Final answer:
To factor the quadratic expression 8x² – 18x – 5 completely, one finds factors of the coefficient product (–40) that sum to the x coefficient (–18). These factors are -20 and +2, which are used to rewrite and group the middle term, allowing us to factor by grouping into (4x + 1)(2x – 5).
Explanation:
To factor the quadratic expression 8x2 − 18x − 5 completely, we need to find two binomials that when multiplied together give us the original quadratic expression. This process generally involves finding two numbers that multiply to give us the product of the coefficient of x2 term (8) and the constant term (-5) and also add to give the coefficient of the x term (-18).
The product of the coefficient of x2 and the constant term is -40 (8 × -5). We need to find factors of -40 that will add up to -18. After testing several combinations of factors, we see that -20 and 2 work since -20 + 2 = -18. Now we rewrite the middle term using these two numbers:
8x² − 20x + 2x − 5
Next, we group the terms to facilitate factoring by grouping:
=(8x² − 20x) + (2x − 5)
Now we factor out the common factors from each group:
=4x(2x − 5) + 1(2x − 5)
At this point, we have a common binomial factor (2x − 5) that can be factored out:
=(4x + 1)(2x − 5)
This is the expression factored completely.
Describe the transformation.
Answer:
Reflection
Step-by-step explanation:
It is reflecting across the Y axis. It is not a dialation, since it is the same shape, but not a different size. Its not rotation, because it wasnt rotated to get to the new shape. And it is not translation, because it is not exactly the same shape (the shape was mirrored)
compare 8 to the power of 0 and 8 to the power of -2. Which is greater?
Answer:
8 to the power of 0
Step-by-step explanation:
[tex]8^{0}[/tex] = 1
[tex]8^{-2}[/tex] = [tex]\frac{1}{64}[/tex]
To compare 8 to the power of 0 and 8 to the power of -2, we focus on understanding negative exponents. The answer is that 8 to the power of 0 is greater than 8 to the power of -2.
To compare 8 to the power of 0 and 8 to the power of -2, we need to understand how negative exponents work. When a power of 10 is transferred from the numerator to the denominator, the sign of the exponent changes. 8 to the power of 0 is 1 and 8 to the power of -2 is 1/64. Therefore, 8 to the power of 0 is greater than 8 to the power of -2.
What is the distance between the points (13, -17) and (-9, -17) in the coordinate plane?
Answer:
The answer is 22.
d=√(−9−13)2+(−17−(−17))^2
d=√(-22)^2+(0)^2
d=√484+0
d=√484
d=22
Step-by-step explanation:
If angle bdc=23 and arc ef=34, determine arc abd using the appropriate theorems and postulates.
m(ar ABD) = 57°
Solution:
The given question have mistake. The correct question is wiiten below.
If angle BCD = 23° and arc EF = 34°, determine arc abd using the appropriate theorems and postulates.
Given data:
m∠BCD = 23° and m(ar EF) = 34°
By central angle theorem,
The measure of a central angle is equal to the measure of the intercepted arc.
m (ar EF) = m∠ECF
m∠ECF = 34°
By vertical angle theorem,
If two lines are intersecting, then vertically opposite angles are equal.
⇒ m∠ACB = m∠ECF
⇒ m∠ACB = 34°
m∠ACD = m∠ACB + m∠BCD
= 34° + 23°
m∠ACD = 57°
By central angle theorem,
m(ar ABD) = m∠ACD
m(ar ABD) = 57°
Translate this sentence into an equation.
33 is the product of Rick's age and 3
Use the variable r to represent Rick's age.
Answer:
r=11
Step-by-step explanation:
3x11=33
so therefore r=11
Kite K L M N is shown. The lengths of sides L M and M N are congruent. The lengths of L K and K N are congruent. Angle K is 99 degrees and angle N is 106 degrees. What is the measure of LMN in kite KLMN? 49° 99° 106° 155°
Answer
[tex]\angle \ LMN=49\textdegree[/tex]
Step-by-step explanation:
The diagonals of kite KLMN meet at 90°
Since, LK and KN are congruent,[tex]\angle KLM[/tex] and[tex]\angle KNM[/tex] form a set of opposite congruent angles. Congruent angles are equal.
