Answer:
-2/3
Step-by-step explanation:
= 1/5 + (-2/3) = -7/15
(A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Rational number can be both positive and negative.)
Select all the correct answers.
Which expressions are equal to
Given the data from the question, the expressions that are equal to 10⁵ are
10³ ⋅ 10²10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10To determine the expressions that are equal to 10⁵, we shall evaluate the options given from the question.
How to evaluate (10⁴)¹Recall
(Aᵐ)ⁿ = Aᵐⁿ
Thus,
(10⁴)¹ = 10⁴
How toevaluate 10³ ⋅ 10²Recall
Aᵐ ⋅ Aⁿ = Aᵐ⁺ⁿ
Thus,
10³ ⋅ 10² = 10³⁺²
10³ ⋅ 10² = 10⁵
How to evaluate 1 / 10⁵Recall
1 / Aᵐ = A⁻ᵐ
Thus,
1 / 10⁵ = 10⁻⁵
How to evaluate (10³)²Recall
(Aᵐ)ⁿ = Aᵐⁿ
Thus,
(10³)² = 10⁶
How to evaluate 10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10Recall
Aᵐ ⋅ Aⁿ = Aᵐ⁺ⁿ
10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 = 10¹⁺¹⁺¹⁺¹⁺¹
10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 = 10⁵
SUMMARY
(10⁴)¹ = 10⁴
10³ ⋅ 10² = 10⁵
1 / 10⁵ = 10⁻⁵
(10³)² = 10⁶
10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 = 10⁵
From the above illustrations, only 10³ ⋅ 10² and 10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 are equal to 10⁵
Complete question
See attached photo
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Find the HCF of
x^2 y and y^2
The highest common factor is [tex]\boxed{y}[/tex].
Which expression is equivalent to
The fences will be aligned with the exterior angles 1 and 2. what are some other relationships you can see between 1,2,a, and b? (2 points)
please help
1.8.4
The relationships between angles 1, a, b, and 2 can be defined using the angles between parallel lines.
In the diagram, we can see the fences, making angles 1 and 2 with the parallel lines X and Y respectively.
Using the angles among parallel lines, we can state the relationships between angles 1, a, b, and 2 as follows:
Angle 1 and Angle a are adjacent angles, thus their sum is 180°, that is m∠ 1 + m∠ a = 180°.Angle 2 and Angle b are adjacent angles, thus their sum is 180°, that is m∠ 2 + m∠ b = 180°.Angle 1 and Angle b are corresponding angles, thus they are equal, that is m∠1 = m∠ b.Angle 2 and Angle a are corresponding angles, thus they are equal, that is m∠2 = m∠ aAngle 1 and angle 2 are co-exterior angles, thus their sum is 180°, that is, m∠ 1 + m∠ 2 = 180°.Angle a and angle b are co-interior angles, thus their sum is 180°, that is, m∠ a + m∠ b = 180°.These were the relations among angles 1, a, b, and 2, using the parallel lines X and Y.
Refer to the diagram for a better understanding.
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im in summer school and i need to pass this please help me
g(x) is a shift of 8 units to the left and 4 units of f(x), then the correct statement is B.
Which statement compares the graph of the two functions?
First, a vertical shift of N units is written as:
g(x) = f(x) + N
if N > 0 the shift is upwards.If N < 0 the shift is downwards.A horizontal shift of N units is written as:
g(x) = f(x + N).
if N < 0, the shift is to the right.If N > 0, the shift is to the left.In this case, we have:
g(x) = f(x + 8) + 4
So g(x) is a shift of 8 units to the left and 4 units of f(x), then the correct statement is B.
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Directions: Find the inverse of each number.
Additive
-2 =
18 =
-30 =
2/5 =
Multiplicative
8/9 =
12/15 =
-6 =
10 =
Answer:
Additive
-2 = 2
18 = -18
-30 = 30
2/5 = -2/5
Multiplicative
8/9 = 9/8
12/15 = 15/12
-6 = -1/6
10 = 1/10
Step-by-step explanation:
an additive inverse is a number you must add to another number to get 0
(think of it as the negative version of the number)
{but WHY? In math, you can imagine comparing numbers on a number line. If we are finding the opposite of a number, we want to find the same distance from 0, but on the opposite side of 0. So, 2 would be two to the right of 0, -2 would be two to the left of 0}
-2 + 2 = 0
18 - 18 = 0
-30 + 30 = 0
2/5 - 2/5 = 0
a multiplicative inverse is a number that you multiply by another number to get 1.
We are finding the "reciprocal" of a number; you are essentially flipping it as a fraction
(reciprocal of 2 = 1/2 {remember, 2 is the same thing as 2/1 } ; reciprocal of 1 / 8 = 8)
note: reciprocal is being used interchangeably with multiplicative inverse here
8/9 · 9/8 = 1
12/15 · 15/12 = 1
-6 · -1/6 = 1 {-6 = -6/1}
10 · 1/10 = 1 {10 = 10/1}
hope this helps!! have a lovely day :)
Answer:
Additive: number that you add to get 0
2
-18
30
-2/5
Multiplicative: number that you multiply to get 1
9/8
15/12
-1/6
1/10
hope this is helpful!! ^u^
NEED HELP ASAP!! In the figure, AC 1 AB and AB 1 BD.
Answer:
d
By the alternate interior angles theorem,
Angles ABD and BAC will be congruentAngles BAD and ABC will be congruentBy the reflexive property, AB is congruent to itself.
Thus, the triangles will be congruent by ASA.
The boarding platform of a Ferris wheel is 4 meters above the ground and the Ferris wheel is 24 meters in diameter and spins once every 7 minutes. How many minutes of the ride are spent higher than 22 meters above the ground
The number of minutes of the ride that are spent higher than 22 meters above the ground is; 2.64 minutes
How to find the number of revolutions?We are given;
bottom of the Ferris Wheel is 4 meters off the ground.
Radius = diameter/2 = 24/2; r = 12 meters.
Thus, the center of the Ferris Wheel is 4 + 12 = 16 meters off the ground.
A horizontal line through the center of the Ferris Wheel is 16 meters off the ground, and therefore the lower half of the Ferris Wheel is always below 22meters.
The distance from the horizontal to 22 meters is 22 - 16 = 6 meters.
The angle between the horizontal and a radius to 22 meters is;
sin(θ) = 6/16
θ = sin⁻¹(6/16)
θ = 22.02°.
This angle height is on both sides of the Ferris Wheel and as such;
180° + (2 * 22.02) = 224.04° is always under 16 meters.
Thus, what is above 16 meters is 360° - 224.04° = 135.96°
Since it takes 7 minutes for 1 revolution, then the amount of time the Ferris Wheel is above 16 meters is;
(135.96/360) * 7 min ≈ 2.64 minutes
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Mike has 63 toys. 18 of them are new and 12 are his favorites, while 4 are new and favorites. Mike is giving away all the toys that are neither new nor favorites. How many toys does mike GIVE AWAY. ASAP ASAP
HELP PLSSSSSS hdghgdhj
Answer:
A
Step-by-step explanation:
Use the Pythagorean Theorem: a^2 + b^2 = c^2
The cable will be the hypotenuse, so c = 11.3 m
One leg is the distance of the anchor, so a = 4.2 m
(4.2)^2 + b^2 = (11.3)^2
17.64 + b^2 = 127.69
Subtract 17.64 from both sides
b^2 = 110.05
Square root both sides
b = ~10.5 m
Line segment KL is tangent to circle J at point K.
Circle J is shown. Line segment J K is a radius with length r. Line segment K L is a tangent with length 24 and it intersects the circle at point K. A line is drawn from point L to point J and goes through a point on the circle. The length from point L to the point on the circle is 16. The length from the point on the circle to center point J is r.
What is the length of the radius, r?
8 units
10 units
12 units
16 units
Using the tangent theorem, the length of the radius is: B. 10 units.
What is the Tangent Theorem?According to the tangent theorem, since KL is tangent to the circle, therefore, angle JKL = 90°.
Since the triangle is a right triangle, apply the Pythagorean theorem:
(r+16)² = r² + 24²
r² + 32r + 256 = r² + 576
r² - r² + 32r + 256 = 576
32r + 256 = 576
32r = 576 - 256
32r = 320
r = 320/32
r = 10
The radius is: B. 10 units.
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Answer:
B. 10 Units
Step-by-step explanation:
Identify the value of a and the length of each secant segment.
x= 10, NL= 8 , NP = 12
What is secant?A secant is a line that intersects a curve at a minimum of two distinct points.
Using secant theorem,
NL* NM = NP* NO
(3+5)*3 = (2+x)*2
24= (2+x)*2
12= 2+x
x= 12-2
x= 10
So, NP= 2+x
NP = 12
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Joe has an ice cream stand. last week he spent $85 for ice cream and supplies. he earned $125. what was his profit?
Answer:
40 dollars
Step-by-step explanation:
Profit is what he earned minus his costs
Profit = 125 -85
Profit = 40
Given triangle ABC, A=105°, a=10cm, b=7cm, find B,C and c.
The value of the side c will be 5.56 cm and angle C is 32.49° and angle B is 42.51°.
What is law of cosine?Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:
a² + b² – 2ab cos C = c²
Given triangle ABC, A = 105°, a = 10 cm, b = 7 cm.
Then we have
7² + c² – (2 · 7 · c) cos 105° = 10²
c² + 3.62c – 51 = 0
On solving, we have
c = 5.56
Then the angle C will be
10² + 7² – 2 · 7 · 10 · cos C = 5.56²
149 – 140 cos C = 30.91
cos C = 0.8435
C = 32.49°
We know that
∠A + ∠B + ∠C = 180°
105° + ∠B + 32.49° = 180°
∠B = 42.51°
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Can anyone help me with this one?
Answer:
c .26
Step-by-step explanation:
Male AND drama is 124 out of 479 total
124/479 = .26
Solve the quadratic function by factoring.
y = 4x² 13x + 10
Answer: [tex]x=-\frac{5}{4}[/tex] and [tex]x=-2[/tex]
Step-by-step explanation:
To factor an equation in the form of [tex]ax^2+bx+c[/tex] you need to find the value of [tex]ac[/tex]. So first solve for that
[tex](4)(10) = 40[/tex]
Now we need to find two numbers that add up to b and multiply together to make ac. In this case those numbers are 5 and 8 since 5+8=13 and (5)(8)=40
Now split 13x into 5x+8x and solve by grouping
[tex]4x^2+5x+8x+10\\(4x^2+5x)+(8x+10)[/tex]
Factor out the GCF in each quantity
[tex](4x^2+5x)+(8x+10)\\x(4x+5)+2(4x+5)[/tex]
Now group x+2 together
[tex](x+2)(4x+5)[/tex]
Finally, set each factor equal to 0 and solve for x
[tex]x+2=0\\x+2-2=0-2\\x=-2\\\\\\4x+5=0\\4x+5-5=0-5\\4x=-5\\\frac{4x}{4} =\frac{-5}{4} \\x=-\frac{5}{4}[/tex]
Janet solves this equation
log(x-3)+logx=1
She finds the two solutions; x=5 and x=-2
Of Janet’s two solutions, ____ correct because _____
A. Neither x=5 nor x=-2 is
B. Only x=5 is
C. Only x=-2 is
D. Both x=5 and x=-2 are
1. x=5 is an extraneous solution
2. Both x=-2 and x=5 are valid solutions
3. Both x=-2 and x=5 are extraneous solutions
4. x=-2 is an extraneous solution
(TWO DIFFERENT ANSWERS FILL IN THE BLANK)
Of Janet’s two solutions, both x=5 and x=-2 are correct because both x=-2 and x=5 are extraneous solutions
Logarithmic functionGiven the log function expressed as:
log(x-3) + logx=1
According to the law of logarithm, addition becomes product to have:
log x(x -3) = log₁₀10
x² - 3x = 10
x² - 3x -10 = 0
x² - 5x + 2x - 10 = 0
x(x-5) + 2(x-5) = 0
(x+2)(x-5)=0
x = -2 and 5
Of Janet’s two solutions, both x=5 and x=-2 are correct because both x=-2 and x=5 are extraneous solutions
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round 68.321 to the nearest tenth
Answer:
When 68.321 rounded to the nearest tenth the result is 68
What is the measure of angle AFR?
O 124 degrees
O 91 degrees
O 13 degrees
O 117 degrees
Answer:
13°Step-by-step explanation:
AFR = VFN (opposite angle rule)
7x + 33 = 9x + 7
33 - 7 = 9x - 7x
26 = 2x
x = 26 : 2
x = 13°
-----------------
check
7 * 13 + 33 = 9 * 13 + 7 (remember PEMDAS)
91 + 33 = 117 + 7
124 = 124
the answer is good
this is not a right angled triangle, but how do i find the 3rd side of a triangle if one side is 50 and the other side is 30?
Use the Pythagorean theorem.
What is the measure of ∠z
Answer:
155°
Step-by-step explanation:
z = 65° + y
y is a right angle
=> y = 90°
=> z = 65° + 90° = 155°
Which of the following points is NOT visible if the viewing window of a graphing utility is set at:
Xmin : 6
Xmaz: 6
Ymin : —6
Ymaz : 6
The points D(-7, 5), E(-8, -3), and H(10, -5) will not be visible the answers are D, E, and H.
What is graphing utility?A graphing calculator is a portable computer that can plot graphs, solve multiple equations at once, and carry out other variable-related activities.
We have points shown in the coordinate plane.
As the window of a graphing utility is set at:
X(min) : -6
X(max): 6
Y(min) : -6
Y(max) : 6
The points out of 6 will not be visible.
We can draw a square as shown in the attached picture.
The points D(-7, 5), E(-8, -3), and H(10, -5) will not be visible.
Thus, the points D(-7, 5), E(-8, -3), and H(10, -5) will not be visible the answers are D, E, and H.
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Which of the following best describes the slope of the line below?
Select the correct answer from each drop-down menu. (Will give brainliest)
(Picture below options are 19.5, 29, 58 for both multiple choice)
The angle BAC will be 29 and the angle BOC will be 58.
What is the circle theorem?The angle in a circle's centre is twice that at its perimeter when two angles are subtended by the same arc. So, angle AOB = 2 angle ACB. Angles that the same arc subtends at its circumference are equal. As a result, angles inside a section are equal.
Here the given angle is ∠BDC = 29 so from the given theorem the angle BEC will be equal to the angle BDC.
∠BDC = 29
The centre angle BOC will be twice the angle at the circumference so the angle will be twice.
∠BOC = 59
Therefore the angle BAC will be 29 and the angle BOC will be 58.
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Each statement describes a transformation of the graph of y= x. Which statement correctly describes the graph of y= x+ 9.5?
a. it is the graph of y= x where the slope is increased by 9.5 .
b. it is the graph of y= x translated 9.5 units to the right.
c. it is the graph of y= x translated 9.5 units up.
d. it I'd the graph of y= x translated 9.5 units down.
Answer: C
Step-by-step explanation: The graph is going to go up because the +9.5 isn't in any parentheses. If it was, that would mean it would move horizontally. I hope this helps!
The correct statement:
It is the graph of y = x translated 9.5 units up.
The correct option is c.
The equation y = x represents a straight line passing through the origin with a slope of 1. When we have the equation y = x + 9.5, it means that for every x-value, the corresponding y-value is obtained by adding 9.5 to the original x-value. This translation in the y-direction shifts the entire graph upward by 9.5 units.
To visualize this, imagine the original line y = x. Each point on this line has an x-coordinate and a corresponding y-coordinate, which are the same due to the equation y = x. When we add 9.5 to each y-coordinate, the line shifts vertically by 9.5 units without any change in slope or horizontal position.
The other options can be eliminated because the statement does not mention changing the slope or the horizontal position of the graph. Instead, it specifically describes a vertical translation, indicating a movement in the y-direction. Therefore, the correct answer is c.
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What is -4(5x-3)+12 simplified
Answer:
20x+24Step-by-step explanation:
-4(5x-3)+12
-20x+12+12
20x+24
my answer is 20x+24.
The simplified form of the given expression -4(5x-3)+12 would be 20x+24.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
Given;
-4(5x-3)+12
Open the bracket
-20x+12+12
Solve the like terms;
20x+24
Hence, the simplified form of the given expression -4(5x-3)+12 would be 20x+24.
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What is 10 1/2÷214 ?
Answer:
21/428 or 0.04 906542056074...
Step-by-step explanation:
the coordinate of two point P(4,6) and Q(5,-7) then find (abicissa of P) -(abicissa of Q)
The value of (abscissa of P) -(abscissa of Q) is -1.
The given coordinates are P(4,6) and Q(5,-7).
We need to find (abscissa of P) -(abscissa of Q).
What is abscissa?The horizontal coordinate of a point in a planar Cartesian coordinate system that is determined by measuring parallel to the x-axis is what abscissa stands for.
Now, (abscissa of P) -(abscissa of Q)=4-5=-1
Hence, the value of (abscissa of P) -(abscissa of Q) is -1.
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The coefficient of 2(3)(6)Q is
The coefficient of the variable Q is 36 , Option A is the correct answer.
The complete question is
The coefficient of 2(3)(6)Q is _____. a.36 b.18 c.12
What is a Coefficient ?Coefficient is the constant term written in front of variable in an expression.
The expression given in the question is
2(3)(6)Q
The coefficient is 2 * 3 * 6 = 36
Therefore , the coefficient of the variable Q is 36 , Option A is the correct answer.
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hi can some one help me
-5≥
so 8 x -5 = -40 - 16 = -56 and that's the smallest number you can get that will be greater than -64 hope this helps! :)
Answer:
x> -6
Step-by-step explanation:
Drag the -16 to -64. This will change the -16 to a positive 16. Add -64 and 16. The answer is -48. All that should be left is 8x>-48. Now we need to divide -48 and 8 so we can leave x. The answer should be -6 on one side, and x on the other side. x> -6
