The two values of x which are root of the given equation are; x = (-3 + √29)/2 and x = (-3 - √29)/2.
What are the two values of x which are root of the given quadratic equation?It follows from the task content that the two values of x which are roots of the given quadratic equation be determined.
Recall that the roots of quadratic equations are given by the formula;
x = {-b ± √(b² - 4ac)} / 2a
Since the given equation is; x² + 3x - 5; it follows that; a = 1, b = 3 and c = -5.
Therefore, the roots are as follows;
x = {-3 ± √(3² - 4•1•-5)} / 2(1)
x = (-3 ± √29)/2
Therefore, the required roots are;
x = (-3 + √29)/2 and x = (-3 - √29)/2
Ultimately, the roots of the given quadratic equation x² + 3x - 5 are; x = (-3 + √29)/2 and x = (-3 - √29)/2.
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Two fire towers are 21 miles apart. Tower B is due East of Tower A. The rangers at Tower A spot a fire at 43°north of east. The rangers at Tower B spot the same fire 31° north of west.
How far is Tower B from the fire? Round to the nearest tenth.
Tower B is 14.9 miles away from the fire.
What is the law of sines?
According to the law of sine, or sine law, the ratio of a triangle's side length to the sine of the opposing angle remains constant for all three sides. The sine rule is another name for it.
Here,
According to the law of sines
BC/sin A = AC/sin B = AB/sin C
∠A = 43°, ∠B = 31°, ∠C = 180° - ∠A - ∠B = 106°
AB = 21 miles
So, BC = (AB/SinC)×SinA
BC = 14.9 miles
Hence, Tower B is 14.9 miles away from the fire.
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whats the quotient for 2.0 and 4.0
The solution to the quotient for 2.0 and 4.0 is 0.50
How to determine the quotient of the numbers?From the question, the mathematical statement is given as
The quotient for 2.0 and 4.0
The quotient of numbers is their division
This in other words mean that:
The quotient for a and b is a/b
Using the above highlights as a guide, we have
The quotient for 2.0 and 4.0 to be 2.0/4.0
Evaluate the quotients
So, we have the following representation
The quotient for 2.0 and 4.0 to be 0.50
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Can anyone write the equation of the graph?
The equation of given graph is y = |x - 3| + 5.
The graph of a absolute or modulus function is a V- shape graph. The function of absolute is f(x) = |x|. The general form of absolute function is f(x)=a |x - h| + k. Where (h,k) is the vertex of graph.
Here, we can see that graph is in the form of V shape, so the function will be absolute function. Now, we have to find the vertex of graph.
As seen from the graph the minimum point on the graph is located at the point (3, 5) and the value of a should be 1.
So, by putting the value of vertex in general equation we get the equation of the graph,
y = |x - 3| + 5
Therefore, the equation of given graph is y = |x - 3| + 5.
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What is 36.9 rounded to the nearest percent
Answer: 37%
Step-by-step explanation:
36.9 rounds up into 37%
pls solve all the question as er the questions given below
1a) The additional information required using SAS Congruency postulate is; ∠AOB ≅ ∠BOD
1b) The additional information required using ASA Congruency postulate is BC ≅ QR
2a) The symbolic form of the congruent triangles is written as;
ΔABC ≅ ΔADC
2b) The congruence Postulate that is used is SAS Congruency postulate.
How to use congruency postulates?1a) We want to prove that the triangles are congruent by SAS Congruency postulate. SAS congruency postulate denotes Side - Angle - Side. That is 2 congruent sides and the included angle. This means we have our additional information as;
∠AOB ≅ ∠BOD
1b) We want to prove that the given triangle ABC is congruent to the other triangle PQR by the ASA Congruency. ASA Congruency means 2 congruent angles and the included side. We are given;
∠Q = ∠B
∠R = ∠C.
Therefore, the additional information is BC ≅ QR
2a) The symbolic form of the given congruent triangles is expressed as;
ΔABC ≅ ΔADC
2b) The congruence postulate that was used here is SAS Congruency postulate.
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-34, -21, -8.5 Complete the recursively defined function to describe this sequence.
