Which expression is equivalent to x² - 4x - 45?
А
(x - 9)(x - 5)
B
(x + 9)(x+5)
(20 +9)(x - 5)
D
(x - 9)(x+5)
Answers
Answer:
D. (x - 9)(x+5)
Step-by-step explanation:
[tex]x^{2} - 4x - 45[/tex] is your expression, so you have to factor it out. Since from the options available it's clear that the factors of -45 you use are some form of 9 and 5, we can use the process of elimination to figure out which are the correct ones.
First, through FOIL u know that in any factored form the last two terms in each bracket multiply together to make the last term in the expanded form.
So first, look at A. the last two terms are -9 and -5, which = 45 when multiplied together. 45 does not = -45, so it can't be A.
B has 9 and 5. When they're multiplied, they = 45, which does not = -45, so its not B
It can't be C either, because the first term of the first bracket in C is 20, and when multiplied with x it doesn't produce x^2.
Therefore it has to be D. u can check this by multiplying -9 and 5, which = -45, the final term in the expanded form. Also, -9 + 5 = -4, which is the middle term of the expanded form.
The equivalent expression to x² - 4x - 45 is (x - 9)(x + 5), which corresponds to option A.
To factor the quadratic expression x² - 4x - 45, we need to find two binomials that, when multiplied, give us the original expression.
We look for two numbers whose product is -45 (the coefficient of the constant term) and whose sum is -4 (the coefficient of the linear term, -4x). After some exploration, we find that the numbers -9 and 5 satisfy these conditions.
Thus, we can express x² - 4x - 45 as (x - 9)(x + 5). This is because when we multiply the two binomials (x - 9) and (x + 5) using the distributive property, we obtain the original quadratic expression.
This factored form, (x - 9)(x + 5), represents the equivalent expression to x² - 4x - 45.
To learn more about the quadratic equation;
https://brainly.com/question/17177510
#SPJ6
Related Questions
Page No.
Date :
33
2
4 Cosin 4 Go + eces4 300 3 citan
60 - tan245) + 5 ecos? 45.
Answers
write an equation of the line that passes through the two given points: (-5, -5) and (1,-3)
Answers
Answer:
slope-intercept formula -----> Y2-Y1/X2-X1
Step-by-step explanation:
X1= -5 X2= 1
Y1= -5 Y2= -3
-3+5/1+5=1/3
PLS PLS PLS HELPPP please...
Answers
Answer: x=12
Step-by-step explanation: 10(x−3)=90
(10)(x)+(10)(−3)=90 (Distribute)
10x+−30=90
10x−30=90
Step 2: Add 30 to both sides.
10x−30+30=90+30
10x=120
Step 3: Divide both sides by 10.
x=12
16. What probability expression is equivalent to P( / z / > 1.96)?
Answers
Answer:
Please check the explanation.
Step-by-step explanation:
Given
[tex]P(Z > 1.96)[/tex]
To determine
What probability expression is equivalent to [tex]P(Z > 1.96)[/tex].
Suppose Z is a standard normal variable.
Therefore,
P(Z > 1.96) = 1 - P(Z ≤ 1.96)
solving
= 1 - Ф(1.96)
[tex]= 1 - 0.9750[/tex]
[tex]= 0.0250[/tex]
The rectangles are similar. What is the value of x?
Answers
Answer:
80
Step-by-step explanation:
30 ÷ 6 = 5
16 × 5 = 80
I hope this helped!
Please help will give brainliestw
Answers
Answer:
6 square units
Step-by-step explanation:
In oder to do this, you need graph paper to make it easier and then mark your graph paper with the quadrants.
I got 3 unites for the height and 4 units for the base
4 x 3 = 12 square units
however the formula for a triangle is Ab/2
so divide 12/2 = 6
So its 6 square units
I will give brainiest. There is 1/ 3 gallon of water in a 3-gallon container. What fraction of the container is filled?
Answers
I really need help. ( Intro to limits )
Answers
Emir flew home from vacation with a heavy bag. With the first airline he flew, Emir had to pay $20 to check his bag, plus $10 for every pound that his bag was over the weight limit. The next flight was with another airline that had the same weight limit. Emir had to pay $5 per pound that his bag was over the weight limit, in addition to the checked bag fee of $30. By coincidence, the fees ended up being the same with both airlines. How large was each airline's fee?
Answers
Answer:
$27.5
Step-by-step explanation:
Let
x = pound over weight limit
Airline 1 = 20 + 10x
Airline 2 = 5 + 30x
Equate the fees
20 + 10x = 5 + 30x
20 - 5 = 30x - 10x
15 = 20x
x = 15/20
x = 0.75 pounds
How large was each airline's fee?
Airline 1 = 20 + 10x
= 20 + 10(0.75)
= 20 + 7.5
= $27.5
Airline 2 = 5 + 30x
= 5 + 30(0.75)
= 5 + 22.5
= $27.5
6 A pair of adjacent angles is formed by lines
AD and CE.
What is the measure of angle ABC?
F 145°
G 217
H 85°
J Not here
Answers
Answer:
x° = 145°
Step-by-step explanation:
x° + (2x - 255)° = 180°
3x = 180 + 255
3x = 435
x° = 145°
What's 9 + 10 ? give me the right answer
Answers
Answer:
19
Step-by-step explanation:
Add 9 to 10
Leticia and Carmen were each given 120 math questions for the month. After 3 weeks,
Leticia completed 75% of the problems and Carmen completed 60% of the problems
How many more questions did Leticia complete thon Carmen?
Answers
A directed line segment begins at F(-8, -2), ends at H(8, 6), and is divided in the ratio 8 to 2 by G. What are the coordinates of G?
Answers
Given:
A directed line segment begins at F(-8, -2), ends at H(8, 6), and is divided in the ratio 8 to 2 by G.
To find:
The coordinates of point G.
Solution:
Section formula: If a point divide a line segment with end points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in m:n, then the coordinates of that point are
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Point G divide the line segment FH in 8:2. Using section formula, we get
[tex]G=\left(\dfrac{8(8)+2(-8)}{8+2},\dfrac{8(6)+2(-2)}{8+2}\right)[/tex]
[tex]G=\left(\dfrac{64-16}{10},\dfrac{48-4}{10}\right)[/tex]
[tex]G=\left(\dfrac{48}{10},\dfrac{44}{10}\right)[/tex]
[tex]G=\left(4.8,4.4\right)[/tex]
Therefore, the coordinates of point G are (4.8, 4.4).
Someone plz help me I will give brainliest
Answers
Answer:
Step-by-step explanation:
3/4 + 3/4 + 3/4 + 3/4 + 3/4 + 3/4 = (6 x 3)/4 = 18/4 = 4 1/2
a=2x3^4x5 b=2^3x3^2x5^5 write down the night common factor of A and B PLEASE HELP ASAP PLEASEE!
Answers
Answer:
The HCF of [tex]a=2^1 \cdot 3^4 \cdot 5^1[/tex] and [tex]b = 2^3 \cdot 3^2 \cdot 5^2[/tex] is [tex]90[/tex].
Step-by-step explanation:
To calculate the HCF of two numbers given their prime factorization, we take the lowest exponent of every prime when comparing the two numbers.
So the HCF of [tex]a=2^1 \cdot 3^4 \cdot 5^1[/tex] and [tex]b = 2^3 \cdot 3^2 \cdot 5^2[/tex] is [tex]2^1 \cdot 3^2 \cdot 5^1 = 90[/tex].
Enter a range of values for x.
a
a
3x-90 930
26
27
[? ]
Answers
Answer:
the answer to your question is 3 and 34
Jada measured the height of a plant in a science experiment and finds that, to the nearest 1/4 of an inch, it is 4 3/4 inches.
a. What is the largest the actual height of the plant could be? Express your answer in decimal form.
Answers
Answer:
I dont know
Step-by-step explanation:
sorrryy
Learning Task 1
4/625
11.
796
A. Simplify the radical expressions
1. V63
6. V24
2. 48
7. 781
3. 775
8. V128
4. 99
9. 340
5. 92
12. 128
13. 4/243
14.
V3000
10. V135
15.
NO
Answers
Answer:
Step-by-step874747634734634347
plss helpppppppppp w,jvkwsvkjbw,vj effvdefv
Answers
Answer:180
Step-by-step explanation:
GEOMETRY Identify the segment bisector of (FG) . Then find (FG)
Answers
Answer:
The segment bisector of FG is HI because it splits it into two equal parts. Since point F to the bisector equals 33 and the bisector to point G is the same, that would also be 33. 33+33=66=FG
Step-by-step explanation:
The measurement of the line segment FG is 66 units.
We need to identify the segment bisector of FG and then find FG.
What is the bisector of the line segment?A segment bisector is a line, a ray, a line segment, or a point that cuts a line segment at the centre dividing the line into two equal parts. The word segment can also be referred to as line segment which means a segment is a part of the line that has fixed endpoints. The word bisect means cutting any object or line into two equal halves. Hence, a segment bisector is referred to as when two line segments bisect or cut each other at a point dividing the lines into equal halves.
From the given figure, HI is the bisector of the line segment FG.
Given that, 1/2 (FG)=33 units
⇒FG=66 units
Therefore, the measurement of the line segment FG is 66 units.
To learn more about the bisector of the line segment visit:
https://brainly.com/question/13792156.
#SPJ2
Help me please......
Answers
Answer:
[tex] \huge \: 19[/tex]Step-by-step explanation:
to understand thisyou need to know about:equationtriangles congruencyPEMDASTIPS AND FORMULAS:when two triangles are congruent the included angles and sides of the triangles are equallet's solve:[tex]step - 1 : define[/tex]
[tex]2x - 9 = x + 5[/tex]
[tex]step - 2 :solve[/tex][tex]2x = x + 5+ 9[/tex]
[tex]2x = x + 14[/tex]
[tex]2x - x = 14[/tex]
[tex]x = 14[/tex]
given:KL=2x-9
=2.14-9
=28-9
=19
Simplify the following:
a) 3^2x3^2
b) 7x7^4
c) 10^9/10^7
d) 5^8/5
Answers
Answer:
see attached
Step-by-step explanation:
pleass see attached
Sam opens a savings account with $800. He saves $50 per month. Assume that he does not withdraw money or make any additional deposits.
Answers
Answer:
wheres the end of the question
Step-by-step explanation:
Sam opens a savings account with $800. He saves $50 per month. Assume that he does not withdraw money or make any additional deposits.
Write a linear model (equation) that represents the total amount of money Sam deposits into his account after m months.
Equation:
b. After how many months will Sam have more than $3500? Show your work.
c. Use the equation and create a table to represent the situation.
Solution:
Savings = 800 + 50m
$800 is the initial savings and $50 are saved every month. By adding these two, we will get the total savings.
B) Use 3500 in the above equation
3500 = 800 + 5m
Taking 800 to other side
5m = 3500 - 800
5m = 2700
m = 2700/5 = 540
It will take him 540 months to save $3500. So we can say that it will take him 541 months to make more than $3500.
C) Make a table with two columns: Months and Total Savings
Take random values of m, put those values in the equation to get total savings for that month.
m savings
0 800
2 810
4 820
6 830
a total of 11℅ students at a large high school are left-handed. A statistics teacher selects a random sample of 100 students and records L = the number of left-handed students in the sample.
a. Explain why L can be modeled by a binomial distribution even though the sample was selected without replacement.
b. use a binomial distribution to estimate the probability that 15 or more students in the sample are left-handed handed.
Answers
The probability that 15 or more students in the sample are left-handed handed is 0.0752
(a) Why L can be a binomial distribution
From the question, we understand that 11% of the students are left-handed; this means that 89% are not left-handed
This, in other words means that:
For each observation, the student is either left-handed or not left-handed
Hence, the distribution can be represented by a binomial distribution
(b) The probability that 15 or more are left-handed
The sample size is given as:
[tex]\mathbf{n = 100}[/tex]
And the proportion is
[tex]\mathbf{p = 11\%}[/tex]
The mean of the dataset is:
[tex]\mathbf{\mu = np}[/tex]
[tex]\mathbf{\mu = 100 \times 11\%}[/tex]
[tex]\mathbf{\mu = 11}[/tex]
The standard deviation of the dataset is:
[tex]\mathbf{\sigma = \sqrt{\mu(1- p)}}[/tex]
So, we have:
[tex]\mathbf{\sigma = \sqrt{11 \times (1- 11\%)}}[/tex]
[tex]\mathbf{\sigma = \sqrt{11 \times 89\%}}[/tex]
[tex]\mathbf{\sigma = \sqrt{9.79}}[/tex]
[tex]\mathbf{\sigma = 3.13}[/tex]
So, the probability is represented as:
[tex]\mathbf{P(x \ge 15)}[/tex]
Using continuity correction, we have:
[tex]\mathbf{P(x \ge 15) = P(x \ge 15.5)}[/tex]
Calculate the z-score for x = 15.5
[tex]\mathbf{z =\frac{x - \mu}{\sigma}}[/tex]
So, we have:
[tex]\mathbf{z =\frac{15.5 - 11}{3.13}}[/tex]
[tex]\mathbf{z =\frac{4.5}{3.13}}[/tex]
[tex]\mathbf{z =1.438}[/tex]
The probability is then calculated as:
[tex]\mathbf{P(x \ge 15) = P(z \ge 1.438)}[/tex]
Using z-tables of probabilities, we have:
[tex]\mathbf{P(x \ge 15) = 0.075217}[/tex]
Approximate
[tex]\mathbf{P(x \ge 15) = 0.0752}[/tex]
Hence, the probability is 0.0752
Read more about binomial distribution at:
https://brainly.com/question/15992180
How many three-digit numbers are divisible by 2,3 or 5? plEASe helP I aM DeSpeRatE
GIVE ME THE RIGHT ANSWER
Answers
Answer:
30
Step-by-step explanation:
- A number is divisible by 2 if its last digit is 2, 4, 6, 8 or 0
- A number is divisible by 3 if ist sum of digits is divisible by 3.
- A number is divisible by 5 if its last digit is a 5 or a 0.
_
The least 3 digit number divisible by 30 is 120 and the greatest is 990.
Answer: 30
Step-by-step explanation:
Divisible by 2,3 and 5 means divisible by 2*3*5=30
So we require to calculate number of multiples of 30 in the range 100 to 999.
The least 3 digit number divisible by 30 is 120 and greatest is 990.
This is an AP series with common difference 30.
First number is 120 and n'th number is 990.
We need to find n.
Using the AP series formula
120 + (n-1)*30= 990
or n= 30
There are 30 3-digit numbers divisible by 2,3 and 5.
Find the value of "n" in the following equation
( n^2 x n = 216 )
plz answer asap
Answers
Answer:
Yoy add them to be 2n squared then divide by 2 on both sides then take the square root
URGENT I need help.
Plzzzzzzzzzzzzzzzzzzzzzz Its Attached
Answers
Answer:
what is you belling? yesterday y monday
Alberto buys a 600 balloons. Some of the balloons are pink.and the rest is green. He wants a estimate of the number of pink balloons in the bag. He ask 4 of his friends to each select a random sample of 10 balloons. Each friend returns the sample before the next friend selects a sample.
What is the estimate number of the pink balloons in the bag
Answers
Answer: there are 120 baloons in the bag
Step-by-step explanation:
10/ 600 = 4/x
10x = 1200
10/1200
x= 120
explain why the miniscus of water is bent downwards
Answers
Answer:
A concave meniscus, which is what you normally will see, occurs when the molecules of the liquid are attracted to those of the container. This occurs with water and a glass tube. A convex meniscus occurs when the molecules have a stronger attraction to each other than to the container, as with mercury and glass.
Can someone tell me if my answer is correct (and correct it if it's not)?
What is the area of an EQUALATERAL triangle with a side length of 6? I'm getting 5.19615242, is this right?
Answers
Answer:
15.59.
Step-by-step explanation:
The altitude of equilateral triangle bisects the base
So 1/2 base = 3.
Altitude of the triangle is found from Pythagoras theorem:
= sqrt(6^2 - 3^2)
= sqrt27
Area = 1/2 base * altitude
= 3 * sqrt27
= 15.59