a) Evaluating the function at x= -2 we get:
[tex]f(-2)=(-2)^2+3(-2)=4-6=-2[/tex]b) Notice that the given function has the form:
[tex]y=ax^2+bx+c[/tex]Therefore f(x) is a quadratic function.
c) Since f(x) is a quadratic function its graph is a parabola.
Emmanuel added two integers Which condition will always give Emmanuel a negative solution when he adds two integers? Both integers have negative values Both integers have positive values O. One integer has a positive value, and one integer has a negative value O The values of the two integers are opposites
Both integers have negative values
Explanation
Let
x and y represents the number
so, the options are
[tex]\begin{gathered} +\text{ + +} \\ +\text{ + -} \\ -\text{ + +} \\ -\text{ +-} \end{gathered}[/tex]a) Both integers have negative values Both integers
[tex]-x-y=-(x+y)\rightarrow you\text{ will always get a negative number}[/tex]b) Both integers have positive values
[tex]x+y=+\text{ + += you will always get a positive number}[/tex]c)One integer has a positive value, and one integer has a negative value
[tex]\begin{gathered} -x+y\text{ or x-y} \\ the\text{ sign of the result depends on the greates absolute value, it means the answer will have the same of the bigger number( absolute value)} \end{gathered}[/tex]d)The values of the two integers are opposites
as the point C , the sign depends on the bigger number
for example
[tex]\begin{gathered} 8-5=3\text{ positive because 8 is the bigger} \\ 5-8=-3\text{ negative because (-8) is has the bigger absolute value} \end{gathered}[/tex]so, the answer is Both integers have negative values
I hope this helps you
7 in. 6in. 9 in. it's the formula of a triangle
Area of a Triangle
Given a triangle of base length B and height length H, the area can be calculated by the formula:
[tex]A=\frac{B\cdot H}{2}[/tex]The base and the height must be perpendicular.
The height of the given triangle is H=7 in. We need to calculate the length of the base.
We are providing a new image where a variable x is introduced to help us calculate the base length:
The triangle formed by the sides 9-7-x is right, so we can calculate the value of x by applying the Pythagora's Theorem:
[tex]7^2+x^2=9^2[/tex][tex]49+x^2=81[/tex]Solving for x:
[tex]\begin{gathered} x^2=81-49=32 \\ x=\sqrt[]{32} \end{gathered}[/tex]The length of the base is:
[tex]B=9+\sqrt[]{32}[/tex]Thus, the area of the triangle is:
[tex]A=\frac{7\cdot(9+\sqrt[]{32})}{2}[/tex]Calculating:
A = 51.3 square inches
Aaron received credit of$48 on a purchase of $960. What percent of$960 is 48%?
we have
[tex]\begin{gathered} \frac{48}{960}=\frac{x}{100} \\ 100\times\frac{48}{960}=100\times\frac{x}{100} \\ x=5 \end{gathered}[/tex]answer: 5%
A line cuts the y-axis at (0, -6) and passes through the point (9, -3). Find the equation of the line.
point 1 (0,-6) and point 2 (9,-3)
the equation is
[tex]y-y1=m(x-x1)[/tex]where m =
[tex]m=\frac{y2-y1}{x2-x1}=\frac{-3-(-6)}{9-0}=\frac{-3+6}{9}=\frac{3}{9}=\frac{1}{3}[/tex]answer: the equation of the line is
[tex]\begin{gathered} y-(-6)=\frac{1}{3}(x-0) \\ y+6=\frac{1}{3}x \\ y+6-6=\frac{1}{3}x-6 \\ y=\frac{1}{3}x-6 \end{gathered}[/tex]Suppose a jar contains 20 red marbles and 31 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
The probability that they are both are red is 0.15.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.
The jar contains 20 red marbles and 31 blue marbles. The total marble is 51.
Therefore, the probability will be:
= P(red) × P(red)
= 20/51 × 19/50
= 380 / 2550
= 0.15
The probability is 0.15.
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What is 2 8/10 in decimal form?
Okay, here we have this:
We are going to convert the following mixed number to decimal: 2 8/10, so we obtain the following:
[tex]\begin{gathered} 2\frac{8}{10} \\ =\frac{2\cdot10+8}{10} \\ =\frac{28}{10} \end{gathered}[/tex]Finally we obtain that 2 8/10 expressed as a fraction is equal to 28/10.
Select the correct answer.What is the range of Piecewise and Absolute Value Functions
Given the function :
g(x) = -1/2 |x-6| + 1
• Th,e, 1 ,, highlighted in yellowabove, indicates the maximum y- intercept that the graph will ever reach .
,• The equation follows y = Mx + b structure , meaning range is from -infinity.
,• So the range of this equation will be (-∞ ; 1]
,• Option A is the correct choice .
Absolute value:
asymptote : none
extreme point (6;1)
critical point : x = 6
Write the sequence of transformations that changes figure ABCD to figure A’B’C’D. Explain your answer and write the coordinates of the figure obtained after each transformation. Are the two figures congruent? Explain your answer.
SOLUTION:
We can compare a point to get the translation.
We can use the point;
[tex]A(-4,4)[/tex]which transforms to;
[tex]A^{\prime}^^{\prime}(3,-4)[/tex]The first transformation is a reflection over the x-axis to map point A to;
[tex]A^{\prime}(-4,-4)[/tex]The next transformation is a translation 7 units to the right.
Therefore, the sequence of transformations are;
Part B: The two figures are congruent because the transformations used are non-rigid.
what percent of 28 is 35? the answer is (blank)%
levon scored 38 points in the first half of the basketball game, and he scored p points in the second half of the game. write an expression to determine the number of points he scored in all. then, find the number of points he scored in all if he scored 20 points in the second half of the game.
By the given information you can raise the following equation, and since levon scored 38 points in the first half of the basketball game, then
[tex]\begin{gathered} TP=38+n \\ \text{Where} \\ TP\colon\text{ the number of points that he scored in total.} \\ n\colon\text{ the number of points that he scored in the second half of the game} \end{gathered}[/tex]So, if n=20
[tex]\begin{gathered} TP=38+n \\ TP=38+20 \\ TP=58 \end{gathered}[/tex]Therefore, if Levon scored 20 points in the second half of the game, in all he scored 58 points.
HEEEEELPPPP
The population of a town is modeled by the equation P=3485e0.12t, where “P” represents the population as of the year 2000.
According to the model, what will the population of the town be in 2010?
In approximately what year will the population reach 50,000 people?
Must answer and show appropriate work for both questions here.
show step bye step explanation
There are 11571 people in the world as of 2010, and would take about 22 years for that number to reach 50,000 of population.
What is termed as the exponential increase?An exponential function's curve is created by a pattern of data called exponential growth, which exhibits greater increases over time. Linear growth, which is additive, and geometric growth can be contrasted with exponential growth, which is multiplicative (that is raised to a power).Let P stand for the population in 2000 (or any other time period). Considering the equation:
P = 3485e∧0.12t,
The population in 2010 (t = 10 years) would be:
P = 3485e∧0.12×10
P = 3485e∧12
P = 11571
When there are 50,000 people in the population:
50,000 = 3485e∧0.12t,
Solving, by log property.
t = 22 years.
Thus, there are 11571 people in the world as of 2010, and would take about 22 years for that number to reach 50,000.
To know more about the exponential increase, here
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Use f(x)=-x-8 and g(x) = x² + 8x − 15 to answer the following: a) f(1) + g(–3) b) g(−9) − f(–7)
ANSWER:
a) -37
b) 9
Given:
f(x)=-x-8 and g(x) = x² + 8x − 15
a) f(1) + g(–3)
f(1) = 1 - 8 = -7
g(-3) = -3² + 8(-3) - 15 = 9 - 24 - 15 = -30
f(1) + g(–3) = -7 + (-30)
= -7 - 30
-37
b) g(−9) − f(–7):
g(-9) = -9² + 8(-9) - 15 = 81 - 72 - 15 = -6
f(-7) = -7 - 8 = -15
Thus,
g(−9) − f(–7) = -6 - (-15)
= -6 + 15
= 9
Graph the line x=3 .
According to the given equation, x=3, the line that represents it is a vertical line that passes throught the x axis at x=3.
This is a constant line, which means that for all the values of y, x will always be 3.
The graph of this line is the following:
the diagram show a side (a) find the height of the top of the side(b) find the length of the side
Part a
Find out the height of the triangle of the figure
we have that
sin(70)=h/2 -----> by opposite side divided by the hypotenuse
solve for h
h=2*sin(70)
h=1.88 mPart b
Find the base of complete triangle
so
Let
x-----> the base of complete triangle
we have that
x=2*cos(70)+h/tan(40)
substitute the value of h
x=2*cos(70)+1.88/tan(40)
x=2.92 mThe answer and how to do it
Answer:
v ≈ 4 cm
Step-by-step explanation:
using the Sine rule in Δ VWX
[tex]\frac{v}{sinV}[/tex] = [tex]\frac{w}{sinW}[/tex]
where v = WX and w = VX
∠ W = 180° - (126 + 21)° = 180° - 147° = 33° , then
[tex]\frac{v}{sin21}[/tex] = [tex]\frac{6}{sin33}[/tex] ( cross- multiply )
v × sin33° = 6 × sin21° ( divide both sides by sin33° )
v = [tex]\frac{6sin21}{sin33}[/tex] ≈ 4 cm ( to the nearest cm )
A population of beetles are growing accordingto a linear growth model. The initial population (week 0) isPo = 5, and the population after 7 weeks is P = 82.Find an explicit formula for the beetle population after n weeks..Pn-After how many weeks will the beetle population reach 258?weeks
Answer:
P(n) = 5 + 11n
n = 23 weeks
Explanation:
The equation for the population as a linear growth model has the form
P = P0 + an
Where P0 is the initial population, n is the number of weeks and a is the rate of increase per week. We know that P0 = 5, so
P = 5 + an
Additionally, when n = 7 the value of P = 82, so we can use this to find the value of a as follows
82 = 5 + a(7)
82 = 5 + 7a
82 - 5 = 5 + 7a - 5
77 = 7a
77/7 = 7a/7
11 = a
Therefore, the equation for the population after n weeks is
P(n) = 5 + 11n
Finally, to know the number of weeks to reach a population of 258, we need to replace P by 258 and solve for n, so
258 = 5 + 11n
258 - 5 = 5 + 11n - 5
253 = 11n
253/11 = 11n/11
23 = n
So, after 23 weeks the population will be 258.
how to find the length of side x. really having a hard time on this
Since the figure is a square the diagonal divide it in two congruent right triangles. One of them is shown below:
Since we have right trisang
For each scenario, use the tape diagram to help answer the question. Think of different labels to use for the diagram depending on the situation. Mai has picked 1 cup of strawberries for a cake, which is enough for 3/4 of the cake. How many cups does she need for the whole cake?Priya has picked 1 1/2 cups of raspberries. which is enough for 3/4 of a cake. How many cups does she need for the whole cake?
Answer:
The number of cups of strawberries needed to make a whole cake is;
[tex]\begin{gathered} \frac{4}{3}\text{ cups} \\ or \\ 1\frac{1}{3}\text{ cups} \end{gathered}[/tex]Explanation:
Given that;
[tex]1\text{ cup of strawberries can make }\frac{3}{4}of\text{ a cake}[/tex]To get the number of cups of strawberries needed for a whole cake.
Let us multiply both sides by 4/3;
[tex]\begin{gathered} 1\times\frac{4}{3}\text{ cup of strawberries can make }\frac{3}{4}\times\frac{4}{3}of\text{ a cake} \\ \frac{4}{3}\text{ cup of strawberries can make 1-whole }of\text{ a cake} \end{gathered}[/tex]Therefore, the number of cups of strawberries needed to make a whole cake is;
[tex]\begin{gathered} \frac{4}{3}\text{ cups} \\ or \\ 1\frac{1}{3}\text{ cups} \end{gathered}[/tex]84 is 75% of what number
Answer:
112
Explanation:
We need to find a number that represents 100% when 84 represents 75%, so we will use the following
[tex]100\text{ \% }\times\frac{84}{75\text{ \%}}=\frac{100\times84}{75}=\frac{8400}{75}=112[/tex]Therefore, 84 is 75% of 112.
Answer:112
Step-by-step explanation: - 84 is 75% of 112. 100% of 112 is 112, hope this helps
what is the perimeter of 6.05m and 3.5m
Recall that the perimeter P of a rectangle is given as
P = 2(L + B)
where L is the length and B is the width of the rectangle
Given that the length is 6.05m and the width is 3.5m
Then the perimeter
= 2(6.05 + 3.5)
= 2 (9.55)
= 19.10m
Hannah bought a total of 5.12 pounds of fruit at the market. she bought 2.5 pounds of pears and she also bought some bananas. how many pounds of bananas did she buy please show work and answer
Hannah bought pears and bananas only, so let's write the following equation:
[tex]\text{total}=\text{pears}+\text{bananas}[/tex]If the total weight bought is 5.12 and 2.5 pounds are pears, we can calculate the weight of bananas bought:
[tex]\begin{gathered} 5.12=2.5+\text{bananas} \\ \text{bananas}=5.12-2.5 \\ \text{bananas}=2.62 \end{gathered}[/tex]So Hannah bought 2.62 pounds of banana.
Fill in the blanks using these answer choices: always, never, sometimes, once.
The complete text would be as following:
Parallel lines cross never
Perpendicular lines cross once
Lines that are neither parallel or perpendicular cross once
Lines that are the same cross always
Perpendicular lines cross at a 90 degree angle
I need help with these two problems.Use the given functions solve:f(x)=6x+7. g(x)= -2x-4. h(x)= -3x/41. g(-6)2. h(-12)I also need help with this.I attached the graph that goes along with the questions.1. If Unit Produced is a function of Labor Hours,f(5)=?A. 3B. 4C. 8D. 102. What can be determined, when f(x)=8?A. Units produced are 5B. Labor hours are 5C. Units produced are 10D. Cannot be determined
We are given the following functions
[tex]f\mleft(x\mright)=6x+7\qquad g(x)=-2x-4\qquad h(x)=-\frac{3x}{4}[/tex]We are asked to find out g(-6) and h(-12)
1. g(-6)
it simply means that we have to plug x = -6 into the function of g(x)
[tex]\begin{gathered} g(x)=-2x-4 \\ g(-6)=-2(-6)-4 \\ g(-6)=12-4 \\ g(-6)=8 \end{gathered}[/tex]Therefore, g(-6) = 8
2. h(-12)
Once again we have to plug x = -12 into the function of h(x)
[tex]\begin{gathered} h(x)=-\frac{3x}{4} \\ h(-12)=-\frac{3(-12)}{4} \\ h(-12)=\frac{36}{4} \\ h(-12)=9 \end{gathered}[/tex]Therefore, h(-12) = 9
x^3-6x^2+12x-8=27
thnk kiu
x^3−6x^2+12x−8=0
⇔x^3−3x^2.2+3.x.2^2−2^3=0
⇔(x−2)^3=0
⇔(x−2)=0
⇔x=2
A sector with a central angle measure of \purpleD{\dfrac{\pi}{6}} 6π start color #7854ab, start fraction, pi, divided by, 6, end fraction, end color #7854ab (in radians) has a radius of \maroonD{12\,\text{cm}}12cmstart color #ca337c, 12, start text, c, m, end text, end color #ca337c.
EXPLANATION:
Given;
We are given a sector of a circle with the following dimensions;
[tex]\begin{gathered} radius=12 \\ central\text{ }angle=\frac{\pi}{6} \end{gathered}[/tex]Required;
We are required to calculate the area of the sector with the details given.
