how do you solve the equation 3(9/4 + 1/4y)-5y=11

Answer:

1 1/4 yard of yarn

Step-by-step explanation:

add 3/4 to 1/2 it's 1 1/4

Answer:

w=0

Step-by-step explanation:

We know a point (3,1) and the slope (-8/3), so we can use point-slope form, which is y-y1=m(x-x1)

For reference, y1 is the y in the point, m is the slope, and x1 is the x in the point

So we subsitute it

y-1=-8/3(x-3)

do distributive prop.

y-1=-8/3x+8

add 1 to both sides

y=-8/3x+9

This is the equation of the line.

Now to find w, which is the x value.

The point will pass through line, so we can susbtitute the point into the equation.

9=-8/3x+9

subtract 9 from both sides

0=-8/3x

multiply by -3/8 on both sides (the reciprocal of -8/3), we need to isolate x

0=x

x=w

therefore, w=0

Hope this helps!

The cliff divers dive headfirst from the top of cliff. 1/2 or 0.5 second is the time period will the diver's height exceed that of the cliff.

An object that moves along the vertical axis due to gravitational acceleration is called a free-falling object. The free fall position is given by the following equation of motion:

yₜ = y₀ + v₀t + 1/2(at²)

Where y₀--> the initial height of the object

v₀--> the initial velocity

t --> time

a --> the acceleration due to gravity and is equal to a = g = - 32.2 ft²/sec

We have given that,

Initial velocity of divers , v₀ = 8 feet/sec

Initial Height of top of cliff , s₀ = 87 feet

position function, s(t) = - 16t²+ v₀t +s₀

Plugging all known values in above position function,

s(t) = -16 t² + 8t + 87

The the diver's height exceed that of the cliff means, s(t) > 87

=> -16 t² + 8t + 87 > 87

Subtract 87 from both sides, we get

-16t^2 + 8t > 0 , now we solve this inequality by changing it in a equality,

-16 t² + 8t = 0

=> -8 t( 2t - 1) = 0 => -8t = 0 , 2t -1 = 0

=> either t = 0 or t = 1/2

So the first half second, the person is above the height of the cliff.

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Complete question:

Use the position function s(t)-16t2+ vot +so position, t time) to answer the following: Divers in Acapulco, Mexico, dive headfirst at 8 feet per second from the top of a cliff 87 feet above the Pacific Ocean. During which time period will a diver's height exceed that of the cliff? (vo initial velocity, so initial.

Here, ΔTPQ is isosceles and TO is the angle bisector of ∠PTO.

[∵ TP=TQ = Tangents from T upon the circle]

⠀⠀⠀⠀⠀⠀⠀⠀∴ OT⊥PQ

⠀⠀⠀

___________________________________________

\(\longmapsto{}\)By Applying Pythagoras Theorem in ∆OPR :

OR = √OP² - PR²

OR = √5² - 4²

OR = 3cm

__________________________________________

Now,

\(\leadsto\)∠TPR + ∠RPO = 90° (∵TPO=90°)

\(\leadsto\)∠TPR + ∠PTR (∵TRP=90°)

\(\leadsto\)∴ ∠RPO = ∠PTR

⠀⠀

∴ Right triangle TRP is similar to the right triangle PRO. [By A-A Rule of similar triangles]

⟼\(\frac{TP}{PO} = \frac{RP}{RO} \)

⟼\(\frac{TP}{5} = \frac{4}{3} \)

⟼\(TP= \frac{20}{3} \)

⠀⠀⠀⠀⠀

The combination of scores that won the National Championship for Baylor are 18 free throws, 24 two point field goals and 6 three-point field goals.

An equation is a mathematical statement containing two expressions on either sides which are connected with an equal to sign.

Either sides of an equation is called as left hand side and right hand side.

Given Baylor University defeated Michigan State University by a score of 84 to 62.

Score of Baylor University = 84

Baylor won by scoring a combination of two-point field goals, three-point field goals, and one-point free throws.

