Translating the situation to a mathematical sentence, and solving, we find that the solutions are: [tex]x = 5 \pm 3\sqrt{2}[/tex]
The translation of the problem given is:
[tex](x - 5)^2 + 1 = 19[/tex]
Then, solving:
[tex](x - 5)^2 = 18[/tex]
[tex]x^2 - 10x + 25 = 18[/tex]
[tex]x^2 - 10x + 7 = 0[/tex]
Which is a quadratic equation with [tex]a = 1, b = -10, c = 7[/tex]. Then:
[tex]\Delta = (-10)^{2} - 4(1)(7) = 72[/tex]
[tex]x_{1} = \frac{-(10) + \sqrt{72}}{2}[/tex]
[tex]x_{2} = \frac{-(-10) - \sqrt{72}}{2}[/tex]
[tex]\sqrt{72} = \sqrt{9 \times 8} = \sqrt{3^2 \times 2^3} = 6\sqrt{2}[/tex], then:
[tex]x_1 = 5 + 3\sqrt{2}[/tex]
[tex]x_2 = 5 - 3\sqrt{2}[/tex]
The solutions are [tex]x = 5 \pm 3\sqrt{2}[/tex]
A similar problem is given at https://brainly.com/question/13094243
if everything in a store is 20% off and the discounted price of an item is $18.00 what is the regular price?
Answer:
14.4 dollars
Step-by-step explanation:
If you buy an item at $18 dollars with a 20% discount, you will pay 18 - 3.6 = 14.4 dollars
7 divided by 9 and 7 simplify
Answer:
Assuming you mean 7 divided by 9/7, the answer would be 5 4/9. If you can clarify your question though if I'm wrong, I'd love to redo the problem and get you the right answer! ^-^
Step-by-step explanation:
When polled to find out if they
preferred hamburgers or hot dogs, all 120
students in the class responded. Sixty-five
percent said they preferred hamburgers,
while the rest preferred hot dogs, The
Picnic Committee decided to order 2
hamburgers or 2 hot dogs for each
student, based on the students' choices.
How many hamburgers were ordered
Answer:
156 hamburgersStep-by-step explanation:
Number of students = 120
Number of those prefer hamburgers:
120*65/100 = 78Number of hamburgers ordered:
78*2 = 156Step-by-step explanation:
[tex]\boxed{\begin{array}{c|c|c} \boxed{\bf hamburgers } & \boxed{\bf hot \ dogs } &\boxed{\bf Students } \\ 65\%& (100-65)=35\% & 120 p \\ \end {array }}[/tex]
Each person is given 2 burgers or 2 hot dogs
Then :
120*2*0,65=156 hamburgers
Which statement is true about the relationship between the height of the plant and the number of days?
A. This relationship is a function because the plant can be more than one height at a time.
B. This relationship is not a function because the plant can be more than one height at a time.
C. This relationship is not a function because the plant can only be one height at a time.
D. This relationship is a function because the plant can only be one height at a time.
This relationship is a function because the plant body can be of only one particular height at a time.
A function can be defined as a relationship between a set of inputs having only one output each. In other words, a function is basically a relationship between inputs and outputs; where each input is related to only one output at a time. Functions are said to occur when the recorded value of x is varied each time. Since we know that the height of the plant (the x-value) varies by each day, Therefore it is a function.
thus we can conclude that the correct option for the relationship between the height of the plant and the number of days is option D, which tells that this relationship is a function because the plant body can only be of one particular height at a time.
To learn more about functions
visit; https://brainly.com/question/12431044
#SPJ1
In a chemical reaction, Substance A reacts with Substance B and forms a new substance AB. The chemical equation for this reaction is A + B = AB where A and B are the reactants and AB is the product. If you add more and more of only Substance A, there will be
Answer:
More and more of product AB but limited to the amount of B
Step-by-step explanation:
Adding more of one substance which makes up the reactant will increase the number of product AB that will be obtained but limited by the amount of B.
The amount of reacting substances is directly proportional to the amount of product yield. This means that adding more and more of the substance which makes up the reactant increases the amount of atoms reacting to form a product.
Hence, adding more and more of only substance A will increase the product AB, however, the amount of B in the product will be limited.
Learn more :https://brainly.com/question/12373196
137.8×3.5 with explanation
Answer:
482.3
Step-by-step explanation:
because 137.8 times 3.5 is
482.3
9/2 + (-8)
Explain the steps
Answer:
nine divided by 2 plus negative eight
Step-by-step explanation:
9/2=4.5
4.5+(-8)= -3.5
Step-by-step explanation:
= 9/2 + -8/1
= 9/2 + 16/2
= 9 + (-16)/2
= -7/2
classify the equation as having one solution no solution or infinite solution
4(9x+6)=36x-7 And the solution is x=
Answer:
[tex]\boxed{\bf {{No\:Solution}}}[/tex]
Step-by-step explanation:
[tex]\bf 4(9x+6)=36x-7[/tex]
Expand: Apply Distributive proprty:
[tex]\bf 36x+24=36x-7[/tex]
[tex]\boxed {\bf \sf {Subtract\:}24\sf {\:from\:both\:sides}}[/tex]
[tex]\bf 36x+24-24=36x-7-24[/tex]
[tex]\bf 36x=36x-31[/tex]
[tex]\boxed {\sf {Subtract\:}36x\sf {\:from\:both\:sides}}[/tex]
[tex]\bf 36x-36x=36x-31-36x[/tex]
[tex]\bf 0=-31[/tex]
Because the sides are not equal there is no Solution
yeah, uhm can someone help me with this?
