Answer:
Step-by-step explanation:
- 4x² + 10x
Answer:
[tex]\fbox{\begin{minipage}{11em}(f - g)(x) = -2x(2x - 5)\end{minipage}}[/tex]
Step-by-step explanation:
Given:
[tex]f(x) = -x^{2} + 6x - 1 \\ g(x) = 3x^{2} - 4x - 1\\[/tex]
Solve for:
[tex](f - g)(x)[/tex]
Solution:
Perform the subtraction:
[tex](f - g)(x) = (-x^{2} + 6x - 1) - (3x^{2} - 4x - 1)[/tex]
Eliminate the parenthesis (notice the change in sign of some components):
[tex](f - g)(x) = -x^{2} + 6x - 1 - 3x^{2} + 4x + 1[/tex]
Rearrange the expression:
[tex](f - g)(x) = (-x^{2} - 3x^{2}) + (6x + 4x) + (1 - 1)[/tex]
Simplify the expression:
[tex](f - g)(x) = -4x^{2} + 10x[/tex]
Perform the inverse of associative property:
[tex](f - g)(x) = -2x(2x - 5)[/tex]
Hope this helps!
:)
plz can someone help me with this plzz
Answer:
p: 42
a: 82.16
Step-by-step explanation:
For perimeter, add all the sides together
For area, multiple the longer side by the shorter side
The graph of a line goes through the points (-4,3) and (6,8). What is the equation
of the line in slope-intercept form?
Answer:
y = 1/2x+5
Step-by-step explanation:
You have two points so you can find the slope
m = (y2-y1)/(x2-x1)
m = (8-3)/(6 - -4)
(8-3)/(6+4)
5/10
1/2
The slope intercept form is y = mx+b where m is the slope and b is the y intercept
y = 1/2 x+b
Substitute a point into the equation
8 = 1/2(6)+b
8 = 3+b
b=8-3 = 5
y = 1/2x+5
A box contains 20 different balls numbered from 1 to 20 (different balls have different numbers). At each step, we select a ball uniformly at random, record the number on it, and put it back in the box. This experiment is repeated 10 times. Find the probability that all the numbers recorded were distinct.
Answer:
P = 0.0655
Step-by-step explanation:
First, we are going to calculate the number of ways in which we can select the 10 balls. This is calculated using the rule of multiplication as:
[tex]T=20*20*20*20*20*20*20*20*20*20\\T=20^{10}\\T=1.024*10^{13}[/tex]
Because we have 20 different balls every time and the experiment is repeated 10 times.
Then, from that [tex]1.024*10^{13}[/tex] ways, there are C ways where all the numbers recorded are distinct. It is calculated as:
[tex]C = 20*19*18*17*16*15*14*13*12*11\\C = 6.704*10^{11}[/tex]
Because, the first time, we have 20 options, the second time, we can just select 19 balls because we can not repeat the numbers, the third time, we can just select 18 balls and we need to keep doing this until get to the 10th time.
Finally, the probability that all the numbers recorded were distinct is calculated as C/T and it is equal to:
[tex]P=\frac{C}{T}=\frac{6.704*10^{11}}{1.024*10^{13}} =0.0655[/tex]
A band is planning a concert at a local theater. The graph below shows the ticket sales per hour.
What is the slope of the line shown in the graph ?
Answer:
A. -400Step-by-step explanation:
Slope of a line is defined as the change in the component of the y- axis to its x axis as shown;
slope = Δy/Δx = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
From the graph, y2 = 0, y1 = 4000, x2 = 10, x1 = 0
slope = [tex]\frac{0-4000}{10-0}[/tex]
[tex]slope = \frac{-4000}{10}\\ slope = -400[/tex]
The slope of the line is a negative slope and it is -400
Answer: A. -400
Step-by-step explanation:
just had this and got in correct
What is StartFraction 11 Over 12 EndFraction divided by one-third? A fraction bar labeled 1. Under the 1 are 3 boxes labeled one-third. Under the 3 boxes are 4 boxes containing one-fourth. Under the 4 boxes are 12 boxes containing StartFraction 1 Over 12 EndFraction. 2 and one-fourth 2 and three-fourths 3 and one-third 3 and two-thirds
Answer:
2 and three-fourthsStep-by-step explanation:
Given the expression [tex]\frac{11}{12}/\frac{1}{3}[/tex], the equivalent expression can be gotten as shown;
[tex]= \frac{11}{12}/\frac{1}{3}\\= \frac{11}{12}*\frac{3}{1}\\ = \frac{11}{4} \\= 2+\frac{3}{4}\\ = 2\frac{3}{4}[/tex]
2 and three-fourth therefore gives the required expression
Answer:
2 and three-fourths
Step-by-step explanation:
Given the expression , the equivalent expression can be gotten as shown;
Step-by-step explanation:
if b=6, what is 12b
Answer:
72
Step-by-step explanation:
12b
Let b = 6
12*6
72
Answer:
72
Step-by-step explanation:
You have to take 12 times 6 because b=6.
so 12b=12 times 6
12 times 6= 72
Which division problem would have an estimated quotient of 3.5 if the divisor and dividend were rounded to the nearest whole number?
Answer:
Step-by-step explanation:
Weren't there possible answer choices from which to choose? If so, please share them.
7 3 + 4
-- is equivalent to ---------- and has an estimated (and exact) quotient of 3.5.
2 2
If the divisor (2) and the dividend (7) were rounded to the nearest whole number (which would be 7), the estimated quotient would still be 3.5.
Answer:
7 3 + 4
-- is equivalent to ---------- and has an estimated (and exact) quotient of 3.5.
2 2
Step-by-step explanation:
Find the slope of the line that passes through (3, 2) and (10, 3).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
m=1/7x
Step-by-step explanation:
Answer:
[tex] slope= \frac{1}{7} [/tex]
Step-by-step explanation:
[tex](3 \: \: \: \: \: \: \: 2) = > (x1 \: \: \: \: \: \: \: x2)\\ (10 \: \: \: \: 3) = > (y1 \: \: \: \: \: \: \: y2)[/tex]
[tex]slope \\ = \frac{y1 - y2}{x1 - x2} \\ = \frac{2 - 3}{3 - 10} \\ = \frac{ - 1}{ - 7} \\ = \frac{1}{7} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
what is the equation of the following line? be sure to scroll down first to see all answer options
Answer:
The equation for the following graph:
[tex]y = -\frac{1}{5}x[/tex]
Step-by-step explanation:
- You first need to find the slope by using the slope formula:
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
(where [tex](x_{1},y_{1})[/tex] is the first point and [tex](x_{2}, y_{2})[/tex] is the second point)
-Use the given points [tex](0,0)[/tex] and [tex](10, -2)[/tex] from the graph for the formula:
[tex]m = \frac{-2 - 0}{10 - 0}[/tex]
Then, you solve:
[tex]m = \frac{-2 - 0}{10 - 0}[/tex]
[tex]m = -\frac{1}{5}[/tex]
After you have found the slope, use the slope [tex]-\frac{1}{5}[/tex] and the first point [tex](0,0)[/tex] for the point-slope formula:
[tex]y - y_{1} = m ( x - x_{1})[/tex]
(where [tex]m[/tex] is the slope and [tex](x_{1}, y_{1})[/tex] is the first point)
[tex]y - 0 = -\frac{1}{5} ( x - 0)[/tex]
Then, you solve:
[tex]y - 0 = -\frac{1}{5} ( x - 0)[/tex]
[tex]y - 0 = -\frac{1}{5}x - 0[/tex]
[tex]y - 0 + 0 = -\frac{1}{5} - 0 + 0[/tex]
[tex]y = -\frac{1}{5}x[/tex]
So, the equation for the following graph is [tex]y = -\frac{1}{5}x[/tex] .
Cheap and fast gas station is conducting a consumer satisfaction survey. Which method of collecting data would most likely lead to a biased sample? Interviewing every 5th customer to come into the station
Given: Z1 is complementary to 22.
What is the missing statement in step 3 of the proof?
22 is complementary to 23.
0 m21 = m22
Prove: mz1 = m 23
OmZ1 + m22 = 90°
OmZ2 = m23
VV
m22 + m23 = 180°
Statements
1. 21 is comp. to 22
2. 22 is comp. to 23
3. ?
4. m21-90°-m22
5 m22+m23-90°
6. m23-90°-m22
7. m 1 m3
1
2.
3
4
5
6.
7
Reasons
given
given
def. of comp. ZS
subtr. equality prop.
def. of comp. ZS
subtr. equality prop
trans. prop.
Answer:
Option (2)
Step-by-step explanation:
Statements Reasons
1). ∠1 is comp. to ∠2 1. Given
2). ∠2 is comp. to ∠3 2. Given
3). ∠1 + ∠2 = 90° 3. def. of comp. angles
4). m∠1 = 90° - ∠1 4. Subtr. equality property
5). m∠2 + m∠3 = 90° 5. def. of comp. angles
6). m∠3 = 90° - m∠2 6. subtr. equality property
7). m∠1 = m∠3 7. Transitive property
Option (2) will be the answer.
Both angle ∠1 and ∠3 are complementary to ∠2, therefore, ∠1 + ∠2 = 90°
and by properties of equality, ∠1 = ∠3.
Response:
The missing statement in step 3 is; m∠1 + m∠2 = 90°Which property or definition is used to find the missing statement?The completed two column proof is presented as follows;
Statements [tex]{}[/tex] Reasons
1. ∠1 is comp. to ∠2 [tex]{}[/tex] 1. Given
2. ∠2 is comp. to ∠3 [tex]{}[/tex] 2. Given
3. m∠1 + m∠2 = 90° [tex]{}[/tex] 3. Definition of complementary angles4. m∠1 = 90° - m∠2 [tex]{}[/tex] 4. Subtraction equality property
5. m∠2 + m∠3 = 90° [tex]{}[/tex] 5. Definition of complementary angles
6. m∠3 = 90° - m∠2 [tex]{}[/tex] 6. Subtraction equality property
7. m∠1 = m∠2 [tex]{}[/tex] 7. Transitive property
The missing statement in step 3 is therefore; m∠1 + m∠2 = 90°Details of the solution:
Given that ∠1 is complementary to ∠2, we have;
∠1 + ∠2 = 90°
Similarly, by definition of complementary angles, we have;
∠2 + ∠3 = 90°
Which gives;
∠3 + ∠2 = 90°
Therefore;
∠1 + ∠2 = ∠3 + ∠2
Subtracting ∠2 from both sides (subtraction property of equality), gives;
∠1 + ∠2 - ∠2 = ∠3 + ∠2 - ∠2
∠1 + 0 = ∠3 + 0
Which gives;
∠1 = ∠3
Learn more about properties of equality here
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the triangle bounded by the lines y = o, y = 2x
and y = -0.5x + k with k positive is equal to 80 square untits find k
Answer
k = 3.575.
Step-by-step explanation:
On a compass, what bearing is South East?
Simplify (4^-2)^5 Pls help
Answer:
4^-10
Step-by-step explanation:
(4^-2)^5
4^-2 x 5
= 4^-10
hope this helped have fun doing school haha
Answer:
[tex]\frac{1}{32768}[/tex]
Step-by-step explanation:
[tex](4^{-2})^{5}[/tex]
[tex](\frac{1}{4^{2} }) ^{5}[/tex]
[tex](\frac{1}{8})^{5}[/tex]
[tex]\frac{1}{32768}[/tex]
∠A and \angle B∠B are complementary angles. If m\angle A=(2x+18)^{\circ}∠A=(2x+18) ∘ and m\angle B=(6x-8)^{\circ}∠B=(6x−8) ∘ , then find the measure of \angle B∠B?
Answer:
[tex]m\angle B=52^{\circ}[/tex]
Step-by-step explanation:
Two or more angles are said to be complementary if they sum up to 90 degrees.
Given that angles A and B are complementary, then:
[tex]\angle A+\angle B=90^\circ\\m\angle A=(2x+18)^{\circ}\\m\angle B=(6x-8)^{\circ}\\$Therefore:\\(2x+18)^{\circ}+(6x-8)^{\circ}=90^\circ\\2x+6x+18-8=90^\circ\\8x+10^\circ=90^\circ\\8x=90^\circ-10^\circ\\8x=80^\circ\\$Divide both sides by 8\\x=10^\circ\\$Therefore:\\m\angle B=(6x-8)^{\circ}\\m\angle B=(6(10)-8)^{\circ}\\=60-8\\m\angle B=52^{\circ}[/tex]
Answer:
56 :)
Step-by-step explanation:
Mrs. Quotient asked her students to simplify each of the expressions below. Which of the numbered choices represents the expressions which simplified to the same result? A 71 B 72 C 73
Answer:
A and B
Step-by-step explanation:
Mrs. Quotient asked her students to simplify each of the expressions below. Which of the numbered choices represents the expressions which simplified to the same result? A 126/2 B 23 × 3 C 3 × 21
When simplifying an algebraic expression, the following steps are needed to be taken.
Firstly, remove parenthesis by multiplying the constant with the term in the parenthesis or remove parenthesis using exponent rules for parenthesis in exponent form.
Secondly Combine terms by adding coefficients of terms with the same order and lastly sum all constant.
A) 126/2
Applying the division rule give:
126/2 = 63
B) 23 × 3
Applying multiplication rule gives:
23 × 3 = 69
C) 3 × 21
Applying multiplication rule gives:
3 × 21 = 63
Both the results of expression A and expression B are simplified to the same result
one x intercept for a parabola is at the point (1,0). use the factor method to find the other x intercept for the parabola defined by y=-5x^2+15x-10
First simplify the equation of parabola y=-5x^2+15x-10 in the following way:
D=(15)^2-4\cdot (-5) \cdot (-10)=225-200=25, \\ \sqrt{D}=5, \\ x_{1,2} = \dfrac{-15\pm 5}{2\cdot(-5)} = 2, 1 \\ -5x^2+15x-10=-5(x-1)(x-2), \\ y=-5(x-1)(x-2).
You can see that if x=1 or x=2, then y=0. Two points of intersection with x-axis are (1,0) and (2,0).
HELPP ITS ABOUT A PYRAMID Explanation needed pleasee
Answer:
A. a triangle with an area of 20 square units
Step-by-step explanation:
note when you cut from top tip to the bottom you will get a triangle with base = 4 and height =10
Area of triangle = 1/2 * base * heighte
Area of triangle = 0.5*10*4
Area of trianle = 20 square units
Suppose that you received an unexpected inheritance of $39,200.You have decided to invest the money by placing some of the money in stocks that pay 4.8% and the rest in bonds that pay 8%.How much should you place in each investment in order to earn 6%or $2352 annually?
Use the synthetic division shown to help factor the polynomial and solve the equation.
What are the solutions of the equation?
1, 4, and –5
1, –4, and 5
–1, –7, and 3
–1, 5, and 9
Answer:
1. x = -5 and x = 1
2. x = 5 and x = -1
3. no integral solutions
4. no integral solutions
Step-by-step explanation:
Answer:
1, 4, and –5
Step-by-step explanation:
on edge
Find the slope of the line will mark as brain
y
=
–9
4
x
−
1
4
.
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer negative 9 is the answer
Step-by-step explanation:
What is the slope of the line that passes through the points (6,-10) and
(3, -13)? Write your answer in simplest form.
Answer:
1
Step-by-step explanation:
The slope intercept form for this problem is y = x - 16
Sandy wants to make a punch recipe with 2 parts pineapple juice to 6 parts ginger ale if you wants to increase the recipe using a parts pineapple juice,
How much ginger-ale should she use?
18
28
(24
Answer:
24
Step-by-step explanation:
If you go from 2 parts pineapple to 8, thats a 4x increase. Therefore 6x4=24 (6 from the Ginger)
A Car travels 42 km
On 7 litres of petrol. How long will it travel
on 12 litres of petrol.
Answer:
The answer is 72
Step-by-step explanation:
You'll do 42 divided by 7 times 2
42/7x2
Hope it helps.
A car travels 72 km on 12 liters of petrol.
What is Division method?
Division method is used to distributing a group of things into equal parts.
Given that;
A Car travels 42 km on 7 liters of petrol.
Now,
Since, On 7 liters of petrol a car travel 42 km
Hence, On 1 liter of petrol distance cover by a car = 42 ÷ 7
= 6 km
So, On 12 liters of petrol distance cover by a car = 6 × 12
= 72 km
Thus, A car travels 72 km on 12 liters of petrol.
Learn more about the division visit:
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Complete the equation of the line through (–6,5) and (-3, -3).
Use exact numbers.
Answer:
-3, -3
Step-by-step explanation:
State true or false
The measure of the supplementary angle of the complementary angle of an angle with measure 35 degree is 125 degree
Answer:
True
Step-by-step explanation:
90-35=55degree
180-55=125°
Write 240 as a product of primes. Use index notation where appropriate.
Answer:
2^4x3x5
Step-by-step explanation:
240=2x120
120=2x60
60=2x30
30=2x15
15=3x5
as an estimation we are told 5 miles is 8km. Convert 84 km to miles
Answer:
52.195 miles
Step-by-step explanation:
84 km to miles is 52.195 miles
The measure of one angle of a triangle is 105°. What do you know about the measures of the other two angles? Check all that apply.
Both angles are acute.
The sum of the measures of the two angles is 75°.
The sum of the measures of the two angles is 155°.
One of the angles is a right angle.
The measure of neither angle is more than 75°.
The measures of the other angles must be 105° too.
The measure of one of the other angles equals 75°.
The measure of one of the other angles must be 45°.
Step-by-step explanation:
The sum of the measures of the two angles is 75° because of the sum of angles in a triangle which means that both angles are acute. This also means that the measure of neither angle is more than 75°.
Answer:
A, B, E
Step-by-step explanation:
both angles are acute
The sum of the measures of the two angles is 75°
The measure of neither angle is more than 75°
if f(x) =5x-2 and g(x) = 2x +1 find(f+g)(x)
Answer & Step-by-step explanation:
When we see (f + g)(x), it means that we are going to be adding f(x) to g(x).
f(x) = 5x - 2
g(x) = 2x + 1
(f + g)(x) = (5x - 2) + (2x + 1)
Combine like terms.
(f + g)(x) = 7x - 1
So, (f + g)(x) equals 7x - 1
