On multiplying (√3+√5)(√3-√5), we get answer as -2
How can square roots be multiplied?1. Split the radicands in half. A number known as a radicand appears underneath the radical symbol.
2. To multiple radicands, multiply the integers as if they were whole numbers. Always keep the item beneath a single radical sign.
3. Use factoring to exclude any perfect squares from the radicand. To achieve this, check whether any perfect squares have the radicand as a factor.
4. Position the square root of the ideal square before the radical sign. Don't change the second component of the radical symbol.
5. Square the square's root. Sometimes it is necessary to multiply a square root by itself.
We are given,
(√3+√5)(√3-√5)
⇒ (√3)² - (√5)²
⇒ 3 - 5
⇒ -2
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Brice worked for 31.5 hours this week. Two-thirds of this time was spent working from home. How many hours did he spend working from home?
Answer:
21 hours
Step-by-step explanation:
If he worked 2/3 at home you need to divide 31.5 by 3 = 10.5
Then multiply by 2 = 21
Hope this helps! Have a great day :)
Does the function below represent a linear function, an exponential function, a quadratic function, or none of these?
function----> f(x)=5*2^x
Question 1 options:
linear
exponential
quadratic
none of these
The equation of the function given as (x)= 5 * 2^x is an exponential function
How to determine the function type?The equation of the function is given as
f(x)= 5 * 2^x
An exponential function is represented as
f(x) = a * b^x
Where
Initial value = a
Rate = b
This means that
a = 5
b = 2
Hence, the equation of the function given as (x)= 5 * 2^x is an exponential function
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Simplify a raised to the negative fourth power over quantity 2 times b squared end quantity all cubed.
The simplified form of the expression ( a⁻⁴ / 2 × b² )³ is a⁻¹² / 8b⁶
Given,
a raised to the negative fourth power over quantity 2 times b squared end quantity all cubed.
The expression : ( a⁻⁴ / 2 × b² )³
Simplify the expression :
( a⁻⁴ / 2 × b² )³
= a⁻⁴⁽³⁾ / 2³ ˣ b²⁽³⁾
= a⁻¹² / 2³ ˣ b⁶
= a⁻¹² / 8b⁶
Therefore, the simplified form of the expression ( a⁻⁴ / 2 × b² )³ is a⁻¹² / 8b⁶
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Write each expression in simplest form. (√y-√3)(√y+2√3)
We write the expression in its simplest form and we are left with.
y²√3 + y - 6
Before proceeding let's define an algebraic expression.
Algebraic expressionAn algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
The first thing we will do is to write the expression:
(√y-√3)(√y+2√3)
Then we perform the multiplication, with the distributive property, which gives as a result
(y + 2√3y - √3y - 6)
y²√3 + y - 6
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Find the area and perimeter.
Answer:
Area: 6[tex]x^{2}[/tex] - 8x
Perimeter: 10x - 8
Step-by-step explanation:
Area:
Multiple the 2 sides together
2x(3x -4) Distribute the 2x
2x(3x)- 2x(4)
6[tex]x^{2}[/tex] -8x
Perimeter:
Add the four sides together
3x -4 + 3x -4 +2x + 2x Combine like terms
10x - 8
Thomas withdrew $55 from his account and later added $30. What was the overall change in his account balance?
It should be noted that when Thomas withdrew $55 from his account and later added $30, the overall change in his account balance is -$25.
How to illustrate the information?It should be noted that regarding a bank account, it should be noted that the withdrawal has to do with the amount of money that the person removes from the account.
It should be noted that deposit is an addition to the amount in the account while the withdrawal is the subtraction.
Therefore, should be noted that when Thomas withdrew $55 from his account and later added $30, the overall change in his account balance will be:
= -$55 + $30
= -$25.
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What are the vertex and x-intercepts of the graph of the function below?
y=(x+4)(x+2)
ООС
A. Vertex: (1,-5); Intercepts: x= -4,2
B. Vertex: (1, -9); Intercepts: x= 4,-2
C. Vertex: (-4, 2); Intercepts: x= 3, -3
OD. Vertex: (-3,-1); Intercepts: x = -4,-2
7
Factor the expression below.
O A. 9(x²-2x+9)
O B.
(x-9)(x + 9)
O C.
(x-9)(x-9)
O D. (x + 9) (x + 9)
4
12 181 +81
_what is this this is futo balis subina to amake dis_
Write two numbers that multiply to the value on top and add to the value on bottom.
100 on top
-20 on bottom
Answer:
-10 and -10
Step-by-step explanation:
Can you use the same number twice?
ANSWEE ASAPP !!!
what point do the equations y=2x+1 , y=3x+1 and 5x+1 have in common?
a) 2,0
b) 0,3
c) the origin
d) they have no point in common
e) 0,1
the answer is the 0,1 because the lines all have different slopes but always start at 1.
the quotient of a number x and five is half the difference of the number and four. write an equation that represents the statement.
The equation that represent the statement "quotient of a number x and five is half the difference of the number and four" is x / 5 = 4 - 1/2x
EquationQuotient means divisionThe unknown number = xx / 5 = 4 - 1/2x
collect like termsx/5 + 1/2x = 4
(2x+5x) / 10 = 4
7/10x = 4
divide both sides by 7/10x = 4 ÷ 7/10
= 4 × 10/7
= 40/7
= 5.714285714285714
Approximately,
x = 5.7
Therefore, the value of x in the equation is approximately 5.7
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pleasem help i dont remember
The line of the graph is a solid line and the region to be shaded depends on the type of the inequality
How to use the graph to determine whether the line will be dashed or solid?The graph represents the given parameter
On the graph, we have a straight continuous line
A straight continuous line is an illustration of a solid line
This means that the line of the graph is a solid line
Hence, the line of the graph is a solid line
How to use the graph to determine whether the graph would be shaded above or below?
The graph represents the given parameter
On the graph, we can see that no region of the graph is shaded
This means that the shaded region would be determined by the type of the inequality
≥ means that the region would be shaded above
≤ means that the region would be shaded below
Hence, the region to be shaded depends on the type of the inequality
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can somebody help me with these questions! helping me instead of giving me the answers is what i want but answers only is okay too ig
can somebody help me with these questions! helping me instead of giving me the answers is what i want but answers only is okay too ?
Here, in the figure we can see a diagram with 3 lines and few points.
1.Name a line that contains point A is A point is an intersection point of 2 lines that are line "l" and line "n".
2.Name a line that contains point D is D point is an intersection point of 2 lines that are "n" and line "m".
3.What is the another name of line m is line BD, B and D point are on the line "m" so we can say as line BD.
4.what is the another name of line n is line AD, A and D points are on the line "n" so we can say as line AD.
5.Name a point not on line AC is there are two points that are not on line AC is D and E points.
6. Name a point not on line BD is there are three points that are not on line BD is A,C and E points.
7.Name the intersection of AC and DB, B is the intersection of AC and DB.
8. Name the intersection of AD and AC, A is the intersection of AD and AC.
9. Name a point not on line l or line m is point E.
10.Name a point not on line n or line m is point E.
Intersection is nothing but a point where lines intersect is the intersection.
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This is a question from line segments part of geometry.
1. A line that contains point A is line l.
2. A line that contains point D is line n.
3. Another name for line m is line BD.
4. Another name for line n is line AD.
5. A point not on the line AC is the point D.
6. A point not on the line BD is the point A.
7. The intersection point of line AC and line DB is the point B.
8. The intersection point of line AC and line AD is the point A.
9. A point not on the line l or line n is the point E.
10. A point not on the line m or line n is the point D.
Geometry is a branch of mathematics that broadly deals with the measurement, characteristics, and connections of points, lines, angles, surfaces, and solids: the study of the characteristics of given elements that hold true even after being transformed in a certain way.
It is from line segments part of geometry.
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Solve for t.
4t + 2 + =18
Please help
Answer:
4
Step-by-step explanation:
18 - 2= 16
16/4=4
Can someone please help me?
Answer: that’s easily C because look down
Step-by-step explanation:
calculator lol I saw it don’t worry niu
PLEASE HELP QUICK!! I’m so irritated!!!
answer: 8 wholes and 3/4
Evaluate
2(-5)(-1)(-1)
Answer:
-10
Step-by-step explanation:
[tex]2\left(-5\right)\left(-1\right)\left(-1\right)\\(-5)(-1) = |5|\\= 2 \times 5\left(-1\right)\\2 \times 5 = 10\\10 \times |-1| = -10\\= -10[/tex]
Answer:
-10
Step-by-step explanation:
Let's solve the problem,
→ 2(-5)(-1)(-1)
→ (2 × -5) × (-1 × -1)
→ -10 × 1 = -10
Thus, the answer is -10.
A frog is about to hop from the bank of a creek. The path of the jump can be modeled
by the equation h(x) = -x² + 4x + 1, where h(x) is the frog's height above the water and
x is the number of seconds since the frog jumped. A fly is cruising at a height of 5 feet
above the water. Is it possible for the frog to catch the fly, given the equation of the
frog's jump?
Answer:
The frog will catch the fly after 2 seconds of his jump.
Step-by-step explanation:
It is given that a frog is about to hop from the bank of a creek. The path of the jump can be modeled by the equation h(x) = -x² + 4x + 1, where h(x) is the frog's height above the water and x is the number of seconds since the frog jumped and a fly is cruising at a height of 5 feet above the water.
Now, let us assume that the frog catches the fly that is cruising at a height of 5 feet above the water;
=> h = 5 feet
So, let us put the value of h = 5 for time x;
=> h(x) = -x² + 4x + 1
=> 5 = -x² + 4x + 1
=> x² - 4x - 1 + 5 = 0
=> x² - 4x + 4 = 0
Now, on solving the above equation we get;
=> x² - 4x + 4 = 0
=> x² - (2 + 2)x + 4 = 0
=> x² - 2x - 2x + 4 = 0
=> x (x - 2) - 2 (x - 2) = 0
=> (x - 2) (x - 2) = 0
On comparing and solving for the value of x we get;
=> (x - 2) = 0
=> x = 2
and
=> (x - 2) = 0
=> x = 2
Therefore, the frog will catch the fly after 2 seconds of his jump.
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(5x^2+8x-4)+(7x^2-11x+3) simplify
m∠ABC=(6x+8)° and m∠DEF=(12x−8)°. If ∠ABC and ∠DEF are supplementary, what is the measure of each angle?
Given that ∠ABC and ∠DEF are supplementary, the numerical value of ∠ABC and ∠DEF are 68° and 112° respectively.
What is the measure of each angle?Supplementary angles are angles that sum up to 180 degrees.
Given the data in the question;
∠ABC and ∠DEF are supplementaryMeasure of ∠ABC = (6x + 8)°Measure of ∠DEF = (12x − 8)°Since ∠ABC and ∠DEF are supplementary, it means they sum up to 180 degrees.
Measure of ∠ABC + Measure of ∠DEF = 180°
Plug in the given values and solve for x
(6x + 8) + (12x − 8) = 180
6x + 8 + 12x − 8 = 180
6x + 12x + 8 - 8 = 180
18x + 0 = 180
18x = 180
x = 180/18
x = 10
Now, the numerical measure of each angle will be;
Measure of ∠ABC = (6x + 8)° = 6(10) + 8 = 60 + 8 = 68°
Measure of ∠DEF = (12x − 8)° = 12(10) - 8 = 120 - 8 = 112°
Given that ∠ABC and ∠DEF are supplementary, the numerical value of ∠ABC and ∠DEF are 68° and 112° respectively.
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Find the least integer greater than each number. Do not use a calculator.
log√₇ √50
It follows that the least integer greater than log√₇ √50 is 3.
We have a logarithm function that is given to us.
Let x = log√₇ √50
We get that:√ 7 ˣ = √ 50
So, we must find an integer x, such that √ 7 ˣ > √ 50.
We know that √ 49 = 7
√ 7 ˣ > 7
7 ⁰°⁵ˣ > √ 7
x / 2 > 1
x > 2
In this case, x = 3 will be the least integer to satisfy this inequality.
Therefore, it follows that the least integer greater than log√₇ √50 is 3.
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Nick estimates that 50% of his income goes toward living expenses. Of the rest 50% goes to paying for his car and 25% of what is left goes to. his other expenses. IF nick has $300 remaining at the end of the month how much does he earn?
Based on the amount that Nick is left with at the end of the month, the amount he earns is $2,400
What does Nick earn?The amount of $300 that is left is 25% of 50% of Nick's income as the other 75% of the 50% went to paying for the car and other expenses.
25% of 50% is:
= 25% x 50%
= 12.5%
The amount Nick makes per month is:
= Amount remaining / Amount remaining in percentage terms
= 300 / 12.5%
= $2,400
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Which of the following statements is true?
A) Two shapes are congruent if their corresponding angles are congruent.
B) Two shapes are not congruent if their corresponding sides and corresponding angles are
congruent.
C) Two shapes are congruent if their corresponding sides and corresponding angles are
congruent.
D) Two shapes are congruent if their corresponding sides are congruent
Answer:
Two shapes are congruent if their corresponding sides and corresponding angles are congruent.
Step-by-step explanation:
This is the definition of congruency.
help me please
show your solution
Step-by-step explanation:
the first suspicion we get from the first terms is that the creation algorithm is a multiplication by 3.
-1/3 × 3 = -1
-1 × 3 = -3
-3 × 3 = -9
then the next term would be
-9 × 3 = -27
and the next
-27 × 3 = -81
and the 7th term, that we have already defined, would be
-81 × 3 = -243
we are correct !
so, the missing terms are
-27, -81
Use the dropdown menus to complete the definition of a midpoint. please help
image below
given that x is (near, between, or before) a and b, x is the midpoint of segment ab (if or if and only if) ax= (xa, ax,ab,xb)
select the right answers for each
X is between A and B, X is the midpoint of segment AB if and only if
AX = XB.
What is a midpoint?A midpoint is a point lying between two points and is in the middle of the line joining the two points.
We have,
A_____X_____B
Given that X is ___________A and B, X is the midpoint of segment AB____________ AX= ______
We need to fill in the blanks.
X would be in between A and B.
X is a midpoint of segment AB if and only if AX = XB.
Thus,
X is between A and B, X is the midpoint of segment AB if and only if
AX= XB.
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Please help and find the value of x at the bottom.
The value of x in the triangle is 100 units.
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees.
The triangles formed are similar, therefore, they form a ratio or proportion.
Therefore, using similarity principle of triangles,
36 / 60 = 60 / x
cross multiply
36x = 60 × 60
36x = 3600
divide both sides by 36
36x = 3600
36x / 36 = 3600 / 36
x = 100
Therefore, the value of x in the triangle is 100 units.
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Solve. Check for extraneous solutions. (2 x+3)³/₄-3=5
x = 13/2 is not an extraneous solution.
[tex](2x+3)^{3/4}[/tex] - 3 = 5
Adding 3 on both the sides of the equation, we get
[tex](2x+3)^{3/4}[/tex] - 3 + 3= 5 + 3
[tex](2x+3)^{3/4}[/tex] = 8
On the right hand side of the equation, 8 can also be written as
[tex](2x+3)^{3/4} = 2^{(3/4)*4}[/tex]
Taking power 4/3 on both the side of the equation, we get
(2x + 3) = 2⁴
2x + 3 = 16
2x = 13
x = 13/2
Check for extraneous solution and putting x = 13/2 in the original equation, we get
[tex](2(13/2) + 3)^{3/4}[/tex] - 3 = 5
[tex]16^{3/4}[/tex] - 3 = 5
8 - 3 = 5
5 = 5
⇒ LHS = RHS
∴ x = 13/2 is not an extraneous solution.
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charlotte is driving at 69.6 mi/h and receives a text message. she looks down at her phone and takes her eyes off the road for 4.06 s. how far has charlotte traveled in feet during this time?
Charlotte traveled in 414.44 feet during the time when she looks down at her phone and takes her eyes off the road for 4.06 s.
The first step is to convert miles per hour to feet per second.
(69.6 mi/hr)* (5280 feet/mi)*(1 hr/3600 sec) = 102.08 feet/sec
We know that,
Speed = [tex]\frac{Distance}{Time}[/tex]
Here, we have given,
Time = 4.06 s
Speed (feet/sec) = 102.08 feet/sec
We need to find, the distance charlotte traveled in feet during the time when she looks down at her phone and takes her eyes off the road for 4.06 s.
Putting the values in the formula, we get
Distance = Speed x Time
= 102.08 x 4.06
= 414.44 Feet
Hence, charlotte traveled in 414.44 feet during the time when she looks down at her phone and takes her eyes off the road for 4.06 s.
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Please Answer Need Badly Will give Brainlyest
What is 9+9
Answer:
that is definitaly 18
Step-by-step explanation:
i will break it down 3+3+3=9 3+3+3=9 again 9+9=18
[tex]answer[/tex]
18
Step by step formula:Break it down: 3+3+3= 9, Another 3+3+3= 9 (3 addition in 6 places will give 18). 9+9 = 18
What is the product of (p3)(2p2 - 4p)(3p2 - 1)? 6p7 4p4 6p7- 2p5 - 12p5 4p3 6p7 - 12p6 - 2p5 4p4 6p12 - 14p6 4p3
The product is 6p⁷ - 2p⁵ - 12⁶ + 4p⁴.
We are provided with expressions in three brackets. Performing multiplication between first two brackets first. This will be followed by multiplication of the product of first two brackets with the expression of third bracket.
For multiplication, the rule of exponents to be used is -
aᵇ×aⁿ = aᵇ⁺ⁿ
Rewriting the expression
Product = (p³)(2p² - 4p) (3p² - 1)
Performing multiplication of first two brackets -
Product = (p³ × 2p² - p³ × 4p) (3p² - 1)
Product = (2p⁵ - 4p⁴) (3p² - 1)
Further performing multiplication of product with third bracket -
Product = (2p⁵ × 3p² - 2p⁵ × 1 - 4p⁴ × 3p² - 4p⁴ × - 1)
Product = 6p⁷ - 2p⁵ - 12⁶ + 4p⁴
Hence, the product of given expressions is 6p⁷ - 2p⁵ - 12⁶ + 4p⁴.
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Answer:
C: 6p7 - 12p6 - 2p5 + 4p4
Step-by-step explanation:
Source: Trust me bro