Answer:
-24
Step-by-step explanation:
[tex]x/4 + 8 = 2\\x/4 = 2 - 8\\x/4 = -6\\x = -6 *4\\x = -24[/tex]
Sven participates in his employer’s 401k plan. His annual salary is $52,000. Sven contributes 7.5% of his annual salary. His employer matches his contributions up to 5% of his salary. How much money will be contributed to Sven’s plan for one year?
Answer:
$ 6,500
Step-by-step explanation:
(52,000)(0.075)+(52,000)(0.05) = 3,900 + 2,600
= 6,500
help me!!!!!!! please please please
Answer:
y and 65 is equal
y= 65°
....................
. Twelve out of 36 students in a class are in the
drama club. What is the ratio of the students in the
drama club to the students who are not in the
drama club?
Is side length 17, 144, and 145 right triangle?
Yes it is.
Use the Pythagorean Theorem:
a²+b²= c²
So, 17²+144²=145²
289+20736=21025
289+20736=21025
21025=21025
Can someone pls help me with this!!!
Answer:
Step-by-step explanation:
Convergent: Two plates are coming together. This results in one or both edges of the plates to move upwards to form mountains. If one plate is pushed down while the second is pused up, a deep trench may form (ocean trenches). Volcanoes and earthquakes may also form along this boundary. The Pacific "Ring of Fire" is due to convergent plate collisions.
Divergent: Divergent boundaries occur when two plates move away from each other. Earthquakes and volcanoes are common as the growing gap allows magma to comes to the surface. Iceland is divided between the North American and Eurasian plates and this has produced an ever-widenng gap down the center of the country, which is both a major tourist attraction and a source for volcanic activity and numerous hot spring pools. One bridge across this gap is known as the "Bridge Between Continents," and is designed to accomodate the Xcm/year stretch as the continents separate even further.
Transform: Two plates slide past each. The San Andreas fault is one of the more famous. Structures, both natural and man-made, that cross a transform boundary can be split into pieces and moved in opposite directions. Rocks along the boundary are pulverized as the plates grind them. This can result in a linear fault valley or undersea canyon. Earthquakes are common along these faults. Unlike convergent and divergent boundaries, crust is cracked and broken at transform margins, but is not created or destroyed as with convergent and divergent boundaries.
how to expand (x+3)(x+4) into algebraic expression
Answer:
x²+7x+12
Step-by-step explanation:
x*x=x²
x*4=4x
3*x=3x
4x+3x=7x
3*4=12
=x²+7x+12=0
Answer: ^2 + 7 + 12
Step-by-step explanation:
(x + 4)(x + 4)
( + 4)+3( + 4)
( + 4)+3( + 4)
^2 + 4 + 3( + 4)
^2 + 4 + 3 + 12
^2 +7 +12
in the diagram, fine pis parallel to side BC. What is the sum of the measures of 21 and 22? B What is the sum of the measures of_1 and _2? P 570 m_1 + m_2= ID 1 A 2 49 c
Answer:
76 women classified with severe hip pain, the WOMAC mean function score was 70.7 with standard deviation of 14.6, and we wish to know if we may conclude that the mean function score for a population of similar women subjects with severe hip pain is less than 75. let alpha is equal
What is the least common denominator (lcd) of 1/2 2/3
Answer:
6
Step-by-step explanation:
Find the least common multiple (LCM) of the denominators in order to find the least common denominator (LCD).
Do you set the legs of an isosceles triangle equal to each other when given one leg and the other is an equation?
Answer:
Yes
Step-by-step explanation:
Both legs of an isosceles triangle are congruent so they can be made to say that one leg=the equation of the other leg.
The line passes the points (-6,2) and (3,-5)
Answer:
Slope-intercept form:
y = -7/9x - 8/3
The slope:
m = -7/9
Picture is of it graphed
Directions: Follow the instructions for the following inequalities. Will give brainlist!
1. 4<7 Multiply both sides by 7, then by 6, then by 3, then by 10
2. 11>-2 Add 5 to both sides, then add 3, then add (-4)
3. -4<-2 Subtract 6 from both sides, then 8, and then 2
4. -8<8 Divide both sides by -4, then by -2
5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
1) 4<7
×7 ×7
28<49
×6 ×6
168<294
×3 ×3
504<882
×10 ×10
5040<8820
2) 11>-2
+5 +5
16> 3
+3 +3
19>6
+-4 +-4
15>2
3) -4<-2
-6 -6
-10<-8
-8 -8
-18<-16
-2 -2
-20<-18
4) -8<8
÷-4 ÷-4
2<-2
÷-2 ÷-2
-1< 1
5) ~The affect of the inequality sign didn't change. If you add or subtract the same positive or negative number to both sides of an inequality or an equation, the inequality stays the same. If you multiply or divide both sides of an inequality or an equation by the same positive number, the inequality stays the same. This is because when manipulating inequalities there are rules this if a < b then a + c < b + c so we get a new number that replaces a and b yet the inequality symbol stays the same so a still is smaller than b.
