Answer:
3 or -3
Explanation:
Let's call the unknown number x. The square of this number is x². The product of 8 and the square of this number is 8x². Finally, it is decreased by 5, so 8x² - 5 and it is equal to 67, then the equation that represents the statement is:
8x² - 5 = 67
Now, we can solve the equation for x. Add 5 to both sides
8x² - 5 + 5 = 67 + 5
8x² = 72
Divide both sides by 8
8x²/8 = 72/8
x² = 9
Find the square root of both sides
x = √9
x = 3 or x = -3
Therefore, the number is 3 or -3
I need help with a math question. I linked it below
1) We can fill in the gaps, this way since we can write the following when we translate into mathematical language:
[tex]\begin{gathered} \frac{b}{55}+8>6 \\ \frac{b}{55}>-8+6 \\ \frac{b}{55}>-2 \\ 55\cdot\frac{b}{55}>-2\cdot55 \\ b>-110 \end{gathered}[/tex]Note that we could do it in two steps. Subtracting and then multiplying and dividing
Which tool would be best to solve this problem?Pythagorean TheoremTriangle Angle Sum TheoremTangent RatioSine RatioCosine RatioUse that tool to solve for x. Show all work on the sketchpad or on your paper.
To get the value of x,
We use triangle sum theorem:
Triangle Sum Theorem:
The sum of all angles in a triangle is equal to 180 degrees.
In the triangle
We have 90 degree, 22 degree and one x
So,
x + 90 + 22 =180
x + 112 = 180
x = 180-112
x = 68 degree
Answer: x = 68
Write a quadratic equationwith vertex (3,-6) and otherpoint (-7,14). Solve for a!
We have to find the parameter a of a quadratic equation knowing the following
• The vertex is (3,-6).
,• A random point is (-7,14).
Based on the given information, we have the following
[tex]\begin{gathered} h=3 \\ k=-6 \\ x=-7 \\ y=14 \end{gathered}[/tex]The vertex form of a quadratic equation is
[tex]y=a(x-h)^2+k[/tex]Replacing all the givens, we have
[tex]14=a(-7-3)^2-6[/tex]Now, we solve for a
[tex]\begin{gathered} 14=a(-10)^2-6 \\ 14=a(100)-6 \\ 14+6=100a \\ 100a=20 \\ a=\frac{20}{100}=\frac{1}{5} \end{gathered}[/tex]Therefore, a is equal to 1/5.find 2x:3y if x:y = 2:5
4 : 15
Explanation:[tex]\begin{gathered} \text{x : y = 2: 5} \\ \frac{x}{y}\text{ = }\frac{2}{5} \\ \\ 2x\text{ : 3y = ?} \end{gathered}[/tex][tex]\begin{gathered} 2x\colon\text{ 3y = }\frac{2x}{3y} \\ 2x\colon3y\text{ = }\frac{2}{3}\times\frac{x}{y} \end{gathered}[/tex][tex]\begin{gathered} \text{substitute for x/y in 2x:3y} \\ \frac{2}{3}\times\frac{x}{y}\text{ =}\frac{2}{3}\times\frac{2}{5} \\ =\text{ }\frac{4}{15} \\ \\ \text{Hence, 2x:3y = }\frac{4}{15} \\ or \\ 4\colon15 \end{gathered}[/tex](4xy³y⁴)(5x²y) expand and simplify
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
(4xy³y⁴)(5x²y)
Step 02:
[tex](4xy^3y^4)(5x^2y)=(4xy^7)(5x^2y)=20x^3y^8^{}[/tex]This is the solution.
[tex]20x^3y^8^{}[/tex]What's the equation of the axis of symmetry of g(x)=x^{2}+4 x+3?A) x=0B) x=-2C) x=2D) x=3
Given a quadratic equation of the form:
[tex]f(x)=ax^2+bx+c[/tex]The equation of the axis of symmetry is obtained using the formula:
[tex]x=-\frac{b}{2a}[/tex]From the given quadratic equation:
[tex]\begin{gathered} g\mleft(x\mright)=x^2+4x+3 \\ a=1 \\ b=4 \end{gathered}[/tex]Therefore, the equation of the axis of symmetry of g(x) is:
[tex]\begin{gathered} x=-\frac{4}{2\times1} \\ x=-2 \end{gathered}[/tex]The correct option is B.
Identify the following forms of factoring with the correct method of solving
Given:
There are given the equation:
[tex]90x^3-20x[/tex]Explanation:
To find the factor of the given equation, first, we need to take a common variable from the given equation:
[tex]90x^3-20x=x(90x^2-20)[/tex]Then,
[tex]\begin{gathered} 90x^3-20x=x(90x^2-20) \\ =10x(9x^2-2) \end{gathered}[/tex]Final answer:
Hence, the factor of the given equation is shown below:
[tex]\begin{equation*} 10x(9x^2-2) \end{equation*}[/tex]If y = (x/x+1)5, then dy/dx
The value of dy/dx is 5x^4 / (x + 1)^6.
What is the derivative?
A function's sensitivity to change with respect to a change in its argument is measured by the derivative of a function of a real variable.
The given function is y = (x / (x + 1))^5
Taking derivative on both sides,
dy/dx = d/dx (x / (x + 1))^5)
Using chain rule,
dy/dx = 5(x / x + 1)^4 x d/dx (x / x + 1)
Using the quotient rule of derivative,
d/dx (x / x + 1) = 1 / (x + 1)^2
So,
dy/dx = 5(x / x+1)^4 x (1 / (x + 1)^2)
dy/dx = 5x^4 / (x + 1)^6
Therefore, the derivative of the given function is, dy/dx = 5x^4 / (x + 1)^6.
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1. Alice made the conjecture below.(a + b)2 = a + b2OWhich values of a and b are not counterexamples to the conjecture?a = 1, b = 1a = 0, b = 1aa = -1, b = 1a = -1, b = 2
the expression is
(a+b)^2=a+b^2
substitute a=1 and b=1
(1+1)^2 = 1+1^2
4=2
that is not possible. so these are the values of a and b that is not counterpart example to the conjecture.
now substitute a=0, b=1
(0+1)^2 = 0+1^2
1=1
so this is true for the above expression.
now for a=-1, b=1
(-1+1)^2 = -1+1^2
0=0
this is true.
now for a=-1, b=2
(-1+2)^2 = -1+2^2
1=3
that is not possible
so a=1, b=1 and a=1,b=2 is the values that not counterpart example to the conjecture.
Choose the algebraic description that maps ΔABC onto ΔA′B′C′ in the given figure.Question 7 options:A) (x, y) → (x + 4, y + 8)B) (x, y) → (x + 8, y + 4)C) (x, y) → (x – 4, y – 8)D) (x, y) → (x + – 8, y – 4)
Step 1
Given the triangle, ABC translated to A'B'C'
Required to find the algebraic description that maps triangle ABC and A'B'C'
Step 2
The coordinates of points A, B,C are in the form ( x,y)
Hence
[tex]\begin{gathered} A\text{ has a coordinate of ( -3,-2)} \\ B\text{ has a coordinate of (-6,-5)} \\ C\text{ has a coordinate of (-1,-4)} \end{gathered}[/tex]Step 3
Find the algebraic description that maps triangle ABS TO A'B'C'
[tex]\begin{gathered} A^{\prime}\text{ has a coordinate of (5,2)} \\ B^{\prime}\text{ has a coordinate of ( 2,-1)} \\ C^{\prime}\text{ has a coordinate of ( 7, 0)} \end{gathered}[/tex]The algebraic description is found using the following;
[tex]\begin{gathered} (A^{\prime}-A^{})=(x^{\prime}-x,\text{ y'-y)} \\ OR \\ (B^{\prime}-B)=(x^{\prime}-x,\text{ y'-y)} \\ OR \\ (C^{\prime}-C)=(x^{\prime}-x,\text{ y'-y)} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} =\text{ ( 5-(-3)), (2-(-2))} \\ =(8,4) \\ \text{Hence the algebraic description from triangle ABC to A'B'C' will be } \\ =(x,y)\Rightarrow(x\text{ + 8, y+4)} \end{gathered}[/tex]Hence the answer is option B
Elsie is moving to iowa city iowa, with her three-year-old daughter. The table shows the results of a family budget estimator for iowa City for Elsie and her daughter."If Elsie earns $45,000 per year at her new job, can she stay on budget in lowa City? A. Yes, because she can easily afford $4020 per month.B. Yes, because she will not actually need all the items that the family budget estimator includes. C. No, because she will only make $3750 per month before taxes are taken out. D.No, because she will not be able to find housing as low as $853 per month?
In order to determine what is the correct statement, calculate the amount of money Elsie can spend per month, based on her earnings per year.
Divide 45,000 by 12:
45,000/12 = 3,750
You can notice that the amount of money Elsie can spend per month is lower than the total expenses shown in the table.
Hence, the correct statement is:
C. No, because she will only make $3750 per month before taxes are taken out.
Write the equation of the line when the slope is 1/5 and the y-intercept is 13.
Given:
• Slope, m = 1/5
,• y-intercept = 13
Let's write the equation of the line.
To write the equation of the line, apply the slope-intercept equation of a line:
[tex]y=mx+b[/tex]Where:
m is the slope
b is the y-intercept.
Thus, we have:
m = 1/5
b = 13
Plug in the values in the equation:
[tex]y=\frac{1}{5}x+13[/tex]Therefore, the equation of the line is:
[tex]y=\frac{1}{5}x+13[/tex]Solve the following simultaneous equation using the inverse matrix method
3x + 4y = 18
4x - y = 5
The values of x and y obtained by inverse matrix method are 2 and 3 respectively
What is an inverse matrix?An inverse of a matrix, A, is a matrix [tex] A^{-1}[/tex], that multiplies matrix A to give an identity matrix.
The inverse matrix method involves defining and making use of a coefficient matrix, A, a variable matrix, X, and a constant matrix, B, which are obtained from the system of equations as follows;
A·X = B
The system of equations is presented as follows;
3·x + 4·y = 18
4·x - y = 5
From the above system of equations, we have:
[tex]The \ coefficient \ matrix, \ A = \begin{bmatrix} 3&4 \\ 4& -1 \end{bmatrix}[/tex]
[tex]The \ variable \ matrix, \ X = \begin{bmatrix} x \\ y \end{bmatrix}[/tex]
[tex]The \ constant \ matrix, \ B = \begin{bmatrix} 18 \\ 5 \end{bmatrix}[/tex]
From the equation, A·X = B, we have;
[tex]\therefore X = \dfrac{B}{A} = A^{-1} \times B[/tex]
Where: A⁻¹ is the inverse matrix of A, which is found as follows;
[tex]If\ A = \begin{bmatrix} a&b \\ c&d \end{bmatrix}[/tex]
[tex]Then, \ A^{-1} = \dfrac{1}{a\cdot d-b\cdot c} \cdot \begin{bmatrix} d& -b \\ -c& a \end{bmatrix}[/tex]
Which gives the value of A⁻¹ obtained from the coefficient matrix, A = [tex]\begin{bmatrix} 3&4 \\ 4& -1 \end{bmatrix}[/tex] as follows;
[tex]A^{-1} = \begin{bmatrix} 3 & 4 \\ 4 & - 1 \end{bmatrix}^{ - 1} = \dfrac{1}{(3 \times - 1) - (4 \times 4)} \times \begin{bmatrix} - 1 & - 4 \\ - 4 & 3 \end{bmatrix}[/tex]
[tex]A^{-1} = \dfrac{1}{(3 \times - 1) - (4 \times 4)} \times \begin{bmatrix} - 1 & - 4 \\ - 4 & 3 \end{bmatrix} = \begin{bmatrix} \dfrac{ - 1}{ - 19} & \dfrac{ - 4}{ - 19} \\\\ \dfrac{ - 4}{ - 19} & \dfrac{3}{ - 19} \end{bmatrix}[/tex]
The variable matrix, [tex]X = A^{-1} \times B[/tex], which gives the value of the variables in the solution is therefore;
[tex]X = \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} \dfrac{ - 1}{ - 19} &\dfrac{ - 4}{ - 19} \\ \\\dfrac{ - 4}{ - 19} &\dfrac{3}{ - 19} \end{bmatrix} \times \begin{bmatrix} 18 \\ 5 \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}[/tex]
[tex]\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}[/tex]
Therefore;
x = 2 and y = 3
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Find the distance between:(4,-9) and(-8,0)Round your answer to the nearest hundredth.
The distance between 2 points (x1, y1) and (x2, y2) is calculated as:
[tex]\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]So, if we replace (x1, y1) by (4, -9) and (x2, y2) by (-8,0), we get:
[tex]\begin{gathered} \text{distance}=\sqrt{(-8-4)^2+(0-(-9))^2} \\ \text{distance}=\sqrt{(-12)^2+(9)^2} \\ \text{distance}=\sqrt{144+81} \\ \text{distance}=\sqrt{225} \\ \text{distance}=15 \end{gathered}[/tex]Answer: the distance is 15
Review: Solve for Area AND Circumference. A giant holiday cookie has a radius of 5 inches. What is the area of the cookie? What is the circumference of the cookie?
Remember that the formual for the area of a circle is:
[tex]A=\pi r^2[/tex]And the formula for the circumference is:
[tex]C=2\pi r[/tex]Using this formulas and the data given,
[tex]\begin{gathered} A=\pi(5^2)\Rightarrow A=78.54 \\ C=2\pi(5)\Rightarrow A=31.42 \end{gathered}[/tex]The cookie has an area of 78.54 square inches and a circumference of 31.42 inches
Find the length of AB given that DB is a median of the triangle AC is 46
ANSWER:
The value of AB is 23
STEP-BY-STEP EXPLANATION:
We know that AB is part of AC, and that DB cuts into two equal parts (half) since it is a median, therefore the value of AB would be
[tex]\begin{gathered} AB=\frac{AC}{2} \\ AB=\frac{46}{2} \\ AB=23 \end{gathered}[/tex]A woman who has recovered from a serious illness begins a diet regimen designed to get her back to a healthy weight. She currently weighs 106 pounds. She hopes each week to multiply her weight by 1.04 each week.
The required exponential function would be W = 106 × 1.04ⁿ for the weight after n weeks.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
The given starting weight for the diet program is 106 pounds. Because the weight is expected to be multiplied by 1.04 pounds each week, the weight will develop exponentially with an initial value of 106 pounds and a growth factor of 1.04 pounds. Then, for the weight after weeks, the exponential function is given by,
W = W(n) = Pb'
Here P = 106 and b = 1.04
Hence the required formula is,
⇒ W = 106 × 1.04ⁿ
Thus, the required exponential function would be W = 106 × 1.04ⁿ for the weight after n weeks.
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The question seems to be incomplete the correct question would be
A woman who has recovered from a serious illness begins a diet regimen designed to get her back to a healthy weight. She currently weighs 106 pounds. She hopes each week to multiply her weight by 1.04 each week. Then, find the exponential function for the weight after weeks.
Can you help me answer part A and part B?
Part A.
Given:
P = (5, 4), Q = (7, 3), R = (8, 6), S = (4, 1)
Let's find the component of the vector PQ + 5RS.
To find the component of the vector, we have:
[tex]=\lparen Q_1-P_1,Q_2-P_2)=<7-5,3-4>[/tex]For vector RS, we have:
[tex]=\lparen S_1-R_1,S_2-R_2)=<4-8,1-6>[/tex]Hence, to find the vector PQ+5RS, we have:
[tex]\begin{gathered} =<7-5,3-4>+5<4-8,1-6> \\ \\ =\left(2,-1\right)+5\left(-4,-5\right) \\ \\ =\left(2,-1\right)+\left(5\ast-4,5\ast-5\right) \\ \\ =\left(2,-1\right)+\left(-20,-25\right) \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} =<2-20,-1-25> \\ \\ =<-18,-26> \end{gathered}[/tex]Therefoee, the component of the vector PQ+5RS is:
<-18, -26>
• Part B.
Let's find the magnitude of the vector PQ+5RS.
To find the magnitude, apply the formula:
[tex]m=\sqrt{\left(x^2+y^2\right?}[/tex]Thus, we have:
[tex]\begin{gathered} m=\sqrt{\left(-18^2+-26^2\right?} \\ \\ m=\sqrt{324+676} \\ \\ m=\sqrt{1000} \\ \\ m=\sqrt{10\ast10^2} \\ \\ m=10\sqrt{10} \end{gathered}[/tex]Therefore, the magnitude of the vector is:
[tex]10\sqrt{10}[/tex]ANSWER:
Part A. <-18, -26>
Part B. 10√10
The question is which of these statements are true about radicals exponents and rational exponents
We have the following:
I)
[tex]\sqrt[n]{a}=a^{\frac{1}{n}}[/tex]It´s true
II)
[tex]a^{\frac{1}{2}}=\sqrt[]{a}[/tex]It´s true
III)
[tex]\begin{gathered} a^{\frac{p}{q}}=\sqrt[p]{a^q}=(\sqrt[p]{a})^q \\ (\sqrt[p]{a})^q=(a^{\frac{1}{p}})^q=a^{\frac{q}{p}} \end{gathered}[/tex]It´s false
IV)
[tex]\sqrt[]{a}[/tex]It´s true
V)
[tex]\begin{gathered} a^{\frac{1}{n}}=\sqrt[]{a^n} \\ \sqrt[]{a^n}=a^{\frac{n}{2}} \end{gathered}[/tex]It´s false
What does the slower car travel at Then what does the faster car travel at
Given that two cars are 188 miles apart, travelling at different speeds, meet after two hours.
To Determine: The speed of both cars if the faster car is 8 miles per hour faster than the slower car
Solution:
Let the slower car has a speed of S₁ and the faster car has a speed of S₂. If the faster speed is 8 miles per hour faster than the slower car, then,
[tex]S_2=8+S_1====\text{equation 1}[/tex]It should be noted that the distance traveled is the product of speed and time. Then, the total distance traveled by each of the cars before they met after 2 hours would be
[tex]\begin{gathered} \text{distance}=\text{speed }\times time \\ \text{Distance traveled by the faster car after 2 hours is} \\ =S_2\times2=2S_2 \\ \text{Distance traveled by the slower car after 2 hours is} \\ =S_1\times2=2S_1 \end{gathered}[/tex]It was given that the distance between the faster and the slower cars is 188 miles. Then, the total distance traveled by the two cars when they meet is 188 miles.
Therefore:
[tex]\begin{gathered} \text{Total distance traveled by the two cars is} \\ 2S_1+2S_2=188====\text{equation 2} \end{gathered}[/tex]Combining equation 1 and equation 2
[tex]\begin{gathered} S_2=8+S_1====\text{equation 1} \\ 2S_1+2S_2=188====\text{equation 2} \end{gathered}[/tex]Substitute equation 1 into equation 2
[tex]\begin{gathered} 2S_1+2(8+S_1)=188 \\ 2S_1+16+2S_1=188 \\ 2S_1+2S_1=188-16 \\ 4S_1=172 \end{gathered}[/tex]Divide through by 4
[tex]\begin{gathered} \frac{4S_1}{4}=\frac{172}{4} \\ S_1=43 \end{gathered}[/tex]Substitute S₁ in equation 1
[tex]\begin{gathered} S_2=8+S_1 \\ S_2=8+43 \\ S_2=51 \end{gathered}[/tex]Hence,
The slower car travels at 43 miles per hour(mph), and
The faster car travels as 51 miles per hour(mph)
Evaluate 2(x - 4) + 3x - x^2 for x = 2.O A. -6O B. -2O C. 6O D. 2
C. 6
Explanation
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.so
Step 1
given
[tex]2(x-4)+3x-x^2[/tex]a)let
[tex]x=2[/tex]b) now, replace and calculate
[tex]\begin{gathered} 2(x-4)+3x-x^2 \\ 2(2-4)+3(2)-(2^2) \\ 2(-2)+6-4 \\ -4+6-4 \\ -4+6-4=6 \end{gathered}[/tex]therefore, the answer is
C. 6
I hope this helps you
Julie wants to purchase a jacket that costs $125. So far she has saved $42 and plans tosave an additional $25 per week. She gets paid every Friday, so she only gets money toput aside once a week. How many weeks, x, will it take for her to save at least $125?
cost of the jacket = $125
money saved = $42
extra savings = $25/week
Ok
125 = 42 + 25w
w = number of weeks
Solve for w
125 - 42 = 25w
83 = 25w
w = 83/25
w = 3.3
She needs to save at least 3.3 weeks
Select the correct answer from the drop-down menu.Find the polynomial,{4'" is the solution set of
Let P(x) be the polynomial such that the given set is its solution set.
Now notice that:
[tex]\begin{gathered} x=-\frac{1}{3}\Rightarrow x+\frac{1}{3}=0\Rightarrow3x+1=0, \\ x=4\Rightarrow x-4=0. \end{gathered}[/tex]Therefore (x-4) and (3x+1) divide to P(x), then:
[tex]\begin{gathered} Exists\text{ k such that:} \\ P(x)=k(x-4)(3x+1). \end{gathered}[/tex]Simplifying the above result we get:
[tex]P(x)=k(3x^2-11x-4).[/tex]Setting k=1 we get that:
[tex]P(x)=3x^2-11x-4.[/tex]Answer: Second option.
what is the area if one of the triangular side of the figure?
Compound Shape
The shape of the figure attached consists on four triangles and one square.
The base of each triangle is B=12 cm and the height is H=10 cm, thus the area is:
[tex]A_t=\frac{BH}{2}[/tex]Calculating:
[tex]A_t=\frac{12\cdot10}{2}=60[/tex]The area of each triangle is 60 square cm.
Now for the square of a side length of L=12.
The area of a square of side length a, is:
[tex]A_s=a^2[/tex]Calculate the area of the square:
[tex]A_s=12^2=144[/tex]The total surface area is:
A = 60*4 + 144
A= 240 + 144
A = 384 square cm
Which best represents the number of square centimeters in a square foot?A 366 square centimeters B 144 square centimeters C 930 square centimeters D 61 square centimeters
Answer:
C. 930 square centimeters
Explanation:
First, recall the standard conversion between cm and ft.
[tex]1\text{ ft}=30.48\operatorname{cm}[/tex]Therefore:
[tex]\begin{gathered} (1\times1)ft^2=(30.48\times30.48)cm^2 \\ =929.03\operatorname{cm}^2 \\ \approx930\text{ square cm} \end{gathered}[/tex]The correct choice is C.
Four points are labeled on the number line. M K L zo 0.5 1 Which point best represents 3? F. Point K G. H. Point 2 Point M Point N J.
The point that best represents 1/3 is point M .
The number line ranges from 0 to 0.5 with 10 divi
In a probability experiment, Craig rolled a six-sided die 62 times. The die landed on a number greater than three 36 times. What is the ratio of rolls greater than three to rolls less than or equal to three?
Answer:
31/55
Step-by-step explanation:
A bus travels 8.4 miles eastand then 14.7 miles north.What is the angle of the bus'resultant vector?Hint: Draw a vector diagram.O[?]
A bus travels 8.4 miles east and then 14.7 miles north.
What is the angle of the bus resultant vector?
see the figure below to better understand the problem
The angle of the bus resultant vector R is equal to
tan(x)=14.7/8.4
mm
In the diagram below, BS and ER intersect as show. Determine the measure of
Find the value of 4v-8 given that 11v-8 = 3.Simplify your answer as much as possible.
Given that 11v - 8 = 3
add 8 to both sides
11v = 3 + 8
11v = 11
Divide both sides by 11
v = 1
to simplify 4v - 8
= 4 (1) - 8
= 4 - 8
= -4
