The function f(x) = −(x + 5)(x + 1) is shown.
What is the range of the function?
a.all real numbers less than or equal to 4
b.all real numbers less than or equal to −3
c.all real numbers greater than or equal to 4
d.all real numbers greater than or equal to −3
Answers
Since the shading would go from 4 all the way to negative infinity, the answer is all real numbers less than or equal to 4.
Best of luck!
Range of the given function is all real numbers less than or equals to 4.
What is the range of the function?The range of a function is the set of all its output values.
According to the given equation we have
f(x) = -(x+5)(x+1)
Let, y = -(x+5)(x+1)
To find the range of the given function, we will substitute different values of x.
At, x = -5
y = f(-5) = -(-5 +5)(-5+1) =0
At, x = -4
y = f(-4) = -(-4 + 5)(-4 + 1) = -(1)(-3) = 3
At, x = -2
y = f(-2) = -(-2+5)(-2+1) = -(3)(-1) =3
At, x = -3
y = f(-3) = -(-3 + 5)(-3 + 1) = -(2)(-2) =4
Similarly, we will find for the other values of x.
So, the coordinates are (-5, 0), (-4, 3), (-3, 4), (-2,3)
And the graph using this coordinates are already given. Here, the set of outputs are the values of y. So we can see that the range of the given function is all real numbers less than or equals to 4.
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Related Questions
Which statement about this product is true? 0.36×(−758)
A.) It is less than −758-758 because multiplying by a number less than 11 gives a smaller number.
B.) It is greater than −4-4 because 0.36×(758)0.36×758 is less than 12×812×8.
C.) It equals −758-758 because 36363636 equals 11, and 11 times any number equals that number.
D.) It equals 00 because 0.360.36 rounded to the nearest whole number is 00, and 00 times any number is 00.
Answers
if you do .036 x (-7 5/8) gives you -2.745
Answer:
B. It is greater than -4 because 0.36*(7 5/8) is less than 1/2 * 8
Step-by-step explanation:
Given the question:
Which statement about this product is true? 0.36*(-7 5/8)
If you replace the multiplication:
0.36*(7 5/8)
by
1/2*8 = 4
You will get a greater result because 1/2 ( or 0.5) is greater than 0.36 and 8 is greater than (7 5/8). Taking into account that the original multiplication involves a negative number, then:
0.36*(7 5/8) < 1/2*8
0.36*(-7 5/8) > 1/2*(-8) (multiply by a negative number at both sides of the inequality change the sign)
In fact 0.36*(-7 5/8) = -2.745.
A local restaurant advertises that the mode cost of their most popular meals is $8. If the costs of their most popular meals are $7, $8, $8, $12, $13, $15, $17, $18, and $20, which word or phrase best describes this kind of advertising?
Answers
Batman is 4 times robins age the sum of their ages equals to 45 how old is batman and robin
Answers
We can set up a system of equations as such with the given information:
[tex]b=4r\\b+r=45[/tex]
Using substitution, we plug-in 4r from the first equation into b in the second equation to get [tex]5r=45 \\ r=9[/tex].
Now, we plug in the value of r into the first equation to get [tex]b=4(9)=36[/tex].
Thus, Batman is 36 years old, and Robin is 9 years old... A little weird?
A spider ate 25%, percent more bugs this month than last month. The spider ate 8 bugs last month. How many bugs did the spider eat this month?
Answers
it ate 10 bugs this month
Jason's insurance company pays 80% of the cost of an ambulance ride, after he pays a $200 deductible. The ambulance ride costs $1200. How much would Jason pay for an ambulance ride?
A. $200B. $240C. $400D. $440
Answers
That's 1200 - 200 = 1000.
The insurance pays 80% of 1000. Percent means "out of 100" (per means "for every" and "cent" means 100 --> think CENTury...100 years). So 80% means 80 out of 100. That is, [tex] \frac{80}{100} [/tex]. To find 80% of 1000 we multiply: [tex] (\frac{80}{100})( 1000) = \frac{80000}{100}=800 [/tex]
If decimals are more your thing then represent 80% as .80 and multiply (1000)(.80) = 800.
Now, that's what the insurance pays. So out of that $1,000 the insurance pays $800 leaving Jason with a bill of $200 plus the deductible (another $200). That means Jason pays $400.
