Solve the following inequalities and represent the solution on the number line.
d) 5x ≥ 15
e) 3(2x + 1) ≤ 15

Answer:

17.1

Step-by-step explanation:

Given we have one side and one degree, we can use the trigonometric function "tangent" to solve this right triangle.

Remember that tangent is opposite side over adjacent side, so lets set up the equation:

[tex]tan(35)=\frac{12}{x}[/tex]

Now solve:

[tex]x(tan(35))=12\\x=\frac{12}{tan(35)}[/tex]

As a result, x is equal to approximately 17.1

Any questions feel free to ask :)

Answer:

fuz what hhde you ha thewebsite and it

Answer:

4:1

Step-by-step explanation

this should be the answer from how  u gave the question, also can i get brainliest ;)

Answer:

a) The mass of a box of bolts is greater.

b) 3/20 kg

Step-by-step explanation:

a) Firstly, you have to make the denominators of the two fractions the same (by finding the LCM of the denominators).

The LCM of 4 and 5 is 20.

Converting 3/4 into denominator 20:

[tex]\frac{3 * 5}{4 * 5}[/tex]

= 15/20

Converting 3/5 into denominator 20:

[tex]\frac{3 * 4}{5 * 4}[/tex]

= 12/20

Now comparing the numerators:

15 > 12

Hence,

3/4 > 3/5

b) Difference of the boxes can be done by subtracting the numbers with the same denominator:

15/20 - 12/20

= 3/20 kg

Hope this helps and feel free to give me brainliest! :)

Answer:

[tex]-\frac{1}{2} \vec {c}[/tex]

Step-by-step explanation:

Look at the component form of each vector.

Note that vector c is <4,4> and vector d is <-2,-2>

If one imagined the line that contained each vector, the line for both would have a slope of 1, because [tex]\frac{4}{4}=1=\frac{-2}{-2}[/tex]

Since they have the same slope they are parallel, but since they are in opposite directions, we often call them "anti-parallel" (simply meaning parallel, but in opposite directions).

If two vectors are parallel, one vector can be multiplied by a scalar to result in the other vector.  This means that there is some number "k", such that [tex]k \vec{c} = \vec {d}[/tex], or equivalently, [tex]kc_x=d_x[/tex] and [tex]kc_y=d_y[/tex].

If [tex]kc_x=d_x[/tex] and [tex]kc_y=d_y[/tex], we just need to substitute known values and solve for k:

[tex]kc_x=d_x\\k(4)=(-2)\\k=\dfrac{-2}{4}\\k=-\frac{1}{2}[/tex]

Double checking that k works for the y-coordinates as well:

[tex]kc_y=d_y[/tex]

[tex](-\frac{1}{2}) (4)[/tex]    ?    [tex](-2)[/tex]

[tex]-2=-2 \text{ } \checkmark[/tex]

So, [tex]-\frac{1}{2} \vec {c} = \vec {d}[/tex]

Answer:

Step-by-step explanation:

Look at the component form of each vector.

Note that vector c is <4,4> and vector d is <-2,-2>

If one imagined the line that contained each vector, the line for both would have a slope of 1, because

Since they have the same slope they are parallel, but since they are in opposite directions, we often call them "anti-parallel" (simply meaning parallel, but in opposite directions).

If two vectors are parallel, one vector can be multiplied by a scalar to result in the other vector.  This means that there is some number "k", such that , or equivalently,  and .

If  and , we just need to substitute known values and solve for k:

Double checking that k works for the y-coordinates as well:

   ?    

So,

Answer:

x = -6

Step-by-step explanation:

5x² + 60x + 180 = 0

5 x 180 = 900

you need 2 numbers that multiplies into 900 and adds into 60. these numbers are 30 and 30. now we can rewrite it

5x² + 30x + 30x + 180 = 0.

split it in half and factorise

5x(x + 6) + 30(x + 6) = 0

this means the brackets are:

(5x + 30)(x + 6) = 0

5x + 30 = 0

5x = -30

x = -6

x + 6 = 0

x = -6

therefore, x = -6.

Answer:

fair share

Step-by-step explanation:

all are equal.

In the given image, the length of JI is 6

From the question, we are to solve for JI

From the given image, we can write that

JI + IH = JH

Then,

2x + 28 + 5 = x + 22

Solving for x

2x + 28 + 5 = x + 22

First, collect like terms

2x - x = 22 - 28 - 5

Simplifying

x = -11

But,

JI = 2x + 28

∴ JI = 2(-11) + 28

JI = -22 + 28

JI = 6

Hence, the length of JI is 6

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Answer:

81 x 10^6

Step-by-step explanation:

x0000000

11111111x

22222222

33333333

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

88888888

99999999

---------------------

The first digit and 8th digit column has only 9 numbers and the rest 6 column have 10 possible numbers

9 x 9 x 10^6 = 81 x 10^6

The composite function (boa)(x) is equivalent to √3x-3

Given the following functions

a(x) = 3x +1

b(x) = √x - 4

To determine the composite function (boa)(x)

b(a(x) = b(3x +1)

Substitute 3x + 1 into b(x) to have:

(boa)(x)= √(3x + 1) - 4

(boa)(x) = √3x-3

Hence the composite function (boa)(x) is equivalent to √3x-3

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Answer: No solution

Step-by-step explanation:

The red line is y=3x+7 and the blue line is y=3x+2

The lines do not intersect at any time. Therefore, this set of equations has no solution. I hope this helps! Pls mark brainliest!! :)

Answer:

24-5=19

Step-by-step explanation:

1. (2b)= 2(12)

2. a=5

3. 24-5

4.9

The number of hours, h it will take 5 people to build the swing set is; 2.4 hours

From the task content, it follows that it took 6 hours for 2 people to build the swing set, hence, it follows that it'd take 12 hours for 1 person to build the swing.

However, when the work is divided between 5 People, the time taken is therefore; 12/5 = 2.4hours.

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Answer:

C

Step-by-step explanation:

given the factors are (x - 7) and (x + 3)

equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x + 3 = 0 ⇒ x = - 3

Answer:

well by using the formulae a²+b²=c² with "a" being the opposite "b" being the adjacent and "c" being hypotenuse

Answer:

BY LEARNING  Pythagorean Theorem Formula Proof using Similar Triangles

Step-by-step explanation:

In a right-angled triangle, the Pythagoras Theorem Formula is expressed as:

c2 = a2 + b2

Where,

'c' = hypotenuse of the right triangle

'a' and 'b' are the other two legs.

[tex] \sf \blue{True✅}[/tex]

Given,

[tex]f(x) = - x + 8 \: and \: f( - 4)[/tex]

Solution:

[tex] f( x) = - ( - 4) + 8 \\ \\ = 4 + 8 \\ \\ = 12[/tex]

Answer:

Step-by-step explanation:

The number of  ways that he can make the fruit salad if it must contain watermelon is 35.

Selection of the one object from the given samples with replacement or without replacement is called as the permutation. The selection of the items from the sample as they are different with each other.

The salad contains water melon, now we have to select 4 more fruits out of 7.

Using combination

[tex]^{n{C}_r[/tex] = n! / r! (n-r)!

[tex]^{7}C_4[/tex] = 7!/ 4! (7-4)!

      = 7*6*5*4! / 4! * 3*2

      = 35

Hence,  number of ways that he can make the fruit salad if it must contain watermelon is 35.

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Answer: 35 on edge got it right

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

[tex]a+b=-5[/tex]

[tex]-(a+b)=-a-b=5[/tex]

[tex]\frac{|-5| + 5}{|5|}[/tex]

[tex]\frac{5+5}{5}[/tex]

[tex]2[/tex]

Answer:

2

Step-by-step explanation:

Given:

To find -a - b  

Factor out the common term -1:

⇒ -a - b = -(a + b)

Substitute a + b = -5:

⇒ -a - b = -(-5)

Apply rule -(-x) = x:

⇒ -a - b = 5

Therefore:

[tex]\begin{aligned}\implies \sf \dfrac{|a+b|+5}{|-a-b|} & = \sf \dfrac{|-5|+5}{|5|}\\\\& = \sf \dfrac{5+5}{5}\\\\& = \sf \dfrac{10}{5}\\\\& = \sf 2\end{aligned}[/tex]

Note:  |-x| = x

Answer:

44 pears and 52 apples

Step-by-step explanation:

pears are 8 more than apple so 52-8 = 44

Number of apples and pears in a box is equals to [tex]30[/tex] and [tex]22[/tex] respectively.

" Number is defined as the count of any given quantity as per given condition."

According to the question,

Given,

Total number of apples [tex]= 52[/tex]

[tex]'x'[/tex] represents the number of pears

[tex]'x+ 8'[/tex] represents the number of apples

As per the given condition required equation we get,

[tex]x + x + 8 = 52\\\\\implies 2x = 52-8\\\\\implies x = \frac{44}{2} \\\\\implies x = 22[/tex]

number of pears [tex]= 22[/tex]

number of apples [tex]= 22+8[/tex]

                              [tex]=30[/tex]

Hence, number of apples and pears in a box is equals to [tex]30[/tex] and [tex]22[/tex] respectively.

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Answer:

y = - 8

Step-by-step explanation:

y = 3 is a horizontal line that includes all of the x coordinates

   just need to find parallel

           y = - 8

Answer:

a)<BAC = EDC,<DEC =ABC,ACB=DFE
b)7

Step-by-step explanation:

According to the definition, two triangles are similar if their corresponding angles are congruent and corresponding sides are proportional. Hence, we can find the dimensions of one triangle with the help of another triangle. If ABC and DEF are two similar triangles, then by the help of below-given formulas, we can find the relevant angles and side lengths.

∠A = ∠D, ∠B = ∠E and ∠C = ∠F

AB/DE = BC/EF= AC/DF

Answer:

2/7

Step-by-step explanation:

To find the fraction that are cherry, take the number that are cherry and put that over the total number of pieces

2 cherry

----------------

7 total

The fraction that are cherry are 2/7

As per the attached picture Option fourth "the probability of all dependent events can be calculated using the OR formula P(A or B) = P(A) + P(B) - P(A and B)" is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

As we know the dependent events are dependent on what happened before.

Let A and B be dependent events:

Event B will be dependent on the Event A

P(A or B) = P(A) + P(B) - P(A and B)

Thus, option fourth "the probability of all dependent events can be calculated using the OR formula P(A or B) = P(A) + P(B) - P(A and B)" is correct.

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The correct answer is option B which is mixture B will have the highest ratio of blue paint.

In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.

The given ratios are:-

Mixture A = [tex]\dfrac{5}{12} = 0.41[/tex]

Mixture B = [tex]\dfrac{6}{6}= 1[/tex]

Mixture C = [tex]\dfrac{4}{12}= 0.33[/tex]

Mixture B = [tex]\dfrac{5}{6}=0.83[/tex]

Here the ratio of mixture B is the highest among all the options available.

Therefore the correct answer is option B which is mixture B will have the highest ratio of blue paint.

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Step-by-step explanation:

Step 1: Setting Up the Factors

Our roots are 3, 2, and -4 so

our factors are

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

Step 2: Initial Test to see if the result equal 30

Let a be a constant, such we have

[tex]a(x - 3)(x - 2)(x + 4) = 30[/tex]

Plug in. 1 for x.

[tex]a(1 - 3)(1 - 2)(1 + 4) = 30[/tex]

[tex]a( - 2)( - 1)(5) = 30[/tex]

[tex]a(10) = 30[/tex]

[tex]a = 3[/tex]

So our equation is

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

Or if you want it simplifed

[tex]3( {x}^{2} - 5x + 6)(x + 4) = 3( {x}^{3} + - {x}^{2} - 14x + 24) = 3 {x}^{3} - 3 {x}^{2} - 42x + 72[/tex]

Answer:

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

Step-by-step explanation:

General form of a cubic polynomial function with 3 roots:

[tex]f(x)=a(x-b)(x-c)(x-d)[/tex]

where:

Given roots:

Substitute the given roots into the general form of the function:

[tex]\implies f(x)=a(x-3)(x-2)(x-(-4))[/tex]

[tex]\implies f(x)=a(x-3)(x-2)(x+4)[/tex]

To find the value of a, substitute the given point (1, 30) into the equation:

[tex]\begin{aligned} f(1) & = 30\\\implies a(1-3)(1-2)(1+4) & =30\\a(-2)(-1)(5) & = 30 \\10a & = 30\\\implies a & = 3 \end{aligned}[/tex]

Therefore, the equation of the cubic polynomial function is:

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

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Answer:

x = 4    y =  1

Step-by-step explanation:

Opposite sides are equal , so

2x-3y = 5  

x+5y =9                <====== multiply this by -2 and add to first equation

-13y = -13

  then y = 1        and x + 5y = 9    so x = 4