Express the quotient as a fraction in simplest form
-5/7 ÷ 6/7
A. 5/6
B. -30/49
C. 30/49
D. 5/6
Answer:
-5/6
Step-by-step explanation:
A great way to divide fractions is to use the "leave it, change it, flip it" method. You leave the first fraction as it is, change the division sign to a multiplication sign, and flip the second fraction so you get the reciprocal. Like this:
-5/7 ÷ 6/7
-5/7 x 6/7
-5/7 x 7/6
Then you multiply through. First -5 x 7, -35, and then 7 x 6, 42, to get -35/42. Because both of these are divisible by 7, we can simplify to get -5/6.
Answer:
-5
6
Step-by-step explanation:
⇒ [tex]\frac{-5}{7}[/tex] ÷ [tex]\frac{6}{7}[/tex]
⇒ [tex]\frac{-5}{7}[/tex] × [tex]\frac{7}{6}[/tex]
(We do this because when dividing a fraction by another fraction we take the inverse of the second fraction and multiply it to the first fraction.)
⇒ -5 × 7 = -35 (to simplify just divide both by 7) = -5
7 × 6 42 6
So the answer is -5
6
Point L is located at (-1,-6). Determine the coordinates of point L’ after a translation 7 units to the left and 6 units up.
Answer:(-8,0)
Step-by-step explanation:
Add (-1,-6) with translation move (-7,6)
-1 , -6
-7 , 6
____
-8 , 0
Which expression is equivalent to 12b + 3a? choices: a (a + b) x 12 b 3 (4b + a) c ab x 12 x 3 d (12 x 3) + (b x a)
Answer:
The answer to the equation is B.
Step-by-step explanation:
Answer:
i took the test and its B
Step-by-step explanation:
In this figure, a || b | c and m/1 = 50°
What is m/3 ?
O 40°
O 50°
O 130°
O I don't know.
The value of m<3= 130
The correct option is (c)
What is alternate interior angle?Given:
m<1= 50
m<1+ m<2= 180 (Linear pair)
m<2= 180-50
m<2=130
Now, m<2 = m<3 [alternate interior angles]
m<3= 130
Hence, the measure of <3 is 130.
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Answer:
The person above me is correct
Step-by-step explanation:
4 Solve these inequalities. Show the solutions on the number lines.
a 4v-2 > 16
b 6 ≥ 2(w-7)
0
5 a Write as a recurring decimal.
b Convert 0.45 to a fraction.
(5 marks)
Answer:
a) v>4.5
b) w<6.5
a) 0.3 recurring
b) 5/11
Solve the system of equations:
y=2x
y=x²-8
75 points! what is the lateral area?
Answer:
48 units²
Step-by-step explanation:
Lateral Surface Area :
Area of the side faces (exclude the base)4 x 1/2 x 8 x 32 x 2448 units²Answer:
48 units²
Step-by-step explanation:
The lateral area of a square based pyramid comprises the four triangular sides.
Area of a triangle = 1/2 × base × height
= 1/2 × 8 × 3
= 1/2 × 24
= 12 units²
Lateral SA = 4 × area of triangle
= 4 × 12
= 48 units²
Match the function in the left column with its period in the right column.
The results for the matching between function and its period are:
Option 1 - Letter DOption 2 - Letter AOption 3 - Letter COption 4 - Letter BWhat is a Period of a Function?If a given function presents repetitions, you can define the period as the smallest part of this repetition. As an example of periodic functions, you have: sin(x) and cos(x).
[tex]\mathrm{Period\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}[/tex]
[tex]\mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\sin \left(x\right)}{|b|}[/tex]
The period of sin(x) and cos(x) is 2π.
For solving this question, you should analyze each option to find its period.
1) Option 1
[tex]\mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}\\ \\ \mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{2\pi }{\frac{1}{2} }=4\pi[/tex]
Thus, the option 1 matches with the letter D.
