The width of the rectangle with an area x² = 19x + 12 is (4x + 3).
What are the area and perimeter of a rectangle?The area of a rectangle is the product of its length and width.
The perimeter of a rectangle is the sum of the lengths of all the sides.
We know the area of a rectangle is (length×widh).
Given, A rectangle has an area of 4x² + 19x + 12 and a length of (x + 4).
∴ width of the rectangle is = (4x² + 19x + 12)/(x + 4).
Or, we know that the product of two linear equations is a quadratic so,
4x² + 19x + 12.
4x² + 16x + 3x + 12.
4x(x + 4) + 3(x + 4).
(x + 4)(4x + 3).
So, the width of the rectangle is (4x + 3).
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In triangle $ABC,$ $AB = BC = 17$ and $AC = 16.$ Find the circumradius of triangle $ABC.$
Answer:
[tex]R = 9.63\ units[/tex]
Step-by-step explanation:
Given
[tex]AB = BC = 17[/tex]
[tex]AC = 16[/tex]
Required
Determine the circumradius, R
The circumradius is calculated as follows;
[tex]R = \frac{AB * BC * AC}{\sqrt{(AB + BC + AC)(AB + BC - AC)(AB + AC - BC)(AC + BC - AB)}}[/tex]
Substitute the values of AB, BC and AC
[tex]R = \frac{17 * 17 * 16}{\sqrt{(17 + 17 + 16)(17 + 17 - 16)(17 + 16 - 17)(16 + 17 - 17)}}[/tex]
Evaluate the denominator
[tex]R = \frac{17 * 17 * 16}{\sqrt{(50)(18)(16)(16)}}[/tex]
[tex]R = \frac{4624}{\sqrt{230400}}[/tex]
Take square root of 230400
[tex]R = \frac{4624}{480}[/tex]
[tex]R = 9.63\ units[/tex] (Approximated)
Hence, the circumradius is 9.63
Answer:
289/30
Step-by-step explanation:
Let the circumcenter be point O. We start by drawing line median BM. Since AB = BC, median BM is perpendicular to side AC.
Therefore, BM is part of the perpendicular bisector of AC and thus, must pass through point O.
We have AM = 8, so the Pythagorean Theorem applied to triangle ABM gives us BM = 15.
Let OA = x, our circumradius. Since O is equidistant from A and B, we have OB = x as well.
Therefore,
OM = BM - BO = 15 - x.
From right triangle OAM, we have (OA)^2 = (OM)^2 + (AM)^2.
Solving for x, we have 30x = 225 + 64.
So, x = 289/30.
Enter a fraction equivalent to 0.8. Use only whole numbers for numerator and denominator.
Answer:
4/5
Step-by-step explanation:
=>0.8
=>8/10
=>4/5
A football kicker boots the ball from the 15 yard line to the 35 yard line. The equation can be modeled by the the following: y = - .054(x - h)(x - k).....where h and k are where the football lands (x-intercepts). What was the maximum height that the football reached?
Answer:
The maximum height that the football reached = 5.4 yards (16.2 feet)
Step-by-step explanation:
The initial location of the ball = 15 yard line
The final location of the ball = 35 yard line
The equation of the ball's motion can be modeled as follows;
y = -0.054·(x - h)·(x - k)
Where;
h and k are the x-intercepts which are the points where the ball lands or where the ball is in contact with the ground
Given that the kicker kicks the ball from the ground on the 15 yard line and the ball lands on the ground at the 35 yard line, we can write
h = 15 yard line
k = 35 yard line
Therefore;
y = -0.054·(x - 15)·(x - 35) = -0.054·x² + 2.7·x-28.35
The maximum height is found by differentiating the function with respect to x and equating the result to 0 as follows;
d(-0.054·x² + 2.7·x-28.35)/dx = 2.7 - 0.108·x = 0
x = 2.7/0.108 = 25
Therefor, at the maximum point, we have;
x = 25
∴ y = -0.054·(25 - 15)·(25 - 35) = -0.054×10×(-10) = 5.4
The maximum height that the football reached = 5.4 yards = 16.2 feet.