Let the number of free throws = x

The number of two-point field goals was six more than the number of free throws.

Number of two point field goals = x + 6

Also, the number of two-point field goals was four times the number of three-point field goals.

Number of two point field goals =  4 (number of three-point field goals)

So, 4 (number of three-point field goals) = x + 6

Number of three-point field goals = (x + 6) / 4

Score for free throw = 1 point × x

Score for 2 point field goal = 2 points × (x + 6)

Score for 3 point field goal = 3 points × [(x + 6)/4]

[1 × x] + [2 (x+6)] + [3 ((x+6)/4] = 84

x + 2x + 12 + 3/4 x + 18/4 = 84

3.75x + 16.5 = 84

3.75x = 67.5

x = 18

Number of free throws = x = 18

Number of two point field goals = x + 6 = 18 + 6 = 24

Number of three-point field goals = (x + 6) / 4 = 24/4 = 6

Hence the combination are 18 free throws, 24 two point field goals and 6 three-point field goals.

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Answer:I think its A.

Step-by-step explanation:

I'm too lazy too explain you got your answer please be happy

Answer:

(8/5) Centimeyers

Step-by-step explanation:

From 1 PM to 6 PM there is a 5 Hour difference.

Mean (total/hours) = 8/5

Answer:

1.6 cm/hour.

Step-by-step explanation:

Yes it is the unit rate.

So mean horly snowfall = total snowfall / time

= 8 / (6 - 1)

= 8/5

= 1.6 cm/hour.

Answer:

Step-by-step explanation:

Use Pythagorean to work out the side length.

The perimeter is:

Answer:

102 cm is the perimeter of the rhombus

The number of ball bearings that can be made based on the volume will be 10 ball bearings.

It should be noted that the volume based on the information given will be:

V = 4/3πr³

= 4/3 × 3.14 × 0.5³

= 0.524

From the information, it takes 5.24 cubic centimeters of molten steel to have a diameter of 1 centimeter.

Therefore, the number of ball bearings will be:

= 5.24/.0524

= 10

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Answer:13.8 is the best answer i could get

Step-by-step explanation:1,077 multiply that × 13.8 =14,862

Answer:

$35

Step-by-step explanation:

50 * 30% = 15$ discount

50 - 15 = 35$ cost

30% discount is additional so based off sales price

Each piece of webbing is either 3/5 yards or 21.6 inches long, depending on the desired unit of measurement.

To find the length of each piece of webbing, we can start by using the formula for dividing a quantity into equal parts. The formula is:

quantity / number of parts = length of each part

In this case, Alexis has 9 yards of webbing, and he wants to divide it into 15 pieces that are each the same length. Therefore, we can plug in the values into the formula as follows:

9 / 15 = length of each part

Simplifying the fraction, we get:

3 / 5 = length of each part

Therefore, each piece of webbing is 3/5 yards long.

We can also express this as a decimal or in inches, depending on the desired unit of measurement. To convert 3/5 yards to inches, we can multiply by the conversion factor of 36 (since there are 36 inches in a yard):

3/5 yards x 36 inches/yard = 21.6 inches

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Answer:

θ = π/3 and 5π/3

Step-by-step explanation:

x = r cos θ and y = r sin θ.  Therefore:

dy/dx = (dy/dθ) / (dx/dθ)

dy/dx = (r cos θ + r' sin θ) / (-r sin θ + r' cos θ)

In this case, r = 1 + cos θ and r' = -sin θ.

dy/dx = ((1 + cos θ) cos θ + (-sin θ) sin θ) / (-(1 + cos θ) sin θ + (-sin θ) cos θ)

dy/dx = (cos θ + cos²θ − sin²θ) / (-sin θ − sin θ cos θ − sin θ cos θ)

dy/dx = (cos θ + cos²θ − (1 − cos²θ)) / (-sin θ (1 + 2 cos θ))

dy/dx = (cos θ + 2 cos²θ − 1) / (-sin θ (1 + 2 cos θ))

The tangent line is horizontal when the numerator of dy/dx is 0 and the denominator of dy/dx is not 0.

0 = 2 cos²θ + cos θ − 1

0 = (cos θ + 1) (2 cos θ − 1)

cos θ = -1 or 1/2

θ = π/3, π, 5π/3

0 = -sin θ (1 + 2 cos θ)

sin θ = 0 or cos θ = -1/2

θ = 0, 2π/3, π, 4π/3

Therefore, the answer is θ = π/3 and 5π/3.

the initial expression is:

Answer:

A

Step-by-step explanation:

Answer:

Z = -15

Step-by-step explanation:

z - 1 +16 = 0

z + 15 = 0

subtract 15 from both side to get z by itself

z+15-15 = -15

so the answer will be z=-15

Answer:

y = \(\frac{3}{4}\) x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = \(\frac{0-(-3)}{4-0}\) = \(\frac{0+3}{4}\) = \(\frac{3}{4}\)

the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = \(\frac{3}{4}\) x - 3 ← equation of line

Answer:

B. 1395 sq. units

Step-by-step explanation:

Since the shape is an octagon, it is also composed of 8 triangles. If you solve the formula for the area of a triangle with those numbers and multiply it by the amount of sides you will have the total area.

Answer:

B. 1395 sq. units

Step-by-step explanation:

A=2(1+\(\sqrt{2}\))a²

A=2(1+\(\sqrt{2}\))17²

A=2(1+\(\sqrt{2}\))289

A≈4.83×289

A≈1395.87

A≈1395 units²

The option that fits this is B. 1395 sq. units

Answer:

67 degrees

Step-by-step explanation:

Angle 2 and angle 7 are vertical angles since l is the transversal.

so that means <2=<7

4x+39=12x-17

Simplify: isolate the variable:

56=8x

divide by 8:

7=x

now plug it in to m<2

4(7)+39=m<2

28+39

67=m<2

i hope this helps!

The total number of bacteria in the dish is 31457280

The expression is given as:

Total = (32)^4 * 30

Start by evaluating the exponent

Total = 1048576 * 30

Next, evaluate the product

Total = 31457280

Hence, the total number of bacteria in the dish is 31457280

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Answer:

A (3^8)

Step-by-step explanation:

I have this question on my test. I'm just assuming the person didn't put ^.

(3^2)^4 times 3^0

Answer:

1/36

Step-by-step explanation:

When you roll it the first time, the chances to get a 1 is 1/6.

when you roll it the second time, the chance is still 1/6, but the chance of rolling one twice in a row, is the product of the probabilities:

1/6 * 1/6 = 1/36

Answer:Angle x is congruent with the interior angle opposite side 8 (alternate interior angles)

Use tangent:

tan x = 8/15

x = arctan (8/15)

x = 28.1° (rounded)

Step-by-step explanation:

The general solution to the system x' = Ax, where A is the given matrix, can be expressed as x(t) = Ce^(At), where C is a constant matrix and e^(At) is the matrix exponential of At. This solution represents a linear combination of exponential functions, where each component of x(t) is determined by the corresponding component of C and the matrix exponential of At.

To find the general solution to the system x' = Ax, we can express the solution in terms of the matrix exponential. The matrix exponential of At, denoted as e^(At), is defined as the power series expansion of the exponential function applied to the matrix At. It can be computed using various techniques, such as diagonalization, Jordan decomposition, or power series.

The general solution to the system x' = Ax can then be written as x(t) = Ce^(At), where C is a constant matrix. This solution represents a linear combination of exponential functions, where each component of x(t) is determined by the corresponding component of C and the matrix exponential of At.

The matrix exponential e^(At) has properties that are analogous to those of the scalar exponential function. It satisfies the initial condition e^(A * 0) = I, where I is the identity matrix, and it can be used to find solutions for different initial conditions by appropriately choosing the constant matrix C.

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Recall that like terms are terms that have the same variables and powers. The coefficients of the terms do not have to match.

a.- Notice that 4z and -3z are like terms since they have the same variables with the same exponents, therefore:

b.- Notice that 3n and -3n are like terms, but 6 is a constant, therefore:

c.- In the given expression, the similar terms are 2g and -8g, and -3 and 11, therefore:

d.- In the last expression, first, we have to apply the distributive property:

Now, adding like terms we get:

Answer:

a.-

b.-

c.-

d.-

The lowest point should be used for measurement. To acquire a correct reading, students must read the meniscus at eye level. In order to read the meniscus at eye level, students need first set the graduated cylinder on the table and then stoop.

A measuring cylinder, often referred to as a graded cylinder, a cylinder measuring cylinder, or a mixing cylinder, is a piece of lab apparatus used to gauge the quantity of fluids, chemicals, or solutions used during a typical lab session. Compared to common laboratory flasks and beakers, graduated cylinders offer higher precision and accuracy. The graduated cylinder is a scientific tool that employs the metric system rather than the American standard system, so measurements are made in millilitres rather than ounces. The volume of an object or quantity of liquid is measured using a graduated cylinder, a common piece of laboratory glassware. It is a glass cylinder with side markings resembling those on a measuring cup, as its name suggests.

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The balance increase for card i is $89.24 greater than the balance increase for card h. Card i has a balance of $1,522.16 and an interest rate of 12.05%, compounded monthly. Now, we can calculate the balance for both cards after three years using the compound interest formula: A = P(1 + r/n)^(nt)

Given, Card h has a balance of $1,186.44 and an interest rate of 14.74%, compounded annually.

Card i has a balance of $1,522.16 and an interest rate of 12.05%, compounded monthly. Now, we can calculate the balance for both cards after three years using the compound interest formula: A = P(1 + r/n)^(nt),

where A = final amount, P = principal (initial balance), r = annual interest rate (as a decimal), n = number of times compounded per year, t = time (in years)

For card h,

A = 1186.44(1 + 0.1474/1)^(1*3)

A = 1883.99

For card i, A = 1522.16(1 + 0.1205/12)^(12*3)

A = 1973.23

Therefore, the balance for card i will have increased more than that of card h, and the difference in the increase is: 1973.23 - 1883.99 = 89.24

The balance increase for card i is $89.24 greater than the balance increase for card h. Hence, the required answer is card i.

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log 30+ log 6 is not equivalent to log 36

Equivalent expressions are expressions that perform the same function not with standing their appearance. If two algebraic expressions are equivalent, they have the same value when the same value(s) for the variable are used (s).

The original phrase is as follows

Log 36

Following that, we write the alternatives (a) log 2+ log 18

Apply the logarithmic rule log 2+ log 18 log (218)

Log 2 plus log 18 log (36)

Remove the bracket

Log 2 plus log 18 log36

(a) Log 2+ Log 18 is the same as log 36.

(b) Log 30 plus log 6

Use the logarithms’ law. 30 logs or more 6 logs (30 x 6)

Log 30 plus log 6 Equals log (180)

Remove the bracket

Log 30-plus log 6-log180

Hence,

(c) Log 30+log 6 does not equal log 36.

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The ordered pair for the equation x-2y=4​ will be (-4,-4).

A mathematical equation is a claim that two expressions, which may contain variables or numbers, are equal. Equations are essential questions, and the main motivations for the development of mathematics have been efforts to methodically discover answers to these questions.

It is given that the equation is x-2y=4​.

We have to find the ordered pair for the triangle.

You may run a test to see whether an ordered pair is a solution to an equation. Put the ordered pair's x-value into the equation after identifying it. It is clear that the ordered pair is a solution to the equation if, after simplifying, the y-value you obtain matches the y-value in the ordered pair.

The question is incomplete.

The complete question is to find the ordered pair of the equation  x-2y=4​ is the coordinates (-4,y)

x-2y=4​

-4-2y=4

-2y=4+4

2y=-8

y= -4

Thus the ordered pair will be (-4,-4).

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