Multiply or divide the following expression: Reduce all answers to lowest terms. Factor the following completely.
Let f(x) = -x^2-4x+5
f(-3) = _______
f(3) + f(-3) = _______
Answers
A function assigns the values. The value of f(-3) and f(3) + f(-3) is 8 and -8, respectively.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the function f(x)=-x²-4x+5, therefore, the value of f(x) when the value of x is -3 is,
f(-3) = -(-3)² - 4(-3) + 5
f(-3) = -9 + 12 + 5
f(-3) = 8
Now, the value of f(x) when the value of x is 3 is,
f(3) = -(3)²-4(3)+5
f(3) = - 9 - 12 + 5
f(3) = -16
further, the value of f(3) + f(-3) is,
f(3) + f(-3) = -16 + 8
f(3) + f(-3) = -8
Hence, the value of f(-3) and f(3) + f(-3) is 8 and -8, respectively.
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Related Questions
The Wilson family had 5 children. Assuming that the probability of a child being a girl is 0.5, find the probability that the Wilson family had
at least 3 girls?
at most 3 girls?
Answers
The expression represents the probability of getting exactly 3 heads is,
[tex]C(n,r)(0.5)^3(0.5)^6[/tex]
We have given
Aron flips a penny 9 times.
We have to determine
Which expression represents the probability of getting exactly 3 heads
What is binomial distribution?The binomial distribution is determined as the probability of mass or discrete random variable which yields exactly some values.
The binomial probability formula shown has variables that represent:
[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]
Where n is the total number of trials (here, we flip penny 9 times, hence n = 9).
r is the number we want to find (here, we want the probability of 3 heads, so r = 3).
p is the probability of success (here, success means getting heads.
So, in a coin flip the probability of heads is always 1/2, so p = 1/2).
Therefore, The expression represents the probability of getting exactly 3 heads is;
[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]
[tex]=C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex]
Hence, the expression represents the probability of getting exactly 3 heads is [tex]C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex].
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The probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.
What is Binomial distribution?A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
Given the probability of a child being girl is 0.5, therefore, the probability of a child being boy is 0.5. Now, the probability of at least 3 girls out of 5 is,
Probability (x≥3)
= ⁵C₃ (0.5)³(0.5)² + ⁵C₄ (0.5)⁴(0.5)¹ + ⁵C₅(0.5)⁵(0.5)⁰
= 0.5
Probability (x≤3)
= ⁵C₃ (0.5)³(0.5)² + ⁵C₂(0.5)²(0.5)³ + ⁵C₁(0.5)¹(0.5)⁴ + ⁵C₀(0.5)⁰(0.5)⁵
= 0.8125
Hence, the probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.
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WILL GIVE THE BRAINLIEST!
If r and s are real numbers such that
r>s>0, then
(A) -s>-r> 0.
(B) 0>-r> -s.
(C) 0> -s> -r.
(D) -s>0> -r.
(E) -r> -s > 0.
Answers
Answer: Choice (C) 0> -s> -r
==========================================================
Explanation:
Let's consider an example. Pick any two positive numbers for r and s, where r is larger than s. I'll go with these:
r = 5s = 2We see that r > s is true since 5 > 2 is true
Also both are larger than 0 so we can say r > 0 and s > 0
This all combines into r > s > 0 being the case.
If we negate each number, then -r > -s would no longer be true. Use a number line to see that -5 is to the left of -2, so -5 > -2 is not true. Instead it would be -5 < -2
You can think of it like floors on a skyscraper. Positive numbers are above ground, while negative numbers are below ground in the basement levels. See the diagram below.
So -r > -s must be -r < -s instead. Both are smaller than 0
-r < 0 and -s < 0
This combines to -r < -s < 0
Flip everything and swap the outer sides to get 0 > -s > -r which leads us to choice C as the final answer
Prove triangle ABC is congruent to triangle DEC.
Answers
Triangle ABC and DEC are said to congruent since all their sides and angles are equal.
