Answer:
y=-3x+14
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-4-26)/(6-(-4))
m=-30/(6+4)
m=-30/10
m=-3
y-y1=m(x-x1)
y-26=-3(x-(-4))
y-26=-3(x+4)
y=-3x-12+26
y=-3x+14
x^2 - 7 = 60
How do I solve the equation?
Answer:
x=√67 or x=−√67
Step-by-step explanation:
Step 1: Add 7 to both sides.
x2−7+7=60+7
x2=67
Step 2: Take square root.
x=±√67
x=√67 or x=−√67
Round 23.5481 to the nearest thousandth
Answer: 23.548
Step-by-step explanation: The thousandths place is 3 places to the right of the decimal point so in this problem, the digit in the rounding place is 8.
The rules of rounding says that if the digit to the right of the rounding place is greater than or equal to 5, we round down but if the digit to the right of the rounding place is less than 5, we round down.
Since the digit to the right of the rounding place, 1, is less than 5, we round down. This means that the digit in the rounding place which is 8 stays the same and we change all digits to the right of 8 to zero.
So we have 23.5480.
Finally, it's important to understand that when rounding decimals, we can drop any zeroes to the right of the decimal point as long as they're also to the right of the rounding place.
This means that 23.5481 rounded to the nearest thousandth is 23.548.
Give a button and a bookmark
to each student who visited the fair. The buttons came in
packages of 30. The bookmarks came in packages of 50.
The committee needed the same number of each left
over for another fair. The committee estimated that
400 students would visit the fair. How many
packages of buttons and packages of bookmarks
did they need?
Let's note the information.
This is what we know:
Every buttons came in packages of 30 per student.
Every bookmark came in packages of 50 per person.
Know, we need to do some multiplying.
30 x 400 & 50 x 400
Now solve.
30 X 400 = 12000.
So we now know that they have an estimated 12000 buttons total.
Now, we find x for bookmarks.
50 x 400 = 20000
That means total that estimated that 20000 bookmarks will be given.
Answer:
15 packages of buttons
9 packages of bookmarks
Step-by-step explanation:
We need to find the least common multiple (LCM) of 30 and 50.
30 = 2×3×5
50 = 2×5²
LCM = 2×3×5²
LCM = 150
Now we need to find a multiple of LCM that is greater than 400.
3LCM = 450
The committee needs at least 450 of each, which means they need at least 15 packages of buttons and 9 packages of bookmarks.
What is the closed linear form for this sequence given a1 = 0.3 and an + 1 = an + 0.75?
Answer:
The closed linear form of the given sequence is [tex]a_{n}=0.75n-0.45[/tex]
Step-by-step explanation:
Given that the first term [tex]a_{1}=0.3[/tex] and [tex]a_{n+1}=a_{n}+0.75[/tex]
To find the closed linear form for the given sequence
The formula for arithmetic sequence is
[tex]a_{n}=a_{1}+(n - 1)d[/tex] (where d is the common difference)
The above equation is of the given form [tex]a_{n+1}=a_{n}+0.75[/tex]
Comparing this we get d=0.75
With [tex]a_{1}=0.3[/tex] and d=0.75
We can substitute these values in [tex]a_{n}=a_{1}+(n - 1)d[/tex]
[tex]a_{n}=a_{1}+(n - 1)d[/tex]
[tex]=0.3+(n-1)(0.75)[/tex]
[tex]=0.3+0.75n-0.75[/tex]
[tex]=-0.45+0.75n[/tex]
Rewritting as below
[tex]=0.75n-0.45[/tex]
Therefore [tex]a_{n}=0.75n-0.45[/tex]
Therefore the closed linear form of the given sequence is [tex]a_{n}=0.75n-0.45[/tex]
B. Consider the total amount you’re willing to spend on the business and how much it will cost you to make your items. Write an inequality that represents the fact that while making each item, you can’t exceed this limit. Be sure to include the cost per item in this inequality.
I have a budget of $140.55 to buy (15 sweatshirts for 7.59 each) and (30 bags $.89 cents each)
write an inequality that can then graphed.
Answer:
$ 140.55 ≤ $ 7.59x + 0.89$ y
$ 140.55 ≤ $ 9.37x where 0≤ x ≤ 15.
Step-by-step explanation:
$ 140.55 ≤ $ 7.59x + 0.89$ y
Let x be the number of sweatshirts and y be the number of bags where y= 2x
and 0≤ x ≤ 15.
$ 140.55 ≤ $ 7.59x + 0.89$ (2x) Putting y= 2x
$ 140.55 ≤ $ 7.59x + $ 1.78x
$ 140.55 ≤ $ 9.37x where 0≤ x ≤ 15.
Answer:
$ 140.55 ≤ $ 7.59x + 0.89$ y
$ 140.55 ≤ $ 9.37x where 0≤ x ≤ 15.
Step-by-step explanation:
$ 140.55 ≤ $ 7.59x + 0.89$ y
Let x be the number of sweatshirts and y be the number of bags where y= 2x
and 0≤ x ≤ 15.
$ 140.55 ≤ $ 7.59x + 0.89$ (2x) Putting y= 2x
$ 140.55 ≤ $ 7.59x + $ 1.78x
$ 140.55 ≤ $ 9.37x where 0≤ x ≤ 15.
Step-by-step explanation:
Quadrilateral ABCD is similar to Quadrilateral EFGH. Diagonal AC has length 7 and diagonal EG has length 13. What is the scale factor that describes a dilation from BC to FG? Give the exact scale factor and state whether the dilation is an expansion or a contraction.
If side AB has length 17/26 what is the length of side EF? Give the exact, un-rounded value.
PLEASE HELP ASAP
If the area of ABCD is 147 square inches, what is the area of EFGH? Give the exact answer.
Answer:
[tex]\large \boxed{\text{A. }\dfrac{13}{7}\text{; B. }\dfrac{17}{14} \text{; C. 507 in}^{2}}[/tex]
Step-by-step explanation:
A. Scale factor
When you dilate an object by a scale factor, you multiply its line lengths by the same number.
If EF/AB = 13/7, the scale factor is 13/7.
B. Length of EF
[tex]\begin{array}{rcl}\dfrac{EF}{AB} & = & \dfrac{13}{7}\\\\\dfrac{EF}{\frac{17}{26}} & = & \dfrac{13}{7}\\\\EF & = & \dfrac{13}{7}\times\dfrac{17}{26}\\\\ & = &\dfrac{1}{7}\times\dfrac{17}{2}\\\\ & = & \mathbf{\dfrac{17}{14}}\\\end{array}\\\text{The length of EF is $\large \boxed{\mathbf{ \dfrac{17}{14}}}$}[/tex]
C. Area of EFGH
If the lengths in a shape are all multiplied by a scale factor, then the areas will be multiplied by the scale factor squared.
ABCD is dilated by a scale factor of 13/7, so its area is dilated by a scale factor of
[tex]\left(\dfrac{13}{7} \right)^{2} = \dfrac{169}{49}[/tex]
The area of its dilated image EFGH is
[tex]\text{Area of EFGH} = \text{147 in}^{2} \times \dfrac{\text{169}}{\text{49}} = 3 \times 169\text{ in}^{2} = 507 \text{ in}^{2}\\\\\text{The area of EFGH is $\large \boxed{\textbf{507 in}^{\mathbf{2}}}$}[/tex]
Mrs. Alveres purchased 3 pounds of oranges for $3.45. At this price, how much do 5 pounds of oranges cost?
Answer:
$5.75
Step-by-step explanation:
3.45 divided by 3 is 1.15. 1.15 times 5 is 5.75.
The cost of 5 pounds of oranges at a unit rate of 1.15 dollars is 5.75 dollars.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Mrs. Alveres purchased 3 pounds of oranges for $3.45.
∴ The cost of 1 pound of orange is (3.45/3) dollars.
= 1.15 dollars.
If the cost of 1 pound of orange is 1.15 dollars,
∴ The cost of 5 pounds of oranges is,
= (5×1.15) dollars.
= 5.75 dollars.
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does y=5/6x+2 and y=5/6x-2 have exactly one solution
Answer:
infinately many solutions
Step-by-step explanation:
Is 18.04 greater or less than 18.4
Step-by-step explanation: To compare decimals such as 18.4 and 18.04, first line up the decimal points of the numbers.
Next, we compare the digits place by place starting on the left.
1 and 1 are the same, 8 and 8 are the same, but notice that 4 is greater than 0.
This means that 18.4 is greater than 18.04.
So to answer your question, 18.04 is less than 18.4
which function is the inverse of y= -3x + 6/7
Answer:
y=-1/3x+2/7
Step-by-step explanation:
y=-3x+6/7
x=-3y+6/7
-3y=x-6/7
y=-1/3x+(6/7)/3
y=-1/3x+(6/7)(1/3)
y=-1/3x+6/21
y=-1/3x+2/7
Where, if any, did Jordana first make a mistake in her work?
Jordana made a mistake when finding the scale factor.
Jordana made a mistake when she calculated the length of side A.
Jordana made a mistake when she calculated the length of side B.
Jordana did not make any mistakes in her work.
Answer:All the answers were correct but her calculating was wrong.
Step-by-step explanation: Jordana could not find the scale factor she was looking in the wrong place but the answer was correct and when she calculated she it wrong but the answer was correct.
Answer:
C
Step-by-step explanation:
Write an equation in slope-intercept form for the line described
Answer:
Step-by-step explanation:
y=mx+b
Luiza is jumping on a trampoline. Ht models her distance above the ground (in m) t seconds after she starts
jumping. Here, t is entered in radians.
H(t) =-0.6 cos (2pi/2.5)t + 1.5
What is the second time when Luiza reaches a height of 1.2 m?
Round your final answer to the nearest hundredth of a second.
Answer:
t=2.08 seconds.
Step-by-step explanation:
Well, in this example, H(t)=-0.6cos(2pi/2.5)t+1.5 should be equal to 1.2. If calculated, -0.6cos(0.8pi)t=1.2-1.5 which is equal to -0.6cos(0.8pi)t=-0.3, then cos(0.8pi)t=0.5. The value of cosine in terms of radians when it is equal to 0.5 is pi/3. So, cos(0.8pi)t=cos(pi/3). If simplified, (0.8pi)*t=5pi/3. pi's are cancelled out and t is calculated as 2.08333... If rounded to the nearest hundredth it is 2.08.
Solve for X if MN =81
A)9
B)10
C)11
D)12
Answer:
D
Step-by-step explanation:
You can see, MN consists of the three lines in the picture. So you just need to sum them tougher in an equation with it's original value 81.
5 + 3x - 8 + 4x = 81
7x = 81 + 3
7x = 84 / : 7
x = 12
The value x from the given line segment is 12 units. Therefore, option D is the correct answer.
What is line segment?A line segment is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon.
Given that, MN=81.
Here, MN=5+3x-8+4x
MN=7x-3
7x-3=81
7x=81+3
7x=84
x=84/7
x=12
Therefore, option D is the correct answer.
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multiplication property of equality and reciprocal of 1/3
Answer:
the answer is 3
Step-by-step explanation:
Final answer:
The multiplication property of equality states that multiplying or dividing both sides of an equation by the same number does not change the equality. The reciprocal of 1/3 is 3/1 or 3. So, if you multiply or divide both sides of an equation by 3/1 (the reciprocal of 1/3), you will maintain the equality.
Explanation:
The multiplication property of equality states that multiplying or dividing both sides of an equation by the same number does not change the equality. In this case, we have the fraction 1/3. The reciprocal of 1/3 is 3/1 or 3. Multiplying both sides of an equation by 3 is equivalent to dividing both sides by 1/3. So, if you multiply or divide both sides by 3/1 (the reciprocal of 1/3), you will maintain the equality.
4. Select all the sentences that describe a
comparison using multiplication.
0 25 is 5 more than b.
64 is 8 times as many as w. i
An ant can carry 50 times its
own weight
There are 7 times as many balls V
as bats.
Each adult ticket costs $5 more than
a student ticket.
64 is 8 times as many as w
There are 7 times as many balls V as bats
The phrase "times as many" signals multiplication.
Final answer:
The answer provides examples of sentences that describe a comparison using multiplication from the options given.
Explanation:
Select the sentence that describes a comparison using multiplication:
64 is 8 times as many as w.
There are 7 times as many balls V as bats.
An ant can carry 50 times its own weight.
Janie took out a loan for $4850 at a 13.8% APR, compounded monthly, to buy
a backyard swimming pool. If she will make monthly payments of $455.50 to
pay off the loan, how many total payments will she have to make?
Answer:
The total payment Janie have to make is $5466 .
Step-by-step explanation:
Given as :
The loan principal = $4850
The rate of interest applied = 13.8% compounded monthly
Let The time period of loan = t years
The monthly payment she make = $455.50 each month
I.e She make payment for t years = $455.50 × n
where n is the number of terms
From Compound Interest
Amount = Principal × [tex](1+\dfrac{\textrm rate}{12\times 100})^{12\times time}[/tex]
Or, $455.50 × n = $4850 × [tex](1+\dfrac{\textrm 13.8}{12\times 100})^{12\times time}[/tex]
Or, [tex]\dfrac{455.50}{4850}[/tex] × n = [tex](1.0115)^{12\times 1}[/tex]
Or, 0.0939 × n = [tex](1.0115)^{12}[/tex]
Or, 0.0939 × n = 1.14707
∴ n = [tex]\dfrac{1.14707}{0.0939}[/tex]
I.e n = 12.21 ≈ 12
So, The number of terms Janie she will pay = 12
So, The total payment she have to make = $455.50 × 12 = $5466
Hence The total payment Janie have to make is $5466 . Answer
Answer:
She will have to make 12 payments
Step-by-step explanation:
College can be expensive, but it is worth the expense. Students should consider financial aid when applying for colleges. Here _______ common ways to fund a college education: earn scholarships, obtain loans, and find a job.
College can be expensive, but it is worth the expense. Students should consider financial aid when applying for colleges. Here are common ways to fund a college education: earn scholarships, obtain loans, and find a job. Therefore, the correct answer choice is: C. are.
In English language, a sentence is a group of words or phrases that comprises a subject and predicate, which are typically used by an author or speaker in order to convey a logical information about a subject matter to an audience (readers or listeners).
A verb is one of the parts of speech in English language and it refers to any word that describes an action, occurrence, or a state of existence.
In this context, we can reasonably infer and logically deduce that the most appropriate word to complete the sentence is "are" because it is a linking verb and it connects the subject with objects in plural form.
What are the roots of the polynomial equation? (picture below)
Answer:
x = - 9, x = 0, x = 7
Step-by-step explanation:
Given
[tex]\frac{1}{2}[/tex] x(x - 7)(x + 9) = 0 ← in standard form
Equate each factor to zero and solve for x
[tex]\frac{1}{2}[/tex] x = 0 ⇒ x = 0
x - 7 = 0 ⇒ x = 7
x + 9 = 0 ⇒ x = - 9
Answer:
-9, 0, 7
Step-by-step explanation:
Finding the roots of a polynomial equation is the same as solving the equation. So, simply figure out which values make the equation equal 0.
If multiplication is involved, then 0 is always an answer (or root). Because anything multiplied by 0 is always 0.
7 is also a root:
7 - 7 = 0
Same with -9:
-9 + 9 = 0
PLZ HELLPPP!!!!!!!!!!!!!!!!1!
Answer:
2 y for every 1 x
Step-by-step explanation:
2 and 1 is the answer
92.0565426965 to the 6 place
Answer:
92.056543
Step-by-step explanation:
Please help me. I'm stupid.
Answer:
[tex]\displaystyle 36\:units[/tex]
Step-by-step explanation:
Split up this Isosceles, Right Triangle into two congruent smaller right triangles. The reflexive side [the line that splits them apart] is 6 units, and both legs are 8 units, leaving the hypotenuses to AUTOMATICALLY be 10 units, according to the Pythagorean Theorem:
[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ 6^2 + 8^2 = 10^2 \\ \\ 36 + 64 = 100 \\ \\ 100 = 100[/tex]
With this Pythagorean Triple, we know that our dimensions are correct. Now, to find the perimeter, just add up all the sides EXCEPT for the divider:
[tex]\displaystyle 2[10] + 2[8] = 20 + 16 = 36[/tex]
I am joyous to assist you anytime.
I need help with his problem with details.
Answer:
The solution is y> -1
Step-by-step explanation:
y- 6 > -7
y> -7+6 (add 6 on both sides)
y> -1
The graph should the the first option from the right, with the dot above -1.
Since y is greater than -1, the dot should be on -1 and the arrow should be pointing towards the right. It shouldn't be a coloured dot because the sign is 'greater than' (>) not 'greater or equal to' (≥)
The side lengths of a triangle are given by the expressions 5x+3,5x+5,and3x-2.write and simplify a linear expression for the perimeter of the triangle.
The perimeter of the triangle is: 13x+6
Step-by-step explanation:
The perimeter is the length of the outer boundary of any closed geometrical shape.
So,
Given
[tex]Side\ 1 = s_1 = 5x+3\\Side\ 2 = s_2 = 5x+5\\Side\ 3 = s_3 = 3x-2[/tex]
The perimeter will be:
[tex]P = s_1+s_2+s_3\\= (5x+3)+(5x+5)+(3x-2)\\=5x+5x+3x+3+5-2\\=13x+6[/tex]
The perimeter of the triangle is: 13x+6
Keywords: Perimeter, geometry
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Solve for x: 6/x = 4/8
A)10
B)12
C)24
D)48
Answer:
B)12
Step-by-step explanation:
6/x = 4/8
6/x = 1/2
6 * 2 = 1 * x
12 = x
x = 12
29 lbs of tomatoes cost $87. How much would 20 lbs cost
Answer:
60
Step-by-step explanation:
87/29=3
3$ for each pound.
20*3= 60.
answer is 60.
Point Q' is the image of Q(-7, -6) under the translation (x, y) + (x + 12, y + 8).
What are the coordinates of Q'?
Answer:
The co-ordinates of Q' is (5,2).
Step-by-step explanation:
Given:
Pre-image point
Q(-7,-6)
To find Image point Q' after following translation.
[tex](x,y)\rightarrow (x+12,y+8)[/tex]
Solution:
Translation rules:
Horizontal shift:
[tex](x,y)\rightarrow (x+k,y)[/tex]
when [tex]K>0[/tex] the point is translated [tex]k[/tex] units to the right.
when [tex]K<0[/tex] the point is translated [tex]k[/tex] units to the left.
Vertical shift:
[tex](x,y)\rightarrow (x,y+k)[/tex]
when [tex]K>0[/tex] the point is translated [tex]k[/tex] units up.
when [tex]K<0[/tex] the point is translated [tex]k[/tex] units down.
Given translation [tex](x,y)\rightarrow (x+12,y+8)[/tex] shows the point is shifted 12 units to the right and 8 units up.
The point Q' can be given as:
Q'=[tex](-7+12,-6+8)=(5,2)[/tex]
So, the co-ordinates of Q' is (5,2). (Answer)
The area of a rectangular patio is square yards, and its length is yards. What is the patios width in yards?
