Answer: z = 7 or z=-5
Step-by-step explanation:
First you need to factor the polynomial.
To factor [tex]z^{2}[/tex] - 2z -35 You will need to find two numbers that their product is -35 and their sum is -2 and the numbers -7 and 5 works out.
Rewrite the polynomial as,
[tex]z^{2}[/tex] - 7z + 5z - 35 = 0 factor the left by grouping
([tex]z^{2}[/tex] -7z) (5z -35) = 0
z(z -7) 5(z - 7) = 0 Factor out z-7
(z-7)(z+5) = 0 Now apply the zero product by setting each of them equal 0.
z-7= 0 or z+5=0
+7 +7 -5 -5
z = 7 or z= -5
(4x-x^3+3)-(2x^2-3x^3+1)
Answer:
2 (x^3 - x^2 + 2 x + 1)
Step-by-step explanation:
Simplify the following:
-(2 x^2 - 3 x^3 + 1) - x^3 + 4 x + 3
Factor -1 out of -3 x^3 + 2 x^2 + 1:
--(3 x^3 - 2 x^2 - 1) - x^3 + 4 x + 3
(-1)^2 = 1:
3 x^3 - 2 x^2 - 1 - x^3 + 4 x + 3
Grouping like terms, 3 x^3 - x^3 - 2 x^2 + 4 x - 1 + 3 = (-x^3 + 3 x^3) - 2 x^2 + 4 x + (3 - 1):
(-x^3 + 3 x^3) - 2 x^2 + 4 x + (3 - 1)
3 x^3 - x^3 = 2 x^3:
2 x^3 - 2 x^2 + 4 x + (3 - 1)
3 - 1 = 2:
2 x^3 - 2 x^2 + 4 x + 2
Factor 2 out of 2 x^3 - 2 x^2 + 4 x + 2:
Answer: 2 (x^3 - x^2 + 2 x + 1)
Answer:
Step-by-step explanation:
4x - x^3 + 3 - 2x^2 + 3x^3 - 1
2x^3 - 2x^2 + 4x + 2 is the solution
Let F(x, y, z) = 3xi+ 2yj and let σ be the cube with opposite corners at (0, 0, 0) and (5, 5, 5), oriented outwards. Find the flux of the flow field F across σ.
Use the divergence theorem,
[tex]\displaystyle\iint_{\partial\sigma}\mathbf F(x,y,z)\cdot\mathrm d\mathbf S=\iiint_\sigma\mathrm{div}\mathbf F(x,y,z)\,\mathrm dV[/tex]
We have
[tex]\mathrm{div}\mathbf F(x,y,z)=\dfrac{\partial(3x)}{\partial x}+\dfrac{\partial(2y)}{\partial y}+\dfrac{\partial0}{\partial z}=5[/tex]
so that the flux across [tex]\sigma[/tex] is equal to 5 times the volume of the cube. The cube itself has edge length 5, so its volume is [tex]5^3=125[/tex], making the flux [tex]5^4=\boxed{625}[/tex].
Find the scale ratio for the map described below 1 mm (map) = 50 km (actual) The scale ratio is 1 to ?
Answer:
1 : 50,000,000
Step-by-step explanation:
The given scale (with units) is ...
1 mm : 50 km
If we convert both units to meters, so we can give the scale as a pure number, then we have ...
10^-3 m : 5×10^4 m = 1 : 5×10^7 = 1 : 50,000,000
Simplify 3x + 3 + 2.
3x + 5
5x + 3
8x
Answer:
3x + 5
Step-by-step explanation:
We are doing variables and simplifying.
You have two types of numbers here, you have a coefficient, and you have regular numbers. Now do keep in mind that you can never add a regular number to a coefficient. So the only thing in this problem you will add is 3 and 2. Because 3x is different
3x + (3 + 2)
3x + 5
The simplified form of the expression is 3x + 5.
Option A is the correct answer.
We have,
Expression:
3x + 3 + 2
Add like terms.
3x + (3 + 2)
3x + 5
This is the simplest simplified form of the expression.
Thus,
The simplified form of the expression is 3x + 5.
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A local gym has 2 types of cardio machines, treadmills and elliptical machines. There are 38 cardio machines in all. There are 10 more treadmills than there are elliptical machines. How many elliptical machines are at the gym? 9 elliptical machines 14 elliptical machines 24 elliptical machines 28 elliptical machines
Answer:
14 elliptical machines
Step-by-step explanation:
t = # of treadmills
e = # of elliptical machines
t + e = 38
t = e + 10
Substitute:
e + 10 + e = 38
2e = 28
e = 14
Find the values for k so that the intersection of x=2k and 3x+2y=12 lies in the first quadrant.
