Point H is between G and I. If HG = 8x + 7, HI = 3x - 2, and GI = 38, what would be the length of GH ?

The ordered pair that is a solution to the system is (A) (−1, −1)

From the question, we have the the system of linear equations to be

x + 3y = −4

y = −3x − 4

By substitution, we have

x + 3(−3x − 4) = −4

Open the brackets

This gives

x - 9x - 12 = -4

Evaluate the like terms

-8x = 8

So, we have

x = -1

Recall that

y = −3x − 4

So, we have

y = −3(-1) − 4

Evaluate

y = -1

Hence, the solution is (A) (−1, −1)

Read more about system of equations at

https://brainly.com/question/13729904

#SPJ1

The absolute value of change in the predicted value of dependent variable Y is 18.

Any variable whose value is influenced by an independent variable is said to be dependent. The thing that is measured or assessed in an experiment or mathematical equation is the dependent variable. The phrase "the outcome variable" is another name for the dependent variable.

Slope = b = -4

Intercept = a = -2.8

So, the equation of the regression line is

y  =  a + bx

y = -2.8 - 4x              ...Equation 1

Now suppose the value of x is changed by adding 4.5

i.e. put x = x + 4.5

So,

y = -2.8 - 4(x + 4.5)

y = -2.8 -4x - 18         ...Equation 2

Comparing 1 and 2 ,

We get the predicted value of dependent variable Y as 18

Therefore The absolute value of change in the predicted value of dependent variable Y is 18

To learn more about dependent variables visit

https://brainly.com/question/1479694

#SPJ4

Answer:

24 sides

Step-by-step explanation:

the sum of the exterior angle and the interior angle = 180° , then

exterior angle = 180° - 165° = 15°

The sum of the exterior angles of a polygon = 360°

Divide the total by 15° to find number of sides n

n = 360° ÷ 15° = 24

Step-by-step explanation:

Number of Yellow tiles = 45 - 15 = 30.

Odds of picking a Yellow tile = Yellow/Total = 30/45 = 2/3. (A)

The odds in favor of drawing a yellow tile is 2:3.

A ratio is a quantitative relationship between two amounts, showing the number of times one value contains or is contained within the other. It is expressed as a comparison of the two values using a colon (:) or as a fraction.

There are 45-15=30 yellow tiles in the bag.

The odds in favor of drawing a yellow tile are the ratio of the number of yellow tiles to the total number of tiles.

So, the odds in favor of drawing a yellow tile are

30:45, which can be simplified by dividing both by 15 to get 2:3.

Thus, the odds in favor of drawing a yellow tile is 2:3.

Learn more about Ratio here:

https://brainly.com/question/13419413

#SPJ2

Answer:

x = 8, y = 1

Step-by-step explanation:

11x - 20y = 28 ...(1)
3x + 4y = 36
or 15x + 20y = 180 ...(2)
Adding (1) and (2),
26x = 208
Or x = 8
Now, 3x + 4y = 36
3(8) + 4y = 36
4y = 36 - 32 = 4
so y = 1

The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

Learn more about trigonometric identities at: https://brainly.com/question/7331447

#SPJ1

The equation of the line passing through the point so that segment of the line i.e. \(y+2x=4\)

The equation of the line be \(y=mx+c\)

Now the line intersects at the x-axis  \((a,0)\) and the point at which the y-axis intersect \((0,b)\)

Plug in the value \((a,0)\\\)

\(ma+c=0\\a=\frac{-c}{m}\)

and now plug in the value \((b,0)\)

\(b=c+0\\b=c\)

now \((1,2)\) is the midpoint of \((a,0)\) and \((0,b)\\\)

\(2=\frac{0+b}{2\\}\\ b=c\\\frac{c}{2} =2\\c=4\)

and

\(1=\frac{a+0}{2}\\1=\frac{-c}{2m} \\m=-2\)

plug in the value of m and c

\(y+2x=4\) is the required equation

Learn more about equations from

https://brainly.com/question/29657983

#SPJ4

The answer: 39 yards

Answer:

Your answer B y=5x

Step-by-step explanation:

I did this got it right

Northside Christian Academy has 528 students enrolled this year. That is an in- crease of 10% over last year's enrollment. How many students were enrolled last year?

Let

x ------> students enrolled last year

we have that

100%+10%=110%=110/100=1.10

so

528=1.10x

solve for x

x=528/1.10

x=480

The pooled standard deviation will be True

The average range of all data points about their group mean is known as the pooled standard deviation (not the overall mean). It is the weighted average of the standard deviations for each group. Larger groups have a proportionately greater impact on the overall estimate because to the weighting.

Compare the ratio of the two sample standard deviations as a quick way to verify this. The ratio would be 1, or, in the event that the two are equal. However, we cannot anticipate the ratio to be exactly 1, as they are samples and as a result, there will be some mistake. A decent Rule of Thumb to apply is to see if the ratio falls between 0.5 and 2 when the sample sizes are nearly equal (granted, "nearly equal" is a bit imprecise, so frequently if sample sizes are small one requires they be equal). In other words, neither sample's standard deviation is greater than its counterpart.

Therefore, the pooled standard deviation will be True

To learn more about the pooled standard deviation

visit: https://brainly.com/question/29642180

#SPJ4

If we reject the global null hypothesis and were interested in all of the possible pairwise comparisons, we would have to perform additional tests equal to the number of pairs of groups.

For instance, if we have 4 groups, there will be 6 pairwise comparisons to be performed. On the other hand, if there are 5 groups, we will have to perform 10 pairwise comparisons. Generally, when we have k groups, there will be k*(k-1)/2 pairwise comparisons.

In pairwise comparisons, we compare one group with another, rather than testing all groups together. Therefore, we perform multiple tests that can increase the possibility of making a type-I error. In order to avoid the inflation of type-I error probability, we use the Bonferroni correction to adjust the significance level.

The Bonferroni correction divides the significance level (α) by the number of comparisons (m), i.e., the new significance level (α_new) becomes α/m. For example, if α = 0.05 and we have 6 pairwise comparisons, then the new significance level will be 0.05/6 = 0.0083. Hence, we will reject the null hypothesis for any p-value less than 0.0083.

To know more about comparisons visit:

https://brainly.com/question/32217736

#SPJ11

The required diameter of the right cone is 6 units.

The volume of a right cone is given by the formula \(V = (1/3)\pi r^2h\), where r is the radius of the base and h is the height of the cone.

Since the cone is a right cone, the radius and height are perpendicular, and we can use the Pythagorean theorem to find the radius.

Let's start by plugging in the given values:

\(18\pi = (1/3)\pi r^2(6)\)

Simplifying:

\(54 = r^2(6)\)

\(r^2 = 9\)

r = 3

Now that we know the radius is 3 units, we can use it to find the diameter:

d = 2r = 2(3) = 6

Therefore, the diameter of the right cone is 6 units.

To know more about cone Visit:

brainly.com/question/29424374

#SPJ1

a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

To know more about maximizes visit:

https://brainly.com/question/30072001

#SPJ11

False. The margin of error only accounts for sampling variability (the fact that my sample will be different that many other people's and therefore provide different statistics.

Statistics is a technique for interpreting, analyzing, and summarizing data in mathematics. In light of these characteristics, the various statistical types are divided into: Statistics that are descriptive and inferential. We analyze and understand data based on how it is presented, such as through graphs, bar graphs, or tables.

Inferential statistics, which draws conclusions from information using statistical tests like the student's t-test, is one of the two main statistical methods used in data analysis. Descriptive statistics presents data using indices like mean and median.

To learn more about statistics visit:

https://brainly.com/question/29093686

#SPJ4

The angle between the line PT and the plane PQRS is 63.4°

In this question, we have been given a rectangular based pyramid PQRST.

A pyramid has height of 10 cm.

We need to find the angle between the line PT and the plane PQRS.

We know that the angle made by triangular plane TPS with the rectangular plane PQRS is same as the angle between the line PT and the plane PQRS.

If we draw a perpendicular through point T and intersects the plane PQRS at point M.

Let R be the midpoint of side PS

Consider a right triangle RMT.

