this case:

N(t)=100

[tex]N_o=53\\t_{1/2}\approx 5730$ years[/tex]

Therefore, the age of the mummy

[tex]t=\dfrac{\ln(53/100)}{-0.693} \cdot 5730\\=5249.43$ years\\t \approx 5249$ years[/tex]

Answer:

the answer is 6349 :)

Step-by-step explanation:

Someone put the correct answer in the comments so I figured I would put it here so you wouldn't miss it :) (It is correct I have tested it)

Answer:

No of rooms in Hotel G = 280

No of rooms in Hotel H = 145

Step-by-step explanation:

I solved the question using Elimination Method.

Answer: m=0.5 or m=1/2

Step-by-step explanation:

To find the slope, you use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. Since we are given the coordinate points, we can directly plug them in.

[tex]m=\frac{0.25-0}{0.5-0} =\frac{0.25}{0.5} =0.5[/tex]

Answer:

  3, 8, 13, 18, 23

Step-by-step explanation:

The recursive definition tells you the first term is 3, and that each successive term is 5 more than the one before. 5 terms are ...

  3, 8, 13, 18, 23

Answer:

not sure if it's 26 or76

Answer:

its 2

Step-by-step explanation:

Answer:

a. The 95% confidence interval for the mean is (33.52, 35.48).

b. The 95% confidence interval for the mean is (34.02, 34.98).  

c. n=49 ⇒ Width = 1.95

n=196 ⇒ Width = 0.96

Note: it should be a factor of 2 between the widths, but the different degrees of freedom affects the critical value for each interval, as the sample size is different. It the population standard deviation had been used, the factor would have been exactly 2.

d. 5. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.

Step-by-step explanation:

a. We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=34.5.

The sample size is N=49.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{49}}=\dfrac{3.4}{7}=0.486[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=49-1=48[/tex]

The t-value for a 95% confidence interval and 48 degrees of freedom is t=2.011.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=2.011 \cdot 0.486=0.98[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 34.5-0.98=33.52\\\\UL=M+t \cdot s_M = 34.5+0.98=35.48[/tex]

The 95% confidence interval for the mean is (33.52, 35.48).

b. We have to calculate a 95% confidence interval for the mean.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{196}}=\dfrac{3.4}{14}=0.243[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=196-1=195[/tex]

The t-value for a 95% confidence interval and 195 degrees of freedom is t=1.972.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=1.972 \cdot 0.243=0.48[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 34.5-0.48=34.02\\\\UL=M+t \cdot s_M = 34.5+0.48=34.98[/tex]

The 95% confidence interval for the mean is (34.02, 34.98).

c. The width of the intervals is:

[tex]n=49\rightarrow UL-LL=33.52-35.48=1.95\\\\n=196\rightarrow UL-LL=34.02-34.98=0.96[/tex]

d. The width of the intervals is decreased by a factor of √4=2 when the sample size is quadrupled, while the others factors are fixed.

Answer:

The correct answer would be C

Step-by-step explanation:

please mark brainliest

The choice which best compares the volume of the cylinders is; Choice B; The volume of cylinder B is the same as that of cylinder A.

From geometry, It can be concluded that the volume of a solid shape is the product of its cross sectional area and the height over which the area spans. On this note, since the volume of a cylinder is dependent on the radius and height of the cylinder, both cylinders have equal volumes.

Read more on cylinders;

https://brainly.com/question/9554871

#SPJ2

Answer:

y= 5x

Step-by-step explanation:

15x - 3y =0

3y= 15x

y= 5x - slope- intercept form

Answer:

a

Step-by-step explanation:

y=5x

Answer:

The probability that the mean of my sample will be between 24 and 25 cm

P(24 ≤X⁻≤25) = 0.4772

Step-by-step explanation:

Step(i):-

Given mean of the Population  'μ'= 25c.m

Given standard deviation of the Population 'σ' = 8c.m

Given sample size 'n' = 256

Let X₁ = 24

[tex]Z_{1} = \frac{x_{1}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{24-25}{\frac{8}{\sqrt{256} } } = -2[/tex]

Let X₂ = 25

[tex]Z_{2} = \frac{x_{2}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{25-25}{\frac{8}{\sqrt{256} } } = 0[/tex]

Step(ii):-

The probability that the mean of my sample will be between 24 and 25 cm

P(24 ≤X⁻≤25) = P(-2≤ Z ≤0)

                     = P( Z≤0) - P(Z≤-2)

                     = 0.5 + A(0) - (0.5- A(-2))

                     = A(0) + A(2)        ( ∵A(-2) =A(2)

                     = 0.000+ 0.4772

                     = 0.4772

Final answer:-

The probability that the mean of my sample will be between 24 and 25 cm

P(24 ≤X⁻≤25) = 0.4772

Answer:

The correct answer is:

The volume of the triangular prism is equal to the volume of the cylinder

Step-by-step explanation:

Given that there are two figures

1. A right triangular prism and

2. Right cylinder

Area of cross section of prism is equal to Area of cross section of cylinder.

Let this value be A.

Also given that Height of prism = Height of cylinder = 6

Volume of a prism is given as:

[tex]V_{Prism} = \text{Area of cross section} \times Height[/tex]

[tex]V_{Prism} = A \times 6 ........ (1)[/tex]

Cross section of cylinder is a circle.

Area of circle is given as: [tex]\pi r^{2}[/tex]

Area of cross section, A = [tex]\pi r^{2}[/tex]

Volume of cylinder is given as:

[tex]V_{Cylinder} = \pi r^{2} h\\\Rightarrow V_{Cylinder} = A \times h\\\Rightarrow V_{Cylinder} = A \times 6 ...... (2)[/tex]

From equations (1) and (2) we can see that

[tex]V_{Prism}=V_{Cylinder}[/tex]

Hence, the correct answer is:

Volume of prism is equal to the volume of cylinder.

Answer:

the answer is C for short

Answer: x=5 and 1/2

Step-by-step explanation:

You have to go to a graph and put it simply it, makes it a lot easier, hope this helps!

Steps to solve:

2x^2 + 5 = 11x

~Subtract 11x to both sides

2x^2 - 11x + 5 = 0

~Factor

(2x - 1)(x - 5) = 0

~Solve each factor

2x - 1 = 0

2x = 1

x = 1/2

x - 5 = 0

x = 5

Best of Luck!

Answer:

Decreases by 2 degrees

Step-by-step explanation:

The expression that describes temperature as a function of latitude is:

[tex]T=110-2(Latitude)[/tex]

This equation represents a linear relationship between latitude and temperature in a way that an increase in latitude causes a decrease in temperature. The magnitude of this decrease is quantified by the slope of the linear equation, which is -2. Therefore, the estimated temperature decreases by 2 degrees when latitude is increased by one.