All interior angles of a kite add up to 180°, therefore:-
[tex]\angle LMN=360\textdegree - 2\times106\textdegree-99\textdegree\\=49\textdegree[/tex]
Answer:
∠LMN = 49°
Step-by-step explanation:
Given that
∠LKN = 99°
∠MNK = 106°.
Because, the lengths of LK and KN are congruent.
LK=KN because congruent lines are equal
Hence, ∠MNK=∠MLK = 106°
Adding all angles together, we have
∠MNK + ∠MLK + ∠LKN + ∠LMN = 360°
By substituton;
We have
106° + 106° + 99° + ∠LMN = 360°
311° + ∠LMN = 360°
Collect like terms
∠LMN = 360° - 311°
∠LMN = 49°
How should the decimal point in 34.05 be moved to determine the product 34.05 × 10 to the power of 6?
Enter your answers in the boxes to correctly complete this statement.
The decimal point should be moved __ places to the right because there are __ zeros in 10 to the power of 6
Answer:
The decimal point should be moved Six places to the right side because there are Six zeros in 10 to the power of 6.
Step-by-step explanation:
As we have to represent the number in the form of [tex]10^{6}[/tex] we need to move the decimal Six places towards left because there are Six zeros in [tex]10^{6}[/tex] i.e. 1000000. For this purpose we will add four zeros to the left of the number.
So the number in the format mentioned in question will look like -
0.00003405 × [tex]10^{6}[/tex].
Match each measurement with the appropriate number.
1. kilo. a. 2000
2. 1 ton. b. 1760
3. 1 mile. c. 1000
Which lengths could represent the side length of a right triangle?
Answer:
as long as
[tex]a^2+b^2=c^2[/tex]
then it’s valid, soo...
the first one is not valid (5,6,sqrt 223)
the second one is Not valid (7,11,sqrt 175)
the third one is correct, since [tex]6^2+15^2=261[/tex]
and [tex]\sqrt 261 = 16.1554944214[/tex] (further info)
Simplify expression
8n+4-6n/2
Step-by-step explanation:
8n+4-6n/2
8n+4-3n
5n+4
Answer:
n+2
Step-by-step explanation:
to simplify this expression 8n+4-6n/2
we have,
{8n-6n + 4}/2
{2n + 4}/2
to further simplify this expression {2n + 4}/2 , we are going to factorize 2 from the numerator ,
we have
=2(n +2)/2
the next step to simplify the 2(n +2)/2 further is to use the factorised 2 at the numerator to divide the 2 at the denominator so that we can have a simplified expression.
we have
=2(n +2)/2
=n+2
therefore the simplified form of the expression 8n+4-6n/2 is n+2
Explain a scenario where using properties of tangent lines to solve problems could be used in real life.
Answer:If we are traveling in a car around a corner and we drive over something slippery on the road (like oil, ice, water or loose gravel) and our car starts to skid, it will continue in a direction tangent to the curve.
Step-by-step explanation:
Tangent lines are essential in real-life scenarios like physics for analyzing motion, such as object velocity and acceleration, enabling accurate predictions in various fields.
**Tangent lines** are crucial in various real-life scenarios. For instance, in **physics**, when analyzing the motion of an object along a curved path, the tangent line at a specific point helps determine the object's instantaneous velocity or acceleration. This is vital in understanding how objects move in the real world.
A practical example is when studying the trajectory of a ball thrown into the air. By using the **tangent line** at different points of its path, we can calculate the ball's velocity or acceleration at those instances, assisting in sports analytics, engineering designs, or even space exploration calculations.
Understanding **tangent lines** is essential in fields like **engineering** and **physics** as it allows for precise calculations and predictions based on the behavior of curved functions and their instantaneous rates of change.
