Which value of x satisfies the equation 5(2x-9)+3=-7

Data:

age of Dollah = x (unknown element)

age of Fatimeh = x + 5 (age of Dollah + 5)

the product is 234

Equation:

x * (x + 5) = 234

x² + 5x = 234

x² + 5x - 234 = 0

Δ = b² - 4 a c = 5² - 4 (1 * -234) = 25 - 4 (-234) = 25 - (-936)

= 25 + 936 = 961

x₁,₂=[tex]\frac{b^{2} ± \sqrt{delta} }{2a}[/tex] = [tex]\frac{5^2 +/- \sqrt{961} }{2}[/tex] = [tex]\frac{25 +/- 31}{2}[/tex]

x1 = (25+31)/2 =  56 / 2 = 28

x2 = (25 -31)/2 = -6 / 2 = -3 [age can't be negative, so the first one is accettable]

So:

Dollah's age (x) = 28 years old

Fatima's age (x + 5) = 28 + 5 = 32 years old

Step-by-step explanation: lol like a dozen

Answer:

Step-by-step explanation:

since it is 100% and the pie chart circle is 360°, then for each % it will be 3.6°

applying this into drawing, just times 3.6° to the percentage and then get the final angle for the data.

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

if you don't need to be so concise, just see as you fit

Answer:

x=8

Step-by-step explanation:

3x -5 =2.5x + 3 - (x-4)

3x - 5 = 2.5x + 3 -x+4

3x - 5 = 1.5x +7

1.5x = 12

x =8

The solution to the linear equation 3x - 5 = 2.5x + 3 - (x-4) is x = 8.

The given expression is,

x-5=2.5x+3-(x-4)

Simplify the equation by combining like terms.

Start with the terms on the right-hand side of the equation:

2.5x+3-(x-4)

= 2.5x + 3 - x + 4 (distributing the negative sign)

= 1.5x + 7

Now let's combine the terms on the left-hand side of the equation:

3x - 5

Now the reduced equation be,

3x - 5 = 1.5x + 7

Isolate the variable (x) on one side of the equation.

Subtracting 1.5x from both sides:

3x - 1.5x - 5 = 1.5x - 1.5x + 7

1.5x - 5 = 7

Add 5 to both sides:

1.5x - 5 + 5 = 7 + 5

1.5x = 12

Solve for x by dividing both sides by 1.5:

1.5x/1.5 = 12/1.5

x = 8

So the solution to the linear equation 3x - 5 = 2.5x + 3 - (x-4) is x = 8.

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Greetings from Brasil....

From Pythagoras we have

AB² = AC² + BC²

13² = 12² + X²

Answer:

5 cm

Step-by-step explanation:

Pythagoras theorem gives us:

[tex]hypotenuse^{2} = side^{2} + side^{2}[/tex]

We know the hypotenuse is 13 cm.

We know one side is 12 cm.

[tex]13^{2} = 12^{2} + side^{2}[/tex]

[tex]169= 144 + side^{2}[/tex]

Subtracting 144 from both sides:

[tex]25 = side^{2}[/tex]

Reversing the sides:

[tex]side^{2}=25[/tex]

[tex]\sqrt{side^{2}}= \±\sqrt{25}[/tex]

[tex]side = \±\sqrt{25}[/tex]

[tex]side = \±5[/tex]

Since a distance can't be negative:

[tex]side=5[/tex]

The third side is 5 cm.

Answer:

Option two and three for the domain and range question

Answer: (0.8115, 0.8645)

Step-by-step explanation:

Let p be the proportion of people who leave one space after a period.

Given:  Sample size : n= 525

Number of people responded that they leave one space. =440

i.e. sample proportion: [tex]\hat{p}=\dfrac{440}{525}\approx0.838[/tex]

z-score for 90% confidence level : 1.645

Formula to find the confidence interval :

[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]0.838\pm (1.645)\sqrt{\dfrac{0.838(1-0.838)}{525}}\\\\=0.838\pm (1.645)\sqrt{0.00025858285}\\\\=0.838\pm (1.645)(0.01608)\\\\= 0.838\pm0.0265\\\\=(0.838-0.0265,\ 0.838+0.0265)\\\\=(0.8115,\ 0.8645)[/tex]

Hence, a 90% confidence interval for the proportion of people who leave one space after a period: (0.8115, 0.8645)

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

Explanation:

Using your calculator, you should find that

Each approximate result has its decimal digits go on forever without any pattern. So we cannot write those values as a fraction of two integers. The decimal expansion must have some kind of pattern that repeats forever, so we could consider it rational.

Only choice B results in a whole number. The value 14 is the same as 14/1, showing it can be written as a fraction of two integers. Therefore choice B is rational.

Answer:

28

Step-by-step explanation:

[tex]5x -7\\x =7[/tex]

Substitute 7 for x in the given equation

[tex]5x -7\\\\= 5(7) -7\\\\= 35-7\\\\= 28[/tex]

Answer:

28 is the answer

Step-by-step explanation:

5(7)= 35

35-7=28

Answer:

B)1-x≤-1 OR 1-x≥1

[tex]S=\{x\in\mathbb{R}| x\le 0\quad \text{or}\quad x\ge 2 \}[/tex]

Step-by-step explanation:

[tex]2|1-x|+1\geq 3[/tex]

[tex]2|1-x|\geq 2[/tex]

[tex]|1-x|\geq 1[/tex]

Once we have an absolute value inequality, remember that:

For a > 0

[tex]\boxed{\text{If } |x|\leq a \Longleftrightarrow -a\leq x \leq a}[/tex]

[tex]\boxed{\text{If } |x|\geq a \Longleftrightarrow x\leq -a \text{ or } x\geq a }[/tex]

Therefore,

[tex]1-x\le -1\quad \text{or}\quad 1-x\ge 1[/tex]

Solving

[tex]1-x\le -1 \Longleftrightarrow x\geq 2[/tex]

[tex]1-x\ge 1 \Longleftrightarrow x\leq 0[/tex]

We have

[tex]x\geq 2 \quad \cup \quad x \leq 0[/tex]

[tex](-\infty, 0] \cup [2, \infty)[/tex]

[tex]S=\{x\in\mathbb{R}| x\le 0\quad \text{or}\quad x\ge 2 \}[/tex]

Answer:

4/6 and 8/12 and 16/24

Step-by-step explanation:

well because it is math and math works like this basically all of theese are equal to 2/3

Answer:

Step-by-step explanation:

-5+1

-4

Answer:

x+4

x+1-2=x-1

Step-by-step explanation:

x+4/x-1=11/16 x should be different than 1 cz 1-1=0

16(x+4)=11(x-1)

16x+64=11x-11

16x-11x=-11-64

5x=-75

x=-15

Answer:  see proof below

Step-by-step explanation:

Proof LHS → RHS

[tex]\dfrac{1}{3-2\sqrt2}-\dfrac{1}{2\sqrt2-7}+\dfrac{1}{\sqrt7-\sqrt6}-\dfrac{1}{\sqrt6-\sqrt5}+\dfrac{1}{\sqrt5-2}\\\\\\\text{Rationalize the denominator (multiply by same numbers but opposite sign)}\\\dfrac{3+2\sqrt2}{1}-\dfrac{2\sqrt2+7}{1}+\dfrac{\sqrt7+\sqrt6}{1}+\dfrac{\sqrt6+\sqrt5}{1}+\dfrac{\sqrt5+2}{1}\\\\\\\text{Group like terms:}\\3+(2\sqrt2-2\sqrt2)+(-\sqrt7+\sqrt7)+(\sqrt6-\sqrt6)+(-\sqrt5+\sqrt5)+2\\\\\\\text{Simplify:}\\3 + 0+0+0+0+2 \\= 5[/tex]

LHS = RHS:  5 = 5  [tex]\checkmark[/tex]

Answer:

160

Step-by-step explanation:

Divide 24 by 15 percent (.15)

24/.15

=160

Answer:

160

Step-by-step explanation:

from the question, we know that 24 balloons are 15% of total.

make equation:

[tex]\frac{15}{100} =\frac{24}{x}[/tex]

calculate:

100*24/15=160 balloons

Answer:

B. No solutions

Step-by-step explanation:

8x+2y=14

8x+2y=4

These linear equations are in standard form, and the Ax values are the same (8x) and the By values are the same (2y).  The only value that is the different is the C values (14 and 4), which will be the cause of a no solution for this system of equations.

Answer:

b

..........

Step-by-step explanation:

0≠14-4

...

Answer:

F: 48

Step-by-step explanation:

Let x be the length of the side of the cube. RQ can be expressed as a triangle consisting of a diagonal of a face of the cube and the side length x. By the pythagorean theorem, we know that a^2+b^2=c^2. So, we can express the diagonal as x^2+x^2=c^2, giving us the value of c to be [tex]x\sqrt{2}[/tex]. Now, we can once again use the pythagorean theorem to find RQ^2=2x^2+x^2=3x^2, so RQ=[tex]x\sqrt{3}[/tex]=12, so x=[tex]4\sqrt{3}[/tex]. To find the area of the shaded part, we multiply the length times width which gives us [tex](4\sqrt{3})^2=48[/tex]. So, the area of the shaded face of the cube is F: 48.

