50.48=-22.02+5x what is the solution to the equation?

Answer:

8 or -4

Step-by-step explanation:

The error is they believed x2 meant x^2 OR they forgot that x could also equal to -4.

x^2 = 16 has two solutions. They are 4 and -4. So the value of x could also be -4.

Answer:

A = π/6 + kπ, or A = 2π/3 + kπ

Step-by-step explanation:

tan A / (1 − tan² A) = √3 / 2

Cross multiply and simplify:

√3 (1 − tan² A) = 2 tan A

√3 − √3 tan² A = 2 tan A

3 − 3 tan² A = 2√3 tan A

0 = 3 tan² A + 2√3 tan A − 3

Solve with quadratic formula:

tan A = [ -2√3 ± √((2√3)² − 4(3)(-3)) ] / 2(3)

tan A = [ -2√3 ± √(12 + 36) ] / 6

tan A = (-2√3 ± √48) / 6

tan A = (-2√3 ± 4√3) / 6

tan A = -√3 or √3/3

Solve for A:

A = 2π/3 + kπ, or A = π/6 + kπ

Answer:

Step-by-step explanation:

So the first step is to simply set up the problem based on what we are given. So here have two numbers, we are going to call the first number x and the second one y. With that now addressed, we can now proceed with the setup.

So the difference between the squares of the numbers is 24. So we have:

[tex]x^{2} -y^{2} = 24[/tex]

Then it says that three times the square of the first number (which we said was x) increased by the square of the second number is 76. So:

[tex]3x^{2} + y^{2} = 76[/tex]

Now we can see that this is simply a system of equations and we can use elimination to solve this! We even have the setup already as the coefficients in front of our y are opposite in sign and are equal. So:

[tex]x^{2} -y^{2} = 24\\3x^{2} +y^{2} = 76[/tex]

We can cancel our y squared terms out and that leaves, when we add the equations together:

[tex]4x^{2} = 100[/tex]

We can then solve for x by diving by four and taking the square root of the result.

[tex]x^{2} = 25\\[/tex]

Therefore, x = ±5

We have both negative and positive answers because if we squared -5 or +5 they would both give us 25. So we cant rule a negative answer out yet.

So now we can plug in x = -5 or +5 to either equation to solve for y as so:

[tex]5^{2} - y^{2} = 24\\25 - y^{2} = 24\\-y^{2} = -1 \\y^{2} = 1[/tex]

So y = ±1

In this case both negative and positive versions of our answer work (you can also double check), so we are left with:

x = ±5 and y = ±1

We can solve the problem by expressing one variable through another from one equation and substituting it into the second equation. Then solve for the first variable and substitute the found value in one of the equations to find the corresponding other variable.

The subject of this question is algebra, specifically equations involving squares of numbers and systems of equations. Let's denote the unknown numbers as 'x' and 'y'. From the problem, we know two equations:

One possible approach to finding the values of x and y would be to use the substitution method. From equation (1), we can express y² as x² - 24 and substitute this into equation (2):

3x² + (x² - 24) = 76

If we simplify and solve for x, we find that x = 4, -4.

Then, substituting 'x' into the first equation will yield corresponding 'y' values. That's how you can solve this kind of problems by using squares of numbers and method of substitution.

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Answer:

25.6

Step-by-step explanation:

Convert the percentage to decimal form by dividing by 100.

4% of 640

= 0.04(640)

= 25.6

Answer:

The equation of the required line is: 2x + y = 8

Step-by-step explanation:

When a point on the line and the slope of the line are given, we use the slope - one - point form to determine the equation of the line.

Say, [tex]$ (x_1, y_1) $[/tex] is the point passing through the line and the slope of the line is say, [tex]m[/tex]. Then the equation would be:

                      [tex]$ (y - y_1) = m(x - x_1) $[/tex]

Here [tex]$ (x_1, y_1) = (7, -6) $[/tex] and slope, [tex]$ m = - 2 $[/tex].

Therefore, the equation of the line becomes:

[tex]$ y - (-6) = -2(x - 7) $[/tex]

[tex]$ \implies y + 6 = -2x + 14 $[/tex]

Rearranging we get:

[tex]$ 2x + y - 8 = 0 $[/tex] which is the required equation of the line.

Answer:

[tex]\angle{A}=53.1^{\circ}[/tex]

[tex]\angle{A}=80.9^{\circ}[/tex]

[tex]b=12.4[/tex]

Step-by-step explanation:

Please find that attachment.

We have been given that in ΔABC, ∠C measures 46° and the values of a and c are 10 and 9, respectively.

First of all, we will find measure of angle A using Law Of Sines:

[tex]\frac{\text{sin(A)}}{a}=\frac{\text{sin(B)}}{b}=\frac{\text{sin(C)}}{c}[/tex], where, A, B and C are angles corresponding to sides a, b and c respectively.

[tex]\frac{\text{sin(A)}}{10}=\frac{\text{sin(46)}}{9}[/tex]

[tex]\frac{\text{sin(A)}}{10}=\frac{0.719339800339}{9}[/tex]

[tex]\frac{\text{sin(A)}}{10}=0.0799266444821111[/tex]

[tex]\frac{\text{sin(A)}}{10}*10=0.0799266444821111*10[/tex]

[tex]\text{sin(A)}=0.799266444821111[/tex]

Upon taking inverse sine:

[tex]A=\text{sin}^{-1}(0.799266444821111)[/tex]

[tex]A=53.060109978759^{\circ}[/tex]

[tex]A\approx 53.1^{\circ}[/tex]

Therefore, the measure of angle A is 53.1 degrees.

Now, we will use angle sum property to find measure of angle B as:

[tex]m\angle{A}+m\angle{B}+m\angle{C}=180^{\circ}[/tex]

[tex]53.1^{\circ}+m\angle{B}+46^{\circ}=180^{\circ}[/tex]

[tex]m\angle{B}+99.1^{\circ}=180^{\circ}[/tex]

[tex]m\angle{B}+99.1^{\circ}-99.1^{\circ}=180^{\circ}-99.1^{\circ}[/tex]

[tex]m\angle{B}=80.9^{\circ}[/tex]

Therefore, the measure of angle B is 80.9 degrees.

Now, we will use Law Of Cosines to find the length of side b.

[tex]b^2=a^2+c^2-2ac\cdot\text{cos}(B)[/tex]

Upon substituting our given values, we will get:

[tex]b^2=10^2+9^2-2(10)(9)\cdot\text{cos}(80.9^{\circ})[/tex]

[tex]b^2=100+81-180\cdot 0.158158067254[/tex]

[tex]b^2=181-28.46845210572[/tex]

[tex]b^2=152.53154789428[/tex]

Upon take square root of both sides, we get:

[tex]b=\sqrt{152.53154789428}[/tex]

[tex]b=12.3503663060769173[/tex]

[tex]b\approx 12.4[/tex]

Therefore, the length of side b is approximately 2.4 units.

Answer:

∠A = 53.1°, ∠B = 80.9°, b = 12.4

Step-by-step explanation:

i got it right on my test

The x-coordinate of the point that divides the  directed line segment from K to J into a ratio of 1:3 is 7

Step-by-step explanation:

The formula for x-cooridnate of a point that divides a line in ratio m:n is given by:

[tex]x = \frac{nx_1+mx_2}{m+n}[/tex]

Given

K(9,2) = (x1,y1)

J(1,-10) = (x2,y2)

m = 1

n = 3

Putting the values in the formula

[tex]x = \frac{(3)(9)+(1)(1)}{1+3}\\x = \frac{27+1}{4}\\x = \frac{28}{4}\\x = 7[/tex]

Hence,

The x-coordinate of the point that divides the  directed line segment from K to J into a ratio of 1:3 is 7

Keywords: Ratio, fraction

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Answer:

the number is X=2

Step-by-step explanation:

Suppose number is X

8X-1 =X+13

8X-X= 13+1

7X=14

X=2

Answer:

8n-1= 13+n is the equation, n=2 is the answer for the variable.

Step-by-step explanation:

8n-1= 13+n

Move the variable to one side.

8n-1= 13+n

-1n         -1n

7n-1= 13

Now, add to both sides, since that is the opposite of subtracting.

7n-1= 13

   +1  +1

Then, divide to both sides by 7 to leave the variable by itself.

7n= 14

7     7

n= 2

Answer:

Ans => 4, 5

Step-by-step explanation:

let the integers be x and y

if they are consecutive, that means the larger integer is one greater than the smaller

=> y = x+1

2 = 3x - 2y

3x - 2(x+1) = 2

3x - 2x - 2 = 2

x = 4

y = 4+1 = 5

Answer:

The statement is false

Step-by-step explanation:

we have

[tex]4y=x[/tex]

Solve for y

That means ----> Isolate the variable y

Divide by 4 both sides

[tex]y=\frac{1}{4}x[/tex]

This is the equation of a proportional relationship between the variable x and the variable y

where the constant of proportionality k or slope m is equal to 1/4

therefore

The statement is false

Answer:

We typically construct graphs with the input values along the horizontal axis and the output values along the vertical axis. The most common graphs name the input value x and the output value y , and we say y is a function of x , or y=f(x) y = f ( x ) when the function is named f .

Step-by-step explanation:

Answer:

Step-by-step explanation:

1)w=−4/3x+−1/3y+2/3z+26/3

2)w=−3/2x+1/2y+−1/2z+7

3)w=1/2x+y+3/2z−9

4)w=2x+2y−z−10

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The slope of given coordinates (0,-2) and (2,-1) is [tex]\frac{1}{2}[/tex]

The slope intercept form is [tex]y = \frac{1}{2}x -2[/tex]

Given that the coordinates are (0,-2) and (2,-1)

To find: slope and slope intercept form

The slope of line is given as:

For a line containing two points [tex](x_1 , y_1)[/tex] and [tex](x_2, y_2)[/tex] , slope of line is given as:

[tex]{m}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Here in this problem,

coordinates are (0,-2) and (2,-1)

[tex]x_{1}=0 ; y_{1}=-2 ; x_{2}=2 ; y_{2}=-1[/tex]

Substituting the values in above formula,

[tex]m=\frac{-1-(-2)}{2-0}=\frac{-1+2}{2}=\frac{1}{2}[/tex]

Thus slope of line is [tex]\frac{1}{2}[/tex]

To find slope intercept form:

The slope intercept form is given as:

y = mx + b

Where "m" is the slope of line and "b" is the y-intercept

Substitute [tex]m = \frac{1}{2}[/tex] and (x, y) = (0, -2) in above slope intercept we get,

[tex]-2 = \frac{1}{2} \times 0 + b[/tex]

b = -2

Thus the required slope intercept is given as:

Substitute [tex]m = \frac{1}{2}[/tex] and b = -2 in slope intercept form,

[tex]y = \frac{1}{2}x -2[/tex]

Thus the slope intercept form is found

Answer:

Step-by-step explanation:

[tex]f(x)=\dfrac{12}{4x+2}\\\\f(-1)-\text{put}\ x=-1\ \text{to}\ f(x):\\\\f(-1)=\dfrac{12}{4(-1)+2}=\dfrac{12}{-4+2}=\dfrac{12}{-2}=-6[/tex]

Answer:

f(-1) = -6

Step-by-step explanation:

substitute -1 into the equation and solve, you'll get -6

Answer:

D. None of the above.

Step-by-step explanation:

OPTIONS A and C. The Olympic final had faster average times and more noticeable variation compared to the top 888 U.S. qualifier times.

Looking at the dot plots, we can draw the following conclusions:

A. The times in the Olympic final were faster on average than the top 888 U.S. qualifier times. - True, since the lower dot plot represents Olympic final times and the lower values (faster times) are more concentrated.

B. All of the times in the Olympic final were faster than all of the top 888 U.S. qualifier times. - False, as there are some times in the U.S. qualifier dot plot that are faster than some times in the Olympic final dot plot.

C. The Olympic final times varied noticeably more than the times of the top 888 U.S. qualifiers. - True, since the spread of dots in the lower plot seems to be wider compared to the upper plot, indicating greater variation in Olympic final times.

So, the correct choices are A and C.

Answer:

(x - 2)(x + 2).

Step-by-step explanation:

This is the difference of 2 squares:

a^2 - b^2 = (a - b)(a + b)

So

x^2 - 4 = (x - 2)(x + 2).

Answer:

6 bicycles and 3 tricycles

Step-by-step explanation:

bicycles have two wheels therefore 6*2=12 total wheels

tricycles have three wheels therefore 3*3=9 total wheels

add the totals up and you have 21 total wheels

Final answer:

The shop can build 6 bicycles and 3 tricycles with the 21 wheels available.

Explanation:

To solve the problem of figuring out how many tricycles and bicycles can be built with 21 wheels, under the condition that there will be half as many tricycles as bicycles, we use algebraic methods.

Let's denote the number of bicycles as B and the number of tricycles as T.

