(10.) The sum of the 6th and 8th terms of an
arithmetic progression is 142. If the fourth
term is 49, find the first term, the common
difference and the sum of the first seven
terms of the progression.

Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

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Answer:

Step-by-step explanation:

TSA of cube = 6a²

side = 2/3

= 6 x (2/3)²

= 6 x 4/9

= 2 x 4/3

=8/3

Ans = 8/3 units or 2.66.. units

HAVE A NICE DAY

STAY SAFE

PLS MARK BRAINLIST IF IT IS CORRECT

Answer:

Length = 10 cm

Width = 10-2 = 8 cm

Step-by-step explanation:

Area formula (L)(W)

80 = 10(x-2)

80 = 10x - 20

Add 20 to both side

100 = 10x

x= 10

Length = 10 cm

Width = 10-2 = 8 cm

Answer:

F(-3)=2(-3)^2-(-3)

      =2(9)+3

      =18+3

      =21

Step-by-step explanation:

Answer:

Conver the sales tax to a decimal and ad it to 1, then multiple that total to the price of the item. Please mark as breinlest

Answer:

just multiply the tax percent to the cost of the product and move the decimal, or you can use a percent calculator

Answer:

x = 50

Step-by-step explanation:

Creating an equation to solve for x using basic geometry rules

Angles in a triangle always add up to 180 degrees.

This means that x + 2x - 10 + 40 must be equal to 180

Solving for x algebraically

x + 2x - 10 + 40 = 180

==> combine like terms

3x + 30 = 180

==> subtract 30 from both sides

3x = 150

==> divide both sides by 3

x = 50

Checking our answer by plugging in x and seeing if the equation created is true

x + 2x - 10 + 40 = 180

==> plug in x = 50

50 + 2(50) - 10 + 40 = 180

==> multiply 2 and 50

50 + 100 - 10 + 40 = 180

==> combine like terms

180 = 180 ( this is true so the answer is indeed x = 50 )

SOLUTION -:

Solve for x

Required Answer -;

By using Sum of triangle property

Let's Begin -:

\( \displaystyle \: x \: + 2x - 10 + 40 = 180 \degree\)

\( \displaystyle \: 3x - 30 = 180 \degree \\ 3x = 180 \degree \: - 30\)

\( \displaystyle \: 3x \: = 150 \degree \\ x \: = \frac{150}{3} \)

\( \bold{x = 50 \degree}\)

thus , the value of x is 50° Ans

They include 14 values in the Class 0.330- 0.339.

Frequency is the measure of number of times an event happen.

Values from  smallest to highest are

0.329, 0.330, 0.331, 0.331, 0.333, 0.333, 0.333, 0.334, 0.334, 0.334, 0.336, 0.337, 0.338, 0.338, 0.338, 0.340, 0.340, 0.341, 0.341, 0.342, 0.342, 0.342, 0.344, 0.344, 0.345, 0.346, 0.349, 0.356, 0.358, 0.366.

The values which fall in the range of 0.330 - 0.339

0.330, 0.331, 0.331, 0.333, 0.333, 0.333, 0.334, 0.334, 0.334, 0.336, 0.337, 0.338, 0.338, 0.338

These are total 14 values

Placing the data in a frequency table ,

the values that will fall into the class 0.330 - 0.339 is the range of number between the class .

They include 14 values in the range.

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Answer:

  see below

Step-by-step explanation:

The graph has two parts. There is one line for x < 2. It has a slope of 1 and a y-intercept of 0.

The line for x > 2 is the horizontal line x=2.

The point at x=2 is not defined by the function you have posted here, so there is a "hole" in the graph at that point.

Answer:

the person above is correct

Step-by-step explanation:

:p

Answer: 70 cats

Step-by-step explanation:

add 2+7 = 9
90/9 = 10
multiply 2x10 = 20 dogs
10x7= 70 cats.

The value of the principal investment is approximately $6,752.18 rounded to the nearest hundredths place.

Simple interest is a technique used to calculate the proportion of interest paid on a sum over a set time period at a set rate. The principal amount remains constant in simple interest. Simple interest is a straightforward and easy technique for calculating interest in money.

The given equation is:

A = \(P(1 + 0.06/4)^4t\)

where A is the amount in the account after t years, P is the principal investment, and 0.06 is the annual interest rate.

We are given that after 15 years, the amount in the account is $16,497.06. So we can substitute A = $16,497.06 and t = 15 into the equation above and solve for P:

$16,497.06 = \(P(1 + 0.06/4)^{4 *15}\)

$16,497.06 = \(P(1.015)^{60}\)

P = \($16,497.06 / (1.015)^{60}\)

Using a calculator, we get:

P ≈ $6,752.18

Therefore, the value of the principal investment is approximately $6,752.18 rounded to the nearest hundredths place.

Hence, the answer is $6,752.18.

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Answer:

22

Step-by-step explanation:

Write an equation:

5x+12=6x-10

Solve.

x=22

Hope I helped!

Answer:

22

Step-by-step explanation:

6x - 10 = 5x + 12 (vertical angles)

6x - 5x = 12 + 10

x = 22

Answer:

1808.64 IN^3

Step-by-step explanation:

Helium needed = volume of spherical shaped ice cream + volume of cone

Volume of a sphere = 4/3 x pi x r^3

4/3 x 3.14 x 6^3 = 904.32 ft^3

Volume of a cone 1/3 x (nr^2h)

n = 22/7

r = radius  = 12/2 = 6

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

h = height

1/3 x 3.14 x 6^2 x 24 = 904.32

helium needed = 2 x 904.32 = 1808.64 in^3

Answer:

.......................

The linear equation that expresses the population P of Pottsville t years since 2010:

\(P = 2141t + 37422\)

The two population values and the time interval between them to construct a linear equation to model the population growth of Pottsville. Let t represent the number of years since 2010.

Using the point-slope form of a linear equation, we have:

\(P - 37422 = m(t - 0)\)

where m is the slope of the line, which represents the rate of change in population over time.

To find the value of m, we can use the two given population values:

\(39583 - 37422 = m(2011 - 2010)\)

\(m = 2141\)

Substituting this value of m into the equation, we have:

\(P - 37422 = 2141t\)

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Answer:

\((2x - 6) + 4(x - 3) \\ 2x - 6 + 4x - 12 \\ 6x - 18\)

hope helpful <3

The expression that describe the end behavior of the expression f(x)= (3.25)^x + 6 is The curve begins infinitely close to the line y equals 6 in the second quadrant.

The behavior of the graph of a function at its "ends" on the x-axis is referred to as the end behavior of a function, f.

For example, if we look at the right end of the x-axis (as x approaches + ∞) and the left end of the x-axis (as x approaches - ∞), the end behavior of a function explains the trend of the graph.

The graph of the function is attached and from the graph it shows that the graph continued to tend towards towards line y = 6

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Answer:

8/20 and 15/20 and then you add to get 23/20 AKA       1   3/20

Step-by-step explanation:

Since you multiply 5 by 4 to get the LCD, apply the same method to the top: 2 times 4 is 8

Next do the same for the other fraction: 4 times 5 is 20 so apply that to get 3 times 5 is 15

Your final fractions will be 8/20 and 15/20

Then add and reduce to get 1 3/20

9514 1404 393

Answer:

  AE = CE = 12 in

Step-by-step explanation:

Angles BDF and BCF are base angles of their respective isosceles triangles. That means the a.pex angle of each, DBF and ABC respectively is ...

  180° -2×30° = 120°

In your diagram, BC is 120° from the -x axis, so is 60° from the +x axis. It bisects the angle DBE. Similarly, BE is 120° from the +x axis, so is 60° from the -x axis. It bisects angle ABC. In an isosceles triangle, the a.pex angle bisector is an altitude and is the perpendicular bisector of the base segment. Any point on that line is equidistant from the base vertices.

Point C lies on the perpendicular bisector of DE, so CD ≅ CE = 12 in.

Point E lies on the perpendicular bisector of AC, so EC ≅ EA = 12 in.

The measurements of interest are ...

  AE = CE = 12 in.

_____

Additional comment

Point F serves no purpose except to confuse the issue. Each of the angles that reference point F could be described equally well using a different point:

  ∠BDF = ∠BDE

  ∠BCF = ∠BCA

This makes it more obvious that the triangles of interest are similar.

Answer:

12

12

Step-by-step explanation:

see the below figure

i got that both triangles are similar

we get that in triangle ABC angle BCF is 30

so angle A is also 30 (isosceles)

so the remaining angle ABC is 120

and angle CBD becomes 180 - 120 = 60

now in triangle BDE angle BDF is 30

so angle BED is also 30

now angle EBC becomes 120 - angle CBD = 120 - 60

and got angles ABE EBC CBD as 60 each

so three 60 degree angles are formed at vertex B as shown in the figure

 tw0 30 30 120 degree triangles are similar

BC becomes perpendicular angular bisector of ED

C is a point on that line which is at equal distance from the base vertices

so CD = CE = 12

here BE is perpendicular bisector of AC

so AE = EC = 12    

The mean of the given data is 1744 days, median of the given data is 1460.5 days, mode of the given data is 1461 days & 4422 days.

To find the mean, median, and mode of the lengths of terms of the US Presidents that preceded Joe Biden:

Mean:

To find the mean, we add up all of the term lengths and divide by the total number of terms:

Mean = (4422 + 2922 + 2865 + 2840 + 2728 + 2041 + 2027 + 1886 + 1654 + 1503 + 1461 + 1460 + 1430 + 1419 + 1262 + 1036 + 969 + 895 + 881 + 492 + 199 + 31) / 44

Mean = 1743.77 days

Median:

To find the median, we need to arrange the term lengths in order from smallest to largest, and then find the middle term. In this case, since we have an even number of terms, we will take the average of the two middle terms:

31 199 492 881 895 969 1036 1262 1419 1430 1460 1461 1503 1654 1886 2027 2041 2728 2840 2865 2922 4422

Median = (1460 + 1461) / 2

Median = 1460.5 days

Mode:

The mode is the most frequently occurring term length. In this case, there are two modes: 1,461 days and 4,422 days.

Since the term length of FDR is much higher than all the other term lengths, it has pulled up the mean to a higher value than the other measures of central tendency. Additionally, the mode being a high value is likely due to the fact that FDR served for more than three terms, which is an outlier in the data set.

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Answer:

Step-by-step explanation:

hope this helps........

Answer:b

Step-by-step explanation:

Answer:

The answer is b

Step-by-step explanation:

-30 x 7= -210

Answer:

B); C).

Step-by-step explanation:

1) if sqrt(x)<5, then x∈(0:25);

2) if x∈(0;25), then the values 17; 22 are correct

The first plane is farther from the airstrip after the second leg

The first plane

Initial distance = 150 miles west

Additional distance = 220 miles 30 degrees SW

This means that

Additional distance = 220 * cos(30) miles SW

Additional distance = 190.53 miles

Total distance = 150 + 190.53 = 340.53

The second plane

Initial distance = 220 miles east

Additional distance = 150 miles x degrees SE

This means that

Additional distance = 150 * cos(x) miles SW

Total distance = 220 + 150 cos(x)

Given that

x < 30

We have

Second plane < First plane

220 + 150 cos(x) < 340.53

Evaluate

cos(x) < 0.8035

Take the arc cos of both sides

x < 36

x < 36 is not the same as x < 30

Hence, the first plane is farther

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The balance for each value of n is calculated by using the formula A = P(1 + r/n) ^nt. The rounded balance values are shown in the last column of the table above.

To complete the table and find the balance A if $3100 is invested at an annual percentage rate of 4% for 10 years and compounded n times a year.

The formula for calculating compound interest is as follows:

A = P(1 + r/n) ^nt,

where P represents the principal investment amount, r is the interest rate, n is the number of times the interest is compounded, t represents the time in years, and A represents the total amount, which includes the principal amount and the interest earned.

The table is given below:
\(\begin{array}{|c|c|c|} \hline \text{n} &

\text{A = P(1 + r/n) }^{nt} &

\text{Balance (rounded to nearest cent)} \\ \hline \text{1} &

\text{3100(1 + 0.04/1)}^{1*10} &

\text{\$4788.03} \\ \hline \text{2} &

\text{3100(1 + 0.04/2)}^{2*10} &

\text{\$4798.76} \\ \hline \text{4} &

\text{3100(1 + 0.04/4)}^{4*10} &

\text{\$4817.46} \\ \hline \text{12} &

\text{3100(1 + 0.04/12)}^{12*10} &

\text{\$4861.94} \\ \hline \end{array}\)

The balance is obtained by substituting the values of P, r, n, and t into the compound interest formula.

In this case, the investment is $3100, the annual interest rate is 4%, the investment is for 10 years, and n is the number of times the interest is compounded.

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Answer:

Sure, here are the answers to your questions:

**A) The value of $f(-5)$ is $-2$.**

To find the value of $f(-5)$, we can simply substitute $x=-5$ into the equation $f(x)=-2x^2-8x+14$. This gives us:

$$f(-5)=-2(-5)^2-8(-5)+14=-2(25)+40+14=-50+54=4$$

**B) The vertex of the parabola is $(2,6)$.**

To find the vertex of the parabola, we can complete the square. This involves adding and subtracting $\left(\dfrac{{b}}{2}\right)^2$ to both sides of the equation, where $b$ is the coefficient of the $x$ term. In this case, $b=-8$, so we have:

$$\begin{aligned}f(x)&=-2x^2-8x+14\\\\ f(x)+20&=-2x^2-8x+14+20\\\\ f(x)+20&=-2(x^2+4x)\\\\ f(x)+20&=-2(x^2+4x+4)\\\\ f(x)+20&=-2(x+2)^2\end{aligned}$$

Now, if we subtract 20 from both sides, we get the equation of the parabola in vertex form:

$$f(x)=-2(x+2)^2-20$$

The vertex of a parabola in vertex form is always the point $(h,k)$, where $h$ is the coefficient of the $x$ term and $k$ is the constant term. In this case, $h=-2$ and $k=-20$, so the vertex of the parabola is $(-2,-20)$. We can also see this by graphing the parabola.

[Image of a parabola with vertex at (-2, -20)]

**C) The $y$-intercept is the point $(0,14)$.**

The $y$-intercept of a parabola is the point where the parabola crosses the $y$-axis. This happens when $x=0$, so we can simply substitute $x=0$ into the equation $f(x)=-2x^2-8x+14$ to find the $y$-intercept:

$$f(0)=-2(0)^2-8(0)+14=14$$

Therefore, the $y$-intercept is the point $(0,14)$.

**D) The two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.**

To find the values of $x$ that make $f(x)=0$, we can set the equation $f(x)=-2x^2-8x+14$ equal to zero and solve for $x$. This gives us:

$$-2x^2-8x+14=0$$

We can factor the left-hand side of the equation as follows:

$$-2(x-2)(x-3)=0$$

This means that either $x-2=0$ or $x-3=0$. Solving for $x$ in each case gives us the following values:

$$x=2\text{ or }x=3$$

However, we need to round our answers to two decimal places. To do this, we can use the calculator. Rounding $x=2$ and $x=3$ to two decimal places gives us the following values:

$$x=2.5\text{ and }x=-3.5$$

Therefore, the two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.

The placement results provided, the student should start with Math 100.

The placement results indicate that the student has placements for Math 111, Math 100, and Math 102+. Math 111 typically corresponds to a higher-level course than Math 100, and Math 102+ implies a placement beyond Math 102.

To progress towards Math 103E, it is essential to follow the recommended course sequence. Usually, Math courses are designed to build upon previously learned concepts and skills. Starting with Math 100 would provide the foundational knowledge necessary to succeed in subsequent courses.

Therefore, the student should first start with Math 100, and upon successful completion, they can proceed to Math 103E. It is important for the student to consult with their academic advisor or the mathematics department at their institution for specific course placement and sequencing information to ensure they are following the appropriate path.

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