What is the numerical expression for 1/4 of the sum of 18 and 6
Answer:
1(18 + 6)/4
Step-by-step explanation:
1(18 + 6)/4
PLEASE MARK ME AS BRAINLIEST!!!
Final answer:
The numerical expression for 1/4 of the sum of 18 and 6 is calculated by adding 18 and 6 to get 24, then multiplying by 1/4 to get 6.
Explanation:
The numerical expression for 1/4 of the sum of 18 and 6 is found by first adding 18 and 6 to get their sum, which is 24. Then, to find 1/4 of this sum, you multiply 24 by 1/4. The calculation step-by-step is as follows:
Add 18 and 6 to get the sum: 18 + 6 = 24.Multiply the sum by 1/4 to get 1/4 of the sum: 1/4 × 24 = 6.Therefore, the numerical expression for 1/4 of the sum of 18 and 6 is 6.
Otis has $6.72, and he wants to buy some pencils that cost $1.12 each. How many pencils can he buy?
Answer: 6 pencils
Step-by-step explanation:
You divide 6.72(amount of money he has) by 1.12(the price of each pencil). You get the answer 6 pencils.
-6y= -20 + 2x
2x – 4y=0
Solve by elimination
Answer:
[tex]x=5\\\\y=2[/tex]
Step-by-step explanation:
Given Equations:
[tex]-6y= -20 + 2x[/tex] Equation:1
Solving Equation:1 Adding '[tex]6y[/tex]' to both the sides:
[tex]2x+6y-20=0[/tex]
Adding '20' both the sides:
[tex]2x+6y=20[/tex] Equation:2
[tex]2x - 4y=0\\[/tex] Equation:3
Subtracting Equation:3 From Equation:2
[tex]2x+6y-(2x-4y)=20-0\\\\2x+6y-2x+4y=20\\\\10y=20\\\\y=\frac{20}{10}\\\\ y=2[/tex]
Putting the value of 'y' in equation:3
[tex]2x - 4y=0\\[/tex]
[tex]2x-4(2)=0\\\\2x-8=0[/tex]
Adding '8' to both the sides
[tex]2x=8\\\\x=8/2\\\\x=5[/tex]
SO,
[tex]x=5\\\\y=2[/tex]
From the picture below, what is the measure of GC?
The measure of arc GC is 90°
Solution:
Given data:
m∠CHD = 90°
Sum of the adjacent angles in a straight line = 180°
⇒ m∠GHC + m∠CHD = 180°
⇒ m∠GHC + 90° = 180°
Subtract 90° from both sides, we get
⇒ m∠GHC = 90°
The angle measure of the central angle is equal to the measure of the intercepted arc.
[tex]m\angle GHD = m (ar \ GC)[/tex]
90° = m(ar GC)
Switch the sides.
m(ar GC) = 90°
The measure of arc GC is 90°.
Bob has 60 coins consisting of quarters and dimes. The coins combined value is $13.35. How many quarters and how many dimes does he have?
Bob has 49 quarters and 11 dimes.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Let there be x quarters.
Then there are 60 - x dimes so using cents as the unit, we get
25x + 10(60 - x) = 1335
25x + 600 - 10x = 1335
15x = 735
x= 49
and 60 - x = 60 - 49 = 11
Hence, Bob has 49 quarters and 11 dimes.
Learn more about Algebra here:
https://brainly.com/question/24875240
#SPJ5
Final answer:
By setting up a system of two equations, where q stands for the number of quarters and d for the number of dimes, and solving this linear system, we find that Bob has 49 quarters and 11 dimes.
Explanation:
To solve this problem, we can set it up as a system of equations. Let's call the number of quarters q and the number of dimes d. We have two pieces of information:
The total number of coins is 60: q + d = 60.The total value of the coins is $13.35. Since each quarter is worth $0.25 and each dime is worth $0.10, the value equation is: 0.25q + 0.10d = 13.35Now, we can multiply the second equation by 10 to eliminate decimals:
2.5q + d = 133.5
Using the first equation (q + d = 60), we can express d as d = 60 - q. Substituting this into the second equation:
2.5q + (60 - q) = 133.5
Simplifying, we get:
1.5q = 73.5
Divide both sides by 1.5 to find q:
q = 49
Now, plug q back into the first equation to find d:
d = 60 - 49 = 11
So, Bob has 49 quarters and 11 dimes.
