In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
8x - 3x + 4x = -36
x = ?
Step 02:
We must apply the algebraic rules to find the solution.
8x - 3x + 4x = -36
12x - 3x = - 36
9x = - 36
x = - 36 / 9
x = - 4
The answer is:
x = - 4
Find the length of the given side for the congruent triangles ABC and A'B'C'.
The length of side AC
The length of side AC is ____.
ABC and A'B'C' are congruent triangle. The length of the side AC is 5.31cm.
congruent triangle - Congruent triangles are those whose two sides and included angle match those of another triangle's matching sides and angle.
rules -
Each of the three sides is equal.A comparable side and two angles share the same properties.The angle between the two sides is also equal, and there are two equal sides.(given)
AB = 17 cm
BC = 34 cm
Using the trigonometric functions
cos x = B/H
cos(81°) = B/34
B = Cos(81°) x 34
B = 5.31.
ABC and A'B'C' are congruent triangle. The length of the side AC is 5.31cm.
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Find the coordinates of the center, vertices, covertices, foci, length of transverse and conjugate axis and the equation of the asymptotes. Then graph the hyperbola.
The given equation is,
[tex]\frac{x^2}{36}-\frac{y^2}{16}=1\text{ ---(1)}[/tex]It can be rewritten as,
[tex]\frac{x^2}{6^2}-\frac{y^2}{4^2}=1\text{ ---(2)}[/tex]The above equation is similar to the standard equation of left-right facing a hyperbola given by,
When you start your career, you decide to set aside $500 every quarter to deposit into an investment account. The investment firm claims that historically their accounts have earned an annual interest rate of 10.0% compounded quarterly. Assuming this to be true, how much money will your account be worth after 25 years of depositing and investing? Round your answer to the nearest cent. Do not include labels or units. Just enter the numerical value.
Given:
The principal amount = $500
Interest rate = 10% quarterly
Required:
Find the deposing amount after 25 years.
Explanation:
The amount formula when the interest is compounded quarterly is given as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where r = interest rate
t = time period
n = The number of compounded times
The amount after 25 years is:
[tex]\begin{gathered} A=500(1+\frac{0.1}{4})^{4\times25} \\ A=500(1+.025)^{100} \\ A=500(1.025)^{100} \end{gathered}[/tex][tex]\begin{gathered} A=500\times11.81371 \\ A=5906.8581 \end{gathered}[/tex]Final Answer:
The amount after 25 years will be &5906.85
Find the percent change to the nearest percent for the function following
f(x) = 3(1 -.2)^-x
The percentage change of the function given in the task content as required is; 20%.
Percent change in exponential functions.It follows from the task content that the percentage change of the function is to be determined.
The percentage change in exponential functions is represented by the change factor, an expression on which the exponent is applied.
On this note, since the function given is an exponential function in which case, the change factor is; (1 - .2).
It consequently follows that the change implies a 20% decrease. This follows from the fact that 20% is equivalent to; 0.2.
Ultimately, the percentage change of the function is; 20%.
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How does a graph of quadratic function (f(x) = ax2 + bx + c) vary when the a,b, c changes from -1 to +1?
When a, b, c changes from -1 to +1, the parabolas opens and widens.
Given,
The quadratic function, f(x) = ax² + bx + c
We have to find the change in graph when a, b, c changes from -1 to 1.
First lets consider:
a and b as constants and c is varying.
That is,
x² + x + c
Then, the parabola will move up and down.
Now, lets consider:
a and c as constants and b is varying.
That is,
x² + bx + 1
Then, the vertex will move but all parabolas passes through the points (0, c)
Now, we can move to the question.
What happens to graph when +1 changes to -1.
So,
b and c should keep constant and a is varying.
Then,
ax² + x + 1
Here, the parabolas opens and widens.
That is,
When a, b, c changes from -1 to +1, the parabolas opens and widens.
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Four friends had dinner at a restaurant. The bill was $45.40, and they added a 20% tip. The 4 friends shared the total cost equally. How much money did each person pay?
Answer:
$13.62
Step-by-step explanation:
To find the tip of 20%, multiply 45.40 by 0.20, and you get 54.48.
Now, since there are 4 friends, divide the amount by 4.
54.48/4=13.62
So each person would pay $13.62.
Hope this helps! :D
If 10 = 1+4, then 1+9= 10substitution property symmetric property transitive propertyreflexive property8*1=8Multiplicative InverseMultiplicative IdentityMultiplicative Property of ZeroAdditive Identity Property
Reflexive Property
In Math, especially in geometry, but also in other fiels.
What we have here is the Reflexive Property, that states that
If a= b+c then b+c=a
Multiplicative Identity
The multiplicative identity is the number 1, so every number times 1 is equal to itself and this property is called multiplicative identity.
Write a formula for the function obtained when the graph is shifted as described. When typing exponents use the carrot key ^ by pressing SHIFT and 6. For example x squared can be typed as x^2. Do not put spaces between your characters and remember to use parentheses in the appropriate places!f(x)=x^2 is shifted up 1 unit and to the left 2 units.The new equations f(x)=Answer
Given the function f(x) defined as:
[tex]f(x)=x^2[/tex]We need to obtain the graph after performing two shifts: 1 unit up and 2 units left. For the first shift, we do the transformation:
[tex]f(x)\rightarrow f(x)+1[/tex]Now, for the second shift:
[tex]f(x)\rightarrow f(x+2)[/tex]Combining these transformations:
[tex]\begin{gathered} f(x)\rightarrow f(x+2)+1 \\ \therefore f(x)=(x+2)^2+1 \end{gathered}[/tex]the number of regular telephones in use is how many times the number of cellular phones? 45% regular phones15% cellular phones6% others34% Cordless phones
Solution
For this case we have the following info:
45% regular phones
15% cellular phones
6% others
34% Cordless phones
We know that the total regular of phones is 45% and the total of cellular phones are 15% then we can find the ratio like this:
45/15 = 3
Triangle RST has the coordinates R(0 , 2), S(2 , 9), and T(4 , 2). Which of the following sets of points represents a dilation from the origin of triangle RST? A. R'(0 , 2), S'(8 , 9), T'(16 , 2) B. R'(0 , 2), S'(2 , 36), T'(16 , 2) C. R'(4 , 6), S'(6 , 13), T'(8 , 6) D. R'(0 , 8), S'(8 , 36), T'(16, 8)
The set of points that represents a dilation from the origin of triangle RST are: D. R'(0 , 8), S'(8 , 36), T'(16, 8).
What is dilation?In Mathematics, dilation is a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
For the given coordinates of triangle RST, the dilation with a scale factor of 4 from the origin (0, 0) or center of dilation should be calculated as follows:
Point R (0, 2) → Point R' (0 × 4, 2 × 4) = Point R' (0, 8).
Point S (2, 9) → Point S' (2 × 4, 9 × 4) = Point S' (8, 36).
Point T (4, 2) → Point T' (4 × 4, 2 × 4) = Point T' (16, 8).
In conclusion, the other sets of points do not represents a dilation from the origin of triangle RST.
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As of the given condition ordered pair in the option D R'(0 , 8), S'(8 , 36), T'(16, 8), represents the dilated coordinates of the former triangle.
Given that,
Coordinates of the triangle, R(0 , 2), S(2 , 9), and T(4 , 2).
The scale factor for the dilation = 4
The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
According to the question,
The dilated coordinate is given as,
R' = (0×4 , 2×4) = (0, 8)
S' = (2×4, 9×4) = (8, 36)
T' = (4×4, 2×2) = (16, 8)
Thus, As of the given condition ordered pair in the option D R'(0 , 8), S'(8 , 36), T'(16, 8), represents the dilated coordinates of the former triangle.
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I need help on number 14!!! Please help and justify your answer!! PLEASE
as the rate of company B is greater, the company B will reach the top first
Explanationto solve this we can find the rate of each company and then compare
let
[tex]rate=\frac{finished\text{ length of construction}}{time\text{ taken}}[/tex]so
Step 1
convert the mixed number into fractions
remember how
[tex]a\frac{b}{c}=\frac{(a*c)+b}{c}[/tex]so
[tex]\begin{gathered} 5\text{ }\frac{1}{2}=\frac{(5*2)+1}{2}=\frac{11}{2} \\ 3\text{ }\frac{1}{2}=\frac{(3*2)+1}{2}=\frac{7}{2} \end{gathered}[/tex]Step 2
Find the rate of each company
A) Company A
replace
[tex]\begin{gathered} rate=\frac{finished\text{ length of construction}}{time\text{ taken}} \\ rate_A=\frac{550}{\frac{11}{2}}=\frac{1100}{11}=100\text{ ft per month} \end{gathered}[/tex]B) Company B
[tex]\begin{gathered} rate=\frac{finished\text{ length of construction}}{time\text{ taken}} \\ rate_B=\frac{385}{\frac{7}{2}}=\frac{770}{7}=110\text{ ft per month} \end{gathered}[/tex]Step 3
finally, compare
[tex]\begin{gathered} 110\text{ ft per month }>100\text{ ft per month} \\ hence \\ rate_B>rate_A \end{gathered}[/tex]as the rate of company B is greater, the company B will reach the top first
Find the time it would take for the general level of prices in the economy to double at an average annual inflation rate of 4%. The doubling time is aboutyears.
The doubling time for the general price levels in the eonomy given the average annual inflation rate is 18 years.
What is the doubling time?Inflation is a period where the general price levels in an economy rise persistently. When there is an inflation, the prices of goods and services increase. Inflation can either be as a result of an increase in the cost of production or an increase in the demand of a good.
The rule of 72 can be used to determine the doubling time. The rule of 72 is a rule of thumb that determines the number of years it would take an investment to double given its rate of growth.
The rule of 72 = 72 / inflation rate
72 / 4 = 18 years
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12x=8x+1 what is the answer
The answer of the given equation is x = 1/4 or 0.25
We are given the equation:-
12x = 8x + 1
We have to solve the equation to find the value of x.
Rearranging the equation to get the like terms on the same side, we get,
12x - 8x = 1
4x = 1
x = 1/4
Hence, the value of x is 1/4 or 0.25.
Like terms
Like terms can be defined as terms that contain the same variables raised to the same power. Only the numerical coefficients are different. In an expression, only we can combine like terms.
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Lily likes to collect records. Last year she had 12 records in her collection. Now she has 15 records. What is the percent increase of
her collection?
The percent increase of her collection is
Clarence is saving money to buy a skateboard that costs $97.50. He has $15.05 already saved and plans to save $5.50 each week from his allowance. He also earns $15.60 every two weeks for walking dogs. Suppose Clarence wants to spend some of the money from walking dogs on other things. To the nearest dollar, how much would he need to save from walking dogs each week in order to buy the skateboard 4 weeks earlier than if he just saves his allowance?
Please explain. Thanks!
Answer:88
Step-by-step explanation:
need help please 16x=-44-4y
-8x=28+4y
Answer: (x,y)= (-2/5,-43/5)
Step-by-step explanation:
Dolphin 1 dove 200 feet underwater. Dolphin 2 dove 30% farther. After dolphin 2 dove down, it ascended 25 1/2 feet, then descended 40 1/2 feet. How far under the water is the dolphin?
Data:
Dolphin 1: 200ft
Dolphin2:
30% farther: 200ft+60ft=260ft
-Find the 30% of 200
[tex]200\cdot\frac{30}{100}=60[/tex]Ascende 25 1/2 feet and then descended 40 1/2 feet:
Substract to the initial 260ft the 25 1/2 ft and add 40 1/2:
[tex]260-25\frac{1}{2}+40\frac{1}{2}[/tex]To sum or substract mixed numbers write it as fractions:
[tex]\begin{gathered} 25\frac{1}{2}=\frac{50}{2}+\frac{1}{2}=\frac{51}{2} \\ \\ 40\frac{1}{2}=\frac{80}{2}+\frac{1}{2}=\frac{81}{2} \end{gathered}[/tex]Then You have:
[tex]260-\frac{51}{2}+\frac{81}{2}[/tex]You can also write the 260 as a fraction with the same denominator (2):
[tex]\begin{gathered} \frac{520}{2}-\frac{51}{2}+\frac{81}{2} \\ \\ =\frac{520-51+81}{2}=\frac{550}{2}=275 \end{gathered}[/tex]Then, the dolphin 2 is 275 feet under the waterGenerate equivalent expressions using properties of operations. 15-(x•9) what do I need to do
Given the expression:
15 - (x • 9)
Let's simplify the expression.
To generate an expression equivalent to the given expression, simplify the expression inside the parentheses.
Thus, we have:
[tex]15-9x[/tex]ANSWER:
[tex]15-9x[/tex]
What is the unknown angle b?
Answer:
48°
Explanation:
A line always equals 180°. The angle on the right is a 90° angle (we know this because or the little red box shown) and the angle in the middle is 42°. We would add 42° and 90° to get the combination of both which is 132°
42+90=132
Then subtract 132° from 180° to find unknown angle b.
180-132=48
Unknown angle b= 48°
4 Consider the quadratic equation below.[tex]4 {x}^{2} - 5 = 3x + 4[/tex] Determine the correct set-up for solving the equation using the quadratic formula.
The equation:
4x² - 5 = 3x + 4
First, we need to re-arrange in the form : ax² + bx + c
4x² - 5 = 3x + 4
4x² - 3x -5 -4 = 0
4x² - 3x -9 =0
comparing the above with ax² + bx + c
a= 4 b= -3 c=-9
we will then substitute the values into the quadratic formula:
[tex]x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex][tex]x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(4)(-9)}}{2(4)}[/tex]When water flows across farmland, some of the soil is washed away, resulting in erosion. Researchers released water
across a test bed at different flow rates and measured the amount of soil washed away. The following table gives the
flow (in liters per second) and the weight (in kilograms) of eroded soil:
The correlation coefficient between flow rate and amount of eroded soil is:
0.967.
Correlation coefficientsThe correlation coefficient is an index that measures correlation between two variables, assuming values between -1 and 1.
If it is positive, the relation is positive, meaning that the variables are direct proportional. If it is negative, the variables are inverse proportional.
If the absolute value of the correlation coefficient is greater than 0.6, the relationship between the variables is strong.
Given a data-set of two points, the correlation coefficient is found inserting points of the data-set into the calculator. In this problem, the points in the data-set are given as follows:
(0.31, 0.82), (0.85, 1.95), (1.26, 2.18), (2.47, 3.01), (3.75, 6.07).
Using a calculator, the coefficient is given as follows:
0.967.
Hence the last option gives the correct coefficient.
Missing informationThe complete problem is given by the image at the end of the answer.
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Find the volume of the cone.9 cmr= 6 cmV = [?] cm3
The radius of cone is r = 6 cm.
The height of cone is h = 9 cm.
The formula for the volume of cone is,
[tex]V=\frac{1}{3}\pi\cdot r^2\cdot h[/tex]Substitute the values in the formula to determine the volume of cone.
[tex]\begin{gathered} V=\frac{1}{3}\pi\cdot(6)^2\cdot9 \\ =339.29 \\ \approx339.3 \end{gathered}[/tex]Thus, volume of cone is 339.3 cm^3.
Consider right triangle PQR what is the value of tan(R)
6/8
8/10
8/6
10/6
The value of tan(R) in the right triangle PQR where Perpendicular=QP, Base=RQ, Tan R=P/B. The slope of a straight line is the tangent of the angle made by the line with the positive x-axis.
What is perpendicular?Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular symbol,⟂, can be used to graphically represent the condition of perpendicularity. It can be defined between two planes, two lines, or two planes and another line.
What is base?The base of a right angle triangle is the side on which it is positioned. The calculation can also be done using any of the two sides other than the hypotenuse as the base. It is the side of the right-angled triangle that is perpendicular to its base.
here,
Perpendicular=QP
Base=RQ
Tan R=P/B
=QP/RQ
Tan R=6/8
The perpendicular QP, base RQ, and tan's (R) values in the right triangle PQR. Tan's (R) = P/B. The tangent of the angle formed by the line with the positive x-axis is what determines a line's slope.
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evaluate each limit. this is in the topic of jump discontinuities.
we have
[tex]\begin{gathered} \lim _{x\to-2}-x^2-4x-5 \\ \lim _{x\to-2}-(-2)^2-4(-2)-5 \\ \lim _{x\to-2}-4^{}+8-5 \\ \lim _{x\to-2}--1 \end{gathered}[/tex][tex]\lim _{x\to-2}-1=-1[/tex]therefore
the answer is -1What is the simplified expression for the expression below?7(x - 4) - 3(x + 5) A. 4x - 43 B. 4x + 1C. 4x - 13D. 4x - 9
Answer:
4x - 43
Step-by-step explanation:
This Question requires the concept of solving algebraic expressions.
Algebraic ExpressionsAlgebraic Expressions are expressions made up of alphabet variables and numbers and can be simplified using order of operations just like numerical expressions.
Example: 8(4x-6) = 32x - 48
ApplicationFor this question, we will use the same concept as above to solve for the expression.
[tex]7(x - 4) - 3(x + 5) = 7x - 28 - (3x + 15) \\ = 7x - 28 - 3x - 15 \\ = 4x - 43[/tex]
I need help with this question... the correct answer choice
Reflection over the x-axis:
(x,y)--->(x, -y)
and the question is what is not a reflection across the x-axis.
so,
the correct option is D which is:
R'(-9, 4) ----> R'(9, -4)
Because it is a reflection over the y-axis.
The perimeter of a rectangle is 36 cm and the length is twice the width. What are the dimensions of this rectangle? What’s the length and width?
Mr. Rodriguez is preparing photos for an international client. The client has requested a photo that is 20 cm by 15 cm. Mr. Rodriguez knows that the formula c = 2.54n can be used to convert n inches to c centimeters. Which formula can he use to convert centimeters to inches?
Given:
The formula to convert from inches to centimeters is c = 2.54n
To find:
The formula that can be used to convert from centimeters to inches
To determine the formula, we need to make n the subject of formula:
[tex]\begin{gathered} \text{c = 2.54n} \\ where\text{ c = value in cm} \\ n\text{ = value in inches} \end{gathered}[/tex][tex]\begin{gathered} To\text{ make n, the subject of formula, we will divide both sides by 2.54:} \\ \frac{c}{2.54}=\text{ }\frac{2.54n}{2.54} \\ n\text{ = }\frac{c}{2.54} \\ This\text{ means when we have a value in cm and substitute, the answer will be in inches} \end{gathered}[/tex][tex]n\text{ = }\frac{c}{2.54\text{ }}\text{ \lparen option B\rparen}[/tex]#8 iOrder the figures described below according to their volumes from least (on top) to greatest (on bottom).= a cylinder with 2-inch radius and 6-inch height= a cube with side length 4 inches= a rectangular prism with a length of 2 inches, a width of 3 inches, and a height of 6 inches
step 1
Find out the volume of each figure
Cylinder
The volume of a cylinder is given by
[tex]\begin{gathered} V=\pi r^2h \\ V=(3.14)(2)^2(6) \\ V=75.36\text{ in}^3 \end{gathered}[/tex]Cube
The volume of the cube is given by
[tex]\begin{gathered} V=b^3 \\ V=4^3 \\ V=64\text{ in}^3 \end{gathered}[/tex]Rectangular prism
The volume of the prism is given by the formula
[tex]\begin{gathered} V=L*W*H \\ V=(2)(3)(6) \\ V=36\text{ in}^3 \end{gathered}[/tex]therefore
The answer is
rectangular prismcubecylinderGraph A) -f(x) B) f(x+2) -4Then find the domain and range of each
a. Graph -f(x):
By the transformations rules for functions, the graph of -f(x) is equal to a reflection over the x-axis, and a change of the y-coordinates:
[tex](x,y)\rightarrow(x,-y)[/tex]Then, given the function:
[tex]f(x)=\sqrt[]{x}[/tex]The graph of -f(x) is:is
The domain of the function is the set of all possible x-values, then it is:
[tex]\lbrack0,+\infty)[/tex]The range is the set of all possible values of the function, then it is:
[tex]\lbrack0,-\infty)[/tex]b. Graph f(x+2)-4:
The transformation f(x+2) is an horizontal translation left 2 units.
And the transformation f(x+2)-4 is a vertical translation down 4 units.
Then, the coordinates of this graph in comparison to the given graph are:
[tex](x,y)\rightarrow(x-2,y-4)[/tex]Then for the point (1,1) the new coordinates are (1-2,1-4)=(-1,-3).
For (4,2): the new coordinates (4-2,2-4)=(2,-2)
For (9,3): the new coordinates (9-2,3-4)=(7,-1)
The graph is:
The domain of this function is:
[tex]\lbrack-2,+\infty)[/tex]And the range is:
[tex]\lbrack-4,+\infty)[/tex]