Hope this helped you- have a good day bro cya)
What is the smallest number greater than 1 that leaves a remainder 1 when divided by each of 2, 3, and 4?
PLS SHOW WORK
Answer:
YOOOO I LOVE YOUR PROFILE PICTURE. SILENT VOICE IS SO SAD BUT SO GOOD <3 :D
if kathy had 1700 apples and split with her 4 friends. and then one friend give her back 15 apples. and she gives then 1 apple back. how. much does she have.
Answer:
439
Step-by-step explanation:
1700/4=425
15-1=14
425+14=439
alr so imma need this answer rn
The answer should be:
x = 5
So the answer is basically 5
The sum of half of a number and 8 less
than the number is 25. Find the number.
Answer:
The number is 22
Step-by-step explanation:
let x = the number
[tex] \frac{1}{2} x + x - 8 = 25 \\ \frac{1}{2} x + x - 8 + 8 = 25 + 8 \\ \frac{1}{2} x + x = 33 \\ factor \: out\: x \: on \: the \: left \\ x( \frac{1}{2} + 1) = 33 \\ divide \: both \: sides \: by \: \frac{1}{2} + 1 \\ \frac{x( \frac{1}{2} + 1) }{ \frac{1}{2} + 1} = \frac{33}{ \frac{1}{2} + 1} \\ x = \frac{33}{ \frac{3}{2} } \\ x = \frac{66}{3} \\ x = 22[/tex]
let's factor out x from the left hand sid
Can someone tell me what 1=x-18 equals
Answer:
19 = x
Step-by-step explanation:
1=x-18
Add 18 to each side
1+18=x-18+18
19 = x
(7a*2b)+3c=3c+(7a*2b)
A.Commutative Property of Addition
B.Commutative Property of Multiplication
C.Associative Property of Addition
D.Associative Property of Multiplication
(7a*2b)+3c=3c+(7a*2b) the property for the given expression is Option A) Commutative Property of Addition.
The given expression is (7a*2b) + 3c = 3c + (7a*2b). This equation demonstrates the Commutative Property of Addition.
The Commutative Property of Addition states that the order in which numbers are added does not affect the result.
In mathematical terms, it can be written as: a + b = b + a.
In your expression, you have terms involving both addition and multiplication. However, since addition is involved on both sides of the equation, we can focus on the addition aspect.
(7a*2b) + 3c = 3c + (7a*2b)
First, we can rearrange the terms on the left side:
7a*2b + 3c = 3c + 7a*2b
Now, observe that the terms on both sides of the equation are the same: 7a*2b and 3c.
They are just arranged in a different order. This aligns with the Commutative Property of Addition, which says the order of addition doesn't matter.
Therefore, the expression is an illustration of this property, and the correct answer is the Commutative Property of Addition (A).
In summary, the expression shows that changing the order of terms within an addition does not change the result, thus demonstrating the Commutative Property of Addition.
To know more about Commutative Property here
https://brainly.com/question/2166345
#SPJ3
brian split 5/6 pounds of candy among 3 people what is the unit rate
Answer:
5/18Step-by-step explanation:
Divide the total by number of people to find the unit rate:
5/6 : 3 = 5/18 pounds per personAnswer:
[tex]\sf\longmapsto \frac{5}{18}pounds \:per\: person [/tex]
Step-by-step explanation:
[tex]\sf\longmapsto \: \frac{5}{6} : 3[/tex]
[tex]\sf\longmapsto \frac{5}{18} pounds \:per\: person [/tex]
Mrs. Larsen wants to get some markers for her class. She notices that they come in boxes of
8.
Write an equation that shows how the total number of markers Mrs. Larsen gets, y, depends
on the number of boxes she buys,X.
y =
(i’ll crown brainliest to whoever answers first, i don’t need the explanation just the answer and how i’m supposed to write it out)
Answer:
y=8x
Step-by-step explanation:
hubsdgvgcsvya
The equation that shows that the total number of markers Mrs. Larsen gets y depends on the number of boxes she buys x, will be;
⇒ y = 8x
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Mrs. Larsen wants to get some markers for her class.
She notices that they come in boxes of 8.
Now,
Let total number of markers = y
And, Number of boxes = x
Here, She notices that they come in boxes of 8.
So, We can formulate;
⇒ y = 8x
Thus, The equation that shows that the total number of markers Mrs. Larsen gets y depends on the number of boxes she buys x, will be;
⇒ y = 8x
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
i need some help on this!
Answer:
4
Step-by-step explanation:
AB=AC
2x-3=x+3
x=6
______________________________
BC=
x-2
(6)-2=4
Find the value of GM If DM = 35