How will the solution of the system change if the inequality sign on both inequalities

Answer:

The sum of the measures of two complementary angles is 90 degrees

Step-by-step explanation:

we know that

If two angles are complementary, then their sum is equal to 90 degrees

In this problem we have that

m∠ABD and m∠DBC are complementary

so

m∠ABD + m∠DBC=90° -----> by complementary angles

and

(m∠ABD + m∠DBC)+m∠EBC=180° -----> by a linear pair

Find the measure of angle EBC

substitute the given values

(90°)+m∠EBC=180°

∠EBC=180°-90°=90°

Answer:

Statements B and A

Step-by-step explanation:

GIven are some statements and we have to identify the one which justifies the measure of angle EBC as 90 degrees.

We have to use two statements here for the complete proof

B) SInce given that  angles ABD and DBC are complementary we have sum of these angles = angle ABC = 90 degrees

A)since linear pair form supplementary angles and since one pair ABC =90 other pair EBC has to be 90 degrees.

Answer:

annual percentage yield

Step-by-step explanation:

APY means annual percentage yield

Answer:

Second option: False.

Step-by-step explanation:

Given the inequality [tex]- 4x > 0[/tex], you need to solve for the variable "x".

To solve for the variable "x" you can divide both sides of the inequality by -4 (Notice that the direction of the symbol of the inequality changes), then:

[tex]- 4x > 0\\\\\frac{- 4x}{-4} > \frac{0}{-4}\\\\x<0[/tex]

Therefore, the solution set in interval notation is:

[tex](-\infty,0)[/tex]

Then the answer is: False.

Answer:

[tex]f(x)=(x-4)^{2}[/tex]

Step-by-step explanation:

we have that

The axis of symmetry shown in the graph is x=4

we know that

The axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex

so

Verify each case

case a) we have

[tex]f(x)=(x+4)^{2}[/tex]

The vertex is the point (-4,0)

therefore

Cannot be the function

case b) we have

[tex]f(x)=x^{2}+4[/tex]

The vertex is the point (0,4)

The axis of symmetry is x=0

therefore

Cannot be the function

case c) we have

[tex]f(x)=(x-4)^{2}[/tex]

The vertex is the point (4,0)

The axis of symmetry is x=4

therefore

Could be the function

case d) we have

[tex]f(x)=x^{2}-4[/tex]

The vertex is the point (0,-4)

The axis of symmetry is x=0

therefore

Cannot be the function

Answer:

Kilograms

Step-by-step explanation:

Answer:

All real numbers

Step-by-step explanation:

f(x) is a polynomial and is well defined for all real values of x

Domain is x ∈ R

The domain of the function[tex]$$f(x)=x^{2}+3 x+5$$[/tex] is (D). All real numbers

It is provided that,

[tex]$$f(x)=x^{2}+3 x+5$$[/tex]

This exists as the equation of a vertical parabola opens upward.

The vertex exists at a minimum

utilizing a graphing tool

The vertex is the point (-1.5,2.75)

The range is the interval -------> [2.75.∞)

[tex]y \geq 2.75[/tex] ------->All real numbers greater than or equal to 2.75

The domain is the interval -------> (-∞,∞) -----> All real numbers

Hence, The domain of the function[tex]$$f(x)=x^{2}+3 x+5$$[/tex] is (D). All real numbers.

To learn more about the Domain of  function refer to:

https://brainly.com/question/13856645

#SPJ2

Answer:

5.8

Step-by-step explanation:

To get the mean, add up all the numbers

9+4+8+3+5 = 29

Then divide by how many numbers there are (5)

29/5 =5.8

The mean is 5.8

Answer: y=2

Step-by-step explanation:

Distribute the numbers -2 and 3...

6y-2y-2=3y-6+6

The -6 and 6 cancel each other out...

6y-2y-2=3y

Combine like terms....

4y-2=3y

Move 4y over....

-2=-y

Multiply both sides by -1.....

2=y

That’s your solution! Hope this helps!

Answer:

x< -1.8

Step-by-step explanation:

-12x+13>35

We leave the variable alone passing the 13 with opposite sign to the other side and subtracting it from 35.

-12x>22

We divide both by the variable, -12x, and it gives x > -1.8. Since the sign of x changed, we flip the sign and the final result is x < -1.8

ANSWER

[tex]x \: < \: - 1\frac{ 5}{ 6} [/tex]

EXPLANATION

The given inequality is

[tex] - 12x + 13 \: > \: 35[/tex]

Add -13 to both sides to obtain;

[tex]- 12x + 13 - 13 \: > \: 35 - 13[/tex]

Simplify to obtain:

[tex]- 12x + 0 \: > \:22[/tex]

[tex]- 12x \: > \: 22[/tex]

Divide both sides by -12 and reverse the inequality sign.

[tex] \frac{ - 12x}{ - 12} \: < \: \frac{ 22}{ - 12} [/tex]

[tex]x \: < \: \frac{ 22}{ - 12} [/tex]

This simplifies to

[tex]x \: < \: - \frac{ 11}{ 6} [/tex]

We rewrite as mixed number

[tex]x \: < \: - 1\frac{ 5}{ 6} [/tex]

Answer:

The probability is [tex]0.7727[/tex]   or  [tex]77.27\%[/tex]

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.  

The size of the sample space is the total number of possible outcomes  

The event space is the number of outcomes in the event you are interested in.  

so  

Let

x------> size of the event space

y-----> size of the sample space  

so

[tex]P=\frac{x}{y}[/tex]

In this problem we have

[tex]x=10+7=17[/tex]

[tex]y=10+7+5=22[/tex]

substitute

[tex]P=\frac{17}{22}=0.7727[/tex]

Convert to percentage

[tex]0.7727*100=77.27\%[/tex]

Answer:

The correct answer is B. b=3a + 2

Step-by-step explanation:

Plug in the values from column A into each equation and find which one works. In this case, the only option that works is B.

x= y/7 + 2/7

I think thats right

All of the months have 28 days. Although some may have more then 28 days they always have AT LEAST 28 days

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Option C is correct.

Step-by-step explanation:

A direct variation function is

y/x = k

i.e. we can say that the ratio of y and x is equal to a constant value k.

We will check for each Option given.

Option A

7/2 = 7/2

8/3 = 8/3

9/4 = 9/4

10/5 = 2

11/6 = 11/6

Option D is incorrect as y/x ≠ k as ratio of y/x for each value of table doesn't equal to constant

Option B

-3/2 = -3/2

-5/4 = -5/4

-6/6 = -1

-7/8 = -7/8

-8/10 = -4/5

Option B is incorrect as y/x ≠ k as ratio of y/x for each value of table doesn't equal to constant

Option C

10/-5 = -2

8/-4 = -2

6/-3 = -2

4/-2 = -2

2/-1 = -2

Option C is correct as y/x = k as ratio of y/x for each value in table c is equal to constant value -2

Option D

-3/-2 = 3/2

-3/1 = -3

-3/0 = 0

-3/1 = -3

-3/2 = -3/2

Option D is incorrect as y/x ≠ k as ratio of y/x for each value of table doesn't equal to constant .

SO, Option C is correct.

Answer: OPTION C

Step-by-step explanation:

The function of direct variation has this form:

[tex]y=kx[/tex]

Where k is the constant of variation.

Let's  check if there is a constant of variation on the Options "a" and "b":

On Option A:

 [tex]\frac{7}{2}=3.5\\\\\frac{8}{2}=4[/tex]

On Option B:

[tex]\frac{-3}{2}=-1.5\\\\\frac{-5}{4}=-1.25[/tex]

There is no constant of variation, then these tables do no represent a direct variation.

On the table shown in Option "d" you can observe that "y" does not change when "x" changes. Then it does not represent a direct variation.

Since on the table shown in Option "c":

[tex]k=-2[/tex]

 This table represents a direct variation.

Answer:

The length = 56 feet and the width = 17 feet.

Step-by-step explanation:

We can set up 2 equations to solve this. Let the length of the rug be x, then

x = 3w + 5    where w = the width.   ( looks like you got the width and the length mixed up. The length is the longest side)

The perimeter = 2x + 2w = 146 so we have the 2 equations:

x = 3w + 5

2x + 2w = 146

Now we substitute for x in the second equation:

2(3w + 5) + 2w = 146

6w + 10 + 2w = 146

8w = 136

w = 17 feet,

and x = 3(17) + 5 =  56 feet.

Answer:

Length is 17 feet and Width is 56 feet.

Step-by-step explanation:

P=2L+2W

146=2L+2(3L+5)

146=2L+6L+10

146=8L+10L

146-10=8L+10-10

136=8L

136\8=8\8

17=L

W=3L+5

  =3(17)+5

  =56

Answer:

7x - 14

Step-by-step explanation:

3(x + 2) + 4(x - 5)

3x + 6 + 4x - 20

7x - 14

For this case we must simplify the following expression:

[tex]3 (x + 2) +4 (x-5)[/tex]

Applying distributive property to the terms within the parenthesis we have:

[tex]3x + 6 + 4x-20 =[/tex]

Adding similar terms:

[tex]3x + 4x + 6-20 =[/tex]

Finally we have that the expression is reduced to:

[tex]7x-14[/tex]

Answer:

[tex]7x-14[/tex]

Answer:

32

Step-by-step explanation:

Possible outcomes in a fair sided die 1,2,3,4,5,6 = 6 possible outcomes

Odd numbers = 1,3,5 = 3 odd numbers

Probability of rolling an odd number = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

Total number of rolls = 64

expected number of odd number rolls in 64 roll,

= [tex]\frac{1}{2}[/tex] x 64 = 32

Answer:

see explanation

Step-by-step explanation:

The exponential function is in the form

y = a [tex](b)^{x}[/tex]

Use points on the graph to find a and b

Using (0, 3), then

3 = a [tex](b)^{0}[/tex] ⇒ a = 3

Using (1, 6), then

6 = 3 [tex](b)^{1}[/tex] ⇒ b = 6 ÷ 3 = 2

The equation is y = 3 [tex](2)^{x}[/tex]

Answer:

y = [tex]3*2^{x}[/tex]

Step-by-step explanation:

The general form for an exponential function is :

y = [tex]ab^{x}[/tex]

We need to find out what a and b are using the values given in the graph.

we can see that (x=0, y = 3) and (x=1, y = 6) are points on the curve. Substitute these into the general equation

for (x=0, y = 3),

3 = [tex]ab^{0}[/tex]

3 = a (1)  or a = 3

for (x=1, y = 6),

6 = [tex]ab^{1}[/tex]

6 = ab (substitute a=3 from previous calculation)

6 = 3b

b = 2

Hence the equation is:

y = [tex]3*2^{x}[/tex]

Edit reason: typo in the final answer

ANSWER

[tex]7 {m}^{2} [/tex]

EXPLANATION

If the area of the circle is 84π m² , then the area of a 30° sector is just a proportion of the full circle.

The area of the 30° sector is

[tex] \frac{30}{360} \times 84\pi \: {m}^{2} [/tex]

[tex] = \frac{1}{12} \times 84 {m}^{2} [/tex]

[tex] = 7 {m}^{2} [/tex]

Hence the area of the 30° sector of this circle is

[tex]7 {m}^{2} [/tex]

The polynomial -2x³ - 4x² - 6x is factored by first factoring out the common term -2x, resulting in -2x(x² + 2x + 3). The quadratic x² + 2x + 3 cannot be further factored over the real numbers, giving the final factored form of -2x(x² + 2x + 3).

To factor the polynomial -2x³ - 4x² - 6x, we first look for any common factors in each term of the polynomial. In this case, we can see that each term includes a factor of -2x. Factoring this out, we get:

-2x(x² + 2x + 3)

However, the quadratic x² + 2x + 3 cannot be factored further over the real numbers because it does not have real roots (its discriminant 22 - 4(1)(3) = 4 - 12 = -8 is negative). Therefore, the fully factored form of the polynomial over the real numbers is:

-2x(x² + 2x + 3)

Answer:

x=3 and y=2

Step-by-step explanation:

The pythagorean triples are generated by two integrers x and y that can be found by solving the following system of equations:

[tex]\left \{ {{x^{2}-y^{2}=5}\atop {2xy=12}} \atop {x^{2}+y^{2}=13}}\right.[/tex]

Solve the system of equations, and we get that the solution is x=3 and y=2.

Therefore, the combination of integrers that ca be used to generate the pythagorea triple are: x=3 and y=2

Answer:

[tex]x=3[/tex] and [tex]y=2[/tex]

Step-by-step explanation:

The Pythagorean triples can be generated by two values x, y, and a given system of equations:

[tex]x^{2}-y^{2}=5\\2xy=12\\x^{2}+y^{2}=13[/tex]

You can see that each coordinate of the triple is included in each equation.

Remember that Pythagorean triples refers to the values of each side of a right triangle, where is used the Pythagorean Theorem. But, at a higher level, to construct this triples we use the system of equations, with two integers x and y., like this case.

Now we solve the system, the best first step is to just sum the first and third equations, because they have like terms:

[tex]2x^{2}=18\\x^{2}=\frac{18}{2}=9\\x=3[/tex]

Now, we just replace it in the second equation:

[tex]2xy=12\\y=\frac{12}{2x}=\frac{6}{3}=2[/tex]

Therefore the integers that generate the Pythagorean triple [tex](5,12,13)[/tex] are [tex]x=3[/tex] and [tex]y=2[/tex]

ANSWER

[tex][1, \infty ][/tex]

EXPLANATION

The given functions are:

[tex]a(x) = 3x + 1[/tex]

[tex]b(x) = \sqrt{x - 4} [/tex]

We want to find the domain of the composite function;

[tex](b \circ \: a)(x) = b(a(x))[/tex]

[tex](b \circ \: a)(x) = b(3x + 1)[/tex]

[tex](b \circ \: a)(x) = \sqrt{3x + 1 - 4} [/tex]

This simplifies to,

[tex](b \circ \: a)(x) = \sqrt{3x - 3} [/tex]

This function is defined for

[tex]3x - 3 \geqslant 0[/tex]

[tex]3x \geqslant 3[/tex]

[tex]x \geqslant 1[/tex]

This can be rewritten as,

[tex][1, \infty ][/tex]

[tex]\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{9-(-3)}{5-1}\implies \cfrac{9+3}{4}\implies \cfrac{12}{4}\implies 3[/tex]

We have

[tex] \mu = 500[/tex]

[tex] \sigma = 100 [/tex]

425 corresponds to a z of

[tex]z_1 = \dfrac{425 - 500}{100} = -\dfrac 3 4[/tex]

575 corresponds to

[tex]z_2 = \dfrac{575 - 500}{100} = \dfrac 3 4[/tex]

So we want the area of the standard Gaussian between -3/4 and 3/4.  

We look up z in the standard normal table, the one that starts with 0 at z=0 and increases.  That's the integral from 0 to z of the standard Gaussian.

For z=0.75 we get p=0.2734. So the probability, which is the integral from -3/4 to 3/4, is double that, 0.5468.

Answer: 55%

Answer:

10.2 cm²

Step-by-step explanation:

The area (A) of a regular hexagon is

A = [tex]\frac{1}{2}[/tex] × perimeter × apothem

Perimeter = 6 × 2 = 12 cm ( hexagon has 6 sides ), hence

A = 0.5 × 12 × 1.7 = 6 × 1.7 = 10.2 cm²

Answer:

10.2cm^2

Step-by-step explanation:

Hello There!

The answer is that the Y intercept is 4.

The y intercept is where the graph crosses the y axis. It goes vertical

Answer: the y intercept is 4.

Step-by-step explanation:

In the graph, if the savings account would’ve started with $8, the y intercept would be 8.

We don’t know what the graph is talking about so it’s not the last option.

The line crossed the x intercept at 8 so it’s not B.