what is the slope of (-5,4) and (7,8)
z−4/9−1/3=5/9 Enter your answer as a fraction in simplest form in the box. z =
Answer:
z=12/9 or 4/3 or 1 1/3
Step-by-step explanation:
1/3 needs to have a denominator of 9 so 3/9 because 3x3=9 and you have to multiply the numerator by 3 also
z-4/9-3/9=5/9
add -4/9 and -3/9 because you add two negative numbers
new equation
z-7/9=5/9
add 7/9 to 5/9
z=12/9 or 4/3 or 1 1/3
Number 14 help I have to zoom with the answer in five minutes
Answer:
31 over -3
Step-by-step explanation:
4.7+1.6=6.3x 5 =31.5-.5=31
Answer: 28
Step-by-step explanation:
5x + 8 verbal expression
Answer:
The sum of 5 times a number x and 8
Step-by-step explanation:
It could also be written as:
The sum of the product of 5 and a number x and 8
i’m not sure about this please help
Answer:
3
Step-by-step explanation:
Evaluate x/4 + 6 (x - 12) where x = 12:
x/4 + 6 (x - 12) = 12/4 + 6 (12 - 12)
Hint: | Reduce 12/4 to lowest terms. Start by finding the GCD of 12 and 4.
The gcd of 12 and 4 is 4, so 12/4 = (4×3)/(4×1) = 4/4×3 = 3:
3 + 6 (12 - 12)
Hint: | Look for the difference of two identical terms.
12 - 12 = 0:
6×0 + 3
Hint: | Any number times zero is zero.
0×6 = 0:
0 + 3
Hint: | Simplify the expression.
Write 3 + 0 as 3:
Answer: 3
The answer is three.
Explanation:
x/4 = 12/4 = 3. 6(x-12) = 6(12-12) = 6(0) = 03+0=3Simplify:
(XY3Z4)4
A.xy3z16
B.xy3z8
C.x4y12z16
D.x5y7z8
Answer:
C
Step-by-step explanation:
(xy^3z^4)^4 =
(x)^4 = x^4
(y^3)^4 = y^12
(z^4)^4 = z^16
Therefore the answer is C. x^4 y^12 z^16
A single card is drawn from a standard 52 card deck.
Work out the probability of choosing the "9 of
spades"
Give your answer in its simplest form
Answer:
Probability of choosing 9 of spades = 1/52
-2(2u-3)+3u=3(u+8)
u=?
Determine which letter on the numberline best represents the radical(photo attached)
Answer:
The square root of 133 is 11.53. The closest to this number would be point D.
Evaluate g(x) = 4 – 3x when x
= -3, 0, and 5.
In the quadratic formula, −b±b2−4ac√2a, what is b2−4ac called?
Answer:
Step-by-step explanation:
In the quadratic formula x = -b±√b²-4ac/2a, the expression b²-4ac inside the square root is called the discriminant. The discriminant is the function that determines the nature of the roots of the equation even without the constant a, b and c
If b²-4ac > 0, the roots of the equation will be real and distinct
If b²-4ac < 0 the roots of the equation will be complex number
If b²-4ac = 0 the roots of the equation will be real and the same
arithmetic sequences are to linear functions as geometric sequences are to
Answer:
exponential functions.
Step-by-step explanation:
Can you help me translate into equations plssssss!!
1. Five more than twice a number is 7.
2. Fourteen more than three times a number is 2.
3. Seven less than twice a number is 5.
4. Two more than four times a number is -10.
6. Eight less than three times a number is – 14.
6. Three more than the quotient of a number and 2 is 7.
7. The product of a number and 4 plus 2 is 14.
8. Eight less than the quotient of a number and 3 is 5.
9. The difference of twice a number and 3 is II.
10. The sum of 3 times a number and 7 is 25.
Answer:
1 is 5+2a =7 and 2is 14+3a=3 and 3 is 7-2a=5
Answer:
1. 2x+5=7
2. 3x+14=2
3. 2x-7=5
4. 4x+2=-10
6. 3x-8=-14
6. (x/2)+3=7
7. 4x+2=14
8. (x/3)-8=5
9. 2x-3=11
10. 3x+7=25
Does every quadratic equation have at
least one real solution? Explain. (1 point)
A. Yes. When the discriminant is zero, there is exactly one solution. When the discriminant is not zero, there are two unique solutions.
B. No. When the discriminant is greater than zero, there are no real solutions.
C. Yes. When the discriminant is zero, there are two unique solutions. When the discriminant is not zero, there is exactly one solution.
D. No. When the discriminant is less than zero, there are no real solutions.
Answer:
D. No. When the discriminant is less than zero, there are no real solutions.
Step-by-step explanation:
We have to notice that quadratic equations are second order polynomials whose standard form is:
[tex]y = a\cdot x^{2}+b\cdot x + c \cdot x[/tex], [tex]\forall \,a,b,c\,\in\,\mathbb{R}[/tex]
The factorized form of this polynomial is:
[tex]y = (x-r_{1})\cdot (x-r_{2})[/tex]
Where [tex]r_{1}[/tex] and [tex]r_{2}[/tex] are the roots of the quadratic equation, which may be real or complex.
If we equalize [tex]y[/tex] to zero and make algebraic handling, we can get the value of each root anatically by the Quadratic Formula:
[tex]r_{1,2} = \frac{-b\pm \sqrt{b^{2}-4\cdot a \cdot c}}{2\cdot a}[/tex]
Where [tex]b^{2}-4\cdot a\cdot c[/tex] is known as the discriminant. Then, we should remember the following rules:
i) If discriminant is greater than zero, then the quadratic equation has two different real roots.
ii) If discriminant is zero, then the quadratic equation has two equal real roots.
iii) If discriminant is less than zero, then the quadratic function has two complex roots.
In consequence, we came to the conclusion that statement is false, as quadratic equation have all roots real or all complex, but not one real and the other complex.
In a nutshell, the correct answer is D.
The histogram shows the heights in meters of trees in a certain section of a park.
How many trees are less than 16 meters tall?
A histogram titled Heights of Trees with Height in meters on horizontal x-axis and Frequency on vertical y-axis
5
9
16
12
Answer:
16
Step-by-step explanation:
2x+4(7−x) HELP PLEASE IM DEPERATEEEEE
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ - 2x + 28}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{2x + 4(7 - x)}[/tex]
Distribute 4 through the parentheses
[tex] \dashrightarrow{ \sf{2x + 28 - 4x}}[/tex]
Collect like terms
[tex] \dashrightarrow{ \sf{2x - 4x + 28}}[/tex]
[tex] \dashrightarrow{ \sf{ - 2x + 28}}[/tex]
Hope I helped!
Best regards! :D
Factor 15 + 50.
5(10 + 3)
5(3 + 10)
3(5 + 25)
10(5 + 5)
Answer:
B
Step-by-step explanation:
So we have the expression:
[tex]15+50[/tex]
Since 5 goes into both 15 and 50, we can factor out a 5. First, rewrite the numbers as:
[tex]5(3)+5(10)[/tex]
Factor out the 5:
[tex]=5(3+10)[/tex]
So, our answer is B
And we're done!
CAN SOMEONE HELP ME PLEASE???
Answer:
[tex]x^3[/tex]
Step-by-step explanation:
To find the greatest common factor of a set of numbers, we need to find the greatest number, that when it's used as a divisor for all the numbers, returns an integer value.
We have the numbers [tex]x^3, x^6,[/tex] and [tex]x^9[/tex].
Exponent rules tell us that [tex]a^b \div a^c = a^{b-c}[/tex].
This means that each of these values must be raised to the power of three. Therefore, each of them can be divided by [tex]x^3[/tex].
[tex]x^3 \div x^3 = 1[/tex]
[tex]x^6 \div x^3 = x^3[/tex]
[tex]x^9 \div x^3 = x^6[/tex]
So [tex]x^3[/tex] is the GCF.
Hope this helped!
What is the equivalent equation to: -6=3y
the answer for your question is y=−2
A scientist was in a submarine below sea level, studying ocean life. Over the next ten minutes, she rose 24.2 feet. How many feet had she been below sea level, if she was 0.5 feet below sea level after she rose?
Answer:
She was initially at a depth of 24.7 feet before she rose
Step-by-step explanation:
To get her initial depth, we need to understand how many feet she sank and rose.
Let us say she was initially at a depth which we can call = x feet.
After 10 minutes she rose for 24.2 feet.
This means her new depth will be x - 24.2 ft.
We are also told that this new depth is actually 0.5 feet below sea level.
This means
x - 24.2 = 0.5
Now that we have this equation we can simply make x the subject of the formula and solve for x
x = 24.2 + 0.5 = 24.7
She was initially at a depth of 24.7 feet before she rose
Answer:
24.7
Step-by-step explanation:
Add 24.2 and 0.5
Please help!,! Once again
Answer:
the answer is "dilation by a scale factor of 2 and a rotation of 90° counter clock wise about the origin"
all linear pairs and vertical pairs share the same...?
Answer:
Lines
Step-by-step explanation:
In both linear and vertical pairs share at least one line.
Hope This Helps :)
All linear pairs and vertical pairs share the same supplementary angle.
Linear pairs and vertical pairs are both types of angle pairs formed by intersecting lines or by the intersection of a line and a transversal.
1. Linear Pairs: A linear pair consists of two adjacent angles formed by two intersecting lines. The two angles in a linear pair are always supplementary, meaning their measures add up to 180 degrees. In other words, if one angle in a linear pair measures x degrees, then the other angle will measure (180 - x) degrees.
2. Vertical Pairs: Vertical angles are formed by the intersection of two lines. They are opposite angles that share a common vertex but are formed by different pairs of intersecting lines. Vertical angles are congruent, meaning they have the same measure. If one vertical angle measures x degrees, then the other vertical angle formed by the same pair of intersecting lines will also measure x degrees.
Therefore, both linear pairs and vertical pairs share the same property of having angles with equal measures. In the case of linear pairs, the angles are supplementary (their measures add up to 180 degrees), while in vertical pairs, the angles are congruent (they have the same measure).
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What is the perimeter of a triangle with the following side lengths?
Side 1=22x-17
Side 2=-15x+12
Side 3=-3x-5
Answer:
p=22x-17-15x+12-3x-5
4x-10
Step-by-step explanation:
hope it is helpful for you if it is follow me
someone please answer and give me a reason. hint: the answer isn’t 49.
Answer:
√37
Step-by-step explanation:
An irrational number is a number that never terminates nor repeats.
Let's go through each of the answer choices.
1) √100 is just 10. This is not irrational.
2) √81 is just 9. This is again not irrational.
3) √64 is 8. Not irrational.
4) √49 is 7. Again, not irrational.
5) √37 is 6.08276253... This number will never end and it doesn't repeat. Therefore, √37 is irrational.
And this is our answer.
And we're done!
could someone please help me
Answer:
x=16°
y=25°
Step-by-step explanation:
7x=112
x=112/7
x=16
90+y=115
y=115-90
y=25
Is −2x=38 a literal equation?
Steps to solve:
-2x = 38
~Divide -2 to both sides
x = -19
Since this equation is solvable, it is a literal equation
Best of Luck!
what is 21000 take away two thirds
Answer:
7000
Step-by-step explanation:
21000/0.667
=14000
21000-14000
=7000