4)
Michael runs 0.18 miles a minute. How many minutes will it
take Michael to run 4.23 miles?
per from tuua dagoltz of mastill

The two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

To solve the system of equations, let's assign variables to the two integers. Let the first integer be represented by 'x' and the second integer by 'y'.

According to the given information:

a. Fourteen more than twice the first integer gives the second integer:

This can be expressed as: 2x + 14 = y

b. The second integer increased by one is the square of the first integer:

This can be expressed as: y + 1 = x^2

Now, we have a system of equations:

1) 2x + 14 = y

2) y + 1 = x^2

To solve this system, we can substitute the value of 'y' from equation 1) into equation 2):

2x + 14 + 1 = x^2

2x + 15 = x^2

Rearranging the equation, we have:

\(x^2 - 2x - 15 = 0\)

Factoring the quadratic equation, we get:

(x - 5)(x + 3) = 0

Setting each factor equal to zero:

x - 5 = 0   -->   x = 5

x + 3 = 0   -->   x = -3

Substituting the values of 'x' back into equation 1), we can find the corresponding values of 'y':

For x = 5:

2(5) + 14 = y

10 + 14 = y

y = 24

For x = -3:

2(-3) + 14 = y

-6 + 14 = y

y = 8

Therefore, the two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

for more such question on integers visit

https://brainly.com/question/929808

#SPJ8

Hello!

We have all angles of the triangle:

We will use the law of cosines. This relation is valid for all sides of any t

We have:

angle A = 12°

côté a = 10

angle B = 150°

This is therefore the first case of application of the sine law.

So:

\(\sf \dfrac{b}{sin~B} = \dfrac{a}{sin~A}\)

\(\sf b =\dfrac{sin~B~*~a}{sin~A} = \dfrac{sin~150~*~10cm}{sin~12} = \dfrac{arcsin~0.5~*~10cm}{arcsin~0.2079116908} = \dfrac{30~*~10cm}{12} = \dfrac{300cm}{12} = \boxed{\sf25cm}\)

If two figures can be mapped onto one another or if all pairings of angles and side lengths are congruent, the figures are said to be congruent.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

If two triangles are the same size and shape, they are said to be congruent. To establish that two triangles are congruent, not all six matching elements of either triangle must be located. There are five requirements for two triangles to be congruent, according to studies and trials. The congruence properties are SSS, SAS, ASA, AAS, and RHS.

here, we have,

Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.

In Δ PQR and ΔXYZ, as shown in figure,

we can identify that PQ = XY, PR = XZ,

and QR = YZ

and ∠P = ∠X,

∠Q = ∠Y and ∠R = ∠Z.

Then we can say that Δ PQR ≅ ΔXYZ.

Learn more about Triangle congruency click here:

brainly.com/question/30256538

#SPJ1

Answer:

7) y = -2

8) x = 4

Step-by-step explanation:

Any straight horizontal/vertical line you find will be x= or y=. The vertical lines are always x= because they only touch the x axis. It's the opposite for horizontal lines. For example, on number 7, the line touches -2 on the y axis. That's why it's "y=-2". Same goes for 8. the line only touches 4.

I hope this helped and wasn't confusing!

Answer:

  k = 110

Step-by-step explanation:

You want the integer multiple of pi that is the area of 300° of a donut with inner radius 8 cm and outer radius of 14 cm.

The area of a circle is given by the formula ...

  A = πr²

Then the area of the outer circle is ...

  A = π(14 cm)² = 196π cm²

The area of the inner circle is ...

  A = π(8 cm)² = 64π cm²

The area of the whole donut is the difference of these areas:

  whole donut area = (196 -64)π cm² = 132π cm²

The shaded area of the figure represents 300° of the 360° full donut. The area is proportional to the central angle, so the shaded area is ...

  shaded area = (300°/360°)×whole donut area

  shaded area = 5/6 × 132π cm² = 110π cm²

Comparing this to the expression kπ cm², we see that ...

  k = 110

I'm not sure if my answer will help, but oh well.

So basically congruent means equal. so with the two photos you should be able to tell if they are congruent by looking and measuring there angles, sizes, etc.