Answer:

D is correct.

Step-by-step explanation:

2x ≤ 14

x  ≤ 7

Answer:

D) x ≤ 7

Step-by-step explanation:

2x + 1 ≤ 15

2x ≤ 15 - 1

2x ≤ 14

x ≤ 14 : 2

x ≤ 7

Answer:

Domain= possible x values

Range= possible y values.

Domain= all real numbers

Range= all numbers greater than -2.

Let me know if this helps :)

Domain = all real numbers and Range = ( -2 , ∞) of the given exponential graph

" Domain of exponential function y = aˣ is all the values of x and range is the all calculated values of 'y' after substituting value of x."

General exponential function

y = aˣ

According to the graph,

Given exponential function,

y = 3ˣ - 2

x represents the domain of the function.

y represents the range of the function

compare with exponential equation

a= 3 >1

As the value of 'x' increases value of 'y' moves to infinity.

Therefore, value of y defined for all the values of 'x'.

Therefore,

Domain is set of all real numbers.

Function y is transformed by -2.

Substitute x=0 in y = 3ˣ-2 we get,

y = -2

Therefore,

Range = (-2 , ∞)

Hence, Domain = all real numbers and Range = ( -2 , ∞) of the given exponential graph.

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Answer:

x = 1

y = 5

Step-by-step explanation:

5x - 2y = -5

5x + 6y = 35

=> 5x + 6y = 35

=> 5x - 5x + 6y = 35 - 5x

=> 6y = 35 - 5x

=> 6y/6 = 35/6 - 5/6x

=> y = 35/6 - 5/6x

=> 5x - 2 (35/6 - 5/6x) = -5

=> 5x - 35/3 + 5/3x = -5

=> 15/3x -35/3 + 5/3 = -15/3

=> 20/3x -35/3 = -15/3

=> 20/3x -35/3 + 35/3 = -15/3 + 35/3

=> 20/3x = 20/3

=> 20/3x * 3 = 20/3 * 3

=> 20x = 20

=> 20x/20 = 20/20

=> x = 1

=> 5x + 6y = 35

=> 5(1) + 6y = 35

=> 5 + 6y = 35

=> 5 -5 + 6y = 35 -5

=> 6y = 30

=> 6y/6 = 30/6

=> y = 5

So, x = 1

     y = 5

Answer:

There are 10 perfect squares between 1 and 100;

A perfect square is basically an integer that is a square of an integer. Or simply the product of an integer with itself.

Explanation:

The perfect squares between 1 and 100 are:

1*1 = 1

2*2 = 4

3*3 = 9

4*4 = 16

5*5 = 25

6*6 = 36

7*7 = 49

8*8 = 64

9*9 = 81

and

10*10 = 100

Answer:

x=2

Step-by-step explanation:

1+4x=7+x

↦4x-x=7-1

↦3x=6

↦x=6/3

↦x=2

.°. x=2

Hope you understand it

Answer:

x = 2

Step-by-step explanation:

For this equation, we simply need to solve for x.

1 + 4x = 7 + x

1 + -1 + 4x = 7 + -1 + x

4x = 6 + x

4x + -x = 6 + x + -x

3x = 6

3x * (1/3) = 6 * (1/3)

x = 2

So the solution to this equation is x = 2.

Cheers.

Answer:

28

Step-by-step explanation:

The first five prime numbers are = 2,3,5,7,11

Addition of the prime nos. = 2+3+5+7+11=28

The first prime numbers are: 2, 3, 5, 7, 11.

The sum is 2 + 3 + 5 + 7 + 11 = 28, so option 4

Answer:

Step-by-step explanation:

That will be 3a + 3b + 3c pounds of mortar.

as there will be 3a pounds of water and 3c pounds of cement.

Answer: $1.8

Step-by-step explanation:

From the question, we are informed that the price for 2 kilograms of ham is $36.00. We should remember that 1000 gram = 1 kilogram; therefore, 2 kilograms = 2000 grams.

