Answer: [tex]x^{2} +4x - 12 = 0[/tex]
Step-by-step explanation:
To find the quadratic equation when the roots are given , we will use the formula:
[tex]x^{2} -[/tex] sum of roots[tex](x)[/tex] + product of roots = 0
sum of roots = -6 + 2 = -4
product of roots = -6(2) = -12
substituting into the formula, we have
[tex]x^{2} - (-4) +(-12) = 0[/tex]
[tex]x^{2} +4x - 12 = 0[/tex]
Find the missing side length in the following triangle.
A 169
B 10
C 1
D 13
The missing side length in the triangle with a hypotenuse of 85 and perpendicular of 84 is 13.
To find the missing side length a in the right triangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
So, in this case, we have:
[tex]\[ \text{hypotenuse}^2 = \text{perpendicular}^2 + \text{base}^2 \][/tex]
Given:
- Hypotenuse ( c ) = 85
- Perpendicular ( b ) = 84
- Base ( a ) = ?
Substituting the given values into the Pythagorean theorem equation:
[tex]\[ 85^2 = 84^2 + a^2 \][/tex]
[tex]\[ 7225 = 7056 + a^2 \][/tex]
Now, subtract 7056 from both sides:
[tex]\[ 169 = a^2 \][/tex]
To solve for a, take the square root of both sides:
[tex]\[ a = \sqrt{169} \][/tex]
a = 13
So, the missing side length ( a ) is 13.
Therefore, the correct answer is option D: 13.
A college has a student to teacher ratio of 30 to 2. If there are 186 teachers at the college, how many students attend the college?
Answer:
2790 college students
Step-by-step explanation:
30 to 2
15 to 1
186 times 15
equals 2790 students
write down the expression for the nth term of the following sequence 7,16,25,34,43 the following patterns are made using small squares write down an expression forthe number of small squares in pattern n
Final answer:
The nth term of the sequence 7, 16, 25, 34, 43 is found using the arithmetic sequence formula and is 9n - 2. The number of small squares in pattern n is expressed as n².
Explanation:
The given sequence 7, 16, 25, 34, 43 is an arithmetic sequence, where each term increases by 9. To find the expression for the nth term, we use the formula for the nth term of an arithmetic sequence, which is an = a₁ + (n-1)d, where a1 is the first term and d is the common difference. In this case, a1 = 7 and d = 9, so the nth term expression would be an = 7 + (n-1)9 = 9n - 2.
For the number of small squares in pattern n, if the expression given is n², it suggests the number of squares grows quadratically with the pattern number. Therefore, the expression for the number of small squares in the nth pattern would be n².
a circle has a radius of the square root of 131 units and is centered at (0, -4.3)
Answer:
x² + (y + 4.3)² = 131
Step-by-step explanation:
Equation of a circle:
(x - h)² + (y - k)² = r²
(x - 0)² + (y - -4.3)² = (sqrt131)²
x² + (y + 4.3)² = 131
Sara creates a box plot using 23, 26, 44, 19, 31, 39, and 43 as the data. Which of the following box plots shows the data accurately?
The box plots show the data accurately is the 3rd box (the one with a median line equal 31).
How to find the median data?Median is such a number for the arranged data set(ascending or descending order) such that to its left and to its right belong a same number of observations.
To identify the correct box plot it is enough to calculate the median value from the given set of data.
When we arranged the data set of all the numbers, we can easily spot which one is in the middle (median):
19, 23, 26, 31, 39, 43, 44
Here we can see that 31 is the median.
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3.9054 to 2 significant figure
Answer:
3.9
Step-by-step explanation:
THIS IS DUE TODAY PLEASE HELP ME OUT!!!!!
Answer:
B
Step-by-step explanation:
It is linear because x+15 is how the number increases. It does not tremendously add up.