Answer:
Values of k can be 0, 1, or 2 such that intersection of the given lines lie in the 1st quadrant.
Step-by-step explanation:
Given two lines:
[tex]x=2k[/tex] and
[tex]3x+2y=12[/tex]
To find:
Values of 'k' such that the intersection of given two lines lie in the first quadrant.
Solution:
In 1st quadrant, the values of [tex]x[/tex] and [tex]y[/tex] both are positive.
So, let us find out intersection of the two lines.
Intersection of the two lines can be found by solving the two equations for the values of [tex]x[/tex] and [tex]y[/tex].
Given that [tex]x=2k[/tex] to be in the first quadrant, the value of k must be positive.
Let us put [tex]x=2k[/tex] in the equation [tex]3x+2y=12[/tex] to find the intersection point.
[tex]3 \times 2k + 2y=12\\\Rightarrow 6k+2y=12\\\Rightarrow 2y=12-6k\\\Rightarrow \bold{y=6-3k}[/tex]
For y to be positive:
[tex]6 - 3k \geq 0\\\Rightarrow 3k \leq 6\\\Rightarrow k \leq 2[/tex]
So, values of k can be 0, 1, or 2 such that intersection of the given lines lie in the 1st quadrant.
Find an equation of a line with slope -7 and y-intercept 2. y=
Answer:
y = -7x + 2
Step-by-step explanation:
Use the slope-intercept form y = mx + b.
Substitute -7 for m, 0 for x and 2 for y. Then
2 = (-7)(0) + b, so b must be 2.
The desired equation is y = -7x + 2.
PLEASE HELP (05.04 LC) The image below is a triangle drawn inside a circle with center O: (5 points) Which of the following expressions shows the area, in square inches, of the circle? (π = 3.14) Select one: a. 3.14 ⋅ 2 b. 3.14 ⋅ 3 c. 3.14 ⋅ 22 d. 2 ⋅ 3.14 ⋅ 22
Answer:
The area of the circle is:
[tex]3.14\, *\,2^2 \,\,in^2[/tex]
Step-by-step explanation:
If the diameter of the circle is 4 inches, then its radius is half of that (that is 2 inches), and we can use the formula for the area of a circle:
[tex]Area=\pi\,R^2\\Area= \pi\,(2\,\,in)^2\\Area=3.14\,(4)\,in^2[/tex]
The area of the circle is : [tex]3.14\, *\,2^2 \,\,in^2[/tex]
What is the sum of the three solutions? (find the values for x, y, and z, then add the answers)
2x + 3y − z = 5
x − 3y + 2z = −6
3x + y − 4z = −8
Answer:
Once we got
[tex]x=-1[/tex]
[tex]y=3[/tex]
[tex]z=2[/tex]
[tex]\boxed{\text{The sum is 4}}[/tex]
Step-by-step explanation:
Given the linear system:
[tex]\begin{cases} 2x + 3y-z = 5 \\ x- 3y + 2z = -6 \\ 3x + y - 4z = -8 \end{cases}[/tex]
Let's solve it using matrices. I will use Cramer's rule
[tex]M=\left[\begin{array}{ccc}2&3&-1\\1&-3&2\\3&1&-4\end{array}\right][/tex]
Considering determinant as D.
[tex]D=\begin{vmatrix}2&3&-1\\1&-3&2\\3&1&-4\\\end{vmatrix}=40[/tex]
[tex]M_x = \left[\begin{array}{ccc}5&3&-1\\-6&-3&2\\-8&1&-4\end{array}\right] \implies D_x = \begin{vmatrix}5&3&-1\\-6&-3&2\\-8&1&-4\\\end{vmatrix}=-40[/tex]
[tex]M_y = \left[\begin{array}{ccc}2&5&-1\\1&-6&2\\3&-8&-4\end{array}\right] \implies D_y = \begin{vmatrix}2&5&-1\\1&-6&2\\3&-8&-4\\\end{vmatrix}=120[/tex]
[tex]M_z = \left[\begin{array}{ccc}2&3&5\\1&-3&-6\\3&1&-8\end{array}\right] \implies D_z= \begin{vmatrix}2&3&5\\1&-3&-6\\3&1&-8\\\end{vmatrix}=80[/tex]
So, we have
[tex]$x=\frac{D_x}{D} =\frac{-40}{40}=-1 $[/tex]
[tex]$y=\frac{D_y}{D} =\frac{120}{40}=3$[/tex]
[tex]$z=\frac{D_z}{D} =\frac{80}{40}=2 $[/tex]
Find sin 2x, cos 2x, and tan 2x from the given information. sin x = -3/5, x in quadrant 3.
Answer:
[tex]\sin 2x = \frac{24}{25}[/tex] , [tex]\cos 2x = \frac{7}{25}[/tex], [tex]\tan 2x = \frac{24}{7}[/tex]
Step-by-step explanation:
The sine, cosine and tangent of a double angle are given by the following trigonometric identities:
[tex]\sin 2x = 2\cdot \sin x \cdot \cos x[/tex]
[tex]\cos 2x = \cos^{2}x -\sin^{2}x[/tex]
[tex]\tan 2x = \frac{2\cdot \tan x}{1-\tan^{2}x}[/tex]
According to the definition of sine function, the ratio is represented by:
[tex]\sin x = \frac{s}{r}[/tex]
Where:
[tex]s[/tex] - Opposite leg, dimensionless.
[tex]r[/tex] - Hypotenuse, dimensionless.
Since [tex]x[/tex], measured in sexagesimal degrees, is in third quadrant, the following relation is known:
[tex]s < 0[/tex] and [tex]y < 0[/tex].
Where [tex]r[/tex] is represented by the Pythagorean identity:
[tex]r = \sqrt{s^{2}+y^{2}}[/tex]
The magnitude of [tex]y[/tex] is found by means the Pythagorean expression:
[tex]r^{2} = s^{2}+y^{2}[/tex]
[tex]y^{2} = r^{2}-s^{2}[/tex]
[tex]y = \sqrt{r^{2}-s^{2}}[/tex]
Where [tex]y[/tex] is the adjacent leg, dimensionless.
If [tex]s = -3[/tex] and [tex]r = 5[/tex], the value of [tex]y[/tex] is:
[tex]y = \sqrt{(5^{2})-(-3)^{2}}[/tex]
[tex]y = -4[/tex]
Then, the definitions for cosine and tangent of x are, respectively:
[tex]\cos x = \frac{y}{r}[/tex]
[tex]\tan x = \frac{s}{y}[/tex]
If [tex]s = -3[/tex], [tex]y = -4[/tex] and [tex]r = 5[/tex], the values for each identity are, respectively:
[tex]\cos x = -\frac{4}{5}[/tex] and [tex]\tan x = \frac{3}{4}[/tex].
Now, the value for each double angle identity are obtained below:
[tex]\sin 2x = 2\cdot \left(-\frac{3}{5} \right)\cdot \left(-\frac{4}{5} \right)[/tex]
[tex]\sin 2x = \frac{24}{25}[/tex]
[tex]\cos 2x = \left(-\frac{4}{5} \right)^{2}-\left(-\frac{3}{5} \right)^{2}[/tex]
[tex]\cos 2x = \frac{7}{25}[/tex]
[tex]\tan 2x = \frac{2\cdot \left(\frac{3}{4} \right)}{1-\left(\frac{3}{4} \right)^{2}}[/tex]
[tex]\tan 2x = \frac{24}{7}[/tex]
WY bisects UV at Y. If UV=x-7 and YV = 3x-29, find UV
Answer:
3.2 units
Step-by-step explanation:
Given that:
WY bisects UV at Y.
[tex]UV=x-7[/tex] and
[tex]YV = 3x-29[/tex],
To find: UV = ?
Solution:
First of all, let us draw the diagram of the given dimensions and bisector line WY of UV.
As UV is bisected i.e. divided in two equal parts at Y by the line WY
Therefore, UY = YV
UV = UY+YV
OR
UV = 2 YV
Now, let us put the given values to solve for [tex]x[/tex]:
[tex]x-7=2 \times (3x-29)\\\Rightarrow x-7=2 \times 3x-2 \times 29\\\Rightarrow x-7=6x-58\\\Rightarrow 6x-x=58-7\\\Rightarrow 5x=51\\\Rightarrow \bold{x =10.2 }[/tex]
Now, we are given that:
[tex]UV=x-7[/tex]
Putting value of [tex]x[/tex] as solved in above step to get the value of UV:
[tex]UV=10.2-7\\\Rightarrow \bold{UV=3.2}[/tex]
So, answer is UV = 3.2 units
Two angles of a triangle measure 12º and 40°.
What is the measure of the third angle of the triangle?
A. 38°
B. 48°
C. 128°
D. 308
Answer:
12+40= 52
180-52=128
Step-by-step explanation:
Angles in a triangle add up to 180
so if two sides are given , they must be added and subtracted from 180.
which gives us 180-52=128
Answer:
the angle is 128°
the right answer is C
Step-by-step explanation:
the angles of a triangle are always 180°
thus
the angle of the the triangle = 180° - (12°+40°)
= 180- 52° = 128°
Two example that show two positive rational number is greater then either factor True?
Answer:
true
Step-by-step explanation:
Simplify (1-√3) (1÷3+√3) leaving your answer in the form p+q√3
Answer:
[tex]1-\dfrac{2}{3}\sqrt{3}[/tex]
Step-by-step explanation:
Maybe you want to simplify ...
[tex](1-\sqrt{3})\dfrac{1}{3+\sqrt{3}}[/tex]
Multiply numerator and denominator by the 'conjugate' of the denominator:
[tex](1-\sqrt{3})\dfrac{1}{3+\sqrt{3}}\cdot\dfrac{3-\sqrt{3}}{3-\sqrt{3}}=\dfrac{(1-\sqrt{3})(3-\sqrt{3})}{9-3}=\dfrac{3-4\sqrt{3}+3}{6}\\\\\boxed{1-\dfrac{2}{3}\sqrt{3}}[/tex]
the question is below, 20 is not the correct answer
Answer:
20
Step-by-step explanation:
Given:
m∠JKL = 3x + 5As per the picture:
m∠JKL = m∠JKM + m∠MKL = 45 + xComparing the two equations above:
3x+5 = 45 + x3x - x = 45 - 52x = 40x = 40/2x = 20x = 20 is the correct answer for this question
Otherwise something is wrong with the question.
what is 1/4 divided by 3/8
Answer: 2/3
Step-by-step explanation:
Answer: 2/3
Step-by-step explanation:It can sometimes be difficult to divide fractions, such as 1/4 divided by 3/8. When we divide two fractions, such as 1/4 ÷ 3/8, we flip the second fraction and then we simply multiply the numerators with each other and the denominator with each other.
The radius of a sphere-shaped balloon increases at a rate of 2 centimeters (cm) per second. If the surface area of
the completely inflated balloon is 784 cm², how long will it take for the balloon to fully inflate?
Use SA=4r2
7 seconds
10 seconds
49 seconds
196 seconds
Answer:
7 seconds
Step-by-step explanation:
The radius of a sphere-shaped balloon increases at a rate of 2 centimeters (cm) per second.
surface area of the completely inflated balloon is 784 cm²
SA=4r²
784= 4r²
784/4= r²
196 = r²
14cm = r
Yhe radius of the complete inflated balloon is 14cm
If the ball inflate at the rate of 2 cm per seconds
Then it took 14/2 = 7 seconds to inflate fully
The advertised weight of a Snickers Fun Size bar is 17 grams. What proportion of candy bars in this sample weigh less than advertised
Answer:
0.412
Step-by-step explanation:
Given the stem plot figure out which ones are below 17g.
So: 7g / 17g = 0.412 which is the proportion
Mitchell travels from the US to Canada, where he exchanges 150 US dollars for Canadian dollars. He then spends 20 Canadian dollars, returns to the US, and exchanges the remaining money back to US dollars. How many US dollars does Mitchell have remaining? 129.46 130.00 130.66 134.59
Answer: $130.66
Step-by-step explanation:
Answer:
130.66
Step-by-step explanation:
i took the asignment
Translate into an equation: y is 37% of x.
Answer:
soln,
y=37/100×x
or, 100y=37x.....is the answer
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The equation of y is 37% of x is
y = 0.37x
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example:
2 + 3x + 4y = 7 is an expression.
2 + 3 - 4 is an expression.
2x4 + 4x = 4 is an expression.
We have,
y is 37% of x.
This can be written as,
y = 37/100 of x
y = 0.37x
Thus,
The equation of y is 37% of x is
y = 0.37x
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If each square in the grid has a side length of 8 mm, what is the width of the rectangle? Do not include units (mm) in your answer. Type your answer below as a number (example: 5, 3.1, 4 1/2, or 3/2)
Answer:
See Explanation
Step-by-step explanation:
The question required attachment; however, follow the following steps to answer your question.
See Attachment
Considering the horizontal plane of the gird.
Count the number of the squares in that plane;
This gives 4
Multiply 4 by length of each side of a square;
[tex]Perimeter = 8mm * 4[/tex]
[tex]Perimeter = 32mm[/tex]
Algebraic expressions
Evaluate
The dog is 4 years older than the cat. The cat is 7 years old. How old is the dog?
Answer:
11 years old
Step-by-step explanation:
Because the dog is 4 years older, add 7+4
Dajia bought 5 shirts online, and in turn receives a 15% discount. She
must pay an additional 4.99 for shipping. Write an algebraic expression
to represent the total cost of the shirts with the discount, if x represents
the cost of each shirt.
Emma jogs 2 miles along the beach in 1 3 of an hour. If she travels at a constant rate, how far will she jog in an hour? 1. Use the known information to write a rate.
Answer:oufonsrgonsrgnrsosgnsogwo0on93rhskgv oaoef
Step-by-step explanation:
iaeiuaefiaef ebf efa fcade emma jog 123e oefofoinsfnfsaefosefnhsfnalnfaogh
Determine if the following table represents a quadratic function. X 1 2 3 4 5 Y 13 22 37 58 85
Answer:
Yes, the table represents quadratic function.
[tex]Y = 3X^2+10[/tex]
Step-by-step explanation:
Given that table of values:
[tex]\begin{center}\begin{tabular}{ c c}X & Y \\ 1 & 13 \\ 2 & 22 \\ 3 & 37 \\ 4 & 58 \\ 5 & 85 \\\end{tabular}\end{center}[/tex]
To find:
Whether the given table represents a quadratic?
Solution:
First of all, let us plot the given values on the coordinate xy plane.
Kindly refer to the attached image for the graph of given values.
The graph seems parabolic in nature which is the graph of a quadratic equation.
Now, let us try to find the equation from the given set of values from hit and trial.
Let Quadratic equation be:
[tex]y=ax^{2} +b[/tex]
If the coefficient a = 1
[tex]f(1) = 13 = 1^2+12[/tex]
[tex]f(2) = 22 = 2^2+18[/tex]
[tex]f(3) = 37= 3^2+28[/tex]
[tex]f(4) = 58 = 4^2+42[/tex]
[tex]f(5) = 85 = 5^2+60[/tex]
value of b is not same in each case.
Now, let us try coefficient a = 3
[tex]f(1) = 13 = 3 \times 1^2+10[/tex]
[tex]f(2) = 22 = 3\times 2^2+10[/tex]
[tex]f(3) = 37= 3\times 3^2+10[/tex]
[tex]f(4) = 58 = 3\times 4^2+10[/tex]
[tex]f(5) = 85 =3\times 5^2+10[/tex]
Value of b = 10
So, we can clearly say that the given table represents a quadratic equation.
and the quadratic equation is:
[tex]Y = 3X^2+10[/tex]
Solve the following
(q+9)/5 +8Q = 11 - Q
Answer:
mark it as brainlist plzz
The within-subjects F is the non-independent groups equivalent of the one-way ANOVA. True or False?
Answer: True.
Step-by-step explanation:
The one-way analysis of variance usually (abbreviated as one-way ANOVA). is a method that is used to compare the means of two or more samples ( by make use of the F distribution). This method only applies to numerical response data, the "Y", usually one variable, and numerical or (usually) categorical input data, the "X", always one variable, hence the reason it’s know as "one-way" beca it takes it account one variae at a time.
Graph y=-1/3x+5. Plsss help hurry
PLEASE HELP ME, I DON'T UNDERSTAND THIS! :(
Hello, please consider the following.
x is obviously different from 0 and then, dividing by x is legit.
For the first 105 miles the speed is x, so the time spent is
[tex]\dfrac{105}{x}[/tex]
For the second part, the speed is 1.4 x, so the time spent is
[tex]\dfrac{105}{1.4x}=\dfrac{75}{x}[/tex]
In total, the time she spent driving is
[tex]\dfrac{105}{x}+\dfrac{75}{x}\large \boxed{=\dfrac{180}{x}}[/tex]
Thank you.
What is “35 is 60% of what number?”
Answer:
58.33
Step-by-step explanation:
35 isn't exactly 60% of an number but by rounding you will get 58.33