In a normally distributed data set with a mean of 24 and a standard deviation of 4.2, what percentage of the data would be between 15.6 and 32.4 and why?
Answer:
About 95% of data lies between 15.6 and 32.4
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 2.4
Standard Deviation, σ = 4.2
We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.
Empirical Formula:
Almost all the data lies within three standard deviation from the mean for a normally distributed data.About 68% of data lies within one standard deviation from the mean.About 95% of data lies within two standard deviations of the mean.About 99.7% of data lies within three standard deviation of the mean.We have to find the percentage of data lying between 15.6 and 32.4
[tex]15.6 = 24 - 2(4.2) = \mu - 2\sigma\\32.4 = 24 + 2(4.2) = \mu + 2\sigma[/tex]
Thus, we have to find the percentage of data lying within two standard deviations of the mean. By Empirical formula about 95% of data lies between 15.6 and 32.4
A fire truck parks 16 feet away from a building. The fire truck extends its ladder 30 feet to the very top of the building. How tall is the building?
The height of the building is 25.38 feet
Explanation:
Let AB denotes the height of the building.
Let BC denotes the distance between the fire truck and the building.
Let AC denotes the length of the ladder.
Using the Pythagorean theorem, we have,
[tex]AC^2=AB^2+BC^2[/tex]
where AC = 30, BC = 16
Substituting the values, we have,
[tex]30^2=AB^2+16^2[/tex]
Simplifying the terms, we get,
[tex]900=AB^2+256[/tex]
Subtracting both sides by 256, we get,
[tex]644=AB^2[/tex]
Taking square root on both sides of the equation, we get,
[tex]\sqrt{644}=AB[/tex]
[tex]25.38=AB[/tex]
Thus, the height of the building is 25.38 feet
Answer:
Step-by-step explanation:
a fire truck parks 16ft away fromm a building. the truck extends its ladder 30 feet. how far up the building from the trucks roof does the ladder reach
Find the slope (-1,-9) and (5,6)
Answer:
m = 5/2
Step-by-step explanation:
Formula for slope: [tex]m =\frac{y_2-y_1}{x_2-x_1}[/tex]
-[tex]\frac{6-(-9)}{5-(-1)}=\frac{15}{6} =\frac{5}{2}[/tex]
Is the product of three negative numbers positive or negative?
Answer:
yup, its positive
two times cancels out, but then the third time made it negative again
Point M is located at (10, 10) and point N is located at (15, 25).
Which point lies on line MN?
(A) (0, 0)
B (11, 13)
C (13, 13)
D (20, 20)
Answer:
That is easy, the answer is B.
Step-by-step explanation:
First you have to graph the points of M and N and then you have to draw a line through the points of M and N and then graph the other points and whichever falls on the M,N line is the answer. So therefor the answer is B, (11,13)
Answer:
B?
Step-by-step explanation:
Triangle ABC is similar to triangle PQR. Solve for n. PLEASE HELP
Answer:
7.5
Step-by-step explanation:
5 x 3 = 15
5.5 x 3 = 16.5
Triangle PQR has 3x the amount as ABC on each side, therefore, n = 7.5
A prism has a length of 6 units, height of 5 units, and width of 4 units. Which is the correct calculation for the volume of the prism?
Answer:
The answer is 120
Step-by-step explanation:
length X width X height
6*4*5
120
Find g o f if f(x) = 2x - 1 and g(x) = x + 2.
Answer:
(g◦f)(x) = 2x +1
Step-by-step explanation:
(g◦f)(x) = g(f(x)) = g(2x -1) = (2x -1) +2
(g◦f)(x) = 2x +1
__
Substitute f(x) for the argument in the function g(x) and simplify.
