1) the initial expression is:
[tex]2x^2+5x-12[/tex]To factor this expression we can use the cuadratic formula that is:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4(a)(c)}}{2(a)} \\ a=2 \\ b=5 \\ c=-12 \end{gathered}[/tex]so we replace the values and we get:
[tex]\begin{gathered} x=\frac{-5\pm\sqrt[]{5^2-4(2)(-12)}}{2\cdot2} \\ x=\frac{-5\pm\sqrt[]{121}}{4} \\ x=\frac{-5\pm11}{4} \end{gathered}[/tex]So now we have two solutions so:
[tex]\begin{gathered} x_1=\frac{-5+11}{4}=\frac{6}{4}=\frac{3}{2}=1.5 \\ x_2=\frac{-5-11}{4}=-\frac{16}{4}=-4 \end{gathered}[/tex]so the factor expression will be:
[tex](x-\frac{3}{2})(x+4)[/tex]2) the initial expression is:
[tex]6x^2-23x+7[/tex]so we repeat the same procedure so:
[tex]\begin{gathered} x=\frac{23\pm\sqrt[]{23^2-4(6)(7)}}{2(6)} \\ x=\frac{23\pm\sqrt[]{529-168}}{12} \\ x=\frac{23\pm\sqrt[]{361}}{12} \\ x=\frac{23\pm19}{12} \end{gathered}[/tex]So the two possible solutions are:
[tex]\begin{gathered} x_1=\frac{23+19}{12}=\frac{42}{12}=\frac{7}{2}=3.5 \\ x_2=\frac{23-19}{12}=\frac{4}{12}=\frac{2}{6}=\frac{1}{3}=0.33 \end{gathered}[/tex]so the factor form is:
[tex](x-\frac{7}{2})(x-\frac{1}{3})[/tex]HELP PLEASEEEEEEEEE!!!!!!!!
Answer:
n∧4 basically its n to the power of 14
Step-by-step explanation:
your work is in the pic below check it out sorry if incorrect have a wonderful day:)
Claire drew a model of five tenths explain how Claire could change her model to show how many hundredths are in five tenths
Let x be the number of hundredths in 5/10. Then 100 times x gives 5/10.
[tex]100x=\frac{5}{10}[/tex]Solve for x.
[tex]\begin{gathered} x=\frac{\frac{5}{10}}{100} \\ =0.005 \end{gathered}[/tex]So, there are 0.005 hundredths in 5/10.
V =Y(r+ B) solve for r
Please help with these two problems.
Answer:
7. x = 25
8. x = 28
Step-by-step explanation:
7. Alternate interior angles are congruent.
[tex]x + 25 = 2x[/tex]
[tex]x = 25[/tex]
8. Consecutive angles add up to 180°.
[tex]4x + 2x + 12 = 180[/tex]
[tex]6x + 12 = 180[/tex]
[tex]6x = 168[/tex]
[tex]x = 28[/tex]
Given the following sets, find the set (A UB) n (AUC).U={1, 2, 3, ...,9}A = {1, 2, 4, 8}B = {3, 7, 9)C={1, 2, 3, 4, 6}Select the correct choice below and, if necessary, fill in the answer box to complete your choice.O A. (AUB) n (AUC)=0(Use a comma to separate answers as needed. Use ascending order.)O B. (A UB) n (AUC) is the empty set.
From the data sets given
(A U B) = ( 1, 2 ,3 ,4 , 7, 8 , 9)
(A U C) = (1, 2 ,3 ,4 ,6 ,8)
(A U B) n ( A U C) = ( 1 ,2, 3, 4 ,8)
Write an exponential function in the form y=ab^xy=ab
x
that goes through points (0, 7)(0,7) and (2, 112)(2,112).
An exponential function in the form y=abˣ is y = 7×4ˣ .
A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.
Write the equation of the function:
y = abˣ
For point (0 , 7)
7 = ab⁰
for point (2 , 112)
x = 2
y = 112
Substitute:
112 = ab²
Swap the sides:
ab⁰ = 7
ab² = 112
Find the quotient of the equations:
ab²/ ab⁰ = 112/7
Simplify the equations:
b² = 16
b = ±√16
Split into two equations: b = +√16 or b = -√16
Simplify the radical expression:
b = 4
b = -4
Combine the results: b = 4 or b = -4
Any fraction with a denominator of 1 is equal to its numerator:
a = 7
7 = a (±4)°
Substitute into one of the equations:
a = 7
b = ± 4
y = 7×4ˣ
Hence , y =7×4ˣ is an exponential function with the formula y=abˣ.
