4x+8 Factorise les expressions
Answer: 4(x+2)
Step-by-step explanation:
1. Take the GCF from both terms and put it on the outside of the parentheses
2. Factor each term inside of the parentheses, in this case, 4
Based on the given information, what is AE?
O 2 units
O 7 units
O 12 units
O17 units
Answer:
the answer is "12 units"
Step-by-step explanation:
edg 2021
The correct option is Option C: the value of AE is 12 units.
What are congruent triangles?Congruent triangles are the triangles whose size and shapes are the same. The angle and the sides of two congruent triangles are also congruent.
Here given in the question
CB = AB
∠DBC = 90°
∠ABE = ∠DBC = 90° (opposite angles formed by the intersection of AC and DE.)
As ∠CBE and ∠ABE are supplementary angles and form a straight line.
∠CBE + ∠ABE =180°
⇒∠CBE = 180° - ∠ABE = 180°- 90°= 90°
Between triangle Δ CBE & ΔABE
∠CBE = ∠ABE = 90°
CB = AB given
BE = BE common
triangle Δ CBE & ΔABE are congruent.
=> Δ CBE ≅ ΔABE( by S-A-S Congruency)
=> CE = AE ( as triangle Δ CBE & ΔABE are congruent then the sides are same.)
=> AE = 12 units
Therefore The correct option is Option C: the value of AE is 12 units.
Learn more about congruent triangles
here: https://brainly.com/question/1675117
#SPJ2
Subtract as indicated.
13
- (
15
6 13
5 15
(Simplify your answer. Type an integer or a simplified fraction.)
(Someone please answer)
-6/5 - (-13/15) = -6/5 + 13/15 =
= -18/15 + 13/15 = -5/15 = -1/3
HELPPPPPP MEEEEE
Question
Use the mapping to determine which of the following are elements of the domain.
Need the map to know the answer the photo of it is up there if you want a better view of it.
110
130
24.0
140
20.6
18.9
Answer:
110, 130, 140
Step-by-step explanation:
The x-values are the elements of the domain.
What is the remainder in the synthetic division problem below?
4 6 - 1
A. 3
B. 7
C. 5
D. 9
Answer:
so,6-1 3+7x5 9
Multiple: 7 * 5 = 35
Divide: the result of step No. 1 / 9 = 35 / 9 = 3.88888889
Add: 3 + the result of step No. 2 = 3 + 3.88888889 = 6.88888889
On a hike, Twyla traveled from an altitude of 527 meters to an altitude of 487 meters. Which statement uses absolute value correctly? *
Answer:
Difference, D = 40
Step-by-step explanation:
This question requires options. Since there's none, I'll answer generally.
Represent the distances with d1 and d2
d1 = 527 Meters
d2 = 487 Meters
Required
Determine the absolute difference
The absolute difference (D) of the given distances can be calculated using the following expression
D = |d1 - d2|
Substitute values for d1 and d2
D = |527−487|
D =|40|
D = 40
Hence, Twyla traveled 40 meters.
Sheila manages a team of editors at a publishing company. To help determine deadlines, she developed a model based on past
projects. In the model below, x represents the number of pages which require editing, and y represents the total number of days required to complete the editing.
y = 1/85x
The linear equation that models the number of days it will take Sheila's team to edit x pages, y = (1/85)·x indicates that the correct statement is option C.
C. Her team can edit 85 pages in one day
What is the slope-intercept form of linear equations?The slope-intercept form of linear equations is; y = m·x + c, where the coefficient m is the slope and c is the y-intercept.
The parameters of the model, y = (1/85)·x are;
x = The number of pages that require editing
y = The number of days required to complete the editing
Therefore, the model is in the slope and intercept form of a linear equation, where;
1/85 = The slope
The y-intercept is zero
The slope indicates that 85 pages can be edited in one day, therefore the number of days to edit 170 (2 × 85) pages is 2 days
Similarly, when the number of days, y = 1, and the number of pages to be edited, x = 1, we get;
y = (1/85)·x
1 = (1/85)·x
x = 1/(1/85) = 85
The number of pages that can be edited in one day is 85 pages
The correct statement is therefore;
C. Her team can edit 85 pages in one day
Learn more on linear equations here: https://brainly.com/question/14323743
#SPJ1
Billy took 5 tests in his math class. He scored an 89,88,93,90 and 81. What is the variance of his grades in these test? If necessary, round to the nearest hundredth.
The variance of Billy's grades obtained from his test scores is 15.76
What is variance?The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.
The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;
The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2
The square of the differences of the values from the mean can be calculated as follows;
(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84
The sum of the square of the differences is therefore;
0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8
The variance is therefore; 78.8/5 = 15.76Learn more on the variance of a set of data here: https://brainly.com/question/30701163
#SPJ1
2+2=
a. 3
b. 5
c. 4
d. 7
Answer:
C
Step-by-step explanation:
2
+2
-----
4
Which mixed number is represented by the shaded
area? 2 2/5, 2 3/5, 2 2/3, 2 3/2?
Answer:
2 3/5
Step-by-step explanation:
A line passes through the point (4,-6) and has a slope of -3/4which is the equation of the line?
Answer:
y=(-3/4)+3
Step-by-step explanation:
PLEASE ANSWER - PLEASE ANSWER
The diagram shows triangle ABC. ABC and BED are straight lines. AB = 12.2cm, CD = 5.8cm, BE:ED = 3:1, Angle ADB = 90°, Angle ABD = 38°.
Work out the size of angle DCE, correct to 1 decimal place. SHOW ALL WORKING IN TEXT FORM, NO IMAGES.
The measure of angle DCE in this problem is given as follows:
m < DCE = 22.5º.
How to obtain the measure of angle DCE?The triangles in this problem are right triangles, meaning that the trigonometric ratios are used to find the measures.
The three trigonometric ratios are given as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.The segment DB is adjacent to angle of 38º, while the hypotenuse is of 12.2 cm, hence the length of segment DB is calculated as follows:
cos(38º) = DB/12.2
DB = 12.2 x cosine of 38 degrees
DB = 9.6 cm.
BE:ED = 3:1, means that segment DE is one-fourth of segment DB, and thus it's length is given as follows:
DE = 1/4 x 9.6
DE = 2.4 cm.
Then for the angle DCE, we have that the opposite side is of 2.4 cm while the adjacent side is of 5.8 cm, hence the tangent is used to find it's measure, as follows:
tan(x) = 2.4/5.8
x = arctan(2.4/5.8)
x = 22.5º
m < DCE = 22.5º.
More can be learned about trigonometric ratios at brainly.com/question/24349828
#SPJ1
Answer:
x = 22.5°
Step-by-step explanation:
BD = cos(38)*12.2 = 9.61DE = 9.61*¼ = 2.4∠DCE = tan(2.4/5.8) = 22.5°Please, help me find the answer
The probability values for the questions posed are :
11/20probability of Public speaking given that student is majoring in Business Administration1/3A.)
Number of students Taking a public speaking class majoring in business administration.
10 + 45 = 55P(PS or BA) = 55/100 = 11/20
Therefore, the probability of PS or BA is 11/20
B.)
For the survey described, P(taken a public speaking class | majoring in Business Administration) represents the probability that a selected student has taken a public speaking class given that the student is majoring in business administration.
Hence, as inferred from P(A|B) ; probability of A given B.
C.)
P(PS|BA) = n(PSnBA) / n(BA)
n(PS) = 10+20 = 30
n(PSnBA) = 10
P(PS|BA) = 10/30 = 1/3
Therefore , the probability of PS|BA is 1/3.
Learn more on probability:https://brainly.com/question/24756209
#SPJ1
A population of values has a normal distribution with �=189.7 and �=96.7. You intend to draw a random sample of size �=62.
Find the probability that a single randomly selected value is between 189.7 and 213.
P(189.7 < X < 213) =
Find the probability that a sample of size �=62 is randomly selected with a mean between 189.7 and 213.
P(189.7 < M < 213) =
Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
The probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213 is approximately 0.9702.
To find the probability that a single randomly selected value is between 189.7 and 213, we can use the standard normal distribution.
Step 1: Calculate the z-scores for the given values using the formula:
z = (x - μ) / σ
For 189.7:
z1 = (189.7 - 189.7) / 96.7 = 0
For 213:
z2 = (213 - 189.7) / 96.7 ≈ 0.2417
Step 2: Utilize a standard typical conveyance table or number cruncher to find the probabilities comparing to the z-scores.
P(189.7 < X < 213) = P(0 < Z < 0.2417) ≈ 0.0939
Therefore, the probability that a single randomly selected value is between 189.7 and 213 is approximately 0.0939.
To find the probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213, we use the central limit theorem. Under specific circumstances, the testing dispersion of the example mean methodologies a typical conveyance
Step 1: Calculate the standard error of the mean (σ_m) using the formula:
σ_m = σ / sqrt(n)
σ_m = 96.7 / sqrt(62) ≈ 12.2878
Step 2: Convert the given qualities to z-scores utilizing the equation:
z = (x - μ) / σ_m
For 189.7:
z1 = (189.7 - 189.7) / 12.2878 = 0
For 213:
z2 = (213 - 189.7) / 12.2878 ≈ 1.8967
Step 3: Utilize a standard typical conveyance table or mini-computer to find the probabilities relating to the z-scores.
P(189.7 < M < 213) = P(0 < Z < 1.8967) ≈ 0.9702
Therefore, the probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213 is approximately 0.9702.
For more such questions on probability, click on:
https://brainly.com/question/7965468
#SPJ8
HELP PLEASE
What is the area of the kite below?
Answer:
Area = 33 inches squared
Step-by-step explanation:
The formula for the area of a kite is:
Area = ½ × (d)1 × (d)2
To find the first diagonal (d1):
d1 = 7 in + 4 in = 11 in
To find the second diagonal (d2):
The triangles on the right of the kite must be 3 4 5 triangle since it is a right triangle with a hypotenuse of 5 and a side of 4, we know half of a diagonal would be 3 inches.
d2 = 3 in + 3 in = 6 in
Now we can plug the diagonals into the area formula.
Area = ½ × 11 × 6 = 33 inches squared
Answer: A = 33 in²
Step-by-step explanation:
Given information:
Longer side = 7 in
Shorter side = 4 in
Shorter Hypotenuse = 5 in
Given formula:
A = (1/2) × (d₁) × (d₂)
A = aread₁ = The longer line (horizontal)d₂ = The shorter line (vertical)Please refer to the attachment below for a graphical understanding
Determine the length of the shorter side (vertical) through the Pythagorean theorem
a² + b² = c² (Pythagorean theorem)
(4)² + b² = (5)² (Substitute values into the equation)
16 + b² = 25
b² = 25 - 16
b² = 9
b = 3 or b = -3 (rej)
Substitute values into the given formula
A = (1/2) × d₁ × d₂
A = (1/2) × (7 + 4) × (3 + 3)
Simplify values in the parenthesis
A = (1/2) × 11 × 6
Simplify by multiplication
A = (11/2) × 6
\(\Large\boxed{A=33}\)
Hope this helps!! :)
Please let me know if you have any questions
8t=56 plsssssss helppp mee
Answer: t=7
Step-by-step explanation:
1. Isolate x or divide both sides by 8: t=56/8
2. Simplify: t=7
Have a nice day! :D
Find the distance between the point (5,12) and the line y = 5x + 12 (rounded to the nearest hundredth).
A. 1.36 units
B. 2.19 units
C. 4.81 units
D. 4.90 units
The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units
How to find the distance between a point and a line?
If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0
Then the distance of a point from the line is given by the formula:
d = (ax₁ + by₁ + c) / √(a² + b²)
Given: the point (5,12) and the line y = 5x + 12. The line can be written as
5x-y+12 = 0. Thus:
x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:
d = (ax₁ + by₁ + c) / √(a² + b²)
d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)
d = 25/√26 = 4.90 units
Therefore, the distance between the point and the line is 4.90 units. Option D is the answer
Learn more about distance between a point and a line on:
https://brainly.com/question/18276750
#SPJ1
What is the domain of the square root function graphed below?
On a coordinate plane, a curve open up to the right in quadrant 4. It starts at (0, negative 1) and goes through (1, negative 2) and (4, negative 3).
x less-than-or-equal-to negative 1
x greater-than-or-equal-to negative 1
x less-than-or-equal-to 0
x greater-than-or-equal-to 0
Mark this and return
The domain of the square root function is x greater-than-or-equal-to 0, since the function is defined for all non-negative x-values or x-values greater than or equal to zero.
The domain of the square root function graphed below can be determined by looking at the x-values of the points on the graph.
From the given information, we can see that the curve starts at (0, -1) and goes through (1, -2) and (4, -3).
The x-values of these points are 0, 1, and 4.
Since the square root function is defined for any non-negative x-values or x-values more than or equal to zero, its domain is x greater-than-or-equal-to 0.
for such more question on domain
https://brainly.com/question/16444481
#SPJ8
A coin is flipped 10 times and the sequence of heads and tails recorded. In how many ways can a sequence consist of exactly 3 heads and the rest tails?
there are 120 different ways a sequence of 10 coin flips can consist of exactly 3 heads and the rest tails.
To solve this problem, we can use the formula for combinations. The number of ways to choose k items from a set of n items is given by the formula n choose k, which is written as C(n,k) or sometimes as nCk.
In this case, we want to choose 3 heads from a set of 10 coin flips. The number of ways to do this is C(10,3) = 120.
Once we have chosen the 3 heads, the remaining 7 flips must all be tails. There is only one way to arrange 7 tails, since they are all the same.
Therefore, the total number of sequences that consist of exactly 3 heads and the rest tails is 120.
Learn more about sequence here:
https://brainly.com/question/30262438
#SPJ11
Which expressions are equivalent to 24-7? Choose all the correct answers. Show your work.
The equivalent expressions to \(24^{-7}\) are given as follows:
C. \(\left(\frac{1}{24^{-7}}\right)^{-1}\)
F. \((24^3 \times 24^4)^{-1}\)
What are are equivalent expressions?Equivalent expressions are expressions that have the same value for all possible values of the variables. In other words, equivalent expressions are different ways of writing the same mathematical idea.
The exponent in the denominator can be moved to the numerator with the changed signal, hence:
\(\left(\frac{1}{24^{-7}}\right)^{-1} = (24^7)^{-1}\)
Applying the power of power rule, we multiply the powers, hence:
\((24^7)^{-1} = 24^{-7}\)
When two terms with the same base and different exponents are multiplied, we add the bases and keep the exponents, hence:
\((24^3 \times 24^4)^{-1} = (24^7)^{-1} = 24^{-7}\)
More can be learned about equivalent expressions at https://brainly.com/question/15775046
#SPJ1
Which of the following angles are congruent?
Answer:
angle B and angle f
Step-by-step explanation:
im not all that smart but goodluck
Ellie fills her car with 14.297 gallons of gas. Alivia fills her car with 14.209 gallons of gas.write an inequality statement comparing the two gas purchase.
Answer:
Ellie is gas.
Step-by-step explanation:
Inequality statement: Ellie is not equal to gas, yet she is all about gas.
Hunter leaves his house to go on a bike ride. He starts at a speed of 15 km/hr. Hunter's
brother decides to join Hunter and leaves the house 30 minutes after him at a speed of
18 km/hr. How long will it take to Hunter's brother to catch up to him?
The time requires to catch up to him will be 3 hours.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance. Speed is a scalar quantity it does not require any direction only needs magnitude to represent.
Given that Hunter leaves his house to go on a bike ride. He starts at a speed of 15 km/hr. Hunter's brother decides to join Hunter and leaves the house 30 minutes after him at a speed of 18 km/hr.
The time will be calculated as below:-
30 minutes = 0.5 hour
15x = 18(x - 0.5)
15x = 18x - 9
-3x = -9
x = 3 hours
Therefore, the time requires to catch up to him will be 3 hours.
To know more about Speed follow
https://brainly.com/question/6504879
#SPJ5
What is the equation of the line that is parallel to the line defined by the equation y = 3x−7 and goes through the point (4, 2)?
Answer:
\(y-2=3(x-4)\)
Step-by-step explanation:
Pre-SolvingWe are given a line contains the point (4, 2).
We also know that the line is parallel to y= 3x - 7.
We want to write the equation of this line.
Parallel lines have the same slopes.
First, let's find the slope of y = 3x - 7.
3 is in the place of where m (the slope) is, so that means it is the slope of that line.
It is also the slope of the line whose equation we want to write.
The equation of the line can be written in three ways:
Slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept. Standard form, which is ax+by=c, where a, b, and c are free integer coefficients. a and b cannot be 0, and a is usually non-negative as well. Point-slope form, which is \(y-y_1=m(x-x_1)\), where m is the slope and \((x_1, y_1)\) is a point.All of these ways are valid, but for this problem, let's write the equation in point-slope form, as it is the easiest.
SolvingSubstitute 3 as m in \(y-y_1=m(x-x_1)\).
\(y-y_1=3(x-x_1)\)
Now, substitute 4 as \(x_1\) and 2 as \(y_1\).
\(y-2=3(x-4)\)
Topic: parallel and perpendicular lines
See more: https://brainly.com/question/7699889
The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair. (1 point)
Function 1
(look at the graph below)
Function 2
f(x) = −x2 + 2x − 15
Function 1 has the larger maximum at (4, 1).
Function 1 has the larger maximum at (1, 4).
Function 2 has the larger maximum at (−14, 1).
Function 2 has the larger maximum at (1, −14).
A function that has a greater maximum include the following: A. Function 1 has a larger maximum at (4, 1).
How to determine the function that has a larger maximum?In order to determine the maximum value of function 2, we would have to take the first derivative with respect to x and then, substitute this x-value into the original function while equating it to zero (0), and then evaluate as follows;
f(x) = −x² + 2x - 15
f(x) = −2x + 2
0 = −2x + 2
2x = 2
x = 2/2
x = 1
For the maximum value of function 2, we have:
f(1) = −(1)² + 2(1) - 15
f(1) = -14
For the maximum value of function 1, we can logically deduce that it is equal to 1 based on the graph in image attached above.
Read more on maximum and function here: https://brainly.com/question/1800006
#SPJ1
Test: Chapter 1-4 Test
Is 9 a solution to the equation x+2=x+2?
Yes
No
Answer:
Yes..............
....
.
The ferry family rented 50 chairs for $150. Which expression can be used to find the cost per chairs.
Answer:
3$per chair
Step-by-step explanation:
50/150$=3
If 3 x 50=150
Answer:
150/50
Step-by-step explanation:
150 divided by 50 = 3
Hope this helps!
3) BRAINLIEST & 10+ POINTS!
Answer:
44rad/sec
Step-by-step explanation:
1rev= 2pie
22 rev= 44pie
I NEED HELP PLEASEEE!!!! I HAVE BEEN WORKING ALL DAY
Answer:
188
Step-by-step explanation:
I found and fixed my mistake sorry
fraction bears the same ratio to 1/27 as 3/7 does to 5/9.then the fraction is?
The fraction that bears the same ratio to 1/27 as 3/7 does to 5/9 is 27/35.
To find the fraction that bears the same ratio to 1/27 as 3/7 does to 5/9, we can set up a proportion.
Let's represent the unknown fraction as x. The ratio can be configured as follows:
x / (1/27) = (3/7) / (5/9)
To solve this proportion, we can cross-multiply:
(x * 5/9) = (3/7) * (1/27)
Simplifying the right side:
(x * 5/9) = 3/189
To eliminate the fraction on the left side, we can multiply both sides by the reciprocal of 5/9, which is 9/5:
(x * 5/9) * (9/5) = (3/189) * (9/5)
Simplifying further:
x = 27/35
Therefore, the fraction that bears the same ratio to 1/27 as 3/7 does to 5/9 is 27/35.
for such more question on fraction
https://brainly.com/question/1622425
#SPJ8