Answer: 2 pens and 4 pencils.
Step-by-step explanation:
If you buy 2 pens it is equal to $2.
If you buy 4 pencils it is also equal to $2.
2+2=4
and 2 pens and 4 pencils is equal to 6 in total.
Answer
[tex]2[/tex] pens and [tex]4[/tex] pencils were bought for [tex]\$4[/tex] such that [tex]6[/tex] pens and pencils are bought for [tex]\$4[/tex] and each pen costs [tex]\$1[/tex] and each pencil costs [tex]\$0.50[/tex].
Linear EquationThe equation whose variables' highest power is one is known as linear equation.
To find the unknown quantities, always assume it to be a variable and then form the equation based on the conditions given in the question.
How to solve the linear equations?Let the number of pens bought be [tex]x[/tex].
and the number of pencils bought be [tex]y[/tex].
The total number of pens and pencils [tex]=6[/tex].
So, the first equation is,
[tex]x+y=6[/tex]
[tex]x=6-y[/tex] ... (i)
And the costs per pen and pencil is [tex]\$1[/tex] and [tex]\$0.50[/tex] respectively.
So, the second equation is,
[tex]x+0.5y=4[/tex] ... (ii)
Now, solve the pair of linear equations.
Put the value of [tex]x[/tex] in the equation (ii),
[tex]6-y+0.5y=4\\-0.5y=-2\\y=4[/tex]
So,
[tex]x=6-4\\x=2[/tex]
Thus, [tex]2[/tex] pens and [tex]4[/tex] pencils were bought for [tex]\$4[/tex].
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Question 13 (5 points)
Find the distance between (-8, 4) and (-8, -2).
6 units
2 units
10 units
8 units
Answer:
Step-by-step explanation:
Find the length of the missing side
Answer:
x is 5 cm
Step-by-step explanation:
From pythogras theorem:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
a is x cm
b is 12 cm
c is 13 cm
[tex] {x}^{2} + {12}^{2} = {13}^{2} \\ {x}^{2} = {13}^{2} - {12}^{2} \\ {x} = \sqrt{ {13}^{2} - {12}^{2} } \\ x = \sqrt{169 - 144} \\ x = \sqrt{25} \\ x = 5 \: cm[/tex]
Distributive Property to find 83x7
Answer:
Step-by-step explanation:
This is a handy thing to know how to do.
83 = 80 + 3
7*(80 + 3)
560 + 21
581
Type the dimensional analysis setup you used to convert 15 years to minutes
Select two ratios that are equivalent to 7:107:107, colon, 10.
Answer:
107:107
Step-by-step explanation:
107:107 are the equivalent ratios as both numbers are same.
Carson is hiking a trail that is 12 kilometers long. one-fourth of the way through the course, he stops to rest. how many meter does carson have left to hike on the trail after he rests?
Answer:
9000 m
Step-by-step explanation:
One: Note that the answer is supposed to be in meters. It's easier if we just convert the 12 kilometers to meters now so we dont' have to worry about it later. 1 kilometer is 1,000 meters, so all we need to do is add three zeros to the end to make it meters:
12km=12,000m
Two: 1/4 means to divide by 4: 12,000/4= 3,000.
Three: The question is asking how much is LEFT. So we would do 12,000-3,000, which is 9000.
pls pls help!!!!!!!!!!
9514 1404 393
Answer:
5
Step-by-step explanation:
Let f represent the number of friends. Their total earnings are ...
21f = 105
f = 105/21 = 5 . . . . . divide by the coefficient of f
There are 5 friends in the group.
simplify square root of 3/8
please give steps!!
Step-by-step explanation:
Write the expression
[tex] \sqrt{ \frac{3}{8} } [/tex]
Let make the denominator a perfect square that is a multiple of 8. 16 is a multiple of 8 and a perfect square so
[tex] \sqrt{ \frac{3}{8} } = \sqrt{ \frac{6}{16} } [/tex]
Know that
[tex] \sqrt{ \frac{x}{y} } = \frac{ \sqrt{x} }{ \sqrt{y} } [/tex]
So
[tex] \sqrt{ \frac{6}{16} } = \frac{ \sqrt{6} }{4} [/tex]
The simplified form of the square root of 3/8 is (√6) / 4.
