\( \frac{1.65}{8} \)
\( \frac{0.825}{4} \)
\( \frac{0.4125}{2} \)
\(0.20625\)
8.2: Word Problems - UNDERLINE key words, set up your division sentence, then solve!
Ms. K's cooking club needs 2 1/4 cups of flour to make enough crepes for everyone in the class. The
club split into 6 smaller groups, each making their own batch. How much flour does each group
need?
Answer:
3/8
Step-by-step explanation:
hope it helps :)
calculate the VAT charged on this amount R1599.00(VAT included)
Answer:
VAT = R239.85
Step-by-step explanation:
VAT = 15%
15/100 = 0.15
R1599 × 0.15 = 239.85
VAT = R239.85
AN EQUilateral triangle has side length 10 centimeters. find its area in square centimeters. Hint: the altitude of an equilateral triangle is the perpendicular bisector of its base
Answer:
Step-by-step explanation:
A cylindrical soup can is 5 inches tall and contains 11.25π cubic inches of soup. What is the diameter of the can to the nearest hundredth of an inch?
\(\\ \sf\longmapsto V=\pi r^2h\)
\(\\ \sf\longmapsto 11.25=5\pi r^2\)
\(\\ \sf\longmapsto 2.25=\pi r^2\)
\(\\ \sf\longmapsto r^2=2.25/3.14=0.71\)
\(\\ \sf\longmapsto r=\sqrt{0.71}\)
\(\\ \sf\longmapsto r=0.84in\)
Answer:
Diameter is 3.00 inches
Step-by-step explanation:
» Volume of a cylindrical soup is given a formula below:
\({ \tt{volume = \pi {r}^{2} h}}\)
r is radiush is height\({ \tt{11.25\pi = \pi( {r}^{2} ) \times 5}}\)
» Divide either sides by 5π
\({ \tt{ \frac{11.25\pi}{ \green{5\pi}} = \frac{\pi {r}^{2} \times 5}{ \green{5\pi}} }} \\ \\ { \tt{2.25 = {r}^{2} }} \\ { \tt{ \sqrt{ {r}^{2} } = \sqrt{2.25} }} \\ { \tt{r = 1.5 \: in}}\)
» From identical circular formulae, diameter is twice radius:
\( { \boxed{ \tt{ \: diameter = 2 \times radius \: }}} \\ { \tt{d = 2 \times 1.5}} \\ { \tt{d = 3 \: inches}}\)
PLEASE HELP I WILL GIVE BRAINLYEST
∠13 = 70.5° [Vertically Opposite angles]
∠13+∠14=180° [Linear pair]
70.5°+∠14=180°
∠14=180-70.5
∠14=109.5
∠15=∠14=109.5 [Vertically opposite angles]
∠13=∠12= 70.5° [Co-interior angles]
∠12=∠10= 70.5° [Vertically Opposite angles]
∠14=∠11=109.5 [Co-interior angles]
∠9=∠11= 109.5 [Vertically opposite angles]
∠13=∠7= 70.5° [Alternate interior angles]
∠7=∠5=70.5° [Vertically Opposite angles]
∠7+∠8=180° [Linear Pair]
70.5+∠8=180
∠8=180-70.5
∠8=109.5°
∠8=∠6= 109.5° [Vertically Opposite angles]
∠6=∠3=109.5° [Co-interior angles]
∠7=∠2=70.5° [Co-exterior angles]
∠2=∠4= 70.5° [Vertically Opposite angles]
∠3=∠1= 109.5° [Vertically Opposite angles]
\(\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}\)
Measures of all angles in sequence⤵️∠1= 109.5°∠2= 70.5°∠3= 109.5°∠4= 70.5°∠5= 70.5°∠6= 109.5°∠7= 70.5°∠8= 109.5°∠9= 109.5°∠10= 109.5°∠11= 70.5°∠12= 109.5°∠13= 70.5°∠14= 109.5°∠15= 109.5°∠16= 70.5°Answer:
Angles 1, 3, 5, 7, 9, 11 and 13 = 70.5°
Angles 2, 4, 6, 8, 10, 12, 14 and 15 = 109.5°
Step-by-step explanation:
Angle Theorems used:
Linear pair : a pair of adjacent angles formed when two lines intersect. The two angles of a linear pair are always supplementary (two angles whose measures add up to 180°)Alternate interior angles : when two parallel lines are cut by a transversal (a line that intersects two or more other, often parallel, lines), the resulting alternate interior angles are congruent.Alternate exterior angles : when two parallel lines are cut by a transversal (a line that intersects two or more other, often parallel, lines), the resulting alternate exterior angles are congruent.Vertical angles : a pair of opposite angles formed by intersecting lines. Vertical angles are always congruent.Angles 1, 3, 5, 7, 9, 11 and 13 = 70.5°
180 - 70.5 = 109.5°
Angles 2, 4, 6, 8, 10, 12, 14 and 15 = 109.5°
a question was asked by a teacher to a student. She gave the student a jumbled word and told him to make words out of it. The jumbled word is gzeysktqix. Now you know what to do. see ya!