Answer:
400
Step-by-step explanation:
Find the annual interest rate. I=$54, P=$900, t=18 months
Answers
[tex]\bf ~~~~~~ \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\$54\\ P=\textit{original amount deposited}\to& \$900\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{18}{12}\to &\frac{3}{2} \end{cases} \\\\\\ 54=(900)(r)\left( \frac{3}{2} \right)\implies \cfrac{54}{(900)\left( \frac{3}{2} \right)}=r\implies \cfrac{1}{25}=r\implies 0.04=r \\\\\\ r\%=0.04\cdot 100\implies r=\stackrel{\%}{4}[/tex]
Answer:
4%
Step-by-step explanation:
yw
If p is true and q is false, then p ∧ ~q is true.
true
false
Answers
Justification
1) ∧ is the and operator
2) ~ is the symbol for negation (which is the same that making false)
3) p ∧ ~q means p and not q.
4) The and operator means that the two joined premises, this is p and ~q, have to be true for the whole statement ve true.
5) It is given that p is true and q is false, then p and ~ q is true.
Answer: true.
Answer:
true
Step-by-step explanation:
A group of 8 friends plan to go watch a movie but they only have 5 tickets. How many different combinations of 5 friends could possibly receive the ticket?
A)13
B)10
C)56
D)64
Answers
Explanation:
1) You have to find the number of ways how you can combine 5 friend (this is form groups of 5 people) out of a group of 8.
2) That is the 5C8
3)The formula for combinatory is: nCm = m! / [ n! (m - n)!]
4) So for m = 8 and n = 5 you get:
5C8 = 8! / [5! (8 - 5)! ] = 8*7*6*5! / [ 5! * 3!] = 8*7*6 / [ 3*2*1] = 8*7 = 56
So, the answer is the option C) 56.
20 POINTS,, PLEASE HELP!!!
Given points K'(1, -2) and L'(1, -4), what are the coordinates of the point J' that produces a triangle J'K'L' congruent to JKL resulting from a rotation of 90 degrees clockwise around the point (1, -6)?
J' ______, _______
Answers
where is point J' that produces a triangle J'K'L' congruent to JKL resulting from a rotation of 90 degrees clockwise around the point (1, -6)
J' (5, 0)
A small plane is 20 miles due north of the airport. a jet at the same altitude as the plane is 64.5 miles west of the airport. to the nearest tenth, what is the distance between the small plane and the jet? enter your answer as a decimal in the box.
Answers
okay realize that the distance traveled by the small plane, distance traveled by jet, and the distance between them makes a right triangle. Using Pythagorean theorem and allowing x be the distance between them, x² = (20 miles)² + (64.5 miles
x = 67.53 miles the distance between the two entities in nearest tenth is approximately 67.5 miles.
Using the Pythagorean theorem, we can calculate the distance between a small plane 20 miles north of an airport and a jet 64.5 miles west of the airport as 67.5 miles to the nearest tenth.
Given that a small plane is 20 miles due north of the airport and a jet is 64.5 miles west of the airport, the scenario forms a right-angled triangle with the legs representing the distances from the airport to each aircraft. To find the distance between the small plane and the jet, we can use the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (the legs).
The equation for the distance (d) between the two planes can be expressed as:
d² = north side² + west side²
d² = 202 + 64.52
d² = 400 + 4160.25
d² = 4560.25
d = √4560.25
d = 67.5 miles (rounded to the nearest tenth)
Thus, the distance between the small plane and the jet is 67.5 miles to the nearest tenth.
How many times greater is the area of circle B compared to the area of circle A?
A.) 15 times greater
B.) 10 times greater
C.) 2.25 times greater
D.) 1.5 times greater
Answers
11. The polygons are similar, but not necessarily drawn to scale. Find the values of x and y.
Answers
ABCD ~ NMPO. Note it's important to match up the corresponding angles.
For similar triangles, the ratio of corresponding sides is the same.
So the ratio of AB to NM equals the ratio of BC to MP.
AB/NM = BC/MP
(y - 1) / 6 = 5/3
Solve for y.
Use the same process to find x.
