Answer:
1) 6x = 21
2) x + y - 3
3) x/z = y
4) 2-x = p
Step-by-step explanation:
1. The product of a number x and 6 is 21
A product is a multiplication. A product of a and b is a * b.
We then have a product of x and 6, that x * 6, which we write usually in the format 6x.
is 21: that means it's equal to 21....
so 6x = 21.
2. The sum of the quantity x- 3 and y
The sum is an addition. The sum of a and b is a + b.
In this case, the first part is x - 3, the second part is y
So, x - 3 + y, which we usually rewrite as x + y - 3
3. The quotient of x and z is y
A quotient is a division.
So, quotient of x and z is x/z.
x/z = y
4. The difference of 2 and x is p.
A difference is a subtraction.
Difference of 2 and x is 2 - x
2 - x = p
The verbal sentences/phrases are translated into algebraic expressions or equations as: 1) 6x = 21, 2) (x - 3) + y, 3) y = x/z, and 4) p = 2 - x. Each expression/equation captures a different mathematical relationship, such as product, sum, quotient, and difference.
Explanation:To translate each verbal sentence/phrase into an algebraic expression or equation, we will take them one at a time:
The product of a number x and 6 is 21: This can be translated into the equation 6x = 21.The sum of the quantity x - 3 and y: The algebraic expression for this is (x - 3) + y.The quotient of x and z is y: This corresponds to the equation x/z = y, or as an expression, y = x/z.The difference of 2 and x is p: This translates to the equation p = 2 - x.Remember to check your final expressions or equations to ensure they make sense and are simplified where possible.
Help me find the which statements are true!!!!
Answer:
C.Step-by-step explanation:
[tex]\text{A. The absolute value of the slope of the line is equal to}\ \dfrac{HJ}{FG}\\\bold{FALSE}\\\text{because the slope of the line is equal to}\ \dfrac{HJ}{KJ}\\------------------------------\\\text{B. The absolute value of the slope of the line is equal to}\ \dfrac{FG}{JK}\\\bold{FALSE}\\\text{because the slope of the line is equal to}\ \dfrac{FG}{FK}\\------------------------------[/tex]
[tex]\text{C. Because triangles FGH and HJK are similar, the slope is the same}\\\text{between any two distinct points on the line.}\\\bold{TRUE}\\------------------------------\\\text{D. Because triangles FGH and HJK are not similar, the slope is found}\\\text{by using two distinct points on one of the triangles}\\\bold{FALSE}\\\text{because triangles FGH and HJK are similar (AAA)}[/tex]
A small pie factory needs to ship 360 pies a day to stay profitable. 180 pies are baked every 3 hours. Of the baked pies, 20% go directly to freezer storage and 80% are loaded on a truck for delivery. Find the constant of proportionality for the number of pies baked and loaded on a truck for delivery. A.48 B. 60 C. 96 D. 144
Answer:
Constant of proportionality should be 48.
Step-by-step explanation:
Given that a small pie factory needs to ship 360 pies a day to stay profitable. 180 pies are baked every 3 hours. Of the baked pies, 20% go directly to freezer storage and 80% are loaded on a truck for delivery.
Now we need to find about what is the constant of proportionality for the number of pies baked and loaded on a truck for delivery.
Number of baked pies = 180
Number of pies loaded on truck for delivery = 80% of baked pies
= 0.80(180)= 144 in 3 hours.
So number of pies loaded per hour = 144/3= 48
Hence constant of proportionality should be 48.
Triangle JKL is a right triangle. What is the length of JK?
Answer:
[tex]H.2\sqrt{2}\ cm[/tex]
Step-by-step explanation:
Hello, I think I can help you with this
To solve this you can use the Pythagorean theorem, which states
in a right triangle:
[tex]side\ length^{2}+side\ length^{2}=hypotenuse^{2} \\[/tex]
the hypotenuse is the longest length of the triangle, in this case JK
Step 1
Let
side1= 2 cm
side2= 2 cm
hypotenuse=unknown=JK
isolate the hypotenuse from the equation
[tex]side\ length^{2}+side\ length^{2}=hypotenuse^{2}\\hypotenuse=\sqrt{side\ length^{2}+side\ length^{2}}[/tex]
It's a distance, we'll only take the positive root
put the values into the formula
[tex]hypotenuse=\sqrt{side\ length^{2}+side\ length^{2}} \\hypotenuse=\sqrt{(2\ cm)^{2}+(2\ cm)^{2}}\\hypotenuse=\sqrt{4\ (cm)^{2}+4\ (cm)^{2}}\\hypotenuse=\sqrt{8\ (cm)^{2}} \\hypotenuse=\sqrt{4\ (cm)^{2}*2} \\hypotenuse=\sqrt{4\ (cm)^{2}} \sqrt{2}\\hypotenuse=2\sqrt{2}\ cm[/tex]
the length JK is
[tex]2\sqrt{2}\ cm[/tex]
have a good day
The scatter plot shows the height and weight of football
players on a team.
How many football players weigh less than 70 kilograms?
Enter your answer in the box.
the answer is two football players weigh less than 70 kilograms
Answer:
Less than 2 players.
Step-by-step explanation:
Given that the scatter plot shows the height and weight of football
players on a team.
WE have to find the number of players who weigh less than 70 kgs.
In the graph of scatter plot we find tha when y<70, there are 2 points in the graph.
Hence only two players in football weight less than 70 kgs.
Suppose f(x) = x^2 and g(x) = (3x)^2 which statement best compares with he graph of g(x) with the graph of f(x)
Answer:
Step-by-step explanation:
f(x) = x^2 and g(x) = (3x)^2. g(x) can be rewritten as 9x^2.
The graph of g(x) is similar to that of f(x), except that the graph of g(x) is the result of vertical stretching of the graph of f(x) by a factor of 9.
Answer: The graph of g(x) is horizontally compressed by a factor of 3.
Step-by-step explanation:
Got this answer right on apex
The 2 ft side length of the scale drawing corresponds to a side length of 120 feet for the actual skate park. What is the scale factor?
Answer:
The scale factor is [tex]\frac{1}{60}[/tex]
Step-by-step explanation:
we know that
The scale factor is equal to the ratio between the side length of the scale drawing to the corresponding side length in the actual
so
[tex]\frac{2}{120}=\frac{1}{60}[/tex]
Answer:
1/60
Divide
Step-by-step explanation:
I really need help please
Answer:
the answer is C
Explanation:
The points (4, 1) and (x, -6) lie on the same line. If the slope of the line is 1 what is the value of x?
A -3
b 3
c 9
d 11
Answer:
x=9
Step-by-step explanation:
The Slope is given by the following equation
m= (y2-y1) / (x2-x1)
Where x2=4, x1=x, y2=1, y1=-6, m=1 by requirements of this problem
Developing the equation we have this:
[tex]1=\frac{1-(-6)}{4-x}[/tex]
Which leaves to the following equation
[tex]5=4-x[/tex]
Resulting that x=9
Help with number four plz!!!!!!
Answer:
Yes
Step-by-step explanation:
First we'll find the number of total bars of soap.
8 + 8 + 11 = 27
Is 27 divisible by 27?
Yes because 27 / 3 = 9
So you could rearrange the soaps to have 9 bars in each basket.
find the solution to the system
y=x^2+8x+2
y=7x+4
A(-2,-10) and (1,11)
B(2,10) and (-1,-11)
C(-2,-34) and (1,11)
D no solution
Answer:
A
Step-by-step explanation:
Given the 2 equations
y = x² + 8x + 2 → (1)
y = 7x + 4 → (2)
Substitute y = x² + 8x + 2 into (2)
x² + 8x + 2 = 7x + 4 ( subtract 7x + 4 from both sides )
x² + x - 2 = 0 ← in standard form
(x + 2)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 1 = 0 ⇒ x = 1
Substitute these values into (2) for the corresponding values of y
x = - 2 : y = - 14 + 4 = - 10 ⇒ (- 2, - 10)
x = 1 : y = 7 + 4 = 11 ⇒ (1, 11)
The solutions are (- 2, - 10) and (1, 11) → A
:0Need Help Please!!!!
Answer:
v = ( D/ 2Z )
Step-by-step explanation:
Equation given : D = 2ZV
In order to find V, we will have to divide both sides by 2Z
: V = D/2Z
An object is translated by (x - 2, y - 6). If one point in the pre-image has the coordinates (-3, 7), what would be the coordinates of its image? (-5, 1) (-1, 13) (-1, 7) (-9, 5)
Answer:
B. (-1,13)
Step-by-step explanation:
Given translation
(x,y)→(x-2,y-6)
moves point 2 units to the left and and 6 units down.
If a point after this translation has coordinates (-3,7), then its preimage has coordinates (-1,13) (translate the image point 2 units to the right and 6 units up to get preimage point).
Answer:
(-5,1)
Step-by-step explanation:
Find the fifth roots of 32(cos 280° + i sin 280°)
Answer:
The fifth root is 2[cos(56°) + i sin(56°)]
Step-by-step explanation:
* To solve this problem we must revise De Moiver's rule
- In the complex number with polar form
∵ z = r(cosФ + i sinФ)
∴ z^n = r^n(cos(nФ) + i sin(nФ))
* In the problem
- The fifth root means z^(1/5)
- We can put 32 as a form a^n
∵ 32 = 2 × 2 × 2 × 2 × 2 = 2^5
∴ z = 2^5[cos(280°) + i sin(280°)]
* Lets find z^(1/5)
[tex]*z^{\frac{1}{5}}=[2^{5}]^{\frac{1}{5} } (cos(\frac{1}{5})(280)+isin(\frac{1}{5})(280)[/tex]
[tex]*(2^{5})^{\frac{1}{5}}=2^{5.\frac{1}{5}}=2[/tex]
∴ z^(1/5) = 2[cos(56) + i sin(56)]
* The fifth root of 32[cos(280°) + i sin(280°)] is 2[cos(56°) + i sin(56°)]
a number is chosen at random from 1 to 50 find the probability of selecting factors of 36
Answer:
9/50 or 18%
Step-by-step explanation:
The factors of 36 are-
123469121836That's 9 factors. 1-50 means that it is a 9 out of 50 chance, or 80%.
When a number is chosen at random from 1 to 50 the probability of selecting factors of 36 is 2/50.
What is probability?Probability is the ratio that shows us how likely an event will occur from a given set of events.
We can find the required probability below:The factors of 36 are:
36 = 2*2*3*3
Therefore the factors of 36 are 2 and 3.
Total number of factors = 2
Total number of numbers from 1 to 50 = 50
The probability of selecting factors of 36 = P(selecting factors of 36)
= 2/50
The probability of getting a factor of 36 when a number is chosen at random is 2/50.
Therefore, we have found that when a number is chosen at random from 1 to 50 the probability of selecting factors of 36 is 2/50.
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A sculptor creates an arch in the shape of a parabola. When sketched onto a coordinate grid, the function f(x) = –2(x)(x – 8) represents the height of the arch, in inches, as a function of the distance from the left side of the arch, x. What is the height of the arch, measured 3 inches from the left side of the arch?
The correct answer is: D) 30 inches
Explanation:
We know that x represents the distance in inches from the left side of the arch. Using 3 for x, we have:
f(3) = -2(3)(3-8)
f(3) = -2(3)(-5)
f(3) = -6(-5)
f(3) = 30
Therefore, the correct answer is 30 inches! Thank you for your inquiry, your welcome for the answer and explanation!
The correct answer is: D) The height of the arch, measured 3 inches from the left side of the arch 30 inches
What is the height?
In math, height can be defined the vertical distance from the top to the base of the object. It is measured in cm, inches, meters, etc.
We know that x represents the distance in inches from the left side of the arch. Using 3 for x, we have:
f(3) = -2(3)(3-8)
f(3) = -2(3)(-5)
f(3) = -6(-5)
f(3) = 30
Therefore, the correct answer is 30 inches
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Identify the equation that represents the line of best fit on this scatter plot.
30 POINTS
[tex]y=\frac{5}{7} x+2[/tex]
How?
The way you find it is easy. +2 means go up 2y. 5 is y too, so you do 2+5=7. Now go 7 positive x. The answer is this.
Hope this helped:)
Answer:
C. [tex]y=\frac{5}{7}x+2[/tex].
Step-by-step explanation:
We have been given a scatter plot. We are asked to find the equation of line of best fit.
First of all, we will find slope of line of best fit using points [tex](0,2)[/tex] and [tex](7,7)[/tex].
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{7-2}{7-0}[/tex]
[tex]m=\frac{5}{7}[/tex]
We can see that y-intercept of line of best fit is 2.
We will write our equation in slope intercept form [tex]y=mx+b[/tex], where,
m = Slope,
b = The y-intercept.
Upon substituting [tex]m=\frac{5}{7}[/tex] and [tex]b=2[/tex] in slope-intercept form, we will get:
[tex]y=\frac{5}{7}x+2[/tex]
Therefore, the equation of line of best fit for given scatter plot is [tex]y=\frac{5}{7}x+2[/tex] and option C is the correct choice.
Information about how the students at vista view High school got to school this morning is shown in the table out of all 252 twelfth graders rode in a car to school
We can actually deduce here that the 114 rode in a car to school out of 252 twelfth graders.
Please, note that the question is incomplete.
What is information?Information actually refers to the available facts and structured data that is given or learnt. Information is very important to achieve and acquire certain knowledge.
Below is the complete question:
Information about how the students at Vista View High School got to school this morning is shown in the table. A 6-column table has 4 rows. The first column has entries Tenth grade, eleventh grade, twelfth grade, Total. The second column is labeled Walk with entries 104, blank, 99, 314. The third column is labeled Bicycle with entries 8, 10, blank, blank. The fourth column is labeled Bus with entries 96, 72, 28, 196. The fifth column is labeled Car with entries blank, 88, blank, 276. The sixth column is labeled Total with entries 282, blank, 252, 815. Out of all 252 twelfth graders, how many rode in a car to school?
A.11
B. 74
C. 111
D. 114
So, in order to find the number of twelfth graders that actually rode in a car, we will have:
Number of twelfth graders that rode in a car = total number of twelfth graders - those that walked - those that rode bicycles - those that went with bus.
Where:
Total number of twelfth graders = 252
Those that walked = 99
Those that rode bicycles = 11
Those that went with bus = 28
Therefore, the number of twelfth graders that rode in a car = 252 - 99 - 11 - 28 = 252 - 138 = 114.
Those that rode in a car = D. 114
We see that out of the information given, one can actually see that 114 rode in a car to school.
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What is the value of h when the function h(x)=x^2−8x+14 is converted to vertex form?
Answer:
h=4
Step-by-step explanation:
The given function is
[tex]h(x)=x^2-8x+14[/tex]
We add and subtract the square of half the coefficient of x.
[tex]h(x)=x^2-8x+(\frac{-8}{2})^2-(\frac{-8}{2})^2+14[/tex]
[tex]h(x)=x^2-8x+(-4)^2-(-4)^2+14[/tex]
The first three terms forms a perfect square trinomial
[tex]h(x)=(x-4)^2-16+14[/tex]
[tex]h(x)=(x-4)^2-2[/tex]
We now compare to the vertex form;
[tex]h(x)=a(x-h)^2+k[/tex]
We have h=4
Make q the subject of the formula 2(q+p) = 1+5q. Give your answer in the form ap-b/c where a,b and c are all positive integers
Answer:
[tex]\frac{2p-1}{3}[/tex]
Step-by-step explanation:
Since you want to get q only and q appears in both side of the equation. Try to isolate q to one side.
1) Expand 2(q+p)
2q + 2p = 1 + 5q
2) Move all q terms to one side
5q - 2q = 2p - 1
3q = 2p - 1
3) Divide 3 on both side (to isolate q)
q = [tex]\frac{2p-1}{3}[/tex]
After making q the subject of the formula in the equation 2(q + p) = 1 + 5q, the resulting solution is:
[tex]q = \frac{2p - 1}{3}[/tex]
The given equation is:
2(q + p) = 1 +5q
To make q the subject of the formula, follow the steps below
Expand the expression using the distributive rule
2q + 2p = 1 + 5q
Collect like terms by subtracting 2q from both sides of the equation
2q - 2q + 2p = 1 + 5q - 2q
2p = 1 + 3q
Subtract 1 from both sides of the equation
2p - 1 = 1 + 3q - 1
2p - 1 = 3q
Divide through by 3
[tex] \frac{2p - 1}{3} = q[/tex]
Therefore after making q the subject if the formula in the equation 2(q + p) = 1 + 5q, the resulting solution is:
[tex] q = \frac{2p - 1}{3}[/tex]
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7x+(2x+7)=9x+7 show work
it is true 9x=9x
7x+(2x+7)=9x+7
7x+2x+7=9x+7
-7. -7
7x+2x=9x
9x=9x
Can some body help me with number 12 it’s due tomorrow.
Answer:
Mean = 51.375
Mode = 55,44
Step-by-step explanation:
add all the numbers up and divide by 8
find the most repeating numbers.
Answer:
Mean: 51.375
Median: 51.5
Mode: 44, 55
Hope This Helps! Have A Nice Day!!
HELP IM ♀️ CONFUSED WILL GIVE BRAINLIEST AND 10 points CAN SOMEONE HELP WITH MY HOMEWORK QUESTIONS
Answer:
1 3/4
Step-by-step explanation:
8.25-6.5
Answer:
I believe it is B
Lowest- 6 1/2 inches
Tallest- 8 1/4 inches
6 1/2-8 1/4= 1 3/4
I am sorry if this is wrong.
If the half-life of K-40 is 1.3 billion years and if a sample rock found on an island is estimated to be 1 billion years old, what percentage of the original parent K-40 would be present in the rock? Round your numerical values to the hundredths decimal place.
Answer Choices
(A) 76.92%
(B) 1.3%
(C) 58.67%
(D) 99.99%
For this case, we must make a rule of three, to find the percentage of the k-40 found in the sample found.
1.3 ----------> 100%
1 -------------> x
Where "x" represents the percentage of k-40 present in the sample found.
[tex]x = \frac {1 * 100} {1.3}\\x = 76.9230[/tex]
Rounding off we have:
76.92%
ANswer:
Option A
The percentage of parent K-40 remaining in the rock is calculated as 76.92% of the original K-40.
Percentage of parent K-40 remaining in the rock:
Calculate the number of half-lives: 1 billion years / 1.3 billion years = 0.7692 or about 0.77 half-lives.
Use the formula[tex](1/2)^n[/tex] where n is the number of half-lives to find the percentage remaining: [tex](1/2)^0.77[/tex] ≈ 0.76.
Convert to a percentage for the original K-40 remaining in the rock: 0.76 * 100% ≈ 76.92%.
can someone help me with this?
V=ABh
S=a +b+c
————-
2
=83.5
How to draw 30/4 in to an mix number
7 1/2
Divide 30 by 4 to get 7 with a remainder of 2. This means the answer is 7 2/4.Simplify the fraction. 2/4 is the same as 1/2, so the answer is 7 1/2.divide 30 by 4. you’ll get 7 remainder:2 take the whole number you got:7 take the remainder:2 (that will be ur numerator) then take the divisor:4
you’ll get 7 2/4
(simplest form is 7 1/2)
PLZZZZZZZZZZZZZ HELP I NEED TO PASS THIS TEST I WILL GIVE BRAINLIST ANSWER TO WHO ANSWERS IT RIGHT
A statue has the shape of a square pyramid. The side length of the square base is 20 feet. The slant height of the monument is 16 feet. What is the height of the monument? Enter your answer, rounded to the nearest tenth of a foot, in the box.
____
|___| ft
Answer:
[tex]b=12.5[/tex] ft
Step-by-step explanation:
From this description we can draw this diagram
Now we can use the Pythagorean theorem to find the height.
[tex]10^2+b^2=16^2\\\\b^2=256-100\\\\b=\sqrt{156}[/tex]
This square root is equal to
[tex]b=12.489[/tex]
Which rounds to
[tex]b=12.5[/tex] ft
Indicate in standard form the equation of the line through the given points P(0,-4), Q(5,1)
bearing in mind that
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex]\bf P(\stackrel{x_1}{0}~,~\stackrel{y_1}{-4})\qquad Q(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-4)}{5-0}\implies \cfrac{1+4}{5}\implies \cfrac{5}{5}\implies 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-4)=1(x-0)\implies y+4=x \\\\\\ y=x-4\implies -x+y=-4\implies \stackrel{\textit{standard form}}{x-y=4}[/tex]
What is the value of log13
log 10=1,
log 2= 0.3010, and
log 3= 0.4771.
From these values, we can find many other log values.
log 5 = log 10 - log 2 = 0.699
log 0.5 = 0–log 2 = -0.301
log 1.5 = log 3 - log 2 = 0.1761
log 2.5 = log 5 - log 2 = 0.398
To find log of any number y:
Express y as (10^m)*(2^n)*(3^p)*(1+x).
Approximate log(1+x) as
(0.4343)*(x-x^2/2+x^3/3)
Or 0.4353*(x-x^2/2)
log y =
m + 0.3010*n + 0.4771*p + (0.4353)*(x-x^2/2+x^3/3)
To find log 13
13=2^2*3*(1+1/12)
log 13
= 2*0.3010 + 0.4771 + (0.4353)*(1/12 - 1/288+1/5184)
= 0.6020 + 0.4771 + 0.034847
= 1.1139
Can someone help ASAP I really need help 15 points
Answer:A=85 E=73 S=37 L=66.5 (or 65) T=82 P=53 D=10 O=89 C=17
Step-by-step explanation:
I am very good at Pythagorean theorem I did it this year.
To do this it is actually like the easiest thing to do in math. The formula is A²+B²=C². To do this it is easier with a scientific calculator. If you don't have one you can use this online calculator: desmos.com/scientific
Step 1. get the two number and square (²) them ( multiply that number by it) For Example 30 multiplied by 30. Or on the calculator I gave you just do 30²+40²
Step 2. After that you will get 2500. Then on the calculator get this symbol √ and but the number 2500 in front of it. it should look like this. √2500.
Step 3. After that you will get 50 which is your answer. And that is how you do Pythagorean theorem.
I hope that helped you. If you don't have a scientific calculator you can use the link I provided above. If you can't use it I reccomend buying one.
What is the slope if the line x+3y = 10
Answer:
the slope is -1/3
the Y intercept is 10/3
Step-by-step explanation:
Answer:
-1/3
Step-by-step explanation:
We want to get the equation in slope intercept form (y=mx+b) where m is the slope and b is the y intercept
x+3y = 10
Subtract x from each side
x-x+3y = -x+10
3y = -x+10
Divide each side by 3
3y/3 = -1/3x +10/3
y = -1/3x +10/3
The slope is -1/3 and the y intercept is 10/3