Find four integers whose sum is 400 such that the first integer is equal to twice the second integer, three times the third integer and four time the fourth integer.

Answer:

9x² + 28x - 32

Step-by-step explanation:

Given

(9x - 8)(x + 4)

Each term in the second factor is multiplied by each term in the first factor, that is

9x(x + 4) - 8(x + 4) ← distribute both parenthesis

= 9x² + 36x - 8x - 32 ← collect like terms

= 9x² + 28x - 32

Answer:

Option D

Step-by-step explanation:

Answer:

[tex]x = 11[/tex]

Step-by-step explanation:

The bases of a trapezoid are parallel

The angles,

[tex](9x) \degree[/tex]

and

[tex](7x + 4) \degree[/tex]

are same side interior angles. These two angles are supplementary.

[tex](7x + 4) + 9x = 180 \degree[/tex]

[tex]7x + 9x = 180 - 4[/tex]

[tex]16x = 176[/tex]

Divide both sides by 16.

[tex]x = \frac{176}{16} [/tex]

[tex]x = 11[/tex]

Answer:

[tex]x=11[/tex]

Step-by-step explanation:

We have been given that a carpenter cuts the corners of a rectangle to make the  trapezoid. We are asked to find the value of x.

Since trapezoid is made of rectangle, so both bases will be parallel to each other.

We know that two consecutive interior angle of parallel lines are supplementary. We can set an equation to solve for x as:

[tex]9x+7x+4=180[/tex]

[tex]16x+4=180[/tex]

[tex]16x+4-4=180-4[/tex]

[tex]16x=176[/tex]

[tex]\frac{16x}{16}=\frac{176}{16}[/tex]

[tex]x=11[/tex]

Therefore, the value of x is 11.

Answer:

The graph in the attached figure ( is the third option)

Step-by-step explanation:

we have the compound inequality

[tex]-18> -5x+2\geq -48[/tex]

Divide the compound inequality in two inequalities

[tex]-18> -5x+2[/tex] -----> inequality A

[tex]-5x+2\geq -48[/tex] -----> inequality B

Step 1

Solve inequality A

[tex]-18> -5x+2[/tex]

[tex]-18-2> -5x[/tex]

[tex]-20> -5x[/tex]

Multiply by -1 both sides

[tex]20<5x[/tex]

[tex]4<x[/tex]

Rewrite

[tex]x > 4[/tex]

The solution of the inequality A is the interval ------>(4,∞)

Step 2

Solve the inequality B

[tex]-5x+2\geq -48[/tex]

[tex]-5x\geq -48-2[/tex]

[tex]-5x\geq -50[/tex]

Multiply by -1 both sides

[tex]5x\leq 50[/tex]

[tex]x\leq 10[/tex]

The solution of the inequality B is the interval -----> (-∞,10]

therefore

The solution of the compound inequality is

(4,∞) ∩ (-∞,10]=(4,10]

All real numbers greater than 4 (open circle) an less than or equal to 10 (close circle)

The solution in the attached figure

Answer:

(x-4)(x-6)(x+3) or in more compressed form x³-7x²-6x+72

Step-by-step explanation:

To find the L.C.M, w first factorize each of the expressions.

x²-10x+24

Two numbers that when added give -10 but when multiplied give 24

will be, -4 and -6

Thus the expression becomes:

x²-4x-6x+24

x(x-4)-6(x-4)

=(x-4)(x-6)

Let us factorize the second expression.

x²-x-12

Two numbers when added give -1 and when multiplied give -12

are 3 and -4

Thus the expression becomes: x²-4x+3x-12

x(x-4)+3(x-4)

(x-4)(x+3)

Therefore the LCM between  (x-4)(x-6) and (x-4)(x+3)

will be

(x-4)(x-6)(x+3)

We can multiply the expression as follows.

(x-4)(x-6)

x²-6x-4x+24 = x²-10x+24

(x+3)(x²-10x+24)

=x³-10x²+24x+3x²-30x+72

=x³-7x²+-6x+72

Find the area of the rug by multiplying the length by the width:

7 x 5 = 35 square meters.

Now multiply the area of the rug by the cost:

35 square meters x 285 pesos per square meter = 9,975 total pesos.

The zeros of the function are 2 and -1.

The zeros of a function are the values of x when f(x) is equal to 0.

Given function is,  [tex]f(x)=\frac{(x-2)(x+1)}{x(x-3)(x+5)}[/tex]

Equate given function to zero.

          [tex]\frac{(x-2)(x+1)}{x(x-3)(x+5)} =0\\\\(x-2)(x+1)=0\\\\x=2,x=-1[/tex]

Learn more about the Zeros of function here:

https://brainly.com/question/446160

[tex]\huge{\boxed{y-3=m(x-2)}}[/tex]

Point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where [tex]m[/tex] is the slope and [tex](x_1, y_1)[/tex] is a point on the line.

Substitute the values. [tex]\boxed{y-3=m(x-2)}[/tex]

Note: This is in point-slope form. Let me know if you need a different form. Also, if you have any more problems similar to this, I encourage you to try them on your own, and ask on here if you are having trouble.

Answer:

y-3 = 3(x-2)  point slope form

y = 3x-3  slope intercept form

Step-by-step explanation:

We can use the point slope form of the equation for a line

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is the point

y-3 = 3(x-2)  point slope form

If we want the line in slope intercept form

Distribute

y-3 = 3x-6

Add 3 to each side

y-3+3 = 3x-6+3

y = 3x-3  slope intercept form

Answer:

Point A' will be located 10 units away from point A along ray PA

Step-by-step explanation:

we have

The scale factor is 3

step 1

Find out the distance PA'

we know that

The distance PA' is equal to multiply the distance PA by the scale factor

so

[tex]PA'=PA*3[/tex]

we have

[tex]PA=5\ units[/tex]

substitute the given values

[tex]PA'=(5)*3=15\ units[/tex]

step 2

Find out how many units away from point A along ray PA will A’ be located

we know that

[tex]PA'=PA+AA'[/tex]

we have

[tex]PA=5\ units[/tex]

[tex]PA'=15\ units[/tex]

substitute the given values and solve for AA'

[tex]15=5+AA'[/tex]

[tex]AA'=15-5=10\ units[/tex]

therefore

Point A' will be located 10 units away from point A along ray PA

Answer:

10 units

Step-by-step explanation:

Answer:

y= 125,000 (1.15x)

Step-by-step explanation:

Answer:

A. [tex]y=125,000\cdot (1.15)^x[/tex]

Step-by-step explanation:

We have been given that Jessa bought her home for $125,000 in 2010 Property values have increased 15% every year since she has owned the home.

We can see that increase in value of house is not constant, so the value of house in increasing exponentially.

We know that an exponential function is in form [tex]y=a\cdot b^x[/tex], where,

a = Initial value,

b = For growth b is in form [tex](1+r)[/tex], where r represents growth rate in decimal form.

[tex]r=\frac{15}{100}=0.15[/tex]

[tex]y=125,000\cdot (1+0.15)^x[/tex]

[tex]y=125,000\cdot (1.15)^x[/tex]

Therefore, the equation [tex]y=125,000\cdot (1.15)^x[/tex] represents the price of the home x years after 2010.

Answer:

y - 1 = -2(x + 1).

Step-by-step explanation:

The slope = (-3-1)/(1 - -1)

= -4 / 2

= -2.

In point slope form:

y - y1 = m(x - x1)

Using m = -2 and the point (-1, 1):

y - 1 = -2(x + 1).

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (1, - 3)

m = [tex]\frac{-3-1}{1+1}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2

Using either of the 2 points as a point on the line, then

Using (- 1, 1)

y - 1 = - 2(x - (- 1)), that is

y - 1 = - 2(x + 1) ← in point- slope form

Answer:

Step-by-step explanation:

A function is a process or a relation that associates each element x of a set X, to a single element y of another set Y.

We have:

{(3, -2), (1, 2), (-1, -4), (-1, 2)}

for x = -1 are two values of y = -4 and y = 2. Therefore this realtion is not a function.

Answer: No, it is not a function.

Step-by-step explanation:

The given relation:  {(3, −2), (1, 2), (−1, −4), (−1, 2)}

According to the above definition, the given relation is not a function because -1 corresponds to two different output values i.e. -4 and 2.

Hence, the given relation is not a function.

Answer:

a = 20 cm

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to solve for a

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

a² + 21² = 29²

a² + 441 = 841 ( subtract 441 from both sides )

a² = 400 ( take the square root of both sides )

a = [tex]\sqrt{400}[/tex] = 20

Answer:

So we have [tex]\csc(\theta)=\frac{3 \sqrt{5}}{5} \text{ and } \tan(\theta)=\frac{-\sqrt{5}}{2}[/tex].

