One plane can travel 10 miles per hour faster than another. One of them goes 510 miles in the same time it takes the other to go 495 miles. What are their speeds?

The planes' speeds would be ____ miles per hour.

This is a proportion math problem.

The shortest distance between planet Q and planet R in standard form is given by

[tex]{1.64 \times 10}^{7} [/tex]

QP =

[tex]3.6 \times {10}^{6} [/tex]

RP =

[tex]1.6 \times {10}^{7} [/tex]

Applying the Pythagorean Theorem

QR² = QP² + RP²

QP² =

[tex] {(3.6 \times {10}^{6} )}^{2} + {(1.6 \times {10}^{7} )}^{2} [/tex]

QP² =

[tex](12.96 \times {10}^{12} ) + (2.56 \times {10}^{14} )[/tex]

Rewriting the expression

QP² =

[tex](12.96 \times {10}^{12} ) + (256 \times {10}^{12} )[/tex]

QP² =

[tex] {268.96 × 10}^{12} [/tex]

Find the square root

QP =

[tex] \sqrt{{268.96 × 10}^{12} } [/tex]

QP =

[tex]{16.4 × 10}^{6} [/tex]

Also written as

QP =

[tex]{1.64 \times 10}^{7} [/tex]

In conclusion, the shortest distance between planet Q and planet R is

[tex]{1.64 \times 10}^{7} [/tex]

Complete question:

The distances between some planets are given below.

Planet Q is 3.6 x 10 to the power of 6 km from planet P.

Planet R is 1.6 x 10 to the power of 7 km from planet P.

Work out the shortest distance between

planet Q and planet R. Give your answer in standard form.

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Answer:

yes, because 130 + 50 = 180 .

Step-by-step explanation:

If the degrees on the inside adds up to 180 then the lines are parallel.

f(x) = (7/4)ˣ is the equivalent exponential function to f(x) = (4/7)⁻ˣ

Equivalent exponential functions are functions that work the same even though they look different.

If two exponential functions are equivalent, then the two functions will have the same value when we substitute the same value(s) for the variable(s)

Given: f(x) = (4/7)⁻ˣ

Expression of this type can be written in two possibles:

1. By interchanging the numerator and denominator, and then changing the negative power to positive. Thus:

f(x) = (4/7)⁻ˣ = (7/4)ˣ

2. By writing the expression as a reciprocal. Thus:

f(x) = (4/7)⁻ˣ =  1/(4/7)ˣ

Therefore, the equivalent exponential function is f(x) = (7/4)ˣ. The 1st option is the answer

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Measure of angle YLA in the given figure is 32°.

Given,

∠LYA = 21°

∠GLA = 32°

A is the incentre of the ΔPQR.

Therefore,

∠YLA = ∠GLA

∠LYA = ∠GYA

=> ∠YLA = 32

Hence, Measure of angle YLA in the given figure is 32°.

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Using Pythagorean Theorem, value of x is 27.2.

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a² + b², are equal to the squares on the legs. To determine the undiscovered side of a right-angled triangle, utilise the Pythagoras theorem. The hypotenuse (third side) of a right-angled triangle, for instance, can be determined using the formula c² = a² + b², where 'c' stands for the hypotenuse and 'a' and 'b' are the two legs.

Given,

Right angled triangle

Base = 16

Height = 22

Using Pythagorean Theorem,

Hypotenuse = √Base² + height²

x = √16² + 22²

x = √256 + 484

x = √740

x = 27.2

Using Pythagorean Theorem, value of x is 27.2.

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The zeros of the function algebraically, by using these values we get, {x = -3/5,  x = 3/5}

What are the zeros of the function algebraically?

The zeros of a function are the points at which the function's value is zero. These are obtained algebraically by setting the function to zero and solving the quadratic.