2) Option 2
[tex]\mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\sin \left(x\right)}{|b|}\\ \\ \mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{2\pi}{4} =\frac{\pi }{2}[/tex]
Thus, the option 2 matches with the letter A.
3) Option 3
[tex]\mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}\\ \\ \mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{2\pi}{2} =\pi[/tex]
Thus, the option 3 matches with the letter C.
4) Option 4
[tex]\mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\sin \left(x\right)}{|b|}\\ \\ \mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{2\pi}{8} =\frac{\pi }{4}[/tex]
Thus, the option 4 matches with the letter B.
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You have combined different polygons to create a polyhedron to approximate a sphere. The sum of all the faces of the polyhedron is about 78.5 square meters. Estimate the radius of the sphere.
Since the polyhedron is about 78.5 m², the radius of the sphere is 2.5 m
Since the sum of the faces of the polyhefron equals the surface area of the sphere, we find its surface area.
What is the surface area of sphere?The surface area of sphere is given by A = 4πr² where r = radius of sphere
Radius of the sphereMaking r subject of the formula, we have
r = √(A/4π)
Given that he sum of all the faces of the polyhedron is about 78.5 square meters, this is equal to the surface area of the sphere.
So, A = 78.5 m²
Substituting this into the equation for r, we have
r = √(A/4π)
r = √(78.5 m²/4π)
r = √(19.625 m²/π)
= √(6.246 m²)
= 2.499 m
≅ 2.5 m
So, the radius of the sphere is 2.5 m
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I'LL MARK BARINLEST!!!(With the help of the drawing tool, create a box plot using the data in Table 1.)
-------------------------------------
TABLE 1
----------------
height(Inches)
--------------------
61-64-62
55-66-65
58-60-63
63-58-59
62-64-67
57-61-57
65-58-59
62-57-61
Answer:
Median
Order the data values from smallest to largest:
55, 57, 57, 57, 58, 58, 58, 59, 59, 60, 61, 61, 61, 62, 62, 62, 63, 63, 64, 64, 65, 65, 66, 67
As there is an even number of values, the median is the mean of the middle two values ⇒ Median = 61
Quartiles
55, 57, 57, 57, 58, 58, 58, 59, 59, 60, 61, 61 || 61, 62, 62, 62, 63, 63, 64, 64, 65, 65, 66, 67
The first quartile is the median of the data points to the left of the median ⇒ first quartile = 58
The third quartile is the median of the data points to the right of the median ⇒ first quartile = 63.5
Five-number summary
Minimum: 55First quartile Q1: 58Median Q2: 61Third quartile Q3: 63.5Maximum: 67Draw a box from the first quartile (58) to the third quartile (63.5)
Add the median (61) as a the vertical line through the box.
The whiskers are horizontal lines from each quartile to the minimum (55) and maximum values (67).
Which shows one way to determine the factors of x³ + 5x² - 6x - 30 by grouping?
O x(x²-5) + 6(x²-5)
O x(x² + 5)-6(x² + 5)
O x²(x - 5) + 6(x - 5)
O x²(x + 5)-6(x + 5)
Answer:
last option
Step-by-step explanation:
hope it helps
One way to determine the factors of x³ + 5x² - 6x - 30 by grouping is shown by option D. x² (x + 5) - 6(x + 5).
What are Polynomials?Polynomials are mathematical expressions which consist of one or more terms involving variables and coefficients connected with operations like multiplication, subtraction, addition and natural number powers of variables.
Given a cubic polynomial,
x³ + 5x² - 6x - 30
Taking the first two terms together and the other two terms together,
(x³ + 5x²) + (- 6x - 30)
Taking x² common from first and -6 common from second,
x² (x + 5) - 6(x + 5)
Hence the correct option is D.
