Answer:
m∠1 = 70
m∠2 = 20
Step-by-step explanation:
41 and 42 are complementary angles: m∠1 + m∠2 = 90
measure of 41 is 50° more than the measure of 42: m∠1 = m∠2 + 50
substitute: (m∠2 + 50) + m∠2 = 90
simplify and solve: 2(m∠2) + 50 = 90
2(m∠2) = 40
m∠2 = 20
You are a store clerk assigned to stack notebooks in a box for shipment. Each notebook is 29 centimeters long, 21.5 centimeters wide, and 1.5 centimeters thick. The box can hold a maximum of 12 notebooks.
To the nearest whole number of cubic centimeters, what is the minimum volume of the box?
A. 64
B. 624
C. 935
D. 7,500
E. 11,223
The minimum volume of the box = 11220 cubic centimeters
What is volume?
In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.
One notebook:
length, l= 29 cm
width = 21.5 cm
height = 1.5 cm
Volume of 1 notebook = l*w*h
= 29*21.5*1.5
= 935.25
≈ 935 cubic centimeters ( nearest whole number )
Volume of 12 notebooks = 935 * 12 = 11220 cubic centimeters
So, the minimum volume of the box = 11220 cubic centimeters
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Answer:
11,223
Step-by-step explanation:
of the car was marked as $14,000.
The price
The end of the month sale has
lowered the price to $12,500. What is the percent decrease to the nearest
percent?
Answer: the percent decrease is 9%
Step-by-step explanation:
Formula :12500/14000x100% and this formula can use in any of question likes this
6/9 times 3/8 and what is equals to
Answer:
1/4
Step-by-step explanation:
Answer:
1/4
Step-by-step explanation:
(6/9) × (3/8)
Cross simplify:
(3/3) × (1/4)
3/12
1/4
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Blake wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Blake has 950 feet of fencing, you can find the dimensions that maximize the area of the enclosure.
a) Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). Write a function for the area A of the enclosure in terms of w . (HINT: First write one equation with w and l and one equation with w and l and A. Solve for l in the first equation and substitute for l in the other). A ( w ) = ____________
b) What width w would maximize the area? w = __________________ ft
c) What is the maximum area? A = ______________ square feet
The maximum width and area of rectangle are 475 feet and 225625 sq. feet respectively.
How we can make the area of rectangle maximum?Any given rectangle has ONE region - there is no base or most extreme, simply a region. To find the region of a rectangle shape, increase the length times the width. For instance, a rectangle shape 4′ long by 5′ wide will have an area of 20 square feet.
According to question:We have
l×w = area of rectangle-------------------------(1)
2w + l = 950
l = 950 - 2w
Put the value if l in equation (1)
(950 - 2w) × w = area
This is a quadratic equation for maximum value of w we have of it one zeros is zero
so,
950 - 2w = 0
w = 950/2
W =475 feet
Te
Then length = 950 - 475 =475
Area of rectangle = 475 × 475 = 225625 sq. feet
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There is a proportional relationship between the weight and total cost of a bag of cherries. One bag weighs 2.1 pounds and costs $7.98. Another bag weighs 2.8 pounds and costs $10.64.
Describe how you would graph the proportional relationship.
PLEASE HELPPP, I got like three different answers
Answer:
y = 3.8x
Step-by-step explanation:
Let y = the cost of the cherries
Let x = pounds of cherries
We can find the unit rate by either:
[tex]\frac{7.98}{2.1}[/tex] = $3.80 per pound
or
[tex]\frac{10.64}{2.8}[/tex] = $3.80 per pound
Now we can write the equation
hy = 3.8x
Jasmine has 38 crayons. Jasmine has 24 fewer crayons than trinity. How many crayons do they have in all?
Suppose that the function f is defined, for all real numbers, as follows.
Answer:
f(-5) = 3f(-2) = -9f(1) = 0Step-by-step explanation:
You have a piecewise defined function f(x) and you want the values of f(-5), f(-2), and f(1).
The first step in finding the value of a piecewise defined function is to determine the function definition on the domain containing the x-value of interest.
F(-5)The value x=-5 is in the interval x < -2, so the first part of the function definition applies: f(x) = 3.
f(-5) = 3
F(-2)The value x = -2 is in the interval -2 ≤ x ≤ 2, so the second part of the function definition applies: f(x) = -(x -1)².
f(-2) = -(-2 -1)² = -(-3)²
f(-2) = -9
F(1)The value x = 1 is in the interval -2 ≤ x ≤ 2, so the second part of the function definition applies: f(x) = -(x -1)².
f(1) = -(1 -1)² = -(0)²
f(1) = 0
Convert the numeral to a numeral in base ten
24^five
Answer:
14 base 10
Step-by-step explanation:
Remember what the digits mean in the base 10 system we use.
For example, the number 539 (base 10) means:
The 5 in the hundreds place means 5 × 100 = 500.
The 3 in the tens place means 3 × 10 = 30.
The 9 in the ones place means 9 × 1 = 9.
The number 539 means
5 × 100 + 3 × 10 + 9 × 1 = 500 + 30 + 9 = 539
Also keep in mind one more thing. The ones digit means the number of ones. 1 = 10^0. The number in the ones digit means the number if 10^0 you have.
The ten digits is the digit of 10^1.
The hundreds digit is the digit of 10^2 since 10^2 = 100.
In other words, the ones digit is the number of 10^0 you have.
The tens digit is the number of 10^1 you have.
The hundreds digit is the number of 10^2 you have.
Now let's look at base 5.
Here, each place to the left is a successively higher power of 5 instead of a power of 10.
Think of the number 432 base 5.
The 2 is in the units place. it represents the number of 5^0 or ones you have. In this case, it is 2 × 5^0 = 2 × 1 = 2
The 3 is in the 5^1 place. It represents the number of fives you have.
3 × 5 = 15
The 4 is in the 5^2 place. It represents the number of 25's you have.
4 × 25 = 100
The number 432 base 5 means:
4 × 5^2 + 3 × 5^1 + 2 × 5^0
= 4 × 25 + 3 × 5 + 2 × 1
= 100 + 15 + 2
= 117 base 10
In other words, 432 base 5 = 117 base 10.
Now we do the same with your number, 24 base 5.
24 base 5 =
= 2 × 5^1 + 4 × 5^0
= 2 × 5 + 4 × 1
= 10 + 4
= 14
Which function is graphed below?
A. f(x) = –cos(x)
B. f(x) = cos(x)
C. f(x) = sin(x)
D. f(x) = –sin(x)
Answer:a
Step-by-step explanation:
If f(1)=3and f(n)=f(n-1)-3 then find the value of f(5)
The required value of f(5) would be 81.
What is the function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
We have been given the function below as:
f(n) = f(n-1) - 3 ....(i)
f(1) = 3
To determine the value of f(5)
Substitute the value of n = 2 in the equation (i);
f(2) = - 3f(1) = - 3;
n = 3,
f(3) = - 3f(2) = 9;
n = 4,
f(4) = - 3f(3) = - 27,
n = 5,
f(5) = - 3f(4) = 81
Thus, the required value of f(5) would be 81.
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. The electricity cost y, in dollars, to use a
hair dryer for x minutes can be represented
by the equation y = 0.002x. The electricity
cost to use a space heater is shown on the
graph. Which appliance is more expensive
to use? Explain. (Example 4)
Space Heater
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
Electricity Cost ($)
y
123456789
Time (min)
X
Answer:
D)The space heater, because it has the greater unit rate for electricity cost.
Step-by-step explanation:
I DID IT AND GOT IT RIGHT!
Find the slope of the line that passes through all of the points
on the table.
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Graph the linear function: f(x)=-2(x+4)
This is high school level math
Algebra:1
PLEASE HELP ME. I DONT UNDERSTAND WHAT IM SUPPOSED TO DO!
Please provide an explanation on how you got your answer. Thank you!
Answer:
Step-by-step explanation:
f(x) =-2 (x+4)
f(x)=2
x+4
Find the missing ange:
RPQ:______
The value of angle RPQ in the circle is 115°.
What is intersecting chords' theorem?The products of the measurements of the segments of two chords are equal if they intersect in a circle.
When two chords intersect inside a circle, the resulting angle's measure is equal to the product of the lengths of the arcs it intercepts and its vertical angle, divided by two.
Therefore,
∠RPQ = 1 / 2 (arc angle RQ + arc angle SA)
arc angle RQ = 175°
arc angle SA = 55°
Hence,
∠RPQ = 1 / 2 (175 + 55)
∠RPQ = 1 / 2 (230)
∠RPQ = 115°.
Therefore, the angle is 115°.
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2y-5+123=180
help me
Answer:
y = 31
Step-by-step explanation:
2y-5+123=180
123 - 5 = 118
2y+118=180
subtract 118 from both sides
2y+118 - 118 = 180 - 118
180 - 118 = 62
2y = 62
divide 2 by both sides
2y/2 = 62/2
y = 31
Answer:
Step-by-step explanation:
2y+−5+123=180
Step 1: (Combine Like Terms)
(2y)+(−5+123)=180
Step 2: (Subtract 118 from both sides)
2y+118−118=180−118
2y=62
Step 3: Divide both sides by 2
2y/2= 62/2
y=31
20 + 0.44x + 4 = 19 + 1.69x. please show how you got it
Answer: x =4
Step-by-step explanation: The solution of the given equation 24 + 0.44x = 19 + 1.69x will be x = 4 thus option (A) will be correct.
What is the equation?
There are many different ways to define an equation.
More than one variable may be present inside a linear equation.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
As per the given equation,
24 + 0.44x = 19 + 1.69x
24 - 19 = 1.69x - 0.44x
5 = 1.25x
x = 4
Hence "The solution of the given equation 24 + 0.44x = 19 + 1.69x will be x = 4".
() Eva left the house at 11:28 A.M. She went to the post office, returned books to the
library, and bought groceries at the store. She returned home at 12:19 P.M. How long was
she running errands?
Eva takes 51 errands (mins) to return home.
What do you mean by errands and give example ?
A short trip either to take a message or to take or collect something.
For example , I'll meet you at six, I have some errands to do/run first.
Given that :
Eva left the house at 11.28 am
Returned house at 12.19 pm
From the given information, we can conclude that how long was
she running errands
11.28 am - 12.00 pm = 32 mins
12.00 pm - 12.19 pm = 19 mins
Totally = 51 mins
Therefore, Eva takes 51 errands to return home.
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A triangle ABC. If a = 100 inches, b = 60 inches, and C= 60°, Find c.
Use the low of cosines
[tex]\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = \sqrt{a^2+b^2-(2ab)\cos(C)} \\\\[-0.35em] ~\dotfill\\\\ c = \sqrt{100^2+60^2~-~2(100)(60)\cos(60^o)} \implies c = \sqrt{ 13600 - 12000 \cos(60^o) } \\\\\\ c = \sqrt{ 13600 - 12000 \cdot \frac{1}{2} }\implies c=\sqrt{7600}\implies c=20\sqrt{19}\implies c\approx 87.18[/tex]
At a furniture store, 20% of chairs are blue, 50% orange and 30% black. A blue chair has a 20% probability of being comfortable. A chair that is not blue has a 5% probability of being comfortable. What is the probability that a comfortable chair in the store is blue?
The probability that a comfortable chair in the store is blue is 4%
How to determine the probability?From the question, we have the following parameters that can be used in our computation:
Proportion of blue chairs = 20%
Proportion of orange chairs = 50%
Proportion of black chairs = 30%
Comfortable Blue chairs = 20%
Comfortable non-blue chairs = 5%
The required probability is then calculated as
Probability = Proportion of blue chairs x Comfortable Blue chairs
Substitute the known values in the above equation, so, we have the following representation
Probability = 20% * 20%
Evaluate
Probability = 4%
Hence, the probability is 4%
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NO LINKS!! Based on each graph below, find the equation of the exponential function y= ab^x
Answer:
[tex]\textsf{a)} \quad y=3\left(\dfrac{5}{3}\right)^x[/tex]
[tex]\textsf{b)} \quad y=40\left(\dfrac{1}{3}\right)^x[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Question (a)From inspection of the diagram, two points on the graph are:
(0, 3)(1, 5)The y-intercept is the y-value when x = 0.
As a is the y-intercept, and the y-intercept is 3:
[tex]\implies y=3 \cdot b^x[/tex]
Substitute point (1, 5) into the equation and solve for b:
[tex]\begin{aligned}(1,5) \implies 5&=3 \cdot b^1\\5&=3b\\b&=\dfrac{5}{3}\end{aligned}[/tex]
Therefore, the equation of the exponential function is:
[tex]y=3\left(\dfrac{5}{3}\right)^x[/tex]
Question (b)From inspection of the diagram, two points on the graph are:
(0, 40)(-1, 120)The y-intercept is the y-value when x = 0.
