Solve the equation.
x2 − 6x − 7 = 0
Answer:
x = 7 and x = -1
Step-by-step explanation:
Step 1: Factor
x^2 - 6x - 7 = 0
(x - 7)(x + 1) = 0
Step 2: Solve for x
(x - 7)(x + 1) = 0
x - 7 = 0 and x + 1 = 0
x - 7 + 7 = 0 + 7 and x + 1 - 1 = 0 - 1
x = 7 and x = -1
Answer: x = 7 and x = -1
The terms in a sequence are given by 3 + 2x. what are the first 6 terms in the sequence?
First 6 terms are 5, 7, 9, 11, 13 and 15
Step-by-step explanation:
Step 1: Given terms in the sequence = 3 + 2x. Find the first 6 terms.a(1) = 3 + 2 × 1 = 3 + 2 = 5
a(2) = 3 + 2 × 2 = 3 + 4 = 7
a(3) = 3 + 2 × 3 = 3 + 6 = 9
a(4) = 3 + 2 × 4 = 3 + 8 = 11
a(5) = 3 + 2 × 5 = 3 + 10 = 13
a(6) = 3 + 2 × 6 = 3 + 12 = 15
The two-way table shows data for a florist’s inventory by flower and color. A 5-column table has 3 rows. The first column has entries roses, tulips, total. The second column is labeled red with entries 25, 11, 36. The third column is labeled Pink with entries 8, 14, 22. The fourth column is labeled white with entries 16, 12, 28. The fourth column is labeled total with entries 49, 37, 86. What is the probability that the florist randomly selects a tulip for a bouquet? P(tulip) = StartFraction 11 Over 37 EndFraction P(tulip) = StartFraction 37 Over 86 EndFraction P(tulip) = StartFraction 37 Over 49 EndFraction P(tulip) = StartFraction 49 Over 86 EndFraction
Answer:
37/86
Step-by-step explanation:
eh
The probability that the florist randomly selects a tulip for a bouquet using the given table is; 37/86
How to find probability from tables?From the given table we see that;
Total number roses = 49
Total number of tulips = 37
Now, we want to find the probability that the florist randomly selects a tulip for a bouquet. Thus;
P(selecting tulip for a bouquet) = total number of tulips/total number of bouquets
Thus;
P(selecting tulip for a bouquet) = 37/(49 + 37)
P(selecting tulip for a bouquet) = 37/86
Read more about probability tables at; https://brainly.com/question/24756209
What value does the red dot represent on the number line?
I think it's 6/7, but i'm not sure
Answer:
The answer is 5/6
Step-by-step explanation:
There are five sections in between 0 and 1; since the dot is five sections away from zero out of six sections, it is 5/6.
I need help with this problem
Yo sup??
net population of Mexico and Canada is= 110.65+33.89
=144.54 million
net population of US=317.64 million
difference=317.64-144.54
=173.1 million
Hope this helps
Hello Red, Need help training your charizard?
Anyways
if you add 110.65million and 33.89million, you would get
144.54
now the united states has a population of 317.64 million
317.64- 144.54= 173.1
so the U.S has 173.1 million more than Canada And Mexico Combined
Change this radical to an algebraic expression with fractional exponents.
[tex]5\sqrt{x^3}[/tex]
Rational exponents
[tex]a^\frac{m}{n}[/tex]
work like this: the numerator is the actual exponent of the base, while the denominator is the index of the root.
In other words, we have
[tex]a^\frac{m}{n}=\sqrt[n]{a^m}[/tex]
So, in you case, we have
[tex]\sqrt[5]{x^3}=x^\frac{3}{5}[/tex]
Assuming that the question contanis a typo. If you actually mean [tex]5\sqrt{x^3}[/tex],
then you can write it as [tex]5x^\frac{1}{3}[/tex]
Mr. Duncan mixed 0.00055 pounds of sulfur and 0.00104 pounds of iron powder in a test tube before heating it. What is the total weight of the mixture in the test tube?
Answer:
1.59 × 10-3 pounds
Step-by-step explanation:
Add the weights of the sulfur and iron powder to find the total weight of the mixture.
First, write both numbers in scientific notation.
Now that both numbers are written in scientific notation, compare the exponents. Since both exponents are not the same, rewrite 5.5 × 10-4 as 0.55 × 10-3. Now the numbers multiplied by the powers of 10 can be added while keeping the power of 10 the same.
So, the total weight of the mixture in the test tube is 1.59 × 10-3 pounds.
The coordinates of triangle BCD are B(8.2), C(11, 13) and D(2,6). Which equality proves that triangle BCD is isosceles? (d =
V(x2-x} + ()2 + y)2)
BC = CD
BC = BD
CD = BD
DB = CB
Answer:
BC=BD
Step-by-step explanation:
This is the correct answer for Usatestprep
Answer:
BC=CD
Step-by-step explanation:
Classify a triangle with angle measures of 63 degrees and 27 degrees.
Acute
Obtuse
Right
Not Possible
Answer:
right
Step-by-step explanation:
The sum of all three angle measures in a triangle will always equal 180 degrees. So, if you subtract 63 and 27 from 180 you will have your third angle measure, which is 90.
So now your 3 measures are 63, 27, and 90. Since one of the angles is a 90-degree angle, the triangle must be a right angle because a right angle has a measure of 90 degrees.
I hope this helps!
Answer:
Right triangle
Step-by-step explanation:
First angle of triangle = 63°
Second angle of triangle = 27°
Third angle of triangle = 180°-(63°+27°) = 90° ∴sum of three angle of triangle is 180°
As one angle is 90°(right angle), therefore it is a right triangle.
What is the solution to the equation x + 14 = 63?
Pleas help
Answer:
x = 49
Step-by-step explanation:
x + 14 = 63
x = 63 - 14
x = 49
Answer:
49
Step-by-step explanation:
Subtract 14 for both sides
Use the distributive property to write the following expression in expanded form. 3(2x+11y)
Answer:
6x + 33y
Step-by-step explanation:
3(2x+11y) Distribute the 3 to the 2x and the 11y separately
6x + 33y This is the expression in expanded form.
If this answer is correct, please make me Brainliest!
Answer: 6x+33y
Step-by-step explanation:
For what number A does the equation 3Ax - 24 = 5x - 9 + x$ have no solutions for x?
HELLLLPPPP
Answer:
A=2
Step-by-step explanation:
3Ax - 24 = 5x - 9 + x (simplifying the right side)
3Ax - 24 = 6x - 9
Equating the term x,
It will have no solution when 3A = 6 ⇒ A = 2
To see why:
3(2)x - 24 = 6x - 24
and this can never equate to 6x - 9 and have no solutions for x.
Thanks if you help and braknly
Answer:
Range: 12 - 32 Median: 15
Step-by-step explanation:
The range is pretty simple... It is the lowest number in the set to the highest number in the set. The lowest number is 12 and the highest number is 32.
The median of a set of numbers is the number that's in the middle. This is different from the mean because you're not finding the average, but actually the middle number.
To find the median, order the numbers from lowest to highest...
12, 13, 13, 15, 16, 19, 32
So, the median of this set is 15, because it is the middle number.
which two beverages have a sum of 5/8 of the students votes favorite beverages iced tea 3/8 fruit juice 2/8 water 1/8 soda 2/8 _fraction of student votes
Answer:
The two beverages can be (iced tea,fruit juice) or (iced tea,soda).
Step-by-step explanation:
Given : Beverages iced tea [tex]\frac{3}{8}[/tex], fruit juice [tex]\frac{2}{8}[/tex], water [tex]\frac{1}{8}[/tex], soda [tex]\frac{2}{8}[/tex].
To find : Which two beverages have a sum of [tex]\frac{5}{8}[/tex] of the students votes ?
Solution :
We have to get the two beverages whose sum became [tex]\frac{5}{8}[/tex] .
The possible ways are
1) Iced tea + Fruit juice = [tex]\frac{3}{8}+\frac{2}{8}[/tex]
Iced tea + Fruit juice = [tex]\frac{5}{8}[/tex]
2) Iced tea + Soda = [tex]\frac{3}{8}+\frac{2}{8}[/tex]
Iced tea + Soda = [tex]\frac{5}{8}[/tex]
Therefore, the two beverages can be (iced tea,fruit juice) or (iced tea,soda).
Tommy wished he practiced more before his violin concert. If he had practiced 1 1/2 more hours one week, he would have averaged 8 hours per week for the four week prior to his concert. How many hours did he practice in the 4 weeks?
Answer:
30.5 hours
Step-by-step explanation:
If he were to average 8 hours PER week for 4 weeks, his total sum would have been:
8 * 4 = 32 hours
But he fell short of it. By how much?
By [tex]1\frac{1}{2}[/tex] hours!
So, he practiced 1 1/2 hours LESS THAN 32 hours, so his practice time is:
[tex]32-1\frac{1}{2}\\=32-1.5\\=30.5\\=30\frac{1}{2}[/tex]
So, he practiced 30.5 hours in the 4 weeks
A farmer has a plot of land
Answer:
good for the farmer
Step-by-step explanation:
Answer:
He can grow stuff
Step-by-step explanation:
Angles P and Q are supplementary. If mZP is
32°, what is the mZQ?
Step-by-step explanation:
Supplementary angles add up to 180°
[tex]\therefore m\angle P + m\angle Q = 180° \\ \therefore 32 \degree+ m\angle Q = 180° \\ \therefore m\angle Q = 180° - 32° \\ \huge \purple{ \boxed{\therefore m\angle Q = 148°}}[/tex]
Are these correct? If not help me please??
Answer: no, no, yes, no, yes, yes
Step-by-step explanation:
x + 1, 2x, these are not equivalent
no
10x, 5(x+5)
5(x+5) distribute the 5 to get 5(x+5) = 5x + 25
5x + 25 is not equal to 10x, so no
no
1 + 2x = 2x + 1, these are equivalent since the constant and coefficients are the same
yes
2x, 2x - 5, these are not equivalent since once has a constant of -5 while the other does not
no
15x -1, 3(x+4x) - (3-2)
3(x+4x) - (3-2) combine like terms
3(5x) - (1) multiply through parentheses
= 15x -1
so 15x - 1 = 3(x+4x) - (3-2), these are equivalent
yes
1/2 * (4x-2),2x-1
1/2 * (4x-2) multiply through parentheses to get
2x - 1
so these two are equivalent
yes
The answer #2 is no and the number #5 is yes.
#2 is no, as you cannot add or subtract if they are not similar. Since in the second part the answer is 5x + 25.
#5 is yes because when there is a subtraction in front of a parenthesis, expressions within the parenthesis must change their sign.
Which of the following is the minimum value of the function y =
x2 + 6x + 6?
Answer:
y=8x+6
Step-by-step explanation: Just add the 2x and the 6x together to get 8x, then add 6. All I did was simplify the equation.
. What is a Golden Rectangle? Why is it important in architecture and art? Look around you right now. Do you see anything that looks like a Golden Rectangle in your classroom?
Answer:
see below
Step-by-step explanation:
A golden rectangle is one that has an aspect ratio of the "golden ratio". That ratio is an irrational number:
Φ = (1+√5)/2 ≈ 1.618034
This number is the positive solution to the equation ...
x = 1/(x -1)
__
Books have been written about the properties of the Golden Ratio and all the ways it shows up in Nature and in mathematics. For example, the ratios of sequential numbers in the Fibonacci sequence approach the Golden Ratio in the limit.
__
The proportion is often called the "divine proportion" because of the ways it shows up in nature. Some say a rectangle with this proportion is most pleasing to the eye. Hence, it may show up in architecture and art for that reason. A 5×8 photo is approximately this shape.
(The 1.6:1 aspect ratio is one that used for some video screens. It isn't quite as wide as the 16:9 aspect ratio seen more commonly. It is somewhat longer and narrower than the aspect ratio of common paper sizes.)
_____
The attached graph shows rectangles with the proportion of Φ.
A Golden Rectangle is a rectangle with side lengths in the golden ratio (approximately 1:1.618), known for its aesthetically pleasing proportions. Its importance in architecture and art stems from its use to create harmonious and balanced designs. Students often study golden rectangles to improve their understanding of symmetry and composition in art and architecture.
A Golden Rectangle is a rectangle whose side lengths are in the golden ratio, approximately 1 : 1.618. This ratio is also known as Phi. The significance of the golden rectangle in architecture and art lies in its aesthetically pleasing proportions which have been utilised since antiquity. It is believed that the human eye finds shapes and proportions based on the golden ratio to be naturally beautiful.
In architecture and art, the golden rectangle has been used to structure designs with a sense of harmony and balance. Modern artists such as Georges Seurat and Piet Mondrian have integrated the golden rectangle into their works to create compositions that are pleasing to the eye.
When constructing a golden rectangle, students may use a computer drawing program, maintaining its proportions even when resizing it. They can use this golden rectangle as a template over scanned images of Renaissance paintings or their own compositions, incorporating elements such as doorways or windows that conform to its proportions.
By understanding and using the golden rectangle, students can explore symmetry and visually satisfying geometrical forms, enhancing their artistic or architectural work.
Find the volume of the prism.
22 m
26 m
The volume of the prism is
The volume of the triangular prism is 2,002 m³.
Step-by-step explanation:
Step 1:
The volume of a triangular prism can be determined by multiplying its area of the triangular base with the height of the prism.
The base triangle has a base length of 26m and a height of 7m.
The area of a triangle is given by; [tex]A = \frac{1}{2} (b)(h)= \frac{1}{2} (26)(7) = 91[/tex].
So the area of the triangle is 91 m².
Step 2:
The volume of the prism is determined by multiplying the area with the height.
The area is 91 m² and the height is 22m.
The volume = (area)(height) [tex]= (91)(22) = 2,002.[/tex]
The volume of the given prism is 2,002 m³.
