Elizabeth bought lemons (l) and apples (a). Each apple costs 35¢ and each lemon costs 15¢. All together, she bought 17 lemons and apples for $3.95. Which system can be used to determine how many of each she bought?

Taking point Z as the origin, the coordinates of the points on ΔBAD are

given by changing the sign of the coordinates of points in ΔDCB.

Reasons:

The given parameters are;

Triangle ΔBAD is the image of ΔDCB following a rotation of 180°.

Required:

The angle congruent to ∠DBA.

Solution:

Given that the rotation of triangle DCB is 180°, we have that the

coordinates of a point (x, y) in ΔDCB is (-x, -y) in ΔDBA.

Therefore, side DC is parallel to side AB

Which gives;

∠DBA is congruent to ∠BDC by alternate interior angles theorem.

∠DBA ≅ ∠BDC

The angle that is congruent to ∠DBA is; option D. ∠BDC

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Given that "Jane wrote all the natural numbers from 5 to k. Including 1 and k"

So Jane wrote k numbers.

lets take an example

if k = 10 , then natural numbers between 1 and 10 are 10 numbers that are 1 , 2 , 3 ,4 ,5 ,6 , 7 , 8 ,9 and 10.

Hence she write k numbers.

Jane wrote k - 4 natural numbers for the given condition.

Natural numbers are defined as which range from 1 to infinity and are the most fundamental sort of numbers. Commonly known as positive numbers or counting numbers, these numbers. Natural Numbers are represented by the symbol N.

Jane wrote all the natural numbers from 5 to k, including 5 and k.

So, she wrote the numbers as 5, 6, 7, 8, 9, ..., k.

To find out how many numbers Jane wrote, we have to subtract 4 from each of these numbers because 4 numbers (1, 2, 3, 4) come before 5.

1, 2, 3, 4, 5, ..., k-1

So, there are k-1 - 4 + 1 = k - 4 natural numbers between 5 and k, inclusive.

Therefore, she wrote k - 4 natural numbers.

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Answer: The equation of a line that passes through the point (8,-4) and has a slope of 3 is y = 3x - 28.

Explanation:

y = -4, x = 8

By putting above values in equation (i)

-4 = 3 (8) + b

-4 = 24 + b

-28 = b

b = -28

y = 3x - 28

I hope this help too.

Answer:-

The linear sequence 27, 25, 23, 21, 19... is an arithmetic progression with (-2) as the common difference.

The nth term of an arithmetic progression is an=a1+(n−1)da_n=a_1+(n-1)dan​=a1​+(n−1)d, where ana_nan​ is the nth term, a1a_1a1​ is the first term, d is the common difference.

In our case, n=50,a1=27,d=−2n=50, a_1=27, d=-2n=50,a1​=27,d=−2 , hence, we get

a50=27+49⋅(−2);a50=27−98=−71.a_{50}=27+49\cdot(-2);\\ a_{50}= 27-98=-71. a50​=27+49⋅(−2);a50​=27−98=−71.

The 50th term of this sequence is (-71).

Answer:

a = 22

AB = 50

Step-by-step explanation:

[tex]a-5=17[/tex]

[tex]a=17+5[/tex]

[tex]a=22[/tex]

Line AB=2a+6

[tex]2(22)+6=44+6=50[/tex]

[tex]AB=50[/tex]

Hope this helps

Answer:

atoc40 /atob40/ctob20

i hope i help

Answer:

67

Step-by-step explanation:

angle c = angle b = 5x + 4

angle a = 46

A + B + C = 180

46 + 10x + 8 = 180

10x = 180 - 54

10x = 126

x = 12.6

5x + 4 = 12.6 x 5 + 4

= 67

Answer:

x=15

Step-by-step explanation:

if you put 8x-10=110 you can solve for x and get 15. this only works because they are opposite & congruent sides

Answer:

  see attached

Step-by-step explanation:

The two inequalities you want to plot are ...

  x + y ≤ 75 . . . . . . . . the auditorium can hold no more than 75 people

  5x +7.5y ≥ 450 . . . a minimum of $450 revenue is needed to cover costs

__

These are probably most easily plotted by graphing their intercepts. The boundary line for the first inequality will have x- and y-intercepts of 75. Shading will be below the line.

The boundary line for the second inequality will have an x-intercept of 450/5 = 90, and a y-intercept of 450/7.5 = 60. Shading will be above the line.

On of the points in the potential solution area is shown in the attached graph:

  (x, y) = (25, 50) . . . . fills the theater, gives $500 revenue

The time it takes to type the document increases proportionately to the

number of words in the document.

Reasons:

From the possible figure from a similar question, we have;

The points on the graph are; (0, 0), (1, 60), (2, 120), (3, 180), (4, 240)

The graph is a straight line, therefore, given that the starting point is at the origin, using the points, (0, 0), (1, 60), we have;

The slope of the graph = 60

The y-intercept = 0

The equation that represents the proportional relationship shown on the graph is therefore;

y = 60·x

Where;

y = The number of words

x = The time it takes to type the document

The time it would take Maya to type the document of 2,160 words is given as follows;

2,160 = 60·x

Therefore;

[tex]\displaystyle Time, \ x = \frac{2,160 \ words}{60 \ words/minute} = \mathbf{36 \ minutes}[/tex]

The time it would take Maya to type the document is x = 36 minutes

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Using the normal distribution, it is found that the percentage of their weekly sales over P4,000 is given by:

C. 5.48%

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

In this problem, the mean and the standard deviation are, respectively, of [tex]\mu = 3200, \sigma = 500[/tex].

The proportion of their weekly sales over P4,000 is 1 subtracted by the p-value of Z when X = 4000, hence:

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

[tex]Z = \frac{4000 - 3200}{500}[/tex]

[tex]Z = 1.6[/tex]

[tex]Z = 1.6[/tex] has a p-value of 0.9452.

1 - 0.9452 = 0.0548 = 5.48%.

Hence option C is correct.

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Answer:

ab hehehe hende ko Alam hahahah

Hence, the area of the square [tex]AB[/tex]  is [tex]5[/tex]

What is the area of square?

The area of a square is equal to

(side) × (side) square units.

Here given that,

Square [tex]ABCD[/tex] is drawn on the coordinate plane (not shown) with vertex [tex]A(-4,-2)[/tex] and the midpoint of side [tex]AB[/tex] at [tex]B(-1.-6).[/tex]

Given ertices are [tex]A(-4,-2)[/tex] and [tex]B(-1.-6).[/tex]

So,

[tex]AB=\sqrt{(-1+4)^2+(-6+2)^2}\\AB=\sqrt{(3)^2+(-4)^2}\\AB=\sqrt{9+16}\\AB=\sqrt{25}\\AB=5[/tex]

Hence, the area of the square [tex]AB[/tex]  is [tex]5[/tex].

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Answer:

105°.

Step-by-step explanation:

1) to calculate m(∠ABC): m(∠ABC)=180-m(∠BAC)-m(∠(ACB)=180-90-65=25°;

2) note, m(∠ABC)=m∠(ABD)=25°, then it is possible

3) to calculate m(∠BAD): m(∠BAD)=180-m(∠ABD)-m(∠ADB)=180-25-50=105°.

Answer:

Step-by-step explanation:

or

Answer:

the answer is 10 :)

Step-by-step explanation:

Answer:

if u are asking how many more pages Matthew read then it's 48 pages. If u are asking how many they read all together then it's 144 pages.

Answer:

8% annual

Step-by-step explanation:

first find the rate of 1 year. 960/3 = 320.

then find what % of 4,000, 320 is.

8%

Answer:

46?

Step-by-step explanation:

23*2=46

Answer:

37.31 cm

Step-by-step explanation:

∡ AB = 180 - 148 = 32° = ∡ DE

∡ CD = 360 - ∡ AE - ∡ AB - ∡ BC - ∡ DE = 360 - 148 - 32 - 87 - 32 =61°

∡ CE = 61 + 32 = 93°

arc length = 2[tex]\pi[/tex]r [tex]\frac{angle}{360}[/tex] = 2×3.14×23×[tex]\frac{93}{360}\\[/tex] = 37.31 cm

Answer:

Line GH or Line HG

Step-by-step explanation:

Hope it help !!

Answer:

Step-by-step explanation:

a point to a point which makes a straight line is called a line segment

Answer:

Step-by-step explanation:

we should divide it by 3 to get a perfect square .and the square root of the perfect square is 49

[tex]\begin{gathered}\:\:\:\:\:\:\:\:\:\:\:\begin{gathered} \begin{array}{c|c} \underline{\sf{3}}& {\sf{ \underline{ \pink{7203} \: } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\ \underline{\sf{7}}&{\sf{ \underline{2401 \: \: \: }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\\underline{\sf{7}}&{\sf{ \underline{343 \: \: \: \: \: }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\\underline{\sf{7}}&{\sf{ \underline{49\: \: \: \: \: }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\\underline{\sf{7}}&{\sf{ \underline{7 \: \: \: \: \: }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\\underline{\sf{}}&{\sf{ 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \end{array}\end{gathered}\end{gathered}[/tex]

[tex]\qquad[/tex][tex]\purple{ \bf\longrightarrow 7203 = 3 \times 7 \times 7 \times 7 \times 7} [/tex]

____________________________________________

Answer:

57kg

Step-by-step explanation:

The maximum weight of a shipping container would be 57 kilograms.

The units of measurement are a collection of units used to quantify various physical quantities. Since ancient times, humans have measured these things using a variety of units, including length, mass, volume, current, and temperature.

The maximum weight of a shipping container is 125 pounds which are given in the question.

We have to determine the maximum weight in kilograms

We know that the unit conversion of pounds to kilograms as

1 pound ≈ 0.45359237 kilogram

Multiply by 125 to get

125 pounds = 0.45359237 × 125 kilograms

125 pounds = 56.69904625 kilograms

Round to the nearest kilogram,

125 pounds = 57 kilograms

Therefore, the maximum weight of a shipping container would be 57 kilograms.

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Answer:

5

Step-by-step explanation:

Answer:

250 boys

Step-by-step explanation:

sum the parts of the ratio, 5 + 3 = 8 parts

Divide the total by 8 to find the value of 1 part of the ratio

400 ÷ 8 = 50 , then

number of boys = 5 × 50 = 250

Answer : There is 250 boys in the sixth grade

Step - by - step explanation :

400 / [ 5 + 3 ] = 400 / 8 = 50

50 x 5 <-- The ratio of boys = 250

Answer:

the desired line is y = 3x - 4

Step-by-step explanation:

The slope formula is not needed here.  If the given line is y = 3x - 2, we can see immediately that the slope is 3, in both cases.

Find the y-intercept as follows:

y = mx + b => 5 = 3(3) + b, or b = -4

Then the desired line is y = 3x - 4

Answer:

Horizontal compression by a factor of 2 followed by a vertical shift by positive 3

Step-by-step explanation:

a*f(k(x-d))+c

k=2

c=3

Answer: D) 10 jerseys

Step-by-step explanation:

Let j represent the number of jerseys and C for total cost

Local company eqn: C = 5.25j + 45

Online company eqn: C = 7.75j + 20

Set both sides equal to solve:

5.25j + 45 = 7.75j + 20

5.25j - 7.75j = 20 -45

- 2.5j = -25

[tex]\frac{-2.5j}{-2.5}=\frac{-25}{-2.5}[/tex]

j = 10

Therefore, the cost is the same for both companies when 10 jerseys are sold

[tex]35m>-30\\\\\implies \dfrac{35m}{35}>-\dfrac{30}{35}\\\\\implies m>-\dfrac{6}{7}[/tex]