It is given that x² - y² = 30 and x - y = 5. Find the value of (x + y)².

Answer:

x < -1

Step-by-step explanation:

Draw a parabola (the graph) passing trough two x-intercepts -1 and 3 and open up.

Answer:

x = 2

Step-by-step explanation:

3x + 1 = 7

3x = 7 – 1

3x = 6

x = 6/3

x = 2

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Answer:  [tex]\textsf{x = 2}[/tex]

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Given:  [tex]\textsf{3x + 1 = 7}[/tex]

Find:  [tex]\textsf{Solve for x}[/tex]

Solution: In order to isolate x we need to subtract 1 from both sides and the divide both sides by 3.

Subtract 1 from both sides

Divide both sides by 3

Therefore, the value of x is equal to 2.

7[tex]\sqrt{2}[/tex]

The triangle shown is a 45-45-90 triangle. This name comes from the fact the 3 angle measurements are 45, 45, and 90 degrees.

If needed, you could find the missing angle using the equation: 180 - (45 + 90) = x.

Special Right Triangles

Special right triangles allow us to use formulas and shortcuts to find missing sides easily. Another type of special right triangle is the 30-60-90 triangle. While both of these are special right triangles, they have different formulas.

Formulas

All 45-45-90 triangles have 2 types of sides: the legs (a and b) and the hypotenuse (c).

In these triangles, both of the legs are congruent.

Solving for c

Since we are given b, we can just plug the b-value into the formula that solves for c.

The answer cannot be simplified further, so this is the final answer.

Answer:

Second option

Step-by-step explanation:

It is a right triangle isosceles

a = b = 7

c = hypotenuse

[tex]c =\sqrt{7^{2}+7^{2} } =\sqrt{49+49} =\sqrt{2(49)}=7\sqrt{2}[/tex]

Hope this helps

Step-by-step explanation:

[tex] \sqrt{ - 64 } = - 8[/tex]

so the answer you got pls mark branlist

Answer:x = 6 , y = 18

Step-by-step explanation:

The sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

The coloured portion of the circle is known as a sector. The formula for calculating the area of a sector is given as:

Area of a sector = θ/360 * πr²

where

θ is the central angle

πr² represents the area of a circle.

Therefore the best statement that explains the formula is expressed as the central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

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Answer:

Its A edge 2023

Step-by-step explanation:

Answer:

One possible answer is:  2.25p + 2.25b + 2.25s

Another possible answer:  2.25(p + b + s)

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

Explanation:

Each item costs $2.25 per box, so,

Add up those subtotals to get the grand total

2.25p + 2.25b + 2.25s

is one possible answer

What we can do is factor out the common 2.25 using the distributive rule in reverse.

Another possible answer is:  2.25(p + b + s)

The statement that must be true about square WXYZ are as follows;

Therefore, the statement that must be true about square WXYZ are as follows;

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The required decreased value is given by 1.2425, 56g, 105.4L, 203m²

What are percentage?

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

1) Decrease 1.25km by 0.6%
    0.6% of 1.25km = 0.0075
    so total decrease = 1.25 - 0.0075
             = 1.2425
similarly,
2.) Decrease 64 g by 12 ½%
  12 ½% of 64g = 8g
   so total decrease = 64-8

                                 = 56g

3. Decrease 124 L by 15%
          15% of 124 = 18.6L
     so total decrease = 105.4L

4. Decrease 350m² by 42%
  42% of 350m² =  147m²
    so total decrease = 203m²

Thus, the required decreased value is given by 1.2425, 56g, 105.4L, 203m²

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The number of diagonals drawn from the vertex of the polygon of n sides is (n−3).

The correct option is C)

⇒  A diagonal is a segment that connects two non-consecutive vertices in a polygon.

⇒  The number of diagonals in a polygon that can be drawn from any vertex in a polygon is three less than the number of sides.

A polygon is a plane figure enclosed by line segments called sides. Polygon is a 2d shape.

Regular polygons contain equal side lengths.

⇒  Let n be the number sides in the polygon.

⇒  So, the number of diagonals drawn from the vertex of the polygon of n sides is (n−3).

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Answer:

Dot number 2. Makayla invests her money 2 years longer.

Step-by-step explanation:

Calvin 400$ with 5% interest compounded monthly will get you to 666.0294029241$ after 13 months or 1 year and 1 month

Makayla 300$ with 6% interest quarterly

1st year 378.743088$(4 quarters)

2nd year 478.1544223592$(+4 quarters)

3rd year 603.6589415506$(+4 quarters)

3rd year and 1 quarter 639.8784780436$

Answer:

So the second option is the answer: Makayla invests her money 2 years longer.

Step-by-step explanation:

Formula for compound interest: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Calvin:

[tex]A=658.80[/tex]

[tex]P=400[/tex]

[tex]r=0.05[/tex]

[tex]n=12[/tex]

[tex]t=?[/tex]

Makayla:

[tex]A=613.04[/tex]

[tex]P=300[/tex]

[tex]r=0.06[/tex]

[tex]n=4[/tex]

[tex]t=?[/tex]

Lets solve for [tex]t[/tex].

1)  Divide both sides of the equation by [tex]P[/tex].

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

2)  Take the natural log of both sides.

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

3)  Rewrite the right side of the equation using properties of exponents.

[tex]ln(\frac{A}{P}) =nt*ln(1+\frac{r}{n})[/tex]

4)  Divide each side of the equation by [tex]n*ln(1+\frac{r}{n})[/tex]

[tex]\frac{nt*ln(1+\frac{r}n)}{n*ln(1+\frac{r}n)}=\frac{ln(\frac{A}{P})}{n*ln(1+\frac{r}n)}[/tex]

5)  Cancel the common factor [tex]n[/tex] on the left side of the equation.

[tex]\frac{t*ln(1+\frac{r}n)}{ln(1+\frac{r}n)}=\frac{ln(\frac{A}{P})}{n*ln(1+\frac{r}n)}[/tex]

6)  Cancel the common factor of [tex]ln(1+\frac{r}{n})[/tex].

[tex]t=\frac{ln(\frac{A}{P)}}{n*ln(1+\frac{r}{n})}[/tex]

Now we have an equation for [tex]t[/tex] that we can use to answer your question.

For Calvin:

[tex]t=\frac{ln(\frac{658.80}{400)}}{12*ln(1+\frac{0.05}{12})}[/tex]

[tex]t=10[/tex]

For Makayla:

[tex]t=\frac{ln(\frac{613.04}{300)}}{3*ln(1+\frac{0.06}{3})}[/tex]

[tex]t=12[/tex]

So the second option is the answer: Makayla invests her money 2 years longer.

Note: This question took me 2 minutes to answer but typing it took 30. lol

Answer: The range of the function is all real numbers less

than or equal to 0.

The correct statement for the given function f(x) = -√x is "The range of the function is all real numbers less than or equal to 0." So, the correct option is C.

The domain of the function is all real numbers that are greater than or equal to 0 but we know that the square root of a negative number is in the real number system.

The graph of the function shows that for each positive input i.e. the range values we get the output values that are negative or zero.

Therefore, the range of the function is all real numbers less than or equal to 0, which is option C.

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The total number of roots of the given polynomial function is 6.

The given polynomial is [tex]f(x)=3x^{6}+2x^{5}+x^{4} -2x^{3}[/tex].

We need to determine the total number of roots of the given polynomial function.

What is the total number of roots of the polynomial function?

The number of roots of any polynomial is depended on the degree of that polynomial. Suppose n is the degree of a polynomial f(x), then fx) has n number of roots.

Here, the degree of the given polynomial function is 6.

Therefore, the given polynomial function will be having 6 roots.

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Answer:

To find out actual distance on earth, we need to measure scale. The scale is 1cm to 15 km. Thus, 10 cm on map is equal to ( 10*15) = 150 km on earth. Thus, actual distance on earth is 150 km.

The infusion time for the IV solution that will be prescribed 480 mins.

The time taken by the saline to be dripped in the infusion is called as the infusion time.

