Answers
Let's first try to rewrite the expression to see if we can write it in a fomr more familiar:
[tex]\begin{gathered} x-\sqrt{10-3x}=0, \\ x=\sqrt{10-3x}, \\ x^2=10-3x, \\ x^2+3x-10=0. \end{gathered}[/tex]This is the same equation, but now we recognize a quadratic expression equal to 0. We can use the quadratic formula to find the solutions of this equation:
[tex]x_{1,2}=\frac{-3\pm\sqrt{3^2-4\cdot1\cdot(-10)}}{2\cdot1}[/tex]And solve:
[tex]\begin{gathered} x_{1,2}=\frac{-3\pm\sqrt{9+40}}{2}=\frac{-3\pm7}{2} \\ x_1=\frac{-3+7}{2}=\frac{4}{2}=2 \\ x_2=\frac{-3-7}{2}=\frac{-10}{2}=-5 \end{gathered}[/tex]Thus, the solution set of the equation is x = -5, x = 2
Related Questions
Evaluate the expression (-4-4i) +(-8-11) and write the result in the form a + bi.The real number a equalsThe real number b equals
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The answer is supposed to be in the form
[tex]a+bi[/tex]Therefore,
[tex](-4-4i)+(-8-1i)[/tex][tex]\begin{gathered} -4-4i-8-1i \\ \end{gathered}[/tex]combine like terms
[tex]-4-8-4i-1i[/tex]Finally,
[tex]-12-5i[/tex]a = -12
b = -5
I need help on this equationTo simplify each and state the excluded value.
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To answer this question, we need to factor each of the polynomials as follows:
First Polynomial
[tex]x^2+4x+3[/tex]To factor it, we need to find two numbers:
a*b = 3
a + b = 4
These numbers are:
a = 3
b = 1
Therefore, we have:
[tex]x^2+4x+3=(x+1)(x+3)[/tex]Find the value of each variable in the parallelogram.5u – 10162u + 2V3U =0V=
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The diagonals of a parallelogram bisect each other. It means the segments, after bisection, are equal to each other.
From the figure, we can write:
[tex]\begin{gathered} 2u+2=5u-10 \\ \text{and} \\ 6=\frac{v}{3} \end{gathered}[/tex]We can solve the first equation and get the value of u:
[tex]\begin{gathered} 2u+2=5u-10 \\ 2+10=5u-2u \\ 12=3u \\ u=\frac{12}{3} \\ u=4 \end{gathered}[/tex]Solving the second equation, we find the value of v:
[tex]\begin{gathered} 6=\frac{v}{3} \\ 6\times3=v \\ v=18 \end{gathered}[/tex]Answer:
u = 4v = 18Three support beams for a bridge form a pair of complementary angles. Find the measure of each angle.(2x - 20)INNISmaller angle:Larger angle:O0UNSFANA(4x - 10)
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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define complementary angles
When the sum of two angles is 90°, then the angles are known as complementary angles.
STEP 2: Write the pairs of the angles formed
[tex]\begin{gathered} (2x-20)\degree \\ (4x-10)\degree \end{gathered}[/tex]STEP 3: find the value of x
Following the definition in step 1, this goes that;
[tex]\begin{gathered} (2x-20)+(4x-10)=90\degree \\ 2x-20+4x-10=90\degree \\ 6x-30=90 \\ 6x=90+30 \\ 6x=120 \\ x=\frac{120}{6}=20 \end{gathered}[/tex]STEP 4: Find the two pair of angles
[tex]\begin{gathered} (2x-20)=2(20)-20=40-20=20\degree \\ 4x-10=4(20)-10=80-10=70\degree \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} smaller\text{ }angle=20\degree \\ Larger\text{ }angle=70\degree \end{gathered}[/tex]14) What is the slope of the line below *
Answers
Solve the system of linear equations using the graphing method. Use “no solution” and “infinitely many” when appropriate.
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Given the system of equations:
[tex]\begin{gathered} y=\frac{1}{2}x+2 \\ \\ y=\frac{1}{2}x+1 \end{gathered}[/tex]Let's solve the system using graphing method.
Let's plot both equations on a graph. The point where both lines meet.