To simplify the square root of 3/8, we can simplify the numerator and denominator separately.
For the numerator, we take the square root of 3:
√3
For the denominator, we take the square root of 8:
√8
Now, let's simplify each of them:
√3 cannot be simplified further because 3 is a prime number.
√8 can be simplified by factoring out the perfect square:
√8 = √(4 × 2)
Since 4 is a perfect square (2² = 4), we can take it out of the square root:
√8 = 2√2
Now, let's put the simplified numerator and denominator together:
√3/8 = √3 / (2√2)
To rationalize the denominator, we multiply the expression by the conjugate of the denominator:
(√3 / (2√2)) × (√2 / √2) = (√3√2) / (2√2√2)
Simplifying the denominator:
(√3√2) / (2√4) = (√6) / (2 × 2)
Simplifying further:
(√6) / (2×2) = (√6) / 4
Therefore, the simplified form of the square root of 3/8 is (√6) / 4.
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Which number is irrational?
Answer:
√11 is the irrational number
Explanation:
Irrational numbers are which numbers that can't be expressed as p/q form that are irrational numbers. root 11 cant be expressed as p/q form so, this is an irrational number.
Hourly rate: $3.82; Hours: 24; What are the total earnings
Answer:
$91.68
Step-by-step explanation:
$3.82 × 24 = $91.68
Answer: $91.68
Step-by-step explanation:
Given information
Hourly rate = $3.82
Hours = 24
Given expression deducted from the given information
Total earning = Hours × Hourly rate
Substitute values into the expression
Total earning = (24) × (3.82)
Simplify by multiplication
Total earning = $91.68
Hope this helps!! :)
Please let me know if you have any questions
Noel can stack 4 blocks in 2 seconds. At this rate, how many blocks can he stack in one minute?
Answer:
120
Step-by-step explanation:
There are 60 seconds in one minute so you would 4 times 30 since Noel can STACK 4 BLOCKS per 2 seconds.
You need to tile 17 kitchen floors in a new apartment building each floor needs 309 tiles how many tiles will you need for all the floors
And explain
Answer:
You will need 5,253 tiles.
Step-by-step explanation:
17 kitchen floors x 309 tiles for each floor = 5,253 tiles total
Answer:
The answer is 5253
Step-by-step explanation:
We will use the unitary method
Make two columns one for kitchen floors and one for tiles
In the first row you will put 1 kitchen floor and 309 tiles
In the second row you will put 17 kitchen floors and x tiles
Then crossmultiply and 17x309 is equal to 5253
Ages Number of students
15-18 5
19-22 7
23-26 8
27-30 7
31-34 2
35-38 4
Based on the frequency distribution above, find the relative frequency for the class with a lower class limit of 35
Give your answer as a percent, rounded to 1 place after the decimal point, if necessary. Type only a number in the answer box (do NOT type "%" after your answer).
Answer:
35 is the answer
Step-by-step explanation:
show that there do not exist scalar c1 c2 and c3 c1(-2,9,6)+c2(-3,2,1)+c3(1,7,5)= (0,5,4)
This is the same as showing the following system of equations doesn't have a solution:
[tex]\begin{cases}-2c_1-3c_2+c_3 = 0 \\ 9c_1 + 2c_2 + 7c_3 = 5 \\ 6c_1 + c_2 + 5c_3 = 4\end{cases}[/tex]
or in matrix form,
[tex]\begin{bmatrix}-2&9&6\\-3&2&1\\1&7&5\end{bmatrix}\begin{bmatrix}c_1\\c_2\\c_3\end{bmatrix} = \begin{bmatrix}0\\5\\4\end{bmatrix}[/tex]
The quickest way to check if there is a solution is to check whether the coefficient matrix is invertible. If its determinant is 0, then it is not invertible.
And the quickest way to show that the determinant is 0 is by observing that the third row is a linear combination of the first two rows:
(-2, 9, 6) - (-3, 2, 1) = (-2 + 3, 9 - 2, 6 - 1) = (1, 7, 5)
So there are indeed no such scalars c₁, c₂, and c₃.