(−3x − 6)(3x2 − 6x + 3)
From Sim’s house to the lake is 30 kilometers. If he completed the round trip on his bike in 2 hours and 30 minutes, what was his average speed in kilometers per hour?
Solution:
Given that,
Distance = 30 km
Time = 2 hours 30 minutes
We know that,
[tex]1\ minute = \frac{1}{60}\ hour\\\\Therefore\\\\30\ minute = \frac{30}{60} = 0.5\ hour[/tex]
Thus,
Time = 2 hour + 0.5 hour = 2.5 hour
The average speed is given as:
[tex]Average\ speed = \frac{ total\ distance}{total\ time\ taken }[/tex]
Therefore,
[tex]Average\ speed = \frac{60}{2.5} = 24[/tex]
Thus average speed is 24 km/hr
What is the slope between (-4,4) and (-6,6)
[tex]\textsf{Let's calculate the slope of the line passing thought the points (-4, 4) and (-6, 6) } \\ \textsf{using the following formula: }\mathsf{m = \frac{\Delta y}{\Delta x}} \textsf{ where m is the slope of the line.}[/tex][tex]\textsf{So:}[/tex]
[tex]\mathsf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{4 - 6}{-4 - (-6)} = \dfrac{-2}{2} = -1}[/tex]
[tex]\textsf{Hence the slope is -1.}[/tex]
2 prime numbers with the sum of 34
Answer:
The two numbers are 15 and 19
Sure, the two prime numbers that add up to 34 are 17 and 17.
The length of a ribbon is 7/ 8 meter. Sun Yi needs pieces measuring 1/ 7 meter for an art project. What is the greatest number of pieces measuring 1 /7 meter that can be cut from the ribbon? How much ribbon will be left after Sun Yi cuts the ribbon?
To find the greatest number of pieces measuring 1/7 meter that can be cut from a ribbon of length 7/8 meter, divide the length of the ribbon by the length of each piece. The greatest number of pieces that can be cut is 6. Subtract the total length of the 6 pieces from the original length of the ribbon to find how much ribbon will be left.
Explanation:To find the greatest number of pieces measuring 1/7 meter that can be cut from a ribbon of length 7/8 meter, we need to divide the length of the ribbon by the length of each piece. So, 7/8 divided by 1/7 is equal to (7/8) x (7/1) = 49/8 = 6.125. Since we can't have a fraction of a piece, the greatest number of pieces that can be cut is 6. This means 6 pieces measuring 1/7 meter can be cut from the ribbon.
To find out how much ribbon will be left after cutting the 6 pieces, we need to subtract the total length of the 6 pieces from the original length of the ribbon. Each piece measures 1/7 meter, so the total length of the 6 pieces is (1/7) x 6 = 6/7 meter. Subtracting this from the original length, we get 7/8 - 6/7 = 49/56 - 48/56 = 1/56 meter. Therefore, there will be 1/56 meter of ribbon left after Sun Yi cuts the ribbon.
Learn more about Division of Fractions here:https://brainly.com/question/17205173
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a farmers land is separated into sections of size 2 1/7 acres. Suppose there are 2 2/3 such sections. how many acres of land does the farmer own
Answer:
5 5/7 acres
Step-by-step explanation:
The product is ...
(2 1/7 acres/section)(2 2/3 sections) = (15/7)(8/3) acres = 40/7 acres
= 5 5/7 acres
The farmer owns 5 5/7 acres of land.
The farmer's land amounts to approximately 5.71 acres. The problem involves conversion of mixed numbers to improper fractions and multiplication.
Explanation:The problem involves the concepts of multiplication and fractional numbers in mathematics. If one section is 2 1/7 acres and there are 2 2/3 such sections, you multiply these two amounts to find the total acreage. First, convert the mixed numbers to improper fractions: 2 1/7 becomes 15/7, and 2 2/3 becomes 8/3. Multiply the numerators together (15*8=120) and the denominators together (7*3=21) to get 120/21, which simplifies to about 5.71 acres.
Learn more about Fractions here:https://brainly.com/question/33564650
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-53 + n = -28 solve for n
Answer:
n will be equal 25
Step-by-step explanation:
-53 + n = -28
collect like terms, and we will have
n = -28 + 53
n = 25
Answer: n = -25
Since, -23 + -25 = -53
Steve os three times as old as Thresa. in four years he will be twice as old as she will be. How old is each one?
Answer:
Theresa is 4 years old while Steve is 12
Consider the expression.
6 · 60 · 6–3
Which statements are true about the expression? Check all that apply.
The 6 without an exponent is equivalent to the 6 having a 0 exponent.
The sum of the exponents is 2.
Multiply the exponents to simplify the expression.
The expression has a value of 1/36.
An equivalent expression is 65 · 6-7.
Answer: its d and e
Step-by-step explanation: