Combine the like terms to create an equivalent expression.
7+4c+2d+3

Answer:

I think the answer is 12 because 8/6 is 1.3333.... Continously so the smaller traingel is 1.33333 times smaller then the bigger one. So you jus do 9 x 1.3333... To get the bigger angels side

[tex]\frac{(-12)(3)+(-5)(9)}{3^2 + 9^2} \langle 3, 9 \rangle \\ \\ =-\frac{9}{10} \langle 3, 9 \rangle \\ \\ =\langle -\frac{27}{10}, -\frac{81}{10} \rangle[/tex]

So, the correct answer is Option 1.

(i) The percentage of students who got high scores in both the subjects English and Mathematics is 46%.

(ii) The total number of students who got high scores either in Mathematics or in English if 300 students had attended the exam exists 138.

The probability exists in the analysis of the possibilities of happening of an outcome, which exists acquired by the ratio between favorable cases and possible cases.

The number of students who got high scores in Mathematics was 75%.

The number of students who got high scores in English was 65%.

(i) The percentage of students who got high scores in both the subjects

100% - 6% = 94%

(75% + 65%) - 94%

= 140% - 94%

= 46%

Therefore, the percentage of students who got high scores in both the subjects English and Mathematics is 46%.

(ii) The total number of students who got high scores either in Mathematics or in English if 300 students had attended the exam

= 300 [tex]*[/tex] 46%

= 300 [tex]*[/tex] (46 / 100)

= 300 [tex]*[/tex] 0.46

= 138.

Therefore, the total number of students who got high scores either in Mathematics or in English if 300 students had attended the exam exists 138.

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Answer:

1. AC is perpendicular to BD

1. Given

2. ACB is a right angle

2. Definition of perpendicular lines

3. Triangle ACB is a right triangle

3. Definition of right triangles

4. Angles 1 and 3 are complementary

4. Interior angles of a triangle add up to 180 degrees (Triangle Interior Angle Sum Theorem), and m<ACB = 90 degrees (definition of right angles), so m<1 + m<3 = 90 degrees (subtraction property of equality). By the definition of complementary angles, angles 1 and 3 are complementary.

The general terms for the given arithmetic sequences are given as follows:

1. [tex]a_n = -2 -3(n - 1)[/tex]

2. [tex]a_n = 22 - 2(n - 1)[/tex]

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The general term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

For sequence 1, given by -2, -5, -8, -11, the first term and the common ratio are given as follows:

[tex]a_1 = -2, d = -3[/tex]

Hence the general term that defines sequence 1 is presented below:

[tex]a_n = -2 -3(n - 1)[/tex]

For sequence 2, represented by 22, 20, 18, 16, the first term and the common ratio are given as follows:

[tex]a_1 = 22, d = -2[/tex]

Hence the general term that defines sequence 2 is presented below:

[tex]a_n = 22 - 2(n - 1)[/tex]

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Answer:

Speed of the plane in still air: [tex]779\; {\rm km \cdot h^{-1}}[/tex].

Windspeed: [tex]100\; {\rm km \cdot h^{-1}}[/tex].

Step-by-step explanation:

Assume that [tex]x\; {\rm km \cdot h^{-1}}[/tex] is the speed of the plane in still air, and that [tex]y\; {\rm km \cdot h^{-1}}[/tex] is the speed of the wind.

The question states that when going against the wind ([tex]v = (x - y)\; {\rm km \cdot h^{-1}}[/tex],) the plane travels [tex]6111\; {\rm km}[/tex] in [tex]9\; {\rm h}[/tex]. Hence, [tex]9\, (x - y) = 6111[/tex].

Similarly, since the plane travels [tex]7911\; {\rm km}[/tex] in [tex]9\; {\rm h}[/tex] when travelling in the same direction as the wind ([tex]v = (x + y)\; {\rm km \cdot h^{-1}}[/tex],) [tex]9\, (x + y) = 7911[/tex].

Add the two equations to eliminate [tex]y[/tex]. Subtract the second equation from the first to eliminate [tex]x[/tex]. Solve this system of equations for [tex]x[/tex] and [tex]y[/tex]: [tex]x = 779[/tex] and [tex]y = 100[/tex].

Hence, the speed of this plane in still air would be [tex]779\; {\rm km \cdot h^{-1}}[/tex], whereas the speed of the wind would be [tex]100\; {\rm km \cdot h^{-1}}[/tex].