Which describes the relationship between the distance and the difference?
Answer:
Which describes the relationship between the distance and the difference? The distance is always the opposite of the difference. ... The distance is the absolute value of the difference.
Helen and Rebecca baked some muffins in the ratio 2:5. After Helen baked another 12 muffins, the ratio become 1:2. How many muffins did Helen bake altogether?
=========================================================
Explanation:
x = some positive whole number
2x = amount Helen baked initially
5x = amount Rebecca baked initially
Notice that the ratio 2x:5x reduces to 2:5 after dividing both parts by x.
So (2x)/(5x) = 2/5
Helen then bakes another 12 muffins, bumping the 2x up to 2x+12. The ratio is now 1:2, which means,
(amount Helen bakes)/(amount Rebecca bakes) = 1/2
(2x+12)/(5x) = 1/2
2(2x+12) = 5x*1 .... cross multiply
4x+24 = 5x
24 = 5x-4x
24 = x
x = 24
From here, we then can say,
Helen = 2x+12 = 2*24+12 = 48+12 = 60Rebecca = 5x = 5*24 = 120Helen baked 60 muffins and Rebecca baked 120 muffins. We see that 60:120 reduces to 1:2 after dividing both parts by the GCF 60.
Furthermore, note how
2x = 2*24 = 485x = 5*24 = 12048:120 reduces to 2:5 after dividing both parts by 24This helps confirm we have the correct answer.
7/9+6/8+6/3=
please help me
Hi ;-)
7/9 + 6/8 + 6/3 = 7/8 + 3/4 + 2 =
= 28/32 + 24/32 + 2 = 52/32 + 2 =
= 1 20/32 + 2 = 3 20/32 = 3 5/8
Answer:
the answer is three and nineteen over thirty-six
[tex]3 \19 \36[/tex]
A 5-foot wide
hallway requires
440.5 ft2 of carpet
to cover. How
long is the
hallway, in feet?
Answer:
length × width = area
440.5 = 5 × length
length = 440.5 / 5
length = 88.1
so haway is 88.1 foot long
the length of the hallway is 88.1 feet. To find the length of the hallway, we need to use the given information about the width of the hallway and the total area of the carpet required to cover it.
Given:
Width of the hallway = 5 feet
Area of carpet required = 440.5 ft^2
Let's denote the length of the hallway as "L" (in feet).
The area of a rectangle (such as the hallway) is given by the formula:
Area = Length * Width
In this case, the area is given as 440.5 ft^2, and the width is given as 5 feet. Now we can set up the equation:
440.5 = L * 5
To find the length (L), divide both sides by 5:
L = 440.5 / 5
L = 88.1
So, the length of the hallway is 88.1 feet.
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solve for m.
-6(1+8m)=-342
Answer:
m is 7
Step-by-step explanation:
[tex]{ \sf{ - 6(1 + 8m) = - 342}}[/tex]
divide all sides by (-6) :
[tex]{ \sf{ \frac{ - 6(1 + 8m)}{ - 6} = \frac{ - 342}{ - 6} }} \\ \\ { \sf{1 + 8m = 57}}[/tex]
make m the subject:
[tex]{ \sf{8m = 56}} \\ { \sf{m = 7}}[/tex]
Jarell is grocery shopping for his BBQ cookout this weekend. He is grilling 13lb. burgers and expects about 20 people. How many whole lbs. of ground beef should be purchase?
Jarrell should purchase 7 lbs of ground beef.
Number of attendees = 20
Fraction of burger per person = 1/3 lbs
Total fraction of burger required to feed 20 persons :
Number of attendees × fraction per person
20 × 1/3 = 6.667
The number of whole grouhd beef that should be purchased is 7 lbs
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Which is an example of a unit rate?
Answer:
A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
What number should be added to 2/8 to -1/12 get ?
Answer:
-1/3
Step-by-step explanation:
this is the best answer
Hello! i need help with these 3 questions.