The teacher's question, the student can provide a List of words including "sixty," "zesty," "skit," "site," "size," "exit," "yeti," "kits," "kite," and "ties."
Let unscramble the jumbled word "gzeysktqix" and find the possible words that can be formed.
Upon unscrambling, we can find several possible words:
1. Sixty
2. Zesty
3. Skit
4. Site
5. Size
6. Exit
7. Yeti
8. Kits
9. Kite
10. Ties
These are some of the words that can be formed from the jumbled letters "gzeysktqix." There may be additional words that can be created, depending on the specific rules or restrictions given by the teacher.
Unscrambling words can be a fun and challenging exercise that helps improve vocabulary, word recognition, and problem-solving skills. It allows students to enhance their language abilities and discover new words they might not have known before.
Remember, the key is to rearrange the given letters systematically and try different combinations until meaningful words are formed.
So, in response to the teacher's question, the student can provide a list of words including "sixty," "zesty," "skit," "site," "size," "exit," "yeti," "kits," "kite," and "ties."
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i need some help plzzzzzzzz
Answer:
help with what?
Step-by-step explanation:
Does this table of values represent a linear relationship? Explain your answer.
Answer:
Yes
Step-by-step explanation:
Yes, because there is a constant rate of change. It is and will always be constantly increasing by 1.5.
To be a linear line you have to have a constant rate of change.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
C
Step-by-step explanation:
cot²θ = 1/tan²θ
plug this in to get
1/(1/tan²θ + 1)
1/tan²θ + 1 = 1/tan²θ + tan²θ/tan²θ = (1+tan²θ)/tan²θ
we then have
1/((1+tan²θ)/tan²θ)
1/(x/y) = y/x, so this is equal to
tan²θ/(1+tan²θ)
tan²θ = sin²θ/cos²θ, so plug this in to get
(sin²θ/cos²θ)/(1+sin²θ/cos²θ)
1+sin²θ/cos²θ = cos²θ/cos²θ + sin²θ/cos²θ
sin²θ + cos²θ = 1, so we have
(cos²θ+sin²θ)/cos²θ = 1/cos²θ. plug this in to get
(sin²θ/cos²θ)/(1/cos²θ)
(a/b)/(c/d) = (d/c) * (a/b), so we have
(sin²θ/cos²θ)/(1/cos²θ) = cos²θ/1 * sin²θ/cos²θ = sin²θ
A dairy needs 285 gallons of milk containing 6% butterfat. How many gallons each of milk containing 8% butterfat and milk containing 3% butterfat must be used to obtain the desired 285 gallons?
The number of gallons of 8% butterfat is 139 and the number of gallons of 3% butterfat milk is 146.
What is equation?An equation is a statement that two mathematical expressions have values that are equal. Simply said, an equation proves that two things are equal. It is denoted by the equals sign, or "=."
Given:
A dairy needs 285 gallons of milk containing 6% butterfat,
The other milk is 8% butterfat and milk containing 3% butterfat,
Assume, the number of gallons of 8% butterfat milk is M then,
The number of gallons of 3% butterfat milk is = 285 - M,
Write the equation as shown below,
M × 8% + (285 - M) × 3% = 6% × 258
Solve for the value of M as shown below,
0.08 M + 8.55 - 0.03 M = 15.48
0.05 M = 6.93
M = 138.6 or 139
The number of gallons of 3% butterfat milk is = 285 - 139 = 146
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NEED HELP!!!!!!!!!!!!!!!!!!!!!!
Answer:
The third answer
Step-by-step explanation:
if p is equivalent to q then q must be equivalent to p. I’m not 100% sure but that’s my best guess. I hope this helps :)
Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
By solving a linear equation, it can be calculated that-
First fourth and fifth option are correct
What is a linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Length of two sides of a right angled triangle = x, x+2
Area = \(\frac{1}{2}\times x \times (x + 2)\)
By the problem,
The linear equation is
\(\frac{1}{2}\times x \times (x + 2) = 24\\\)
0.5x(x + 2) = 24
First option is correct
x(x + 2) = 48
\(x^2 + 2x - 48 = 0\)
Fourth option is correct
For the sixth option,
\(x^2 + (x + 2)^2 = 100\\x^2 + x^2 + 4x + 4 - 100 = 0\\2x^2 + 4x - 96 = 0\\2(x^2 + 2x - 48) = 0\\x^2 + 2x - 48 = 0\)
Which is the third option.
First fourth and fifth option are correct
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Express the first quantity as percentage of the second of 45g and 75g
The first quantity (45g) as 60 percentage of second (75g).
What do you mean by Percentage?A part of whole expressed in Hundredth. Percentage is a fraction of a number out of 100%. It can be in fraction or in decimal.
To convert the given percentage value in decimal, divide the given value by 100.
For example:
1. 50% in decimal or fraction will be 50/100 = 0.5.
2. 20% in decimal or fraction will be 20/100 = 0.2.
How to calculate Percentage?1. Finding the total amount from which we need to find the percent.
2. Dividing the required amount to find the percentage by total amount.
3. Multiply it by 100.
For example:
1. It rained 10 of the 30 days in April.
Percentage will be 10/30 = (1/3) x 100
Percentage = 33.33%
Here, we have given that:
Total amount = 75g
Required amount for percent = 45g
Now, to find the percentage:
Percentage = 45/75
Percentage = 0.6 x 100
Percentage = 60%
Hence,
The first quantity (45g) as 60 percentage of second (75g).
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11. Mike has a 792-page book. If he reads 36 pages each day,
how many days will it take him to finish reading the book?
Answer:
22 days
Step-by-step explanation:
Number of pages divided by number of pages he reads per day
792 ÷ 36 = 22
Hope this helped :)
Answer:
22
Step-by-step explanation:
792÷36=22
ok??:)) isksjsix
Jacob invests $8,634 in a savings account with a fixed annual interest rate of 2.67% compounded continuously. How long will it take to reach $25,000 dollars?
After answering the provided question, we can conclude that As a result, with continuous compounding at a fixed annual interest rate of 2.67%, Jacob's investment will reach $25,000 in approximately 30.6 years.
what is interest ?In mathematics, interest refers to the amount of revenue raised or owed on an original cost or loan. You can use either simple or compound interest. Simple interest is determined by a proportion of the original amount, whereas compound interest is calculated on the principal amount and as well as any previously earned interest. If you put money $100 at a 5% yearly simple interest rate, visitors will earn $5 in interest every year for three years, for a total of $15.
To solve this problem, we can use the continuous compounding formula:
\(A = Pe^(rt)\\25000 = 8634e^(0.0267t)\\e^{(0.0267t)}= 2.893\\0.0267t = ln(2.893)\\t = ln(2.893) / 0.0267 ≈ 30.6 years\\\)
As a result, with continuous compounding at a fixed annual interest rate of 2.67%, Jacob's investment will reach $25,000 in approximately 30.6 years.
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The pressure, P (in lbs/ft2 ), in a pipe varies over time. Five times an hour, the pressure oscillates from a low of 90 to a high of 230 and then back to a low 90. The pressure at t = 0 is 90.
Question: Find a possible formula for P=f(t)
P=160-70*cos(2π*(1/12)*t)
• Pressure in mathematics or physics is defined as force per unit area. The pressure exerted by a solid object which is resting on top of a solid surface is the weight divided by the area of the object . SI unit of force is Newton (N).
First, we find the amplitude by taking the difference between the peak values and dividing by two:
Amplitude=(230+90)/2=70
We can find the center value by either adding 70 to the minimum or subtracting 70 from the maximum:
90+70=160
230-70=160
This tells us that the Center Value=160
The frequency that we are operating at is given as:
f = 5/hour
so in minutes
f=5*(1/60)/minute=5/60=1/12 per minute
So, combining everything we get
P=160-70*cos(2π*(1/12)*t)
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plz answer will give brainliest
help meeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
Step-by-step explanation:
if a teenager receives 4 tokens for finishing first place in an arcade game, which table correctly represents the realtionship between the number of tokens the teenager receives and the number of first place finishes the teenager completes?
Answer:
The first chart.
Step-by-step explanation:
The first table. The chart gives a ratio of 1:4, which is the same as the amount the teenager made.
can someone help me solve this ill mark u as brainlest
Answer:
-13 ≤ x ≤ 11
Step-by-step explanation:
|x+1| ≤12
There are two solutions, one positive and one negative, remembering to flip the inequality for the negative
x+1 ≤12 x+1 ≥-12
Subtract 1 from each side
x+1-1 ≤12-1 and x+1-1 ≥-12-1
x ≤11 and x ≥-13
-13 ≤ x ≤ 11
Equation A is equal to (C + D) x (C + D). Equation B is equal to 2 x (C + D). If C and D were numbers that were greater than zero, which equation would give you a bigger value ? Equation A or Equation B ? Give an example for C and D that supports your answer. PLEASE HELP TIMED EXAM!!!!!
According to the question an example of C = 3 and D = 2 supports the answer that Equation A gives a bigger value than Equation B.
What is equation?Two equations are considered to be comparable when their roots and solutions line up. To create an equivalent equation, the identical quantity, symbol, or expression has to be added to or removed from both of the equation's two sides. We can also create a similar equation by dividing or multiplying each component of an equation with a nonzero value.
given,
To determine which equation would give a bigger value, we can compare the expressions obtained by expanding Equation A and simplifying Equation B.
Expanding Equation A, we get:
A = (C + D) x (C + D) = C² + 2CD + D²
Simplifying Equation B, we get:
B = 2 x (C + D) = 2C + 2D
To compare the values of A and B, let's choose some values for C and D that are greater than zero. Let's choose C = 3 and D = 2.
Plugging these values into Equation A, we get:
A = 3² + 2(3)(2) + 2² = 9 + 12 + 4 = 25
Plugging these values into Equation B, we get:
B = 2(3 + 2) = 2(5) = 10
Since A is greater than B for the values of C = 3 and D = 2, we can conclude that Equation A gives a bigger value than Equation B for positive values of C and D.
Therefore, an example of C = 3 and D = 2 supports the answer that Equation A gives a bigger value than Equation B.
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You deposit $500 at 6% interest annually. After 6 months, how much money will you earn?
Write an equation in slope-intercept form of the line shown.
An equation is
Using the slope intercept formula, the equation for the line in slope intercept form is y = -x - 4
Slope intercept equationThe slope intercept equation can be describe as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore,
(-4, 0)(1, -5)
m = -5 - 0 / 1 + 4 = -5 / 5 = -1
Therefore, let's find b using (1, -5)
-5 = -1(1) + b
-5 = -1 + b
b = -5 + 1
b = -4
Therefore, the equation is y = -x - 4
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Which equation can be used to solve for x xx in the following diagram? Choose 1 answer: (Choice A) A ( 5 x + 30 ) − 5 x = 90 (5x+30)−5x=90left parenthesis, 5, x, plus, 30, right parenthesis, minus, 5, x, equals, 90 (Choice B) B ( 5 x + 30 ) + 5 x = 180 (5x+30)+5x=180left parenthesis, 5, x, plus, 30, right parenthesis, plus, 5, x, equals, 180 (Choice C) C ( 5 x + 30 ) + 5 x = 90 (5x+30)+5x=90left parenthesis, 5, x, plus, 30, right parenthesis, plus, 5, x, equals, 90 (Choice D) D 5 x = ( 5 x + 30 ) 5x=(5x+30)
Answer: answer is C
Step-by-step explanation:
for find x
(5x+30)+5x=90
5x+30+5x=90 add like terms
after,
10x+30=90
10x+30-30=90-30
10x/10=60/10
x = 6
to obtain answer as C
it mean
(5x+30)+5x=90
(5(6)+30)+5(6)=90 we know x=6 so add 6 to x and multiply and obtain answer is correct!
30+30+30=90
The value of a certain collectible card in dollars from January 2020 to May 2021 can be modeled by the function V(m)=250m2 – 3,500m + 18,000, where m is the approximate number of months since the start of 2020.
Over what period was the value of the card declining?
< m
If the value of a certain collectible card in dollars from January 2020 to May 2021 can be modeled by the function V(m)=250m² – 3,500m + 18,000, the value of the card was declining over the period 0 < m < 7.
To determine when the value of the collectible card was declining, we need to look for when the first derivative of the function is negative. If the first derivative of the function is negative over a certain period, then the function is decreasing over that period. The first derivative of the function V(m) is:
V'(m) = 500m - 3,500
To find when the value of the card was declining, we need to solve the inequality V'(m) < 0. Solving for m, we get:
500m - 3,500 < 0
500m < 3,500
m < 7
Therefore, the value of the card was declining over the period 0 < m < 7. This corresponds to the months from January 2020 to July 2020. During this period, the first derivative of the function V(m) is negative, which means the value of the card was decreasing.
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Find the equation of a sphere if one of its diameters has endpoints: (-9, -12, -6) and (11, 8, 14).
= 0
Answer:
Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is \((x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30\).
Step-by-step explanation:
There are two kew parameters for a sphere: Center (\(h\), \(k\), \(s\)) and Radius (\(r\)). The radius is the midpoint of the line segment between endpoints. That is:
\(C(x,y,z) = \left(\frac{-9+11}{2},\frac{-12+8}{2},\frac{-6+14}{2} \right)\)
\(C(x,y,z) = (1,-2,4)\)
The radius can be found by halving the length of diameter, which can be determined by knowning location of endpoints and using Pythagorean Theorem:
\(r = \frac{1}{2}\cdot \sqrt{(-9-11)^{2}+(-12-8)^{2}+(-6-14)^{2}}\)
\(r = 10\sqrt{3}\)
The general formula of a sphere centered at (h, k, s) and with a radius r is:
\((x-h)^{2}+(y-k)^{2}+(z-s)^{2} = r^{2}\)
Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is \((x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30\).
x power 8 + x power 4 + 1
factorize
Answer:
\(1(x {}^{8} + x {}^{4} + 1)\)
Step-by-step explanation:
\(x {}^{8} + {x}^{4} + 1 =1( x {}^{8} + x {}^{2} + 1)\)
Hope this helps ;) ❤❤❤
Let me know if there is an error in my answer.
find the steps to find the inverse
The inverse of f(x) = x^(7/9) using exponential notation is f(x) = x^(9/7)
what are inverse functions?An inverse function in mathematics is a function that "undoes" another function.
In other words, if f(x) yields y, then y entered into the inverse of f yields the output x.
An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹.
How to find the inverse functionThe given function is of the form
f(x) = x^(7/9), this is equivalent to ⁹√x⁷
say f(x) = y, then
f(x) = y = x^(7/9)
y = x^(7/9)
solving for the inverse, of y = x^(7/9)
y = x^(7/9)
y^(9/7) = x
interchanging the letters
y = x^(9/7)
hence the inverse function is solved to be f⁻¹(x) = x^(9/7)
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Find the value of x.
Answer:
\(\huge\boxed{x=\sqrt{66}}\)
Step-by-step explanation:
ΔADC and ΔABD are similar (AAA)
Therefore the cooresponging sides are in proportion:
\(\dfrac{AD}{AC}=\dfrac{AB}{AD}\)
Substitute
\(AD=x;\ AC=6+5=11;\ AB=6\)
\(\dfrac{x}{11}=\dfrac{6}{x}\) cross multiply
\((x)(x)=(11)(6)\\\\x^2=66\to x=\sqrt{66}\)
Please help!!!
A movie theatre sold tickets to three movies. The tickets to the
first movie were $16, the tickets to the second movie were $13,
and the third movie was $18. 100 tickets were sold to the first
movie. The total number of tickets sold was 310, for a total
revenue of $4,980. How many tickets for each movie were sold?
Answer:
100, 197, 13
Step-by-step explanation:
Total revenue from 1st movie
16×100 = 1600
Revenue from 2nd and 3rd movie = 4980 - 1600 = 3380
Total number of tickets sold = 310
Number of tickets sold for 2nd and 3rd movie combined = 310 - 100 = 210
Let x be number of 2nd movie tickets, y be number of 3rd movie tickets
x + y = 210, multiplying this by 13,
13x + 13y = 2730 (1)
13x + 18y = 3380 (2)
(2) - (1)
5y = 650
y = 13
x = 197