How to prove the statementThe angle for triangle ABC lies in angle B
The angle for triangle DEC lies in angle E
From the diagram, angles B and E are alternate angles and alternate angles are equal.
A corresponds to D
B corresponds to E
The measure of their angles are also equal
Note, congruent triangles are triangles with three corresponding sides and angles
Therefore, triangle ABC and DEC are said to congruent since all their sides and angles are equal.
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Think about all of the ways in which a circle and a parabola can intersect.
Select all of the number of ways in which a circle and a parabola can intersect.
00
1
2
03
04
05
DONE
Answers
There will be four ways a circle and a parabola can intersect because the solution of the quartic equation will be 4.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have a circle and a parabola:
As we know the standard form of a circle:
[tex]\rm (x-h)^2 +(y-k)^2=r^2[/tex]
The standard form of the parabola:
[tex]\rm y = a(x-h)^2+k[/tex]
If we plug the value of y from the parabola equation in the circle equation, we get a quartic equation(4th order equation)
The solution of the quartic equation will be 4.
Thus, there will be four ways a circle and a parabola can intersect because the solution of the quartic equation will be 4.
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Find the slope of the line passing through the points (3,-9) and (2, -3).
Answers
Answer:
The slope of the line passing through is -6.
1
0/1 point
A student wants to write an expression for, "all of the elements which are not in set A but are in set B".
Answers
The way to write this expression in mathematics is A'∩B
How to solve for the expressionIn order to get the right way to write this expression we have to break it down in two parts.
First we are told that some of the elements are not in A.
This is represented as A'.
Then we are told that they are in the set B. Hence we have it written as B.
Then the expression not in set A but are in set B would be written as
A'∩B.
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solve the system of equations for one of the variables x+4y=5 x-4y=5
Answers
Answer:
x=5 y=0
Step-by-step explanation:
cancel out the 4y's and then add the x's together. also add the 5s together. 2x = 10, x = 5, and plug it in, and 5 cancels out, leaving y by itself.
Suppose that
f
(
x
,
y
)
=
x
+
5
y
f
(
x
,
y
)
=
x
+
5
y
at which
−
1
≤
x
≤
1
,
−
1
≤
y
≤
1
-
1
≤
x
≤
1
,
-
1
≤
y
≤
1
.
Absolute minimum of
f
(
x
,
y
)
f
(
x
,
y
)
is
Absolute maximum of
f
(
x
,
y
)
f
(
x
,
y
)
is
Answers
========================================================
Explanation:
The range of x values is [tex]-1 \le x \le 1[/tex] which means x = -1 is the smallest and x = 1 is the largest possible.
Similarly the smallest y value is y = -1 and the largest is y = 1.
----------
Plug in the smallest x and y value to get
f(x,y) = x+5y
f(-1,-1) = -1+5(-1)
f(-1,-1) = -6
Therefore, the absolute min is -6
----------
Now plug in the largest x and y values
f(x,y) = x+5y
f(1,1) = 1+5(1)
f(1,1) = 6
The absolute max is 6
Which expression is equivalent to (a²b¹c)²(6a³b)(2c³)³₂ 4ab¹2c3 ?
Answers
The expression (a²b¹c)² × (6a³b) × (2c³)³ × (4ab¹) × (2c³) is equivalent to the expression 384a⁸b⁴c¹⁴.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
The expression is given below.
⇒ (a²b¹c)² × (6a³b) × (2c³)³ × (4ab¹) × (2c³)
By simplifying, we have
⇒ a⁴b²c² × 6a³b × 8c⁹ × 4ab¹ × 2c³
⇒ 384a⁸b⁴c¹⁴
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What is −7.6 − 2(2.2)
Answers
Answer:
-12
Step-by-step explanation:
Order of operations:
PEMDAS
First, do parenthesis, 2 x 2.2 = 4.4 then do -7.6 - 4.4 = -12
1) When the polynomial P(x) is divided by x+5, the remainder is 3. Which of the following is definitely true?
a) P(3) = 5
b) P(-5) = 3
c) P(5) = 3
d) P(-3) = 5
2) P is a degree 3 polynomial with real coefficients and three zeros. Two of the zeros are 5 and 3+4i. What is the other zero?
a) 4-3i
b) 4+3i
c) -5
d) 3-4i
Answers
1) The definitely true for the statement is b) P(-5) = 3.
2) The three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.
What is the remainder theorem for polynomials?If there is a polynomial p(x), and a constant number 'a', then
[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]
where g(x) is a factor of p(x)
Given;
1) When the polynomial P(x) is divided by x+5, the remainder is 3.
If a polynomial P(x) is divided by (x-a), then the remainder is P(a).
If the polynomial P(x) is divided by (x+5), then the remainder will be P(-5).
So, P(-5) = 3
Therefore, the definitely true for the statement is b) P(-5) = 3.
2) P is a 3 degree polynomial with real coefficients and three zeros. Two of the zeros are 5 and 3+4i.
The complex roots always exist in conjugate pairs so,
3 + 4i and 3 - 4i
Thus, the three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.
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Please solve this equation, I don't understand...
show all work!
Answers
Answer:
x = - 5/2
Step-by-step explanation:
Using the law of indices
. a^-n = 1/a^n
. (a^4)^5 = a^5×4 = a^20
Note : When two base are equal , we equate the Exponents.
3^4x-5 = (1/27)^2x+10
= 3^4x-5 = (27^-1)^2x+10
= 3^4x-5 = (3^-3)^2x+10
= 3^4x-5 = 3^ -3(2x+10)
= 3^4x-5 = 3^ -6x-30
The two base are 3 so we equate the exponents.
= 4x - 5 = -6x - 30
= 4x + 6x = -30+5
= 10x = -25
= 10x/10 = -25/10
x = -25/10
x = - 5/2
X is -5/2
If f(x) = x + 8 and g(x) = –4x – 3, find (f + g)(x).
A. (f + g)(x) = 5x + 11
B. (f + g)(x) = –3x + 5
C. (f + g)(x) = –5x – 11
D. (f + g)(x) = 3x – 5
Answers
Answer:
B
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= x + 8 - 4x - 3 ← collect like terms
= - 3x + 5
Answer:
[tex]\huge\boxed{\sf (f + g)(x) = -3x + 5}[/tex]
Step-by-step explanation:
Given functions:f(x) = x + 8g(x) = -4x - 3Solution:Add both functions
(f + g)(x) = x + 8 + (-4x - 3)
(f + g)(x) = x + 8 - 4x - 3
(f + g)(x) = x - 4x + 8 - 3
(f + g)(x) = -3x + 5
[tex]\rule[225]{225}{2}[/tex]
Which number comes next in this series 1/64 1/32 1/16 1/8 1/4 1/2
Answers
Answer:
1/1
Step-by-step explanation:
As the question is halfing by 2
So
2 divide 2 equals 1
Answer:
1
Step-by-step explanation:
it's fractions of divided half. next one will be number 1
46. Machine A produces 500 springs a day. The number of defective springs produced by this machine each day is recorded for 60 days. Based on the distribution given below, what is the expected value of the number of defective springs produced by Machine A in any single day?
F. 0.00
G. 0.45
H. 0.70
J. 1.00
K. 1.50
Answers
Answer:
G. 0.45
Step-by-step explanation:
To find expected value, you simply multiply the value of each outcome (the numbers in the left column) by its probability
(the numbers in the right column) and then add them all together.
0(0.7) + 1(0.2) + 2(0.05) + 3(0.05)
0 + 0.2 + 0.1 + 0.15 = 0.3 + 0.15 = 0.45
The expected value is 0.45. Thus, the correct option is G.
What is the expected value?In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.
The expected value is given below.
E(x) = np
Where n is the number of samples and p is the probability.