Jamal ran 6 miles in 30 minutes which expression shows how to correctly determine his speed in miles per minute
Answer:
d= r/t
Step-by-step explanation:
i dont know if this is what youre looking for because i cant see the expression options but maybe it would be 6=r/30
Adele's grandmother is 56 years older than she is. Let a represent Adele's age . Write an expression for Adele's grandmother's age.
Carrie gave her hair stylist a $4.20 tip. The tip was 15% of the cost of the
haircut. What is the total cost of the haircut?
The total cost of her haircut was 28 dollars
step by step:
(percentage) 15 x 6 = 90
4.20 x 6 =25.2
(perscentage) 15 divided by 3 = 5
4.20 divided by 3 = 1.4
1.4 + 1.4 = 2.8
25.2 + 2.8 =28
Final answer:
The total cost of the haircut before adding the tip was $28.00, found by setting up an equation where 15% of the total cost is equal to the $4.20 tip and solving for the total cost.
Explanation:
To calculate the total cost of the haircut that resulted in a $4.20 tip given at the rate of 15%, we need to set up a proportion where 15% of the total cost equals $4.20.
Step 1: Represent the unknown total cost of the haircut by the variable x.
Step 2: Set up the equation representing the tip as 15% of the total cost (0.15x = $4.20).
Step 3: Solve for x by dividing $4.20 by 0.15.
x = $4.20 / 0.15
x = $28.00
Therefore, the total cost of the haircut before adding the tip was $28.00.
A monkey is swinging from a tree. On the first swing, she passes through an arc whose length is 24 m.
With each swing, she travels along an arc that is half as long as the arc of the previous swing.
Which expression gives the total length the monkey swings in her first n swings?
24 divided by .5 or 1/2 (probably .5 tho)
Answer: 24 times 1-.5 divided by .5
Step-by-step explanation:
what is the constant term in the expression 24xy -5yz + 82z - 62
[tex]\text{The constant term is the term that doesn't have a variable in it}\\\\\text{As you can see in the expression 24xy -5yz + 82z - 62, the only term}\\\text{that doesn't have a variable is -62}\\\\\text{This means that -62 would be your constant term}\\\\\boxed{\text{Constant term: -62}}[/tex]
A regular hexagon and a regular octagon are joined as shown on the diagram.
Work out the size of angle x.
The interior angle of a regular hexagon is 120°. As two hexagons share a side, [tex]\( x \)[/tex] equals 120°.
In the given diagram, two regular hexagons share a common side, and an interior angle marked as [tex]\( x \)[/tex] is formed by the sum of the interior angles of the two hexagons. The interior angle of a regular hexagon is [tex]\( \frac{{180^\circ \times (n-2)}}{n} \)[/tex], where [tex]\( n \)[/tex] is the number of sides. For a hexagon [tex](\( n = 6 \))[/tex], this angle is [tex]\( \frac{{180^\circ \times (6-2)}}{6} = 120^\circ \)[/tex].
Considering the interior angles of both hexagons and the angle [tex]\( x \)[/tex], the equation [tex]\( 120^\circ + 120^\circ + x = 360^\circ \)[/tex] arises, as the sum of angles around a point is 360°. Solving for [tex]\( x \) yields \( x = 120^\circ \).[/tex] Therefore, the measure of angle [tex]\( x \)[/tex] in the diagram is 120°.
This solution demonstrates the application of the interior angle formula for a regular hexagon and the consideration of the total angle around a point, resulting in the determination that [tex]\( x \) is indeed \( 120^\circ \).[/tex]
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Jackie created a diagonal cross section cut on a sphere. What plane figure did she discover after making the cut?
If you cut a sphere diagonally or along any of its diameters, you will always get a circle as the plane figure because all diameters of a sphere are of equal length.
Explanation:In the field of mathematics, specifically in solid geometry, if Jackie created a diagonal cross section cut on a sphere, the plane figure that she would have discovered is a circle.
The concept behind this is that a sphere is a perfectly symmetrical three-dimensional figure. When we make a cross sectional cut along any diameter of the sphere (which is what Jackie did by making a diagonal cross section), we will always reveal a circular plane figure irrespective of the direction of this cut because all diameters of a sphere are of equal length, thus ensuring the cut is always a circle.