-Let U= {1,2,3,4,5,6,7,8,9,10}, A={2,4,6,8} B={1,2,3,4}, C={5,6,9}
Answer:
10 is B
11 is C
12 is C. Simple set rules
11) There are 32 students in a closs. Nine of those students are
women. What percent ere mena (round to the nearest tenth)
Find the area of the sector of the circle Radius. 7kmCentral angle. 2pi over 3
Show steps
9514 1404 393
Answer:
51.3 km²
Step-by-step explanation:
The area formula is ...
A = 1/2r²θ . . . . where θ is the central angle in radians
A = 1/2(7 km)²(2π/3) = 49π/3 km² ≈ 51.3 km²
Is 66.06 a irrational number
Answer:
No.
Step-by-step explanation:
No because it can be written as a fraction, 6606/10
6. Find the sum of whole number divisible by 3 and lies between 100 and 200.
Answer:
4950
Step-by-step explanation:
first find the smallest multiple of 3 thats >100, 3*33=99, so 3*34=102 is the smallest multiple of 3 >100.
next find the greatest multiple of 3 <200, 3*66=198 which is the greatest multiple of 3<200
34-66+1=number of terms=33. then find the average of the terms: 102+198/2=150. 150*33=4950. the answer should be 4950
Answer:
Step-by-step explanation:
The first number in the sequence = 102
The last number = 198
The number of terms =
L = a1 + (n-1)*d
198 = 102 + (n- 1)*3 Subtract 102
198 - 102 = (n - 1)* 3
96 = (n - 1)*3 divide by 3
32 = n - 1 add 1
33 = n
Sum = (a1 + L ) * n/2
sum = (102+198)*33/2
sum = 300 * 33/2
sum = 150 * 33
sum = 4950
Tavon has a gift card for $65 that loses $3 for each 30-day period it is not used. He has another gift card for $55 that loses $2.50 for each 30-day period it is not
used
a. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal.
b. What will the value of each card be when they have equal value?
a. If x is the number of 30-day periods, then the equation can be used to find the number of 30-day periods until the values of the gift cards will be equal.
(Type an equation. Use integers or decimals for any numbers in the equation)
Answer:
a. 65 - 3 x = 55 - 2.5 x
ab. 20
b. 5
Step-by-step explanation:
The equations are y = 110 - 2.5x and y = 90 - 2x. Then the value of each card, when they have equal value, will be $10.
What is a linear equation?The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let x be the number of days and y be the value of the card.
Tavon has a gift card for $110 that loses $2.50 for each 30-day period it is not used. He has another gift card for $90 that loses $2 for each 30-day period it is not used. Then the equations will be
y = 110 - 2.5x ...1
y = 90 - 2x ...2
From equations 1 and 2, we have
110 - 2.5x = 90 - 2x
20 = 0.5x
x = 40
And the value of y will be
y = 110 - 2.5(40)
y = 110 - 100
y = $10
The equations are y = 110 - 2.5x and y = 90 - 2x. Then the value of each card, when they have equal value, will be $10.
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Complete the missing ? That will make the sentences true
I’m confused on what to do please help!!
Answer:
1.21 ) 8
1.22) 6
1.23) €
1.24)⊂
1.25)=
Answer:
[tex]1)7 \\ 2)6 \\ 3) > \\ 4)0 \\ 5)phy[/tex]
Find an equation of the set of all points equidistant from the points
A(−2, 6, 3) and B(5, 3, −3).
We need to find the equation which is equidistant to the given points.
[tex]A(-2,6,3)[/tex] and [tex]B(5,3,-3)[/tex]
This can be done using the distance formula.
Let us take a point [tex]P(x,y,z)[/tex] which is equidistant from both points so
[tex]\sqrt{(x+2)^2+(y-6)^2+(z-3)^2}=\sqrt{(x-5)^2+(y-3)^2+(z+3)^2}\\\Rightarrow y^2-12y+x^2+4x+z^2+49-6z=y^2-6y+x^2+z^2+6z+43-10x\\\Rightarrow 7x-3y-2z+1=0[/tex]
The required equation is [tex]7x-3y-2z+1=0[/tex]
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