What is the slope of the line

Answer:

[tex]=50m^{\frac{5}{3}}n^{\frac{3}{8}}[/tex]

Step-by-step explanation:

[tex]\left(5m^{\frac{4}{3}}\cdot \:5n^{\frac{1}{4}}\right)\left(m^{\frac{1}{3}}\cdot \:2n^{\frac{1}{8}}\right)[/tex]

[tex]=m^{\frac{4}{3}}\cdot \:5^{1+1}n^{\frac{1}{4}}m^{\frac{1}{3}}\cdot \:2n^{\frac{1}{8}}[/tex]

[tex]=m^{\frac{4}{3}}\cdot \:5^2n^{\frac{1}{4}}m^{\frac{1}{3}}\cdot \:2n^{\frac{1}{8}}[/tex]

[tex]=5^2n^{\frac{1}{4}}m^{\frac{4}{3}+\frac{1}{3}}\cdot \:2n^{\frac{1}{8}}[/tex]

[tex]=5^2m^{\frac{4}{3}+\frac{1}{3}}\cdot \:2n^{\frac{1}{4}+\frac{1}{8}}[/tex]

[tex]=5^2\cdot \:2m^{\frac{5}{3}}n^{\frac{1}{4}+\frac{1}{8}}[/tex]

[tex]=5^2\cdot \:2m^{\frac{5}{3}}n^{\frac{3}{8}}[/tex]

[tex]=50m^{\frac{5}{3}}n^{\frac{3}{8}}[/tex]

Answer:-4x+3y=1

Step-by-step explanation:

First put the equations above one another

-2x+7y=-5

-2x-4y= 6

Just add the corresponding number from the top from the one right below it

-2x plus -2x is 4x

7y plus -4y is 3y

-5 plus 6

Then bring down the equal sign

And you get

-4x+3y=1

The addition of the two equations -2x+7y=-5 and -2x-4y=6 is -4x +3y = 1.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the two equations are -2x+7y=-5 and -2x-4y=6. The equations can be added as below,

Write the two equations with the like terms adjacent to each other than perform the algebraic operation and get the final solution.

-2x+7y=-5

-2x-4y=6

________

-4x + 3y = 1

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Answer:1/4

Step-by-step explanation:there are four sides one is shaded so the answer is 1/4

The shaded area is equal to 1/4

Answer: The weight of mail at noon is 104 pounds.

Step-by-step explanation:

Given that , At a post office, the weight of the mail at 10.00 A.M was 80 pounds.

Two hours later, the weight of the mail had increased by 30%.

Since , time after 2 hours of 10 A.M would be 12 P.M which is known as noon.

Mathematically , the weight of the mail at noon = (Weight at 10 AM) +30% of (Weight at 10 AM)

= 80 + 0.30(80) pounds

= 80 (1+0.30) pounds

= 80 (1.30) pounds

= 104 pounds

Hence, the weight of mail at noon is 104 pounds.

Answer:

The factors are 7 * 2 * 2 * 2

Step-by-step explanation:

Step 1:  Find all of the factors

                     56

               28        2

          14        2

      7        2

Answer: The factors are 7 * 2 * 2 * 2

Answer:

15/8

Step-by-step explanation:

The tangent of an angle is the opposite side over the adjacent side. In this case, the opposite side length is the square root of 17^2-8^2=15. This means that the tangent of angle R is 15/8. Hope this helps!

108 / 1376 is the probability that a student participates in both sports and music.

Step-by-step explanation:

It is given that,

A suburban high school has a population of 1376 students.

The number of students who participate in sports is 649.

The number of students who participate in music is 433.

To find the probability of event A (sports) :

P(sports) = No.of students participated in sports / Total students.

⇒ 649 / 1376

∴ P(A) = 649 / 1376

To find the probability of event B (music) :

P(music) = No.of students participated in music / Total students.

⇒ 433 / 1376

∴ P(B) = 443 / 1376

From the question, we know that the probability that a student participates in either sports or music is 974 /1376.