The recursive definition of the arithmetic sequence -34, -21, -8 is:
f(1) = -34.f(n + 1) = f(n) + 13.What is an arithmetic sequence?It is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the rule presented as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term of the sequence.
An arithmetic sequence can also be defined recursively, as follows:
[tex]f(1) = a_1[/tex]f(n + 1) = f(n) + d.In this problem, the sequence is given as follows:
-34, -21, -8.
Hence the first term and the common ratio are given as follows:
First term: -34.Common ratio: 13, as each term is the previous term added to 13.Hence the recursive definition of the sequence is:
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A single bathc of your mother resipe for slalsa call for 3 tomatos. 1/4 cup cilantro,1/2 onion, and spices. you are having a party and need 5 batches of salsa how many cups of onions do you need?
To produce five constructive batches of salsa, 2.5 cups of onion will be needed.
What is unitary method of problem solving?
The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.
Given, the number of onions required to produce one batch = 0.5 cup(s)
∴ The number of onions required to produce five batches = 0.5×5
= 2.5 cup(s)
Thus, to produce five constructive batches of salsa, 2.5 cups of onion will be needed.
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Gabriel Harris earns an annual salary of $156,000 as CFO of
TechMedia, Inc. He is married and claims three dependents. TechMedia
recently converted from a weekly pay plan to a monthly pay plan.
How much more will Gabriel have deducted from his monthly pay
than from his weekly pay for state income tax?
Answer:
Step-by-step explanation:
Gabriel Harris earns an annual salary of $156,000 as CFO ofTechMedia, Inc. He is married and claims three dependents. TechMediarecently converted from a weekly pay plan to a monthly pay plan.How much more will Gabriel have deducted from his monthly paythan from his weekly pay for state income tax?
Find the slope of the line(4,9) and (4,13)
Answer:
the slope of the line is undefined
Please answer part d
Answer:
∆JGF ≅ ∆GJH by the SAA Postulate
Step-by-step explanation:
Given a figure showing two triangles with a common side, and two marked angles not at either end of that side, you want to know the applicable congruence postulate.
SAAThe letters S and A in the congruence postulate references refer to "Side" and "Angle". The sequence of the letters corresponds to the sequence of corresponding parts in the triangles.
In the given figure, two angles in each triangle are marked with a single arc and a double arc. The triangles share a side that has the double-arc angle at one end. Hence, the sequence of corresponding parts can be seen to be (common) Side - (double-arc) Angle - (single-arc) Angle. The SAA congruence postulate applies.
∆JGF ≅ ∆GJH by the SAA Postulate
One type of plant root splits 4 times while growing in the ground. The number of new roots after each split can be modeled by the function f(x)=3x, where x is the number of times the root splits. What is the domain of f(x)? CLEAR CHECK All positive integers All positive integers less than or equal to 4 All integers All positive integers greater than or equal to 4
The domain of the function represented as .f(x) is (b) All positive integers less than or equal to 4
How to determine the representation of the domain?The equation of the function is given as
f(x) = 3x
Where
x = Number of splits
f(x) = number of new roots in each split
From the question, we have
Splits = 4
This means that the maximum value of x is 4
The other values of x would be
x = 1, 2, 3, 4
This can be represented as
0 ≤ x ≤ 4
The interpretation of the above notation is all positive values less than or equal to 4
Hence, the domain value is option (b)
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PLS HELP!!!
30 = y/2 + 8
y = ____
Answer:
y = 44
Step-by-step explanation:
y = 300
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Steps are in the attached picture!
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Joke: What runs around a farm but doesn’t move?
Answer: A fence.
Have a great day and God bless! :D
What’s is the equation of this line in slope intercept form? 2x+3y=-6
Answer:
[tex]y=-\frac{2}{3}x-2[/tex]
Step-by-step explanation:
To find the equation in slope-intercept form, isolate [tex]y[/tex].
[tex]2x+3y=-6 \\ \\ 3y=-2x-6 \\ \\ y=-\frac{2}{3}x-2[/tex]
Heather is planning her birthday party at the rink. the graph below shows the total cost including the fee to rent the party room and the price for each guest.
