√x+7 The solution to the equation is x=-3.
Square root: If we take the square root of a number and then take the square of the outcome, we get the original number back again.
e.g. 4 = 2 and 22 = 4.
We can say that the square root and the square cancel each other out. They are the inverse of each other.
If we have a number written with the index 2 ( squared) then taking the square root simply means that we leave out the 2 ( this only applies to positive numbers ).
We can therefore take any squared numbers that are under the square root sign out from under the root sign by leaving out the power 2.
The solution to the equation√x+7= -2.
√x+7= -2
First we take Squaring on both sides
(√x+7)2= (-2)2
x+7 = 4
x=-3.
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∠
ABC = 40° and
x
= 9 cm.
Find the length of AC.
Give your answer rounded to 1 DP.
The length of AC is 6.228 cm.
Here the angle of the triangle ∡ABC is 40°, AB = BC = 9.
We have to find the length of AC which is opposite to ∡B.
Let AB = BC = x , AC = c
From the cosine formula, we know that
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab cos α
Here c is the length of the side opposite to the angle α, and a, b is the side adjacent to the angle α.
So from the cosine formula we have
[tex]c^{2}[/tex] = [tex]x^{2}[/tex] + [tex]x^{2}[/tex] -2[tex]x^{2}[/tex]cos α
[tex]c^{2}[/tex] = 2[tex]x^{2}[/tex] - 2[tex]x^{2}[/tex] cos 40°
= 2[tex]x^{2}[/tex](1- cos 40°)
= 2 ×[tex]9^{2}[/tex] ( 1 - 0.76)
= 2 × 81 × 0.24
c = 2 × 9 × 0.2×√3
=3.6 × 1.73
= 6.228cm
Therefore the length of the side AC is 6.228cm.
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help me understand this
Answer:
59,049
Step-by-step explanation:
Since 3^2 is basically 3 times 3 which is 9, then what's 9 times 9, 9, 9, 9, 9 (9^5)?
Answer: 3¹⁰
Step-by-step explanation:
[tex]\displaystyle\\(3^2)^5=\\\\3^{2*5}=\\\\3^{10}[/tex]
A recipe requires 11 pints of water. How many fluid ounces of water are in 11 pints of water?
A study was performed with a random sample of 513 bolts produced at one factory. What population would be appropriate for generalizing conclusions from the study, assuming the data collection methods used did not introduce biases?.
Given that the study was conducted using a sample of 513 bolts produced at a single facility when there is no bias resulting from data gathering procedures, broad inferences may then be drawn.
All bolts manufactured by that factory would be covered by the conclusion?
Due to the fact that bolts made in the same factory will follow the results of an analysis of a sample made up of bolts from the same factory. The finding or conclusion would therefore be applicable to all bolts produced in the same factory because the environment for experimentation and production is the same there while it may differ in other factories. Conclusions from the study may not apply to the bolts made by other companies as a result of this bias.
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suppose that mean retail price per gallon of regular grade gasoline is with a standard deviation of and that the retail price per gallon has a bell-shaped distribution. note: please use empirical rule approximations for this problem.
68.26 % of regular gasoline sold between $ 3.25 & $ 3.65.
What do you mean by the term standard deviation?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. In contrast, a high or low standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean. the curve at the top is more dispersed and has a greater standard deviation than the curve at the bottom, which is more concentrated around the mean and has a lower standard deviation.
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Find the perimeter of a rectangle whose width is 16 and whose length is 12 square feet
Answer:
56 square feet
Step-by-step explanation:
a rectangle has 4 sides, and two of each are the same;
12 is the length
16 is the width
12 + 12 + 16 + 16 = 56
final answer is 56 square feet
hope this helped xx
Find the 8th term of the arithmetic sequence 3x+13x+1, -2x+7−2x+7, -7x+13,
pls help me I will give brainlist
Answer: =38x+16.
a_{\color{red}{8}}=(\color{blue}{3x-5}) + (\color{red}{8}-1)(\color{green}{5x+3})
a
8
=(3x−5)+(8−1)(5x+3)
a_{8}=3x-5+ 7(5x+3)
a
8
=3x−5+7(5x+3)
a_{8}=3x-5+35x+21
a
8
=3x−5+35x+21
seven times the quantity of the difference of a number cubed and eleven
write into algebraic expression
Answer:
7x(y^3-11)
Step-by-step explanation:
The label on a car's antifreeze container claims to protect the car between −30°C and 130°C. To covert Celsius temperature to Fahrenheit temperature, the formula is C equals five ninths times the quantity F minus thirty two.. Write a compound inequality to determine the Fahrenheit temperature range at which the antifreeze protects the car.
Answer:
he. haha. shyw sjIana d auhaabab ssbajiaan s
The formula d = 16t to the second power describes the number of feet d a skydiver falls in t seconds of free fall assuming there is not air resistance. How far does a skydiver fall between the third and fourth seconds?
Answer:
D=16(3)
=48 feet
D=16(4)
=64 feet
The distance between third and fourth second=64 feet-48 feet
=16 feet
a portion of a map with cites A and B is shown. The map uses a scale of 1 inch to 30 miles a new map has a scale of 2 inches = 15 miles. how far apart are cites A and B on the new map?
1in=15 then it’s 75. For 2in=25 then it’s 62.5
Pleas help me it would be so nice
Answer:
1. 0.003
2. 0.5
3. 0.001343
4.0.05003
5. 0.670570
6. 1.01
Molli purchased 9 apples for $3.96. While looking at her receipt, Molli divided $3.96 by 9.
Why might Molli perform this calculation?
Answer:
To find out how much each apple cost
Step-by-step explanation:
If Molli bought 9 apples for a total of $3.96, she could divide her total by 9 to figure out how much each individual apple cost.
Joe has a mullet ratio of 1.5 (a) Find 2 possibilities for his hair lengths.
Mullet ratio of 1.5 is 1.8
Given:
The mullet ratio is 1.5
Rm=[tex]\frac{party}{buisness}[/tex]
Rm = 17/9
Rm=1.8
The ratio to their Mullet and several other higher-level extension questions.
Trimmed short in the front and sides, but left wild and long in the back. Mullet begins the experience with intuition, the lowest rung on the ladder of abstraction, asking students to decide using nothing more than their gut “which one is more Mullet-y” By the end, they’ve named variables and defined operations, entirely abstracting the context.
The pipe cleaner was inserted along the hair, and the students straightened it on their rulers to determine the size of the Party. The Business was often rather honest.
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how are the cards and the proportional relationships useful for determining the diameter of the sun?
This investigation's goal is to demonstrate how quickly and easily we can determine the diameter of the sun using basic geometry.
How to determine the diameter of the sun?The cards must remain parallel and separated by a predetermined amount. Then, a tiny hole must be cut on one card so that sunlight can pass through and create the sun's picture on the other card. We base the formula described above on the diameter of this photograph of the sun. The diameter of the sun's picture on the card is now measured because we can choose the distance between the cards, and we already know that the sun is nearly 150 million kilometers away from the earth. i.. e. Since three of the values are known, we can use the technique above to determine the fourth unknown quantity and measure the diameter.
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An automobile purchased for $37000 is worth $2600 after eight
years. Assuming that the value decreased steadily each year,
what was the car worth at the end of the fifth year?
The car has a value of $ 15 500 at the end of the fifth year.
What is the value of a car in time?
In accordance with the statement, the value of an automobile decreases in time and decreases steadily. A stead decrease means that the value decreases linearly in time, whose formula is shown below:
C' = C + r · t (1)
Where:
C - Initial value of the car, in dollars.C' - Final value of the car, in dollars.r - Decrease rate, in dollars per time.t - Time.If we know that C = $ 2 600, C' = $ 37 000 and t = 8, then the value of the car at the end of the fifth is:
r = (C' - C) / t
r = (2 600 - 37 000) / 8
r = - 4 300
t = 5
y = 37 000 - 4 300 · 5
y = 15 500
The car has a value of $ 15 500 at the end of the fifth year.
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a scientist measured the weights (in grams) of 11 female guinea pigs (cavia porcellus) and got the following: 582 904 311 410 688 541 470 709 525 478 402 calculate the iqr
278 is the value of IQR.
What do we mean by IQR?The interquartile range (IQR) is a way of measuring statistical dispersion, or the spread of data, in descriptive statistics. The IQR is also known as the midspread, the middle 50%, the fourth spread, or the Spread. It is defined as the difference between the data's 75th and 25th percentiles. To calculate the interquartile range (IQR), first, compute the median (middle value) of the data's lower and upper halves. These are quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The IQR is the distinction between quarters three and one.To find the IQR:
Arrange in ascending order as follows:
311, 402, 410, 470, 478, 525, 541, 582, 688, 709, 904The middle value or the median is 525.
IOR = Q₃ - Q₁Q₁ from the lower half is 410 and Q₃ from the upper half is 688.
So, IOR = 688 - 410 = 278Therefore, the value of IQR is 278.
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George is making a peperoni pizza using a circular pan with a 14-inch diameter. What is the area
of the pizza that George will cover with sauce?
The area of the pizza that George is 153.938040026 [tex]inch^{2}[/tex].
What is area?The area of the pizza that George is [tex]\pi r^{2}[/tex]
area = [tex]\pi[/tex]×[tex]7^{2}[/tex] = 153.938040026 [tex]inch^{2}[/tex]
The number of unit squares that are equivalent in size to the surface, which is included inside a set of lines; see Metric System Table, Weights and Measures Table.
The extent of a notion, action, or activity: the entire realm of international policy.
The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
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Find these common multiple for five and nine
Answer: 45
Step-by-step explanation:
The LCM of 5 and 9 is 45. To find the least common multiple of 5 and 9, we need to find the multiples of 5 and 9 (multiples of 5 = 5, 10, 15, 20 . . . . 45; multiples of 9 = 9, 18, 27, 36 . . . . 45) and choose the smallest multiple that is exactly divisible by 5 and 9, i.e., 45.
Margaret drove to a business appointment at 70 mph. Her average speed on the return trip was 60 mph. The return trip took 1/3 hr longer because of heavy traffic. How far did she travel to the appointment?
Answer:
70t = 60t + 10
10t = 10
t = 1 hour
----------
1 hour 70 mi/hr = 70 miles
Step-by-step explanation:
Solve the absolute value equation - 5 | x + 1 | + 2 = 12 if there is no solution, state no solution
Answer:
Let's solve your equation step-by-step.
−5(|x+1|)+2=12
Step 1: Add -2 to both sides.
−5(|x+1|)+2+−2=12+−2
−5(|x+1|)=10
Step 2: Divide both sides by -5.
−5(|x+1|)
−5
=
10
−5
|x+1|=−2
Step 3: Solve Absolute Value.
|x+1|=−2
No solutions. (Absolute value cannot be less than 0.)
Step-by-step explanation:
Which table shows a function that is decreasing only over the interval (–1, ∞)?
Answer:
The 4th option.
Step-by-step explanation:
f(x) is increasing from x = -3 to x = -1 then it starts to decrease as x increases.
The larger bag of ferret food is on sale at the SuperPetMart
for $89. Ferroza made the following table. Explain to
Ferroza why the cost of food at SuperPetMart is not a
proportional relationship.
Ferret Food
Weight
(pounds)
0
5
30
Cost
($)
$0
17.50
89
Relationships that have a uniform or constant rate are said to be proportional relationships. Because it does not employ a uniform rate, the price of food does not follow a proportional connection.
The missing table looks like this:
Bag cost
0 0
5 17.5
30 89
First, we calculate the slope (m) of the table using:
(x₁ y₁) = (0,0)
(x₂ y₂) = (5,17.5)
m₁=(y₂-y₁)/(x₂ -x₁)
m₁=(17.5-0)/(5-0)
m₁=3.5
The slope for the following points
(x₁ y₁) = (0,0)
(x₂ y₂) = (30,89)
m₂=(y₂-y₁)/(x₂ -x₁)
m₂=(89-0)/(30-0)
m₂=2.97
3.5 ≠2.97
Hence, the cost of food is not a proportional relationship because it does not use a uniform rate.
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must first specify a coordinate system in order to find the components of each arrow.) this problem gives you some practice with the components. let vectors a⃗
The calculated vectors are:
[tex]\vec{A}-\vec{B}[/tex]=(3,-5,-4)
[tex]\vec{B}-\vec{C}[/tex]=(-5,4,0)
[tex]-\vec{A}+\vec{B}-\vec{C}[/tex]=(-6,4,3)
[tex]3 \vec{A}-2 \vec{C}[/tex]=(-3,-2,-11)
Calculate the following, and express your answers as ordered triplets of values separated by commas.?Generally, the equation for is mathematically given a
[tex]\vec{V}+\vec{W}=\left(V_1, V_2, V_3\right)+\left(W_1, W_2, W_3\right)\\\\\vec{V}+\vec{W}=\left(V_1+W_1, V_2+W_2, V_3+W_3\right) \text { }[/tex]
[tex]\vec{V}-\vec{W}=\left(V_1, V_2, V_3\right)-\left(W_1, W_2, W_3\right)\\\\\vec{V}-\vec{W}=\left(V_1-W_1, V_2-W_2, V_3-W_3\right)[/tex]
[tex]\alpha \cdot \vec{V}=\alpha \cdot\left(V_1, V_2, V_3\right)\\\\\alpha \cdot \vec{V}=\left(\alpha \cdot V_1, \alpha \cdot V_2, \alpha \cdot V_3\right)[/tex]
[tex]\vec{A}-\vec{B}=(1,0,-3)-(-2,5,1)\\\vec{A}-\vec{B}=(3,-5,-4) \\\\&\vec{B}-\vec{C}=(-2,5,1)-(3,1,1)\\&\vec{B}-\vec{C}=(-5,4,0) \\\\&-\vec{A}+\vec{B}-\vec{C}=-(1,0,-3)+(-2,5,1)-(3,1,1)\\-\vec{A}+\vec{B}-\vec{C}=(-6,4,3) \\\\&3 \vec{A}-2 \vec{C}=3(1,0,-3)-2(3,1,1)\\3 \vec{A}-2 \vec{C}=(3,0,-9)-(6,2,2)\\3 \vec{A}-2 \vec{C}=(-3,-2,-11)[/tex]
In conclusion,
[tex]\vec{A}-\vec{B}[/tex]=(3,-5,-4) [tex]\vec{B}-\vec{C}[/tex]=(-5,4,0) [tex]-\vec{A}+\vec{B}-\vec{C}[/tex]=(-6,4,3) [tex]3 \vec{A}-2 \vec{C}[/tex]=(-3,-2,-11)Read more about Vectors
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CQ
In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors A rightarrow = (1,0, -3), rightarrow = (-2,5,1), and C rightarrow = (3,1,1). Calculate the following, and express your answers as ordered triplets of values separated by commas.
−4 3/3 − 5/3 subtract then simplify
8. Karen earned $81.00 at her job last week. Kimberly earned 33% as much money as Karen. How much money did Kimberly earn?
Answer:
$26.73
Step-by-step explanation:
Karen: $81
Kimberly: 33% of $81
33% of $81 = 0.33 × $81 = $26.73
..., -39, ______, ______, -45,....
Find the missing term
multiple choice question. with explanation
Answer:
(1)
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180° .
consider the inner triangle where
a + b + 58° = 180° ( subtract 58° from both sides )
a + b = 122°
consider the outer triangle where
c + d + 63° = 180° ( subtract 63° from both sides )
c + d = 117°
Then
a + b + c + d = 122° + 117° = 239°
question 4(multiple choice worth 1 points) (01.02 mc) bruno solved the following equation: 4x (10x − 4)
The justifications are 1. Distributive Property 2. Combine like terms 3. Addition Property of Equality 4. Division Property of Equality (Option 3 and 4).
What is a linear equation?It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.The equation is referred to as a linear equation in one variable if just one variable is contained in the equation.Now,
We are given the linear equation: [tex]4x + \frac{1}{2}(10x-4)=6[/tex]
4x + 5x -2 = 6 (Distributive property)9x - 2 = 6 (combining the like terms)9x = 8 (additive property of equality)x = 8/9 (division property of equality)Hence, The third and fourth solutions are correct when using the division property of equality, i.e., The justifications are 1. Distributive Property 2. Combine like terms 3. Addition Property of Equality 4. Division Property of Equality (Option 3 and 4).
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solve the equation 6x = 12
Answer: x=2
Step-by-step explanation:
[tex]6x=12[/tex]
[tex]\frac{6}{6}x=\frac{12}{6}[/tex]
[tex]x=2[/tex]