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Do ∠ABE and ∠DBC share a ray
Answer:
yes they do
Step-by-step explanation:
they share a ray
Cindy wants to put new carpet in her entryway. The entryway is 15ft. long and 7ft. wide. She wants to buy 10% extra carpet in case it is needed. How much carpet will she need to order?
Answer:
10.5
Step-by-step explanation:
quick math
the average of 5 girls is 6 yrs. the average of 4 of them is 16½. what is d age of d fifth gal
Answer:
This assumes the question should read:
"The average of 5 girls is 16 [not 6] yrs. the average of 4 of them is 16½. what is d age of d fifth gal
The age, d, is 14 years.
Step-by-step explanation:
When the girl with age d is not included, the average goes up to 16.5 years. Let's define GroupA as the sum of the ages of the 4 girls whose average age is 16.5 years. d is the age of the girl that is removed from the average.
We know that all the girls (GroupA + d) have an average age of 16 years:
(GroupA + d)/5 = 16 years [Add the ages for all the girls (GroupA and d) and divide by 5 to obtain the average age for the larger group].
We know that when d is removed, the average for the 4 remaining girls (GroupA) is 16.5 years:
(GroupA)/4 = 16.5 years
This tells us the sum of the ages for GroupA:
GroupA = 4*(16.5)
GroupA total = 66 years
From above: (GroupA + d)/5 = 16 years
Since GroupA = 66 years, (66 years + d)/5 = 16 years
(66 years + d) = 90 years
d = 14 years
What is the slope of the line y=-2x+3?
A. 3
B. -2
C. -3
D. 2
The first step that we must take before solving a problem is to understand what the problem statement is asking us to do and what is given to us to do so. Looking at the problem they are asking what the slope of the line is. What is provided to us is an equation which was captured as [tex]y=-2x + 3[/tex].
The next step that we must take is to determine what the slope of the line is. Let us first define what slope is.
Slope ⇒ Slope is the rate of change which can be expressed in an equation. For example, if a student buys 4 books per semester, the rate of change would be 4 as for every semester the student would add another 4 books.Slope-Intercept form is a form in which an equation can be expressed in and it follows the y = mx + b format. M is equal to the slope while b displays the y-intercept of the expression.
The easiest way to determine the slope using slope-intercept form us by looking at the coefficient of the variable x (in this case) which is also known as m. Looking at our equation, we can see that the coefficient in front of the variable x is -2.
Therefore, the option that would best match the details that we provided would be option B, -2.
Answer:
B. -2
General Formulas and Concepts:
Algebra I
Slope-Intercept Form:
[tex]\displaystyle y = mx + b[/tex]
Step-by-step explanation:
Step 1: Define
Identify given equation.
[tex]\displaystyle y = -2x + 3[/tex]
Step 2: Find Slope m
Let's compare our given equation to the general equation Slope-Intercept Form to identify our values for slope m and y-intercept b:
Compare:We can see that our y-intercept b is equal to 3 and that our slope m is equal to -2.
∴ the slope of the given line is equal to -2 and the answer choice that correlates with this is answer choice B.
___
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___
Topic: Algebra I
2а + 20 = -3а - 5 pls help
Answer: A= -5
Step-by-step explanation:
Answer: a = 5
Step-by-step explanation:
To solve, we will isolate the variable a.
Given:
2а + 20 = -3а - 5
Add 3a to both sides of the equation:
5а + 20 = - 5
Subtract 20 from both sides of the equation:
5а = 25
Divide both sides of the equation by 5:
a = 5
What is the solution of 5/2-7= 3/4x+14,
O A.
x=-6
O B.
x=6
OC.
X=8
O D. x=12
Answer:
D) x = 12
Step-by-step explanation:
Given:
[tex]\sf{\dfrac{5}{2}x-7=\dfrac{3}{4}x+14 \implies \dfrac{10}{4}x-7=\dfrac{3}{4}x+14}[/tex]
1. Multiply both sides by 4
[tex]\sf{4\left(\dfrac{10}{4}x-7\right)=4\left(\dfrac{3}{4}x+14\right)}\\\\\implies 10x-28=3x+56[/tex]
2. Subtract 3x from both sides
[tex]\sf{10x-3x-28=3x-3x+56}\\\\\implies 7x-28=56[/tex]
3. Add 28 to both sides
[tex]\sf{7x-28+28=56+28}\\\\\implies 7x=84[/tex]
4. Divide both sides by 7 to isolate the variable:
[tex]\sf{\dfrac{7x}{7}=\dfrac{84}{7}}\\\\\implies x=12[/tex]
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Write an inequality for the graph shown below.
Use x for your variable.
-11-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0
4
2
w.
O
ロマロ
X
S
6 7 8
口<口
S
9 10 11 X
OSO
?
Step-by-step explanation:
x is less than or equal to 0.
so click x than the choose the third option then click 0
what is the the value of m in the equation 1/2m-3/4n=16, when n=8
5x – 2x + 7 – x = ?x + ?
I need the answer for "no solution" and "infinite solutions".
(preferably with an explanation)
thanks to anyone who helps
Step-by-step explanation:
5x – 2x + 7 – x = ?x + ?
I need the answer for "no solution" and "infinite solutions".
NO SOLUTION:
no solution because any value you give to x is not solvable, it remains +7
5x – 2x + 7 – x = ?x + ?
2x = 2x + 7
INFINITE SOLUTION
infinite solutions because any value you give to x is solvable
5x – 2x + 7 – x = ?x + ?
5x – 2x + 7 – x = 2x + 7
2x + 7 = 2x + 7
PLEASE HELPP! ILL GIVE BRAINLIEST!
Which graph represents a quadratic function that has exactly one real zero?
There exists one real zero when the vertex lies on the x-axis, from that we conclude that the correct option is A.
Which quadratic function has only one real zero?
The real zeros of a quadratic function are the values of x at which the graph of the quadratic function intercepts the x-axis.
If we want only one real zero, then we must have only one intercept. And this only can happen if the vertex of the quadratic function lies on the x-axis.
As you can see, the only graph where that happens is the one in option A, so we conclude that option A is the correct one.
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Guys, can you please help me with The Question #47 of The Quadratic Relations for me, please? :)
Answer:
[tex]y=\dfrac{1}{2}(x+5)^2-3[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
Parent function
[tex]y=-x^2[/tex]
Reflected in the x-axis
[tex]-f(x) \implies y=-(-x^2)\implies y=x^2[/tex]
Compressed vertically by a factor of 1/2
Multiply the whole function by the given scale factor:
[tex]\dfrac{1}{2}f(x)\implies y=\dfrac{1}{2}x^2[/tex]
Translated 3 units down
Subtract 3 from the whole function:
[tex]f(x)-3 \implies y=\dfrac{1}{2}x^2-3[/tex]
Translated 5 units left
Add 5 to the variable of the function:
[tex]f(x+5) \implies y=\dfrac{1}{2}(x+5)^2-3[/tex]
To sketch the parabola
Vertex = [tex](-5, -3)[/tex]
Axis of symmetry: [tex]x = -5[/tex]
Plot points:
[tex]x=-9 \implies \dfrac{1}{2}(-9+5)^2-3=5 \implies (-9,5)[/tex]
[tex]x=-7 \implies \dfrac{1}{2}(-7+5)^2-3=-1 \implies (-7,-1)[/tex]
[tex]x=-3 \implies \dfrac{1}{2}(-3+5)^2-3=-1 \implies (-3,-1)[/tex]
[tex]x=-1 \implies \dfrac{1}{2}(-1+5)^2-3=5 \implies (-1,5)[/tex]
4+√x+1=5
I need the answer to this question
Answer:
x=0
Step-by-step explanation:
Expand the equation 4 + [tex]\sqrt{x}[/tex]+1=5
[tex]\sqrt{x} +5=5[/tex]
-5 -5
subtract 5 from both sides
[tex]\sqrt{x} = 0[/tex]
x=0
square both sides
True= x=0
Answer:
the answer is x=0
Step-by-step explanation:
[tex]4+\sqrt{x} +1=5[/tex]
add "4 +1" which equals 5
[tex]\sqrt{x} +5=5[/tex]
now -5 on both sides :)
[tex]\sqrt{x}[/tex]
now you're left with a square root
[tex]\sqrt{x}=0[/tex]
what is the slope-intercept equation of the line that includes the points in the table?