130 for 2
140 for 4
150 for 6
how much for the party room
how much for each guest
what's the equation for the total cost for the party
how much for 15 people and the party room
Step-by-step explanation:
I skipped the answer line because they are pasted below.
Since there is a ten dollar difference for two people, each guest is 5 dollars. If each guest is 5 dollars, the party room is 120. If we want to create an equation, we have:
y=5x(each guest is 5 dollars)+120(the basic fee).
If we use 15 here, we have that it will be $195.
ANSWERS DOWN HERE:
1. $120
2. $5
3. y=5x+120
4. $195
What are some Mathematical Concepts for Slopes and equations? Any kind of help would be much appreciated.
Answer:25256
Step-by-step explanation:
The rectangular floor of a classroom is 36 feet in length and 28 feet in width. a scale drawing of the floor has a length of 9 inches. what is the perimeter, in inches, of the floor in the scale drawing?
The perimeter of the floor in the scale drawing is 32 inches.
Using ratio and proportion, determine the width of the scale drawing of the floor.
actual length / scale length = actual width / scale width
36 feet / 9 inches = 28 feet / scale width
scale width = 28 feet (9 inches / 36 feet)
scale width = 7 inches
Perimeter is defined as distance around a two-dimensional shape.
The perimeter of a rectangle can be calculated using the formula below.
P = 2(l + w)
where P = perimeter
l = length
w =width
Plug in the values of the dimension of the scale drawing and determine its perimeter.
P = 2(l + w)
P = 2(9 inches + 7 inches)
P = 32 inches
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Apply the distributive property to
create an equivalent expression.
(-7c + 8d)0.6
Answer: -4.2c + 4.8d
Step-by-step explanation:
Multiply each number by 0.6 to get -4.2c + 4.8d.
Find x
35°
100°
X
algebra 1
Answer:
X would be 135 degrees
Step-by-step explanation:
35 is a vertical angle
180-(100+35) = 45
By supplements, 180-45 = 135 which would be your answer
hope this helps
the value o f x is 135, it mean x=135°
which expressions are equivalet to the one below check all that apply (7^3) * (7^x)
A. 49^3x
B. (7 * x)^3
C. 343 * 7^x
D. 7^(3+x)
E. 7^(3x)
F. 7^(3-x)
For given expression (7^3) * (7^x) equivalent expressions are:
343 * 7^x and 7^(3+x)
The correct options are option (C) and option (D)
In this question, we have been given an expression (7^3) * (7^x)
We need to find expressions that are equivalent to given expression.
Consider given expression (7^3) * (7^x)
We know that 7^3 = 343
So given expression becomes, (7^3) * (7^x) = 343 * (7^x)
For given expression, the bases of the exponents are equal.
so, by the properties of exponents
(7^3) * (7^x) = 7^(3 + x)
Therefore, for given expression (7^3) * (7^x) equivalent expressions are:
343 * 7^x and 7^(3+x)
The correct options are option (C) and option (D)
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4. A farmer is taking a break
to watch a movie that is 25
minutes long. He doesn't have
time to watch the whole thing
in one day. So he watched 20
minutes the first day and 12
minutes the next day. How
much more of the movie does
he have left to watch?
A cake is made of 300 grams of flour,150 grams of sugar powder, and 0.75 liters of
water. Find the ratio of the floor to the total mass of the mixture.
Answer: 1/4
Step-by-step explanation:
0.75 liters is the same as 750 grams.
So, the total mass of the mixture is [tex]300+150+750=1200[/tex] g.
This means the ratio is [tex]\frac{300}{1200}=\frac{1}{4}[/tex].
Answer:
Flour : total mass = 1 : 4
Step-by-step explanation:
Given ingredients for the cake:
Flour = 300 gSugar = 150 gWater = 0.75 LFirst convert the mass of the water to the same SI units as the other ingredients.
1 liter = 1000 g
⇒ Water = 0.75 liters = 750 g
Total mass of the mixture:
= flour + sugar + water
= 300 g + 150 g + 750 g
= 1200 g
Therefore, the flour to total mass ratio is:
⇒ Flour : total mass = 300 : 1200 = 1 : 4
a restaurant manager collected data to predict monthly sales for the restaurant from monthly advertising expenses. the model created from the data showed that 36 percent of the variation in monthly sales could be explained by monthly advertising expenses. what was the value of the correlation coefficient? responses 0.64 0.64 0.60 0.60 0.40 0.40 0.36 0.36 0.13
The value of the correlation coefficient is 0.60.
There is a 0.6 correlation coefficient between two variables, which measures the strength of the relationship.
R² is the coefficient of determination, which measures how much variation can be explained by the regression line.
This means that, the R² value of the data is 36%
R² = 36% = 0.36
Correlation coefficients measure the strength of relationships between variables in the form of square roots.
That is ; R = √R²
R = √0.36
Hence, the correlation Coefficient, R is 0.60
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you are going to paint the 6-sector spinner shown. there are 4 colors to choose from. 0 how many different ways can you paint the spinner, if each color can be used more than once, and: there are no other restrictions?
The different ways can paint the spinner is [tex]4^{6}[/tex].
Permutation and Combination:
A permutation is an act of arranging objects or numbers in order. Combinations are the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.
Here it is given that to paint the 6-sector spinner shown there are 4 colors to choose from.
The total number of ways to color this spinner with 6 different parts and 4 different colors is 4 × 4 × 4 × 4 × 4×4 = [tex]4^{6}[/tex] ways
Therefore the ways is [tex]4^{6}[/tex].
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in the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a
If all other values remain constant, an increase in sample size will result in a broader confidence interval when constructing one.
The definition of the MoE, or margin of error, is
MoE = sigma ÷ sqrt(n)
The population standard deviation is represented by sigma. If you don't know sigma, utilize s to get a rough idea of it. The sample standard deviation is denoted by the variable s.
The MoE increases along with the sigma. The width or narrowness of the confidence interval is directly determined by the MoE. A smaller MoE indicates greater confidence with less error, whereas a larger MoE indicates greater net casting but increased error.
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What is the answer to x - 5 > 12?
Answer:
x > 17
Step-by-step explanation:
x - 5 > 12 ( isolate x by adding 5 to both sides )
x > 17
-------------- from your comment
x - (- 5) > 12 , that is
x + 5 > 12 ( subtract 5 from both sides )
x > 7
EASY POINTS WILL GIVE BRAINLIST TO BEST ASWER!!
write the point slope form of the equation of the line through the given point with the given slope
through: (-1, -2) slope =3
Answer:
y=3x+1
Step-by-step explanation:
we know slope so just fill in the rest
y=3x
-2=3(-1)
-2=-3
We add 1 to make the equation true so the y intercept is 1
Hopes this helps please mark brainliest
Expand and simplify (x + 3)(x + 5)
Answer:
expanded: x^2+8x+15
Step-by-step explanation:
(x+3)(x+5)
x^2+5x+3x+15
kara categorized her spending for this month into four categories: rent, food, fun, and other. the amounts she spent in each category are pictured here. rent $500 food $400 fun $300 other $600 [graphs generated by this script: initpicture(-5.5,5.5,-5.5,5.5);circle([0,0],5);line([0,0],[5,0]);line([0,0],[-.868,4.924]);text([1,2],'rent','right');text([1,1],'$500','right');line([0,0],[-5,0]);text([-1,2],'food','left');text([-1,1],'$400','left');line([0,0],[2.5,-4.33]);text([1,-1],'fun','right');text([1,-2],'$300','right');text([-1,-1],'other','left');text([-1,-2],'$600','left');] what percent of her total spending did she spend on fun? answer to the nearest whole percent. %
Answer: is 16.6%
Step-by-step explanation: Use the rule of three (mathematic).
I need help please because I am failing in math
Answer:
what do you need help with?
Answer:
Step-by-step explanation:
You need a picture of the item.
Andy needs to solve
3/5
A. No, because and are not equivalent.
3
OD. Yes, because
3. In order to do this, he multiplies. Will Andy's method work?
OB. Yes, because dividing by a fraction is the same as multiplying by the reciprocal of the fraction.
OC. No, because one strategy involves division and the other involves multiplication.
3/6
and are equivalent