CD/PO = BC/MP
Can anyone please help me with this problem? I got my answer incorrect, and I don’t understand why.
Answers
a) is asking what is the initial height, and that occurs right before the balloon is shot up, at 0 seconds, namely at x = 0.
Solve the equations to find the number and type of solutions. The equation 8 − 4x = 0 has real solution(s).
Answers
Answer:
The number of solution is, 1 and the type of solution is, Integer solution.
Step-by-step explanation:
Given the equation:
[tex]8-4x=0[/tex]
Add 4x to both sides we have;
[tex]8 = 4x[/tex]
Divide both sides by 4 we have;
[tex]2 = x[/tex]
or
x = 2
Solution for this equation is, 2
Therefore, The number of solution is, 1 and the type of solution is, Integer solution.
The equation has a single real solution, x = 2.
The equation 8 − 4x = 0 can be solved as follows:
8 − 4x = 0
4x = 8
x = 2
The equation has one real solution, x = 2.
A real solution is a solution that is a number. The number 2 is a real number, so the equation has one real solution.
Here is a more detailed explanation of the solution:
We subtract 8 from both sides of the equation.
We divide both sides of the equation by -4.
We simplify both sides of the equation.
The answer is x = 2, which is a real number. So, the equation has one real solution.
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Maya's standard deduction on her federal income tax return is $8350. If she paid $5980 in state taxes and $2430 in mortgage interest last year, should she use her standard deduction?
Answers
Answer: b no because it is less then the deduction she would get from itemizing
AB=2y+1, BC=y+1,CD=7x-3,DA=3x what is x and y
Answers
Answer:
x = 2
y = 5
Explanation:
ABCD is a parallelogram. This means that each two opposite sides are equal.
This means that:
1- AB = CD
2y + 1 = 7x - 3 ...........> equation I
2- AD = BC
3x = y + 1
This can be rewritten as:
y = 3x - 1............> equation II
Substitute with equation II in equation I and solve for x as follows:
2y + 1 = 7x - 3 ...........> equation I
2(3x - 1) + 1 = 7x - 3
6x - 2 + 1 = 7x - 3
6x - 1 = 7x - 3
7x - 6x = -1 + 3
x = 2
Substitute with x in equation I to get y as follows:
y = 3x - 1
y = 3(2) - 1
y = 6 - 1
y = 5
Hope this helps :)
Given the segments of a quadrilateral, the steps show that for it to be closed, the expression 3y + 10x + 1 = 0 must hold. Additional information would be needed to find unique values for x and y.
Given the segments AB, BC, CD, and DA of a quadrilateral:
AB = 2y + 1BC = y + 1CD = 7x - 3DA = 3xFor a quadrilateral to be closed, the perimeter equations must be equal. Thus, we set up the equality:
AB + BC + CD + DA = 0
Substituting the given segment expressions:
(2y + 1) + (y + 1) + (7x - 3) + (3x) = 0
Simplifying this equation:
3y + 4 + 10x - 3 = 0
Combine like terms:
3y + 10x + 1 = 0
This represents a linear equation involving x and y.
Assuming the quadrilateral is closed, another equation or condition is needed to solve for x and y simultaneously. If additional geometric or numeric information is provided about the quadrilateral, it can help solve the system.
here is complete question-Find the values of x and y in ABCD. 9. AB=2y,BC=y+3,CD=5x-1,DA=2x+4 10. AB=2y+1,BC=y+1,CD=7x-3,DA=3x (6.3) Determine whether the quadrilateral must be a parallelogram.
A carpenter has a piece of wood that is 10 Yards long and a piece that is 5 Feet Long . How many Feet of wood does the carpenter have ?
Answers
10 yd = 10 * 1 yd
10 * 1 yd = 10 * 3 ft
10 yd = 30 ft
The 10-yard piece is 30 ft long.
Then you add to it the 5-foot long piece.
30 ft + 5 ft = 35 ft
Answer: He has 35 ft of wood.
Given that lines a and b are parallel and that m∠8 = 108°, find m∠3.
Answers
Answer:
The answer would be 72
Find the unknown side length, x. Write your answer in simplest radical form.
Answers
Answer: The required value of x is 32.
Step-by-step explanation: We are given to find the length of the unknown side.