We need to find angle TRM.

Here, MT = 10 cm, MR = 5 cm (1/2 × length of the rectangle)

Consider the tangent of the angle TRM

tan(∠TRM) = TM / RM

tan(∠TRM) = 10 / 5

∠TRM = tan^(-2)[2]

∠TRM = 63.4°

Therefore, the angle between the line PT and the plane PQRS is 63.4°

Learn more about the rectangular pyramid here:

https://brainly.com/question/13087776

#SPJ1

Answer:

Elena is correct

Step-by-step explanation:

She is correct because in both the answer will be 702.

Answer:

Elena is correct

Step-by-step explanation:

pls make brainliest

Answer:

8 years.

Step-by-step explanation:

Mara is 6.

6+8=14

Alberto is 20.

20+8=28

14*2=28.

In 8 years, Alberto will be twice Mara's age.

Answer: To find the equation of the tangent line y(x) of the curve r(t) = (t^9, t^5), we need to find the derivative of the curve and then evaluate it at the point where we want to find the tangent line.

The derivative of r(t) is:

r'(t) = (9t^8, 5t^4)

To find the equation of the tangent line at a specific point (x0, y0), we need to evaluate r'(t) at the value of t that corresponds to that point. Since r(t) = (t^9, t^5), we can solve for t in terms of x0 and y0:

t^9 = x0

t^5 = y0

Solving for t, we get:

t = (x0)^(1/9)

t = (y0)^(1/5)

Since these two expressions must be equal, we have:

(x0)^(1/9) = (y0)^(1/5)

Raising both sides to the 45th power, we get:

(x0)^(5/9) = (y0)^(9/45)

(x0)^(5/9) = (y0)^(1/5)

(x0)^(9/5) = y0

So the point where we want to find the tangent line is (x0, y0) = (t0^9, t0^5) = (x0, x0^(5/9 * 9/5)) = (x0, x0).

Now we can evaluate r'(t) at t0:

r'(t0) = (9t0^8, 5t0^4) = (9x0^(8/9), 5x0^(4/9))

The slope of the tangent line at (x0, y0) is given by the derivative of y(x) with respect to x:

y'(x) = (dy/dt)/(dx/dt) = (5t^4)/(9t^8) = (5/x0^4)/(9/x0^8) = 5x0^4/9

So the equation of the tangent line is:

y - y0 = y'(x0) * (x - x0)

y - x0 = (5x0^4/9) * (x - x0)

y = (5/9)x + (4/9)x0

Therefore, the equation of the tangent line y(x) of the curve r(t) = (t^9, t^5) at the point (x0, y0) = (x0, x0) is y = (5/9)x + (4/9)x0.

To find the equation of the tangent line at a point on the curve, we need to find the derivative of the curve at that point. So, we start by finding the derivative of r(t):

r'(t) = (9t^8, 5t^4)

Now, let's find the tangent line at the point (1, 1):

r'(1) = (9, 5)

So, the slope of the tangent line at (1, 1) is 5/9. To find the y-intercept, we can use the point-slope form:

y - y1 = m(x - x1)

where (x1, y1) is the point on the curve. Plugging in (1, 1) and the slope we just found, we get:

y - 1 = (5/9)(x - 1)

Simplifying, we get:

y = (5/9)x + 4/9

So, the equation of the tangent line at the point (1, 1) is y = (5/9)x + 4/9.

To know more about tangent line , refer here :

https://brainly.com/question/31179315#

#SPJ11

The conclusion regarding the publisher's claim is that it is incorrect if the potential advertiser rejects the null hypothesis. A newsletter publisher believes that less than 65% 65 % of their readers own a personal computer. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.02 0.02 level of significance, the advertiser decides to reject the null hypothesis.

What is a null hypothesis?

The null hypothesis is a fundamental idea in inferential statistics that represents the null assumption. It's frequently utilized to compare datasets and decide whether any differences between them are real or just by chance.

It is also called H0. It is the default theory that no difference exists between two tested populations or data sets.

A hypothesis test is a way of deciding whether the data supports or disproves the null hypothesis. If the null hypothesis is incorrect, it is referred to as a Type I error. If it is true and the data leads to its rejection, it is known as a Type II error.