• Equation 1:
Let's plot using 3 points.
Substitute random values of x and solve for y.
We have:
[tex]\begin{gathered} x=-4;\text{ y = }\frac{1}{2}(-4)+2=-2+2=0 \\ \\ x=0;y=\frac{1}{2}(0)+2=0+2=2 \\ \\ x=4;y=\frac{1}{2}(4)+2=2+2=4 \end{gathered}[/tex]For equation 1, we have the points:
(x, y) ==> (-4, 0), (0, 2), (4, 4)
Plot the points and connect the points with a straight line.
• Equation 2:
Let's create 3 points:
[tex]\begin{gathered} x=-2;y=\frac{1}{2}(-2)+1=-1+1=0 \\ \\ x=0;y=\frac{1}{2}(0)+1=0+1=1 \\ \\ x=2;y=\frac{1}{2}(2)+1=1+1=2 \end{gathered}[/tex]FOr equation 2, we have the points:
(x, y) ==> (-2, 0), (0, 1), (2, 2)
Now, plot the points and connect using a straight line.
We have the graph of both equations below:
From the graph, we can see that both lines do not meet at any point.
They are parallel lines,
Since they will not meet at any point, there is NO SOLUTION.
ANSWER:
No solution.
Square Root Function and inverse
Answers
Answer:
[tex]f^-^1(x)=\frac{x+1}{8}[/tex]
Step-by-step explanation:
f(x) = 8x - 1
==> replace "f(x)" with y
y = 8x - 1
==> inter exchange x and y
x = 8y - 1
==> solve for y now, first step would be to add 1 to both sides
x + 1 = 8y
==> divide both sides by 8
(x+1)/8 = y
==> replace y with f^-1(x)
f^-1(x)=(x+1)/8y
on a graph if it has (-5,5) and (5,5) is it proportional or non- proportional
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A proportional graph is when y increases/decreases, if x increases. The graph shows that as x increases, the value of y stays the same, therefore it is not proportional.
what is the name of the geometric figure that begins at a point and is a set of all points that make a never-ending straight path extending in only one direction?
Answers
hi.
to start this exercise, let's remember some definitions about the alternatives:
a. ray
distance between the center of the circle and a point on its circumference (one straight line)
b. vertex
is a point where two edges meet
c. angle
is formed by two semi-straights that come from the same origin
d. opposite rays
is the same definition of radius, only now it considers two rays: one and its opposite. joining a radius to its opposite, we get a straight line.
Can you help me please? If there is a solution what’s the solution as well
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Solution:
Given;
[tex]-7y^2+7y+1=0[/tex]Where;
[tex]a=-7,b=7,c=1[/tex]Thus;
[tex]\begin{gathered} b^2-4ac=7^2-4(-7)(1) \\ \\ b^2-4ac>0 \end{gathered}[/tex]Hence, the quadratic equation has two different real solutions.
Then;
[tex]\begin{gathered} y=\frac{-7\pm\sqrt{7^2-4(-7)(1)}}{2(-7)} \\ \\ y=1.13,y=-0.13 \end{gathered}[/tex]I need help finding my equation for the question. I’m very confused
Answers
1)
The ratio of cookies to hours spent cooking = C : H
= 300 : 4
= 75 : 1
2)
How many hours does it take to bake 225 cookies
[tex]\begin{gathered} =\text{ }\frac{225}{75}\text{ } \\ =\text{ 3 hours} \end{gathered}[/tex]Piper works at a camera store. He is paid an hourly rate plus 16% commission on everything he sells. One week, he was paid $515 for working 20 hours and selling $1,500 worth of camera equipment. What is his hourly rate?
