Based on the fact that no less than a third of the juniors went to prom and there were 37 juniors, the minimum amount of juniors at the school was 111 juniors
How to find the juniors who went to prom?The school paper reported that out of the total juniors in school, no less than a third juniors went to prom.
We also know that 37 juniors went to prom. Assuming that 37 juniors represents a third of the juniors, the minimum amount of juniors at the school can be found as:
= Number of juniors who went to prom / Proportion of juniors who went to prom
Solving for the minimum amount of juniors at the school gives:
= 37 / 1/3
= 37 x 3/1
= 111 juniors
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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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PLEASE HELP QUICK!! I’m so irritated!!!
answer: 8 wholes and 3/4
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_
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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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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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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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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(5x^2+8x-4)+(7x^2-11x+3) simplify
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
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
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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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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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 :)
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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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?
Pluto is approximately 2.7 miles from the Sun. Venus is approximately 6.7 miles from the Sun.
Approximately how many times greater is the distance of Pluto from the Sun than the distance of Venus from the Sun?
Answer:
C. 40 times greater is the distance of Pluto from the Sun than the distance of Venus from the sun.
Solve each equation by factoring. Check your answers.
3 x²+8 x+4=0
The factors for given equation are -2/3 and -2.
Rewriting the equation firstly -
3x² + 8x + 4 = 0
ax² + bx + c = 0
Factorizing the equation as per mentioned two rules -
Sum of the factors should be equal to b (8 in this question)Product of the factors should be equal to product of a and c (12 in this question)6 and 2 are the suitable factors for given expression -
3x² + 6x + 2x + 4 = 0
3x (x + 2) + 2(x + 2) = 0
(3x + 2) (x + 2) = 0
3x + 2 = 0
3x = -2
x = -2/3
x + 2 = 0
x = -2
So, the two factors of equation are -2/3 and -2.
To check the factors, we will keep the value of x in equation -
When x = -2/3
3x² + 8x + 4 = 0
3(-2/3)² + 8(-2/3) + 4 = 0
3(4/9) - 16/3 + 4 = 0
4/3 - 16/3 + 4 = 0
Multiplying the equation with 3/4
1 - 4 + 3 = 0
- 3 + 3 = 0
0 = 0
When x = -2
3x² + 8x + 4 = 0
3(-2)² + 8(-2) + 4 = 0
12 - 16 + 4 = 0
- 4 + 4 = 0
0 = 0
Since for both values of x, Left hand Side and Right Hand Side of equation is same, the two resultant factors are correct.
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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 woman looks out a window of a building. She is 94 feet above the ground. Her line of sight makes an angle of θ with the building. The distance in feet of an object from the woman is modeled by the function d=94 secθ. How far away are objects sighted at angles of 25° and 55°?
The required distance of object far from 25° and 55° are 103.71feet and 163.88feet respectively.
Function and values in trigonometry identityTrigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given the trigonometry identity;
d=94 secθ.
If the object is sighted at an angle of 25°, then;
d=94 sec25
d = 94 × 1/cos25
d = 94 × 1.1033
d = 103.71feet
If the object is sighted at an angle of 55°, then;
d=94 sec55
d = 94 × 1/cos55
d = 94 × 1.7434
d = 163.88feet
Hence the required distance of object far from 25° and 55° are 103.71feet and 163.88feet respectively.
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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
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.
I need the word problem translated to an inequality.
Half of 7 added to product of h and 4 is at least 1
Based on theword problem, the inequality of the word problem is 7/2 + 4h >= 1
What are inequalities?Inequalities are used to represent expressions that do not have equal values i.e. unequal expression
How to translate the word problem to an inequality?The word problem is given as
Half of 7 added to product of h and 4 is at least 1
At least 1 means greater than or equal to 1
So, the word problem becomes
Half of 7 added to product of h and 4 is at least 1 ⇒ Half of 7 added to product of h and 4 >= 1
The product of h and 4 means 4h
So, the word problem becomes
Half of 7 added to product of h and 4 is at least 1 ⇒ Half of 7 added to 4h >= 1
Half of 7 means 7/2
So, the word problem becomes
Half of 7 added to product of h and 4 is at least 1 ⇒ 7/2 added to 4h >= 1
added to means +
So, the word problem becomes
Half of 7 added to product of h and 4 is at least 1 ⇒ 7/2 + 4h >= 1
Hence, the inequality of the word problem is 7/2 + 4h >= 1
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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.
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 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
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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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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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
A cool rock is quickly rolling down one side of a volcano. Compared with the same mass of hot lava that is slowing flowing down the other side, the rock has _____.
1. more thermal energy and more mechanical energy
2. less thermal energy and more mechanical energy
3. less thermal energy and less mechanical energy
4. more thermal energy and less mechanical energy
When the cool rock that is rolling down the side of the volcano is compared to the mass of hot lava that is slowly flowing, the rock has 2. less thermal energy and more mechanical energy.
What is mechanical energy?The mechanical energy that an object has refers to the combination of kinetic and potential energy. The rock will have more mechanical energy than the hot lava as it is moving faster.
Thermal energy on the other hand refers to how much heat/ energy is in an object. The rock is cool as opposed to the hot lava which would have more thermal energy as a result of its heat.
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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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