Step-by-step solution;
To calculate the area of a sector with the central angle given in radians, we will use the following formula;
[tex]Area\text{ }of\text{ }a\text{ }sector=\frac{\theta}{2\pi}\times\pi r^2[/tex]We can now substitute and solve;
[tex]Area=\frac{\frac{\pi}{6}}{2\pi}\times\pi r^2[/tex][tex]Area=(\frac{\pi}{6}\div\frac{2\pi}{1})\times\pi r^2[/tex][tex]Area=(\frac{\pi}{6}\times\frac{1}{2\pi})\times\pi\times12^2[/tex][tex]Area=\frac{1}{12}\times144\times\pi[/tex][tex]Area=12\pi[/tex]ANSWER:
In terms of pi the area of the sector is
[tex]undefined[/tex]write the given equation in slope intercept form. 5x-3y = -9
Thae equation is given as :
5x - 3y = -9
The equation can be written in slope intercept form as;
y= mx + c where m is the gradient and c is the y-intercept
So this will be;
5x = 3y -9
5x + 9 = 3y
5/3 x + 9/3 = 3y/3
5/3 x + 3 = y
y= 5/3 x + 3
Answer
y = 5/3 x + 3
question 1 estimated number of dogs = 6.99 × 107=6.99 • 10,000,000=69,900,000estimated number of cats = 3.61 × 107=3.61 • 10,000,000= 36,100,000estimated number of birds = 8.3 × 106= 8.3 • 1,000,000= 8,300,000-------------------------------------------Question 2The estimated number of dogs is 6.99 x 10⁷The estimated number of cats is 3.61 x 10⁷The estimated number of birds is 8.3 x 10⁶The power of 10 in 8.3 x 10⁶ is 6 which is less than the power of 10 in the other two numbers. To make the calculation simpler, convert this number so the exponents are all the sameMultiply and divide 8.3 x 10⁶ by 10 to increase its exponent by 18.3x 10⁶= 10/10 • 8.3x 10⁶=8.3/10 •10⁶ •10= 0.83 x 10⁷
SOLUTION
For question 1, we have
[tex]\begin{gathered} 6.99\times10^7=69,900,000 \\ 3.61\times10^7=36,100,000 \\ 8.3\times10^6=8,300,000 \end{gathered}[/tex]Take the sum of the number above, we have
[tex]\begin{gathered} 69,900,000+36,100,000+8,300,000 \\ =114,300,000 \end{gathered}[/tex]For Question 2, we have
We need to add the number without converting to the ordinary form i.e will add the number in thier exponential form.
[tex]6.99\times10^7+3.61\times10^7+0.83\times10^7[/tex]The exponent is the common factor, hence we add the other numbers
[tex]\begin{gathered} (6.99+3.61+0.83)\times10^7 \\ =11.43\times10^7 \end{gathered}[/tex]Changin the result in question 2 to ordinary form, we have
[tex]11.43\times10^7=11.43\times10,000,000=114,300,000[/tex]Hence
Yes the answer in question 1 and question 2 are the same.
We can tell this because the nunbers have the same values(they are the same) but are in different forms(ordinary form and the exponential form). Hence the numbers can be use interchangeably.
a. Reflect y = x^2 – 2 across the x-axis.
Given;
We are to reflect the function:
[tex]y=x^2\text{ -2}[/tex]Given a function f(x), the rule for reflecting across the x-axis is:
[tex]\begin{gathered} f(x)\text{ }\rightarrow\text{ -f'(x)} \\ \text{where the arrow represents the transformation} \end{gathered}[/tex]Hence, the reflection of the given function gives:
[tex]\begin{gathered} y=f(x)=x^2\text{ -2} \\ f^{\prime}(x)=-(x^2-2) \\ =-x^2+2 \end{gathered}[/tex]Thus the reflected function would be:
[tex]y^{^{\prime}}=-x^2+2[/tex]Show how Aaliyah can finish her work using complexnumbers. As a reminder, her last step before requiringassistance is:(x- 3)2=1Be sure to show ALL steps that lead to your finalsolution set!
aAs given by the question
There are given that the equation
[tex]x^2-6x+10=0[/tex]Now,
The solution of the Aaliyah is:
[tex](x-3)^2=-1[/tex]Then,
The next step of the given solution is:
[tex]\begin{gathered} (x-3)^2=-1 \\ x-3=\sqrt[]{-1} \end{gathered}[/tex]According to the concept of complex number
[tex]i=\sqrt[]{-1}[/tex]So,
[tex]\begin{gathered} x-3=\sqrt[]{-1} \\ x-3=i \\ x=i+3 \end{gathered}[/tex]Provide reasons for the proofGiven line m is parallel to line nprove angle 1 is supplementary to angle 3
The first reason is Given.
The second is corresponding angles theorem.
The third one is definition of congruent angles.
The fourth is definition of linear pair.
The fifth is linear pair theorem.
The sixth is definition of supplementary angles.
The seventh is addition property of equality.
The eighth is definition of supplementary angles.