The expected value is calculated as,
E(x) = 0 x 0.70 + 1 x 0.20 + 2 x 0.05 + 3 x 0.05
E(x) = 0 + 0.20 + 0.10 + 0.15
E(x) = 0.45
Thus, the correct option is G.
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Consider the proof.
Given: In △ABC, BD ⊥ AC
Prove: the formula for the law of cosines, a2 = b2 + c2 – 2bccos(A)
Triangle A B C is shown. A perpendicular bisector is drawn from point B to point D on side A C. The length of B C is a, the length of D C is b minus x, the length of A D is x, the length of A B is c, and the length of B D is h.
Statement
Reason
1. In △ABC, BD ⊥ AC 1. given
2. In △ADB, c2 = x2 + h2 2. Pythagorean thm.
3. In △BDC, a2 = (b – x)2 + h2 3. Pythagorean thm.
4. a2 = b2 – 2bx + x2 + h2 4. prop. of multiplication
5. a2 = b2 – 2bx + c2 5. substitution
6. In △ADB, cos(A) = StartFraction x Over c EndFraction 6. def. cosine
7. ccos(A) = x 7. mult. prop. of equality
8. a2 = b2 – 2bccos(A) + c2 8. ?
9. a2 = b2 + c2 – 2bccos(A) 9. commutative property
What is the missing reason in Step 8?
Pythagorean theorem
definition of cosine
substitution
properties of multiplication
Answers
The missing reason in Step 8 is substitution
When a triangle is not a right triangle and when either the lengths of two sides and the measurement of the included angle are known (SAS) or the lengths of the three sides are known (SSS), the Law of Cosines is used to discover the remaining pieces of the triangle.
According to the law of cosine, if a, b, and c are any triangle's three sides, then a² = b² + c² - 2bcosa
The x in statement 5 of the preceding proof is changed to c cos A from statement 6 in statement 8 of the proof.
Option C, from the list of alternatives, is the one that best explains statement 8.
Hence missing reason in Step 8 is substitution
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Answer: OPTION C
Step-by-step explanation:
EDGE22
There were 582 students enrolled in a freshman-level chemistry class. By the end of the semester, the number of students who passed was 5 times the number of students who failed.
Answers
Answer:
let the no. of students who failed the examination be X
therefore, no. of students passed = 5x
total no. of students = 582
5x + X = 582
6x = 582
x = 97
no. of students failed the examination = 97
no. of students passed = 97*5 = 485
Which expression can be used to find the difference of the polynomials?
Answers
The expression that can be used to find the difference of the polynomials is (4m - 5) + ( -6m + 7 - 2n). D
How to find the difference
Given the expression:
(4m - 5) - (6m - 7 + 2n)
Note that - * - = +
+ * - = -
So in finding the difference, we have
(4m - 5) - ( 6m + 7 - 2n )
It could as be written as
(4m - 5) + ( -6m + 7 - 2n)
Therefore, the expression that can be used to find the difference of the polynomials is (4m - 5) + ( -6m + 7 - 2n) . D
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Your mother is out of toothpicks, and suggests you use cotton swabs instead. You measure them, and they are 7.5 cm tall. How many cotton swabs tall will your model be? If necessary, round your answer to the nearest whole number.
Answers
Answer:
6.3 *30= 189; so 4 cotton swabs
Determine the equation of the line that passes through the given points. (If you have a graphing calculator, you can use the table feature to confirm that the coordinates of both points satisfy your equation.) (-5, 10) and (5, -10) a. y = 2x-10 b. C. d. y = 2x y = -2x+ 20 y=-2x A
Answers
Answer:
y = -2x
Step-by-step explanation:
It passes through -5, 10 and 5, -10
gradient = Δy/Δx
gradient = -10 - 10 / 5 -- 5
gradient = -20 / 10
gradient = -2
let's use -5, 10 for y = mx + b
10 = -2(-5) + b
10 = 10 + b
b = 10 - 10
b = 0.
the equation of the line is just y = -2x
Help! I need help with this math problem
Answers
Answer:
h(-1) is -1, h(-0.5) is 0 and h(1) is 1.
Step-by-step explanation:
functions :- an expression, rule or law that defines relationship between one variable and another variable. When a certain condition is fulfilled, then the result is corresponding to that condition.
h(-1)In the function it is given that when x∈(-2,-1] then we get -1. Now here x=-1 satisfies the given condition. So, the answer will be -1.
h(-0.5)In the function it is given that when x∈(-1,0] then we get 0. Now here x=-0.5 lies in the range (-1,0]. So, the answer is 0.
h(1)In the function it is given that when x∈(0,1] then we get 1. Clearly, x=1 satisfies this range of values. So, we get 1.
Hence, the Answer is h(-1) = -1, h(-0.5) = 0 and h(1) = 1.
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A car has a maximum speed of 355.7 feet/second. Convert this speed to miles/hour.
Answers
Answer:
242.5226626 mphStep-by-step explanation:
1 ft/s = 0.681818 mph
355.7 * 0.681818 = 242.5226626
355.7 ft/s = 242.5226626 mph
A farmer has 250 ft of fencing and wants to enclose a rectangular area of 3750 ft². What dimensions should she use?
The length of the longer side of the fence is:
The length of the shorter side of the fence is:
Answers
Answer:
Longer side is 75 feet, shorter side is 50 feet.
Step-by-step explanation:
Let l be the length of the longer side and w be the length of the shorter side.
2l + 2w = 250, which simplifies to
l + w = 125. Solving for w, we have
w = 125 - l.
lw = l(125-l) = 3750
[tex] {l}^{2} - 125l - 3750 = 0[/tex]
[tex]( l - 50)(l - 75) = 0[/tex]
l = 75, w = 50
Simplify the expression -3z(1.8z-2.2).
-5.4z² + 6.6z
-5.4z²-6.6z
-1.2z²+5.2z
-1.2z²-5.2z
Mark this and return
Save and Exit
Next
Submit
Answers
Answer:
[tex] - 5.4z {}^{2} + 6.6z[/tex]
Step-by-step explanation:
Given:
[tex]-3z(1.8z-2.2)[/tex]
Solution:
Applying Distributive property,we obtain
[tex](−3z)(1.8z)+(−3z)(−2.2)[/tex]Simplifying using PEMDAS:
[tex] - 5.4z {}^{2} + 6.6z[/tex]Done!
Answer:A
Step-by-step explanation:
Seismology In 1812, an earthquake of magnitude 7.9 shook New Madrid,
Missouri. Compare the amount of energy released by that earthquake to the
amount of energy released by each earthquake below.
magnitude 9.5 in Valdivia, Chile, in 1960
Answers
Given mCT=26 and m/CAT =124° find the length of CA, the radius in Circle A. Use
π = 3.14 in your calculation and round to the nearest tenth.
Answers
Answer:
[tex]\text{length of \textit{CA}} \ = \ 12.0 \ \ \ (\text{nearest tenth})[/tex]
Step-by-step explanation:
Radian measure is the ratio of the length of a circular arc to its radius.
A radian is the measurement of the central angle which subtends an arc whose length is equal to the length of the radius of the circle.
In the case of the unit circle, as shown in the figure below, one radian is the angle of the sector with a radius of 1 and circular arclength of 1.
Following this definition, the magnitude, in radians, of one complete revolution of a unit circle is the circumference of the unit circle divided by its radius, [tex]\displaystyle\frac{2\pi}{1}[/tex] or [tex]2\pi[/tex]. Thus, [tex]2\pi[/tex] radians is equal to [tex]360^{\circ}[/tex] degrees. Alternatively, one radian is equal to [tex]\displaystyle\frac{180^{\circ}}{\pi} \ \approx \ 57.296^{\circ} \ \ \ (3 \ d.p.)[/tex].
