What is the solution of the system? {5x−y=−21x+y=−3 Enter your answer in the boxes. ( , )

Total surface area

=2 ×(area of triangle) +( area of rectangle 1) + (area of rectangle 2) + (area of rectangle 3)

2×(1/2 × 16 ×12) + (10×12)+(16×10)+(20×10)

=672 cm²

Answer:

i think four but im prolly wrong

Step-by-step explanation:

Answer:

\(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\)

Step-by-step explanation:

Integrate v(t) with respect to time

\(\displaystyle \int(3t^3+30t^2+5)\,dt\\\\=\frac{3}{4}t^4+10t^3+5t+C\)

Plug-in initial condition to get C

\(\displaystyle s(0)=\frac{3}{4}(0)^3+10(0)^3+5(0)+C\\\\3=C\)

Thus, the position function is \(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\) given the velocity function and initial condition.

We have the function

then

therefore f(10)=-130.

Answer:

A linear function is a special type of function whose graphs are straight lines (as their name suggests). Let’s look at a straight line and find out what this particular shape of graph tells us about the relationship between the input  and the output  of a linear function.

Step-by-step explanation:

pls mark as brainliest

Answer:

b= (3z-6)/(1+3z)

Step-by-step explanation:

z=(-b+6)/(3b-3)

cross multiple

z(3b-3)=-b+6

open the bracket

3bz-3z=-b+6

make -b the subject of the formula

-b = 3bz-3z-6

-b - 3bz = -3z - 6

factorize the left hand side...

-b(1+3z) = -3z-6

make -b the subject of the formula again

-b = -(3z-6)/(1+3z)

cancel the minus at both sides...

b = (3z-6)/(1+3z)

Answer:

b = \(\frac{3z + 6}{3z+1}\)

Step-by-step explanation:

Simply solve for "b" , so the formula will be

b = .....

z = \(\frac{-b+6}{3b-3}\) ( b > 0 )

z(3b - 3) = - b + 6

3zb - 3z = - b + 6

3zb + b = 3z + 6

b( 3z + 1 ) = 3z + 6

b =  \(\frac{3z + 6}{3z+1}\)

Using the property of similar triangles, we found that the value of n is 5.

This is the length of the side RQ.

What are similar triangles?

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are similar. Similar figures are described as items with the same shape but varying sizes, such as two or more figures. Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are identical, their respective sides are equal in number and their corresponding angles are congruent.

The given triangles are both right triangles.

So they can be considered similar triangles.

One of the properties of similar triangles is that the ratio of corresponding sides is always equal.

Then we can write for the given triangles,

  BA/RQ = AC/QS

 2/n = 4/10

n = 2 * 10 / 4 = 5

Therefore using the property of similar triangles, we found that the value of n is 5.

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Answer:

The slope is \(-\frac{3}{4}\)

Step-by-step explanation:

To find the slope, you take 2 points and use rise/run. I used (0,1) and (4,-2) because they look like they are being touched by the line. So by looking at the graph, I have to look at how I can get from (0,1) to (4,-2). So from (0,1), I go down 3 units which makes my number -3, over the run which is 4 units to the right, which makes it positive. so I went down 3 and then went right 4, making this    \(-\frac{3}{4}\). You could also use point-slope which means \(\frac{y2-y1}{x2-x1}\) or \(\frac{-2-1}{4-0}\) which equals the same thing

Answer:

\( \frac{ {x}^{ - 2} {y}^{ \frac{1}{2} } }{ \sqrt{36x {y}^{2} } } = \frac{ \sqrt{y} }{ {x}^{2} \sqrt{36x {y}^{2} } } = \frac{ \sqrt{y} }{6 {x}^{2}y \sqrt{x} } = \frac{1}{6 {x}^{ \frac{5}{2} } {y}^{ \frac{1}{2} } } = \frac{1}{6} {x}^{ - \frac{5}{2} } {y}^{ - \frac{1}{2} } \)

\( \frac{1}{6} \times - \frac{5}{2} \times - \frac{1}{2} = \frac{5}{24} \)

Using fractional operation, since Jack ate ¹/₂ of the delicious pizza with ¹/₆ left, Jill ate ¹/₃ of it.

The fractional operations involve mathematical operations using fractions, which are parts or portions of the whole value or quantity.

Some of the mathematical operations include addition, subtraction, multiplication, and division.

The fraction ate by Jack = ¹/₂

The fraction of the pizza left over after Jack and Jill have eaten = ¹/₆

The fraction or portion that Jill ate = ¹/₃ [1 - (¹/₂ + ¹/₆)]

Thus, we can conclude that Jill ate ¹/₃ of the delicious pizza.

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Answer:

That handy button allows you to instantly change a positive number into a negative number, or, to change a negative number to a positive one

Answer: c. (5,2)

Step-by-step explanation:  We have two equations here and need to calculate the value of x and y.

The two equations are:

2x+5y = 20

3x - 4y = 7

Using the Substitution method,

2x=20-5y

x=(20-5y)/2

Now substitute the value of x in equation (2)

3 × \(\frac{20-5y}{2} - 4y = 7\)

60-15y-8y = 14

60-23y=14

-23y = -46

y=2

Now put the value of y in any equation.

x = (20-10)/2

x=5          

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Answer:

y = - 2x - 6

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 )

Here m = - 2 , then

y = - 2x + c ← is the partial equation

To find c substitute (- 4, 2 ) into the partial equation

2 = 8 + c ⇒ c = 2 - 8 = - 6

y = - 2x - 6 ← equation of line

Answer:

No solution

Step-by-step explanation:

5x−4≥12 AND 12x+5≤−4

solve it separately

5x - 4>=12

add 4 on both sides

5x >= 16

Divide both sides by 5

x > = 16/5

12x+5≤−4

subtract 5 from both sides

12x <= -9

divide both sides by 12

x<= -9/12

x<=-9/12   and x>= 16/5

There is no intersection between the inequalities

so there is no solution

The lengths of LV and OE are 15cm, and the lengths of LD and EV are 3√7 cm and 9/√7 cm, respectively.

Since LOVE is a kite, LV and OE are perpendicular bisectors of each other. Let the length of LD be x, and the length of EV be y. Then, we can use the Pythagorean theorem and the fact that the diagonals bisect each other to set up two equations:

x² + (LV/2)² = DV²/4

y² + (OE/2)² = LE²/4

Simplifying each equation and substituting the given values, we get:

x² + (LV/2)² = 81/4

y² + (OE/2)² = 225/4

We also know that the diagonals bisect each other, so we can set up another equation:

LV/2 + OE/2 = LO = VE

Substituting the given value for LE, we get:

LV/2 + OE/2 = 15

Solving this equation for one of the variables, we get:

LV = 30 - OE

Substituting this expression into the first equation above, we get:

x² + ((30 - OE)/2)² = 81/4

Simplifying and rearranging, we get:

OE² - 60OE + 675 = 0

Using the quadratic formula, we get:

OE = (60 ± √(3600 - 2700)) / 2

OE = 15 or 45

If OE = 15, then LV = 30 - 15 = 15, and we can solve for x and y:

x² + 7.5² = 81/4

y² + 7.5² = 225/4

Solving these equations, we get:

x = 3√7

y = 9/√7

If OE = 45, then LV = 30 - 45 = -15, which is impossible for a length. Therefore, the solution is:

LV = OE = 15

x = 3√7

y = 9/√7

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Complete question:

LOVE is a kite. LV and OE are diagonals. The segments DV = 9cm and LE = 15cm are given. Find the lengths of the other segments of the diagonals, DV, OE, and LV.

When testing HA: µ > 45, if the test statistic is t = 2.052, n = 16, and the level of significance is 0.05, the p-value is 0.028.

The following information is given:-

The level of significance is 0.05-

The sample size (n) is 16-

The test statistic is 2.052

The p-value is the probability that the t-value or another statistic would be observed when the null hypothesis is true, given the data.

In this situation, the p-value is the area to the right of the test statistic in the t-distribution with (n - 1) degrees of freedom. The t-distribution is symmetric about the mean (0), so the p-value can also be calculated as the area to the left of the negative test statistic.

The p-value for a one-tailed test with a t-statistic of 2.052 and 15 degrees of freedom can be determined using a t-distribution table. Because this is a right-tailed test, the area in the right-tail with 15 degrees of freedom and a t-value of 2.052 should be looked up, giving the probability of 0.028.

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Both -5 and 1 are extraneous solution to the equation

A quadratic equation is a second-order polynomial equation in a single variable x ax2+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

c²+2c-4-1-2c = 0

c²+2c-2c -4-1 = 0

c²-5 = 0

Therefore both -5 and 1 are extraneous solution in the equation.

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Answer:

1.5

Step-by-step explanation:

3÷2=1.5

The given differential equation with variable separation will be cosy = -1/2 sin2x + C.

A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions.

Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.

Due to the prevalence of these relationships, differential equations are widely used in many fields, including engineering, physics, economics, and biology.

So, we have the differential equation:

csc(y) dx + sec2(x) dy = 0

We, are aware that:
csc(y) = 1/ siny

sec(x) = 1/ cosx

We can also write it:

dx/siny = dy/cos2x

Cross multiplication with variable separation:

siny dy = cos2x dx

Differentiate:
cosy = -1/2 sin2x + C

As a result, the given differential equation with variable separation will be

cosy = -1/2 sin2x + C.

Therefore, the given differential equation with variable separation will be cosy = -1/2 sin2x + C.

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Answer:

a) Domain 0 ≤ x ≤ 4

B) Range 0 ≤y ≤ 2

C) 1.5 hours.

Sorry, I do not know what they are looking for in the blank

Step-by-step explanation:

The domain is the x values.  If you look at the numbers on the horizontal axis.  It starts at zero and goes to 4.

The range is the y values.  If you look at the number on the vertical axis.  It starts at zero and goes to 2.

He is not moving when you see the flat, horizontal lines.  That is from (1,2) to (2,2)  That is a time of 1 hour.  The x values tell us the time.  The y tells us the distance.  There is also no movement at  (3, .5)  and (3.5, .5)  
This is half of an hour.  The total would be 1.5 hours.

Answer:

138 : 269

Step-by-step explanation:

Last year, the number of bicyclists that showed up was 1345.

This year, there were 690 bicyclists.

The ratio of the number of bicyclists that showed up for the past two years is the ratio of those that showed up this year to those that showed up last year:

690 : 1345

Let us put it in simplest terms:

138 : 269

The equation of the line through \((1,2)\) which make equal intercepts on the axis \(x+y=3\)

The equation of the line through (1,2) makes an equal intercept on the axis

The formula of the intercept form is

\(\frac{x}{a} +\frac{y}{b} =1\)

If they make an equal intercept

\(a=b\\\frac{x}{a} +\frac{y}{a} =1\\x+y=a\)

Put the value of the point in the axis, and we get.

\(1+2=a\\a=3\)

Put the value in the equation, and we get.