Since each bicycle needs 2 wheels and each tricycle needs 3, we can establish the following equations based on these facts and the condition given:

Substituting T from the second equation into the first gives:

2B + 3(0.5B) = 21

2B + 1.5B = 21

3.5B = 21

B = 21 / 3.5 = 6

So, there are 6 bicycles. To find T, plug B back into the equation T = 0.5B:

T = 0.5×6 = 3

Therefore, the shop can build 6 bicycles and 3 tricycles with the 21 wheels available.

Answer:

y-4=3/4(x+8)

Step-by-step explanation:

y-y1=m(x-x1)

y-4=3/4(x-(-8))

y-4=3/4(x+8)

Abdul drove the truck for 177 miles.

To find the number of miles driven by Abdul, we need to subtract the base fee from the total amount he paid and then divide the result by the additional charge per mile. Let's represent the number of miles driven by x.

Total amount paid - Base fee = Additional charge per mile * Number of miles driven

$146.16 - $16.95 = $0.73 * x

Simplifying the equation: $129.21 = $0.73x

Dividing both sides by $0.73, we get: x = 177

Therefore, Abdul drove the truck for 177 miles.

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From Patrick's gains, tax rates, and the inflation rate, the following are true: $346.25, $1,731.25, $145.43 and $4,702.08.

State tax on initial profit can be calculated by;

= (17,000 - 10,000 - 25 - 25 - 25) x 5%

= $346.25

The federal tax is:

= 25% x (17,000 - 10,000 - 25 - 25 - 25) x 25%

= $1,731.25

Inflation after taxes is:

= (17,000 - 7,000 - 25 - 25 - 25 - 346.25 - 1,731.25) * (1% + 1% + 1%)

= $145.43

Real value in profit is:

= 17,000 - 7,000 - 25 - 25 - 25 - 346.25 - 1,731.25 - 145.43

= $4,702.08

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Patrick's initial profit is $7,000, and after state and federal taxes, he has $4,900. When adjusted for a 1% annual inflation rate over three years, the real value of his profit is approximately $4,805.03.

Patrick's profit from selling his stock is calculated by subtracting the initial investment from the current value, $17,000 - $10,000 = $7,000. The state tax he must pay on this profit is 5% of $7,000, which equals $350. Similarly, the federal tax on the profit is 25% of $7,000, equaling $1,750. After state and federal taxes, the remaining amount is $7,000 - $350 - $1,750 = $4,900. Lastly, the inflation effect over three years at 1% per year diminishes the purchasing power of the remaining amount. The cumulative effect of inflation can be calculated by the formula P = P0 * ((1 - r)^n), where P is the future value, P0 is the present value, r is the inflation rate, and n is the number of years. Thus, Patrick's remaining profit adjusted for inflation would be $4,900 * ((1 - 0.01)^3), which gives a result of approximately $4,805.03. This is the real value of Patrick’s profit after taxes and inflation adjustments.

Answer:

[tex]\frac{n^{2} }{n+5}[/tex]

Step-by-step explanation:

We can see that for nth term of this sequence,numerator is square of the term number([tex]n^{2}[/tex]) and denominator is 5 added to the term number(n+5).

Therefore , the nth term of this sequence is

[tex]\frac{n^{2} }{n+5}[/tex]

Answer: 44

Step-by-step explanation:

we will find RN and NQ, then add together to give us RQ.

To find RN;

RP= 17 PN = 15 and RN =?

using pythagoras theorem,

adj^2 = hyp^2 - opp^2

RN^2 = RP^2 - PN^2

?^2 = 17^2 - 15^2

?^2 = 17^2 - 15^2

?^2 = 289 - 225

?^2 = 64

? = √64

? = 8

RN=8

To find NQ,

PN = 15 PQ=39 and NQ=?

using pythagoras theorem

NQ^2 = PQ^2 - PN^2

?^2 = 39^2 - 15^2

?^2 = 1521 - 225

?^2 = 1296

? = √1296

? = 36

NQ= 36

RQ = RN + NQ

RQ= 8 + 36

RQ=44

Answer:

[tex](2x+5)(4x^{2} -10x+25)=0[/tex]

Step-by-step explanation:

Given:

The given equation is.

[tex]8x^{3} +125=0[/tex]

Find the some of cube.

Solution:

[tex]8x^{3} +125=0[/tex]

[tex]2^{3}x^{3} +5^{3}=0[/tex]

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

The sum of the cube formula is given below.