The cost of a gram of ham will then be:

= $36.00/2000

= $0.018

The unit price of ham per 100 grams will be:

= 100 × 0.018

= $1.8

Answer:  see proof below

Step-by-step explanation:

Use the following Product to Sum Identities:

2 sin A sin B = cos (A - B) - cos (A + B)

2 sin A cos B = sin (A + B) + sin (A - B)

Use the Unit Circle to evaluate: cos 120 = -1/2    &      sin 60 = √3/2

Proof LHS → RHS

LHS:                                            sin 20 · sin 40 · sin 80

Regroup:                              (1/2) sin 20 · 2 sin 40 · sin 80

Product to Sum Identity:     (1/2) sin 20 [cos(80-40) - cos (80+40)]

Simplify:                                (1/2) sin 20 [cos 40 - cos 120]

Unit Circle:                            (1/2) sin 20 [cos 40 + (1/2)]

Distribute:                             (1/2) sin 20 cos 40 + (1/4) sin 20

Product to Sum Identity:       (1/4)[sin(20 + 40) + sin (20 - 40)] + (1/4) sin 20

Simplify:                                 (1/4)[sin 60 + sin (-20)] + (1/4) sin 20

                                           = (1/4)[sin 60 - sin 20] + (1/4) sin 20

Unit Circle:                             (1/4)[(√3/2) - sin 20] + (1/4) sin 20

Distribute:                              (√3/8) -  (1/4) sin 20 + (1/4) sin 20

Simplify:                                  √3/8

LHS = RHS:   √3/8 = √3/8  [tex]\checkmark[/tex]

We are given the equation cos(20°)(cos(40°)(cos(60°)(cos(80°) = √3 / 8. Let's once again start by applying the identity 'sin(s)sin(t) = - cos(s + t) + cos(s - t) / 2. In this case if we focus on the expression 'cos(20°)(cos(40°),' s would be = 20°, and t = 40°.

[tex]\mathrm{Use\:the\:following\:identity}:\quad \sin \left(s\right)\sin \left(t\right)=\frac{-\cos \left(s+t\right)+\cos \left(s-t\right)}{2}[/tex]

[tex]\sin \left(20^{\circ \:}\right)\sin \left(40^{\circ \:}\right)=\frac{-\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}[/tex]

[tex]\mathrm{Substitute}:\frac{-\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}\sin \left(80^{\circ \:}\right)[/tex]

[tex]\mathrm{Multiply\:fractions}:\frac{\sin \left(80^{\circ \:}\right)\left(-\cos \left(60^{\circ \:}\right)+\cos \left(-20^{\circ \:}\right)\right)}{2}[/tex]

Remember that cos(- x) = cos(x). Respectively cos(- 20°) = cos(20°). Let's substitute and afterwards apply the identity 'cos(60°) = 1 / 2.'

[tex]\frac{\sin \left(80^{\circ \:}\right)\left(-\cos \left(60^{\circ \:}\right)+\cos \left(20^{\circ \:}\right)\right)}{2} = \frac{\sin \left(80^{\circ \:}\right)\left(-\frac{1}{2}+\cos \left(20^{\circ \:}\right)\right)}{2}[/tex]

And if we further simplify the expression, we should receive the following...

[tex]\frac{\sin \left(80^{\circ \:}\right)\left(-1+2\cos \left(20^{\circ \:}\right)\right)}{4}[/tex]

Now we want to prove that this expression = √3 / 8. The denominator here is 4 so we can multiply the whole thing by 2 to have a denominator of 8. 2((sin(80°)(- 1 + 2cos(20°)) when simplified = √3. Therefore the expression is true.

Answer:

2x + 22

Explanation

2(4x + 7) -2(3x -4)

Factor 2 out of  the Expression

2(4x + 7 -(3x -4)

- × - is +

2(4x + 7 - 3x +4)

Collect like terms

2(x+7+4)

2(x+11)

2x + 22

☆ The relation between x and y is y = a cos x° +b

Taking 1st condition from the table .

→ x = 0 and y = 9

→ y = a + cos 0° + b

→ 9 = a + cos 0° + b

☆ We know that cos 0° = 1

→ 9 = a(1) + b

Now taking other condition

→ x = 90° and y = 1

→ y = a cos 90° + b

→ 1 = a cos 90° + b

☆ We know that cos 90° is 0

→ 1 = a(0) + b

Putting the value of b in equation 1st .

→ 9 = a + 1

→ a = 8 .

Now taking the value of x according to the question .

☆ x = 45 °

→ y = 8 ( cos 45°) + 1

☆ We know that cos 45° is 1/√2

→ y = 8(1/√2) + 1

→ 8 = 4×√2×√2

So the answer is 4√2+1

Answer:

E. - 7

Step-by-step explanation:

2x2-X2+5X-10-4=0

X2+5X-14=0

X2-2X+7X-14.=0

X(X-2). 7(X-2)=0

(X+7). (X-2)

X=-7, X=2

Answer:

the answer is -7 and 2

Step-by-step explanation: