first know it in a simple way
that,3-1=2 right so if we add base and numbers in power , because it has same base when x i.e x to the power 1 goes up
Step-by-step explanation:
x^3/x^1
now
x^3 *x^-1
x^3-1
x^2
proved
Match the systems of equations with their solution sets.
Answer:
1. y + 12 = x^2 + x
2. y - 17 = x^2 -9x
3. y + 5 = x^2 - 3x
4. y - 15 = -x^2 + 4x
A box has twice as many grapes as a basket. Once 2kg of grapes were added to the basket, it contained 0.5 kg more than the box. How many kilograms of grapes are in the basket now?
By solving a system of equations, we will see that now there are 3.5kg of grapes on the basket.
How many kilograms of grapes are in the basket now?Let's define the variables:
x = kg of grapes on the box originally.y = kg of grapes on the basket originally.We know that:
x = 2y
When we add 2kg to the basket, it has 0.5k more than the box, then:
y + 2 = x + 0.5
Then we have a system of equations:
x = 2y
y + 2 = x + 0.5
We want to solve this for y, then we can replace the first equation into the second one:
y + 2 = (x = 2y) + 0.5
y + 2 = 2y + 0.5
2 - 0.5 = 2y - y
1.5 = y
This means that, originally, there are 1.5 kg of grapes on the basket. And then we added 2kg, so now there are:
1.5kg + 2kg = 3.5kg
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Answer:
There are now 3.5kg of grapes.
What is the value of 12⁰?
Hello,
Answer:
12⁰ = 1
Step-by-step explanation:
We have any number with exponent 0 = 1
(a⁰) = 1
Find two negative odd integers such that 5 times the first plus the square of the second equals -14
The two negative odd integers such that 5 times the first plus the square of the second equals -14 are: -3 and -1.
What are negative odd integers?In a multiplication or division issue, an odd number of negatives will always result in a negative odd integer.
A negative odd integer carries a negative sign and is not exactly divisible by 2.
According to the question, an equation can be formed as follows:
[tex]5a+b^{2}=-14[/tex]
Here, a and b are the two negative odd integers.
Let a= -3 and b= -1,
[tex]5a+b^{2}=5(-3)+(-1)^{2}\\[/tex]
= -15+1
= -14
Thus, the required negative odd integers are -3 and -1.
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Solve the rational equation
and check for extraneous solutions
5 = 4x+1
— ——-
x x^2
(1) x= 1; x = 0 is an extraneous solution
(2) x=0; x = 1 is an extraneous solution
(3) x= -1; x = 0 is an extraneous solution
(4) x=0; x = -1 is an extraneous solution
Answer:
1) x=1; x= 0 is an extraneous solution
Step-by-step explanation:
5 = 4x + 1
5 = 4 x 1 + 1
5 = 5
x = 1
______________________
x x^2
0 x 0^2
0 x 0 = 0
x = 0
:)
Eduardo’s average speed on his commute to work was 55 miles per hour. On the way home, he hit traffic and only averaged 40 miles per hour. If the round trip took him 1. 25 hours, which expression represents the distance, in miles, for his trip home that is missing from the table?.
40(1.25-t) is missing from the table
Time, speed, and distance are the three factors must be taken into account.
How to solve such time related questions?
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed X Time
We provide both time and speed.
It is necessary to compute the distance.
55 miles per hour is the commuter speed
Worktime equals 1.25-T
Home-bound speed is 40 miles per hour.
1.25 seconds to get home
Time in Total = T + t = 1.25
Travel distance to home
Distance/Time x Speed
40 = Total Distance/t
Distance overall = 40 (1.25-t)
As a result, 40(1.25-t) is the right response.
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Add: (3g^8-4h) + (-6g*8)
pls answer asap
The sum of the expression is 3g^8 - 4h - 48
How to add the expressionGiven that;
(3g^8 - 4h) + ( -6 × 8)
Expand the brackets,
3g^8 - 4h - 6 × 8
Multiply the values
3g^8 - 4h - 48
Therefore, the sum of the expression is 3g^8 - 4h - 48
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Ravi makes lemonade by mixing lemon juice and water.
For every 1 cup of lemon juice, he uses 4 cups of water.
Drag the correct number of each ingredient into the box that would make 10 cups of
lemonade.
What is 3(4x-2x)
5+3*2 simplified?
Answer:
30x+6Step-by-step explanation:
What is 3*(4x-2x)*5+3*2 simplified?
3*(4x-2x)*5+3*2=
3*2x*5+6 =
6x*5+6=
30x+6
can someone please help me, as well as factoring the expression
The value of U and V will be (x – 3) and 8y, respectively. Then the correct option is A.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The expression is given below.
⇒ (U + V)(U – V)
Where U and V are either constant or single variable expression.
Then the expression will be
⇒ U² – V²
Then the value of U and V will be (x – 3) and 8y, respectively.
Then the correct option is A.
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3. What additional information do you need to prove AABC = ADEF by the SAS Postulate?
Answer:
∠ACB = ∠DFE
Step-by-step explanation:
In SAS postulate,
S refers to Side.
A refers to Angle.
In the triangles, △ABC and △DEF,
AC = DF ( Side )
CB = FE ( Side )
The additional information required to prove is Angle.
Angle between sides AC and CB in △ABC and Angle between sides CB and FE in △DEF respectively.
Angle between sides AC and CB is ∠ACB.
Angle between sides CB and FE is ∠DFE.
So according to SAS postulate,
∠ACB = ∠DFE
The triangles are congruent by the SSS congruence theorem.
Triangles A B C and F E D are shown. Triangle A B C is reflected across A C and then is shifted down and to the left to form triangle F E D.
Which rigid transformation(s) can map TriangleABC onto TriangleFED?
reflection, then dilation
reflection, then translation
rotation, then translation
rotation, then reflection
The rigid transformations that maps ΔABC onto ΔFED by reflection then translation.
The correct option is (B).
What is Reflection?Reflection is a from of transformation whereby a figure is flipped over a line of reflection, making both figures exactly the same shape and size after the transformation.
given:
ΔABC ≅ ΔFED are congruent by the SSS Congruence Theorem.
Hence, the rigid transformations that maps ΔABC onto ΔFED by reflection then translation.
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Answer:
B
Step-by-step explanation:
Trust me bro
In the rhombus below, solve for x and y. (Round to the nearest tenth as needed.)
The value of x and y in the rhombus are 5 and 25 respectively.
How to find the angles of a rhombus?The sum of angles of a rhombus is 360 degrees. The opposite angles of a rhombus is equal.
Therefore,
11x = 55
x = 55 / 11
x = 5
Therefore,
5y + 5y + 55 + 55 = 360
10y + 110 = 360
10y = 360 - 110
10y = 250
y = 250 / 10
y = 25
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a bag contains Stephanie five marbles, some red some blue. The ratio of red marbles to blue ones is 3:2. how many red marbles are there?
Answer:
There are 3 red marbles.
Step-by-step explanation:
The ratio of red marbles to blue marbles is 3:2, so for every two blue marbles there are three red marbles. This means that there are three red marbles for every four marbles in the bag. Therefore, if there are five marbles in the bag, there must be three red marbles and two blue marbles.
How many three digits numbers are divisible by 7? ( Please help )
Please give it step-by-step, I will give you a brainlist! Also some points!
Thank you,
Answer:
128 3 digit number which are divisible by 7
Answer:
128
Step-by-step explanation:
I just looked it up because the only way I know would take a lot of time.
Know the times table?
You can make a chart that starts from 100 to 999 and circle every single number you know can be divided by 7. That's 128 numbers.
I hope the answer helps, but I hope someone can actually find a formula or something for you to use. Best of luck.
helppp solve step 2 and 3 pleasee quick
Answer:
Step-by-step explanation:
What is the ratio of the area of the inner square to the area of the outer square?
The area of the inner square to the area of the outer square ratio is: [tex]\frac{(a-b)^2+b^2}{a^2}[/tex]
Given a figure in which an inner square is inscribed inside the outer square.
The area of a square is the product of the two sides of the square. Also known as side square.
Firstly, we will find the side of the inner square by finding the distance between the points (0,b) and (a-b,0)
S₁=√(a-b-0)²+(b-0)²
S₁=√(a-b)²+b²
Now, we will find the area of the inner square, we get
The area of the inner square=(side)²
A₁=(S₁)²
A₁=(√(a-b)²+b²)²
A₁=(a-b)²+b²square cm.
Further, we will find the side of the outer square by finding the distance between the points (0,0) and (a,0).
S₂=√(a-0)²+0²
S₂=√a²
S₂=a
Furthermore, we will find the area of the outer square, we get
The area of the outer square=(side)²
A₂=(S₂)²
A₂=a² square cm.
Hence, the area of the inner square to the area of the outer square ratio is [tex]\frac{(a-b)^2+b^2}{a^2}[/tex].
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The electric field strength between the plates of a simple air capacitor is equal to the voltage across the plates divided by the distance between them. When a voltage of 96.6 V is put across the plates of such a capacitor an electric field strength of 1.8 KV/cm is measured. Write an equation that will let you calculate the distance d between the plates.
The distance can be expressed in equation d=5.3*[tex]10^{-4}m[/tex].
Given voltage of 96.6 V and electric field strength of 1.8 KV/cm.
We know that d=V/E
We have to find the distance in equation form.
We know that electric field strength between the plates of a parallel plate capacitor is
E=V/d
Distance is the measurement between two sides or points.
where E=electric field strength
V=potential difference
d=distance between the plates
In equation form distance looks like:
d=V/E
from the question we are that V=96.6 V
E=1.8KV/cm.
Converting to V/m
E=180000V/m
d=96.6/180000
=0.00053
d=5.3*[tex]10^{-4}m[/tex].
Hence the distance can be expressed as d=[tex]5.3*10^{-4} m[/tex].
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Patty is a customer service representative for a company. She earns $18 an hour, plus an additional $2.50 each time one of her customers completes a company survey. This week, Patty plans to work 38 hours.
If Patty wants to earn at least $750 this week, which inequality could she solve to find the number of surveys, s, she needs her customers to complete this week?
Considering the definition of an inequality, the inequality she could solve to find the number of surveys, s, she needs her customers to complete this week is 18(38)- 2.50s ≥ 750
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Inequality in this caseIn this case, Patty earns $18 an hour, plus an additional $2.50 each time one of her customers completes a company survey. This week, Patty plans to work 38 hours and she wants to earn at least $750.
Being "s" number of surveys Patty needs her customers to complete this week, the inequality that expresses the previous relationship is
18× 38 hours - 2.50×s ≥ 750 or, which is the same, 18(38)- 2.50s ≥ 750
Finally, the inequality she could solve to find the number of surveys, s, she needs her customers to complete this week is 18(38)- 2.50s ≥ 750
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Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
1st.) x = 5 /Sin(30°)
x = 10
!) sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°) = 3√3 / x
x = 3√3 / 3
W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3 = 4√3 / 3
S) Sin(60°) = x / (10/3)
x = 5√3 / 3
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In the expansion of (2a + 3b), which of the following are possible variable terms? Explain your reasoning.
a²b³; a5b³; ab8; b8; a4b4; a8; ab7; a6b5
The possible variable terms are a^5b^3, b^8, a^4b^4, a^8, ab^7
How to determine the possible variable term?The expression is given as:
(2a + 3b)^8
The power of the above expression is 8
When expanded, the sum of powers on each variable must be 8.
Using the above explanation, we have the following possible variable terms:
a^5b^3, b^8, a^4b^4, a^8, ab^7
This is because the sum of powers equals 8
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The range of Y = x³ is
Answer:
(-2,-8)
(-1,-1)
(0,0)
(1,1)
(2,8)
Step-by-step explanation:
y = x^3
y = -2^3
= -8
y = -1^3
= -1
y = 0^3
= 0
y = 1^3
= 1
y = 2^3
= 8
HELP GEOMETRY) Fill in the blanks:
Measure of angle GFJ is ___ degrees.
Measure of arc FH is ___ degrees.
Part 1
By the inscribed angle theorem, arc GFJ measures 55 degrees.