Complete Question:
As you missed to add the area and length value. So, after a little research I was able to find the complete question. I will answer the question based on this complete question I am mentioning, but hopefully it would clear your concept anyways. So, here is the complete question.
The Area of a rectangular patio is 5 5/8 square yards, and it's length is 1 1/2 yards.What is the patio's width,in yards?
Answer:
The width of patios is [tex]w = \frac{15}{4} yards[/tex].
Step-by-step explanation:
As the area of a rectangular patio is [tex]A = 5\frac{5}{8}[/tex] square yards.
⇒ [tex]A = 5\frac{5}{8}[/tex]
⇒ [tex]A = 5\frac{5}{8}[/tex] can be written as : [tex]A = \frac{45}{8}[/tex]
The length of a rectangular patio is [tex]l = 1\frac{1}{2}[/tex] square yards.
⇒[tex]l = 1\frac{1}{2}[/tex]
⇒[tex]l = 1\frac{1}{2}[/tex] can be written as : [tex]l = \frac{3}{2}[/tex]
As the area of rectangular patio can be computed by multiplying the length and width. So, width [tex](w)[/tex] can be computed by dividing the Area by length.
[tex]A = lw[/tex]
[tex]w = \frac{A}{l}[/tex]
So, [tex]w = \frac{\frac{45}{8}}{\frac{3}{2} }[/tex]
[tex]w = (\frac{45}{8}) (\frac{2}{3} )[/tex]
[tex]w = \frac{90}{24}[/tex]
[tex]w = \frac{15}{4}[/tex] or [tex]w = 3\frac{3}{4}[/tex]
Hence, the width of patios is [tex]w = \frac{15}{4} yards[/tex].
Keywords: area of rectangle, width, length
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what fraction of 2 1/2 is 4/5
Answer:
2!
Step-by-step explanation:
To find out what fraction of 2 1/2 is 4/5, convert 2 1/2 to a fraction (5/2), then multiply 4/5 by the reciprocal of 5/2 which gives 8/25. So, 4/5 is 8/25 of 2 1/2.
Explanation:
The question is asking about what fraction of 2 1/2 is 4/5. In order to solve this, we should firstly convert the mixed number 2 1/2 to a fraction, which is 5/2. Then we have to divide 4/5 by 5/2 to find out the fraction. To divide fractions, we multiply the first fraction (the dividend) by the reciprocal of the second fraction (the divisor).
So, the problem becomes 4/5 * 2/5, and the solution is 8/25. Therefore, 4/5 is 8/25 of 2 1/2.
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What is the volume of this rectangular prism 7/5 CM by 5 cm and 7/2 cm
Answer:
[tex]V=\frac{49}{2}\ cm^3[/tex]
or
[tex]V=24.5\ cm^3[/tex]
Step-by-step explanation:
we know that
The volume of the rectangular prism is
[tex]V=LWH[/tex]
where
L is the length
W is the width
H is the height
substitute the given values in the formula
[tex]V=(\frac{7}{5})(5)(\frac{7}{2})[/tex]
[tex]V=\frac{245}{10}\ cm^3[/tex]
Simplify
[tex]V=\frac{49}{2}\ cm^3[/tex] ---> fraction form
or
[tex]V=24.5\ cm^3[/tex] ----> decimal form
The volume of the rectangular prism is 24.5 cm³.
To find the volume of a rectangular prism, you use the formula Volume = length × width × height. Given the dimensions of the prism are 7/5 cm by 5 cm and 7/2 cm, we calculate the volume by multiplying these three dimensions together.
Volume = (7/5) cm × 5 cm × (7/2) cm
First, simplify the calculation by multiplying the whole numbers: Volume = (7 × 5 × 7) / (5 × 2) cm³, which simplifies to Volume = 49/2 cm³. Then, divide 49 by 2 to get Volume = 24.5 cm³.