Solve for ∠X.
A) 82°
B) 87°
C) 90°
D) 96°
Answer: D. 96
Step-by-step explanation:
1/2 (82 + 110)
1/2 (192) = 96
96°
∠X = 1/2(82 + 110)
∠X = 96°
solve for −4.2y+2.1>−2.52
Answer:
y < 1.1
Step-by-step explanation:
Step 1: Subtract 2.1 from both sides
-4.2y + 2.1 - 2.1 > -2.52 - 2.1
-4.2y > -4.62
Step 2: Divide both sides by -4.2
-4.2y / -4.2 > -4.62 / -4.2
Since you divided by a negative, that flips the sign.
y < 1.1
Answer: y < 1.1
Answer: Y < 1.1
Step-by-step explanation: I took the quiz, i hope this helps! :)
Write the equation of this line in slope-intercept form
Answer:
y = - [tex]\frac{2}{5}[/tex] x + 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (5, 2) ← 2 points on the line
m = [tex]\frac{2-4}{5-0}[/tex] = [tex]\frac{-2}{5}[/tex] = - [tex]\frac{2}{5}[/tex]
Note the line crosses the y- axis at (0, 4) ⇒ c = 4
y = - [tex]\frac{2}{5}[/tex] x + 4 ← equation of line
Answer:
y = -2/5 +4
Step-by-step explanation:
Create the equationpoints are :
(0 , 4 ) and ( 5,2)
midpoint = (0 + 5 )/2 and ( 4 + 2 )/2
= (2.5 , 3 )
the gradient = (2 - 4 )/ ( 5 - 0)
= -2/5
now create the equation using both gradient and midpoint
Y - y1 = m (X - x1)
y-3 = -2/5 (x - 2.5)
y = -2/5 x +1 +3
y = -2/5 +4
Find the product.
(2x+3)(2x-3)
A. 4x2 - 9
B. 4x2 +9
C. 4x2 –5x+9
D. 4x2 - 5x-9
Answer:
A. 4x^2 - 9
Step-by-step explanation:
2x * 2x = 4x^2
2x * -3 = -6x
3 * 2x = 6x
-3 * 3 = -9
-6x + 6x = 0, so we're left with 4x^2 - 9
Answer:
B. (2x − 3)(2x + 3)(4x2 + 9)
Step-by-step explanation:
word puzzle!!!!
Karen's friends want to buy her a wedding gift. Originally ten friends were going to chip in equally, but then two or them dropped out. Each of the remaining eight friends had to chip in another dollar to bring the total back up to the original amount. How much money did they plan to collect?
Answer:
$4
Step-by-step explanation:
10x = 8(x+1)
2x = 8
x = 4
Answer:
40 dollars
Step-by-step explanation:
We can say
x=amount each friend has to pay
Then, the price of the gift would be 10x because there are 10 friends and each pays x dollars. But since two friends dropped out, it will now become 8x. Also, each of the 8 friends has to pay an extra dollar to go back to the original amount, so 8x+8 is also the price of the gift. We set these two expressions equal to each other (because they both represent the price of the gift) so
10x=8x+8. Using the subtraction property of equality (which says if a=b, then a-c=b-c) we subtract 8x from both sides to get
2x=8. Using the division property of equality (which says if a=b, then a/c=b/c) we divide by 2 on both sides to get x=4. But the question asked how much money they planned to collect, or what was the price of the gift, which is 10x, 10*4=40, 40 dollars.
What is the product of the polynomials below?
(6x2-3x-6)(4x2 +5x+4)
Answer:
24x^4+18x^3-15x^2 -42x-24
Step-by-step explanation:
(6x^2-3x-6)(4x^2 +5x+4)=
6x^2*4x^2 +6x^2*5x+6x^2*4
-3x*4x^2 - 3x*5x-3x*4
- 6*4x^2 -6*5x-6*4=
24x^4+30x^3+24x^2-12x^3-15x^2 -12x
-24x^2-30x-24=
24x^4+18x^3-15x^2 -42x-24