∴ P(A∪B) = 974 / 1376

To find the probability that a student participates in both sports and music :

The formula used here is,

P(A∩B) = P(A) + P(B) - P(A∪B)

⇒ 649 / 1376 + 433 / 1376 - 974 /1376

⇒ 108 / 1376

∴ P(A∩B) = 108 / 1376

The probability that a student participates in both sports and music is 108/1376

The given parameters are:
Total = 1376

Sport = 649

Music = 433

P(Sport or Music) = 974/1376

The required probability is:

P(Sport and Music) = P(Sport) + P(Music) - P(Sport or Music)

This gives

P(Sport and Music) = 649/1376 + 433/1376 - 974/1376

Evaluate the expression

P(Sport and Music) = 108/1376

Hence, the probability that a student participates in both sports and music is 108/1376

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Answer:

Compare the equivalent temperatures as a ratio; if the ratios are equivalent, then the temperatures vary directly.

Step-by-step explanation:

Took the test - answer got deleted :/

Answer:

The independent variable is the variable that can be changed.

The dependent variable is wjat you measure in an experiment

Answer:

[tex]5x + 2 - x + 10 \\ 5x - x + 2 + 10 \\ 4x + 12 \\ = 4(x + 3)[/tex]

hope this helps you....

Answer:

There were 60 nano-related patents granted in 1991

Step-by-step explanation:

Given:

The figure contains a right triangle.

The two angles of the triangle are 45° each.

The length of one leg is 3 units.

The length of the hypotenuse is x units.

We need to determine the value of x.

Value of x:

The value of x can be determined using the formula,

[tex]cos \ \theta=\frac{adj}{hyp}[/tex]

where [tex]\theta=45^{\circ}[/tex], adj = 3 and hyp = x.

Substituting these values, we get;

[tex]cos \ 45^{\circ}=\frac{3}{x}[/tex]

Simplifying, we get;

[tex]x=\frac{3}{cos \ 45^{\circ}}[/tex]

[tex]x=\frac{3}{\frac{\sqrt{2}}{2}}[/tex]

[tex]x=3 \times \frac{2}{\sqrt{2}}[/tex]

[tex]x=\frac{6}{\sqrt{2}}[/tex]

Thus, the value of x is [tex]x=\frac{6}{\sqrt{2}}[/tex]

Answer:

Step-by-step explanation:

[tex]\frac{4}{5}(\frac{1}{4}-5)=\frac{4}{5}*\frac{1}{4}-\frac{4}{5}*5\\\\=\frac{1}{5}-4\\\\=\frac{1}{5}-\frac{4*5}{1*5}\\\\=\frac{1}{5}-\frac{20}{5}\\\\=\frac{1-20}{5}\\\\=\frac{-19}{5}[/tex]

We have been given that a person invests 5500 dollars in a bank. The bank pays 6.75% interest compound monthly. We are asked to find the time that will take the amount to 13,200 dollars.

We will use compound interest formula to solve our given problem.  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,

A = Final amount,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year,

t = Time in years.

[tex]6.75\%=\frac{6.75}{100}=0.0675[/tex]

Upon substituting our given values in above formula, we will get:

[tex]13200=5500(1+\frac{0.0675}{12})^{12\cdot t}[/tex]

[tex]13200=5500(1+0.005625)^{12\cdot t}[/tex]

[tex]13200=5500(1.005625)^{12\cdot t}[/tex]

[tex]\frac{13200}{5500}=(1.005625)^{12\cdot t}[/tex]

[tex]2.4=(1.005625)^{12\cdot t}[/tex]

Now we will take natural log on both sides.

[tex]\text{ln}(2.4)=\text{ln}((1.005625)^{12\cdot t})[/tex]

Using natural log property [tex]\text{ln}(a^b)=b\cdot \text{ln}(a)[/tex], we will get:

[tex]\text{ln}(2.4)=12t\cdot \text{ln}(1.005625)[/tex]

[tex]t=\frac{\text{ln}(2.4)}{12\cdot \text{ln}(1.005625)}[/tex]

[tex]t=13.00635[/tex]

Upon rounding to nearest tenth, we will get:

[tex]t\approx 13.0[/tex]

Therefore, it will take approximately 13.0 years for the amount to reach $13200.

Answer:

(C) Nathaniel can build at most 3 birdhouses.

Step-by-step explanation:

Given that:

[tex]43B+215H \leq 3000[/tex]

where:

Nathaniel wants to build 50 birds(B) using lego Blocks, we want to determine how many birdhouses(H) he can build with the remaining Lego blocks.

If B=50

[tex]43(50)+215H \leq 3000\\2150+215H \leq 3000\\\text{Subtract 2150 from both sides}\\215H \leq 3000-2150\\215H \leq 850\\\text{Divide both sides by 215}\\H \leq 3.95[/tex]

Therefore, Nathaniel can build at most 3 Birdhouses.

Answer: 3

Step-by-step explanation:

We are given that the number of birds Nathaniel wants to build using Lego blocks is \blue{50}50start color #6495ed, 50, end color #6495ed. When we substitute \blue B = \blue {50}B=50start color #6495ed, B, end color #6495ed, equals, start color #6495ed, 50, end color #6495ed in the given inequality, we will obtain an inequality for HHH alone:

\begin{aligned}43B+215H &\leq 3000\\\\ 43(\blue {50})+215H &\leq 3000 \\\\ 215H &\leq 850\\\\ H&\leq 3 \dfrac{41}{43}\end{aligned}

43B+215H

43(50)+215H

215H

H

​

≤3000

≤3000

≤850

≤3

43

41

​

​

Hint #22 / 3

So HHH must be less than or equal to 3\dfrac{41}{43}3

43

41

​

3, start fraction, 41, divided by, 43, end fraction. However, we should remember that the number of birdhouses Nathaniel can build must be an integer.

Since 333 is the biggest integer less than or equal to 3\dfrac{41}{43}3

43

41

​

3, start fraction, 41, divided by, 43, end fraction, Nathaniel can build 333 birdhouses at most with the remaining Lego blocks.

Hint #33 / 3

Nathaniel can build at most 3 birdhouses.

Answer:

that is the answer to the question

Answer: 1.875 days

Step-by-step explanation:

Hi, to answer this question we simple have to divide the total day of the month (30 days) by the number of days that she offers tutoring (16).

Mathematically speaking:

30 /16 =1.875 days

1.875 days is equivalent to the fraction of days that tutoring was offered in November

Feel free to ask for more if needed or if you did not understand something.

Answer:0.533

Step-by-step explanation:

Sam's mathematics teacher offered after school tutoring 16 days out of the 30 days that were in November in order to help students review for the mid-term exam.

To convert this to a decimal, we divide the number of days tutorial was offered in November by the number of days in November. This will be:

= 16/30

= 0.533

The decimal that is equivalent to the fraction is 0.533.

To rewrite the integral over an appropriate region G in the​ uv-plane, we need to use the given transformation x = u/v and y = uv. The region G is defined by certain constraints on u and v, which can be found by solving the inequalities derived from the boundaries of R in the xy-plane. Finally, we can set up and evaluate the double integral over G.

To rewrite the integral over an appropriate region G in the​ uv-plane, we need to use the given transformation x = u/v and y = uv. Let's consider each boundary of R separately:

Now, we need to find the region G in the uv-plane that corresponds to R in the xy-plane. The region G is defined by the following constraints: u^2 ≤ v, 9v ≥ u^2, uv ≤ u/v, and uv ≥ 4(u/v). Combining these constraints, we get u^4 ≤ v^2 ≤ 9u^3 and u^2 ≤ 4v. The boundaries of G can be found by solving these inequalities.

To evaluate the integral over G, we need to determine the limits of integration for u and v. Once we have the limits, we can set up the double integral of the function over G and evaluate it.