The total number of pears consumed by all the 6 partridges is given by the equation A = 84 pears

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of pears be represented as A

Let the number of partridges be n = 6

Now , Pete the partridge eats 4 pears in 30 minutes

So , the number of pears in 1 hour = 2 x 4

The number of pears in 1 hour = 8 pears

The number of pears in 1 hour 30 minutes = 8 + 4 pears

The number of pears in 1 hour 30 minutes = 12 pears

The number of pears in 1 hour 45 minutes = 12 + 2 pears

The number of pears in 1 hour 45 minutes = 14 pears

So ,

The total number of pears by all 6 partridges A = 6 x number of pears in 1 hour 45 minutes

Substituting the values in the equation , we get

The total number of pears by all 6 partridges A = 6 x 14

On simplifying the equation , we get

The total number of pears by all 6 partridges A = 84 partridges

Therefore , the value of A is 84 partridges

Hence , the number of partridges is 84

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

Answer:  

Step-by-step explanation:

Add the exponents \(x^{2} x^{9} = x^{11}\)

Answer:

1 = 7x=42 (divide both sides by 7)

7x/7 =42/7

x=6

2.=9y=81 (divide both sides by 9)

9y/9y= 81/9

y=9

3.= –40=8a (divide both sides by 8)

–40/8= 8a/8

a=5

4.=y divided 11=12

y=11 multiplied by 12

y= 132

5.= –15y=135( divide both sides by –15)

–15y/–15=135/–15

y= –9

6.= 17p=51(divide both sides by 17)

17p/17=51/17

p=3

7.= –65= –13w (divide both sides by 13)

–65/–13=–13w/–13

w=5

8.=y/–2=4

(cross multiply)

y/–2=4/1

4 multiplied by –2= –8

therefore:y= –8

Step-by-step explanation:

I HOPE THIS HELPED :)

Answer:

a) 7x=42

Step-by-step explanation

use the co-efficient of the unknown to divide both sides

7x=42

7x/7=42/7

x=6

9y=81

9y/9=81/9

y=9

-40=8a

is the same thing as

-8a=40

-8a/-8=40/-8

a=-5

y+11=12

y=12-11

y=1

-15y=135

-15y/-15=135/-15

y=9

17p=51

17p/17=51/17

p=3

-65=-13w

13w=65

13w/13=65/13

w=5

y/-2= 4

cross multiply y=-8

Answer:

Tan(x)

Step-by-step explanation:

JUST TOOK THE TEST

tan(x) is equivalent to 1/sin2x - cos2x/sin2x. Option a is correct.

To determine equivalent 1/sin2x - cos2x/sin2x.

tan(x) is tangent of x here, tan is trigonometric operator.

Here,
= 1/sin2x - cos2x/sin2x
= (1-cos2x)/sin2x
= (2sin²x)/2sinxcosx
= sin(x)/cos(x)
= tan(x)

Thus, tan(x) is equivalent to 1/sin2x - cos2x/sin2x.

Learn more about tan(x) here:

https://brainly.com/question/15391269

#SPJ5

Answer:

Supplementary

x = 31

Step-by-step explanation:

The given angles are supplementary which means their sum is equal to 180

3x + 25 + 2x = 180 add like terms

5x + 25 = 180 subtract 25 from both sides

5x = 155 divide both sides by 5

x = 31

Product B performed worse in the study because 26% failed to get relief with this product whereas only 20% failed to get relief with product A.

From the information given, it was illustrated that

20 people were given Product A, and all but 4 experienced relief. The percentage for those relieved will be:

= 16/20 × 100

= 80%

Those relived = 100% - 20%

= 80%

Also, 50 people were given Product B, and all but 13 experienced relief. Those relieved will be:

= 37/50 × 100

= 74%

Therefore, product A performed better.

Learn more about percentages on:

brainly.com/question/29592182

#SPJ1

Answer:

$77.514

Step-by-step explanation:

28.6 x 1.74 + 27.75 =  77.514

Answer:

5/14

Step-by-step explanation:

You multiply the recripricoal in division problems:

5/2  ÷ 7/1 =

5/2 × 1/7 =

5/14

Answer:

5 / 14

Step-by-step explanation:

will make it simple... the technique is to flip the either 5/2 or 7/1

then multiply.

5/2 x 1/7 = 5 / 14

Answer:

Hope you find this helpful:

Step-by-step explanation:

Answer: The least common denominator (LCD) is 1015.

a) A negative number on the x-axis (-a, b) would move in the left direction by one unit.

To find out why, check point (0, b) on the y-axis and point (-a, b) on the x-axis.

The distance between these two points is a unit, meaning that the point (-a, b) is one unit to the left of the point (0, b).

b) A positive number on the x-axis (+a, b) would move in the right direction by a unit.

Again, let's look at the point (0, b) on the y-axis and the point (+a, b) on the x-axis.

The distance between the two points is also one unit, which means the point (+a, b) is one unit to the right of the point (0, b).

c) A negative number on the y-axis (a, -b) would move in the downward direction by b units.

Assume that point (a, 0) is on the x-axis and point (a, -b) is on the y-axis. The distance between them is b units, which means that the point (a, -b) is b units below the point (a, 0).

d) A positive number on the y-axis (a, +b) would move in the upward direction by b units.

Also, check the point (a, 0) on the x-axis and point (a, +b) on the y-axis. The distance between these two points is b units, which means that the point (a, +b) is b units above the point (a, 0).

A number is a mathematical term used to show the quantity or value of a thing. It can be depicted using numerals, symbols, or words.

Examples include 30, hundred, -8, 6x, "5", 0.67, etc.

Numbers can be Positive - numbers greater than zero, or negative - numbers less than zero.

Learn more about numbers at brainly.com/question/17200227

#SPJ1

Answer:

1) Y-6=-3/2(X-0)     2) Y= -3/2x+6   3) 3x+2y=12

Step-by-step explanation:

Answer:

144 196 256

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

Answer: 18

Step-by-step explanation:

Multiply number of each item possible

3*2*3=18

Answer:

  y = x³ -2x² -13x -10

Step-by-step explanation:

You want a polynomial with x-intercepts -2, -1, and 5, and a y-intercept of -10.

A polynomial with zero x = p will have a factor of (x -p). The three given zeros mean factors of the desired polynomial will be ...

  p(x) = (x -(-2))(x -(-1))(x -5) = (x +2)(x +1)(x -5)

Expanding this gives ...

  p(x) = (x +2)(x² -4x -5) = x³ -2x² -13x -10

This polynomial has a constant of -10, which will be its y-intercept. No additional scaling is needed.

The polynomial function is ...

  y = x³ -2x² -13x -10

The lengths of the segments x and y in the right triangles are x = 6√2 and y = 12√2

The given shape is the right-angled triangle

Such that

We have angles = 30 degrees and 45 degrees

The measure of y can be calculated using the following sine ratio

sin(45) = y/24

Make y the subject

So, we have

y = 24 * sin(45)

When evaluated, we have

y = 12√2

The length x is calculated as

sin(30) = x/y

So, we have

x = y * sin(30)

This gives

x = 12√2 * 1/2

Evaluate

x = 6√2

Hence, the value of x in the triangle is 6√2

Read more about triangles at

https://brainly.com/question/2437195

#SPJ1

Answer:

The 99.9% confidence interval for the difference between these results is between 12.09 and 25.91 hours per week.

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

Subtraction of normal variables:

When two normal variables are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of variances.

Ohio had an average of 52, standard deviation of 7.22, sample of 40.

This means that \(\mu_O = 52, s_O = \frac{7.22}{\sqrt{40}} = 1.1416\)

Pennsylvania had an average of 33, standard deviation of 10.11, sample of 33.

This means that \(\mu_P = 33, s_P = \frac{10.11}{\sqrt{33}} = 1.76\)

Distribution of the difference:

\(\mu = \mu_O - \mu_P = 52 - 33 = 19\)

\(s = \sqrt{s_O^2 + s_P^2} = \sqrt{1.1416^2 + 1.76^2} = 2.1\)

Confidence interval:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.999}{2} = 0.0005\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.0005 = 0.9995\), so Z = 3.29.

Now, find the margin of error M as such

\(M = zs\)

\(M = 3.29*2.1 = 6.91\)

The lower end of the interval is the sample mean subtracted by M. So it is 19 - 6.91 = 12.09 hours per week

The upper end of the interval is the sample mean added to M. So it is 19 + 6.91 = 25.91 hours per week.

The 99.9% confidence interval for the difference between these results is between 12.09 and 25.91 hours per week.

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

Option D is the correct answer.

We have,

We need to isolate the absolute value |x + 2| on one side of the inequality.

We subtract 7 from both sides.

|x + 2| > 3

Next, we can split this inequality into two separate inequalities, one for when the expression inside the absolute value is positive, and one for when it is negative:

x + 2 > 3

or

- (x + 2) > 3

Solving for x in the first inequality.

x > 1

Solving for x in the second inequality.

-x - 2 > 3

Adding 2 to both sides and multiplying by -1.

x < -5

So the solution set for the inequality |x + 2| + 7 > 10 is the set of all x-values that satisfy either x > 1 or x < -5.

Using interval notation.

(-∞, -5) U (1, ∞)

Thus,

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ1

Maria’s vegetable garden measures 5⅔ feet by 6⅚ feet. 38.72 feet² is the area of the garden. This can be solved using the concept of the area of rectangle.

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposing sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Each and every square is a rectangle since it is a quadrilateral with right angles on all four sides. But not all rectangles are squares; for a shape to be a square, all of its sides must have the same length.

So a square is also a rectangle and a rhombus. There is no square shape in the rectangle or rhombus. The trapezium shape is a parallelogram.

Maria’s vegetable garden measures 5⅔ feet by 6⅚ feet.

So, it is a rectangular garden.

Now, area = 5⅔ feet × 6⅚ feet

or, area = 17/3 feet × 41/6 feet

or, area = 697 /18 feet²

or, area = 38.72 feet²

To know more about area of rectangle refer to:

https://brainly.com/question/2607596

#SPJ1