Step-by-step explanation:

Ok so we are in quadrant 2, that means sine is positive while cosine is negative.

We are given [tex]\cos(\theta)=\frac{-2}{3}(\frac{\text{adjacent}}{\text{hypotenuse}})[/tex].

So to find the opposite we will just use the Pythagorean Theorem.

[tex]a^2+b^2=c^2[/tex]

[tex](2)^2+b^2=(3)^2[/tex]

[tex]4+b^2=9[/tex]

[tex]b^2=5[/tex]

[tex]b=\sqrt{5}[/tex]  This is the opposite side.

Now to find [tex]\csc(\theta)[/tex] and [tex]\tan(\theta)[/tex].

[tex]\csc(\theta)=\frac{\text{hypotenuse}}{\text{opposite}}=\frac{3}{\sqrt{5}}[/tex].

Some teachers do not like the radical on bottom so we will rationalize the denominator by multiplying the numerator and denominator by sqrt(5).

So [tex]\csc(\theta)=\frac{3}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}=\frac{3 \sqrt{5}}{5}[/tex].

And now [tex]\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}=\frac{\sqrt{5}}{-2}=\frac{-\sqrt{5}}{2}[/tex].

So we have [tex]\csc(\theta)=\frac{3 \sqrt{5}}{5} \text{ and } \tan(\theta)=\frac{-\sqrt{5}}{2}[/tex].

Answer:

[tex]tan\theta{3}=-\frac{\sqrt5}{2}[/tex]

[tex]cosec\theta=\frac{3}{\sqrt5}[/tex]

Step-by-step explanation:

We are given that [tex]\theta[/tex] be an  angle in quadrant II and [tex]cos\theta=-\frac{2}{3}[/tex]

We have to find the exact values of [tex]cosec\theta[/tex] and [tex]tan\theta[/tex].

[tex]sec\theta=\frac{1}{cos\theta}[/tex]

Then substitute the value of cos theta and we get

[tex]sec\theta=\frac{1}{-\frac{2}{3}}[/tex]

[tex]sec\theta=-\frac{3}{2}[/tex]

Now, [tex]1+tan^2\theta=sec^2\theta[/tex]

[tex]tan^2\theta=sec^2\theta-1[/tex]

Substitute the value of sec theta then we get

[tex]tan^2\theta= (-\frac{3}{2})^2-1[/tex]

[tex]tan^2\theta=\frac{9}{4}-1=\frac{9-4}{4}=\frac{5}{4}[/tex]

[tex]tan\theta=\sqrt{\frac{5}{4}}=-\frac{\sqrt5}{2}[/tex]

Because[tex] tan\theta [/tex] in quadrant II is negative.

[tex]sin^2\theta=1-cos^2\theta[/tex]

[tex]sin^2\theta=1-(\farc{-2}{3})^2[/tex]

[tex]sin^2\theta=1-\frac{4}{9}[/tex]

[tex]sin^2\theta=\frac{9-4}{9}=\frac{5}{9}[/tex]

[tex]sin\theta=\sqrt{\frac{5}{9}}[/tex]

[tex]sin\theta=\frac{\sqrt5}{3}[/tex]

Because in quadrant II [tex]sin\theta[/tex] is positive.

[tex]cosec\theta=\frac{1}{sin\theta}=\frac{1}{\frac{\sqrt5}{3}}[/tex]

[tex]cosec\theta=\frac{3}{\sqrt5}[/tex]

[tex]cosec\theta[/tex] is positive in II quadrant.

C

By the law of sines, [tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex] where A, B, C are the angles and a, b, c are the lengths of the sides opposite their respective angles. In this case, [tex]110^{\circ}[/tex] is opposite 4.6 and A is opposite 3.2, so [tex]\frac{sinA}{3.2}=\frac{sin(110^{\circ})}{4.6}[/tex], giving the answer.

Answer:

it’s c

Step-by-step explanation:

Answer:

A should be the answer

Step-by-step explanation:

ok so first find area of a circle the area of this circle

pi r sqared

the area of the circle is 3.14

since the raduis is diamter ÷ 2

the area of the small rectangle would be 2a sqared

so if i did it right the answer should be A

I could be wrong tho

hope this helped

Answer:

[tex]\large\boxed{-2(10r+4)+10(7r+2)=50r+12}[/tex]

Step-by-step explanation:

[tex]-2(10r+4)+10(7r+2)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=(-2)(10r)+(-2)(4)+(10)(7r)+(10)(2)\\\\=-20r-8+70r+20\qquad\text{combine like terms}\\\\=(-20r+70r)+(-8+20)\\\\=50r+12[/tex]

Answer:

Part A)

x=-3i

x=3i

Part B)

(x+3i)(x-3i)

Step-by-step explanation:

Given:

Part A)

x^2+9=0

x^2=-9

x= √-9

x=√-1 *√9

x=± i *3

x=±3i

Part B)

x^2+9=0

x^2 - (-9)=0

x2-(3i)^2=0

(x-3i)(x+3i)=0 !

Answer:

Two line segments are congruent if they have the same length. Two angles are congruent if they have the same measure.

Two angles are said to be congruent if they are equal. For example, if two triangles each have an angle of 42 degrees, then those angles are congruent.

Answer:

−5 + 5 = 0

-6+6=0

14+-14=0

70+-70=0

100+-100=0

Step-by-step explanation:

hope this helps

Answer:

The second layer of skin is the dermis, located under the epidermis. It contains connective tissue, nerve endings, and hair follicles.

The dermis layer of the skin contains hair follicles.

The layer of the skin that contains hair follicles is the dermis.

The dermis is the layer of skin directly under the epidermis, and it is made of tough connective tissue. It contains hair follicles, sweat glands, oil glands, and blood vessels.

For example, when you pluck a hair from your skin, you are pulling it out from the dermis.

Answer:

The correct answer is option a.  400

Step-by-step explanation:

Points to remember

Area of square = a²

Where 'a' is the side length of square

To find the area of square

It is given that, the side length of square is 20 inches.

Here a = 20 inches

Area = a²  

 = 20²

 = 400

Therefore the correct answer is option a.  400

Answer:

[tex]5+\sqrt{x+4}[/tex]

Step-by-step explanation:

The conjugate of the radical expression [tex]a+\sqrt{b}[/tex] is  [tex]a-\sqrt{b}[/tex]

The conjugate of the radical expression [tex]a-\sqrt{b}[/tex] is  [tex]a+\sqrt{b}[/tex]

The sign of the radical becomes its additive inverse in the conjugate,

The given expression is

[tex]5-\sqrt{x+4}[/tex] where [tex]x>-4[/tex] (domain)

The conjugate of this expression is [tex]5+\sqrt{x+4}[/tex]

Answer:

The conjugate is 5+√x+4

Step-by-step explanation:

To find the conjugate of of expression 5-√x+4

when x>-4

First let us understand that in simple terms terms the conjugate of a radical simply involves the change in sign of the radical

in the problem the conjugate of

5-√x+4 is 5+√x+4

it is that simple Just alternate the sign and you are done!!!

The answer is:

A.

[tex]h(x)=9x-13[/tex]

To solve the problem, we need to perform the shown operation.

We have the functions:

[tex]f(x)=2x-1\\g(x)=7x-12[/tex]

So, performing the following operation, we have:

[tex]f(x)+g(x)=h(x)[/tex]

[tex]h(x)=f(x)+g(x)=(2x-1)+(7x-12)=7x+2x-1-12=9x-13[/tex]

[tex]h(x)=9x-13[/tex]

Hence, we have that the correct option is:

A. [tex]h(x)=9x-13[/tex]

Have a nice day!

Answer: A

Step-by-step explanation:

Answer:

c. 19.73

Step-by-step explanation:

The Cosine rule shows states that:

a²=b²+c²-2bcCos A, where a, b and c are the sides of the triangle and A is the angle at vertex A.

A=108°

b=9

c=15

Substituting with the values above gives:

a²=9²+15²-(2×9×15 Cos 108)

a²=389.4346

a=19.73

Answer:

150 bags

Step-by-step explanation:

Given the total area:

The area will be:

=75*50

= 3750 square feet

As it is given that one bag covers 25 square feet. To find the total number of bags we have to find how many 25s will be in 3750 square feet.

So,

Total number of bags = 3750 / 25

= 150 bags

Hence, total number of bags that will be used are 150 ..

Answer:

Statement 2 (The ages of the Stars are the most dispersed from the team’s mean).

Step-by-step explanation:

Standard deviation is one way to measure the average of the data by determining the spread of the data. It actually explains how much the observation points are further away from the mean of the data. Higher the standard deviation, higher the spread of the data and higher is the uncertainty. This means that the team with the highest standard deviation will have the most dispersion. In this case, the standard deviation of 4.1 is the largest number, therefore, the statement "The ages of the Stars are the most dispersed from the team’s mean." is true i.e. the option 2!!!

Answer:

B.The ages of the Stars are the most dispersed from the team’s mean

Step-by-step explanation:

Answer: The temperature change is 19 degrees Fahrenheit.

Step-by-step explanation: Put a circle at -9 and 10. You can count the numbers in between them to get 19. Or you can add the two numbers. 9 + 10 = 19.

Answer:

The mode is 4 and the median is 8

Step-by-step explanation:

The mode is the number the occurs the most in the set, and as you can see 4 appears twice. The median is the number that lies in the middle of the set when put together from least to greatest. When you write it out it results in 2,4,4,8,9,10,12. As you can see the number 8 lies right in the middle, with three numbers on it's left and three numbers on it's right. Hope this helps :)

Final answer:

median: 8

mode: 4

Explanation:

Calculate the median and mode for a data set, including step-by-step instructions.

Median: To find the median, arrange the data set in numerical order first. As the data set has seven values, the median will be the fourth value, which is 8. Median represents the middle most value of the data

Mode: The mode is the value that appears most frequently in the data set. In this case, the mode is 4 as it occurs twice. Mode represents the maximum frequency.

Answer:

(k ∘ p)(x)=2x^2-12x+13

Step-by-step explanation:

(k ∘ p)(x)=k(p(x))

(k ∘ p)(x)=k(x-3)

(k ∘ p)(x)=2(x-3)^2-5

(k ∘ p)(x)=2(x-3)(x-3)-5

Use foil on (x-3)(x-3) or use this as a formula:

(x+a)^2=x^2+2ax+a^2.

(k ∘ p)(x)=k(p(x))

(k ∘ p)(x)=k(x-3)

(k ∘ p)(x)=2(x-3)^2-5

(k ∘ p)(x)=2(x-3)(x-3)-5

(k ∘ p)(x)=2(x^2-6x+9)-5

Distribute: multiply terms inside ( ) by 2:

(k ∘ p)(x)=2x^2-12x+18-5

(k ∘ p)(x)=2x^2-12x+13

The composite function is [tex]k(p(x))=2x^{2} -12x+13[/tex]

Option b is correct.

Given function are,

               [tex]k(x)=2x^{2} -5,p(x)=(x-3)[/tex]

We have to find composite function [tex]k(p(x))[/tex].

                  [tex]k(p(x))=k(x-3)\\\\k(p(x))=2(x-3)^{2}-5\\ \\k(p(x))=2(x^{2} +9-6x)-5\\\\k(p(x))=2x^{2} +18-12x-5\\\\k(p(x))=2x^{2} -12x+13[/tex]

Thus, the composite function is [tex]k(p(x))=2x^{2} -12x+13[/tex]

Learn more about the composite function here:

https://brainly.com/question/10687170

Answer:

116500

Step-by-step explanation:

We are looking for the number of twin births in 2000.

Let the number of twin births in 2000 be x.

The number of twin births in 2000 is 100% of the number of births in 2000 since 100% of something is the entire thing.

The number of twin births went up 15% from 2000 to 2014, so in 2014, the number of twin births was 100% of the number of twin births plus another 15% of the number of twin births.

100% + 15% = 115%

The number of twin births in 2014 was 115% of x.

The number of twin births in 2014 was 133975.

115% of x = 133975

115% * x = 133975

1.15x = 133975

x = 133975/1.15

x = 116500

The number of twin births in 2000 was 116500.

An increase by 15% means 15 added to per cent (per = each; cent=100).

If the population was 100 in the year 2000 then it would be 115 in the year 2014. (adding 15 to 100)

The population was 116500 in the year 2000 and it increased to 133975 in the year 2014.

Let the population be x in the year 2000.

Using ratio and proportion

Year 2000 : Year 2014

100              :       115

x                  :    133975

Applying cross product rule

x × 115= 100× 133975

x= 100× 133975/115

x= 116500

The population was 116500 in the year 2000 and it increased to 133975 in the year 2014.

https://brainly.com/question/14039286