13. The length of a rectangle is 5 cm less than 3 times the width. Theperimeter of the rectangle is 94 cm. What is the length of the rectangle?C. 33 cmA 31 cmD. 34 cmB. 32 cm

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-11)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 4 ( x +3) \\\\\\ y+11=4x+12\implies {\Large \begin{array}{llll} y=4x+1 \end{array}}\)

The equation is:

Work/explanation:

Recall that the point slope formula is \(\rm{y-y_1=m(x-x_1)}\),

where m is the slope and (x₁, y₁) is a point on the line.

Plug in the data:

\(\rm{y-(-11)=4(x-(-3)}\)

Simplify.

\(\rm{y+11=4(x+3)}\)

Simplified to slope intercept:

\(\rm{y+11=4x+12}\)

\(\rm{y=4x+1}\) <- this is the simplified slope intercept equation

The solution by substituting 15 for b in the Original equation. The answer is true.

The steps needed to solve the equation b + 6 = 21 are:

Subtract 6 from both sides of the equation: b + 6 - 6 = 21 - 6, which simplifies to b = 15.

Check the solution by substituting 15 for b in the original equation: 15 + 6 = 21, which is true.

Therefore, the correct steps to solve the equation are:

Subtract 6 from both sides of the equation. The answer is b = 15

the solution by substituting 15 for b in the original equation. The answer is true.

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Answer:  Portfolio 1:

Tech Company Stock: $2,800 * 2.95% = $82.60

Government Bond: $3,200 * 4.56% = $145.92

Total return for Portfolio 1 = $82.60 + $145.92 = $228.52

Portfolio 2:

Junk Bond: $950 * (-3.75%) = -$35.63

Common Stock: $1,500 * 7.18% = $107.70

Total return for Portfolio 2 = -$35.63 + $107.70 = $72.07

From the calculations, we can see that Portfolio 1 earns $228.52 in returns, while Portfolio 2 earns $72.07. Therefore, Portfolio 1 earns $228.52 - $72.07 = $156.45 more than Portfolio 2.

Step-by-step explanation:

The tip of the minute hand on a clock travels a distance of 4π inches in 15 minutes.

The distance traveled by the tip of a minute hand on a clock can be calculated using the circumference formula.

The circumference of a circle is given by the formula:

C = 2πr C is the circumference, π is pi (approximately 3.14159) and r is the radius.

The distance from the center of the clock to the tip of the minute hand is the radius is 8 centimeters.

The circumference of the circle traced by the tip of the minute hand is:

\(\text{C} = 2\pi \text{r}\)

\(= 2\pi (8)\)

\(= 16\pi \ \text{centimeters}\)

Since the minute hand travels the full circumference of the circle in 60 minutes, in 15 minutes it will cover 15/60 = 1/4 of the circumference.

The distance traveled by the tip of the minute hand in 15 minutes is:

\(\text{Distance} = \huge \text(\dfrac{1}{4}\huge \text) \times C\)

\(= \huge \text(\dfrac{1}{4}\huge \text) \times (16\pi)\)

\(= 4\pi \ \text{centimeters}\)

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Answer:

4π cm ≈ 12.6 cm

Step-by-step explanation:

The clock can be modelled as a circle, where the radius (r) is equal to the length of the minute hand:  r = 8 cm.

A clock face is divided into 12 equal sectors (numbered 1 to 12).

It takes 60 minutes for the minute hand to complete one revolution of the clock. Therefore, each sector represents the passing of 5 minutes.

This means that 15 minutes equals 3 sectors, which is a quarter of the circle.

To find the distance the tip of the minute hand travels in 15 minutes, we need to find a quarter of the circumference of a circle with radius 8 cm.

The formula for the circumference of the circle is C = 2πr, where r is the radius. Therefore, the equation to find the distance the tip of the minute hand travelled in 15 minutes is:

\(\sf Distance=\dfrac{2 \cdot \pi \cdot 8}{4}\)

Simplifying, we get:

\(\sf Distance=\dfrac{16 \cdot \pi}{4}\)

\(\sf Distance=4 \pi\)

Therefore, the minute hand will travel 4π cm or approximately 12.6 cm (to the nearest tenth) in 15 minutes.

Answer:

256

Step-by-step explanation:

calculator app

       The equation representing the relationship between Electricity and  Gas used, and your Bill is:

      T  =  0.25 * k + 0.97 * t

        Make a plan:

We need to find the equation that represents the relationship between the total monthly bill (T), The Kilowatt Hours of Electricity used (k), and the Terms of Gas used (t).