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His hourly rate is $13.75
Here, we want to get Piper's hourly pay at work
Let the hourly rate be h
Thus, for working 20 hours, the amount for this will be; 20 * h = 20h
Now, out of the $1500 sales, he is entitled to 16%
That means;
[tex]\frac{16}{100}\times\text{ 1500 = 240}[/tex]Thus, we have it that;
[tex]\begin{gathered} 20h\text{ + 240 = 515} \\ 20h\text{ = 515-240} \\ 20h\text{ = 275} \\ h\text{ = }\frac{275}{20} \\ h\text{ = \$13.75} \end{gathered}[/tex]Distributive Property equation8x4=(_x_)+(_x_)
Answers
Answer:
8 x 4 = (8 x 2) + (8 x 2)
Explanation:
The distributive property says that:
a x (b + c) = (a x b) + (a x c)
Then, we can write 4 as (2 + 2), so:
8 x 4 = 8 x ( 2 + 2)
Now, we can apply the distributive property:
8 x 4 = (8 x 2) + (8 x 2)
Therefore, the answer is:
8 x 4 = (8 x 2) + (8 x 2)
Find the scale factor of the two prisms, the ratio of their surface areas, and the ratio of theirvolumes. List the larger values first.6 cm8 cm9 cm10 cm12 cm15 cmScale FactorSurface AreasVolumesBlank 1:Blank 2:Blank 3:Blank 4:Blank 5:Blank 6:
Answers
We will operate as follows:
*Scale factor:
We determine the scale factor using two respective sides, that is:
[tex]9x=6\Rightarrow x=\frac{6}{9}\Rightarrow x=\frac{2}{3}[/tex]So, the scale factor is 2 : 3.
*Surface area:
We determine the surface are of each prism:
[tex]S_{A1}=(9\cdot12)+2(\frac{15\cdot9}{2})+(12\cdot\sqrt[]{15^2+9^2})+(15\cdot12)\Rightarrow S_{A1}=(108)+(135)+(36\sqrt[]{34})+(180)[/tex][tex]\Rightarrow S_{A1}=423+36\sqrt[]{34}\Rightarrow S_{A1}=632.9142682\ldots[/tex][tex]S_{A2}=(6\cdot8)+2(\frac{6\cdot10}{2})+(10\cdot8)+(8\cdot\sqrt[]{6^2+10^2})\Rightarrow S_{A2}=(48)+(60)+(80)+(16\sqrt[]{34})[/tex][tex]\Rightarrow S_{A2}=188+16\sqrt[]{34}\Rightarrow S_{A2}=281.2952303\ldots[/tex]Now:
[tex](423+36\sqrt[]{34})x=188+16\sqrt[]{34}\Rightarrow x=\frac{188+16\sqrt[]{34}}{423+36\sqrt[]{34}}\Rightarrow x=\frac{4}{9}[/tex]So, the ratio of the surface areas is 4 : 9.
*Volume:
We determine the volume of each prism and proceed as before:
[tex]V_1=\frac{9\cdot15\cdot12}{2}\Rightarrow V_1=810[/tex][tex]V_2=\frac{6\cdot10\cdot8}{2}\Rightarrow V_2=240[/tex]Now:
[tex]810x=240\Rightarrow x=\frac{240}{810}\Rightarrow x=\frac{8}{27}[/tex]So, the ratio for the volumes is 8 : 27.
e inverse operations to solve the equations below. x^2+3=19
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We have the expression:
[tex]x^2+3=19\Rightarrow x^2=16[/tex][tex]\Rightarrow x=\pm4[/tex]based on the graph which equation can be used to describe the relationship between x and y?
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hello
to solve this problem, we can easily find the slope of the line
this will give us the an insight to the answer
[tex]\text{slope(m)}=\frac{y_2-y_1}{x_2-x_1}[/tex]now let's identify our points
[tex]\begin{gathered} y_2=2 \\ y_1=-4.5 \\ x_2=-13.5 \\ x_1=6 \end{gathered}[/tex][tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{2--4.5}{-13.5-6} \\ m=\frac{6.5}{-19.5} \\ m=-\frac{1}{3} \end{gathered}[/tex]the slope of the line is -1/3 and this corresponds to option B
the equation of the line is given as
[tex]y=-\frac{1}{3}x-2.5[/tex]Given triangle ABC below, if angle B=(x-60)^ and angle C=(x- 45)^ find the measure of angle x
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Given:
m∠B = (x - 60)°
m∠C = (x - 45)°
Opposite angle = x°
Let's find the measure of angle x.