Answer:y=5x+1
Step-by-step explanation:the y intercept is the y value when x=0 which we can read off as run. Slope =rise/run=(change in y value)/(change in x value) for any two points.
What is the value of a in the equation? 22 = startfraction a over 11 endfraction 2 33 222 242
Answer:
D / 242
Step-by-step explanation:
hope this helps!
The Answer please!!!!!!!!!!
The number of seeds in 2 ounce package is 6.7 × 10⁷ seeds
Calculating quantityFrom the question, we are to determine the number of seeds in 2 ounce package
From the given information,
An orchid seed weighs 3.2 × 10⁻⁸ ounces
If an orchid seed weighs 3.2 × 10⁻⁸ ounces
Then,
2 ounce package will contain [tex]\frac{2}{3\times 10^{-8} }[/tex] seeds
= 0.67 × 10⁸
= 6.7 × 10⁷ seeds
Hence, the number of seeds in 2 ounce package is 6.7 × 10⁷ seeds
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If the bowl contains 5 red marbles 7 blue marbles and 8 white marbles what is the probability you will draw a blue and red marble when you pick one out?
5/20
15/20
7/20
2/5
Answer:
none of those are correct.
Step-by-step explanation:
5 red
7 blue
8 white
5 red + 7 blue= 12
5 red + 7 blue + 8 white= 20
=12/20
=6/10
=3/525 Select the correct answer. What is the average rate of change of f(x), represented by the graph, over the interval [-1, 2]? A. -2.5 B. -2 C. 2.5 D. 3 E. 6
The average rate of change of the function over the interval [-1, 2] is: C. 2.5.
How to Find the Average Rate of Change?The average rate of change over an interval of a function is: f(b) - f(a) / b - a.
Given the interval [-1, 2]:
a = -1; f(a) = -5
b = 2; f(b) = 2.5
Average rate of change = (2.5 - (-5)) / (2 - (-1)) = 7.5/3
Average rate of change = 2.5 (option C).
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5. What is the measurement of each angle?
Answer:
x=14
Step-by-step explanation:
The sum of a interior angle is 180°
(7x-11)+(2x-3)+(5x-2)°=180°
7x+2x+5x=180+11+3+2
14x/14=196/14
x= 14
Hope this answers your question!! :)
PLEASE HELP ILL MAKE YOU BRAINIEST
Answer:
obtuse
Step-by-step explanation:
A "form factor" can be computed whose sign will tell you the classification of the triangle. For short sides a, b and long side c, the form factor is ...
f = a² +b² -c²
And the interpretation is ...
f > 0 . . . acutef = 0 . . . rightf < 0 . . . obtuse__
form factorFor the given side lengths, the form factor is ...
f = 11² +15² -20² = 121 +225 -400
f = -54
interpretationThe value is less than zero, signifying an obtuse triangle.
_____
Additional comment
The value f/(2ab) = -54/(2·11·15) = -9/55 is the cosine of the largest angle. Here, the largest angle is arccos(-9/55) ≈ 99.4°. This is greater than 90°, hence an obtuse angle.
This cosine relation comes from the Law of Cosines. The interpretation of the "form factor" can be developed by considering the Pythagorean theorem (f=0 ⇒ right triangle) and the relationship between sides and angles. If the longest side is longer than necessary for a right triangle, the largest angle will be greater than 90°.