To calculate the infusion time the formula for IV drip rate is used which is;

Drip rate = volume/time × Drop factor

Drip rate = 5gtt/min

Volume = 120mL

Drop factor= 20 gtt/mL

Time = ?

From the formula above, make time the subject of the formula. That is,

Time = vol × drop factor/drip rate

Time = 120 × 20/5

Time= 120 x 4

Time= 480 mins

Therefore, the infusion time for the IV solution that was prescribed = 480 mins

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Using limits, the end behavior of the functions are given as follows:

a. Rises to the left and falls to the right.

b. Rises to the left and rises to the right.

c. Falls to the left and rises to the right.

The end behavior of a function f(x) is given by the limit of f(x) as x goes to infinity.

In item a, we have that, respectively, to the left and to the right.

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -5x^3 = -5(-\infty)^3 = \infty[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} -5x^3 = -5(\infty)^3 = -\infty[/tex]

Hence it rises to the left and falls to the right.

In item b, we have that, respectively, to the left and to the right.

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 3x^6 = 3(-\infty)^6 = \infty[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 3x^6 = 3(\infty)^6 = \infty[/tex]

Rises to the left and rises to the right.

In item c, we have that, respectively, to the left and to the right.

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 20x^3 = 20(-\infty)^3 = -\infty[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 20x^3 = 20(\infty)^3 = \infty[/tex]

Falls to the left and rises to the right.

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Jeremy's debt-to-credit ratio is 0.471.

debt-to-income ratio is the percentage of a consumer's monthly gross income that goes toward paying debts.

Here, Based on the given conditions,

formulate = Total debt / total credit limit

                 = 2355 / 5000

                = 471/1000

Cross out the common factor: 471/1000

Round 471/1000 to the required place:: 0.471

Thus, Jeremy's debt-to-credit ratio is 0.471.

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The answer for the exponential expressions 1,2,3 and 4 will be [tex]4.5,\frac{1}{2},2,1[/tex] respectively.

Exponential notation is a type of mathematical shorthand that allows us to write complex formulas in a more concise manner.

The basis of an exponent is a number or letter. It means that the base will be raised to a given level of power. The base is X, and the power is n.

The properties of the exponent used;

[tex]\rm m^a \times m^b = m^{a+b} \\\\ m^a \times n^a = {mn}^a \\\\ m^a \times m^b = m^{a-b} \\\\ m^0 = 1[/tex]

Expression 1;

[tex]\frac{(2.3^{-2})^2(5.3^2.2)^2}{(3)^-2(5.2)^2} \\\\ \frac{2^3.3^{-6}.5^2.3^6}{3^{-2}.5^2.2^2} \\\\ 4.5[/tex]

Expression 2;

[tex](3^3)(4^0)(3.2)^{-3}(2)^2 \\\\ 3^3.1.3^{-3}.2^{-3}.2^2 \\\\ \frac{1}{2}[/tex]

Expression 3;

[tex]\frac{(3^7.4^7)(2.5)^{-3}(5)^2}{12^7.5^{-1}.2^{-4}} \\\\ \frac{3^7.4^7.25^{-3}.5^{-3}.5^2}{12^7.5^{-1}2^{-4}} \\\\ 2[/tex]

Expression 4;

[tex]\frac{(2.3)^{-1}.2^0}{(2.3)^{-1}}\\\\ \frac{2^{-1}.3^{-1}.1}{2.3}\\\\ 1[/tex]

Hence, the answer for the exponential expressions 1,2,3, and 4 will be [tex]4.5,\frac{1}{2},2,1[/tex] respectively.

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The 15 are women, keeping track of the number of men chosen is Not binomial the trials are not independent.

We have given that,

The given procedure results in a binomial distribution. If not, state the reason why. Choosing 5 people (without replacement) from a group of 58 people, of which 15 are women, keeping track of the number of men chosen.

In samples with replacement, the probability has to be the same for each trial, that is, they are independent.

Hypergeometric distribution

Samples without replacement, as the probabilities depend on the previous outcomes, that is, they are not independent.

In this question

Marbles are chosen without replacement, which means that for each trial the probabilities of choosing a red marble are different, which means that the trials are not independent. So the answer is:

Not binomial the trials are not independent.

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Answer:

now we have to follow up with the formula n² - n¹

which is 7-1= 6

n³-n²

which is 13-7=6

so therefore the nth term=6

Answer:

I assume you meant "y = -x+7" not "= -x +7". If that is correct then the slope is -1.

Step-by-step explanation:

The slope is the coefficient of the x in slope-intercept form. Therefore, the slope is -1.

Please give me Brainliest if this answer is correct.

Explanation:

A slope of zero means there isn't any change in the y value. The graph isn't going upward, and it's not going downward either. We have a flat horizontal line. All horizontal lines have a slope of zero.

You can think of it like this

slope = rise/run = 0/1 = 0

rise = 0 means the y value isn't changing.

Answer:

x ≤ - 1

Step-by-step explanation:

2x - 8 ≤ - 10 ( add 8 to both sides )

2x ≤ - 2 ( divide both sides by 2 )

x ≤ - 1

Answer:

x ≤ -1

Step-by-step explanation:

Given,

2x - 8≤ -10

Solution:

Add 8 to both sides:

Divide both sides by 2:

Value of x is ≤ -1.

Answer:

(2,3) ; (-2.11)

Step-by-step explanation:

Answer:

(2, 3); (-2, 11)

Step-by-step explanation:

f(x) = x² - 2x + 3

f(x) = -2x + 7

f(x) = f(x)

x² - 2x + 3 = -2x + 7

x² = 4

x = ±2

x = 2

f(2) = -2(2) + 7 = -4 + 7 = 3

x = -2

f(-2) = -2(-2) + 7 = 4 + 7 = 11

Answer: (2, 3); (-2, 11)

The actual height of the building is 67 1/2 feet

The courthouse is the tallest building in the city. If it is 7 1/2 inches tall in the model, how tall is the actual building?

Scale factor: 1 inch = 9 feet

The given parameters are:

This means that:

7 1/2 inches : Actual = 1 inch = 9 feet

So, we have:

Actual =7 1/2 * 9 feet

Evaluate the product

Actual = 67 1/2 feet

Hence, the actual height of the building is 67 1/2 feet

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The function that has an x-intercept of - 4 and a y-intercept of 3 when graphed is f(x) = 3/4x + 3

The x-intercept of a line is the point where the line crosses the x-axis while the y-intercept of a line is the point where the line crosses the y-axis.

For the x-intercept, y = 0

For the function f(x) = 3/4x + 3

0 = 3/4x + 3

0 = 3x + 12

-3x = 12

x = -4

This shows that the function has an x-intercept of -4

For the y-intercept, x = 0

For the function f(x) = 3/4x + 3

y = 3/4(0) + 3

y = 3

This shows that the function has an y-intercept of 3

Hence the function that has an x-intercept of - 4 and a y-intercept of 3 when graphed is f(x) = 3/4x + 3

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Answer:

y = 4x

Step-by-step explanation:

Equation of line in point -y intercept form:

    [tex]\sf \boxed{\bf y-y_1=m(x- x_1)}[/tex]

[tex]\sf x_1 = 1 \ ; \ y_1=4 \ \& \ m = 4[/tex]

  y - 4 = 4(x -1)

  y - 4 = 4*x - 4*1

  y - 4 = 4x - 4

Add 4 to both sides

       y = 4x - 4 + 4

      y =4x

Answer:

continuous random variable

The answer for the following part is

Surface area is the amount of space covering the outside of a three-dimensional shape.

Surface Area of Cone,

= πrl + πr²

=3.14*8*15.77 + 3.14* 8*8

= 597.61804 mm²

Surface Area of triangular pyramid,

= apothem * slant height * length

= 73.6 m²

Surface Area pentagonal pyramid

= B + LA

= 247.75 + 5 ( 1/2*12*19.5)

= 247.75 + 5 ( 117)

= 832.75 in²

Surface area of square pyramid

= P*l /2

= 2400 ft²

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