Answer:
-2 is an extraneous solution because it creates 0 in the denominator.
There is one acceptable solution to the equation
Step-by-step explanation:
x² + 5x + 6 = x² + 2x + 3x + 6
= x(x + 2) + 3(x + 2)
= (x + 2)(x + 3)
[tex]\frac{x}{x+2}+\frac{2}{x^{2}+5x+6}=\frac{5}{(x+3)}\\\\\frac{x}{x+2}+\frac{2}{(x+2)(x+3)}=\frac{5}{(x+3)}\\\\\frac{x*(x+3)}{(x+2)(x+3)}+\frac{2}{(x+2)(x+3)}=\frac{5*(x+2)}{(x+3)(x+2)}\\\\\frac{x^{2}+3x+2}{(x+2)(x+3)}=\frac{5x+10}{(x+3)(x+2)}\\\\[/tex]
x² + 3x + 2 = 5x + 10
x² + 3x - 5x + 2 - 10 = 0
x² - 2x - 8 = 0
x² + 2x - 4x - 8 = 0
x(x + 2) - 4(x + 2) = 0
(x + 2)(x - 4) = 0
x +2 = 0 or x - 4 = 0
x = - 2 or x = 4
What type of line is PQ?
A. side bisector
B. altitude
C. median
D. angle bisector
Answer:
D
Step-by-step explanation:
Since ∠ RPQ = ∠ SPQ = 60° , then
PQ bisects ∠ RPS and is an angle bisector
PQ exists the angle bisector of angle RPS. It means PQ divides the angle RPS in two equivalent parts.
What is angle bisector?
Angle bisector in geometry directs to a line that divides an angle into two equivalent angles. A bisector represents the thing that bisects a shape or an object into two equivalent regions. If we draw a ray that bisects an angle into two equivalent parts of the exact measurement, then it exists named an angle bisector.
It is given that ray PQ is the angle bisector of angle RPS. It means PQ divides the angle RPS in two equivalent parts.
[tex]$m \angle R P Q=m \angle QP S=60^{\circ}$[/tex]
Now, [tex]&m \angle R P S=m \angle R P Q+m \angle Q P S \\[/tex]
[tex]&m \angle R P S=60^{\circ}+60^{\circ} \\[/tex]
[tex]&m \angle R P S=120^{\circ}[/tex]
Therefore, the measure of angle RPS is [tex]$60^{\circ}$[/tex].
Therefore, the correct answer is option D. angle bisector.
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Cassie paid 55% of the bill. The remaining $18 was covered by her friend. What was the total bill
-80% + 50/54 (fraction) - 0.25
Answer:
-67/540
Step-by-step explanation:
I just converted - 80% to a decimal which is - 0.8 and then used a calculator for the rest.
Bryan has a square parcel of land that is 120 yards long and 120 yards wide. The land is planted with Bermuda grass and surrounded by a fence. So
that his cattle will not ruin the grass, Bryan decides to split the field into two halves and rotate his cattle on the land every 30 days. He plans to build a
fence diagonally across the field. How many feet of fencing will Bryan need to split the parcel of land in half? Round your answer to the nearest yard.
A sphere has a radius of 8cm.Find its volume
Answer:
[tex]\displaystyle V = \frac{2048 \pi}{3} \ cm^3[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Volume of a Sphere Formula: [tex]\displaystyle V = \frac{4 \pi}{3}r^3[/tex]
r is radiusStep-by-step explanation:
Step 1: Define
Identify variables
r = 8 cm
Step 2: Find Volume
Substitute in variables [Volume of a Sphere Formula]: [tex]\displaystyle V = \frac{4 \pi}{3}(8 \ cm)^3[/tex]Evaluate exponents: [tex]\displaystyle V = \frac{4 \pi}{3}(512 \ cm^3)[/tex]Multiply: [tex]\displaystyle V = \frac{2048 \pi}{3} \ cm^3[/tex]Answer:
sphere
Step-by-step explanation:
volume of a sphere = 4/3πr³
= 4/3*22/7 * 8³
= 2145.5
5. Find the measures of the following. Round to the nearest whole number. (2 points)
a. "HT
H
b. 2T
15 cm
c.
ΖΗ
W
8 cm
T
[tex] \\ \sf \longmapsto \: HT=√15^2+8^2[/tex]
[tex] \\ \sf \longmapsto \: HT=√225+64[/tex]
[tex] \\ \sf \longmapsto \: HT=√289[/tex]
[tex] \\ \sf \longmapsto \: HT=17cm[/tex]
Solution:-2Angle T=15x
Let others be 8x and 17x
[tex] \\ \sf \longmapsto \: 8x+17x+15x=180[/tex]
[tex] \\ \sf \longmapsto \: 40x=180[/tex]
[tex] \\ \sf \longmapsto \: x=\dfrac{180}{40}[/tex]
[tex] \\ \sf \longmapsto \: x=4.5[/tex]
[tex] \\ \sf \longmapsto \: 15x=15(4.5)[/tex]
[tex] \\ \sf \longmapsto \: \angle T=67.5°[/tex]
Solution:-3[tex] \\ \sf \longmapsto \: \angle H=8x[/tex]
[tex] \\ \sf \longmapsto \: \angle H=32.5°[/tex]
A box contains eight cards labeled P, Q, R, S, T, U, V, and W. One card will be randomly chosen.
What is the probability of choosing a letter from Q to W?
Write your answer as a fraction in simplest form.
Answer:
7/8
Step-by-step explanation:
Probability= (Cards having letter Q to W)/(All cards) = 7/8
In a fruit cocktail, for every 15 ml of orange juice you need 5 ml of apple juice and 50 ml of coconut milk. What is the ratio of apple juice to coconut milk to orange juice expressed in its simplest form?
Answer:
1:10:3
Step-by-step explanation:
Which number belongs to the solution set of the equation?
x + 3 = 45
A. 15
B. 48
C. 43
D. 42
Answer:
D
Step-by-step explana
[tex] \sf \: The \: value \: of \: x \: is \: the \: number \: that \: belongs \: to \: the \: solution \: \\ \sf \: set \: of \: the \: equation. \: So \: we \: need \: to \: find \: x.[/tex]
[tex] \sf \: x + 3 = 45 \\ \sf \: x = 45 - 3 \\ \sf \: x = \underline{42}[/tex]
Answer ⟶ [tex]\boxed{\bf{D.42}}[/tex]
what multiplies to get 56 and adds to get 15
Answer:
8 & 7
Step-by-step explanation:
x*y = 56
x+y = 15
y = 15-x
x(15-x)=56
15x-x^2 = 56
x^2 -15x + 56 = 0
Factored Form: y= (x-8)(x-7)
What’s 4 divided by $5.32
Answer:
0.752
Step-by-step explanation:
Simplify the expression 5(x-3)(x^2+4x+1)
Simplify the expression 5(x-3)(x^2+4x+1)
it would be I think answer number 3
How many L of a 10% alcohol solution must be mixed with 9l of a 80% alcohol solution to make a 55% solution
Answer:
Step-by-step explanation:
The best thing to do for these solution/mixture problems is to make a table:
#L * %alcohol = L alcohol
10% sol.
+ 80% sol.
55% sol.
In this way, we can keep track of our information AND figure out the equation we need to use to solve it. Notice first, the equation along the top of the table:
#L * %alcohol = L alcohol This tells us that we are multiplying the #L column times the %alcohol column to get the L alcohol column. Notice second, that there is a + sign to the far left, indicating that we are ADDING rows 1 and 2 together to get the mix. Let's start filling this in. The easy part is the % alcohol column. 10% alcohol has .10 alcohol as a decimal, likewise for the 80% and 55%:
#L * %alcohol = L alcohol
10% sol. .10
+ 80% sol. .80 =
55% sol. .55
Now to fill in the first column. We know that our unknown, from the problem, is the number of Liters, #L in the 10% solution, so that is x, and we also know that we have 9 L of the 80% alcohol. Filling that in:
#L * %alcohol = L alcohol
10% sol. x * .10
+ 80% sol. 9 * .80
55% .55
Now look back at the + sign. We are told that we are mixing the 10% with the 80%, so we are adding them together. So let's do that. We will also follow the rule for the table and multiply the first column times the second column to fill in the last column to complete the table:
#L * %alcohol = L alcohol
10% sol. x * .10 = .10x
+ 80% sol. 9 * .80 = 7.2
55% sol. (9 + x) * .55 = .55x + 4.95
If we add the 2 solutions together to get the new solution in the first column, we will also add the L alcohol in the last column to get our equation:
.10x + 7.2 = .55x + 4.95 and
- .45x = - 2.25 so
x = 5L
We need 5 Liters of the 10% solution if we want to mix that with 9L of 80% solution to get 14 L of 55% solution.
[tex]\frac{x+4}{2} -\frac{3}{x-3} =1[/tex]
Quadratics null factor the given answer is x= 4,−3 but I don't know how to work it out
Answer:
Hello,
Step-by-step explanation:
[tex]x\neq 3\\\\\dfrac{x+4}{2} -\dfrac{3}{x-3} =1\\\\\dfrac{(x+4)(x-3)-2*3-2(x-3)}{2(x-3)} =0\\\\x^2+4x-3x-12-6-2x+6=0\\\\x^2-x-12=0\\\\x^2-4x+3x-12=0\\\\x(x-4)+3(x-4)=0\\\\(x-4)(x+3)=0\\\\x=4\ or\ x=-3\\[/tex]
Plz someone do this for me I’ll give a lot of points
Answer:
RW is congruent to WX
Step-by-step explanation:
We know that PW and WV and Angle W is vertical angle so We need to include that RW congruent to WX.
Which shows a difference of squares?10 y squared minus 4 x squared16 y squared minus x squared8 x squared minus 40 x 2564 x squared minus 48 x 9
Answer:
16 y squared minus x squared
Step-by-step explanation:
The other all expressions except 16y²-x² doesn't complete the square and its difference. Then we can check 16y²-x²,
Now take the expression 16y²-x² and we can try to solve it.
We can simplify the terms separately to associate them as perfect squares,
→ 16y² = (4y)² --- (1)
→ x² = (1x)² --- (2)
Now we can take the difference of eq. (1) and eq. (2),
→ 16y²-x²
→ (4y)²-(1x)² --- (3)
Now eq. (3) shows a difference of squares.
Another representation is,
→ (4y - x) (4y + x)
→ 16y²- x²
→ (4y)²- (1x)²
Therefore, the expression 16y²-x² shows a correct difference of squares.
Answer:
its b trust
Step-by-step explanation:
Which is the graph of f(x) = (x - 1)(x + 4)?
6
4
2
2
22
2
4
6
2
B42
2
O
O
4
2
2
Answer:
Graph DStep-by-step explanation:
f(x)=(x-1)(x+4
roots x=1,-4,
x=0, y=-4
OAmalOHopeO
A box contains 6 red, 3 white, 2 green, and 1 black (in total 12) identical balls. What is the least number of balls necessary to take out randomly (without looking) to be sure of getting at least two white balls?
Answer:
Pick at least 4 balls to be sure that you are getting balls with the same color.
Step-by-step explanation:
Here, you want to know the least number of balls to be taken out of the box to be sure that you have all the three colors represented.
You know there are 12 identical balls, with the least numbers of balls being 1 and 2. Hence, to be able to know you have all the colors of balls represented, you will need to have taken all the less represented ones i.e the 1 and 2 , and this means that the next number of ball which would be taken will confidently confirm that you have taken all the colors since you would have exhausted picking other balls at this point.
So you shall be needing at least 4 balls picked to ensure that you have all the colors represented
PLEASE HELP!!
A 16 ft ladder is propped up against a building at an angle of 52°. How far up the wall does the ladder go?
a. 20.3 ft
b. 9.9 ft
c. 25.9 ft
d. 12.6 ft
Answer:
The correct answer is a) 12.6 ft
Step-by-step explanation:
I took the test and got it right:)
The branch of mathematics deals with the relations of the sides and angles of triangles and with the relevant functions of any angles. The ladder goes at a height of 12.6082 feet.
What is trigonometry?The branch of mathematics deals with the relations of the sides and angles of triangles and with the relevant functions of any angles.
Given that the length of the Ladder is 16 feet while the angle between the ladder leaning against the wall is 52°.
Trigonometric Ratios are the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
Using Trigonometric Ratios of sin because of opposite over hypotenuse,
sin ∅=perpendicular/hypotenuse
sin(52) = x/16
16sin(52) = x
By calculating,
x = 12.6082 feet
Hence, the ladder goes at a height of 12.6082 feet.
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Grade improvement and study motivation
Answer:
yes because we are leraning new things
Angle ADB and CD are straight lines.
angle ADC = 5 x angle CDB
Work out the size of angle ADC.
Answer:
150 degrees
Step-by-step explanation:
5 + 1 = 6
180 : 6 = 30
30 x 5 = 150
Karma was given some birthday money. She puts money in an account. Every month after that, she deposits the same amount of money. The equation that models this situation is y=75x+60, where y is the amount of money in the account and x is the number of deposits. What does the y-intercept mean in this situation
Answer:
y represents the amount in the bank account after 7 months.
Step-by-step explanation:
Let karma gets x money on his birthday.
He has 60 in his account initially
He deposits teh same money for the seven months
So, the money he has after the seven months is 7 x + 60
According to the question,
y =7 x + 60
It shows that the amount after seven months is y.
10)
Ka
The longer base of a trapezoid has endpoints of (-2,- 4) and (4,0). The shorter base contains the point (3, 1).
(40)
(2)
We an equation of the line that contains the shorter base of the trapezoid. Provide valid mathematical reasoning and calculations to
you derived your equaiton.
of a trapezoid are parallel
Suation and explanation in the space provided.
Math symbols
Relations
Geometry
Answer:
y = 2·x/3 - 1
Step-by-step explanation:
The endpoints of the longer base of the trapezoid = (-2, -4), and (4, 0)
The point contained on the shorter base = (3, 1)
The slope of the line representing the longer base, m, is given as follows;
m = (0 - (-4))/(4 - (-2)) = 2/3
The slope of the shorter base = The slope of the longer base = m = 2/3
The equation of the line representing the shorter base in point and slope form is therefore;
y - 1 = (2/3)·(x - 3)
∴ y = 2·x/3 - 2 + 1 = 2·x/3 - 1
The equation of the shorter side of the trapezoid is y = 2·x/3 - 1
Question 4 of 25
Suppose a normal distribution has a mean of 62 and a standard deviation of
4. What is the probability that a data value is between 58 and 64? Round your
answer to the nearest tenth of a percent.
A. 53.3%
B. 54.3%
C. 52.3%
D. 51.3%
Answer:
Step-by-step explanation:
We are looking for P(58 < x < 64). We need to find the percentage to the left of the z-scores for each of these numbers. To find the z scores, use the formula:
[tex]z=\frac{x_i-\bar{x}}{\sigma}[/tex]
[tex]z=\frac{58-62}{4}[/tex] which gives us a z-score of -1. The percentage of numbers to the left of a z-score of -1 is .1586553
Now for the other z-score:
[tex]z=\frac{64-64}{4}[/tex] which gives us a z-score of .5. The percentage of numbers to the left of a z-score of .5 is .69146246
The lower percentage subtracted from the higher gives the area in question:
.69146246 - .1586553 = .53280716, or as a percentage, 53.3%, choice A.
Complete the sentence. The amount of time it takes to drive from your house to the library is most likely to be a function of the _____.
Answer:
D. distance
Step-by-step explanation:
really ? given the choices you needed help with that ?
only D makes sense. the rest is completely ridiculous and has nothing to do with driving from the house to the library.
if V = 1/3 BH, what is h expressed in terms of B and V?
A) 1/3VB
B) V/3B
C) 3V/B
D) 3VB
V=(1/3)(B)(h)
multiply both sides by 3
3V=Bhdivide both sides by B
3V/B=hsomeone please help me
Step-by-step explanation:
D) (A³/2)³ = A⁹/8
A³ whole to the power 3 is A⁹
2³ is 8
Moosonee: -1.5°C
Cold Lake: -4.5°C
Anchorage: -9.5°C and
Moscow: -1°C
Which city is warmer?
Answer:
Moscow
Step-by-step explanation:
In negatives the greater number is less. So -1 is the greatest, and thus, Moscow is the answer.
Moscow with a temperature of -1°C is warmer than Moosonee (-1.5°C), Cold Lake (-4.5°C), and Anchorage (-9.5°C).
The temperatures provided for the cities are as follows:
Moosonee: -1.5°C
Cold Lake: -4.5°C
Anchorage: -9.5°C
Moscow: -1°C
To determine which city is warmer, we compare the temperatures.
The higher the temperature, the warmer the city.
Moscow has the highest temperature of -1°C.
Therefore, Moscow is the warmest city compared to Moosonee, Cold Lake, and Anchorage, as it has a temperature that is closer to 0°C (warmer) compared to the other cities.
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Add 1,249 and 594.
what is their sum rounded to the nearest hundred?
A. 700
B. 1,800
C. 1,900
Answer:
1249+592=1843, rounding that you get B, 1,800
Anyone? Ive tried and its not clicking
Answer:
Hello Bro How Are You....?