\(x+y=3\)

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Answer:

274 square units

Step-by-step explanation:

Surface Area of the prism

Here :

Solving

Answer:

\(274\ units^2\)

Step-by-step explanation:

Step 1:  Determine the area of top and bottom

\(A = l * w\)

\(A = 13\ units * 4\ units\)

\(A = 52\ units^2\)

Top and bottom gives us (52 units^2 * 2) = 104 units^2

Step 2:  Determine the area of the sides

\(A = l * w\)

\(A = 4\ units * 5\ units\)

\(A = 20\ units^2\)

Sides gives us (20 units^2 * 2) = 40 units^2

Step 3:  Determine the area of the front and back

\(A = l * w\)

\(A = 13\ units * 5\ units\)

\(A = 65\ units^2\)

Ffront and back gives us (65 units^2 * 2) = 130 units^2

Step 4:  Add up the areas to get the total surface area

\(104\ units^2 + 40\ units^2 + 130\ units^2\)

\(274\ units^2\)

Answer:  \(274\ units^2\)

The equation that passes (6,0) and (3,4) is -3y=4(x-6)

What are the different forms of straight lines ?

The following information about the straight line is required if we wish to obtain the equation for it.

1. The y-intercept and slope

2. Two-point and slope

3. Two things.

4. the intersection of the x- and y-axes

the straight line that passes through (6,0) and (3,4).

The equation can be expressed in a point-slope form which is ,

y/x-6=4/-3

∵ -3y=4(x-6)

Hence,

The equation that passes (6,0) and (3,4) is -3y=4(x-6)

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Answer:

2\(\frac{7}{9} \\\)

Step-by-step explanation:

-(2/9) + 3

= 27/9 - 2/9

= 25/9

= 2\(\frac{7}{9} \\\)

Answer:

Cube root of 16​

Step-by-step explanation:

x^m/n =n/x^m

4^2/3 = 3/4^2=3/16

So it is Cube root of 16​

Hope This Helped

Find the equation of the line through point (-2,-2) and parallel to 3+4=12.

\(( - 2 \: - 2)\)

Factor out the negative sign

\( - ( 2 + 2)\)

Calculate

\( - 4\)

\(3 + 4 = 12\)

Calculate

\(7 = 12\)

Check the equality

\(false\)

Hence, we have proved that Xn → X implies f(Xn) → f(X).Therefore, we can say that f is a continuous function of X. Therefore, f(Xn) 4.8 f(X) as n +00.

Given, X, X1, X2, ... be a sequence of random variables defined on a common probability space (12, F,P) and f:R + R is a continuous function.

To prove that Xn → X implies f(Xn) → f(X)We are given that Xn 4.0 X. This implies that for every ε > 0, we can find N ε such that for all n ≥ N ε, we have |Xn − X| < ε.

For a continuous function f, we know that for every ε > 0, we can find δε such that for all x, y with |x − y| < δε, we have |f(x) − f(y)| < ε.Using this, we have for any ε > 0 and δ > 0, |Xn − X| < δ implies |f(Xn) − f(X)| < ε.Finally, we get |f(Xn) − f(X)| < ε whenever |Xn − X| < δ.Substituting δ = ε in the above expression, we get |f(Xn) − f(X)| < ε whenever |Xn − X| < ε.

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In order to prove that if Xn -> X, then f(Xn) -> f(X) as n -> infinity, the function f must be continuous. f is said to be continuous at a point x if the limit of f(y) as y -> x exists and is equal to f(x).f: R -> R is a continuous function and Xn -> X as n -> infinity.

To prove that if Xn → X, then f(Xn) → f(X) as n approaches infinity, we need to show that for any given ϵ > 0, there exists a positive integer N such that for all n > N, |f(Xn) - f(X)| < ϵ.

Since f is a continuous function, it is continuous at X. This means that for any ϵ > 0, there exists a δ > 0 such that |x - X| < δ implies |f(x) - f(X)| < ϵ.

Now, since Xn → X, we can choose a positive integer N such that for all n > N, |Xn - X| < δ.

Using the continuity of f, we can conclude that for all n > N, |f(Xn) - f(X)| < ϵ.

Therefore, we have shown that for any given ϵ > 0, there exists a positive integer N such that for all n > N, |f(Xn) - f(X)| < ϵ. This proves that if Xn → X, then f(Xn) → f(X) as n approaches infinity.

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