Since radian measure is defined as the ratio of the arc length of a sector to its radius, hence
[tex]\displaystyle\frac{s}{r} \ = \ \theta \\\\ s \ = \ r\theta[/tex]
where [tex]s[/tex] is the arclength, [tex]r[/tex] is the radius, and [tex]\theta[/tex] is the central angle, in radians.
Therefore, the length of CA is
[tex]\displaystyle\frac{s}{\theta} \ = \ r \\ \\ r \ = \ \displaystyle\frac{26}{124^{\circ} \ \times \ \displaystyle\frac{\pi}{180^{\circ}} \ \text{rad}} \\ \\ r = \displaystyle\frac{26 \ \times \ 45}{31 \ \times \ 3.14} \\ \\ r\ = \ 12.0 \ \ \ \ \left(\text{nearest tenth}\right)[/tex]
PLEASE HELP AND SHOW WORK PLEASE.
How is this a no solution answer? I came out with the answer x < -2 and x ≥ 5
5 - x > 7 and 2x + 3 ≥ 13
Answers
Inequalities help us to compare two unequal expressions. There exists no solution to the given set of inequalities.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The given Inequalities can be solved as,
5 - x > 7
-x > 7 - 5
-x > 2
x < -2
2x + 3 ≥ 13
2x ≥ 10
x ≥ 5
As per the solution of the two inequalities, the value of x should be less than -2 but at the same time, it should be more than or equal to 5, which is impossible. Thus, there is no solution for the given inequalities.
This can be confirmed by graphing the two inequalities, as shown below. Since there is no area in common between the two inequalities, there exists no solution to the given set of inequalities.
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If 3x − 6 ≤ f(x) ≤ x2 − 3x + 3 for x ≥ 0, find lim x→3 f(x).
Answers
Answer:
Step-by-step explanation:
How do you solve 32-34?
Answers
Answer:
32. {-4, 1, 2, 12}
33. {2, 6, 9, 31, 65}
34. No
Step-by-step explanation:
32. The domain of a relation is the set that contains all the x-coordinates of all the ordered pairs of the relation.
domain = {-4, 1, 2, 12}
33. The range of a relation is the set that contains all the y-coordinates of all the ordered pairs of the relation.
range = {2, 6, 9, 31, 65}
34. No since the same number, 2, appears twice as an x-coordinate. In a function, no two ordered pairs can have the same x-coordinate.
NEED ASAP
The scatter plot below shows the amount of profit earned per month by a bagel shop over a period of 11 months.
Write an equation for the line of best fit that models the relationship between profit in thousands, p, and time in months,m. Then, use your equation to predict the profit the bagel shop will earn in month 12. Round slope and -y intercept to the nearest tenth.
Answers
The bagel shop will earn $9625 in 12 months.
What is a Scatter Plot ?Scatter plot are graphs that identifies relation between x and y variables.
The scatter points are given in the graph and we have to determine the equation that best fits the data .
the points in the scatter plot is
(3,4) and (8,6)
The slope of the equation
y = mx +c is given by
m =(y2 - y1)/(x2-x1)
m = (9-4)/(11-3)
m = 5/8 = 0.625
The equation is
y= 0.625x +2.125
for 12 months
y = 9.625 thousand = 9625 thousand in 12 months
Therefore the bagel shop will earn $9625 in 12 months.
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Answer:
$9,625 is the answer, and $9,300 is the rounded answer
Step-by-step explanation:
general formula: y=ax-b
required form: p=am-b
choose two dots: (11,9), (3,4)
find the slope: 9-4/11-3=5/8 -> p=5/8
put it into an equation: f(11)=6&7/8-b=9, f(3)=1&7/8-b=4
finding the y-intercept: -9+6&7/8=2&1/8, -4+1&7/8=2&1/8 -> b=2&1/8
forming a whole equation: p=5/8m+2&1/8
predict the profit in December: p=7&4/8+2&1/8=9&5/8
the bagel shop will earn $9,625 in December
round them to the nearest tenth: p=0.6m+2.1
predict the profit in December: p=7.2+2.1=9.3 -> $9,300
