Answer:
[tex](x+4)(x+5)[/tex]
Step-by-step explanation:
To factorize [tex]x^2+9x+20[/tex]
[tex]\textsf{for} \ ax^2+bx+c \ \textsf{find} \ v, w \ \textsf{such that} \ v \cdot w=a \cdot c \ \textsf{and} \ v+w=b\\ \textsf{ and group into} \ (ax^2+vx)+(wx+c)[/tex]
[tex]a \cdot c=1 \cdot 20=20[/tex]
[tex]b=9[/tex]
Therefore, the 2 numbers that multiply together to give 20 and add together to give 9 are: 4 and 5
[tex]\implies x^2+4x+5x+20[/tex]
[tex]\implies (x^2+4x)+(5x+20)[/tex]
Factor the parentheses:
[tex]\implies x(x+4)+5(x+4)[/tex]
Factor out the common term [tex](x+4)[/tex]:
[tex]\implies (x+4)(x+5)[/tex]
[tex]\\ \rm\rightarrowtail x^2+9x+20[/tex]
Use mid term splitation[tex]\\ \rm\rightarrowtail x^2+4x+5x+20[/tex]
[tex]\\ \rm\rightarrowtail x(x+4)+5(x+4)[/tex]
[tex]\\ \rm\rightarrowtail (x+5)(x+4)[/tex]
Done!
find 3 different ratios that are equivalent 7:3 explain why these ratios are equivalent
Answer:
7:3, 14:6, 28:12
multiples.. hope that helps.
If DF=7x-3 and EG=5x+9, find the value of X
Answer:
[tex]x=6[/tex]
Step-by-step explanation:
Using the given measurements of the angles and the lengths of the sides, we can determine that this figure must be a rectangle.
Diagonals of a rectangle are always equivalent/congruent.
We can use this information to set up an equation:
[tex]DF=EG\\7x-3=5x+9[/tex]
Add 3 to both sides:
[tex]7x-3+3=5x+9+3\\7x=5x+12[/tex]
Subtract 5x from both sides:
[tex]7x-5x=5x-5x+12\\2x=12[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{12}{2}\\x=6[/tex]
Answer:
6[tex] \: [/tex]
Step-by-step explanation:
A rectangle is a parallelogram with equal angles and the diagonals of a rectangle are of equal length.
[tex] \: [/tex]
Therefore,
[tex] \\ { \longrightarrow \qquad{ \sf{ \pmb {DF = EG}}}} \: \: \\ \\[/tex]
[tex]{ \longrightarrow \qquad{ \sf{ \pmb {7x - 3 = 5x + 9}}}} \: \: \\ \\[/tex]
Subtracting 5x from both sides we get :
[tex] \\ { \longrightarrow \qquad{ \sf{ \pmb {7x - 5x - 3 = 5x - 5x + 9}}}} \: \: \\ \\[/tex]
[tex]{ \longrightarrow \qquad{ \sf{ \pmb {2x - 3 = 9}}}} \: \: \\ \\[/tex]
Adding 3 to both sides we get :
[tex] \\ { \longrightarrow \qquad{ \sf{ \pmb {2x - 3 + 3 = 9 + 3}}}} \: \: \\ \\[/tex]
[tex]{ \longrightarrow \qquad{ \sf{ \pmb {2x = 12}}}} \: \: \\ \\[/tex]
Dividing 2 from both sides we get :
[tex] \\ { \longrightarrow \qquad{ \sf{ \pmb { \frac{2x}{2} = \frac{12}{2} }}}} \: \: \\ \\[/tex]
[tex]{ \longrightarrow \qquad{ \frak{ \pmb {x = 6}}}} \: \: \\ \\[/tex]
Therefore,
The value of x is 6It takes Sally 15 min to pick the apples from the tree in her backyard. Lisa
can do it in 25 min. How long will it take them working together?
The answer for this problem is that the number is 31p
Playing cards numbered from 1 to 20 are mixed thoroughly and kept it in a box. One card is taken at random from the box. What is the probability of the selected/drawn playing cards?1. Is a Prime number.2. A factor of 20.3. A composite number.4. A multiple of 3.5. A perfect square.
Step-by-step explanation:
Probability is the ratio of the expected outcome (event) to the total outcome (sample space)
Probability = expected outcome/total outcome
If Playing cards numbered from 1 to 20 are mixed thoroughly and kept it in a box, the total number of sample space is 20
1) To calculate of getting a prima number.
Events = {2, 3, 5, 7,11,13,17,19}
n(events) = 8 elements
Pr(selecting a prime) = 8/20 = 2/5
2) If a factor of 20 is selected
Factor of 20 F = {2, 4, 5, 10, 20}
n(F) = 5
Pr(factor of 20) = 5/20 = 1/4
3) A composite number are 2 digits numbers.
Composite number C = {10,11,12,13,14,15,16,17,18,19,20}
n(C) = 11
Pr(a composite number) = 11/20
4) For multiple of 3.5
Multiple of 3.5 M = {3.5, 7.0, 10.5, 14.0, 17.5}
n(M) = 5
Pr(multiple of 3.5) = 5/20 = 1/4
5) For perfect squares
Perfect squares P = {1, 4, 9, 16}
n(P) = 4
Pr(perfect squares) = 4/20 = 1/5
HELPP! The perimeter of a rectangle is 104 inches. The width is 6 inches less than 3 times the length. Find the
width of the rectangle.Show each step and explain what was performed for each step.
Answer:
Length of the rectangle = 14.5 inches
Width of the rectangle = 37.5 inches
Step-by-step explanation:
Let the length of a rectangle = a inches
Since, width of the rectangle is 6 inches less than 3 times the length,
w = 3a - 6
Perimeter of the rectangle = 104 inches
Formula to calculate the perimeter of a rectangle = 2(length + width)
104 = 2[a + (3a - 6)]
2a + 2(3a - 6) = 104 → [Starting equation]
8a - 12 = 104 → [Distributive property]
8a - 12 + 12 = 104 + 12 → [Addition property of equality]
a = [tex]\frac{116}{8}=14.5[/tex] → [Division property of equality]
a). width of the rectangle = (3a - 6) = 37.5 inches
b). length of the rectangle = 14.5 inches
The width of the rectangle is 37.5 inches and the length of the rectangle is 14.5 inches.
The perimeter of a rectangle is represented as follows:
perimeter = 2l + 2w
where
w = width
l = length
Therefore,
perimeter = 104 inches
let
the length = a
Therefore,
width = 3a - 6
Therefore,
104 = 2a + 2(3a - 6)
104 = 2a + 6a - 12
116 = 8a
a = 116 / 8
a = 14.5 inches
width = 3(14.5 ) - 6 = 37.5 inches
Therefore, the width of the rectangle is 37.5 inches and the length of the rectangle is 14.5 inches.
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Translate this sentence into an equation,
42 is the difference of Julie’s age and 14. Use the variable j to represent Julie’s age
Answer:
x-14=42
Step-by-step explanation:
let x be Julies age x= the difference between julies unknown age and 14
Someone please help
Answer:
63%
Step-by-step explanation:
Volume=(l)(w)(h)
V= (12.9)(5.5)(4.7)
V= 333.465 cubic feet
The tank contains: 210 cubic feet of water
To find percentage: current amount / maximum capacity (this would be our volume) multiplied by 100% =
210/333.465 = .6297
.6297 x 100% = 62.97%
Round to a whole number:
63%
Quadrilateral MNOP with verticles M(3,-1), N(8,-4), (6,-6), and P(1,-7); is rotated 180 degrees. What are the new points?
Answer:
The new points after a rotation of 180 degrees is;
M’ = (-3, 1)
N’ = (-8,4)
O’ = (-6,6)
P’ = (-1 , 7)
Step-by-step explanation:
Given a point (x , y) and we rotate by 180 degrees , the new point will be (-x , -y)
So to the question;
M’ = (-3, 1)
N’ = (-8,4)
O’ = (-6,6)
P’ = (-1 , 7)
what is the value of the digit 3 in 17039 in words?
Answer:
30
Step-by-step explanation:
Since the 3 is in the tenths column, it therefore equals 30.
Answer:
thirty
Step-by-step explanation:
the value of the 3 in 17039 is 30
Is this correct? Ive done this a million times and they always come out the same, but I still get it wrong.
Answer:
No, the correct answer is 32cm.
Step-by-step explanation:
First of all, lets cut the shape into two. A rectangle and a triangle. This will help us find the slanted side of the shape.
We will use the pythagorean theorem to find the length of the slanted line.
The pythagorean theorem is [tex]a^{2} +b^{2} =c^{2}[/tex].
Input the given information of the triangle lengths that we know; that is the length= 6 and the base=3.
[tex]c= \sqrt{a^{2}+b^{2} } =\sqrt{6^{2}+\ 3^{2} } = 6.7082[/tex]
Now, we round.
6.7082≈ 6.7
We have found the length of the slanted line of the shape.
Now, let's add all the lengths together.
8+6+6.7+11= 31.7
Now, lets round.
31.7 ≈ 32cm
Hope this helps!
A city has a population of 2,549,786 people. Estimate this population to the nearest million. Express your answer as the product of a single digit and a power of 10. Rounded to the nearest million, the population is about? Written as the product of a single digit and a power of ten, this number is blank X 10 to the power of what?
Solution,
The population of a city is 2,549,786.
We can convert it into nearest million as follows :
Million = 10 lakhs
Rounding off to the nearest million
2,549,786 = 3,000,000
There are 6 zeroes after 3. We can express as the product of a single digit and a power of 10 as follows :
[tex]3,000,000=3\times 10^6[/tex]
Hence, the population of the city is 2,549,786 or [tex]3\times 10^6[/tex].
5. If the number of employees is represented by x, which function represents the
amount each received?
a. f(x) = 65000x
b. f(x) = x + 65000
c. f(x)
d. f(x) = x - 65000
65000
Consider the missing lines of question are "Due to the Enhanced Community Quarantine, Grand Royal Spa temporarily stopped its operation and to help the employees, the owner decided to split evenly its total revenue of 65,000.00".
Given:
Total revenue = 65000
Number of employees = x
To find:
The function which represents the amount each received.
Solution:
We know that,
[tex]\text{Amount each received}=\dfrac{\text{Total revenue}}{\text{Number of employees}}[/tex]
Substitute the given values in the above formula.
[tex]\text{Amount each received}=\dfrac{65000}{x}[/tex]
So, the function which represents the amount each received is
[tex]f(x)=\dfrac{65000}{x}[/tex]
Therefore, the required function is [tex]f(x)=\dfrac{65000}{x}[/tex].
Note: Given options are not correct and option C is incomplete.
Kaitlin drove 567 miles in 9 hours. At the same rate, how long would it take her to drive 819 miles? hours
Answer:
13 hours
Step-by-step explanation:
567/9= 63 mile per hour
819/63 = 13
13 hours
Answer:
13 hours
Step-by-step explanation:
how long does she drive in one hour?
567/9=63
she drives 63mph
819/63=13
it will take her 13 hours to drive 819 miless
I have no idea plz help
Answer:
a
Step-by-step explanation:
Ian earns x dollars a month. He received a 10% raise in his paycheck. Which expression represents Ian’s new monthly paycheck?
x + 0.10x
x + 1.10
x + 1.10x
I need this fast, please with the work
The expression is
[tex]\\ \rm\Rrightarrow x+(1+0.10)x[/tex]
[tex]\\ \rm\Rrightarrow x+1.10x[/tex]
Whats the domain and range?
what is the median score on the exam ?
a) 70
b) 75
c) 77.5
d) 85
Answer:
b) 75
Step-by-step explanation:
The median (middle quartile) marks the mid-point of the data and is shown by the line that divides the box into two parts.
Therefore, from inspection of the box plot diagram, the median is 75
Additional information
Lower quartile (Q1) = 70
Median (Q2) = 75
Upper quartile (Q3) = 85
IQR = Q3 - Q1 = 85 - 70 = 15
Minimum value = 55
Maximum value = 100
Range = Max - Min = 100 - 55 = 45
10. Which of the following are true of the equation x = log10 (12,500)? Select all that apply.
A. x < 4
B. X = 4
C. x > 4
D. x < 5
E. X = 5
F.x > 5
Answer: C, D
Step-by-step explanation:
can someone help me asap
Answer:
I think it's 31
Step-by-step explanation:
Answer:
x = 31°
Step-by-step explanation:
The two triangles seem to be identical.
All angles of a triangle must add up to 180° to make a triangle.
So, 53° + 96° = 149°
Subtract 149° from 180°
180° - 149° = 31°
So x = 31°
Hope I helped :)
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Marco runs 22 miles in four hours. What is his unit rate?
Answer:
5.5 maybe..
Step-by-step explanation:
Write a system & solve: A farm has only chickens & cows. In total, there are 145 animals. However, there are only 324 animal legs. How many cows are there?
Answer:
x=17 y=128
Step-by-step explanation:
x-cows
y=chicken
x+y=145
4x+2y=324
x=145-y
4(145-y)+2y=324
580-4y+2y=324
580-2y=324
580-324=2y
256=2y
y=128
x=145-128
x=17
In a lab, a substance was heated by 2c each hour for 6 hours. What was the total change in temperature?
Answer:
12 c
Step-by-step explanation:
You can add up the hourly changes, or you can use multiplication to do the repeated addition. The increase in temperature over 6 hours is ...
2c +2c +2c +2c +2c +2c
= 6 × 2c
= 12c
The total change in temperature was an increase of 12c over the 6-hour time period.
Stella has x in her checking account. She goes to the Dollar Store and spends $23.75. Now she has $9.30 left in the account. How much did Stella have in her account before she went to the store?
Answer:
$33.05
Step-by-step explanation:
Add 23.75 + 9.30
A triangle has two sides of length 6 and 12. What is the smallest possible whole-number length for the third side?
Which expression is equivalent to StartFraction 5 y cubed Over (5 y) Superscript negative 2 Baseline EndFraction? y5 y6 125y3 125y5.
The expression which is equivalent to Start Fraction 5 y cubed Over (5 y) Superscript negative 2 Baseline End Fraction is
[tex]125y^5[/tex]
How to find the equivalent expression?Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.
To find the equivalent expression, simplify the provided function using the mathematical operations.
The given algebraic expression is,
[tex]\dfrac{5y^3}{(5y^{-2})}[/tex]
Suppose the equivalent expression of this fraction is n. Thus,
[tex]n=\dfrac{5y^3}{(5y^{-2})}\\\\n=\dfrac{5y^3}{((5)^{-2}y^{-2})}\\[/tex]
In the division the power of the same number is subtracted. Therefore,
[tex]n=(5)^{1-(-2)}(y)^{3-(-2)}\\n=5^3\times y^5\\n=125y^5[/tex]
Hence, the expression which is equivalent to StartFraction 5 y cubed Over (5 y) Superscript negative 2 Baseline EndFraction is
[tex]125y^5[/tex]
Learn more about the equivalent expression here;
https://brainly.com/question/2972832
Answer:
The answer is D.
Step-by-step explanation:
Hope this helps! Pls give brainliest!
Help I need to hand this in soon
Answer:
∠x = 50°
Step-by-step explanation:
All external angles of a polygon add up to 360°.
Therefore,
78° + ∠x + 95° + ∠x + 37° + ∠x = 360°3∠x + 210° = 360°3∠x = 150°∠x = 50°
Find the distance between Point A (9, -3) and Point B (16,
7), correct to 2 decimal places.
Answer:
8.06
Step-by-step explanation:
use distance formula
y=mx+b
solve for x
please it is due today if right ill give brain list
Answer:x=y-bm
Step-by-step explanation:
Answer:
x = y-b/m
Step-by-step explanation:
Step 1: y = mx + b
Step 2: Bring b to the left side of the equation
Step 3: y - b = mx
Step 4: To isolate for x, we must get rid of m. Therefore, divide m on both sides of the equation
Step 5: y-b/m = mx/m
Step 6: On the right side of the equation, m and m crosses out.
Step 7: All we have left is: y-b/m = x
(Or you can write it as x = y-b/m)
Hope this helps.
A researcher administers a treatment to a sample of participants selected from a population with µ = 80. If a hypothesis test is used to evaluate the effect of the treatment, which combination of factors is most likely to result in rejecting the null hypothesis?
a. a sample mean near 80 with a=.05b. a sample mean much different than 80 with a=.05c. a sample mean much different than 80 with a=.01d. a sample mean near 80 with a=.01
Answer:
The answer is "Option c"
Step-by-step explanation:
In the given question, in choice c the numerice value is missing, that is "0.05".
The null hypothesis can only be rejected whether there is enough statistical data than that of the critical values.
The options A and B are not accurate, because the mean test of around 80 means that now the check-in and check number is lower, giving small statistics of the experiment and resulting in the null hypothesis is not rejected. In the C or D is true, however, the importance or alpha level need to be tested Alpha level 0.05 is 5% likely to reject an absolute zero hypothesis so, although 0.01 alpha level is 1% more likely to oppose an absolute zero hypothesis, Therefore, the alpha 0.05 rating is stronger.Which temperature is colder? -10 degrees or -13 degrees
Answer:
-13
Step-by-step explanation:
The more negative the number, the colder it is
-13 is more negative than -10
-13 < -10
-13 is colder