[tex](a^{3} +b^{3})=(a+b)(a^{2} -ab+b^{2} )[/tex]-----------(2)

By comparing equation 1 and equation 2

[tex]a=2x, b=5[/tex]

substitute a and b value in equation 2

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

[tex]((2x)^{3} +5^{3})=(2x+5)(4x^{2} -(10x)+25)[/tex]

[tex]((2x)^{3} +5^{3})=(2x+5)(4x^{2} -10x+25)[/tex]

Therefore the sum of the cube [tex](2x+5)(4x^{2} -10x+25)=0[/tex]

Answer:

Yes, △ABC ∼ △FED by AA postulate.

Step-by-step explanation:

Given:

Two triangles ABC and FED.

m∠A = m∠B

m∠C = m∠A + 30°

m∠E = m∠F = [tex]x[/tex]

m∠D = [tex]2x-20[/tex]°.

Now, let m∠A = m∠B = [tex]y[/tex]

So, m∠C = m∠A + 30° = [tex]y+30[/tex]

Now, sum of all interior angles of a triangle is 180°. Therefore,

m∠A + m∠B +  m∠C = 180

[tex]y+y+y+30=180\\3y=180-30\\3y=150\\y=\frac{150}{3}=50[/tex]

Therefore, m∠A = 50°, m∠B = 50° and m∠C =  m∠A + 30° = 50 + 30 = 80°.

Now, consider triangle FED,

m∠D+ m∠E + m∠F = 180

[tex]2x-20+x+x=180\\4x=180+20\\4x=200\\x=\frac{200}{4}=50[/tex]

Therefore,  m∠F = 50°  

m∠E = 50° and  

m∠D =  [tex]2x-20=2(50)-20=100-20=80\°[/tex]

So, both the triangles have congruent corresponding angle measures.

m∠A = m∠F = 50°

m∠B = m∠E = 50°

m∠C = m∠D = 80°

Therefore, the two triangles are similar by AA postulate.

Answer:

[tex]AB=\dfrac{38}{3}\ units[/tex]

Step-by-step explanation:

ABCD is a rhombus, then

[tex]AB=BC=CD=DA[/tex]

Since

[tex]BC=2x+8\\ \\CD=5x+1,[/tex]

then

[tex]BC=CD\Rightarrow 2x+8=5x+1[/tex]

Solve this equation:

[tex]2x-5x=1-8\\ \\-3x=-7\\ \\3x=7\\ \\x=\dfrac{7}{3}[/tex]

Then

[tex]BC=2\cdot \dfrac{7}{3}+8=\dfrac{14}{3}+8=\dfrac{14+8\cdot 3}{3}=\dfrac{14+24}{3}=\dfrac{38}{3}\ units[/tex]

Therefore,

[tex]AB=\dfrac{38}{3}\ units[/tex]

Find base and height of the triangle to find area.

Base=Perimeter/3

Base=36/3=12 cm

Height²=12²-6²

Height²=108

Height=(6√3) cm

area=base×height

area=1/2×12×6√3=62 cm² approx.

answer: 3rd choice

Answer:

Find base and height of the triangle to find area.

Base=Perimeter/3

Base=36/3=12 cm

Height²=12²-6²

Height²=108

Height=(6√3) cm

area=base×height

area=1/2×12×6√3=62 cm² approx.

answer: 3rd choice

Step-by-step explanation:

Answer:

The function is y = 2x + 1.

And mike graphed the function correctly.

Menna took the point where the function touches x-axis incorrectly.

Instead of (-1/2,0), Menna took it as (-2,0)

Step-by-step explanation:

The equation y = mx +c indicates a straight line whose slope is m

And y-intercept is c.

y-intercept is nothing but the distance between origin and point where the graph crosses the y-axis (0,c).

Now, this graph crosses x-axis when y = 0.

⇒ mx + c = 0;       ⇒ x = [tex]\frac{-c}{m}[/tex].

Now, by comparing y = 2x + 1 with y = mx + c.

m=2 and c=1

⇒ the graph should crosses y-axis at (0,c) = (0,1)

And touch x-axis at ([tex]\frac{-c}{m}[/tex] , 0) = ([tex]\frac{-1}{2}[/tex],0)

⇒ mike graphed the function correctly.

Menna took the point where the function touches x-axis incorrectly.

Instead of (-1/2,0), Menna took it as (-2,0)

Answer:

Step-by-step explanation:

y = 2x + 1.