what’s the value of y ?

Answer:

A) 41 laps

Step-by-step explanation:

Round 17 4/7 to the nearest whole number:

18

Round 23 5/14 to the nearest whole number:

23

18 + 23 = 41

Final answer:

By rounding the fractional laps to the nearest whole numbers (18 for Monday and 23 for Wednesday), and adding them together, we estimate that Kira swam a total of 41 laps. Option A is the closest answer.

Explanation:

To estimate the total number of laps Kira swam on Monday and Wednesday, we should round the numbers to the nearest whole number and then add them together. Kira swam 17 4/7 laps on Monday, which we can round to 18 laps for estimation purposes. On Wednesday, she swam 23 5/14 laps, which rounds to 23 laps. Adding the estimated numbers together, we get:

Monday: 18 (estimated from 17 4/7)

Wednesday: 23 (estimated from 23 5/14)

Therefore, the estimated total number of laps is 18 + 23 = 41 laps.

The closest answer to our estimation is Option A: 41 laps.

Answer:

[tex]y=\frac{3}{2} x+\frac{20}{3}[/tex]

Step-by-step explanation:

First, to find the original line, employ the slope formula.

[tex]\frac{y2-y1}{x2-x1} \\\\\frac{6-8}{4-1} \\\\\frac{-2}{3}[/tex]

The slope of your original line is [tex]-\frac{2}{3}[/tex].

Next, plug in your slope and the third point to the point-slope formula.

[tex]y-y1=m(x-x1)\\\\y-8=-\frac{2}{3} (x+2)\\\\y-8=-\frac{2}{3} x-\frac{4}{3}\\\\y=-\frac{2}{3} x+\frac{20}{3}[/tex]

To find the line which is perpendicular to the line, take the opposite reciprocal of the slope.

To find the opposite, flip the sign. [tex]-\frac{2}{3}[/tex] is negative, so it will become [tex]\frac{2}{3}[/tex], which is positive.

To find the reciprocal, flip the fraction. [tex]\frac{2}{3}[/tex] would become [tex]\frac{3}{2}[/tex].

Your slope for the perpendicular line is [tex]\frac{3}{2}[/tex], so your line is:

[tex]y=\frac{3}{2} x+\frac{20}{3}[/tex]

Answer:

y=x

Step-by-step explanation:

If you draw the line y=x on the shown graph a and a' are the same distance away from the line. This is the same for all the other points and its prime.

Answer:

true

explanation:

because vertical angles are congruent.

Answer:

10 different groups of three CDs are possible

Step-by-step explanation:

Total CDs are five and 3 has to be chosen where order doesn't matter.

In these kind of scenarios, combinations are used for calculating different ways in which the CDs can be given.

So,

Number of ways in which groups of CDs are possible = ⁵C₃

[tex]= \frac{n!}{r!(n-r)!} \\= \frac{5!}{3!(5-3)!}\\=\frac{5!}{3!2!}\\=\frac{5*4*3!}{3!2!}\\=\frac{5*4}{2}\\=\frac{20}{2}\\=10[/tex]

Therefore, 10 different groups of three CDs are possible ..

Answer:

65

Step-by-step explanation:

25+2x8+3x8

Answer:

25 + 8(2 + 3)

Step-by-step explanation:

Answer:

Hi there!

The answer to this question is 3

Step-by-step explanation:

You first distribute the four into the parenthesis to get: 12x-24+15+ 27

Next you add -24 to 15 to get: -9 your equation should now look like 12x-9=27

Then you add 9 on both side to get 12x=36

Last you divide twelve on both sides to x=3

Answer:

3

Step-by-step explanation:

Answer:

9 or -6

Step-by-step explanation:

To solve, I would suggest factoring.

You need to find two numbers which can be multiplied for 54 and also combined in some way to get 3. In this case, 9 and 6 are perfect.

[tex]x^2-3x-54=0\\(x-9)(x+6)=0[/tex]

Next, you can set both of your terms equal to zero to find your possible solutions.

[tex]x-9=0\\x=9\\[/tex]

or

[tex]x+6=0\\x=-6[/tex]

Answer:

g(x) = 7x^2

Step-by-step explanation:

Given a function f(x), the function kf(x) is stretched by a factor of k. In this case, if we stretch the function f(x) = x^2 by a factor of seven, the new function is going to be the base function multiplied by 7, as follows:

g(x) = 7x^2

Answer:

0.015

Step-by-step explanation:

The probability two independent events take place is the product of their individual probabilities.

p(shoes & book) = p(shoes) * p(book) = 0.15 * 0.10 = 0.015

Answer:

0.015 ~apex

Step-by-step explanation:

Answer:

x<-1

Step-by-step explanation:

-5x-15>10+20x

Add 5x to each side

-5x+5x-15>10+20x+5x

-15> 10+25x

Subtract 10 from each side

-15-10 > 25x

-25 >25x

Divide each side by 25

-25/25 >25x/25

-1>x

x<-1

Answer:

9/4  or 2 1/4.

Step-by-step explanation:

3/4 / 1/3

=3/4 * 3/1

= 9/4

Answer:

3/4 ÷ 1/3 equals

(3/4 x 3/1) = 9/4

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

Given

9x - 10 = 3x + 2 ( subtract 3x from both sides )

6x - 10 = 2 ( add 10 to both sides )

6x = 12 ( divide both sides by 6 )

x = 2

Answer:

x=2

Step-by-step explanation:

Given

9x - 10 = 3x + 2 ( subtract 3x from both sides )

6x - 10 = 2 ( add 10 to both sides )

6x = 12 ( divide both sides by 6 )

x = 2

Answer:

So x=4 and y=-5 would work.

Step-by-step explanation:

When you multiply complex conjugates, you get a real result.

Example:

[tex](a+bi)(a-bi)=a^2-b^2i^2=a^2+b^2[/tex]

I replace [tex]i^2[/tex] with -1 since [tex]i^2=-1[/tex].

[tex]a^2+b^2[/tex] is a real number (there is no imaginary part, no i).

So what is the conjugate of 4+5i?

4-5i

So x=4 and y=-5 would work.

A multiple of the complex conjugate would work as well.

[tex](a+bi)(ca-cbi)[/tex]

[tex]c(a+bi)(a-bi)[/tex]

[tex]c(a^2-b^2i^2)[/tex]

[tex]c(a^2+b^2)[/tex]

This is still a real number; there is no imaginary part,no i.

Answer:

n=5   n=9

Step-by-step explanation:

n^2 − 14n = -45

Add 45 to each side

n^2 − 14n +45 = -45+45

n^2 -14n +45 = 0

Factor the equation

What 2 number multiply to 45 and add to -14

-5*-9 = 45

-5+-9 = -14

(n-5) (n-9) =0

Using the zero product property

n=5   n=9

You are told the middle part is a square, so all 4 sides are equal.

The height is shown as 4 feet, so the width of the square is also 4 feet.

This means the height of the 2 triangles is 7 - 4 = 3 feet, so each triangle is 1.5 feet high ( 3 feet / 2 = 1.5).

The area of the square is 4 x 4 = 16 square feet.

The area of 1 triangle is 1/2 x base x height = 1/2 x 4 x 1.5 = 3 square feet.

The total area = 16 + 3 + 3 = 22 square feet.

Answer:

[tex] a = \frac{100}{3}[/tex]

Step-by-step explanation:

We have the following equation:

[tex]\frac{1}{2} a + \frac{2}{3} b = 50[/tex]

If [tex]b=50[/tex], then:

[tex]\frac{1}{2} a + \frac{2}{3}[/tex]×50 [tex] = 50[/tex]

Solving for 'a':

[tex]\frac{1}{2} a = \frac{50}{3}[/tex]

[tex]\frac{1}{2} a = \frac{50}{3}[/tex]

[tex] a = 2\frac{50}{3}[/tex]

[tex] a = \frac{100}{3}[/tex]

Answer a=60 (3rd option)

Step-by-step explanation:

Answer:

Article I, Section 8.

Step-by-step explanation:

The expressed powers of the federal government are given in Article I, Section 8 of the Constitution. This includes the many specific powers which the framers intended for the federal government to have, such as to declare war, regulate commerce, establish post offices, and establish rules of naturalization.

Answer:

They are directly listed in the Constitution.

Answer:

A. $2,506.50

Step-by-step explanation:

Step-by-step explanation:

After the raise, his pay is:

62000 + 0.05×62000

62000 (1 + 0.05)

65100

His pay after one year is $65,100.

To calculate Carlos's new salary after a 5% raise on his initial $62,000 salary, you multiply $62,000 by 0.05 to find the raise amount of $3,100, and then add it to the initial salary, resulting in a new salary of $65,100.

The question involves calculating the new salary of Carlos after a 5% raise following his initial year of employment. Carlos's starting salary is $62,000 per year. After one year, he receives a 5% raise. To calculate Carlos's new salary, follow this step:

Now, let's do the math:

Therefore, after a 5% raise, Carlos's new annual pay will be $65,100.

Answer:

[tex]\large\boxed{\dfrac{(2a+1)^2}{50a}}[/tex]

Step-by-step explanation:

[tex]10a-5=5(2a-1)\\\\4a^2-1=2^2a^2-1^2=(2a)^2-1^2\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(2a-1)(2a+1)\\\\\dfrac{2a+1}{10a-5}\div\dfrac{10a}{4a^2-1}=\dfrac{2a+1}{5(2a-1)}\div\dfrac{10a}{(2a-1)(2a+1)}\\\\=\dfrac{2a+1}{5(2a-1)}\cdot\dfrac{(2a-1)(2a+1)}{10a}\qquad\text{cancel}\ (2a-1)\\\\=\dfrac{2a+1}{5}\cdot\dfrac{2a+1}{10a}=\dfrac{(2a+1)^2}{50a}[/tex]

Answer: The answer is D

Step-by-step explanation: got it right 2023 edge

Answer:

(2y-4)cm

Step-by-step explanation:

In the given question we have (4y-8) divided by 2

which can be written mathematically as [tex]\frac{\left ( 4y-8 \right )cm}{2}[/tex]

Now (4y-8) is a quatity  with unit cm. and the whole expression is in parentheses. Moreover, two quatity can only be added or subtracted only when their units are same. Therefore 4y and 8 must have same unit that is cm.

Therefore, [tex]\frac{\left ( 4y-8 \right )cm}{2}=(2y-4)cm[/tex] and not anything else

Answer:

=56°

Step-by-step explanation:

The degree measure of an angle is the measure of the central angle that intercepts the arc at the circumference.

The central angle is bound by two radii.

In the provided question, the central angle ACB=56° and intercepts the circle at A and B, with the vertex at C the center of the circle.

Answer:56

Step-by-step explanation:

[tex]\displaystyle\tt\left(\frac{xy^4}{x^{-5}y^5}\right)^{-3} =\frac{x^{-3}y^{4\cdot(-3)}}{x^{-5\cdot(-3)}y^{5\cdot(-3)}}=\boxed{\tt\frac{x^{-3}y^{-12}}{x^{15}y^{-15}}}[/tex]

Answer:

[tex]log_{3}(x-4)= 3log_{3}(2)[/tex]

Step-by-step explanation:

The given equation is:

[tex]x-4=2^{3}[/tex]

We have to find the logarithmic equation with same solution as the given equation.

If we take the log of both sides, we can get a logarithmic equation. Since the log operation is applied to both sides the solution of the equation will stay the same.

Taking the logarithm to the base 3 of both sides, we get:

[tex]log_{3}(x-4)= log_{3}(2)^{3}\\\\ log_{3}(x-4)= 3log_{3}(2)[/tex]

Answer: The CORRECT answer is C: log2(x-4)=3

Answer:

135°

Step-by-step explanation:

In a parallelogram the opposite angles are congruent, so

∠BCD = ∠BAD = 135°

Answer:

$39

Step-by-step explanation:

Let original price be x, so we need to subtract 16 2/3 % from that to get 32.50

So we can write:

[tex]100x-16\frac{2}{3}x=3250\\83\frac{1}{3}x=3250\\x=39[/tex]

So basically, the original price was $39.

Answer:

Option C is correct

Step-by-step explanation:

The two triangles are similar if there sides are proportional to each other

So, In Triangle ABC and Triangle DEF

AB/DE=BC/EF=AC/FD

according to definition of similar triangles.

We are given AC = 8

and FD = 4

So, AC/FD = 8/4 = 2/1

or 2:1

So, Option C is correct

Answer: Option C

2:1

Step-by-step explanation:

Two triangles are similar if the ratio of their sides is proportional.

In this case we have the triangle ∆ABC and ∆DEF so for the sides of the triangles they are proportional it must be fulfilled that:

[tex]\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}[/tex]

In this case we know that:

[tex]AC=8[/tex]

[tex]DF=4[/tex]

Therefore

[tex]\frac{AC}{DF} = \frac{8}{4}\\\\\frac{AC}{DF} = \frac{2}{1}[/tex]

The similarity ratio of ∆ABC to ∆DEF is 2:1

Answer:

(- ∞, - 4 ] ∪ [7, + ∞ )

Step-by-step explanation:

Determine the zeros by equating to zero, that is

x² - 3x - 28 = 0 ← in standard form

(x - 7)(x + 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x + 4 = 0 ⇒ x = - 4

The zeros divide the domain into 3 intervals

(- ∞ , - 4 ], [ - 4, 7 ], [ 7, + ∞)

Choose a test point in each interval and compare value with required solution

x = - 5 : (- 5)² - 3(- 5) - 28 = 25 + 15 - 28 = 12 > 0

x = 0 : 0 - 0 - 28 = - 28 < 0

x = 10 : 10² - 3(10) - 28 = 100 - 30 - 28 = 42 > 0

Solutions are the first and third interval, that is

x ∈ (- ∞, - 4 ] ∪ [ - 7, + ∞)

Answer:

it's C on edge

Step-by-step explanation:

got it right:)

Answer:

1/16

Step-by-step explanation:

2 ^ -4

The negative puts the number in the denominator

1 / 2^4

1/16