As a is the y-intercept, and the y-intercept is 40:
[tex]\implies y=40 \cdot b^x[/tex]
Substitute point (-1, 120) into the equation and solve for b:
[tex]\begin{aligned}(-1,120) \implies 120&=40 \cdot b^{-1}\\\dfrac{120}{40}&=\dfrac{1}{b}\\b&=\dfrac{40}{120}\\ b&=\dfrac{1}{3}\end{aligned}[/tex]
Therefore, the equation of the exponential function is:
[tex]y=40\left(\dfrac{1}{3}\right)^x[/tex]
A man pays a total of 4800 in flat rental for 3 months. Find his monthly rental rate.
Answer:
The man's monthly rental rate is $1600.
Step-by-step explanation:
To figure out the answer to your question, it says to find how much is monthly rental is. So, we can do this by simply dividing the two numbers:
4800 ÷ 3 = $1600
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The next model of a sports car will cost 5.1% less than the current model. The current model costs $37,000 how much will the price decrease in dollars? What will be the price of the next model?
Decrease in the price is $1887, the price of the next model car is $35,113.
What is percentage?Percentage is a measurement to find value of the given number out of hundred.
Given that,
Price of current model = $37,000
The price of next model car is 5.1% less than the current model.
The price of the next model car = 94.9% of price of current model car
= 94.9 x 37,000/100
= 35,113
The decrease in the price = 37,000 - 35,113 = 1887
The price of the next model car is $35,113 and decrease in the price is $1887.
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please help me! i have a test rn and i am struggling. please send answer ASAP!!
Find an equation for line l,m,n,p
The linear functions in this problem are given as follows:
Line l: y = 4.Line m: y = -2x + 4.Line n: y = x - 1.Line p: x = -4.How to define the linear functions?First we define the horizontal line l, given as follows:
l: y = 4.
(as no matter the value of x, the output variable assumes a value of 4).
Then the vertical line p is defined as follows:
p: x = -4.
(as no matter the value of the output y, the input variable x assumes a value of -4).
For the remaining two lines, they are defined in the slope-intercept format, as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope, representing by how much y changes when x is increased by one.b is the y-intercept, representing the value of y when the function crosses the x-axis, that is, when x = 0.More can be learned about linear functions at https://brainly.com/question/24808124
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which of the following rational functions is graphed below? A. F(x)=(x+2)/(x-2) B. F(x)=(x-1)/x(x-2) C. F(x)= (x+2)/(x+1) D. F(x)= (x+1)/(x+2)(x-2)
Answer:
[tex]C. \; \dfrac{x+2}{x+1}[/tex]
Step-by-step explanation:
Since the vertical asymptotes are at x = -1
This means the denominator must have x + 1 in it
The only expression is the one in choice C
What is 3 3/4 ft to yards as a mixed number?
The value of 3¾ft in yards would be = 1 6/25 yard
What is a mixed number?A mixed number is the type of number that is made up of three parts such as the whole number, a numerator and a denominator.
To convert to yards;
1 ft = 0.33 yard
3¾ = X yards
make x yards the subject of formula;
X yards = 3¾ × 0.33
X yards = 3.75×0.33
X yards = 1.24 yards
X yards in mixed number= 124/100 = 31/25 = 1 6/25 yard.
Note that the final value which is 124/100 is reduce to the lower figure by dividing through with 4 to arrive at the mixed number 1⁶/25
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A kindergarten teacher has five books to distribute to 20 children in her class.
(a)
How many ways are there for her to distribute the books if they are all the same and no child gets more than one?
(b)
How many ways are there for her to distribute the books if they are different and no child gets more than one? If Charlie gets Green Eggs and Ham and Amanda gets The Cat in the Hat, that is a different distribution from one in which Amanda gets Green Eggs and Ham and Charlie gets The Cat in the Hat.
(c)
How many ways are there for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child?
Answer:
(a) There are 20 ways for her to distribute the books if they are all the same and no child gets more than one. Each of the 20 children can receive one of the five books.
(b) There are 100 ways for her to distribute the books if they are different and no child gets more than one. Each of the 20 children can receive one of the five different books, so there are 5x4x3x2x1 = 100 possible ways for her to distribute the books.
(c) There are 3,628,800 ways for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child. This is because each child can receive any number of books from 0 to 5. Therefore, there are 6x6x6x6x6 = 6^5 = 3,628,800 possible ways for her to distribute the books.
Step-by-step explanation:
Help i think it’s b i don’t know!!
