Directions: Plot the positive rational numbers on the number line. 12 134.16 310 / 8 0 1 - 2.05 Warm-Up 2 + 3 4 5​

The missing angles of the isosceles triangle are as follows:

An isosceles triangle is a triangle that has two sides equal to each other and two angles congruent to each other.

The base angles of an isosceles triangles are congruent and the two legs are also equal.

Therefore, ΔHIJ

where

HI ≅ IJ

m∠H  = 3x + 10

m∠I = 6x - 20

Therefore,

m∠H ≅ m∠J

m∠H  + m∠I+ m∠J = 180

3x + 10 + 6x - 20 + 3x + 10 = 180

12x  = 180

x = 180 / 12

x = 15

Hence,

m∠H  = 3(15) + 10 = 55 degrees

m∠I = 6(15) - 20 = 90 - 20  = 70 degrees

m∠J = 55 degrees.

learn more on isosceles triangle here: https://brainly.com/question/29410755

#SPJ1

Answer:

the ture was

0.6 • 25 = x

6/10=x/25

x/25=60/100

the fault

6.0 • 25 = x

x • 1.6 = 25

60/100=25/x

The perimeter of the whole diagram in cm is derived as 86.6158 cm using trigonometric ratios.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the angle P for right-angled triangle formed by extending the line PQ to the base of the trapezium, so that we have opposite side of 7 cm (22 cm - 15 cm)

so; sinP = 7/25.3

P = sin^(-1)(7/25.3)

P = 16.06

The isosceles triangle PQR have the angle;

Q = 180 - 2(16.06) {sum of interior angles of Isosceles triangle with two equal base angles}

Q = 147.88°

Considering the smaller right-angled triangle formed by the height of the trapezium and one side of the Isosceles triangle, we have its angle;

Q = 180° - 147.88° {sum of angles on a straight line}

Q = 32.12

also;

sin32.12 = 7/hypotenuse (one of the equal sides of the Isosceles triangle)

hypotenuse = 7/sin32.12

hypotenuse = 13.1655

The length TS is equal to the adjacent side of the smaller triangle, so;

cos32.12 = TS/13.1655

TS = 13.1655 × cos32.12

TS = 1.51503

Therefore, the perimeter of the whole diagram is;

25.3 cm + 22 cm + 15 cm + 13.1655 cm + 11.1503 cm = 86.6158 cm.

Learn more about perimeter here:https://brainly.com/question/27405967

#SPJ1

The expanded equation of the function f(x) = (3x + 2)⁴ is f(x) = 81x + 216x³ + 216x² + 96x + 16

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

f(x) = (3x + 2)⁴

Using the pascal triangle at n = 4, we have the coefficients to be

Coefficient = 1     4     6     4     1

So, when the function f(x) = (3x + 2)⁴ is expanded, we have

f(x) = 1 * (3x)⁴ + 4 * (3x)³ * 2 + 6 * (3x)² * 2² + 4 * (3x) * 2³ + 1 * 2⁴

Evaluate

f(x) = 81x + 216x³ + 216x² + 96x + 16

Hence, the solution is f(x) = 81x + 216x³ + 216x² + 96x + 16

Read more about functions at

https://brainly.com/question/25638609

#SPJ1

A dot plot is a graph of each data value plotted as a point.

In the given question, we have to fill in the blanks.

A _______ is a graph of each data value plotted as a point.

As we know that;

Data points are represented as dots on a graph with an x- and y-axis in a dot plot, sometimes referred to as a strip plot or dot chart, which is a straightforward type of data visualisation.

These kinds of graphs are employed to visually represent particular data trends or groupings. The distribution of a collection of data is shown by a dot plot, which is comparable to a histogram in that it shows the proportion of data points that fall into each category or value on the axis.

Hence, a dot plot is a graph of each data value plotted as a point.

To learn more about data visualization link is here

brainly.com/question/18597103

#SPJ4

Answer:

  368

Step-by-step explanation:

You want the 41st term of the arithmetic sequence that starts 8, 17, 26.

The n-th term of an arithmetic sequence is given by ...

  an = a1 +d(n -1)

for first term a1 and common difference d.

The difference between terms is ...

  d = 17 -8 = 9

The first term is a1 = 8, so the 41st term is ...

  a41 = a1 +d(41 -1) = 8 +9(41 -1) = 368

The 41st term of the sequence is 368.

<95141404393>

i'm kind of sure it's -4.7

Answer:

0

Step-by-step explanation:

Answer:

Step-by-step explanation:

2; <3 is congruent to <6. Option B is correct.

Angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Given that Corey is making a wall-mounted bookshelf.

It has 2 shelves, with a third piece of wood intersecting them. to support the shelves, corey orders some l-brackets to put between the shelves and the crosspiece.

To find a congruent angle you must find what can fit inside the giving number the best. If we compare all of the answer is wouldn't make sense, since 7 is greater than 6 it would be wrong. So, A is Incorrect.

C is about 3 and 7. C would fit but 7 wouldn't. So, C is incorrect.

D has both 2 and 3 but also have 4 and 7 which wouldn't match. So, D is incorrect.

Hence, option B is correct,  2; <3 is congruent to <6.

To learn more on Angles click:

https://brainly.com/question/28451077

#SPJ1

The ordered pair -2,2 makes the inequalities y < –x + 1 and y > x true. Therefore, option B is true.

Inequality is the absence of an equality link between two expressions or values. An ordered pair is made up of the x and y coordinates, with two values stated in a certain order inside parenthesis.

Substitute the values from the given ordered pair one by one to check whether the given inequalities are true.

Substituting (-2,2) in y < –x + 1 and y > x,

For,  y < –x + 1

2<2+1

2<3

For, y > x

2>-2

This ordered pair (-2,2) makes the given inequalities true.

To know more about inequalities:

https://brainly.com/question/29166625

#SPJ4

Leah currently has 14.55 out of the total of 48.50, which is approximately 30% of the total amount.

To calculate the exact percentage, you would divide 14.55 by 48.50 and then multiply the result by 100. If you do this, you find that Leah has exactly 29.941%, which rounds up to 30%.

The remaining amount of money that Leah needs to buy the necklace is 33.95, which is approximately 70% of the total. To calculate the exact percentage, you would divide 33.95 by 48.50 and then multiply the result by 100. If you do this, you find that Leah needs exactly 69.907%, which rounds down to 69%.

Therefore, Leah currently has 30% of the total amount of money needed for the necklace, and she needs 69% of the total amount of money to buy the necklace for her mother's birthday.

Learn more about how to find percentages:

brainly.com/question/24877689

#SPJ4

if the pile contains only 25 quarters and only 40 dimes but at least 50 of each other kind of coin, then 20,281 collections of 50 coins can be chosen.

what are quarters?

Given that:

25 quarters and only 40 dimes

No. of. Ways with at least 26 quarters and 41 dimes.

26 + 41 = 67 coins, but we have only 50 coins.

There are 0 ways to select at least 26 quarters and 41 dimes.

[tex]A_{1}[/tex] = at least 26 quarters

[tex]A_{2}[/tex] = at least 41 dimes

Using inclusion / exclusion rule for the two sets:

N([tex]A_{1} U A_{2}[/tex]) = N ( [tex]A_{1}[/tex]) + N ( [tex]A_{2}[/tex])- N ([tex]A_{1}[/tex] ∩ [tex]A_{2[/tex])

                = 2925 + 220 - 0

                = 3145

Therefore, no . of . ways with at most 25 quarters and at most 40 dimes are

= 23426 - 3145

= 20,281 ways

To learn more about exclusion rule check the given link

https://brainly.com/question/12239906

#SPJ4

Answer:

[tex](x-3)^2+(y+7)^2=\dfrac{361}{13}[/tex]

Step-by-step explanation:

The tangent of a circle is always perpendicular to the radius.

Therefore, the center is on a line that is perpendicular to the tangent.

Rearrange the equation of the tangent to make y the subject:

[tex]\begin{aligned}2x+3y-4&=0\\3y&=-2x+4\\y&=-\dfrac{2}{3}x+\dfrac{4}{3}\end{aligned}[/tex]

Therefore, the slope of the tangent line is -²/₃.

If two lines are perpendicular to each other, their slopes are negative reciprocals.  Therefore, the slope of the perpendicular line is ³/₂.

To write the equation of the line perpendicular to the tangent, substitute the found slope and the center point into the point-slope formula:

[tex]\begin{aligned}y-y_1&=m(x-x_1)\\\implies y-(-7)&=\dfrac{3}{2}(x-3)\\y+7&=\dfrac{3}{2}x-\dfrac{9}{2}\\y&=\dfrac{3}{2}x-\dfrac{23}{2}\end{aligned}[/tex]

The point on the circle is the point of intersection of the tangent line and the perpendicular line.  

To find the point of intersection, substitute the equation for the perpendicular line into the equation for the tangent line:

[tex]\implies \dfrac{3}{2}x-\dfrac{23}{2}=-\dfrac{2}{3}x+\dfrac{4}{3}[/tex]

[tex]\implies \dfrac{13}{6}x=\dfrac{77}{6}[/tex]

[tex]\implies x=\dfrac{77}{13}[/tex]

Substitute the found value of x into one of the linear equations and solve for y:

[tex]\implies y=-\dfrac{2}{3}\left( \dfrac{77}{13} \right)+\dfrac{4}{3}[/tex]

[tex]\implies y=-\dfrac{34}{13}[/tex]

Therefore, the point of intersection and hence the point on the circle is:

[tex]\left( \dfrac{77}{13}, -\dfrac{34}{13}\right)[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

To find r², substitute the given center of the circle (3, -7) and the found point into the equation of the circle:

[tex]\implies \left(\dfrac{77}{13} -3 \right)^2+ \left(-\dfrac{34}{13}+7\right)^2=r^2[/tex]

[tex]\implies \left(\dfrac{38}{13} \right)^2+ \left(\dfrac{57}{13}\right)^2=r^2[/tex]

[tex]\implies \dfrac{1444}{169} + \dfrac{3249}{169}=r^2[/tex]

[tex]\implies \dfrac{4693}{169}=r^2[/tex]

[tex]\implies \dfrac{361}{13}=r^2[/tex]

Therefore, the equation of the circle whose center is P(3, -7) and tangent to 2x+3y-4=0 is:

[tex]\boxed{(x-3)^2+(y+7)^2=\dfrac{361}{13}}[/tex]

The number which would be the next in the sequence of number is sixty-four i.e., 64.

In mathematics, a geometric progression is a sequence of non-zero numbers where each term after the first multiplies the previous term by a fixed non-zero number called the common ratio. In other words, a geometric progression has consecutive terms with a common ratio. Example: a , a², a³, ..., where aₙ₊₁/aₙ= a

We have , Jamie noted the following sequence: 4, 8, 16, 32, . .. on a sheet of paper. After careful study of the sequence we have provided, is a geometric sequence and the ratio between consecutive terms in the geometric sequence is : (8/4), (16/8), ....

= 2, 2, .....

We have to locate the next number in sequence. To find the next term in a geometric sequence, simply multiply the last term given by the common ratio of the sequence. So, the next number in the sequence is 32 × 2 = 64. Hence, required number is 64.

To learn more about Geometric sequence, refer:

https://brainly.com/question/2515230

#SPJ4

Complete question:

Jamie wrote out the following sequence of numbers: 2, 6, 14, 30,...on a sheet of paper. What number would be the next in the equence of number?

Answer:

just write the value of y in the y table and replace x with the given value above : for example if x is -4

then,

y = 20*(-4)-5

In linear equation, For 20 Months Dagogo requires to upload videos to get 90,000,000  views on his channel.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.        

                                   The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

Dagogo uploads 3 videos on his channel each month.

Each video gets an average of 1500000 views.

