2. Identify the proportional relationship.
7x-2=y y + 1 = 3x y = 5x y=2x +4 ​

Answer:

3.09

Step-by-step explanation:

check the file attached

The value of Angle DAF, x is 21°

Given,

Line BC parallel to line DE

The value of Angle ABC = 54°

The value of Angle BAC = 105°

We have to find the value of angle DAF

Here,

Angle DAF = x

Now,

Angle ABC = Angle DAB (Alternate interior angles)

So,

Angle DAB = 54°

Then,

Angle DAF, x = 180 - (105 + 54) (Linear pair of angles)

Linear Pair of Angles;

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.

That is,

Angle DAF, x = 180 - 159

Angle DAF, x = 21°

Therefore,

The value of Angle DAF, x is 21°

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Answer:

25

Step-by-step explanation:

the equation is a^2+b^2=c^2

7^2=49

24^2=576

49+576=625

the square root of 625 is 25

When the product of 6 and the square of a number is increased by 5 times the number, the result is 4. then the values of the number is x = 1/2 and -4/3

The product of 6 and the square of a number

Consider the number as x

Then the product of 6 and the square of a number = [tex]6x^2[/tex]

The product of 6 and the square of a number is increased by 5 times the number, the result is 4

Then the equation will be

[tex]6x^2[/tex] + 5x = 4

Move 4 to the left hand side of the equation

[tex]6x^2[/tex] + 5x - 4 = 0

We have to solve the quadratic equation

Split the middle terms

[tex]6x^2[/tex] + 8x - 3x -4 = 0

2x(3x+4) -1(3x+4) = 0

(2x-1)(3x+4)= 0

Then the value of x will be

2x- 1 = 0

2x = 1

x = 1/2

Similarly

3x+4 = 0

3x = -4

x = -4/3

Hence, when the product of 6 and the square of a number is increased by 5 times the number, the result is 4. then the values of the number is x = 1/2 and -4/3

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Answer :

9 girls and 18 boys don't have a voucher

Step-by-step explanation :

There are 38 boys and 22 girls.  The total number of children is 60.  We know that 33 children have a voucher.  27 children don't have a voucher. ( 60 - 33 = 27 ) .

"Twice as many boys as girls do not have a voucher."

We can now make an equation.

The girls who do not have a voucher will be x, boys who don't have a voucher will be 2x, since it says twice as many boys.

We can now make our equation.

x + 2x = 27

Add x and 2x

3x = 27

Divide both sides by 3

x = 9

We know now that girls who don't have a voucher is 9.

The boys who don't have a voucher is 2x, so we plug 9 instead of x.

2(9) = 18.

18 boys do not have a voucher.

If you would like the rest for the frequency tree...

Total students : 60

Boys : 38

Boys who don't have a voucher : 18

Boys who have a voucher : 20

Girls : 22

Girls who don't have a voucher : 9

Girls who have a voucher : 13

Hope this helped.

Answer:

Exponent: B

Base: A

Scientific Notation: C

Step-by-step explanation:

vocabulary

Answer:

Exponent and A

Base and B

Scientific Notation and C

Step-by-step explanation:

Because the Exponent is the number that is going to raise the Base and that Base is the number that you are going to multiply by.

Using the general addition rule, p(F or G) = 0.667.

What is sample space?

In probability theory, the set of all feasible outcomes or outcomes of an experiment or random trial is referred to as the sample space. The sample points, or potential ordered outcomes, are listed as elements in the set used to represent the sample space.

Let,

S = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}

F = {8, 9, 10, 11, 12, 13}

G = {12, 13, 14, 15}

n(S) = number of elements in set S are 12.

n(F) = 6

n(G) = 4

n(F and G) = common elements in F and G = 2

n(F or G) = n(F) + n(G) - (F and G)

n(F or G) = 6 + 4 - 2

n(F or G) = 8

Now, using the general addition rule,

P(F or G) = P(F) + P(G) - P(F and G)

Here,

P(F) = n(F)/n(S) = 6/12 = 1/2

P(G) = n(G)/n(S) = 4/12 = 1/3

P(F and G) = n(F and G)/n(S) = 2/12 = 1/6

⇒ P(F or G) = 1/2 + 1/3 - 1/6

                   = 5/6 - 1/6

                   = 4/6

⇒ P(F or G) = 0.667

Hence, using the general addition rule, P(F or G) = 0.667.

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The monthly payment for the first condition is $1750.11 and the total number of payments is 156.

What is the monthly payment?

Monthly payment is defined as the amount paid every month depending on the terms of the mortgage loan. This includes the principal, which is the actual balance on the loan, and the interest on the loan.