To find the measure of angle x, apply the Exterior Angle Theorem which states that the exterior angle of a triangle is equal to the sum of the two opposite angles.
Thus, we have:
∠B + ∠C = x
(x - 60) + (x - 45) = x
Solve for x.
• Remove the parentheses and combine like terms:
x - 60 + x - 45 = x
x + x - 60 - 45 = x
2x - 105 = x
• Move all terms containing x to the left, then move 105 to the right
2x - x = 105
x = 105°
Therefore, the measure of angle x is 105°
ANSWER:
x = 105°
Are the triangle below congruent? If so, write a congruence statement and say why
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Yes, they ARE congruent. Even if the shape has been reflected/flipped or rotated and is the same size, the shapes will always stay congruent.
If it wasn’t congruent:
If the size has changed between shapes, it would NOT be congruent.
6)Find the solution set of the quadratic equation over the set of complex numbers.5x2 + 12x + 8 = 0A)x = −34 − i4 or −34 + i4B)x = −65 − 2i5 or −65 + 2i5C)x = −25i(11 − 2i) or −25i(11 + 2i)D)x = −16i(11 − 2i) or −16i(11 + 2i)
Answers
The given quadratic equation is expressed as
5x^2 + 12x + 8 = 0
The standard form of a quadratic equation is expressed as
ax^2 + bx + c = 0
By comparing both equations, we have
a = 5, b = 12, c = 8
We would solve for x by applying the general formula for solving quadratic equations which is expressed as
[tex]\begin{gathered} x\text{ = }\frac{-\text{ b }\pm\sqrt[]{b^2-4ac}}{2a} \\ By\text{ substituting the values, we have} \\ x\text{ = }\frac{-\text{ 12}\pm\sqrt[]{12^2-4(5\times8)}}{2\times5}\text{ } \\ x\text{ = }\frac{-\text{ 12 }\pm\sqrt[]{144\text{ - 160}}}{10}\text{ = }\frac{-\text{ 12}\pm\sqrt[]{-\text{ 16}}}{10} \\ x\text{ = }\frac{-\text{ 12}\pm4i}{10} \\ x\text{ = }\frac{-\text{ 12 + 4i}}{10}\text{ or x = }\frac{-\text{ 12 - 4i}}{10} \\ x\text{ = }\frac{-\text{ 12}}{10}\text{ + }\frac{4i}{10}\text{ or x = }\frac{-\text{ 12}}{10}\text{ - }\frac{4i}{10} \\ x\text{ = }\frac{-\text{ 6}}{5}+\text{ }\frac{2i}{5}\text{ or x = }\frac{-6}{5}-\text{ }\frac{2i}{5} \end{gathered}[/tex]What type of angle is shown on the protractor below?
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Given data:
The given angle .
The given angle AOB is an obtuse angle.
Thus, third option is correct.
What is the domain of the cubic function f(x)= 9x³ + 2x-12 ?
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GIVEN:
We are given the function below;
[tex]f(x)=9x^3+2x-12[/tex]Required;
To find the domain of the cubic function.
Step-by-step solution/explanation;
The domain of a function is the set of all input values (that is, x values) for which the function is defined.
For the function given, there is no constraint, which means the function is always true for any value of x.
Therefore,
ANSWER:
[tex]Domain=(-\infty,+\infty)[/tex]The domain is the set of all real numbers.
Option B
Solve the system using the addition method 5x-2y=32x-y=0What is the y-valueA. 3B. 6C. -3D. none of the above
Answers
First, we multiply the first equation by "2":
[tex]\begin{gathered} 2\times\lbrack5x-2y=3\rbrack \\ 10x-4y=6 \end{gathered}[/tex]Then, we multiply the second equation by "-5":
[tex]\begin{gathered} -5\times\lbrack2x-y=0\rbrack \\ -10x+5y=0 \end{gathered}[/tex]The two new equations are:
[tex]\begin{gathered} 10x-4y=6 \\ -10x+5y=0 \end{gathered}[/tex]We add both equations and solve for y. The steps are shown below:
[tex]\begin{gathered} 10x-4y=6 \\ -10x+5y=0 \\ ----------- \\ y=6 \end{gathered}[/tex]The correct answer is y = 6.
AnswerBChoose the graph that illustrates both g (x) andg (x+4)
Answers
Explanation:
If we have a function f(x) = g(x + c), we can say that f(x) is g(x) shifted c units to the left.
So, the graph of g(x + 4) will be the same graph of g(x) shifted 4 units to the left
Answer:
The only graph that has two functions and one if equal to the other shifted 4 units to the left is the following:
the paper didnt explain how to do this clearly could you take me step by step how to do this
Answers
Given data:
The given point is (2,-2).
The equation of the line is y= -2x+3.
The standard equation of the line is,
[tex]y=mx+c[/tex]Compare the given equation with the above equation.
[tex]m=-2[/tex]Two parallel lines have equal slope, the equation of the line parallel to the given line and passing through (2, -2) is,
[tex]\begin{gathered} y-(-2)=m(x-2) \\ y+2=-2(x-2) \\ y+2=-2x+4 \\ y=-2x+2 \end{gathered}[/tex]Thus, the equation of the line is y= -2x+2.
Please help!! I keep getting crazy fractions for the one for equation of a line and for the other one I have no idea how to solve. I'll be eternally grateful!
Answers
We will find the equation of the line passes through the points:
[tex](\frac{5}{8},\frac{31}{16})and(-\frac{-5}{7},\frac{13}{14})[/tex]The general neral
What is the approximate area of the shaded region? 6 5 3 a 2 1 X 0 1 2 3 4 5 6 O A. 3 units? B. 6 units c. 10 units D. 13 units
Answers
Area aof shaded region is
Difference of areas between square, and circle
Area of square is = (5-1)^2 = 16
Area of circle is = π•[(5-1)/2]^2 = π•2^2 = π•4
Shaded Area = 16 - (π•4) = 16 - 12.564 = 3.436
THEN option A , is the value most aproximate to 3.436
What is the measure of the 5x+25
Answers
As you can see:
RM+MT = RT
Where:
RM = 5x + 9
MT = 8x - 6
RT = 198
Replacing the data:
5x + 9 + 8x - 6 = 198
Add like terms:
(5x + 8x) + (9 - 6) = 198
13x + 3 = 198
Solve for x:
Subtract 3 from both sides:
13x + 3 - 3 = 198 - 3
13x = 195
Divide both sides by 13:
13x/13 = 195/13
x = 15
The sequence below shows the number of trees that a nursery plants each year.2, 8, 32, 128 ...Let an represent the current term in the sequence and an-1 represent the previous term in thesequence. Which formula could be used to determine the number of trees the nursery will plantin year n?
Answers
According to the given sequence, the formula that could be used to determine the number of trees the nursery will plant in year n is [tex]a_{n}= 4a_{n-1}[/tex]. Thus, option (A) is correct.
The given sequence of the number of trees that a nursery plants each year is -
2, 8, 32, 128, .....
[tex]a_{n}[/tex] = The current term in the sequence
[tex]a_{n-1}[/tex] = The previous term in the sequence
We have to find out the formula that could be used to determine the number of trees that the nursery will plant in the year n.
From the sequence we can see that -
8 = 2*4
32 = 8*4
128 = 32*4
So, this can be said that the current term in the sequence ([tex]a_{n}[/tex]) is 4 times the previous term in the sequence ([tex]a_{n-1}[/tex]).
=> [tex]a_{n}= 4a_{n-1}[/tex]
Thus, according to the given sequence, the formula that could be used to determine the number of trees the nursery will plant in year n is
[tex]a_{n}= 4a_{n-1}[/tex]
Thus, option (A) is correct.
To learn more about sequence visit https://brainly.com/question/21961097
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Nancy bought a pack of 10 cookies for her 3 children to share equally. How many cookies should each child get if the cookies are shared equally between the 3 children?
Answers
Given:
Total pack is 10.
Share divied in 3 children.
So each children share is:
[tex]\begin{gathered} 3\text{ total share is 10} \\ for\text{ each share}=\frac{10}{3} \\ =3.33 \end{gathered}[/tex]each children share is 3.33 cookies.
homework practice what is the 5th term of this sequence?