  3 Video get Views  = 3 * 1500000

                                = 4,500,000 Views

Views per month  =   4,500,000 Views

      Total Views = 90,000,000 views

Number of months = Total Views/Views per month

Number of months  = 90,000,000/4,500,000

      Number of months  20 Months

For 20 Months Dagogo requires to upload videos to get 90,000,000  views on his channel.

Learn more about linear equation

brainly.com/question/11897796

#SPJ4

The complete question is -

Dagogo uploads 3 videos on his channel every month. Each video averages 15 minutes in length and gets an average of 150,000 new views. The average ratio of likes-to-views of Dagogo videos is 1:5. Dagogo wants to reach a total of 9,000,000 views on his channel. Assuming these rates continue, for how many months does Dagogo need to upload videos to get to 9,000,000 views on his channel?

Answer:

2000 likes per minute

Step-by-step explanation:

If each video averages 15 minutes and he gets an average of 150000 new views, we can divide.

150000/15=10000

If the ratio of likes to views is 1:5, we can assume 10000 is the "5" and divide it by 5.

10000/5=2000

2000:10000 = 1:5

2000 likes per minute

(KHAN)

Answer:

.

Step-by-step explanation:

The correct equation is p - 53 = 118.

⇒ p - 53 = 118

Therefore, the correct equation is p - 53 = 118.

Answer:

32

Step-by-step explanation:

Answer:

[tex]x=60[/tex]

Step-by-step explanation:

[tex]3x=180\\x=\frac{180}{3} \\x=60[/tex]

The factorization of y²+7y-8 is (y+8)(y-1).

y²+7y-8

=y²+8y-y-8

=y(y+8)-1.(y+8)

=(y+8)(y-1)

The factors are (y+8), (y-1).

The method we are following here is factorize by grouping.

To learn more about factorization,

brainly.com/question/26791528

The correct question is-

Factor y²+7y-8.

Answer:

The answer is that there are 2 green pins and 5 yellow pins remaining in the bag.

Step-by-step explanation:

There are 3 green pins in the bag at the start and Yaqub gives one to his sister, so there are 3 - 1 = <<3-1=2>>2 green pins remaining in the bag. The rest of the pins in the bag must be yellow, so there are 2 green and 7 - 2 = <<7-2=5>>5 yellow pins remaining in the bag.

Answer:2 green 5 yellow

Step-by-step explanation:

If both bouquets have 6 tickseeds, the first bouquet ( roses + tickseeds) has more flowers.

The problem can be solved using ratio.

Bouquet 1 :

Every 2 tickseeds there are 7 roses

Hence, the ratio

Tickseed : rose = 2 : 7    

If there are 6 tickseeds, then

2 : 7 = 6 : rose

rose = (6/2) x 7 = 21

Number of flowers = 6 tickseeds + 21 roses = 27 flowers

Bouquet 2 :

Every 3 tickseeds there are 4 daisies

Hence, the ratio

Tickseed : daisy = 3 : 4

If there are 6 tickseeds, then

3 : 4 = 6 : daisy

daisy = (6/3) x 4 = 8

Number of flowers = 6 tickseeds + 4 daisies = 10 flowers

Hence, if there are 6 tickseeds in each bouquet, the first bouquet contains more flowers.

Learn more about ratio here:

https://brainly.com/question/29145263

#SPJ4

x = random variable = number of successful trials = 4

n = number of trials = 6

P = likelihood of success = 0.55

Q = likelihood of failure = 0.45

nCx = number of combinations of n objects taken x at a time

.

Binomial Distribution

b(x; n, P) = nCx * P^x * Q^(n - x)

.

b(4; 6, 0.55) = 6C4 * (0.55)^4 * (0.45)^2 = (15)(0.09150625)(0.2025) = 0.2779502

[tex]$W(\mathbf{x})$[/tex]is a linear transformation. it is not onto .The given statement is false.

The objective is to determine whether the following statement is true or false.

"If [tex]$$T_1(\mathbf{x})$ and $T_2(\mathbf{x})$[/tex] are onto linear transformations from [tex]$\mathbf{R}^n$[/tex] to [tex]$\mathbf{R}^m$[/tex] then [tex]$W(\mathbf{x})=T_1(\mathbf{x})+T_2(\mathbf{x})$[/tex] is an onto linear transformation."

To check whether [tex]$W(\mathbf{x})$[/tex] is a linear transformation or not:

For a, b ∈ R and for x, y ∈ [tex]$\mathbf{R}^n$[/tex],

[tex]$$\begin{aligned}W(a \mathbf{x}+b \mathbf{y})= & T_1(a \mathbf{x}+b \mathbf{y})+T_2(a \mathbf{x}+b \mathbf{y}) \quad\left(\text { Since } W(\mathbf{x})=T_1(\mathbf{x})+T_2(\mathbf{x})\right) \\= & {\left[a T_1(\mathbf{x})+b T_1(\mathbf{y})\right]+\left[a T_2(\mathbf{x})+b T_2(\mathbf{y})\right] } \\& \quad\left(\text { Since } T_1(\mathbf{x}) \text { and } T_2(\mathbf{x}) \text { are onto linear transformations }\right) \\\end[/tex]

[tex]= & a\left[T_1(\mathbf{x})+T_2(\mathbf{x})\right]+b\left[T_1(\mathbf{y})+T_2(\mathbf{y})\right] \\\\= & a W(\mathbf{x})+b W(\mathbf{y})\end{aligned}$$[/tex]

Therefore, [tex]$W(\mathbf{x})$[/tex] is a linear transformation.

To check whether [tex]$W(\mathbf{x})$[/tex] is onto:

Define the linear transformations:

[tex]$$T_1: \mathbf{R} \rightarrow \mathbf{R}$ such that $T_1(\mathbf{x})=\mathbf{x}$[/tex]

[tex]$$T_2: \mathbf{R} \rightarrow \mathbf{R}$ such that $T_2(\mathbf{x})=-\mathbf{x}$[/tex]

Then, [tex]$T_2(\mathbf{x})=-\mathbf{x}=-T_1(\mathbf{x}) \Rightarrow T_2(\mathbf{x})=-T_1(\mathbf{x})$[/tex]

The range of both functions [tex]$T_1, T_2$ is $\mathbf{R}$[/tex] This is same as the co-domain of [tex]$T_1, T_2$[/tex]. So, they are onto functions.

If A and B are the two sets, if for every element of B, there is at least one or more element matching with set A, it is called the onto function.

Therefore, [tex]$T_1, T_2: \mathbf{R} \rightarrow \mathbf{R}$[/tex]are onto linear transformations.

And, [tex]$W=T_1+T_2: \mathbf{R} \rightarrow \mathbf{R}$[/tex] is a mapping.

Now, [tex]$W(\mathbf{x})=T_1(\mathbf{x})+T_2(\mathbf{x})$[/tex]

[tex]$$\begin{aligned}& =T_1(\mathbf{x})-T_1(\mathbf{x}) \\& =0\end{aligned}$$[/tex]

So, the range of [tex]$$W(\mathbf{x})$ is $\{0\} \neq \mathbf{R}($[/tex] co-domain of [tex]$W(\mathbf{x}))$[/tex]

Then, is [tex]$W(\mathbf{x})$[/tex] not onto.

So, the given statement is false.

Hence, the correct answer is 5th option

For more such questions on linear transformations.

https://brainly.com/question/16287383

#SPJ4

The initial purchase price of the best fit function is; $2500

The equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

The formula to find the slope between two coordinates is;

m = (y₂ - y₁)/(x₂ - x₁)

If we take the coordinates (4, 5000) and (12, 10000), we have;

Slope = (10000 - 5000)/(12 - 4)

Slope = 625

Thus, the equation will be;

5000 = 625(4) + c

5000 - 2500 = c

c = $2500

y-intercept represents the intital price which is when x = 0 years.

Read more about linear best fit function at; https://brainly.com/question/1564293

#SPJ1

Answer:

C. detail-oriented

Step-by-step explanation:

Haute cuisine is typically characterized by careful preparation and detail-oriented presentation.