Thus, after performing the test at the 0.02 level of significance, if the potential advertiser decides to reject the null hypothesis, the publisher's claim is incorrect.

for such more question on publisher's claim

https://brainly.com/question/28159262

#SPJ11

Answer:

Mid point of A(9,2) and B(6,44) is (7.5, -1)

Step-by-step explanation:

I. If mid point = \(\frac{x_{a} +x_{b} }{2}\), \(\frac{y_{a}+ y_{b} }{2}\)

 So (x) = (9 + 6) / 2 = 7.5

       (y) = (2 + (-4)) / 2 = -1

So (x,y) = (7.5, -1)        

Leave more question below, I don't understand you question well.

The height of the tower is equal to the length of the side opposite the angle of elevation plus the length of the side opposite the angle of depression.

The angle of elevation and angle of depression in this problem can be used to solve for the height of the tower.

Since the angle of elevation is the angle from the window to the top of the tower and the angle of depression is the angle from the window to the bottom of the tower, the height of the tower can be determined by finding the length of the side opposite the angle of elevation and adding it to the length of the side opposite the angle of depression.

Using trigonometry, we can solve for the two lengths using the sine and cosine functions. The sine of the angle of elevation is equal to the length of the side opposite the angle divided by the hypotenuse. The hypotenuse is the distance from the window to the tower, which is known to be 275 feet. Therefore, we can solve for the side opposite the angle of elevation by multiplying the sine of the angle of elevation by 275. The cosine of the angle of depression is equal to the length of the side opposite the angle divided by the hypotenuse. We can solve for the side opposite the angle of depression in the same way.

Once the two lengths are calculated, we can add them together to find the height of the tower.The height of the tower is equal to the length of the side opposite the angle of elevation plus the length of the side opposite the angle of depression.

Learn more about angle of elevation here:

https://brainly.com/question/21137209

#SPJ4

Answer:

no po ang answer ko

Step-by-step explanation:

thanks choi

The acceleration of the box is 0.4 m/s².

The magnitude of the force that Rory applies is 20.12 N.

(a)

The acceleration of the box can be calculated using the formula:

\(a = (v_f^2 - v_i^2) / (2d)\)

where vf is the final velocity, vi is the initial velocity, and d is the distance traveled.

Substituting the given values, we get:

a = (1.2² - 0²) / (2 x 1.8)

a = 0.4 m/s²

(b)

To find the magnitude of the force that Rory applies, we can use Newton's second law, which states that the net force on an object is equal to its mass times its acceleration:

F(net) = ma

The resistance force is acting in the opposite direction to the force applied by Rory.

F(applied) - F(resistance) = ma

Substituting the given values.

F(applied) - 19 = 2.8 x 0.4

F(applied) = 19 + 1.12 = 20.12 N

Therefore, the magnitude of the force that Rory applies is 20.12 N.

Thus,

The acceleration of the box is 0.4 m/s².

The magnitude of the force that Rory applies is 20.12 N.

Learn more about force here:

https://brainly.com/question/30526425

#SPJ1

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The table tells you all you need to know. Put values from the table in the corresponding answer slots.

Answer:

i think original price Php656.25

Step-by-step explanation:

original price Php x

80%x = 575

x = 575×100/80

x = 656.25

original price Php656.25

Answer:

(-2, 3)

Step-by-step explanation:

For x-4 you go left four places and y+6 go up 6 places

Answer:

(-2, 3)

Step-by-step explanation:

Point P has coordinates (2, -3).

The translation is (x - 4, y + 6) which means subtract 4 from the x-coordinate and add 6 to the y-coordinate.

The x-coordinate of point P is 2. Subtract 4 from it, you get -2.

The y-coordinate of point P is -3. Add 6 to it to get 3.

The coordinates of the translated point are (-2, 3).

Answer:

50/3

Step-by-step explanation:

For x

3x-2(2+1)=4

3x-2(3)=4

3x-6=4

3x=4+6

3x=10

x=10/3

 as we have to find 5x=?

    5(10/3)

50/3