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A diagonal cross-section cut on a sphere will reveal a circle.
When Jackie made a diagonal cross-section cut on a sphere, she discovered a circle. Regardless of the angle or position of the cut, the intersection of a plane and a sphere always results in a circular shape. This fundamental geometric property arises from the symmetrical nature of spheres, where every cross-section manifests as a circle.
Thus, Jackie's diagonal cut revealed a circular plane figure, showcasing the inherent relationship between spheres and circles in geometry.
Suppose that a Navy submarine is submerged 500 feet below sea level.
Answer:
B) A and D
Step-by-step explanation:
Below sea level already implies negative.
And on a number line, it should be -500
In the image shown, line n is a transversal cutting parallel lines l and m.
∠1 = x + 40
∠5 = 2x + 10
What is the measure of ∠5?
A) 65°
B) 67°
C) 70°
D) 72°
Answer:
it is 70 on usatestprep.
Step-by-step explanation:
x + 40 = 2x + 10
x = 30
So, ∠5 = 2x + 10 = 2(30) + 10 = 70
Answer:
The answer is C.) 70
Step-by-step explanation:
Corresponding angles are congruent. So, set the angles equal to each other and solve for x.
x + 40 = 2x + 10
x = 30
So, ∠5 = 2x + 10 = 2(30) + 10 = 70°
what whole number does x represent
Which scatterplot would have a trend line with a negative slope
Answer: B
Step-by-step explanation:
Answer: B
What is an example of a negative slope?
For example, as more people quit smoking (x), fewer people develop lung cancer (y). The graph for this relationship has a negative slope. If the gradient is negative, then the gradient and the gradient must be opposite, one must be positive and the other must be negative.
In other words, you go up and down or left and right. The positive area of a function is the interval at which the function is on the x-axis. Where the y value is positive (not zero). The negative area of a function is the interval at which the function is below the x-axis.
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effrey typed 110 words in 2 2/3 minutes. At this rate, how many words can he type in 4 1/4 minutes?
First, you find the rate at which Jeffery types.
110 divides by 2.75. This makes 40.
Then to find the amount of words he types in 4.25 minutes,
40 x 4.25. This makes 170.
So Jeffery can type 170 words in 4 1/4 minutes.
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What is the prime factorization for 160 using exponents?
Answer:
[tex]2^5*5[/tex]
Step-by-step explanation:
Step 1: Prime Factorization
[tex]160[/tex] → [tex]2 * 2 * 2 * 2 * 2 * 5[/tex]
[tex]2 * 2 * 2 * 2 * 2 * 5[/tex] → [tex]2^5*5[/tex]
Answer: [tex]2^5*5[/tex]
4. Which two numbers have an absolute value of 2.67?
Answer:
2.67 & -2.67 both have an absolute value of 2.67
Step-by-step explanation:
The absolute value is the distance between a number and zero. the distance between 2.67 and zero is 2.67, and the distance between -2.67 and zero is also 2.67.
Which of the following equations could be the result of using the comparison method to solve the system shown? x - 4y - 1 = 0 x + 5y - 4 = 0
4y + 1 = 4 - 5y
-4y + 1 = 4 - 5y
4y + 1 = 5y - 4
Answer:
Option A.
Step-by-step explanation:
The given system of equations is
[tex]x-4y-1=0[/tex]
[tex]x+5y-4=0[/tex]
The given equations can be rewritten as
[tex]x=4y+1[/tex]
[tex]x=4-5y[/tex]
Using comparison method, compare the values of x.
[tex]4y+1=4-5y[/tex]
Therefore, the correct option is A.
Answer:
number 1:
4y +1 = 4 - 5y
Malachi bought a new fishing rod. The regular price of the fishing rod was $125.99. He bought it on sale with a 15% discount. A sales tax of 3% is applied to the discounted total. What was the sale price with tax of Malachi’s fishing rod to the nearest cent? *
Answer:
110.30
Step-by-step explanation:
125.99-(125.99X0.15)= 107.09
107.09+(107.09X0.03)= 110.30
Gertrude makes a one time deposit of $1200 into an account that pays 7% annual interest compounded continuously. Assuming Gertrude makes no additional deposits or withdraws. how much money would be in the account after 3 years? Round to the nearest penny.
Answer:$14701
Step-by-step explanation:
1) at the end of the first year the account will be 1*(12 000)+0,07*(12 000)=1,07*12 000,
2) at the end of the second year 1*(1.07*12 000) + 0.07*(1.07*12 000) = 1.1449*12 000,
3) at the end of the third year 1*(1,1449*12 000) + 0.07*(1,1449*12 000) = 1.225*12 000 = 14,700.516 = 14701
Answer: $14701
how many thirds are in 4/5? complete an area model and give the quotient.
Explain when the median of a data set is a better
measure of center than the mean.
Answer:
The median of a data set is better when you have a term or terms that are not close to the other terms
Step-by-step explanation:
For example:
Say you have the data set
1, 15, 17, 18, 22, 84
The median of these terms would be 17.5
(it is the exact center of the data group)
17 + 18 = 35
35/2 = 17.5
The mean of these terms would be 26.17
(this number is not close to the center because the numbers 1 and 84
are not close enough to the other terms)
1 + 15 + 17 + 18 + 22 + 84 = 157
157/6 = 26.17
Answer:
Sample Response: When there is an outlier in the data set, the dot plot or histogram will be skewed. In a skewed representation, the mean is pulled up or down toward the tail of the data. Therefore, skewed data affects the mean more than the median.
What did you include in your response? Check all that apply.
The dot plot or histogram will be skewed.
The mean is pulled up or down toward the tail.
The mean is affected more than the median.
If the sales tax is 7% on all purchases, how much must you set aside for sales tax on $300? Show your work.
Answer:
$321
Step-by-step explanation:
Because if you use a calculator u put in 300 + 7% you get 321
Answer: $8.04
Step-by-step explanation: First you add on 7% to all of the amounts, then you get the new answer and subtract it by the old answer, finally you add up the subtracted amounts together. (Sorry if its wrong it tried my best)
Won has a container with the shape below.
A rectangular prism with length of 18 centimeters, width of 10 centimeters, and height of 12 centimeters. A rectangular pyramid has a base of 18 centimeters by 10 centimeters and height of 10 centimeters.
Which statements are true about the container? Select three options.
The shape can be broken into a rectangular prism and a triangular prism.
The shape can be broken into a rectangular prism and a rectangular pyramid.
The formula for the volume of this figure is V = B h + one-third B h.
The volume of the container is 2,760 centimeters cubed.
The volume of the container is 3,060 centimeters cubed.
Answer:
B. The shape can be broken into a rectangular prism and a rectangular pyramid.
C. The formula for the volume of this figure is V = B h + one-third B h.
D. The volume of the container is 2,760 centimeters cubed.
Step-by-step explanation:
I did the edge test.
Answer:
B, C, ,D
DID HE ES
Step-by-step explanation:
Let f(x) = 5x - x+1 and g(x) = -3x. Evaluate the composition (f • g)(1).
Replace the variable x with 1 in the expression
f(1)=5(1)−(1)+1
f(1) = 5
Replace the variable x with 1 in the expression.
g(1)=−3⋅1
g(1) = -3
Multiply 5 by −3
.
−15⋅1
Multiply −15
by 1
.
−15
Thus, the answer is -15
I am unsure about this answer, I have doublechecked it several times. Please take this with a grain of salt
Te game started at 7:50pm. It ended at
10:04pm. How long was the game?
Answer:
134 minutes or 2 hours and 14 minutes
Step-by-step explanation:
Answer:
2 hours and 14 minutes
Step-by-step explanation: