Answer:
1:3
Step-by-step explanation:
if a + b = 4a then b has to be 3a
(1) + (3) = 4(1)
(2) + (6) = 4(2)
it works no matter what you plug in for a
To find the ratio a:b given that a+b=4a, we rearrange the equation to find b=3a, and then simplify the ratio to get 1:3.
Explanation:To find the ratio a:b, given that a+b=4a, we first need to express b in terms of a. This can be done by subtracting a from both sides of the equation:
a + b - a = 4a - a
b = 3a
Now that we have b expressed as 3a, we can find the ratio of a to b:
a : b = a : 3a
As we can simplify the ratio by dividing both terms by a (assuming a is not zero):
a : b = 1 : 3
Therefore, the ratio of a to b is 1:3.
Which ordered pair is a solution of this equation? -7x - 5y = 42
(-5,0)
(0,-5)
(0,-6)
(-6,0)
(-6,0) is the ordered pair for this solution, you might want to double check though
-6,0 is the answer just substitute the numbers and boom
In order to go on the field trip, you must accrue 75 positive behaviors points. You found out that you have 45% of the points necessary to go. How many points do you have?
Answer:
Step-by-step explanation:
I think 33 : this i got by multiplying 75 by 45%
or 166: i got this by dividing 75 by 45%
The total points for 75 positive behaviors points are 33.45.
We have given that,
n order to go on the field trip, you must accrue 75 positive behavior points. You found out that you have 45% of the points necessary to go.
We have to determine the points.
What are the positive behavior points?Positive behavior strategies are evidence-based, proactive approaches to changing challenging student behavior.
We have 75 are the positive points so we have,
[tex]75\times 0.45=33.75[/tex]
Therefore we get the total points are 33.45.
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The area of the triangle is 3ft2. The height of the triangle is 2ft and the base of the triangle is ft
Answer: 3
Step-by-step explanation: 1/2 times, the height which is 3 and times 2 equals the base which is 3.
Determine the area of the composite figure to the nearest whole number
Check the picture below.
so, let's notice, is really just a 2x20 rectangle with a quarter of a semicircle with a radius of 11.
[tex]\bf \stackrel{\textit{area of a circle}}{A=\pi r^2}~~ \implies A=\pi 11^2\implies A=121\pi \implies \stackrel{\textit{one quarter of that}}{\boxed{A=\cfrac{121\pi }{4}}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\underline{\textit{area of the figure}}}{\stackrel{\textit{rectangle's area}}{(2\cdot 20)}+\stackrel{\textit{circle's quart's area}}{\cfrac{121\pi }{4}}\qquad \approx \qquad 135.03\implies \stackrel{\textit{rounded up}}{135}}[/tex]
Answer:
i think its A
Step-by-step explanation:
Find the number a such that the line x = a divides the region bounded by the curves x = y^2 − 1 and the y-axis into 2 regions with equal area. Give your answer correct to 3 decimal places.
[tex]x=y^2-1\implies y=\pm\sqrt{x+1}[/tex]
We want to find [tex]a[/tex] such that
[tex]\displaystyle\int_{-1}^a2\sqrt{x+1}\,\mathrm dx=\int_a^02\sqrt{x+1}\,\mathrm dx[/tex]
On the left,
[tex]\displaystyle\int_{-1}^a2\sqrt{x+1}\,\mathrm dx=4(x+1)^{3/2}\bigg|_{x=-1}^{x=a}=4(a+1)^{3/2}[/tex]
and on the right,
[tex]\displaystyle\int_a^02\sqrt{x+1}\,\mathrm dx=4(x+1)^{3/2}\bigg|_{x=a}^{x=0}=4-4(a+1)^{3/2}[/tex]
For the areas to be equal, we need
[tex]4(a+1)^{3/2}=4-4(a+1)^{3/2}\implies(a+1)^{3/2}=\dfrac12[/tex]
[tex]\implies a=\dfrac1{2^{2/3}}-1\approx-0.370[/tex]
To find the value of 'a' for which the line x = a splits the region into two equal areas, integrate the curve starting from -sqrt(a+1) to sqrt(a+1) and set it equal to the area of the region between the curve and the y-axis.
Explanation:This question pertains to the concept of finding the area under curves in Calculus. To solve this problem, we need to set up an equation that represents the given situation and solve for 'a'. The line 'x = a' splits the region into two equal areas, meaning the area on the right of the line is equal to the area on the left of the line.
Starting from the x-axis, the curve 'x = y^2 - 1' intersects the line at y = sqrt(a+1) and y = -sqrt(a+1). Thus, we want the integral from -sqrt(a+1) to sqrt(a+1) of the curve to be equal to the area of the region between the curve and the y-axis. Formulate and solve the intergral problem to get the desired value of 'a'.
Additionally, this problem might involve the use of numerical methods like the Simpson's rule or midpoint rule to get an accurate result.
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Jesse is baking several cakes for a bake sale. A pound bag of flour is enough to make 4 cakes. How much flour is needed to make 1 cake?
Answer:
4 ounces of flour will make 1 cake.
Step-by-step explanation:
16 ounces = 1 pound
16 ounces divided by 4 cakes = 4 ounces for 1 cake
Jesse needs ⅔ pound or 0.125 pounds (2 ounces) of flour to make one cake, calculated by dividing the half-pound bag of flour by the number of cakes it can produce (4 cakes).
Explanation:Jesse is baking cakes for a bake sale and needs to know how much flour is needed for one cake.
From the information provided, we know that a ½ pound bag of flour is enough to make 4 cakes.
To determine how much flour is needed for one cake, we use a simple division.
To find the amount of flour per cake, we divide the total amount of flour by the number of cakes that can be made from it. That gives us:
½ pound flour ÷ 4 cakes = ⅔ pound flour per cake.
Therefore, Jesse needs ⅔ pound (which is 0.125 pounds or 2 ounces) of flour to make one cake.
Which of the following tables shows the correct steps to transform x2 + 8x + 15 = 0 into the form (x − p)2 = q? [p and q are integers] (5 points) Step 1 x2 + 8x + 15 − 2 = 0 − 2 Step 2 x2 + 8x + 13 = −2 Step 3 (x + 4)2 = −2 Step 1 x2 + 8x + 15 − 1 = 0 − 1 Step 2 x2 + 8x + 14 = −1 Step 3 (x + 4)2 = −1 Step 1 x2 + 8x + 15 + 2 = 0 + 2 Step 2 x2 + 8x + 17 = 2 Step 3 (x + 4)2 = 2 Step 1 x2 + 8x + 15 + 1 = 0 + 1 Step 2 x2 + 8x + 16 = 1 Step 3 (x + 4)2 = 1
The correct steps are:
start with
[tex]x^2+8x+15=0[/tex]
Add 1 to both sides:
[tex]x^2+8x+16=1[/tex]
The left hand side is a perfect square:
[tex](x+4)^2=1[/tex]
Answer:
Option D
Step-by-step explanation:
The given expression is x² + 8x + 15 = 0
We have to solve it further to transform into the form ( x - p )² = q
x² + 8x + 15 = 0
[ x² + 8x + 15 ] + 1 = 0 + 1
x² + 8x + 16 = 1
( x + 4 )² = 1
Option D is the answer.
Solve.
x2 + x – 6 = 0
{2, –3}
{6, –1}
{3, –2}
{2, 3}
Answer:
x = - 3, x = 2
Step-by-step explanation:
Given
x² + x - 6 = 0 ← in standard form
To factorise the quadratic
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (+ 1)
The factors are + 3 and - 2, since
3 × - 2 = - 6 and 3 - 2 = + 1, hence
(x + 3)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 2 = 0 ⇒ x = 2
A $4,500 savings account earns $540 in interest. What is the percent of increase on the original value? Show work please
540:4500*100 =
(540*100):4500 =
54000:4500 = 12%
What is the area of parallelogram
H=4 in b=7 in
Answer:
A = 28 in²
Step-by-step explanation:
Equation for the area of a parallelogram: A = b * h
Plug in: A = 7 in * 4 in
Solve: A = 28 in²
Answer:
its 28
Step-by-step explanation:
The following dot plot shows how many pets each customer owned before entering Jeremy's Pet Store today. Each dot represents one customer.
Based on this data, what is a reasonable estimate of the probability that the next customer to enter Jeremy's Pet Store has exactly 333 pets?
Choose the best answer.
Choose 1 answer:
Choose 1 answer:
Answer:
c
Step-by-step explanation:
Probability that the next customer to enter Jeremy's Pet Store has exactly 3 pets is 0.23.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that a dot plot shows how many pets each customer owned before entering Jeremy's Pet Store today.
Based on this data we need to find the reasonable estimate of the probability that the next customer to enter Jeremy's Pet Store has exactly 3 pets.
The total number of customer enter Jeremy's Pet Store is 13.
Probability that the next customer to enter Jeremy's Pet Store has exactly 3 pets= 3/13
=0.23
Hence, Probability that the next customer to enter Jeremy's Pet Store has exactly 3 pets is 0.23.
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In parallelogram DEFG, DH = x + 2 HF = 2y, GH = 4x-3 and HE = 4y + 1. Find the values of x and y. The diagram is not drawn to scale.
Final answer:
The problem involves finding the values of x and y in a parallelogram, using given segment lengths. Without an additional equation, we can only express one variable in terms of the other, resulting in the equation 4 = 3x + 2y.
Explanation:
The question is asking us to find the values of x and y in a parallelogram DEFG, where we know the lengths of some segments inside the parallelogram, specifically DH, HF, GH, and HE. As properties of a parallelogram dictate that opposite sides are equal in length, and segments DH and HF form one side, while segments GH and HE form the opposite side, we conclude that DH + HF must equal GH + HE.
Setting up the equation (x + 2) + (2y) = (4x - 3) + (4y + 1), we combine like terms, which gives us x + 2y + 2 = 4x + 4y - 2. Upon further simplification, by subtracting x and 2y from both sides, we get 4 = 3x + 2y. This equation allows us to express one variable in terms of the other.
Finding a specific value for x and y would require additional information, such as another equation involving x and y to solve this system of equations. Without this, we are limited to only expressing one variable in terms of the other.
Mike wants to paint one wall of his room.
The wall measures 12 feet by 9 feet. On the
wall is one square window that measures 4
feet on each side. Which of the following best
describes the number of square feet Mike will
paint?
Answer:
92 squre feeeet you willllll paintttttttttttttttttttttt
Step-by-step explanation:
Which expression is equivalent to
Step-by-step explanation:
[tex]\log_{12}\left(\dfrac{\frac{1}{2}}{8w}\right)=\log_{12}\left(\dfrac{1}{16w}\right)\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\=\log_{12}(16w)^{-1}\qquad\text{use}\ \log_ab^n=n\log_ab\\\\=-1\log_{12}(16w)\qquad\text{use}\ \log_a(bc)=\log_ab+\log_ac\\\\=-\left(\log_{12}16+\log_{12}w\right)=-\log_{12}2^4-\log_{12}w\qquad\text{use}\ \log_ab^n=n\log_ab\\\\=-4\log_{12}2-\log_{12}w[/tex]
You are packaging expansion packs for the game of checkers. The table below lists the number
of each part needed per expansion pack, as well as the number of each part that you have
available.
_
- "Let's see how many packs of each item we can make and what's left over. That's the remainder.
287 = 6(287/6) = 6(47) + 5
143 = 3(143/3) = 3(47) + 2
341 = 7(341/7) = 7(48) + 5
So on that 48th pack we have 5 people markers so need 1 more and 2 dice, so we need one more. We have enough teleport markers for the 48th pack.
Choice A."
Help me answer this question please
Answer:
Step-by-step explanation:
f⁻¹(x) is the inverse of f(x).
y = 4x − 9. To find the inverse, switch x and y and solve for y.
x = 4y − 9
x + 9 = 4y
y = (x + 9) / 4
So the inverse function is:
f⁻¹(x) = (x + 9) / 4
ANSWER
[tex]{f}^{ - 1}(x) = \frac{x + 9}{4} [/tex]
EXPLANATION
The given function is
f(x)=4x-9
Let
y=4x-9
Interchange x and y.
x=4y-9
Add 9 to both sides,
x+9=4y
Divide both sides by 4
[tex] \frac{x + 9}{4} = y[/tex]
[tex]y = \frac{x + 9}{4} [/tex]
Therefore,
[tex] {f}^{ - 1}(x) = \frac{x + 9}{4} [/tex]
The following table gives the apples eaten in a week and the times sick in the year of 10 friends:
Describe the correlation between the apples eaten per week and the times sick per year.
Answer:
The correlation coefficient is 0 which implies no association between the number of apples eaten per week and the times sick in a year.
Step-by-step explanation:
The correlation coefficient between paired data gives information on the strength and the direction of the relationship between the paired data sets. The coefficient of correlation can imply strong or weak association as well as positive or negative association between data sets.
In the data given, the number of apples eaten per week can be used to explain the number of times an individual falls ill per year. This implies that the number of apples eaten per week is our explanatory or independent variable while times sick in a year is our response or dependent variable.
We can use Ms.Excel to compute the correlation coefficient between these two variables;
The first step is to enter the data in two adjacent columns in an excel workbook. We then type;
=CORREL
In an empty cell and enter the data arrays. This is an in-built function that computes the correlation coefficient.
Ms. Excel returns a correlation coefficient of 0. The correlation coefficient of 0 implies no association between the number of apples eaten per week and the times sick in a year.
The cube of a number divided by two
The cube of a number (n) divided by two can be mathematically represented as n³/2.
Explanation:The cube of a number is achieved when you raise that number to the power of 3. If we have a number, let's denote it as 'n', and we cube it, and we get n³. Now, if you are to divide the cube of a number by two, the formula would be n³/2. For example, if n = 2, the cube of 2 is 8, divided by two equals 4.
The cube of a number divided by two means that you take a number raise it to the power of 3, and then divide the result by 2. For example, if the number is 4, the cube of 4 is 4 × 4 × 4 = 64. Dividing 64 by 2 gives you a result of 32.
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Find the average of these numbers to the nearest whole number. 516,497,501,528,476
Answer:
504
Step-by-step explanation:
To find the average of a series of numbers one must add them all then divide by the amount of numbers.
So....
516+497+501+528+476= 2,518
then...
2,518/5 = 503.6
6> 5 so you would round UP
ROUNDED : 504
Which of the following expressions is true?
A. 8^3 • 8^2 < 8^4
B. 4^4 • 4^4 = 4^16
C. 2^2 • 2^6 < 2^8
D 3^3 • 3^3 > 3^5
Answer:
The answer is D.
Step-by-step explanation:
A. 8^3 x 8^2 < 8^4
8^3 = 512 8^2 = 64 512 x 64 = 32768
8^4 = 4096 32,768 < 4096 is NOT true
B. 4^4 x 4^4 = 4^16
4^4 = 256 256 x 256 = 65536
4^16 = 4294967296
256 = 4294967296 is NOT true
C. 2^2 • 2^6 < 2^8
2^2 = 4 2^6 = 64 64*4 = 256
2^8 = 256 256 < 256 is NOT true
D. 3^3 • 3^3 > 3^5
3^3 = 27 27*27 = 729
3^5 = 243
729 > 243 IS true
(a + 3)(a - 2) whats the answer
(a+3)(a-2)
a^2-2a+3a-6
a^2+a-6
Answer is a^2+a-6
You must FOIL (first, outside, inside, last)
First (The first number/variable of each parentheses must be multiplied together)
(a + 3)(a - 2)
[tex]a^{2}[/tex]
Outside (The outside number/variable of each parentheses must be multiplied together)
(a + 3)( a - 2)
-2a
Inside (The inside number/variable of each parentheses must be multiplied together)
(a + 3)(a - 2)
3a
Last (The last number/variable of each parentheses must be multiplied together)
(a + 3)( a - 2)
-6
Now add/subtract each FOIL answer according to its sign
[tex]a^{2}[/tex] - 2a + 3a - 6
Combine like terms
[tex]a^{2}[/tex] + a - 6
Hope this helped!
~Just a girl in love with Shawn Mendes
estimations please!! asap (22 points)
Answer:
1) 15/32
2) 2
Step-by-step explanation:
1) 3 /8 / 5/4
= 3 · 5 /8 · 4
= 15 /32
2) 4/5 * 2 1/2
First solve --> 2 1/2 = 2 · 2 + 1 /2
= 5 /2
Then solve: 4 /5 * 5 /2
= 4 · 5 /5 · 2
= 20 /10
= 2 · 10 /1 · 10
= 2
Which of the following statements is true?
Answer: OPTION D
Step-by-step explanation:
We know that the function [tex]y=log(x)[/tex] is not defined for values of x less or equal than zero, therefore its domain is [tex](x|x>0)[/tex] and the range is all real numbers.
In this case we have the function [tex]y=log(x-2)+1[/tex], then [tex]x-2[/tex] must be greater than zero.
Then:
[tex]x-2>0\\\\x>2[/tex]
Therefore, the domain of the function is:
[tex]x>2[/tex] or [tex](2, \infty)[/tex]
And the range is:
All real numbers.
Answer:
the answer is D the other guy was right i just tried it.
Step-by-step explanation:
What is the difference? -6-(11)
Answer: [tex]=-17[/tex]
Step-by-step explanation:
The first thing you must remember is the mulplication of signs. You know that:
[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-[/tex]
You can observe that the number inside the parentheses is positive (+) and the sign that is outside the parentheses is negative (-), therefore, when you multiply these signs you get a negative sign (-). Then you get:
[tex]-6-(11)=-6-11[/tex]
Now, you need to add these numbers. And the result obtained is:
[tex]=-17[/tex]
Answer:
It’s -17
Step-by-step explanation:
I just got it right in the quiz
the Drama club is running a lemonade stand to raise money for it's new production. A local grocery store donated cans of lemonade and bottles of water. Cans of lemonade sell for $2 each and bottles of water sell for $1.50 each. The club needs to raise at least $500 to cover the cost of renting costumes. The students can accept a maximum of 360 cans and bottles.) Write a system of inequalities that can be used to represent this situation.) quick please I'm being timed
Answer:
Here's what I get.
Step-by-step explanation:
You have two conditions.
1. The club must raise at least $500, and that comes from the sale of lemonade and water.
Let c = cans of lemonade
and b = bottles of water
Then the first condition is
(1) 2c + 1.50b ≥ 500
2. The club can accept a maximum of 360 cans and bottles
Your second condition is
(2) c + b ≤ 360
Your system of inequalities is
[tex]\left[ \begin{array}{rcl}2c + 1.50b & \geq & 500\\c+b & \leq&360\\\end{array}\right][/tex]
Any good mathematicians out there that would help me understand this concept?
Please please...explain
The correct answer is (D) because 3 multiple 1/3, the 3 go with 3 and we get the 1. And 9 multiple 1/3, the 9 go with 3 and we will go 3 multiple 1 and we will get 3.
What is the relationship between Jack and praiseworthy
Answer:
Praiseworthy is a main character in Sid Fleischman's 'By the Great Horn Spoon!' Praiseworthy is an incredibly likable guy who is able to help his fellow travel partner - Jack - out of some pretty sticky situations.
Step-by-step explanation:
Praiseworthy is a main character in Sid Fleischman's 'By the Great Horn Spoon!' Praiseworthy is an incredibly likable guy who is able to help his fellow travel partner - Jack - out of some pretty sticky situations.
Petra jogs 2 miles in 24 minutes. At this rate, how long would it take her to jog 13 miles?
To find out how long it would take Petra to jog 13 miles at the same rate, we can set up a proportion and solve for the unknown variable. The answer is approximately 156 minutes.
Explanation:To find out how long it would take Petra to jog 13 miles at the same rate, we can set up a proportion using the given information. Since Petra jogs 2 miles in 24 minutes, the rate at which she jogs is 2 miles / 24 minutes. We can use this rate to find out the time it would take her to jog 13 miles.
Set up the proportion: 2 miles / 24 minutes = 13 miles / x minutes. Cross multiply and solve for x to find the answer.
2 miles / 24 minutes = 13 miles / x minutes
2x = 24 × 13
2x = 312
x = 156
So, it would take Petra approximately 156 minutes to jog 13 miles at the same rate.
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what is equivalent to (3+5i) - (7-2i)
Answer:
- 4 + 7i
Step-by-step explanation:
Solving (3+5i) - (7-2i)
= 3 + 5i - 7 + 2i
=3 - 7 + 5i + 2i
= - 4 + 7i
So, (3+5i) - (7-2i) is equivalent to - 4 + 7i
What is (a+2)(a+2) make sure to multiply
Answer:
a² + 4 a + 4
Step-by-step explanation:
( a + 2 ) ( a + 2 )
Expand brackets
a² + 2 a + 2 a + 4
Simplify
a² + 4 a + 4
[tex]\text{Hey there!}[/tex]
[tex]\text{(a + 2)(a + 2)}[/tex]
[tex]\text{In order for you to solve this, you need to DISTRIBUTE}[/tex]
[tex]\text{a(a) = a}^2[/tex]
[tex]\text{a(2) = 2a}[/tex]
[tex]\text{2(a) = 2a}[/tex]
[tex]\text{2(2) = 4}[/tex]
[tex]\text{Next, combine your like terms: 2a \& 2a}[/tex]
[tex]\text{2a + 2a = 4a}[/tex]
[tex]\text{Everything else stays the same because they aren't like terms}[/tex]
[tex]\boxed{\boxed{\bf{Thus,\ your\ answer\ is:a^2+4a+4}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]