We have,

f(x) = -25x⁴ + 9x²

= (25 • (x⁴)) -  32x²

= (5)²x⁴ -  (3)²x²

= 25x⁴ - 9x²

= x² • (25x²- 9)

25x² - 9

  A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

25  is the square of  5

9 is the square of 3

x²  is the square of  x¹

Factorization is  (5x + 3)  •  (5x - 3)

x² * (5x+3) * (5x-3)

x = -3/5,  x = 3/5

Hence, the zeros of the function algebraically, by using these values we get, {x = -3/5,  x = 3/5}

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Answer:

24

Step-by-step explanation:

Solving with decimals

.15 * ? = 3.6

Divide each side by .15

? = 3.6/.15

Multiply the top and bottom by 100

? = 360/15

? = 24

1) The regression equation that predicts the dog's weight based on cups of food per day is of:

Weight = -29.7 + 22.93 x Consumption.

2) Each additional cup increases the estimated weight by 22.93 pounds.

To obtain the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.

The input and the output in the context of this problem are given as follows:

The points are given on the spreadsheet, and inserting them into the calculator, the equation is given as follows:

Weight = -29.7 + 22.93 x Consumption.

Each additional cup increases the estimated weight by 22.93 pounds, because the slope of the linear function is of 22.93.

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Answer:

x=3

Step-by-step explanation:

since f(X)=4 we just fill it in on the equation to find x

4=3x-5

+5.   +5

9=3x

/3. /3

3=x

Hopes this helps please mark brainliest

Answer:

[tex]\huge\boxed{\sf x = 3}[/tex]

Step-by-step explanation:

f(x) = 3x - 5

Given that, f(x) = 4

So, we can find x by inserting the value of f(x) in the above equation.

4 = 3x - 5

Add 5 to both sides

4 + 5 = 3x

9 = 3x

Divide 3 to both sides

3 = x

OR

[tex]\rule[225]{225}{2}[/tex]

The estimate of the amount 28,945,000 is 3 × 10⁷

An estimate is a rough or approximate calculation or judgement value.

The question is with regards to the scientific notation which is of the form a × 10ᵇ, where absolute a is of a value 1 ≤ a < 10

The scientific notation form of a number is found as follows;

The decimal point on the number is moved from its position to the point such that the number of non zero numbers to the left of the decimal point is 1

The number b is the number of places to which the decimal point is moved.

b is positive when the decimal point is moved to the left

b is negative when the decimal point in the number is moved to the right

b is zero when the decimal point is not moved

The scientific notation number formed, a × 10ᵇ, which is read as a times 10 raised to the power b.

The zeros in the tail to the right of the decimal point are removed

The number 28,945,000 in scientific notation is 2.8945 × 10⁷

The number part of the scientific notation is approximated to the next higher whole number, as follows;

The first digit to the right of the decimal point is 8 which is larger than 5, therefore the 2 is increased to 3

The approximated number is therefore;

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By using the formula for simple interest, it can be calculated that-

7) Simple Interest = $24.75

   Amount =  $924.75

8) Simple Interest = $126.255

   Amount = $8543.255

9)   Simple Interest = $271.25

   Amount = $1821.25

10) Rate is 9.5%

11) Time is 4 years

12) Noah pays $6591 as interest on his car loan

What is simple interest?

Simple interest ( SI) is the interest earned on a certain principal at a certain rate over a certain period of time,

If P is the principal, rate is r %, time is t years,

SI = [tex]\frac{p \times r \times t}{100}[/tex]

Adding Principal and simple interest will give the amount

7) Principal = $900

   Rate = 11 %

  Time = 3 months = [tex]\frac{3}{12} = \frac{1}{4}[/tex] years

    Simple Interest = [tex]\frac{900 \times 11 \times 1}{100 \times 4}[/tex]

                              = [tex]\frac{99}{4}[/tex]

                              = $24.75

  Amount = $(900 + 24.75) = $924.75

8) Principal = $8417

   Rate = 18 %

   Time = 1 months = [tex]\frac{1}{12}[/tex] years

    Simple Interest = [tex]\frac{8417 \times 18 \times 1}{100 \times 12}[/tex]

                              = $126.255

   Amount = $(8417 + 126.255) = $8543.255

9)  Principal = $1550

  Rate = [tex]8\frac{3}{4}[/tex] % = [tex]\frac{35}{4}[/tex] %

  Time = 24 months = 2 years

    Simple Interest = [tex]\frac{1550 \times 35 \times 2}{100 \times 4}[/tex]

                              = $271.25

   Amount = $(1550 + 271.25) = $1821.25

10) Let the rate be r %

Principal = $7200

  Rate = r %

   Time = 15 months = [tex]\frac{15}{12} = \frac{5}{4}[/tex]  years

    Simple Interest = [tex]\frac{7200 \times r \times 5}{100 \times 4}[/tex]

                              = $90r

By the problem,

90r = 855

[tex]r = \frac{855}{90}[/tex]

r = 9.5%

11)  Let the time be t years

Principal = $4500

   Rate = 5.75 %

   Time = t years

    Simple Interest = [tex]\frac{4500 \times 5.75 \times t}{100 }[/tex]

                              = $258.75t

By the problem,

258.75t = 1035

t = 4 years

12) Cost of Noah's car = $25350

    Down payment = 20%

    Remaining cost = $([tex]25350 -\frac{20}{100}\times 25350}\\[/tex])

                                = $(25350 - 5070)

                                = $20280

Rate = 6.5%

Time = 5 years

Simple Interest = [tex]\frac{20280 \times 6.5 \times 5}{100}[/tex]

                          = $6591

13) Question 13 is incomplete

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Answer:

D

Step-by-step explanation:

The only point we see on the graph is (0, -4).

The only table that includes point (0, -4) is D

Answer:

44 i think <333

Step-by-step explanation:

Answer:

lmfa you answer my questions i recently posted ill answer yours.

Step-by-step explanation:

please tho

The correct solution is x=(+11 , +3)

Step-by-step solution:

2(x-7)²=32

⇒2(x-7)(x-7)=32

⇒(x-7)(x-7)=(32/2)

⇒(x-7)(x-7)=16

⇒(x-7)²=16

⇒[tex](x-7)=\sqrt{16}[/tex]

⇒(x-7) = ±4

⇒(x-7) = +4   or   ⇒(x-7) = -4

⇒x = +4+7   or   ⇒x = -4+7

⇒x = +11  or   ⇒x = +3

Therefore, the correct solution is x = (+11 , +3)

The length of EP is 8 units, in the triangle.

What is are of the triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

In geometry, a line segment bisecting one side of a triangle by connecting one of its vertices to the opposing side's midpoint is referred to as the triangle's median. Every triangle has exactly three medians, one from each vertices. The centroid of the triangle is where these medians cross.

Given in the diagram in PU = 4units.

We know that PU is 1/3rd of the side EU

So the length of EP = 2* PU = 2*4 = 8unit.

Hence the length of EP is 8unit.

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(7, 14)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

   Brackets

   Parenthesis

   Exponents

   Multiplication

   Division

   Addition

   Subtraction

   Left to Right

Equality Properties

Algebra I

   Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

4x + y = 42

y = x + 7

Step 2: Solve for x

Substitution

   Substitute in y:                    4x + (x + 7) = 42

   Combine like terms:           5x + 7 = 42

   Isolate x term:                     5x = 35

   Isolate x:                              x = 7

Step 3: Solve for y

   Define equation:                    y = x + 7

   Substitute in x:                       y = 7 + 7

   Add:                                        y = 14

We can use the distance formula to determine the side lengths of DEF.

D (3, -1)

E (7, -4)

F (4, -4)

DE --> √((7 - 3)^2 + (-4 - (-1))^2) = √(4^2 + (-3)^2) = √(16 + 9) = √25 = 5

DF --> √((4 - 3)^2 + (-4 - (-1))^2) = √(1^2 + (-3)^2) = √(1 + 9) = √10 ≈ 3.2

EF --> √((7 - 4)^2 + (-4 - (-4)^2) = √(3^2 + 0^2) = √9 = 3

Notice DEF is congruent to ABC because due to SSS (side-side-side) congruency; DE = AB, DF = AC, EF = BC. Because DEF and ABC are congruent, DEF and ABC must have congruent angles.

angleBAC = angleEDF = 34.7 degrees

angleACB = angleDFE = 108.4 degrees

angleCBA = angleFED = 36.9 degrees

Answer:

4.6

Step-by-step explanation:

we can use the Pythagorean theorem of

A^2 + B^2 = C^2

where A and B are the (lengths of) short sides of a right triangle and C is the (length of) long side.

Here, we have an unknown side, let's call it X, and we know that:

2^2 + X^2 = 5^2

So

4 + X^2 = 25

X^2 = 25 - 4 = 21

X^2 = 21

X = [tex]\sqrt{21}[/tex]

Let's find the root of 21 rounded to the nearest tenth (or you can probably use a calculator, the method I show below is mathematically proper but not part of the curriculum).

the root of 21 is bigger than the root of 16 but smaller than the root of 25. So the number we're looking for is between 4 and 5.

21 is pretty much in the middle, so let's start by checking if it's bigger than 4.5

4.5^2 = 20.25

So 4.5 is a bit too small

Let's check 4.6

4.6^2 = 21.16

So 4.6 is a bit too big.

So we know our number is between 4.5 and 4.6 now. To have a good rounding to the nearest tenth, we only need to find out if it's over or below 4.55 (as this gives us direct rounding to the nearest tenth).

4.55^2 = 20.7025

So X is bigger than 4.55 and smaller than 4.6, hence the answer rounded to the nearest tenth is 4.6

Answer:

Step-by-step explanation: Let x = 2, y = 5 and z=?

Here z is the unknown length.

here z is 4.6

Yes! they can afford an $85,000 house with a $65,000 mortgage requiring payments of $720 per month.

What is in a mortgage?

Principal, interest, taxes, and insurance make up the majority of mortgage payments. Your outstanding loan balance is reduced by the amount of the principal part. Borrowing money has a cost, which is interest.

Given data:

Annual Salary =$42,000

Cost =$85,000

Mortgage = $65000

Monthly Payment = $720

First Criterian : - Never Spend more than 2.5 times of your Annual Income.

2.5 * 42,000

= 105,000

it can be afforded.

Second Criterian : - Monthly Payment should not exceed Weekly Income

Monthly Payment = 720

Weekly earnings = 42000 / 52 weeks = 807

it can afforded.

Third Criterian : - monthly payment should not exceed 28% of monthly earnings.

Monthly payment = 720

Monthly earnings = 42,000 / 12 = 3500

28% * 3500

= 980

it can be afforded.

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Answer:

SAS is where two sides(S) of a triangle are equal and one angle(A) is equal

SSS is where all three sides(S) of a triangle are equal

Answer:

- 7

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

There is a total of 720 students are in Ridgewood Junior High School.

5% of students brought their lunch.

36 students brought their lunch.

the percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Let there be x students in the Ridgewood Junior High School.

5% of students brought their lunch and equal to 36

so 5% of x = 36

5/100 * x = 36

x = 36*100/5

x = 36*20

x = 720

There is a total of 720 students are in Ridgewood Junior High School.

Answer:

x log (7) -2

Step-by-step explanation:

Answer: x = 85° ,   y =45°

Step-by-step explanation:

x + 95 = 180°

x = 180° - 95°

x = 85°

In a triangle,

50° + x + y = 180°

50° + 85° + y = 180°

135° + y = 180°

y = 45°

From the above given expression

x = 35°

y = 95°

In a straight line, the angle is 180°

given angles are  50° internal angle and 95° external angle

then   x + 50° + 95° = 180°

          x + 145° =  180°

          x = 180° - 145°

          x = 35°

so in a triangle total angle is 180°

then  50° + x + y = 180°

         50° + 35° + y 180°

         y = 180° - 85°

         y = 95°

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The unknown value is [tex]\frac{a}{b} *100[/tex]

Let the unknown value is x

From the question, we have

a/b = x/100

[tex]x = \frac{a}{b} *100[/tex]

Percentage:

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed.

A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %. The ratio of the increased value to the original value, multiplied by 100, is the percentage increase formula. It is outlined as a percentage. Anything's value will increase if it is valued more, so will its proportion.

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Answer:

x - y = 3

Step-by-step explanation:

Answer:

2x - 5y = 20

Step-by-step explanation:

Standard form should look like:

Ax + By = C

and the numbers A,B, and C have to be whole numbers (actually integers, because negative is okay too except A has to be positive)

You have been given a point and the slope. There is a shortcut, fill-in-the-blank equation called point-slope that you can just fill in a point and the slope. Then we can change that equation into standard form.

Point-slope equation:

y - Y = m(x - X)

Fill in (5, -2), which is the (X, Y). 5 in place of X and -2 in place of Y. Fill in 2/5 for the m which is slope.

y - Y = m(x - X)

y - -2 = 2/5(x - 5)

simplify, and distribute.

y + 2 = 2/5x - 2

Multiply through by 5 to get rid of the fraction.

5y + 10 = 2x - 10

Subtract 10.

5y = 2x -20

Subtract 2x.

5y - 2x = -20

Rearrange the terms.

-2x + 5y = -20

Multiply through by -1 (because that A has to be positive)

2x - 5y = 20

The equation in standard form is:

2x - 5y = 20

The length of the shadow to the nearest tenth is 24.6 metres.

A 29 metres tall building casts a shadow.  The distance from the top of the building to the tip of the shadow is 38 metres.

The length of the shadow can be calculated as follows;

The situation forms a right angle triangle.

Hence, the length of the shadow can be found using Pythagoras's theorem.

c² = a² + b²

38² - 29² = b²

1444 - 841 = b²

b²= 603

b = √603

b = 24.5560583156

b = 24.6 metres

Therefore,

length of the shadow = 24.6 metres.

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The value of h in the equation h = 6q - 2u , when q = 3 and u = -5 is h = 28 .

In the question ,

it is given that ,

the equation is h = 6q - 2u ,

we have to find the value of h , when q = 3 and u = -5 .

Substituting the value of q = 3 and u = -5 in the equation ,

we get,

h = 6q - 2u

h = 6(3) - 2(-5)      ....because 6(3) = 18   and -2(-5) = 10

h = 18 + 10

Simplifying the above equation further ,

we get ,

h = 28

Therefore , The value of h in the equation h = 6q - 2u , when q = 3 and u = -5 is h = 28 .

The given question is incomplete , the complete question is

Find the value of h in the equation h = 6q - 2u , when q = 3 and u = -5  ?

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Answer:

You do it as solving by substitution.So first make x the subject of the formula in eqn1

substitute eqn1 into eqn two and solve After getting y substitute in the equation* and get x

The value of x and y in the system of equations are 8 and -5 respectively.

Given,

2x + 5y = -9

3x + 4y = 4

Now,

To solve the system of equation,

Let us make the coefficient of x same in both the equations to eliminate x.

2x +5y = -9

3x + 4y = 4

Multiply equation 1 with 3 and equation 2 with 2.

6x + 15y = -27

6x + 8y = 8

Now subtract both the equations,

7y = -35

y = -5

Now substitute y in equation,

2x + 5(-5) = -9

2x - 25 = -9

x = 8

Thus the system of equation solutions are x = 8 and y = -5.

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