That is, x = ?
From the figure, we see a right-angled triangle with
length of the hypotenuse, h = 68 units,
length of the other two sides, a = 60 units and b = x.
Using Pythagoras theorem in the given right-angled triangle, we have
[tex]h^2=a^2+b^2\\\\\Rightarrow 68^2=60^2+x^2\\\\\Rightarrow x^2=68^2-60^2\\\\\Rightarrow x^2=4624-3600\\\\\Rightarrow x^2=1024\\\\\Rightarrow x=\pm32.[/tex]
Since x is the length of a side of the triangle, so it cannot be negative.
Therefore, x = 32 units.
Thus, the required value of x is 32.
The first team of workers received 50 kg of cement less than the second team. for every hour of work the first team was using 150 kg of cement, while the second team was using 200 kg. in three hours the first team had 1.5 times as much remaining cement as the second team. how much cement was delivered to each team of workers?
Answers
the amount of cement the first team received is termed as 'x' hereafter
the cement the second team received is termed as 'y'
the first team received 50 kg less, the 1st equation is as follows;
x = y - 50 after rearranging
1) x-y = -50
for every hour 150 kg and 200 kg were used by the two teams separately
after three hours first team used up 150*3 = 450 kg
the second team used up 200 * 3 = 600 kg
however the first team had 1.5 times as much as second team had after three hours.
After three hours;
the amount second team had leftover was y - 600
the amount first team had leftover was x - 450
the amount the second team had ,multiplied by 1.5 is equal to what the first team had
we can build the 2nd equation using this information
1.5 * (y-600) = x-450
1.5y - 900 = x - 450
rearrange the equation,
1.5y - x = -450 +900
2) 1.5y - x = 450
add 1st and 2nd equations to eliminate x
1) + 2) (x - y = -50) + (1.5y - x = 450)
1.5y - y = 450 -50
0.5y = 400
y = 400/ 0.5
y = 800 kg
substitute y = 800 in x = y - 50
x = 800 - 50
x = 750 kg
first team received 750 kg and second team received 800 kg
What is the value of x in the figure shown?
A quadrilateral is shown with the measurements of four angles shown. The first angle measures 65 degree sign. The second angle measures 123 degree sign. The third angle measures 87 degree sign. The fourth angle measures x degree sign.
A. x = 85 B. x = 95 C. x = 150 D. x = 208
Answers
360-(65+123+87)=360-275=85
x=85
A quadrilateral is shown with the measurements of four angles shown. The fourth angle is 85 degrees.
What is the angle sum property?The angle sum property of a quadrilateral states that the sum of the interior angles of a triangle is 360 degrees.
A quadrilateral is shown with the measurements of four angles shown. The first angle measures 65 degree sign.
The second angle measures 123 degree sign.
The third angle measures 87 degree sign. The fourth angle measures x degree sign.
The total amount of angles in a quadrilateral is 360:
x + 65 + 123 + 87 = 360
x = 360-(65+123+87)
x =360-275
x=85
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A cylindrical candle has a height of 11 cm and a diameter of 10 cm.
what is the volume of the candle, rounded to the nearest whole number?
Answers
The answer is 864 cm³
Find the area of each figure.
Answers
141.3ft^2 second
(50 points worth ) A rectangular prism fish tank a length of 5 1/2 in., a width of 7 in., and a height of 2 1/2 in. Use this to answer questions (a) and (b) below.
A) What’s the volume of this fish tank? Show all work and express your answer as a mixed number in its most simplified form!
B) Could this fish tank hold 100 in³ of water? Answer yes or no, then explain why in one or more sentences.
Answers
By definition we have that the volume of a rectangular prism is given by:
V = (w) * (l) * (h)
Where,
w: width
l: long
h: height
We then have to replace the values:
V = (7) * (5.5) * (2.5)
V = 96.25 in ^ 3
Equivalently:
V = 96 1/4 in ^ 3
B) Could this fish tank hold 100 in³ of water? Answer yes or no, then explain why in one or more sentences.
No, this fish tank could not hold 100 in³ of water.
This is because the prism volume (part A) is less than 100 in ^ 3.
In other words;
96 1/4 in ^ 3 <100 in ^ 3
simplify the expression 5+4•(8-6)^2
Please show steps.
Answers
( 8 - 6 ) = 2
E- exponents
2^2 = 2 × 2 = 4
M- multiplication / division
4 × 4 = 16
D- division
N/A
A- addition / subtraction
5 + 16 = 21
S- subtraction
N/A
~~
Answer : 21
Simplify the expression 75/153 completely.
Answers
GCD of 75 and 153 is 3
Divide both the numerator and denominator by the GCD
75 ÷ 3
153 ÷ 3
Reduced fraction:
25/51
So,its 25/51 hope this helps
75 / 3 = 25
---- ---
153 / 3 51
if you want to check it then simply multiply both the numerator and denominator 25/51 by 3 to get 75/153
Identify the type of sequence shown in the table below and select the appropriate response. n f(n) 1 540 2 500 3 460 4 420 5 380 arithmetic sequence; common difference is −40 arithmetic sequence; common difference is 40 geometric sequence; common ratio is −40 geometric sequence; common ratio is 40
Answers
Answer:
arithmetic sequence; common difference is −40
Step-by-step explanation:
An arithmetic sequence is a sequence in which each term is found by adding a constant, called the common difference, to each previous term.
In this sequence, we go from 540 to 500 to 460, etc. Each time we are subtracting 40. This is the same as adding -40; this makes the sequence arithmetic.
The common difference of the arithmetic sequence will be negative 40. Then the correct option is A.
What is an arithmetic sequence?A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.
Let a₁ be the first term and d be a common difference.
Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
The table is given below.
n f(n)
1 540
2 500
3 460
4 420
5 380
The first term is 540 and the common difference of the arithmetic sequence is given as,
d = 500 - 540
d = - 40
The common difference of the arithmetic sequence will be negative 40. Then the correct option is A.
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3. Triangle ABC has angle measures as shown.
a) What is the value of x? Show your work.
Answers
(x -5) +(3x +30) +35 = 180
4x +60 = 180 . . . . . . . . . . . . . collect terms
4x = 120 . . . . . . . . . . . . . . . . . subtract 60
x = 30 . . . . . . . . . . . . . . . . . divide by 4
a) The value of x is 30.
[tex](x - 5) + (3x + 30) + 35 = 180[/tex]
[tex]x - 5 + 3x + 30 + 35 = 180[/tex]
Sum up x + 3x
[tex]4x - 5 + 30 + 35 = 180[/tex]
Sum up all the numbers
[tex]4x + 60 = 180[/tex]
Substract 60 from both sides
[tex]4x = 120[/tex]
And finally divide by 4 (on both sides)
[tex]x = 30[/tex]
PLEASE HELP WITH THIS I HAVE NO IDEA HOW TO SOLVE!!!!
PLEASE DON"T IGNORE THIS ONE
PLEASE HELLLP
consider the following graph of a quadratic function. Write the euqation for the quadratic function in standard form.
The graphs y-intercept is 7 and vertex is (-3,-2)
Answers
.. y = a*(x +3)^2 -2
.. = ax^2 +6ax +9a -2
You require the y-intercept to be 7. So, for x=0, you have
.. 9a -2 = 7
.. 9a = 9
.. a = 1
The equation you seek is
.. y = x^2 +6x +7
Classify the polynomial according to its degree and number of terms.
7b^3 + 3b^2 − 7b
A. linear monomial
B. quartic monomial
C. linear trinomial
D. cubic trinomial
HELP ASAP!!
Answers
The degree of this polynomial is 3 and the number of terms is 3 which makes it a cubic trinomial.
The equation given to us here is
[tex]7b^3+3b^2-7b[/tex]
Data Given;
[tex]7b^3+3b^2-7b[/tex]From this equation above, we have to know the degree of the polynomial. This will enable us to know what type of polynomial is this.
Degree of PolynomialThe degree of the polynomial is the highest value of the power in any of the variable.
In this question, the highest degree of polynomial here is 3 and this makes it a cubic polynomial.
However, it have only three variables also which makes it a trinomial. Put together it becomes cubic trinomial.
Generally, the degree of polynomials and their names are,
2 degree = quadratic3 degree = cubic4 degree = quarticLearn more on polynomials here;
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