Answer: It is B
Step-by-step explanation:
If you put leg a (3) and leg b (4) into a Pythagorean equation it will turn out like this
3^2+4^2=x^2
9+16=x^2
25=x^2
√25=√x
5=x
5 is the missing side length, which corresponds to option b
1)What value of b will complete the square in the expression below and make the expression a perfect square trinomial? X^2+bx+16/49
2) Enter the perfect square trinomial as a squared binomial.
The value of b in x²+ bx + 16/49 is 8/7 and the squared binomial is (x + 4/7)²
How to determine the value of b?From the question, we have the following parameters that can be used in our computation:
X^2+bx+16/49
Rewrite properly
So, we have the following representation
x²+ bx + 16/49
When represented as a square, we have
x²+ bx + 16/49 = (x + a)²
Expand the bracket
So, we have the following representation
x²+ bx + 16/49 = x² + 2ax + a²
By comparison, we have
bx = 2ax
a² = 16/49
Take the square root of both sides
a = 4/7
Substitute a = 4/7 in bx = 2ax
bx = 2 * 4/7x
So, we have
b = 2 * 4/7
Evaluate
b = 8/7
The squared binomialIn (a), we have
x²+ bx + 16/49 = (x + a)²
Where
a = 4/7
So, we have
x²+ bx + 16/49 = (x + 4/7)²
Hence, the binomial is (x + 4/7)²
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Answer:
[tex]\textsf{1)} \quad b = \dfrac{8}{7}[/tex]
[tex]\textsf{2)} \quad \left(x+\dfrac{4}{7}\right)^2[/tex]
Step-by-step explanation:
Perfect Square Trinomial
A trinomial that can be written as the square of a binomial.
For example the perfect trinomial x²+2dx+d² can be written as (x+d)².
Given trinomial:
[tex]x^2+bx+\dfrac{16}{49}[/tex]
To express the given trinomial as a perfect square trinomial, determine the value of b.
As the coefficient of the x² term is one, b equals twice the square root of the constant of the trinomial:
[tex]\implies b = 2 \sqrt{\dfrac{16}{49}}[/tex]
[tex]\implies b = 2 \cdot \dfrac{4}{7}[/tex]
[tex]\implies b = \dfrac{8}{7}[/tex]
Therefore, the perfect square trinomial is:
[tex]x^2+\dfrac{8}{7}x+\dfrac{16}{49}[/tex]
To factor in the form of a squared binomial (x + d)², d is half the value of b:
[tex]\implies d = \dfrac{1}{2}b[/tex]
[tex]\implies d = \dfrac{1}{2} \cdot \dfrac{8}{7}[/tex]
[tex]\implies d=\dfrac{8}{14}[/tex]
[tex]\implies d=\dfrac{4}{7}[/tex]
Therefore, the perfect square trinomial as a squared binomial is:[tex]\implies \left(x+\dfrac{4}{7}\right)^2[/tex]
You are saving to buy a brand new car in 6 years? You predict the car will cost $32000 but you have already saved $6500.
How much work do you have if you put the $6,500 in an account paying 5% APR compounded continuously?
How much should you invest into an account paying 5% APR compounded continuously to have the entire $32000 in the 6 years?
The amount you will have $6,500 with 5% in six years using continuous compounding is of:
$8,774.
The amount you will need to have the entire $32000 in the 6 years is of:
$18,890.46.
What is continuous compounding?The balance of an account after t years, using continuous compounding, is given as follows:
[tex]B(t) = Pe^{kt}[/tex]
In which the parameters are given as follows:
P is the principal, which is the initial investment.k is the APR, as a decimal.Putting the $6,500 into the account, the values of the parameters are given as follows:
P = 6500, k = 0.05, t = 6.
Hence the balance will be of:
B(6) = 6500 x e^(0.05 x 6) = $8,774.
The balance to have the entire $32,000, considering what you already have, will be of:
32000 - 6500 = 25500
Hence the principal is obtained as follows:
Pe^(0.05 x 6) = 25500
P = 25500/e^(0.3)
P = $18,890.46.
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Find the missing number so that the equation has no solutions
–2x + 11 = x + 21 + __x
a 5
b 2
c -2
d -3
Answer: d -3
Step-by-step explanation:
The answer I got was 11 = 21, which does not make sense
–2x + 11 = x + 21 + (-3)x
+3x +3x
x + 11 = x + 21
-x -x
11 = 21
Answer:
-3
Step-by-step explanation: