Match each piece of the function with its domain.(6, oo)(-00, 1)(1,00)(-oo, -2)(-00, 6)(-2, 6)(3,00)(1, 4)
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Explanation
The question wants us to select all the domains in the set of functions graphed.
The domain of a function is the set of all possible inputs for the function.
To do so, we have to be aware that there are 3 pieces of functions
These are shown below
These are
[tex]\begin{gathered} (-\infty,-2) \\ \\ (-2,6) \\ \\ (6,\infty) \end{gathered}[/tex]
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PLEASE HELP!!
Write an equation of a quadratic function with the given properties: f(3)=f(-5)=0; f(-6)=-36
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The equation for a quadratic function with given properties is, f(x) = -201.5 (x² +2x - 15)
Given,
f(3) = f(-5) = 0;
f(-6) = -36
Here,
The x intercepts of the quadratic equation are;
x₁ = 3 , x₂ = -5
The quadratic equation in factored form is equal to
f(x) = a(x - x₁) (x - x₂)
Substitute x₁ = 3 , x₂ = -5 in f(x)
Then,
f(x) = a(x - 3) (x - -5)
f(x) = a(x - 3) (x + 5)
We have;
f(-6) = -36
That is, if x = -6 then f(x) = -36
So,
f(x) = a(x - 3) (x + 5)
-6 = a(-36 - 3) (-36 + 5)
-6 = a x - 39 x - 31
-6 = 1029a
a = -1029/6
a = -201.5
Here,
f(x) = -201.5(x - 3) (x + 5)
Apply distributive property;
f(x) = -201.5(x² +5x - 3x - 15)
f(x) = -201.5 (x² +2x - 15)
That is,
The equation for a quadratic function with given properties is, f(x) = -201.5 (x² +2x - 15)
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Evaluate 7a - 5b when a = 3 and b = 4 .
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A committee of eight math instructors and ten science instructors need to select two people from each group to send to a conference. What is the probability of selecting two math instructors and two science instructors?
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Choosing two math instructors out of 8 would be
[tex]P=\frac{2}{8}=\frac{1}{4}[/tex]Choosing two science instructors out of 10 would be
[tex]P=\frac{2}{10}=\frac{1}{5}[/tex]Given that they are independent events, we multiply their probabilities
[tex]P=\frac{1}{4}\times\frac{1}{5}=\frac{1}{20}[/tex]Hence, the probability of selecting two math instructors and two science instructors is 1/20.
Solve 5x² + 25 = 0Ox= -5x = -5 and x = 5Ox=5No Real Solutions
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Solve for x:
Subtract 25 from both sides:
[tex]\begin{gathered} 5x^2+25-25=-25 \\ 5x^2=-25 \end{gathered}[/tex]Divide both sides by 5:
[tex]\begin{gathered} \frac{5x^2}{5}=-\frac{25}{5} \\ x^2=-5 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} x=\pm\sqrt{-5} \\ x=\pm\sqrt{5}i \end{gathered}[/tex]Therefore, there are no real solutions
Answer:
No Real Solutions
9) Write an equation of a line that is steeper than y- 6x + 2
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Which graph represents 2x + 3y < 6?Choose 1 answer:
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Given: An inequality
[tex]2x+3y<6[/tex]Required: To determine the graph of the inequality.
Explanation: The inequality represent an area either inside or outside a line determined by repl
100 points!!!!
PLS WRITE IN SLOPE INTERCEPT FORM
–18y + 8 = 12x
SOLVE FOR Y
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Answer: y = (-2/3)x + (4/9)
Step-by-step explanation:
y = mx + b is the form expected
-18y + 8 = 12x
subtract 8 from both sides
-18y = 12x - 8
divide both sides by -18
y = (12x/-18) - (8/-18)
Simplify the negatives and pull x out of the parenthesis (this only works if x is in the numerator).
y = (-12/18)x + 8/18
Simplify the fractions
y = (-2/3)x + 4/9
Answer:
The required value of y is,
y = -(2/3)x + (4/9)Step-by-step explanation:
Given equation,
→ -18y + 8 = 12x
The slope-intercept form is,
→ y = mx + b
Let's rewrite the equation,
→ y = mx + b
→ -18y + 8 = 12x
→ -18y = 12x - 8
→ -y = (12x - 8)/18
→ -y = (2/3)x - (4/9)
→ y = -(2/3)x + (4/9)
Hence, this is the answer.
If two lines intersect and one of the angles formed has a measure of 67°, which of the following statements are true? Explain your answers.
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Intersecting Lines
When two lines intersect, four angles are formed at the point of intersection.
Two pairs of angles are vertical, i.e., they have the same measure.
Two pairs of angles are complementary (or linear) therefore their sum adds up to 180°.
We are given one of the angles that has a measure of 67°.
Then, another angle also measures 67° (the vertical peer).
One of the other angles is 180° - 67° = 113°
The other angle also measures 113° (the other vertical peer).
According to the facts found above, the following statements are true:
* Vertical angles are congruent, therefore another angle must equal 67°
* The lines form linear pairs
* The lines form complementary angles
* Two of the angles formed measure 113°
* Two of the angles formed will have a sum of 180°
Note: The last statement should read "Two pairs of angles formed..."
f(x) = -5x -4 and g(x) = x^2 + 3 find (g+f)(x)
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f(x) = -5x -4
g(x) = x^2+3
To find (g+f)(x) , simply add both equations:
(g+f)(x)= x^2+3 + (-5x -4 )
(g+f)(x)= x^2+3 -5x -4
Combine like terms
(g+f)(x)= x^2-5x+3-4
(g+f)(x)= x^2-5x-1
Use the fact that 521•73=38, 033.Enter the exact product of 5.21•7.3
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Answer: 38.033
5.21 x 7.3
= 38.033
I’m stuck on this one need a push in Wright direction
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In the graph it is observed that staright line is drawn between y-axis and x-axis. The graph of a linear function is always a straight line. So function represented in graph is linear.
Answer: Yes function is linear
Alberto is saving money to buy a pair of shoes that cost $50 he has already saved $32 he still needs to save D dollars explain how to solve your equation to find how much money Alberto needs to save how much more does he need to save
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This is the formula that represents how much money needs Alberto to buy a pair of shoes.
To solve this equation, first, subtract 32 to both sides of the equation:
[tex]32\text{ - 32 + x = 50 - 32}[/tex][tex]x\text{ = 50 - 32}[/tex][tex]x\text{ = 18}[/tex]Thus, he still needs to save $18 to buy the shoes.
Do you know anything about dilation!?
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Find how many years it would take for an investment of $4500 to grow to $7900 at an annual interest rate of 4.7% compounded daily.
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To answer this question, we need to use the next formula for compound interest:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]From the formula, we have:
• A is the accrued amount. In this case, A = $7900.
,• P is the principal amount. In this case, $4500.
,• r is the interest rate. In this case, we have 4.7%. We know that this is equivalent to 4.7/100.
,• n is the number of times per year compounded. In this case, we have that n = 365, since the amount is compounded daily.
Now, we can substitute each of the corresponding values into the formula as follows:
[tex]A=P(1+\frac{r}{n})^{nt}\Rightarrow7900=4500(1+\frac{\frac{4.7}{100}}{365})^{365t}[/tex]And we need to solve for t to find the number of years, as follows:
1. Divide both sides by 4500:
[tex]\frac{7900}{4500}=(1+\frac{0.047}{365})^{365t}[/tex]2. Applying natural logarithms to both sides (we can also apply common logarithms):
[tex]\ln \frac{7900}{4500}=\ln (1+\frac{0.047}{365})^{365t}\Rightarrow\ln \frac{7900}{4500}=365t\ln (1+\frac{0.047}{365})[/tex]3. Then, we have:
[tex]\frac{\ln\frac{7900}{4500}}{\ln(1+\frac{0.047}{365})}=365t\Rightarrow4370.84856503=365t[/tex]4. And now, we have to divide both sides by 365:
[tex]\frac{4370.84856503}{365}=t\Rightarrow t=11.9749275754[/tex]If we round the answer to two decimals, we have that t is equal to 11.97 years.
hello,Can you please help me with question # 25 in the picture?Thank you
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To find the sum of an arithmetic sequence up to the nth term, we use the sum formula, which is
[tex]S_n=n(\frac{a_1+a_n}{2})[/tex]where a1 represents the first term, and an the nth term.
