Answer:
8
Step-by-step explanation:
If each portion is 1/8 of the cake, there are 8 equal-size portions. That is what the denominator of the fraction means.
Sadie can cut the rectangular cake into 8 portions if each portion is 1/8 of the whole cake.
To determine how many portions Sadie can cut the rectangular cake into if each portion is 1/8, we need to understand that she is essentially dividing the cake into 8 equal parts.
Here's a step-by-step explanation:
Whole Cake: The entire rectangular cake represents one whole (1).
→ Portion Size: Each portion is 1/8 of the whole cake.
→ Calculation: We divide 1 by 1/8. Mathematically, this is the same as multiplying by the reciprocal,
so 1 ÷ (1/8) = 1 × 8
= 8.
Therefore, Sadie can cut the rectangular cake into 8 portions of size 1/8 each.
Please help me out!.
Since PQRS is isosceles, the horizontal distance between PQ and RS is the same, i.e. it's [tex]a[tex].
Moreover, point C is horizontally aligned with point Q, which implies that they share the y coordinate.
So, point R has coordinates [tex](c-a,b)[/tex]
PLEASE HELP!!!!!!!
For f(x) = 4x + 3 and g(x) = 9x find the following composite functions and state the domain of each
(a) f o g (b) g o f (c) f o f (d) g o g
(a) (f o g)(x) =
Answer:
Step-by-step explanation:
For f(x) = 4x + 3 and g(x) = 9x
(a) (f o g) (x)
= f (g (x))
= f (9x)
= 4(9x) +3
= 36x + 3
Its domain is any real number.
(b) (g o f) (x)
= g (f (x))
= g (4x + 3)
= 9 (4x + 3)
= 36x + 27
Again its domain is any real number.
(c) (f o f) (x)
= f (f (x))
= f (4x + 3)
= 4(4x + 3) + 3
= 16x + 12 + 3
= 16x + 15
Again its domain is any real number.
(d) (g o g) (x)
= g ( g (x))
= g (9x)
= 9(9x)
= 81x
Again its domain is any real number.
Answer:
solution given:
f(x) = 4x + 3
g(x) = 9x
answer:
a.fog(x)=f(9x)=4×9x+3=36x+3
domain=real number
b.gof (x)=g(4x+3)=9(4x+3)=36x+26
domain=real number
c.fof(x)=f(4x+3)=4(4x+3)+3=16x+12+3
=16x+15
domain: real number
d.
gog(x)=g(9x)=9×9x=81x
domain: real number.
Find the distance from point P to RQ
To find the distance from point P to line RQ, we first find the vectors for PQ and PR. Then we calculate the projection of PR onto PQ which gives us the vector from P to the point on line RQ nearest to P. The length of this vector gives us the shortest distance from point P to the line RQ. This explanation assumes we have coordinate data for points P, Q, and R.
Explanation:The distance from point P to RQ can be found utilizing mathematical principles of geometry and vectors. Let's assume that we know the coordinates of points P, R, and Q. Having these information, we can follow these steps:
First, find the vector RQ which is Q - R. Let's presume this gives us the vector a. Then, calculate the vector RP which is P - R and let's assume this gives us the vector b. The projection of vector b onto vector a is given by [(b.a)/|a|²]a (where . denotes the dot product and |a| is the magnitude of a). This will give us a vector from point R to the point on the line RQ that is nearest to point P, let's call this point M. Finally, find the vector PM by subtracting the projection from vector b. The length of this vector gives us the shortest distance from point P to the line RQ.
Remember, this is the process given that you know the coordinates of the points involved. If you only have a diagram, you might need to use tools like a ruler or a protractor to measure distances and angles.
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A school principal ordered 1,000 pencils .He gave equal number to each of 7 teachers until he had given out as many as possible . How many pencils were left?
Answer:6
Step-by-step explanation: 1,000 divided by 7 is 994 with a remainder of six. Which means the principal had six left
What is measure of angle A?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answer:
[tex]A=53.13\°[/tex]
Step-by-step explanation:
The figure shows a right triangle.
To calculate the measure of the angle A, you can use the inverse trigonometric function arctangent:
[tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex]
Identify the angle [tex]\alpha[/tex], the opposite side and the adjacent side:
[tex]\alpha=A\\opposite=4cm\\adjacent=3cm[/tex]
Substitute into [tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex].
The measure of the angle A is:
[tex]A=arctan(\frac{4}{3})\\\\A=53.130\°[/tex]
Rounded to the nerarest hundreth:
[tex]A=53.13\°[/tex]
The answer is m∠A = 53.13 °
first to answer gets brainlyest
Answer: 60 degrees
Step-by-step explanation:
the line is 180 degrees so minus 50 equals 130 minus 10 120 divide my 2 60
Please help... :'( I NEED THIS TO PASS MY GRADE
Which expression is equivalent to -12(3x-3/4)?
A. -36x-8
B. -36x+8
C. -36x-9
D. -36x+9
Answer:
D. -36x+9
Step-by-step explanation:
−12(3x−
3/4)
=(−12)(3x+ −3/
4)
=(−12)(3x)+(−12)(
−3/4)
=−36x+9
Answer:
D. -36x + 9
Step-by-step explanation:
[tex]-12[3x - \frac{3}{4}] \\ -36x + 9[/tex]
I am joyous to assist you anytime.
Please help me solve this as soon as possible.
Thanks!!
BRAINLIEST TO FIRST WHO ANSWERS
Answer:
x=-5
Step-by-step explanation:
Set up the rational expression with the same denominator over the entire equation.
2x-2/6=3x+3/6
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
2x−2=3x+3
Move all terms containing x to the left side of the equation.
−x−2=3
Move all terms not containing x to the right side of the equation.
-x=5
Multiply each term in x=−5 by −1
x=−5
For the geometric series given by 5 + 10 + 20+ . . . , which of the following statements is FALSE?
None of the other 3 statements here are False.
S₅₀₀ > S₄₉₉
S₅₀₀ > a₅₀₀
S1 = a1
Answer:
All statements are true
Step-by-step explanation:
1. The statement [tex]S_{500}>S_{499}[/tex] is true, because [tex]S_{499}[/tex] is the sum of first 499 terms, [tex]S_{500}[/tex] is the sum of first 500 terms, and all these terms are positive, then the sum of smaller number of terms is less than the sum of larger number of terms.
2. The statement [tex]S_{500}>a_{500}[/tex] is true, because [tex]S_{500}[/tex] is the sum of first 500 terms, [tex]a_{500}[/tex] is 500th term and the sum of 500 terms is greater than the 500th term.
3. The statement [tex]S_1=a_1[/tex] is true, because [tex]S_1[/tex] is the sum of first 1 term that is exactly [tex]a_1.[/tex]
All statements are true.
A square and a rhombus have the same perimeter. What about their areas? Are they the same? If not then which is bigger?
The area of a square is always larger than the area of a rhombus when they have the same perimeter.
Explanation:The areas of a square and a rhombus with the same perimeter are not equal. The square will always have a larger area than the rhombus.
To understand why, let's compare the sides and angles of a square and a rhombus.
Therefore, the square will always have a bigger area than the rhombus when both shapes have the same perimeter.
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1. In the figure below, ABC ~ PQR.
in given figure, ABC is 4 cm and PQR is 6 cm
If the area of ABC is 40 cm2, what is the area of PQR? Show your work.
2. A science museum has a spherical model of the earth with a diameter of 8.5 m. What is the volume of the model? Use 3.14 for and round your answer to the nearest whole number. Show your work.
(4 points: 1-Work shown, 1-Calculations, 1-Area, 1-Units)
Answer:
1. The area of the triangle PQR is 40 cm^2.
2. 321.4 cubic cm
Step-by-step explanation:
1. We are given two triangles, ABC and PQR, which are similar to each other.
Given that area of the triangle ABC is [tex]40cm^2[/tex], we are to find the area of the triangle PQR.
For that, we can use the ratio method:
[tex] \frac { P Q R } { 4 0 } = \frac { 6 } { 4 } [/tex]
Area of triangle PQR = [tex] \frac { 6 \times 40 } { 4 } = 60cm^2 [/tex]
2. We are given the diameter of a spherical model to be 8.5 cm so its radius will be 4.25 cm.
Finding the volume of the spherical model as we know that the volume of a sphere is given by:
[tex]\frac{4}{3} \pi r^3[/tex]
Substituting the given value of radius in the formula to get:
Volume of spherical model = [tex]\frac{4}{3} \times 3.14 \times (4.25)^3[/tex] = 321.4 cubic cm
Place the circles in order from the circle with the largest area to the circle with the smallest area.
a circle with a diameter
of 8 metersa circle with a radius
of 7 metersa circle with a circumference
of 37.68 metersa circle with a diameter
of 16 meters
Answer:
Diameter 16, radius 7, circumference 37.68, diameter 8
Step-by-step explanation:
Largest area will be in a circle with the largest radius. So let's find all radii.
d = 8, so r = 4;
r = 7;
circumference = 2pi*r = 37. 68, so r = 6
diameter 18, so r = 8
Explain how to determine if the number is a solution to the equation. 56 = 8 + 4n for n = 6
To determine if the number is a solution to the equation, we have to substitute n with the number given.
56= 8 + 4(6)
56= 8 + 24
56= 32
So no, the number is not a solution to the equation.
The number is a solution of a linear equation if both sides of the equation namely RHS and LHS are equivalent.
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here, the equation as 56 = 8 + 4n and to verify for n=6
Here, LHS =56 and RHS when n=6 is 8+4×6=32
Thus LHS≠RHS
Hence n=6 is not a solution to the equation.
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What is the length of the missing side of the triangle in simplest radical form? the figure is not drawn to scale.
Answer:
option (c)
4√34
Step-by-step explanation:
Given in the question is a right angle triangle
height of triangle = 20 cm
base of triangle = 12 cm
To find the length of missing side of the triangle we will use pythagorus theorem
hypotenuse² = height² + base²hypotenuse² = 20² + 12²
hypotenuse² = 400 + 144
hypotenuse² = 544
take square root on both sides
√hypotenuse² = √544
hypotenuse = 4√34 cm
Hence, the length of missing side of the triangle is4√34 cm
Given: Circles k1(A) and k2(O)ext. tangent
KE- tangent to k1(A) and k2(O)
AK=5, OE=4 Find: KE
There is a visual
AO is a line segment containing the radii of both circles, which are AK and OE, so AO = AK + OE = 9.
Extend AO to a point P on the line KE. Then we get two similar triangles APK and OPE. Let [tex]x[/tex] be the length of KE, [tex]y[/tex] the length of EP, and [tex]z[/tex] the length of OP.
By similarity, we have
[tex]\dfrac{OE}{AK}=\dfrac{EP}{KP}=\dfrac{OP}{AP}\iff\dfrac45=\dfrac y{y+x}=\dfrac z{z+9}[/tex]
OPE is a right triangle, so
[tex]OP^2=OE^2+EP^2\implies z=\sqrt{16+y^2}[/tex]
Now,
[tex]\dfrac45=\dfrac y{y+x}\implies 4(y+x)=5y\implies 4x=y[/tex]
and we also have
[tex]z=\sqrt{16+(4x)^2}=\sqrt{16+16x^2}=4\sqrt{1+x^2}[/tex]
Substituting this into the expression containing [tex]z[/tex] gives us an equation that we can solve for [tex]x[/tex]:
[tex]\dfrac45=\dfrac z{z+9}=\dfrac{4\sqrt{1+x^2}}{4\sqrt{1+x^2}+9}[/tex]
[tex]16\sqrt{1+x^2}+36=20\sqrt{1+x^2}[/tex]
[tex]9=\sqrt{1+x^2}[/tex]
[tex]\implies KE=x=\sqrt{80}=3\sqrt{10}[/tex]
(6CQ) Evaluate the limit, or state that the limit does not exist. 2n+7n/13n
Answer:
option(b)
9/13
Step-by-step explanation:
Given the expression
[tex]\frac{2n+7n}{13n}[/tex]
=[tex]\frac{9n}{13n}[/tex]
n will cancel out on both sides
so,
9/13 will remain
As 9/13 is a constant so any value of n when approaches to a constant will not affect it. Hence limit = 9/13
It is one of the limit laws thatThe limit of a constant function is equal to the constant.
Answer:
B
Step-by-step explanation:
A winter jacket is marked down 75% from its original price. According to the new price tag, it now costs $52.50. What was the original price?
Answer:
x = 70
Step-by-step explanation:
70 % of x = 52.50
75 out of 100 X = £ 52.50
Answer:
The Original Price of the Winter Jacket is $70
Step-by-step explanation:
The Original Price is calculated by using the given information on a Simple Rule of Three formula, which looks like the following.
X --------> 100%
$52.50 --------> 75%
The Rule of Three simply asks if $52.50 is 75% then What is 100%? We solve the Rule of Three by multiplying $52.50 by 100 and then dividing the result by 75.
[tex]X = \frac{52.50*100}{75}[/tex]
[tex]X = 70[/tex]
According to the formula the Original Price of the Winter Jacket was $70
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
3x/5-0.5=1.9
a: 0.16
b: 16
c: 4
d: 2.3
Answer:
C. 4
Step-by-step explanation:
(3x/5) - 0.5 = 1.9
+ 0.5 +0.5
3x/5 = 2.4
*5 *5
3x = 12
— —
3 3
X = 4
Answer is C
I hope I helped!
Let me know if you need anything else!
~Zoe
You roll a number cube numbered from 1 to 6. What is the probability that the number is 2,6,3,4,or 1
[tex] \frac{5 \: = \: number \: of \: favorable \: outcomes}{6 \: = \: number \: of \: possible \: outcomes} [/tex]
Since there are 6 possible outcomes, that will become the denominator. In addition, since we are trying to find the probability of rolling 5 numbers out of that 6, 5 would be the numerator.
So the answer is,
[tex] \frac{5}{6} [/tex]
The probability that the number is 2,6,3,4, or 1 is 5/6.
What is probability?Probability is the ratio that shows the likelihood that an event will occur from a given set of events.
The probability of the given event can be found as shown below:A cube has six sides. Each side has a unique number.
We have to find the probability of getting 2,6,3,4, or 1.
The total number of favorable events = 5
The sample space has 6 events.
Therefore, the probability is given by 5/6.
Therefore, we have found the probability that the number is 2,6,3,4, or 1 to be 5/6.
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A coin is tossed. The probability of getting tails is 1?2. What is the likelihood of getting tails?
It’s a 50/50 chance since there is only 2 sides. (1?2)
John picks 150 apples on the first day, 250 on the second day, 350 on the third day, and so on. How many apples does John pick on the 10th day?
1250
1150
1050
950
To determine the number of apples John picks on the 10th day, we use the formula for the nth term of an arithmetic sequence. Given the first day's pick at 150 apples and an increase of 100 apples each day, we find that John picks 1050 apples on the 10th day.
Explanation:An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant difference to the preceding term.
In this case, the first term (the number of apples picked on the first day) is 150, and the common difference (the increase each day) is 100 apples.
To find the number of apples picked on the 10th day, we use the formula for the nth term of an arithmetic sequence, which is:
an = a1 + (n - 1) × d
Where an is the nth term, a1 is the first term, n is the term number, and d is the common difference. For the 10th day:
a10 = 150 + (10 - 1) × 100
a10 = 150 + 9 × 100
a10 = 150 + 900
a10 = 1050
Therefore, John picks 1050 apples on the 10th day.
help 23 points 2 questions
A)
The lawyer in 20 years earns 3,620,000
The mathematician in 40 years earns 3,160,000
Subtract to find the difference:
3,620,000 - 3,160,000 = 460,000
The answer is the first one.
B)
Interest would be a credit of 27.23, balance = 700 + 27.23 = 723.23
Transfer would be a debit of 176.02 balance = 723.23 - 176.02 = 547.21
Deposit would be a credit of 157.00 balance = 547.21 + 157.00 = 704.21
A check would be a debit of 47.13 balance = 704.21 - 47.13 = 657.08
A plumber charges $55 per hour plus a $50 service charge. Kevin hired the plumber to install a new hot water heater. What are the total charges if the plumber took 4 hours to complete the installation?
A.
$220
B.
$250
C.
$255
D.
$270
The correct answer is D.
$55 per hour x 4 hours = $220
$220 + $50 service charge = $270 total
Hope this help.
Answer:
D. $270
Step-by-step explanation:
$55 per hour for 4 hours = $55 * 4 = $220
$50 service fee
total = hourly amount + service fee
total = $220 + $50
total = $270
70 POINTS!!!! HURRY PLEASEE!
A lab assistant tracked an object’s travel time in hours. However, the lab director wants the time tracked in minutes. customary system Help the lab assistant complete the table. How many minutes did the object travel after 2.5 hours? 100 120 150 180
Answer:
150 minutes
Step-by-step explanation:
Since your solving for minutes you need to change the 2.5 hours into minutes. There is 60 minutes in 1 hour. you take 60 and multiply it by 2.5 because you need to find the total minutes. When you multiply those teo you get 150 minutes. Please give me the brainliest answer.
:D Hoped this helped!!! Have a good day!! <3
Answer:
150 minutes
Step-by-step explanation:
1 hours = 60 minutes
We need to use the conversion factor with minutes on top
2.5 hours * 60 minutes
-------------
1 hour
Canceling hours
2.5 *60 minutes
150 minutes
Randy took out a subsidized student loan of $7,000 at a 3.6% APR, compounded monthly, to pay for his last semester of college. If he will begin paying off the loan in 10 months with monthly payments lasting for 20 years, what will be the total amount that he pays in interest on the loan?
A.) 10,128.00
B.) 9,830.40
C.) 2,830.40
D.) 3,128.00
Answer: 2830.40
Step-by-step explanation:
By using mathematical formulas for calculating compound interest and the total payment of an installment loan, and then subtracting the original loan principal, the total interest paid on the loan is identified as $9,830.40.
Explanation:To solve this problem, use the formula for the compound interest on a loan: A = P(1 + r/n)^(nt), where:
A is the total amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money). r is the annual interest rate (in decimal) (3.6% APR). t is the number of years the money is invested or borrowed for. n is the number of times that interest is compounded per unit t.
Since Randy is not going to start paying off his loan until 10 months later, the money will compound for 20 years and 10 months. Convert 10 months into years we get 10/12 = 0.833 years. Therefore, t = 20 + 0.833 = 20.833 years.
The loan was compounded monthly which means n = 12 and the rate is r = 3.6/100 = 0.036. Now you can substitute these values into the formula.
Next, find the total amount paid over the entire period of the loan by using the formula for the total payment of an installment loan: M = P*r*(1 + r)^n / [(1 + r)^n – 1], where M is monthly payment.
Subtract the principal from the total payment to find the total interest paid. From the given options, it appears that the answer is B.) $9,830.40
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A team is excavating an archeological site. The original plan was to excavate a rectangular area 35 ft long
by 20 ft wide. Instead, the team decided to excavate a similar rectangle that is 50 ft wide. Find the length
and the area of the new rectangle.
CAN SOMEONE HELP??
Answer:
Part 1) The length of the new rectangle is [tex]87.5\ ft[/tex]
Part 2) The area of the new rectangle is [tex]4,375\ ft^{2}[/tex]
Step-by-step explanation:
we know that
If two rectangles are similar, then the ratio of its corresponding sides is proportional
step 1
Find the length of the new rectangle
Let
L-----> the length of the new rectangle
[tex]\frac{50}{20}=\frac{L}{35}\\ \\ L=50*35/20\\ \\L=87.5\ ft[/tex]
step 2
Find the area of the new rectangle
we know that
The area of the rectangle is
[tex]A=LW[/tex]
we have
[tex]L=87.5\ ft[/tex]
[tex]W=50\ ft[/tex]
substitute
[tex]A=(87.5)(50)=4,375\ ft^{2}[/tex]
Five people will equally share 2 pizzas.How much pizza will each person will receive?
Answer:
⅖ pizza
Step-by-step explanation:
Divide each pizza into five slices.
Then there will be 10 slices, and each person will get two slices.
Two slices = ⅖ pizza
Each person will receive ⅖ pizza.
Each of the five people will receive 2/5 of a pizza when two pizzas are shared equally amongst them.
Explanation:The student asked how much pizza each person will receive if five people are sharing two pizzas equally. To answer this, we divide the total number of pizzas by the number of people. Since there are 2 pizzas and each pizza is usually considered to be 1 whole, when split among 5 people, each person will get 2/5 of a pizza.
What is the measure of angle A?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answer:
20
Step-by-step explanation:
You multiply the 80 and the 18 and then you add 82
Consider the line that passes through the point P(l,-3) and is parallel to the line -3x-4y=9. Write the point-slope equation of the line. Use exact values.
parallel slopes always has the same exact slope.
The equation of required line is [tex]y=-\frac{3}{4} x-\frac{9}{4}[/tex]
Slope-intercept equation :Equation of line which is given,
[tex]-3x-4y=9\\\\y=\frac{-3x+9}{4} =-\frac{3}{4}x+\frac{9}{4}[/tex]
Compare above equation with [tex]y=mx+c[/tex]
Where m is slope of line, [tex]m=-\frac{3}{4}[/tex]
The slope of parallel lines are always equal.
So that, slope of required line is also [tex]-\frac{3}{4}[/tex].
[tex]y=-\frac{3}{4} x+c[/tex]
the line that passes through the point [tex]P(1,-3)[/tex]
Substitute given point in required equation of line.
[tex]-3=-\frac{3}{4} *1+c\\\\c=-3+\frac{3}{4} \\\\c=-\frac{9}{4}[/tex]
The equation of required line is [tex]y=-\frac{3}{4} x-\frac{9}{4}[/tex]
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How many Cubes with the side length of 1/4 unit would it take to make a unit cube
Answer:
4
Step-by-step explanation:
1/4 is a quarter at up 1/4 4 time and it gives you a whole, 1/4+1/4+1/4+1/4=1