The account balance of each of three children at the end of a month is shown below:


Daniel has −$1.25

Libby has −$2.00


Sandra has as much savings in her account as the amount Daniel owes the bank.


Part A: On a blank paper, draw a number line from −4 to +4. Plot points on the number line to show the account balances of the three children. Label the points using the name of each child. Describe in detail how you created and labeled this number line, and what it looks like in detail. (5 points)


Part B: Determine whether Daniel or Libby owes the bank more. Use absolute values and inequalities to write statements that justify your conclusion. (5 points)

Answer:

True, True, False

Step-by-step explanation:

Answer:

1764

Step-by-step explanation:

[tex]from \: the \: question \: rt {}^{2} \\ were \: r =9 \\ and \: t = 14 \\ rt {}^{2} = 9 \times (14) {}^{2} = 9 \times 196 = 1764[/tex]

Hii!

__________________________________________________________

[tex]\rightsquigarrow\circ\boldsymbol{Answer.}\circ \leftharpoonup[/tex]

1764

[tex]\rightsquigarrow\circ\boldsymbol{Explanation.}\circ\leftharpoonup[/tex]

Stick in the values: 9 for r and 14 for t, and simplify.

[tex]\twoheadrightarrow\sf 9\cdot14^2}[/tex]

[tex]\bullet[/tex] Square 14 first

[tex]\twoheadrightarrow\sf 9\cdot196}[/tex]

[tex]\bullet[/tex] Multiply the numbers

[tex]\twoheadrightarrow\sf 1764}[/tex]

[tex]\bullet[/tex] Great job! We found the answer

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

--

The values of x and y at t=3 are -4.95 and 0.423 respectively.

The value of dx/dt and dy/dt are 0.71 and -2.97 respectively.

The value of the tangent slope at t=3 is 4.21.

The speed at t=3 is 3.05 units/sec.

Given the equation of x as the function of t is

x= 5 cos t

similarly, the equation of y as the function of t is

y= 3 sin t

At t=3 the value of x will be

x (at t=3) = 5 cos 3= 5(-0.989)= -4.95

At t=3 the value of y will be

y (at t=3) = 3 sin 3= 3(0.141)= 0.423

The derivative of the function of x with respect to t will be

dx/dt= d(5 cos t)/dt= 5d(cos t)/dt= -5 sin t

at t=3 the value of dx/dt will be

dx/dt (at t=3) = -5 sin 3= -5(0.141)= 0.71

The derivative of the function of y with respect to t will be

dy/dt= d(3 sin t)/dt= 3d(sin t)/dt= 3 cos t

at t=3 the value of dy/dt will be

dy/dt (at t=3) = 3 cos t= 3(-0.989)= -2.97

The tangent slope is dy/dx which can be calculated by

dy/dx= (dy/dt)(dt/dx)= (dy/dt)/(dx/dt)= 3 cos t/ -5 sin t=  (-3/5) cot t

at t=3 the value of tangent slope will be

dy/dx (at t=3) = (-3/5) cot 3= 4.21

The speed at t=3 will be

speed v= [tex]\sqrt{v_{x} ^{2} + v_{y} ^{2} }[/tex]

= √(dx/dt)²+(dy/dt)²

at t=3

= √(0.71)²+(-2.97)²

= √9.325

= 3.05 unit/sec

Therefore the values of x and y at t=3 are -4.95 and 0.423 respectively.

The value of dx/dt and dy/dt are 0.71 and -2.97 respectively.

The value of the tangent slope at t=3 is 4.21.

The speed at t=3 is 3.05 units/sec.

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Answer:

Solution:

Here,

[tex]\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline 13 \rm{m}& \rm{23.4kg} \\ \hline \rm{6m}&?\\ \hline\end{array}[/tex]

Weight of 13 m of rod=23.4 kg

Weight of 1 m of rod=23.4/13 kg

[less length,less weight]

Weight of 6 m of rod=23.4/13 ×6 kg=10.8 kg

[more length,more weight]

Thus,the weight of 6 m of rod is 10.8 kg.

Alternative method:

Let,the required weight be x kg.

Then,

[tex]\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline \rm{13m}& \rm{23.4 \: kg }\\ \hline \rm{6m}& \rm{x =? } \\ \hline\end{array}[/tex]

We know that,

More length of iron rod([tex]\red{\uparrow}[/tex]) will have the more weight([tex]\red{\uparrow}[/tex]).

So,using the rule of direct proportion;

i.e. Ratio of length=Ratio of weight

[tex] \displaystyle{ \frac{13}{6} = \rm\frac{23.4}{x} }[/tex]

[tex] \rm{13x = 6 \times 23.4}[/tex]

[tex] \rm{x = \displaystyle{ \frac{6 \times 23.4}{13} }}[/tex]

[tex] \therefore{x = 10.8}[/tex]

Thus,the weight of 6 m long iron rod is 10.8 kg.

Answer:

sure how can I help you? please tell me

Answer:

u = -18

Step-by-step explanation:

[tex]\frac{-5u}{6} =15[/tex]

Multiply both sides by 6.

-5u = 15 × 6

-5u = 90

Divide both sides by -5.

u = -18

The triangle ABC and triangle CDA are congruent by AAS [Angle - Angle-Side] property.

If two triangles are congruent, this means they are the same shape and the same size. By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.

In the given triangles we can see that:-

Therefore we can see that the triangle ABC and triangle CDA are congruent by AAS [Angle - Angle-Side] property.

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Answer:

ANSWER IS B

Step-by-step explanation:

NEXT TIME USE any graph website online

Answer:

[tex]a = 7[/tex]

Step-by-step explanation:

[tex]1. \: 7a - 70 = 13 - 4a - 6 \\ 2. \: 7a - 70 = - 4a + 7 \\ 3. \: 7a = - 4a + 7 + 70 \\ 4. \: 7a = - 4a + 77 \\ 5. \: 7a + 4a = 77 \\ 6. \: 11a = 77 \\ 7. \: a = \frac{77}{11} \\ 8. \: a = 7[/tex]

Answer:

1491 girls (99.4 percent)

Step-by-step explanation:

explanation is in the attached picture

Answer:

21

Step-by-step explanation:

[tex]3t-7=5t[/tex]

subtract 3t from both sides

[tex]-7 = 2t[/tex]

multiply both sides by 3

[tex]-21 = 6t[/tex]

so 6t = -21

Part A:

The greatest common factor is 2k

2k(2ck + 5k - 8c - 20)

Part B:

factor by grouping

2k(k - 4)(2c + 5) is the final factored form

Answer:

33, 792

Step-by-step explanation:

first convert the 8 miles to feet because our answers are in feet.

1 mile= 5280 feet

therefore 8 miles= 5280×8

= 42240

Dale and son covered 4/5 of the 42240 feet

= 4/5×42240

= 33,782 feet

The value of m∠G = 48.6° .

A triangle is a polygon with three sides , angles and vertices.

It is given that

In ΔFGH, FH = 9 ft, FG = 11 ft, and m∠F = 65°

m∠G = ?

well, using the law of cosines,

GH ² = 9² + 11² - 2(9)(11) cos65°

f = 10.88 ft

now, using the law of sines,

sinG/9 = sin65°/10.88

m∠G = 48.6°

Therefore the value of m∠G = 48.6° .

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Answer:

slant length (l) = 7.5 m

perimeter of base P = 40 m

area of base B = 100 m^2

Surface Area = 250 m^2

Step-by-step explanation:

Surface area of a pyramid formula

1/2Pl + B

1/2 (40)(7.5) + 100

150 + 100 = 250 square meters

Step-by-step explanation:

{-1,2,3,4,5,6,8} is the answer

Answer:

10

Step-by-step explanation:

24/30 = 0.8

24+x/30+x =0.85

10=x

If you want more clarification just ask

Total games Chase has to win in a row to achieve an 85% win percentage would be 10.

We can write the total number game won by Chase as -

w = 80% of 30

w = 80/100 x 30

w = 4/5 x 30

w = 24

Assume that he wins {x} games after winning 24 games to achieve 85% win percentage. Now, we can write that out of (30 + x) number of games played, Chase won (24 + x) games to achieve 85% win percentage. So, we can write that -

(24 + x)/(30 + x) = 85/100

(24 + x)/(30 + x) = 0.85

(24 + x) = 0.85(30 + x)

24 + x = 25.5 + 0.85x

0.15x = 1.5

x = 10

Total games Chase has to win in a row to achieve an 85% win percentage would be 10.

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b. Total fixed cost are $49885

Sometimes production of a product may increase or decrease, but the cost which do not change with the change of output is called fixed cost of the product.

Highest monthly total cost = $83800

Highest monthly production units = 3500 desks

Lowest monthly total cost = $61900

Lowset monthly production units = 1240 desks

So, variable cost per unit = (Highest cost-lower cost)/(highest production units-lowest production units)

= ($83800-$61900)/(3500-1240)

= $21900/2260

= $9.7

∴ Total fixed costs=Highest monthly total cost-(highest production units×variable cost per unit)

= $83800-(3500×$9.7)

= $83800-$33950

= $49850

Nearest value is $49885, whch is the correct one.

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Answer:

(x-5)²+(y+2)²=200.

Step-by-step explanation:

1) using the given coordinates it is possible to calculate

- the centre of the given circle:

[tex]x_0=\frac{10+0}{2}=5; \ y_0=\frac{2-8}{2}=-2;[/tex]

- the radius of the given circle:

[tex]r=\sqrt{(10-0)^2+(2+8)^2} =\sqrt{200} ;[/tex]

2) finally, the required equation (common form is (x-x₀)²+(y-y₀)²=r²):

(x-5)²+(y+2)²=200.

Answer:

angle 1 is 105degrees and angle 2 is 75degrees

Step-by-step explanation:

The angle below angle 2, presumably angle 6, is also 75 degrees since line c and line d are parallel. If angle 2 is 75 degrees then we know that angle 1 is 105 degrees since both angles equal a straight line and a straight line has 180 degrees.

Answer:

[tex]P = A - I[/tex]

Step-by-step explanation:

Answer:

I think it's 80%

Step-by-step explanation:

Method 1: (40/50)*100 = 80%

Method 2: [tex]\frac{40*2}{50*2} = \frac{80}{100}[/tex] = 80%

Answer:

25%

Step-by-step explanation:

In the sentence "15 is 25% of 60.", 25% is the percentage.

15 is the partial amount and 60 is the total amount.

15/60 = .25

convert a decimal to a percentage by multiplying by 100

.25 × 100 = 25

Some people use a shortcut of moving the decimal two places to the right. This is the same as multiplying by 100.

15/60 is 25%

Answer:

hi

Step-by-step explanation:

no

Step-by-step explanation:

please attach a picture for us to see the choices

Another way to write the equation is 7x + 54 = 0

Given the equation;

[tex]\frac{7}{8}x + \frac{3}{4} = -6[/tex]

Find the LCM on the left side, which is 8

[tex]\frac{7x + 6}{8} = -6[/tex]

Cross multiply

[tex]7x + 6 = -6[/tex] × [tex]8[/tex]

[tex]7x + 6 = -48[/tex]

Collect like terms

[tex]7x = -48 - 6[/tex]

[tex]7x = -54[/tex]

Take all to one side

[tex]7x + 54 = 0[/tex]

Thus, another way to write the equation is 7x + 54 = 0

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The function has a local minima at  ( 20 , -7 )

Function is a mathematical statement formed when two algebraic expression are equated by an equal sign.

The expression given is

y = -2 +5sin ( (π/12) (x-2))

the minima of the given expression will be when

the sine term = -1

as the lowest value sin can have is -1

y = -2 +5 * (-1)

y = -7

The sin ( (π/12) (x-2)) = -1

(π/12) (x-2) = 3π /2

On solving this

x = 20

Therefore the function has a local minima at  ( 20 , -7 )

It can also be confirmed form the graph attached with the answer.

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Answer:

$800

Step-by-step explanation:

per hour $40×10hours=$400

$400÷$50=8 times initial fee

8×$50=$400 total initial fee

$400hours fee+$400 initial fee=$800 total payment