The formula for monthly payments on the mortgage is given:

                                [tex]MP = \frac{P(\frac{r}{n}) }{1- (1+\frac{r}{n})^{-nt} }[/tex]

where, MP = monthly payment

            P = principal amount

             r = rate of interest

             n = number of payments per year

              t = number of years

Given, a couple buys a house for $290000 and makes a down payment of 15%

Down payment = 0.15*290000 = $ 43500

First condition,

Present value of loan (P) = $290000 - $43500 = $246500

rate of interest (r) = 3.4% = 0.034

number of payments per year (n) = 12

number of years (t) = 15 years

Then, the monthly payment is calculated by:

             [tex]MP = \frac{246500(\frac{0.034}{12}) }{1- (1+\frac{0.034}{12})^{-12*15} } = 1750.11[/tex]

Therefore, monthly payment = $1750.11

Second condition,

monthly payment (MP) = $1950

Present value of loan (P) = $290000 - $43500 = $246500

rate of interest (r) = 3.4% = 0.034

number of payments per year (n) = 12

time in years (t) = x years

Then,

or,  [tex]1950 = \frac{246500(\frac{0.034}{12}) }{1- (1+\frac{0.034}{12})^{-12*x} }[/tex]

or, [tex]x = 13.06 = 13[/tex]

So, the total number of payments =  13*12 = 156

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Answer:

1. 5x +2

2. 6x/5

Step-by-step explanation:

If Kelley family went on a tour this afternoon and they bought 4 tickets and 3 pictures. The total cost of the Kelley family's tour is $55.

Given data

Total price =  10t+5p dollars

Where:

t = tickets =4

p = pictures = 3

Now let find the total cost

Total cost =  10t+5p

Total cost = 10(4) + 5(3)

Total cost =40 +15

Total cost =$55

Therefore we can conclude that the total cost is the amount of $55.

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Answer:

Her piggy bank can hold 720 pennies.

Step-by-step explanation:

1/2= 3/6, and 2/3=4/6, meaning the difference of 1/6=120 pennies. 120x6=720.

Less than 10 attempts were successful in this situation. due to the fact that 5 is less than 10. The data does not satisfy the requirement as a result.

Because the data don't fit the success or failure criteria, it is not appropriate to adopt a normal model for the sampling distribution of the sample.

50 students make up the sample. The likelihood that she assumes 10% of the class will attend is 10%. It will be demonstrated by:

1 - p = 1 - 10%

⇒ 1 - 0.10 = 0.90

np = 50 × 0.1

np = 5

This suggests the number of victories.

In this case, fewer than 10 efforts have been successful. Since 5 is less than 10, this is the situation. The data does not meet the criteria as a result.

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Answer:

it's not possible

because Z^2 = Z*Z

and the condition to multiply two arrays is :

( the column in first array have to equal the row in the second array)

Answer:

  (4)  5 m

Step-by-step explanation:

You want the length of side x of a right triangular prism with base edge lengths of 2.5 m and 2 m, and a volume of 12.5 m³.

The volume of the prism is given by the formula ...

  V = Bh

where B is the area of the base:

  B = 1/2bh . . . . where b and h are the leg dimensions of the right triangle

Using these formulas together, we have ...

  V = 1/2(2.5 m)(2 m)x

  12.5 m³ = 2.5x m²

Dividing by 2.5 m², we find x to be ...

  (12.5 m³)/(2.5 m²) = x = 5 m

The dimension labeled x has length 5 meters.

Amoli is Correct, where distributive property is used to multiply two expressions.

What is Distributive property?

The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.

What is Associative property?

A mathematical principle known as the associative property states that grouping the factors in a multiplication problem does not affect the solution.

Step-by-step explanation:

According to distributive property:

= (125 * (1/2y)) +( y * (1/2y))

= 125/2y + 1/2

Here, Associative property does not held.

Hence, Distributive property should be used.

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Answer:

$22,000 at 5%, $10,000 at 11%

Step-by-step explanation:

Let x be the amount invested at 5%.

[tex].05x = .11(32000 - x)[/tex]

[tex].05x = 3520 - .11x[/tex]

[tex].16x = 3520[/tex]

[tex]x = 22000[/tex]

$22,000 at 5%, $10,000 at 11%

Part A:because the data points are far away from each other.

Part B: A casual relationship would be: the number of strawberries picked and the amount of fertilizers used.

What is Correlation Coefficient?

Correlation coefficient, r, is quantitative measure that measures the extent to which two variables are associated.

The closer the data points are on a scatter plot, the closer the value of r is to 1 or -1.

Part A:

The data points in the scatter plot are farther apart and the trend slopes upwards to the right, this means that the correlation coefficient, r, would be positive but very low.

Thus, based on the scatter plot given, the correlation coefficient of r = 0.01 is most likely accurate because the data points are far away from each other.

Part B:

A casual relationship would be: the number of strawberries picked and the amount of fertilizers used.

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Answer:

Read the given problem, look at the given figure of intersecting lines, and identify the angle given and the unknown angles.

Step-by-step explanation:

Answer:

  227.7 in²

Step-by-step explanation:

You want to know the area that is 30% of a canvas that is 23 inches by 33 inches.

The area of the canvas is the product of its length and width.

  A = LW

  A = (33 in)(23 in) = 759 in²

The rose covers 30% of that area, so an area of ...

  rose = 0.30 × 759 in² = 227.7 in²

The area of the canvas covered by the rose was 227.7 square inches.

The value of the equation g(x+1) is -2x²-x

Given equation,

g(x) = -2x²+3x-1

Replacing x in the equation by x+1

g(x+1) = -2(x+1)² +3(x+1) -1

g(x+1) = -2(x²+1+2x) +3x +3 -1

g(x+1) = -2x² -2 -4x +3x +3 -1

g(x+1) = -2x²- x

Hence the final answer is g(x+1) = -2x²-x

Since this, the question says to find the value g(x+1) we need to replace the value of x in the given equation g(x) by x+1 to find value. After replacing we get -2(x+1)² +3(x+1) -1. Next, we need to solve the bracket (x+1)² which will give us x²+1+2x. We will multiply this by -2, which will give us -2x² -2 - 4x. Next, we will solve 3(x+1) which will give us 3x+3. Finally, we need to solve the whole equation to get the answer -2x²- x

I hope this answer helps.

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Answer:

A=-3,b=1,C=19

Step-by-step explanation:

y-7=3(x+4)

we will just simplify the bracket like this

y-7=3x+12

y=3x+12+7

y=3x+19

y-3x=19

A=-3,b=1,C=19

if u find the answer correct mark as brainliest

The vertex of the parabola is at (-2, 2), the line of symmetry of the parabola is at x = -2 and the parabola is open downwards

From the given parabola

The vertex of the parabola is at (-2, 2)

The vertex of the parabola is defined as the the point at the intersection of the parabola and its line of symmetry.

The line of symmetry is at x = -2

The parabola is open downwards

Hence, the vertex of the parabola is at (-2, 2), the line of symmetry of the parabola is at x = -2 and the given parabola is open downwards

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Answer:

6666667

Step-by-step explanation:

Answer:

0.64 feet

Step-by-step explanation:

make h the subject of this expression

[tex]t = \sqrt{ \frac{h}{16} } [/tex]

[tex] {t}^{2} = \frac{h}{16} [/tex]

[tex]h = 16 {t}^{2} [/tex]

then substitute in the value of t=0.2 into the equation of h:

h = 16 × (0.2)² = 0.64 feet(answer)

Problem 13

Reason:

If a > 0, then the statement would always be true. However, if 'a' was negative, then the statement is false.

For example, if a = -2 then:

[tex]a^{-1} = (-2)^{-1} = \frac{1}{(-2)^1} = -\frac{1}{2} = -0.5[/tex]

In short,

[tex]a^{-1} = -0.5 \ \ \text{ when } a = -2[/tex]

This is one of infinitely many counter-examples to prove the original statement isn't always true.

===================================================

Problem 14

Reason:

The rule to use here is [tex]a^b*a^c = a^{b+c}[/tex]

We add exponents b and c, while the base 'a' stays the same the whole time.

In this problem we have: [tex]3^n*3^{-n} = 3^{n+(-n)} = 3^{n-n} = 3^0 = 1[/tex]

Therefore [tex]3^n*3^{-n} = 1[/tex] is always true regardless of what you replace n with. The variable n doesn't have to be an integer.

===================================================

Problem 15

Reason:

Let's say p = -1 is plugged into the expression

[tex]6^p = 6^{-1} = \frac{1}{6^1} = \frac{1}{6} \approx 0.1667[/tex]

which is a positive outcome showing that [tex]6^p > 0[/tex] doesn't automatically guarantee that p > 0. Feel free to try other negative values as counter-examples. Also p = 0 works as well. It turns out that [tex]6^p[/tex] is always positive regardless of what real number you use for p.

===================================================

Problem 16

Reason:

The rule used here is [tex]a^{-b} = \frac{1}{a^b}[/tex]

An equivalent rule is [tex]\left(\frac{a}{b}\right)^{-c} = \left(\frac{b}{a}\right)^c[/tex]

The idea is to flip the fraction to turn the exponent positive.

Examples: [tex]2^{-5} = \frac{1}{2^5} \ \ \text{ and } \ \ \left(\frac{7}{9}\right)^{-3} = \left(\frac{9}{7}\right)^{3}[/tex]

===================================================

Problem 17

Reason:

This is similar to problem 15 in that [tex]2^m[/tex] is always positive regardless if m is negative, zero, or positive. It might help to graph out [tex]y = 2^x[/tex] and see that the curve never dips below the x axis.

Price of one pair of socks are $5.00

The total of 5 sisters each bought scarves and 2 pairs of socks.

Socks price variable defined as x.

Total scarves bought by the sisters are:

5 × 1 = 5

Total socks bought by the sisters are:

5 × 2 = 10

Equation for total bill:

$125.00 = 5 × $15.00 + 10 × x

$125.00 = $75.00 + 10x

10x = $125.00 - $75.00

10x = $50.00

x = $50.00/10

x = $5.00

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