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Essential Question How can you write an algebraic expression?
Answer:
Step-by-step explanation:
In algebraic expressions that use variables (written as letters), you can write them directly after a normal number, with no symbol between them.
...
Use a ⋅ or × sign if you see words like double, per, or product.
Twice 16 → 2 ⋅ 16.
Five per day → 5 ⋅ d or 5d. ...
The product of 8 and 20 → 8 ⋅ 20.
help please for my homework
A. The similar triangles are: B. ΔABC ~ ΔDBE
B. AC = 16
What is the Angle-Angle Similarity Theorem (AA)?The angle-angle similarity theorem (AA) states that two triangles are similar to each other if two angles in one triangle are congruent to two corresponding angles in the other triangles.
The side lengths of two similar triangles are proportional to each other, which means they have ratio that is equal to one another.
Part A:
In the given diagram, triangles ABC and DBE have two pairs of corresponding angles that are congruent to each other which are: angle ABC ≅ DBE, and angle BCA ≅ BED.
Therefore, based on the AA similarity theorem: B. triangle ABC ~ triangle DBE.
Part B:
Since triangles ABC and DBE are similar triangles, therefore, BC/BE = AC/DE
Substitute
12/15 = (x + 1)/(x + 5)
Cross multiply
12(x + 5) = 15(x + 1)
12x + 60 = 15x + 15
Combine like terms
12x - 15x = -60 + 15
-3x = -45
-3x/-3 = -45/-3
x = 15
AC = x + 1 = 15 + 1
AC = 16
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5. A ja contains 11 green marbles, 7 red marbles, and 6 blue marbles. A marble is selected at random, not replaced, and then a second marble is selected. What is the probability ofselecting a blue marble followed by a green marble?
Answer: 11/92
Explanation:
Probability is expressed as
number of favorable outcomes/number of total outcomes
From the information given,
number of green marbles = 11
number of red marbles = 7
number of blue marbles = 6
Total number of marbles = 11 + 7 + 6 = 24
Probability of selecting a blue marble = 6/24 = 1/4
Since the marble is not replaced, total number of marbles left = 24 - 1 = 23
Probability of selecting a green marble = 11/23
The probability of selecting a blue marble followed by a green marble is
1/4 x 11/23
= 11/92
Which of these is the northern-most countries? Responses
A Colombia
B Brazil
C Ecuador
D Peru
a regular octagon (a polygon with 8 equal sid3s) is inscribed in a circle of radius 19.9cm. find the perimeter of the octagon
Perimeter of an octagon
radius R = 19.9 cm
then To find perimeter
Multiply 8 times lenghts of octagon
with height=
internal angle is= 360/8 = 45°
Now apply rule of Sines
then sin 45/ lside = sin ( 180-45)/2/ radius
Therefore
Lside = sin 45• (19.9) / sin (67.5) = 15.23 cm
Now multiply 8 times this lenght side to find perimeter
8x 15.23 = 121.84 cm
Formula?
$268 is deposited into savings account at 4% interest, compounded quarterly. To the nearest year, how long will it take for the account balance to reach $427?
Answer: 12 years
A quadrilateral has two angles that measure 210° and 82º. The other two angles are in aratio of 7:10. What are the measures of those two angles?o andSubmit
Solution
The interior angles of a quadrilateral measure to 360 degrees
Two of them are known and are 210 and 82. They add to 292 degrees.
The other two angles must sum to (360-292)=68 degrees.
They are in a ratio of 7:10
The sum of these two numbers is 17
[tex]\frac{68}{17}=4[/tex][tex]\begin{gathered} 7\times4=28^0 \\ 10\times4=40^0 \end{gathered}[/tex]The other two angles are 28 and 40 degrees respectively.
The sum of all 4 angles is 360 degrees.
The final answer
The other two angles are 28 and 40 degrees respectively.
Help me pleaseeeeeeeeee
The side lengths of the right triangle in exact form are z = (15√3)/2, x = 15/2, y = (15√3)/4, a = 15/4 and b = 45/4.
How determine the sides of a right triangle using trigonometric ratios?Three out of the six functions used in trigonometry is expressed as;
sin = opposite / hypotenuse
cos = adjacent / hypotenuse
tan = opposite / adjacent
From diagram, we solve for side z of the right triangle.
cosθ = adjacent / hypotenuse
cos( 30° ) = z / 15
Solve for z
z = cos( 30° ) × 15
z = (√3)/2 × 15
z = (15√3)/2
Next solve for side x
sinθ = opposite / hypotenuse
sin( 30° ) = x / 15
x = sin( 30° ) × 15
x = 15/2
Solve for side y
sinθ = opposite / hypotenuse
sin( 60° ) = y / 15/2
y = sin( 60° ) × 15/2
y = (15√3)/4
Solve for side a
cosθ = adjacent / hypotenuse
cos( 60° ) = a / 15/2
a = cos( 60° ) × 15/2
a = 15/4
Solve for side b
b = 15 - a
b = 15 - 15/4
b = 45/4
Therefore the length of side of b is 45/4
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There are 2 buses. Bus A can travel 125 miles in 3 hours, and bus B can travel 85 more miles than bus A within the same time what is the speed of bus B?
Answer:
70 miles an hour
Step-by-step explanation:
First, you want to know how fast bus A can go. So you want to do 125/3 since the bus travels 3 hours. you get 41.6666667. keep that number. then you want to divide 85 by 3 since bus B is going for 3 hours. you get 28.3333333. then you add those numbers to get how fast bus B is going and you get 70 miles per hour for bus B
what is the slope of the line through (-9, 6) and (-3,9)
Solution
For this case we have the following points:
(-9, 6) and (-3, 9)
and we can find the slope with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{9-6}{-3+9}=\frac{3}{6}=\frac{1}{2}[/tex]Then the solution would be:
B ) 1/2
The stingray population in a particular reef is decreasing at a rate of 1.4% per year. The population was 3800 in the year 2008. What is the best prediction of the population in the year 2013? Round to the nearest whole number, Show all work for full credit.
We have a initial population P(0) of 3800.
We know that the population is decreasing by 1.4% each year, so the population at year 1 (2009) we will have a population of:
[tex]\begin{gathered} P(1)=P(0)-0.014\cdot P(0) \\ P(1)=(1-0.014)\cdot P(0) \\ P(1)=0.986\cdot P(0) \end{gathered}[/tex]We can generalize this for P(n), where n is the number of years from 2008.
[tex]\begin{gathered} P(2)=0.986\cdot P(1)=0.986\cdot(0.986\cdot P(0))=0.986^2\cdot P(0) \\ \Rightarrow \\ P(n)=0.986^n\cdot P(0)=0.986^n\cdot3800=3800\cdot0.986^n \end{gathered}[/tex]From 2008 to 2013 we have 2013-2008=5 years, so for the year 2013, the value of n is n=5.
Then, the population for 2013 will be P(5) and can be calculated as:
[tex]P(5)=3800\cdot0.986^5\approx3800\cdot0.932\approx3541[/tex]Answer: the predicted population for the year 2013 is 3541.
Tell whether the data represents a linear, an exponential, or a quadratic function. Then, write the function. Picture is attached. I need help!
SOLUTION:
Case: Equations
Method:
The table:
Plotting the points
Studying the points, could either be quadratic or exponential.
We will proceed to test the points but because the increase of the y values as x increases from left to right is not a fine pattern, it will most likely not be exponential.
Next, we test a quadratic model on the graph
[tex]y=ax^2+bx+c[/tex]Final answer:
Quadratic function
[tex]y=x^2+4x-12[/tex]To be linear, you'd need a fixed increase in the y-values for a constant increase in the x-values. As x increases by 1 in each new point, your y-values increase by 1, 3, 5, and 7 respectively. That is not the same increase each time. This is not linear.
To be exponential, you need a fixed percent increase in the y-values between the points. From (-2,-16) to (-1,-15), your increase is 1/16 or 6.25%. From (-1,-15) to (0,-12), your increase is 3/15 or 20%. That is not a constant percent increase.
The only option left is quadratic.
To find the function, start with c = -12, based on the point (0,-12).
This gives you f(x) = ax^2 + bx -12
Next plug in (2,0) into f(x): 0 = 4a + 2b - 12
And plug in (1,-7) into f(x): -7 = a + b -12
You now have two equations with two unknowns.
Solve equation 2 for a:
5-b = a
Substitute that into equation 1
0 = 4(5-b) + 2b - 12
0 = 20 -4b + 2b - 12
-8 = -2b
4 = b
Substitute that b-value into 5-b=a
5 - 4 = a
1 = a
You have your three values and have your function:
f(x) = 1x^2 + 4x - 12 or f(x) = x^2 + 4x - 12
You can confirm that the other points also fit with this function.
Just need a simple explanation.
The square roots for each side of the equation are not correct, as the square root of 36 is of -6 or 6, not -36 or 36, hence the correct solutions are:
x = -3 or x = 9.
Are the steps correct?The equation in Step 6 is given as follows:
[tex]\sqrt{(x - 3)^2} = \sqrt{36}[/tex]
Simplifying the square roots, the variable x can be isolated, as follows:
x - 3 = 6.x - 3 = -6.Both -6 and 6 are correct results for the square root of 36, because:
6² = 36.(-6)² = 36.His mistake when removing the square root is that he did not calculate the root, he just removed the square root from the 36, hence the correct solutions will be found as follows:
x - 3 = 6. -> x = 9.x - 3 = -6. -> x = -3.From the (x - 3)² term, the square root is removed along with the square. However 36 = (6)² or (-6)², hence sqrt(36) = 6 or sqrt(36) = -6.;
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Apply the Pythagorean theorem to find the distance between two points in a coordinator system
Using pythagoras theorem to find the distance between two points in a coordinate:
[tex]\begin{gathered} A=(-5,5) \\ B=(-1,1) \end{gathered}[/tex][tex]\begin{gathered} A=(-5,5)\longrightarrow x_1=-5,y_1=5 \\ B=(-1,1)\longrightarrow x_2=-1,y_2=1 \\ \text{vertical line = opposite =5-1=4} \\ \text{horizontal line = adjacent = -5--1=-5+1=-4} \end{gathered}[/tex]To calculate the distance between the points AB = hypotenuse
[tex]\begin{gathered} \text{Hypotenuse}^2=opposite^2+adjacent^2 \\ AB^2=4^2+(-4)^2 \\ AB^2=16+16 \\ AB^2=32 \\ AB=\sqrt[]{32} \\ AB=4\sqrt[]{2} \end{gathered}[/tex]Therefore the distance between the points in the coordinate system = 4√2
Sarah has 3 candy bars. She wants to share the candy bars with her friends that everyone gets a serving that is equivalent to 2/5 of a candy bar. To determine how many servings Sarah can make, she dividends 3 divided by 2/5 and get gets 7 1/2
Sarah is unsure this is correct. Use the diagram below and the dropdown menus to help explain if Sarah is correct or not.
I need to solve this to get zero can you help?
sin 0 = 26/30
sin 0 = 0.87
0 = 60°
Result 0 = 60°
Given the right triangle shown, solve for X, Y and Z. The triangle may not be drawn to scaleA. x=1.86feet, y=4.41 feet and z=65 degreeB.x=4.41 feet, y=1.69 feet, and z=155 degreeC. x=8.58 feet, y=9.46 feet and z=65 degreeD.x=9.46 feet, y=8.58 feet and z=155 degree
Since the triangle is a right-angled triangle, we can use SohCahToa to find x
Using the ratio
[tex]Tan25=\frac{\text{opposite}}{\text{adjacent}}[/tex]Opposite = 4ft
adjacent = x
Substituting these values yield
[tex]\begin{gathered} \text{Tan 25 =}\frac{4}{x} \\ x\text{ =}\frac{4}{\tan 25} \\ x\text{ =8.57}8ft \\ x\approx8.58ft \end{gathered}[/tex]To find Z we use the fact that the sum of angles in a triangle is 180 degrees
so that in triangle XYZ
90 + 25 +Z = 180
Z = 180 - 115
Z= 65 degrees
We will now use Pythagoras theorem to find y
[tex]\begin{gathered} \text{For that} \\ y^2=x^2+4^2 \\ \text{but x = 8.58ft} \\ y^2=8.58^2+4^2 \\ y=\sqrt[]{73.6164\text{ +16}} \\ y\text{ =9.46 ft} \end{gathered}[/tex]
Hence x= 8.58 ft, y= 9.46ft and Z = 65 degrees, Option C
For the polynomial f(x) = 2x3 – 9x2 +117 - 20 as x → -0,f(x) > 0 O A. True O B. False
Given the function;
[tex]\begin{gathered} f(x)=2x^3-9x^2+11x-20 \\ \end{gathered}[/tex]The leading exponent is odd and the leading coeeficient is positive, so as x tends to positive infinity, f(x) also tends to positive infinity and as x tends to negative infinity, f(x) also tends to negative infinity.
Thus, the correct answer is FALSE.
A restaurant bill for four people is 122 route leave the $8018 tip what percentage tip is that A restaurant beer for four people is 120 the group me is a tip of $18 what percent of tip is that
The total tip for a four-person meal at a restaurant is $122, people $8018. The percentage of the tip is 22%.
Given that,
The total tip for a four-person meal at a restaurant is $122, people $8018. What proportion of a tip is that? Four restaurant beers cost 120 each, and the group tip is $180.
We have to calculate the how much percentage of a tip is there.
In a variety of situations, such as restaurants, hotels, salons, and other establishments in the service sector, leaving a tip is common. Knowing how to compute a tip and knowing how much to tip is crucial for a variety of reasons, including the fact that many service sector personnel, like waiters, rely heavily on gratuities for the majority of their income. This means that these experts might not be able to support themselves and their families without tips.
Percentage= tip/amount
Percentage= $180/$8018
Percentage= 22%
Therefore, the percentage of the tip is 22%
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which is more 95 fluid ounces or 3 quarts
95 fluid ounces or 3 quarts.
To solve htis problem, convert the ounces to quarts and compare the results.
1 ounce ----------------------- 0.03125 quart
95 ounces ------------------- x
x = (95 x 0.03125) / 1
x = 2.97 quarts
2.97 ounces < 3 quarts
Three quarts is more
It takes bbb minutes for Sylvia's bathtub to fill with water.
How many minutes will it take to fill 333 same-size bathtubs?
Write your answer as an expression.
Time taken to fill 3 same-size bathtubs is 3b minutes.
Its given in the question that it takes b minutes to fill Sylvia's bathtub with water.
Time taken to fill same-size bathtub as an expression = 3*b
= 3b minutes.
Hence, time takes to fill 3 bathtubs of the same size as of Sylvia's bathtub to fill with water is 3b minutes.
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express in simplest form: sec 0 • cot 0 • sin 0
Note that;
secθ = 1/cosθ cotθ= cosθ/sinθ
substitute into into the expression
[tex]\sec \theta.\cot \theta.\sin \theta=\frac{1}{\cos\theta}.\frac{\cos \theta}{\sin \theta}\text{. sin}\theta[/tex]cosθ at the numerator will cancel out the cosθ at the denominator, also sinθ at the numerator will cancel out the sinθ at the denominator
[tex]=1[/tex]How does the graph of the transformed function g(x) = log7(3x-9) compare to the graph of its parent function f(x) = log7x
The correct option is A
The graph has been horizontally stretched, 9 units to the right.
Explanation:Given the function:
[tex]f(x)=\log _7x[/tex]The function:
[tex]f(x)=\log _7(3x-9)[/tex]is a horizontally stretched transformation, 9 units to the right.
Angie is working on solving an exponential equation 23^x=6; however, she’s not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation using the change of base formula.
we have the equation
[tex]23^x=6[/tex]Remember the definition of logarithm
[tex]\begin{gathered} If \\ a^x=b \\ then \\ x=\log_ab \end{gathered}[/tex]Applying the definition of a logarithm to this problem
we have that
[tex]x=\log_{23}6[/tex]Apply change of base formula
Remember that
[tex]\log_bM=\frac{\log_{10}M}{\log_{10}b}=\frac{logM}{logb}[/tex]so
[tex]\log_{23}6=\frac{log6}{log23}[/tex]therefore
The answer is
[tex]x=\frac{log6}{log23}[/tex]