Answer:

  180 yards

Step-by-step explanation:

The number of yards she sprints on day 21 can be found by evaluating the formula with n=21.

  a21 = 100 +(21 -1)4 = 100 +(20)(4) = 100 +80 . . . . . use 21 in place of n

  a21 = 180

Marika sprints 180 yards on day 21.

The correct option is B.

Rank

The RANK function in a Microsoft Excel spreadsheet enables users to order the various pieces of data by their numerical values. By entering an absolute value for the range of cells the user wants to rank, they can also use the rank function. If an absolute value is not specified, the program's auto-formula may cause the rank of the various cells to alter.

A spreadsheet is a computer program used for organizing, organizing, analyzing, and storing tabular data. Spreadsheets were created as electronic alternatives to paper accounting worksheets. Data typed into table cells serves as the program's input.

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Answer:

I forgot the name but I can show you how to do it lol

Step-by-step explanation:

x+5(-2)-1

x-10-1 we multiplied 5 and -2

x-11

x=11

how I did the last one is there is a non-existent 0 with an equal sign like my teacher says  so we added 11 to both sides.

Answer:

I am not 100% confident, but I think that she is 11.

Step-by-step explanation:

Answer:

14 years old

Step-by-step explanation:

Define the variable

Let x be the actual age of Zeba (in years).

Create an equation using the give information and the variable x:

[tex](x - 5)^2=5x+11[/tex]

To find Zeba's age now, solve the equation for x.

Expand the brackets:

[tex]\implies x^2-10x+25=5x+11[/tex]

Subtract 5x from both sides:

[tex]\implies x^2-10x+25-5x=5x+11-5x[/tex]

[tex]\implies x^2-15x+25=11[/tex]

Subtract 11 from both sides:

[tex]\implies x^2-15x+25-11=11-11[/tex]

[tex]\implies x^2-15x+14=0[/tex]

Factor the found quadratic

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex], then rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies x^2-14x-x+14=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x-14)-1(x-14)=0[/tex]

Factor out the common term (x - 14):

[tex]\implies (x-1)(x-14)=0[/tex]

Apply the zero product property:

[tex]\implies (x-1)=0 \implies x=1[/tex]

[tex]\implies (x-14)=0 \implies x=14[/tex]

Therefore, Zeba's age now is either 1 or 14 years.

As the question states "If Zeba were younger by 5 years" then 1 must be an extraneous solution since 1 - 5 = -4 and Zeba cannot be -4 years old.

Therefore, Zeba's age now is 14 years old.

Check

Given the actual age of Zeba is 14 years old.

Therefore, If Zeba were younger by 5 years, she would be 9 years old as:  14 - 5 = 9

The square of 9 is:  9² = 81.

5 times her actual age:  5 × 14 = 70

81 is 11 more than 70, hence verifying that her actual age is 14 years old.

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The lower and the upper class limit are as follows

interval  lower limit  upper limit

10-14          10                14

15-19          15                19

20-24         20              24

25-29           25            29

This is further explained below.

Generally, The lower class limit and the upper-class limits are just the minima and maximum values that are allowed in each class, respectively: The gap that exists between the upper-class limit and the lower class limit is referred to as the class interval.

In conclusion, The lower and the upper class limit are as follows

interval  lower limit  upper limit

10-14          10                14

15-19          15                19

20-24         20              24

25-29           25            29

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Answer: i believe the answer is 26

Step by step explanation

Total no. of observation = (12+13) = 25

Median = Average of 18/2 observation + (18/2+1)

=1/2 (12th observation + 13 observation)

1/2 × (25 +27) = 1/2 × 52

=26

The reliability of two components in series is 0.996.

To find the reliability of the engine, we need all the two components to work. Each components has a reliability of 0.998, so to find the reliability of the engine we need to find the probability of all two components working.

Reliability is defined as the probability that a product, system, or service will perform its intended function adequately for a specified period of time, or will operate in a defined environment without failure.

We can find this probability multiplying all the ten reliabilities:

P = 0.998^2 = 0.996004

Rounding to three decimal places, we have P = 0.996

The reliability of the engine is 0.996.

Hence,

The reliability of two components in series is 0.996.

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The equation of the circumference of a circle in terms of [tex]\pi[/tex] is [tex]2\pi r[/tex] or [tex]\pi d[/tex].

The circumference for a circle with diameter 10 is [tex]10\pi[/tex].

The circumference for a circle with diameter 19 is [tex]19\pi[/tex].

The circumference for a circle with diameter 30 is [tex]30\pi[/tex].

The circumference for a circle with diameter 16 is [tex]16\pi[/tex].

Relatively easy, right?

The equation of the area of a circle in terms of [tex]\pi[/tex] is [tex]\pi r^2[/tex].

The area of a circle with radius 5 is [tex]25\pi[/tex].

The area of a circle with radius 9.5 is [tex]90.25\pi[/tex].

The area of a circle with radius 15 is [tex]225\pi[/tex].

The area of a circle with radius 8 is [tex]64\pi[/tex].

Hope this helped!

(By the way, I don't know why you're using hard formulas for trying to find the radius or diameter. The diameter is simply twice the radius, and the radius is simply half the diameter.)

Answer:

Circumference = 10[tex]\pi[/tex], 19[tex]\pi[/tex], 30[tex]\pi[/tex], 16[tex]\pi[/tex]

Area = 25[tex]\pi[/tex], 90.25[tex]\pi[/tex], 225[tex]\pi[/tex], 64[tex]\pi[/tex]

Step-by-step explanation:

For the first row we have the radius which is 5, the diameter is 10. The formula for circumference is 2[tex]\pi[/tex]r. So for this one its gonna be 2[tex]\pi[/tex]5 or 10[tex]\pi[/tex]

radius = 5

diameter = 10

circumference = 2[tex]\pi[/tex]5 or 10[tex]\pi[/tex]

area = [tex]\pi[/tex][tex]5^{2}[/tex] or 25[tex]\pi[/tex]

for the second row

radius = 9.5

diameter = 19

circumference = 2[tex]\pi[/tex]9.5 or 19[tex]\pi[/tex]

area = [tex]\pi[/tex][tex]9.5^{2}[/tex] or 90.25[tex]\pi[/tex]

for the third row

radius = 15

diameter = 30

circumference = 2[tex]\pi[/tex]15 or 30[tex]\pi[/tex]

area = [tex]\pi[/tex][tex]15^{2}[/tex] or 225[tex]\pi[/tex]

for the fourth row

radius = 8

diameter = 16

circumference = 2[tex]\pi[/tex]8 or 16[tex]\pi[/tex]

area = [tex]\pi[/tex][tex]8^{2}[/tex] or 64[tex]\pi[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{Equation:}[/tex]

[tex]\mathsf{2[(8 \div 4)-(-5)] + 6}[/tex]

[tex]\huge\textsf{Solving:}[/tex]

[tex]\mathsf{2[(8 \div 4)-(-5)] + 6}[/tex]

[tex]\mathsf{= 2[((2 - (-5)] + 6}[/tex]

[tex]\mathsf{= 2(7) + 6}[/tex]

[tex]\mathsf{= 2 \times 7 + 6}[/tex]

[tex]\mathsf{= 14 + 6}[/tex]

[tex]\mathsf{= 20}[/tex]

[tex]\huge\textbf{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\frak{20}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

▪ [tex] \sf{2[(8 ÷ 4)-(-5)] + 6}[/tex]

First, we will start with the division:

[tex]\longrightarrow \sf{2[(2) − (−5)] +6}[/tex]

Now we will resolve what is inside the bracket:

[tex]\longrightarrow \sf{2[2+5] +6}[/tex]

[tex]\longrightarrow \sf{2 \times 7 +6}[/tex]

Now we will solve the multiplication:

[tex]\longrightarrow \sf{14 +6= 20}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex] \bm{2[(8 ÷ 4)-(-5)] + 6 = \boxed{\bm {20}}}[/tex]

Answer:

a = 97° , b = c = 146°

Step-by-step explanation:

a and 83° are same- side interior angles and sum to 180°

a + 83° = 180° ( subtract 83° from both sides )

a = 97°

34° and b are same- side interior angles and sum to 180°

b + 34° = 180° ( subtract 34° from both sides )

b = 146°

b and c are corresponding angles and are congruent , so

c = b = 146°

Answer:

< a = 97 degrees.

< b = 146 degrees.

< c = 146 degrees.

Step-by-step explanation:

We have 2 lines crossing 2 parallel lines.

Internal angles between the 2 parallel lines add up to 180 degrees, so

34 + <b = 180

<b = 180 - 34 = 146 degrees

Also

<a + 83 = 180 degrees (also internal angles)

---> <a = 97 degrees

< c and < b are corresponding angles so are congruent, therefore

<c = < b = 146 degrees.

Answer:

(-5, 2)

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}-2x-5y=20\\y=\dfrac{4}{5}x+2\end{cases}[/tex]

Both equations are linear equations.

Rearrange Equation 1 to make y the subject:

[tex]\implies -2x-5y=20[/tex]

[tex]\implies -5y=2x+20[/tex]

[tex]\implies y=-\dfrac{2}{5}x-4[/tex]

Therefore, the graph of this equation is a straight line with a negative slope and a y-intercept of (0, -4).

Find two points on the line by substituting two values of x into the equation:

[tex]x = 0\implies y=-\dfrac{2}{5}(0)-4=-4 \implies (0,-4)[/tex]

[tex]x = 5 \implies y=-\dfrac{2}{5}(5)-4=-6 \implies (5,-6)[/tex]

Plot the found points and draw a straight line through them.

The graph of this equation is a straight line with a positive slope and a y-intercept of (0, 2).

Find two points on the line by substituting two values of x into the equation:

[tex]x = 0 \implies y=\dfrac{4}{5}(0)+2=2 \implies (0,2)[/tex]

[tex]x = 5 \implies y=\dfrac{4}{5}(5)+2=6 \implies (5,6)[/tex]

Plot the found points and draw a straight line through them.

The solution(s) to a system of equations is the point(s) of intersection.

From inspection of the graph, the point of intersection is (-5, -2).

To verify the solution, substitute the second equation into the first and solve for x:

[tex]\implies \dfrac{4}{5}x+2=-\dfrac{2}{5}x-4[/tex]

[tex]\implies \dfrac{6}{5}x=-6[/tex]

[tex]\implies 6x=-30[/tex]

[tex]\implies x=-5[/tex]

Substitute the found value of x into one of the equations and solve for y:

[tex]\implies \dfrac{4}{5}(-5)+2=-2[/tex]

Hence verifying that (-5, -2) is the solution to the given system of equations.

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First simplify first one

Another one is

On first line

at x=0

At x=5

On second line

At x=0

At x=5

Graph attached

Solution is (-5,-2)

The value of x in the triangle is 4

The complete question is added as an attachment

From the question, the given parameters are as follows:

Hypotenuse = 8

Adjacent = x

Angle = 60

The cosine of the angle is then calculated as:

cos(angle) = Adjacent/Hypotenuse

Substitute the known values in the above equation

cos(60) = x/8

Multiply both sides by 8

x = 8 * cos(60)

Evaluate the product

x = 4

Hence, the value of x in the triangle is 4

So, the complete parameters are:

Hypotenuse = 8

Adjacent = x

Angle = 60

x = 4

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Answer:

Secant 60 degrees = StartFraction 8 Over x EndFraction. 2 = StartFraction 8 Over x EndFraction. 2 x = 8. x = 4.

Step-by-step explanation:

The answer above is correct.

Answer: B

Step-by-step explanation: what I did was I drew a square and folded it if both sides matched i knew that that was a line of symmetry

⟨A = 7•x + 40° and ⟨B = 3•x + 112°

From a possible diagram of the question, ⟨A = ⟨B, which gives;

Given;

⟨A = 7•x + 40°

⟨B = 3•x + 112°

In the diagram from a similar question posted online, we have;

Corresponding angles formed by parallel lines having a common transversal are congruent, therefore;

Which gives;

7•x + 40° = 3•x + 112°

7•x - 3•x = 112° - 40° = 72°

7•x - 3•x = 4•x = 72°

x = 72° ÷ 4 = 18°

Therefore;

Which gives;

⟨A = 7•x + 40°

⟨A = 7 × 18 + 40° = 166°

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Answer:d

Step-by-step explanation:

khan

Answer:

15

Step-by-step explanation:

from the first then it is 0+7=7

and from the last it is 0+8=8

then the number of cars available in the station is 8+7=15

The graph in the question is of the function f(x)=[tex]log _{0.2}x[/tex] which is option a.

Given a graph which is downward sloping and we are required to find the function whose the graph is.

Function is like a relationship between two or more variables expressed in equal to form. It may be a linear function,exponential function, logarithmic function or quadratic function.

In the given graph the values of y becomes negative when the curve crosses then x axis. For all x>1 the value of log x is greater than 0. So the value of [tex]log_{2}x,log_{4}x,log_{20}x[/tex] should be greater than 0 for x greater than 1. But in graph it is negative. That's why the graph will be of y=[tex]log_{0.2}x[/tex].

Hence the given graph is of the function f(x)=[tex]log _{0.2}x[/tex] which is option a.

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The terms of this series may be arranged without changing the value of the series. The sum of the reciprocals of the squares of the odd positive integers is [tex]\pi ^{2} /8[/tex].

In mathematics, a sequence is the cumulative sum of a given collection of terms. Usually, those phrases are actual or complicated numbers, but plenty of extra generalities are feasible.

A series is described as an arrangement of numbers in a specific order. then again, a chain is described as the sum of the factors of a sequence.

In mathematics, a series is, more or less speaking, a description of the operation of including infinitely many quantities, one after the alternative, to a given beginning quantity. The look at of series is a primary part of calculus and its generalization, mathematical analysis.

k=1

1/(1)2+1/(2)2+1/(3)2+1/(4)2+1/(5)2+1/(6)2+1/(7)2+.

up to ∞ terms = 2/6

[1/(1)2+1/(3)2+1/(5)2+1/(7)2+]+[1/(2)²+1/(4)²+1/(6)²+

..∞0] = T²/6

→ [1/(1)² + 1/(3)² + 1/(5)2+1/(7)2+......00] + [1/4 (1)² + 1/4(2)²+

1/4(3)²+....0] =²/6

[1/(1)²+1/(3)²+1/(5)2+1/(7)2+.......)] + 1/4[1/(1)² + 1/(2)²+

1/(3)²+....x] = 2/6

⇒ [1/(1)² + 1/(3)² + 1/(5)²+1/(7)²+..] + 1/4 [π²/6] = 2/6

⇒ [1/(1)² + 1/(3)² + 1/(5)²+1/(7)²+] = (1-1/4)/6

⇒ [1/(1)²+1/(3)2+1/(5)2+1/(7)2+..∞ = 3/4 x π²/6

=

↑

[1/(1)2+1/(3)2+1/(5)2+1/(7)²+] = 2/8

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Use BODMAS and algebra to arrive at the values of P = 5/2, q = -25/4 and r = -9/2.

Then substitute the values of p and q into p+2q to get -10

Using the fundamental theorem of calculas the derivative of function g(x)=[tex]xt^{3}+t^{5}[/tex] at x=0 is [tex]t^{3}[/tex].

Given a function g(x)=[tex]xt^{3}+t^{5}[/tex].

We are required to find the derivative of the function g(x) at x=0.

Function is relationship between two or more variables expressed in equal to form. The values entered in a function are part of domain and the values which we get from the function after entering of values are part of codomain of function. Differentiation is the sensitivity to change of the function value with respect to a change in its variables.

g(x)=[tex]xt^{3}+t^{5}[/tex]

Differentiating with respect to x.

d g(x)/dx=[tex]t^{3}[/tex]+0  [Differentiation of x is 1 and differentiation of constant is 0]

=[tex]t^{3}[/tex]

Hence using the fundamental theorem of calculas the derivative of function g(x)= [tex]xt^{3}+t^{5}[/tex] at x=0 is [tex]t^{3}[/tex].

The function given in the question is incomplete. The right function will be g(x)=[tex]xt^{3}+t^{5}[/tex].

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.

Answer:

The function is increasing from x = 0 to x = 1.

Step-by-step explanation:

A function is increasing when the y-value increases as the x-value increases.

A function is decreasing when the y-value decreases as the x-value increases.

From x = -2 to x = -1 the function is decreasing as the y-value decreases as the x-value increases:  

From x = -1 to x = 0 the function is increasing as the y-value increases as the x-value increase:  

From x = 0 to x = 1 the function is increasing as the y-value increases as the x-value increase:  

Step-by-step explanation:

since the 2 arc angles cover the full circle, we know their sum must be 360°.

so,

23x - 5 + 37x + 5 = 360

60x = 360

x = 6

and so the angle at V = 5×6 + 17 = 30+17 = 47°

Answer:51 crates could have 12 oranges and one crate could hold 11 oranges.

Step-by-step explanation: 623 / 12 is 51.9... 51 x 12 is 612. 612 + 11 is 623 math checks out.

Answer: 57

I'm pretty sure that's what it is

Step-by-step explanation:

Answer:

4) 7a+20

5) 14+2b

6) 25c² - 15

Step-by-step explanation:

4) 9a+7-2a+13= 9a-2a+7+13 = 7a+20

5) 21-3b+5b-7= 21-7+5b-3b = 14+2b

6) (3c)² + (8c)² - 15 = 9c² + 16c² - 15 = 25c² - 15