The general term of our sequence is
[tex]a_n=3n+2[/tex]We want to sum up to the 16th term. Evaluanting n = 16 and n = 1 on this expression, we get the terms to plug in our formula
[tex]\begin{gathered} a_1=3(1)+2=3+2=5 \\ a_{16}=3(16)+2=48+2=50 \end{gathered}[/tex]Then, the sum is equal to
[tex]\sum_{i\mathop{=}1}^{16}(3i+2)=16(\frac{50+5}{2})=8\cdot55=440[/tex]The result of this sum is 440.
What fraction is bigger 25/5 or 24/6?
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many solutions can be found for the system of linear equations represented on the graph?A. no solution B. one solution C. two solution D. Infinity many solutions
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The lines are not intersecting. The system of linear equations has a solution only if the lines corresponding to the equations intersect.
The general linear equation is,
y=mx+c, where m is the slope.
The slopes of lines m=2.
Since the graphs are parallel or have the same slope and will never intersect, the system of linear equations have no solution.
Consider the following equation of a parabola.(y- 7)? = -4(x - 3)Step 1 of 3: Find the focus of the parabola.
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Answer
Focus = (2, 7)
Explanation
Given:
The following is the equation of a parabola
[tex](y-7)^2=-4x(x-3)[/tex]What to find:
To find the focus of the parabola.
Step-by-step solution:
The general equation of a parabola can be given as,
[tex](y-k)^2=4p(x-h)[/tex]Comparing the general equation of a parabola with the given equation of a parabola, we have
4p = -4
∴ p = -4/4 = -1
Also,
h = 3
k = 7
Since h ± c = F
We have,
3 - 1 = 2
Therefore, the focus will be (h ± c, k) = (2, 7)
A cubic equation has zeros at -2, 1, and 3 a) Write an eqn for a polynomial function that meets the given conditions.b) Draw the graph of a polynomial function that meets the given conditions.
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we know that
A cubic equation has zeros at -2, 1, and 3
so
the factors of the cubic equation are
(x+2), (x-1) and (x-3)
Part a
The equation of a polynomial is
[tex]P(x)=(x+2)\cdot(x-1)\cdot(x-3)[/tex]Applying distributive property
[tex]\begin{gathered} P(x)=(x^2-x+2x-2)\cdot(x-3) \\ P(x)=(x^2+x-2)\cdot(x-3) \end{gathered}[/tex]Applying distributive property again
[tex]P(x)=x^3-3x^2+x^2-3x-2x+6[/tex]Combine like terms
[tex]P(x)=x^3-2x^2^{}-5x+6[/tex]Part b
using a graphing tool
see the attached figure below
Triangle DEF is rotated 60⁰ clockwise about the vertex to obtain triangle LMN. if the m
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EXPLANATION
The measure of the angle LMN is equal to 40 degrees, then the measure of the angle LMN is the same because the rotation does not modify the angle.
0 Rick has been losing weight at a constant rate since he began his new fitness plan. The table below shows Rick's weight for the first four weeks, 2 3 I 220.2 218.6 221.8 223.4 Weight (lbs) a) Write an equation to represent this sequence. b) Find Rick's weight after 16 weeks. ter your answer(s) here
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To make the equation lets us find the rate of change of the weight
The form of the equation is y = m x + b
where:
m is the rate of change (slope)
b is the y-intercept (value y when x = 0)
To find m use two-point from the table
(1, 223.4) , (2, 221.8)
[tex]m=\frac{221.8-223.4}{2-1}=-\frac{8}{5}=-1.6[/tex]Substitute it in the form of the equation
[tex]y=-1.6x+b[/tex]To find b use any point in the table
(1, 223.4)
x = 1 , y = 223.4
[tex]\begin{gathered} 223.4=-1.6(1)+b \\ 223.4=-1.6+b \end{gathered}[/tex]Add 1.6 for both sides to find b
[tex]\begin{gathered} 223.4+1.6=-1.6+1.6+b \\ 225=b \end{gathered}[/tex]Substitute value b in the equation
[tex]y=-1.6x+225[/tex]The equation of the sequence is y = -1.6 x + 225
to find his weight after 16 weeks substitute x by 16
[tex]\begin{gathered} y=-1.6(16)+225 \\ y=-25.6+225 \\ y=199.4 \end{gathered}[/tex]His weight after 16 weeks is 199.4 Ibs
In a sourball game, a fizzy is worth 2 points and a X is worth 5 points. K and W recently played for the sourball game. During the game, K scored eight more fizzles than the W, but scored 5 fewer Y than the W. Together the two teams scored 93 pints total. What was the final score?
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Using mathematical operations of addition, multiplication, division, and subtraction, the final score was:
K = 42 pointsW = 51 points.What are mathematical operations?The basic mathematical operations for getting mathematical results from numbers, values, and variables include addition, multiplication, division, and subtraction.
In this situation, we apply these four basic mathematical operations.
Fizzy = 2 points
X = 5 points
Total scores = 93 points
The points in 8 Fizzys = 16 points (8 x 2)
The points in 5 Xs = 25 points (5 x 5)
The equation showing the total scores of K = total scores + 16 - 25
= (93 + 16 - 25)/2
= 42 points
The equation showing the total scores of W = total scores - 16 + 25
= (93 - 16 + 25)/2
= 51 points
Final scores are K = 42 and W = 51.
Thus, applying mathematical operations, the final score shows that K scored 42 points while W scored 51 points, totaling 93 points for the two teams.
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coupon A 60% off of $87 pants coupon B $55 rebate on $87 pants
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We are given two coupons A and B. Coupon A gives a 60% discount on a $87 item. Let's calculate the amount to pay by subtracting 60% of 87. We do that by multiplying 87 by 60/100, like this:
[tex]87(\frac{60}{100})=52.2[/tex]Now we subtract this from the initial price, like this:
[tex]87-52.2=34.8[/tex]therefore, using coupon A she must pay $34.8
For coupon B there's a rebate of $55. We calculate the amount to pay by subtracting 55 to the total price of 87, like this:
[tex]87-55=32[/tex]Therefore, using coupon B she must pay $32.
Coupon B gives the lowest price, the price of coupon B compared to coupon A is calculated by subtracting both prices:
[tex]34.8-32=2.8[/tex]Therefore, with coupon B she pays $2.8 less than the price with coupon A.
give two-sided of a triangle, find a range of a possible side length of the third side 24 and 52
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For a triangle to be possible with 3 given lengths, the largest side must be lower than the sum of the two remaining sides.
Let L be the length of the third side. There are two cases:
If L is the largest side, then:
[tex]\begin{gathered} L<24+52 \\ \Rightarrow L<76 \end{gathered}[/tex]If L is not the largest side, then the largest side has a measure of 52 and:
[tex]\begin{gathered} 52<24+L \\ \Rightarrow52-24Since both conditions should meet for a triangle to be formed, then:[tex]28Therefore, the range of possible values for L is:[tex]undefined[/tex]Eric takes classes at both Westside Community College and Pinewood Community College. At Westfield class fees are $98 per credit hour and at Pinewood, class fees are $115 per credit hour. Eric is taking a combined total of 17 credit hours at the two schools. Suppose that he is taking W credit hours at Westside. Write an expression for the combined total dollar amount he paid for class fees. Total paid ( in dollars) =
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Let W = number of credit hours at Westside
Since the total credit hours is 17, the number of credit hours at Pinewood is :
[tex]17-W[/tex]To find the expression for the combined total dollar amount for both class.
Multiply each hours by the corresponding fees.
The expression will be :
[tex]\begin{gathered} 98(W)+115(17-W) \\ =98W+1955-115W \\ =1955-17W \end{gathered}[/tex]The correct answer is :
1955 - 17W
What should you do to finish solving this equation?6y + 4y + 90 = 36010y + 90 = 360Add 90 then divide by 102 subtract 90 then multiply by 10Add 10 then multiply by 904Subtract 90 then divide by 10O 102O 304h
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answer is substract 90 then divide by 10
How do I simplify 5 8/48
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Given:
[tex]5\frac{8}{48}[/tex][tex]5\frac{8}{48}=\frac{248}{48}[/tex][tex]5\frac{8}{48}=\frac{31}{6}[/tex][tex]5\frac{8}{48}=5.1667[/tex]what can divide into 8 and 48
if you need to you can do small numbers like 2
but you can divide 4 and 8
you don’t have to worry about 5 because that a whole number so pretend that’s not that there until you break down the fraction till you can’t anymore
once you can’t break down the fraction anymore and the 5 back
hope this helped
Olivia goes out to lunch. The bill, before tax and tip, was $13.90. A sales tax of 6% was added on. Olivia tipped 23% on the amount after the sales tax was added. How much was the sales tax? Round to the nearest cent.
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According to the information given in the exercise, the bill before the tax and tip was $13.90 and the sales tax of 6% was added to that amount.
By definition, you can write 6% as a Decimal number by dividing it by 100. Then, this is:
[tex]\frac{6}{100}=0.06[/tex]Let be "t" the amount (in dollars) of the sales tax.
To find the value of "t", you can set up the following equation:
[tex]t=(13.90)(0.06)[/tex]Finally, evaluating, you get that this is:
[tex]t=0.834[/tex]Rounded to the nearest cent, this is:
[tex]t\approx0.83[/tex]The answer is: $0.83
The numerator of a certain fraction is five times the denominator. If nine is added to both the numerator and the denominator, the resulting fraction is equivalent to two. What was the original fraction (not written in lowest terms)?
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Explanation
To solve the question,
Let
The numerator = x
The denominator = y
So that the original equation will be
[tex]\frac{x}{y}[/tex]Next, we are told that the numerator is five times the denominator.
So that
[tex]x=5y[/tex]Again, we are told that If nine is added to both the numerator and the denominator, the resulting fraction is equivalent to two. so
[tex]\frac{x+9}{y+9}=2[/tex]Hence
we can substitute x =5y into the above
[tex]\begin{gathered} \frac{5y+9}{y+9}=2 \\ \\ cross\text{ multiplying} \end{gathered}[/tex][tex]\begin{gathered} 5y+9=2(y+9) \\ 5y+9=2y+18 \\ Taking\text{ like terms} \\ 5y-2y=18-9 \\ 3y=9 \\ \\ y=\frac{9}{3} \\ \\ y=3 \end{gathered}[/tex]Thus, the denominator is 3
The numerator will be
[tex]\begin{gathered} x=5y \\ x=5\times3 \\ x=15 \end{gathered}[/tex]The numerator is 15
Therefore, the fraction is
[tex]undefined[/tex]Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree. a. 87 ft b. 74 ft c. 65 ft d. 63 ft
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Given the information on the picture, we have the following right triangle:
we can use the tangent trigonometric function to find the height of the tree:
[tex]\begin{gathered} tan(44)=\frac{\text{opposite side}}{adjacent\text{ side}}=\frac{h}{90} \\ \Rightarrow\tan (44)=\frac{h}{90} \end{gathered}[/tex]solving for h, we get:
[tex]\begin{gathered} \frac{h}{90}=\tan (44) \\ \Rightarrow h=90\cdot\tan (44)=86.9\approx87 \\ h=87ft \end{gathered}[/tex]therefore, the height of the tree is 87 ft