Answer:

x = 15.65

y = 3.5

Step-by-step explanation:

Step 1

Find the equation for x and y

Equation for x is given as

x² = 7( 7+28) ..........Equation 1

14(14 + y) = x²........ Equation 2

Solving for Equation 1

x² = 7( 7+28)

x² = 7(35)

x² = 245

x = √245

x = 15.65

From Equation 1 , x² has been determined to be 245

Therefore we substitute 245 for y in Equation 2

14(14 + y) = x²........ Equation 2

14(14 + y) = 245

196 + 14y = 245

14y = 245 - 196

14y = 49

y = 49 ÷ 14

y = 3.5

Answer:

4/h+7

Step-by-step explanation:

4 is on top of H+7

Answer:

See below.

Step-by-step explanation:

RSTV is a quadrilateral. We see that segments RV and RS are congruent. We also see that segments TV and TS are congruent. That makes quadrilateral RSTV a kite. A kite is a quadrilateral that has one set of congruent adjacent sides and a second set of congruent adjacent sides. One set of congruent adjacent sides may or may not be congruent to the second set of congruent adjacent sides. In this case they are not.

The diagonals of a kite are perpendicular which is shown in your figure with segment VS perpendicular to segment RT. The diagonals form 4 right triangles. The 4 right triangles are VRW, SRW, VTW, and STW.

Triangles VRW and SRW are congruent.

Triangles VTW and STW are congruent.

Let's work on the angles first.

Let's work on triangle VTW.

Angle VWT is a right angle.

m<VWT = 90

m<WVT = 42

m<VWT + m<VTW + m<WVT = 180

90 + 42 + m<WVT = 180

m<WVT + 132 = 180

m<WVT = 48

Triangle SWR is a right triangle.

m<RWS + m<RSW + m<SRW = 180

90 + m<RSW + 21 = 180

m<RSW + 111 = 180

m<RSW = 69

Triangles WVR and WSR are congruent with corresponding angles WVR and WSR.

m<WVR = m<WSR = 69

m<TVR = m<WVT + m<WVR

m<TVR = 48 + 69 = 117

m<TVR = 117

Now we deal with sides.

Let's look at triangle VWT.

Side VT is the hypotenuse.

m<VTW = 42 deg

VT = 15

For angle VTW, VW is the opposite leg, and VT is the hypotenuse.

The trig ratio that relates the opposite leg and the hypotenuse is the sine.

[tex] \sin \angle A = \dfrac{opp}{hyp} [/tex]

[tex] \sin \angle VTW = \dfrac{VW}{VT} [/tex]

[tex]\sin 42^\circ = \dfrac{VW}{15}[/tex]

[tex]VW = 15 \sin 42^\circ[/tex]

VW = 10

Since triangles RVW and RSW are congruent, corresponding sides VW and SW are congruent.

SW = VW = 10

Trianlge RSW is a right triangle with right angle RWS.

For angle WRS, SW is the opposite leg. RW is the adjacent leg.

[tex] \tan A = \dfrac{opp}{adj} [/tex]

[tex] \tan \angle WRS = \dfrac{SW}{RW} [/tex]

[tex] \tan 21^\circ = \dfrac{10}{RW} [/tex]

[tex] RW \tan 21^\circ = 10 [/tex]

[tex] RW = \dfrac{10}{\tan 21^\circ} [/tex]

RW = 26

We now know VW and RW. Using the Pythagorean theorem we can find RV.

(RW)^2 + (VW)^2 = (RV)^2

26^2 + 10^2 = (RV)^2

RV = 28

Perimeter:

Triangles RVT and RST are congruent, so we have:

RV = RS = 28

VT = ST = 15

perimeter = RS + RV + VT + ST

perimeter = 28 + 28 + 15 + 15

perimeter = 86

Answer:

4^-2

Step-by-step explanation:

4^4(4^-7)(4)      I solved this separately

256(0.00006103515625)(4)         Multiply

0.015625(4)                                    Multiply

0.0625

This decimal is equivalent to 4^-2

4^-2 = 0.0625

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Final answer:

The expression [tex]4^4(4^-7)(4[/tex]) simplifies to [tex]4^-2[/tex] by adding the exponents of the same base, resulting in a single exponent expression.

Explanation:

To simplify the expression [tex]4^4(4^-7)(4)[/tex] using a single exponent, you'll need to apply the rules of exponents. When you have the same base being multiplied, you can add the exponents. Start by looking at the terms 4^4 and 4^-7. The rule says to add the exponents when multiplying: 4 + (-7) = -3. So those two terms combine to make 4^-3.

Next, we have the single 4, which can also be written as 4^1 since any number to the power of 1 is itself. Now add the exponents again: -3 + 1. This gives us[tex]4^-2[/tex], which is the expression simplified with a single exponent.

The correct answer to this problem is therefore [tex]4^-2.[/tex]

The transformation (x, y) → (x, 2y) doubles the y-coordinates of the parallelogram ABCD vertices, resulting in a new parallelogram with doubled height and consequently doubled area, demonstrating that the change in height is proportional to the original height.

The question posed relates to the effect of a transformation on the coordinates of a parallelogram's vertices. Specifically, we look at the transformation (x, y) → (x, 2y), which stretches the y-coordinates of the vertices while keeping the x-coordinates unchanged. For the given parallelogram ABCD with vertices A(0, 0), B(1, 1), C(3, 1), and D(2, 0), we apply the transformation to each vertex:

The transformation doubles the height (y-coordinate) of the parallelogram, while the base (x-coordinate) remains the same. Consequently, the area of the parallelogram also doubles, confirming that the change in height is proportional to the original height. By applying the transformation to a simple geometric figure, students can visualize and understand the properties of transformations and their effects on the shapes.

Answer:

it's C my doods

Step-by-step explanation:

Yes, 9²+40²=41²

Pythagoras theorem states that, a right-angled triangle, the square of the one side is equal to the sum of the squares of the other two sides.

Pythagorean Triples where any 2 side the sum of the squares adds up to be equal the other side.

A triangle has side lengths are 40, 9 and 41

∵ 41 is the longest side length and that makes it the hypotenuse

The square of the two other sides is 9²+40² = 1,681

Also, 41² = 1,681

As we can see, the sum of the squares equal the square of the hypotenuse

Since this triangle follows the theorem, we can conclude that the triangle is a right triangle

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There is no answer, there is no table.

Answer:

k=8

Step-by-step explanation:

You can solve this by setting up an equation.

7*(k-5)=21

k-5=3

k=8

Hope this helps!

Answer:

Option A) 0.588

Step-by-step explanation:

We are given the following in the question:

In triangle ABC

AC = 8 cm

AB = 13.6 cm

We have to find the sine ratio of angle B.

We define sine ratio of angle B as:

[tex]\sin B = \dfrac{\text{Perpendicular}}{\text{Base}}[/tex]

Putting values, we get,

[tex]\sin B = \dfrac{AC}{AB} = \dfrac{8}{13.6} = 0.588[/tex]

The attached image shows the triangle.

The correct ansqwer is

Option A) 0.588

Answer:

Length: 7 units

Width: 1 unit

Step-by-step explanation:

The length of rectangle is 7 units.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the length of rectangle be x.

Then, width of the rectangle = x - 6

Also, Area of rectangle = 7 units

So, length x width = 7

x(x- 6)= 7

x² - 6x = 7

x² -6x -7 =0

x² -7x + x - 7=0

x( x- 7) +1 (x- 7)= 0

(x+ 1)(x- 7)=0

x= -1 or 7.

Hence, the length of rectangle is 7 units.

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Step-by-step explanation:

1 pie in total: $13.66

1 slice: $1.70

1 pie in total: $20.11 (75+1.36×4)÷4

1 slice: $1.67

Answer:

y = 225x + 28,000 (please give branliest)

Step-by-step explanation:

X = amount of tickets