T  =  0.25  *  k  +  0.97  *  t

1 - Write the Equation for the cost of Electricity:

        0.25 * k

2 - Write the Equation for the Cost of Gas:

       0.97 * t

3 - Combine the Equations to Represent the total Monthly Bill (T):

       T  =  0.25 * k + 0.97 * t

Hence,  The equation representing the relationship between Electricity and  Gas used, and your Bill is:

       T  =  0.25 * k + 0.97 * t

I hope that helps!

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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Answer:

$0.60

Step-by-step explanation:

the question ask us to find the amount of the markup on Flora’s roses. The amount of markup is given by:

markup rate x original price = amount of markup

the markup rate is in decimal form

since the original price was $0.05 and the markup price is 80% = 0.80, we have

0.80 x .075 = 0.60

thus, the amount of the markup on Flora’s roses was $0.60

What is parallelogram side theorem?

The parallelogram side theorem simply means that the opposite sides of a parallelogram are equal and also parallel to each other.

Proof: We have AD || BC [Opposite sides of parallelogram ABCD]

∠BAC= ∠ACD …(i) [Alternate angles with transversal AC]

Now, AB || CD [Opposite sides of parallelogram ABCD]

∠DAC = ∠ACB …(ii) [Alternate angles with transversal AC]

In ΔABC and ΔACD, we have

∠1 = ∠3 [From (i)]

∠2 = ∠4 [From (ii)]

and AC = CA [Common]

∴ ΔABC≅ ΔCDA [By ASA Congruence]

Hence Proved.

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ΔABC≅ ΔCDA By ASA Congruence, therefore m∠ BAC ≅ m∠ DCA, hence proved using parallelogram side theorem.

What is parallelogram side theorem?

The parallelogram side theorem simply means that the opposite sides of a parallelogram are equal and also parallel to each other.

Proof: We have AD || BC [Opposite sides of parallelogram ABCD]

∠BAC= ∠ACD …(i) [Alternate angles with transversal AC]

Now, AB || CD [Opposite sides of parallelogram ABCD]

∠DAC = ∠ACB …(ii) [Alternate angles with transversal AC]

In ΔABC and ΔACD, we have

∠1 = ∠3 [From (i)]

∠2 = ∠4 [From (ii)]

and AC = CA [Common]

∴ ΔABC≅ ΔCDA [By ASA Congruence]

Hence Proved.

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The triangles ΔUVW and ΔYXW congruent to each other by ASA postulates. Then the correct option is D.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain one if two triangles are comparable to one another.

In the triangles ΔUVW and ΔYXW, then we have

∠VUW = ∠XYW           (Given)

VW = XW                     (Given)

∠UWV = ∠XWY           (vertically opposite angle)

The triangles ΔUVW and ΔYXW congruent to each other by ASA postulates. Then the correct option is D.

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Answer:

green line or "b"

Step-by-step explanation:

we can set this up into the slope intercept form

y=mx+b

where m is the slope and b is y intercept

12=3x+4y

-3x -3x

-3x+12=4y

/4.  /4.  /4

-3/4x+3=y

we can see the only line with a negative slope and a y intercept at 3 is the green line or "b"

hopes this helps please mark rainliest

Answer:

259200

Step-by-step explanation:

so there are 86400 in one day. multiply by 3.

Answer:

259200

Step-by-step explanation:

60x24x3x60=

According to the information we can infer that it will take approximately 31 years for the wolf population to reach 500.

The given function, w(x) = 14 * 1.08^x, models the number of wolves (w) in the years since 1995 (x).

To find the number of years it will take for the population to reach 500 wolves, we can set up the equation:

Dividing both sides by 14, we get:

Taking the logarithm (base 1.08) of both sides to solve for x:

Using a calculator, we find that x ≈ 31.

According to the above it will take approximately 31 years for the wolf population to reach 500 based on the given model.

Note: This question is incomplete. Here is the complete information:
Attached image

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Answer:

Step-by-step explanation:

Angles <5 and <1 are adjacent to <6.

Adjacent angles refer to those angles that share a common side and common vertex but at the same time, not overlap with each other. In this question , angle <6 is sharing a side and a common vertex  with <5 and <1 without overlapping each other. Therefore, we can say that the angles are adjacent to each other.

Similarly, if we were supposed to find the adjacent angles of <1, then, the adjacent angles would be angles <6 and <2, as they are sharing the same side and common vertex with that of <1, and are not overlapping each other.

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Answer:

41.60

Step-by-step explanation:

\(\sqrt{108}\)=10.39230485=10.40

10.40+10.40+10.40+10.40=41.60

10.40*2=20.80

\(20.80^{2}\)=432.64

Answer:

i think that the answer is 16√5

Step-by-step explanation:

4 + 4 + 4 + 4 = 16, and 4 times 4 =16

We have proven that △ABD ≅ △CBD based on the given information and the SAS congruence criterion.

To prove that △ABD ≅ △CBD, we can use the SAS (Side-Angle-Side) congruence criterion.

Given:

∠BDA ≅ ∠BDC (Both are right angles)

D is the midpoint of AC¯¯¯¯¯

AB¯¯¯¯¯ ≅ BC¯¯¯¯¯

BD¯¯¯¯¯ bisects ∠B

Proof:

Since D is the midpoint of AC¯¯¯¯¯, we have AD ≅ CD by the definition of a midpoint.

AB¯¯¯¯¯ ≅ BC¯¯¯¯¯ (Given)

BD¯¯¯¯¯ is a common side for both triangles.

∠BDA ≅ ∠BDC (Given)

To apply the SAS congruence criterion, we need to show that one pair of corresponding sides and the included angle are congruent in both triangles.

AD ≅ CD (Side) - This is true as D is the midpoint of AC¯¯¯¯¯.

∠BDA ≅ ∠BDC (Included Angle) - Both are right angles.

By the SAS congruence criterion, we can conclude that △ABD ≅ △CBD.

Therefore, we have proven that △ABD ≅ △CBD based on the given information and the SAS congruence criterion.

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Answer:

36 miles

Step-by-step explanation:

Since there are 60 minutes in a hour, you can see that 20 minutes is a third of that time. To find the answer, you multiply the values by 3 to equal on hour. 20x3 = 60 and 12x3 = 36, meaning he drove 36 miles in a hour.

(-4-3) (5+5) = -7,10

Answer:

96*48=4608

Step-by-step explanation:

4*24=96

6*8=48

am I right to think that this is multiplication

if not then use the 2 numbers and their sign whatever it may be.

fixed cost= $8

cost= $4.50

payed= $50

recieved= $10.50

how many days Hannah rented the bike.

let the unknown be ( x )

\(x = 50 - (10.50 + 8)\)

\(x = 50 - 18.50\)

\(x = 13.50\)

\(x = \frac{13.50}{4.50} \)

\(x = 7\)

hence, Hannah rented the bike for 7 days.

The equation of the circle is (x - 4)^2 + (y - 5)^2 = 4

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

The graph

A circle equation is represented as

(x - a)^2 + (y - b)^2 = r^2

Where

Center - (a, b)

From the graph, we have

(a, b) = (4, 5)

So, we have

(x - 4)^2 + (y - 5)^2 = r^2

The radius is 2

So, we have

(x - 4)^2 + (y - 5)^2 = 2^2

Evaluate

(x - 4)^2 + (y - 5)^2 = 4

Hence, the equation is (x - 4)^2 + (y - 5)^2 = 4

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Answer:

740

Step-by-step explanation:

2500 x 4 x 0.074 = 740

Answer:

11/2 times 1/3 is 11/6

Step-by-step explanation:

11/2 times 1/3,

We have to multiply the numerators and denominators,

\((11/2)(1/3) = (11*1)/(2*3) = 11/6\\11/6\)

hence we get 11/6

Answer:

$10300

Step-by-step explanation:

Given data

Marked price= Rs 10,000

discount= 10%

VAT= 13%

Let us compute the discount and the VAT

Discount

=10/100*10,000

=0.1*10,000

=$1000

VAT

=13/100*10,000

=0.13*10,000

=$1300

Hence the cost of the good will be

=10000-1000+1300

=$10300

Answer:

a. addition property of Equality

Answer:

-57

Step-by-step explanation:

4x2y + x

4(-1)*2(7) -1

-4*14 - 1

-56 -1

-57

Answer:

33.3%

Step-by-step explanation:

To get the gain percent, first we need to calculate the unit selling price and cost of each cosmetics.

If a person bought some cosmetics from wholesale market at the rate of Rs 360 per dozen., then one cosmetic will cost 360/12 = Rs. 30

Also if he sells it at Rs 80 a pair, then he sold one cosmetic at 80/2 = Rs. 40

Selling price = Rs. 40

Cost price = Rs. 30

% gain = SP-CP/CP * 100%

% gain = 40-30/30 * 100

% gain = 10/30 * 100

% gain = 100/3

% gain = 33.3%

Hence the percentage gain is 33.3%

Answer:

its ok! I accept apologies

Step-by-step explanation: