what is the smallest number that you can add to 17,438 that will make the sum divisible by 25?

Answer:

y=−3x-5

Step-by-step explanation:

Answer:

Find the slope of the original line and use the point-slope formula y−y1=m(x−x1)to find the line parallel to y=−3x+4y

y=−3x−5y

Answer: - 9/8

Step-by-step explanation:

Answer:

Your answer is D.Divide

Step-by-step explanation:

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\(\frac{x}{3x}+\frac{8x}{3x}=\frac{1}{3}+\frac{8}{3}=3\)

Answer:

-5/2

Step-by-step explanation:

(9,-4) and (5,6)

Slope = y2-y1/x2-x1

(6-(-4)/5-9

10/-4

-5/2

Hope this helps!

Answer:

The coordinates of point X that divides the line in 1:4 are: (3,8/5)

Step-by-step explanation:

When a point divides a line with coordinates (x1,y1) and (x2,y2) in ratio m:n,

the coordinates of point are given by:

\((x,y) = (\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n})\)

Given points are:

(x1,y1) = (5,1)

(x2,y2) = (-5,4)

Putting the values in the formula

\(X(x,y) = (\frac{(1)(-5)+(4)(5)}{1+4} , \frac{(1)(4)+(4)(1)}{1+4})\\= (\frac{-5+20}{5}, \frac{4+4}{5})\\=(\frac{15}{5}, \frac{8}{5})\\=(3,\frac{8}{5})\)

Hence,

The coordinates of point X that divides the line in 1:4 are: (3,8/5)

The piecewise function for this problem is defined as follows:

B.

The function is a piecewise function, as the function has different definitions based on the input of the function.

The different definitions for the graph are given as follows:

To the left of x = 0, we have a linear function with intercept of 2 and slope of 2, hence it is given as follows:

y = 2x + 2, x ≤ 0.

To the right of x = 0, we have a linear function with intercept of 4 and slope of -4/3, hence it is given as follows:

y = -4/3x + 4, x > 0.

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Answer:

\((f + g)(4) = 191\)

Step-by-step explanation:

Given

\(f(x) = 5x^2 - 5x + 15\)

\(g(x) = 6x^2 + 7x - 8\)

Required

\((f + g)(4)\)

First, calculate \((f + g)(x)\)

This is calculated as:

\((f + g)(x) = f(x) + g(x)\)

So, we have:

\((f + g)(x) = 5x^2 - 5x + 15+6x^2 + 7x - 8\)

Collect like terms

\((f + g)(x) = 5x^2 +6x^2 - 5x+ 7x + 15 - 8\)

\((f + g)(x) = 11x^2 + 2x + 7\)

Substitute 4 for x

\((f + g)(4) = 11*4^2 + 2*4 + 7\)

\((f + g)(4) = 191\)

We can simplify cosec(t)tant(t) to sec(t). A trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of its sides.

The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

To simplify the expression cosec(t)tant(t), we need to use the trigonometric identity:

cosec(t) = 1/sin(t)

tant(t) = sin(t)/cos(t)

Substituting these expressions into the original expression, we get:

cosec(t)tant(t) = (1/sin(t))(sin(t)/cos(t))

The sin(t) term in the numerator and denominator cancel out, leaving:

cosec(t)tant(t) = 1/cos(t)

Recalling the definition of secant, sec(t) = 1/cos(t), we can express the simplified expression as:

cosec(t)tant(t) = 1/sec(t)

Therefore, we can simplify cosec(t)tant(t) to sec(t).

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-8/27

Step-by-step explanation:

Just multiply this fraction by itself 3 times and you will get the answer then simplify.

Answer:

3 weeks and 4 days.

Step-by-step explanation:

If the plant grows 1 1/6 inches every week, then that means 1/6 inch everyday. 1 1/6 x 3 = 3 3/6

3 3/6 + (1/6 x 4) = 4 1/6

3 weeks and 4 days

Answer:

111.6

Step-by-step explanation:

92.8+28.7=121.5

121.5-9.9=111.6

Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

Answer:

15 smukeroos

Step-by-step explanation:

The cost of an entrance ticket on the trip to Spring Shot trampoline park is equal to $ \(16\frac{1}{2}\).

What do you mean by algebraic expressions ?

Algebraic expression is an equation which consists of variables and the arithmetic operations such as division , multiplication , etc.

It is given that the total cost of trip for Lorenzo and his friends is $68.

Let's assume the cost of the entrance ticket be x.

The cost of entrance ticket for all of them = 4x

The fee added to entrance ticket is $2.

So , the algebraic expression can be written as :

2 + 4x = 68

reordering the like terms :

4x = 68 - 2

4x = 66

Dividing by 2 on both sides :

2x = 33

or

x = \(\frac{33}{2}\)

or

x = \(16\frac{1}{2}\)

Therefore , the cost of an entrance ticket on the trip to Spring Shot trampoline park is equal to $ \(16\frac{1}{2}\).

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Answer:

M, t, h, and s are the consonants in the word maths.

Answer:

If you are asking for a definition, a constant is the letter in aan algebraic expression that never changes.

For Example: 5x + y

y is the constant.

Answer:

The value 155 is zero standard deviations from the [population] mean, because \( \\ x = \mu\), and therefore \( \\ z = 0\).

Step-by-step explanation:

The key concept we need to manage here is the z-scores (or standardized values), and we can obtain a z-score using the next formula:

\( \\ z = \frac{x - \mu}{\sigma}\) [1]

Where

Carefully looking at [1], we can interpret it as the distance from the mean of a raw value in standard deviations units. When the z-score is negative indicates that the raw score, x, is below the population mean, \( \\ \mu\). Conversely, a positive z-score is telling us that x is above the population mean. A z-score is also fundamental when determining probabilities using the standard normal distribution.

For example, think about a z-score = 1. In this case, the raw score is, after being standardized using [1], one standard deviation above from the population mean. A z-score = -1 is also one standard deviation from the mean but below it.

These standardized values have always the same probability in the standard normal distribution, and this is the advantage of using it for calculating probabilities for normally distributed data.

A subject earns a score of 155. How many standard deviations from the mean is the value 155?

From the question, we know that:

Having into account all the previous information, we can say that the raw score, x = 155, is zero standard deviations units from the mean. The subject   earned a score that equals the population mean. Then, using [1]:

\( \\ z = \frac{x - \mu}{\sigma}\)

\( \\ z = \frac{155 - 155}{50}\)

\( \\ z = \frac{0}{50}\)

\( \\ z = 0\)

As we say before, the z-score "tells us" the distance from the population mean, and in this case this value equals zero:  

\( \\ x = \mu\)

Therefore

\( \\ z = 0\)

So, the value 155 is zero standard deviations from the [population] mean.

∠G+∠H+∠J=180 and ∠K+∠L+∠M=180 from the angle sum property of triangle, ∠H=∠L (3rd Angle Theorem) and ∆GHJ≅∆KLM from ASA congruency theorem.

In the given question we have to prove ∆GHJ congrurnce ∆KLM.

Given that: ∠G≅∠K, ∠J≅∠M, \(\over{HJ}\) ≅ \(\over{LM}\).

As given that;

∠G≅∠K

∠J≅∠M

\(\over{HJ}\) ≅ \(\over{LM}\)

So from the angle sum property of triangle

∠G+∠H+∠J=180................(1)

∠K+∠L+∠M=180.................(2)

Now equation equation 1 and 2

∠G+∠H+∠J=∠K+∠L+∠M

As we know that ∠G=∠K, ∠J=∠M

So now the expression is

∠G+∠H+∠J=∠G+∠L+∠J

After solving ∠H=∠L (3rd Angle Theorem)

Since, ∠H=∠L, HJ=LM and ∠G=∠K, so from the theorem Angle Side Angle(ASA) congruency,

∆GHJ≅∆KLM

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Answer:

60.8

Step-by-step explanation:

Step 1: Go on g oogle

Step 2: Type "79% of 77"

Step 3: Round your answer 60.83 to 60.8 because it said round to the nearest tenth.

THIS ANSWER WAS DELETED DUE TO NOT BEING TRUE.

Answer:

  (a)  $479.50

Step-by-step explanation:

You want to know how much the friend with the smaller bedroom will pay for rent if they split the $975 cost based on the square footage of each bedroom. The two bedrooms in the 1225 square foot property are 130 and 150 square feet.

Apparently, the cost of the non-bedroom area is to be split evenly. That common area is ...

  1225 ft² -(150 +130) ft² = 945 ft²

Then the proportion due from the occupant of the smaller bedroom is ...

  (945/2 +130)/1225 = 241/490 ≈ 0.49184

That fraction of the rent is ...

  0.49184 · $975 = $479.54

The nearest answer choice is $479.50.

__

Additional comment

If we were to assume the split is based only on bedroom size, then the rent paid for the 130 ft² space would be (13/28)($975) ≈ $452.68. This would be equivalent to splitting the rent for the common area in the same proportion as for the bedrooms.

We note that half the rent is $487.50, a number less than either of the last two answer choices. Those can be rejected for that reason. (The smaller bedroom is expected to pay less than half of the rent.)

Answer:

The sales tax rate is 7.96%.

Step-by-step explanation:

To determine the sales tax rate, we need to first calculate the amount of the discount on the tablet by multiplying the regular price by the discount percentage:

Discount = Regular price * Discount percentage

Discount = $330 * 15%

Discount = $49.50

Next, we can calculate the total price of the tablet before taxes by subtracting the discount from the regular price:

Total price before taxes = Regular price - Discount

Total price before taxes = $330 - $49.50

Total price before taxes = $280.50

Finally, we can calculate the sales tax rate by dividing the total amount of taxes paid by the total price of the tablet before taxes and multiplying by 100% to express the result as a percentage:

Sales tax rate = (Total amount of taxes paid / Total price before taxes) * 100%

Sales tax rate = ($302.94 - $280.50) / $280.50 * 100%

Sales tax rate = $22.44 / $280.50 * 100%

Sales tax rate = 7.96%

Therefore, the sales tax rate is 7.96%.

Answer:

(- 3, 1.5)

--------------------------

Given system:

The first expression is ready to be substituted as no further operation is required to simplify it.

Find x:

Answer: 4000

Step-by-step explanation:

Three different expressions that simplify to x^6​ are

x¹²/x⁶

x¹⁸/x¹²

x¹. x¹⁰/x⁵

Index forms are defined as mathematical expressions used to write numbers too small or large in more convenient forms.

Other names for index forms are standard forms and scientific notations.

Note some rules of indices, they are;

Then, we have;

x¹²/x⁶

x¹⁸/x¹²

x¹. x¹⁰/x⁵

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The perimeter of the square is 16√5 mm, and the area of the square is 80 mm².

To calculate the perimeter and area of the square, we can use the formulas:

Perimeter = 4 * side length

Area = side length * side length

Substituting the given side length of 4√5mm into the formulas, we have:

Perimeter = 4 * 4√5mm = 16√5mm

Area = (4√5mm) * (4√5mm) = 16 * 5mm = 80mm²

Therefore, the perimeter of the square is 16√5mm, and the area of the square is 80mm².

Please note that the values are based on the provided side length of 4√5mm. If there are any changes to the side length, the perimeter and area will differ accordingly.

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The perimeter of the square is 16√5 mm, and the area of the square is 80 mm².

I took the test on plato.

Answer:

Step-by-step explanation:

The downstream speed is ...

  speed = distance / time

  speed = 36 km/(3 h) = 12 km/h

The upstream speed is ...

  12 km/(3 h) = 4 km/h

__

If b and c represent the speeds of the boat and current, respectively, then we have ...

  b + c = 12

  b - c = 4

Adding these gives ...

  2b = 16

  b = 8

  c = b -4 = 4

The rate of the rowing team in calm water is 8 km/h; the rate of the current is 4 km/h.

Answer:

The team is 8

The current is 4