Part 2
By the inscribed angle theorem, arc FH measures 72 degrees.
a pole that is 3m tall casts a shadow that is 1.72m long. at the same time, a nearby building casts a show that is 50.5 m long. how tall is the building
Answer:
88.08 m tall
Step-by-step explanation:
Pole:
tall/long
3/1.72
Building:
tall/long
x/50.5
Solve for x:
3/1.72 = x/50.5
1.72x = 151.5
x ≈ 88.08
After 1 year, $70,060 deposited in a savings account with simple interest had grown to a total of $77,136.06. What was the interest rate?
Answer:
10.1%
Step-by-step explanation:
Interest = PRT/100
Interest = 77136.06 - 70060 = 7076.06
Interest = PRT/100
7076.06 = [(70060) × R × 1] / 100
7076.06 = 70060R/100
Cross multiply
(7076.06 × 100) = 70060R
707606 = 70060R
R = 707606/70060
R = 10.1%
Air pressure may be represented as a function of height above the surface of
the Earth as shown below.
P(h) = Pe-.00012h
In this function, Po is air pressure at sea level, and his measured in meters.
Which of the following equations will find the height at which air pressure is
75% of the air pressure at sea level?
OA..75P, Pe
-.00012h
- .00012h
OB. Po=.75Pe
O c..75=h.e-.00012
OD. h= .75e00012
Answer:
A
Step-by-step explanation:
75% of the air pressure at sea level is simply
0.75 × Po
this is what we need to set as the expected result of the function, and it becomes the left side of the equation.
we don't change anything on the right side for this, as the full, unchanged function has to be used to find the h for the desired result.
Please help.
True or false
Answer:
True
Step-by-step explanation:
That is the distance formula.
Answer:
FALSE
Step-by-step explanation:
Distance Formula: [tex]\sqrt{(x_{2}-x_1)^2 + (y_2-y_1)^2}[/tex]
An engineering firm designs a custom hexagonal screw for a computer board. A sketch of the top of the screw is below. To the nearest tenth,
what is the area of the screw head?
Given that the screw is a regular hexagon with side length 6 mm, the area of the screw is 93.5 mm^2
How can the area of the screw be found?The area of an hexagon can be found using the following equation;
[tex]A = \mathbf{ \frac{3 \cdot \sqrt{3} }{2} \times {a}^{2}} [/tex]
Where a = The side length
However the side lengths are not equal, and the figure is a composite figure with two triangles and one rectangle;
Base length of the triangles = 12
Height of the triangles = 3
Area of each triangle = 0.5 × 12 × 3 = 18
Width of the rectangle = 12
Height of the rectangle = 6
Area of the rectangle = 12 × 6 = 72
Area of the screw = 18 + 18 + 72 = 108
However taking the screw as a regular hexagon, with side length a = 6, we have;
[tex]A = \frac{3 \cdot \sqrt{3} }{2} \times {6 \: mm}^{2} = 93.5 \: mm^2 [/tex]
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Question in the picture please help
The tabulated form of Two column proof attached below.
Two column proof is just tabulated form of statements and reason.
We are adding the key points to the table. As per the required questions
Thus the table formed by is attached below.
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find the unknown sizes of angles
(Urgently needed please help to solve)
Answer:
x=70, y=40, z=70
Step-by-step explanation:
So whenever you have a straight line, the angle is going to be 180 degrees, and whenever you have multiple angles that make up one angle, the sum of the multiples angles is going to be the angle of the one angle.
So let's look at x. The 180 degree angle consists of 110 degrees and x, the sum of these two should add up to 180 degrees, you can set up an algebraic equation to solve for x, but you can also do some simple mental math to see that x=70, so that 110+70=180. You do the same thing for the other angles
For y, you simply need to know 140+y = 180 so y=40
For z there is two methods, you can use the fact that opposite angles are congruent, or you can use the fact that the sum of the interior angles of a triangle is 180 degrees. This means that x+y+z=180 and since we know that x=70 and y=40 then 70+40=z so 110+z=180 so z=70, which is also the same as the opposite angle, you could use either method although knowing that opposite angles are congruent is much more easier. It's called the vertical angles theorem.