Answer:
The correct option is 3.
Step-by-step explanation:
The given expression is
[tex]7\sqrt{28}-5\sqrt{63}[/tex]
It can be written as
[tex]7\sqrt{4\times 7}-5\sqrt{9\times 7}[/tex]
[tex]7\sqrt{2^2\times 7}-5\sqrt{3^2\times 7}[/tex]
Using product property of radical expressions, we get
[tex]7(\sqrt{2^2}\times \sqrt{7})-5(\sqrt{3^2}\times \sqrt{7})[/tex] [tex][\because \sqrt{ab}=\sqrt{a}\sqrt{b}][/tex]
[tex]7(2\times \sqrt{7})-5(3\times \sqrt{7})[/tex]
[tex]14\sqrt{7}-15\sqrt{7}[/tex]
Taking out common factors.
[tex]\sqrt{7}(14-15)[/tex]
[tex]\sqrt{7}(-1)[/tex]
[tex]-\sqrt{7}[/tex]
Therefore the correct option is 3.
What is the missing term in the factorization? 18x2−32=2(3x+?)(3x−4)
Answer:
4.
Step-by-step explanation:
[tex]18x^{2} -32 = 2(9x^{2} -16)[/tex]
we apply difference of squares
2(3x-4)(3x+4)
So, the missing term is 4.
The missing term in the factorization 18x² − 32 = 2(3x + ?)(3x − 4) is 4.
What is Factorization ?Factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form. Factorization is expressing a mathematical quantity in terms of multiples of smaller units of similar quantities.
For an integer, Factorization is decomposition of that integer in terms of smaller integers; when multiplied with each other give back that considered number. Those composing integers are called factors of that considered integers.
WE have given an expression as;
18x² − 32 = 2(3x + ?)(3x − 4)
Now we apply difference of squares;
2(9x² - 16)
2(3x + 4)(3x - 4)
OR
2(3x-4)(3x+4)
Therefore, the missing term is 4.
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How do transformations in m and b effect the graph of y=mx+b
How many 12ths are equivalent to 1/3?
Find the value of x so that f || g. The diagram is not to scale.
Lines f and g are parallel with a transversal forming same side interior angles with measures 3x and 5x + 36.
Theorem: If parallel lines are cut by a transversal, then same side interior angles are supplementary.
The angles measuring 3x and 5x + 36 are supplementary, so their measures add up to 180 degrees
3x + 5x + 36 = 180
8x + 36 = 180
8x = 144
x = 18
The answer is x = 18.
Answer:
18
The answer is 18
Step-by-step explanation:
Donald baked 77 cookies in the morning and 83 cookies in the afternoon for 14 days how many total cookies did he bake
Which is an x-intercept of the graphed function?
The x-intercepts of the graphed function are -2, -1, 1, and 2
How to determine the x-intercept?The x-intercept is the point where the graph crosses the x-axis
This means that the point on the x-axis where y = 0
From the graph, we have:
x = -2, -1, 1, and 2 when y = 0
Hence, the x-intercepts of the graphed function are -2, -1, 1, and 2
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A basketball team played 14 games. the team's mean score was 66 points. how many total points did they score in the 14 games?
given the equation -2x-13=8x+7, which order of operations completely solves for x
Trina employer purchased a health insurance plan that's costs $550 per month. Trina pays $85 toward the plan each month. What is the annual value of the employer contribution?
subtract the amount Trina pays from the total:
550 - 85 = 465 per month employer pays
12 months per year
465 * 12 = $5,580 per year is what the employer pays
Answer: $5580.00
Step-by-step explanation:
Which graph is represented by the following table?
The pictures show the table and graphs. The graphs are what can show which one is the answer.
A quantity x varies directly with y and inversely with z. Which expression represents the constant of variation,k?
the answer is xz/y.
Answer:
The expression represents the constant of variation k is [tex]\frac{xz}{y}[/tex].
Step-by-step explanation:
As given
A quantity x varies directly with y and inversely with z.
[tex]x \propto y[/tex]
and
[tex]x \propto \frac{1}{z}[/tex]
Than combined the above equation.
[tex]x \propto \frac{y}{z}[/tex]
[tex]x = k\frac{y}{z}[/tex]
Where k is the constant of variation.
Than
[tex]k = \frac{xz}{y}[/tex]
Therefore the expression represents the constant of variation k is [tex]\frac{xz}{y}[/tex].
The distributive property to express 48+72
Answer:
24(2+3)=24.2+24.3=48+72
Step-by-step explanation:
Given form of number is 48+72.
we have to apply the distributive property to express the above number.
The distributive property is
a(b+c)=ab+ac
Multiply the common term with the term inside the parentheses
So to express 48+72 we have to take the highest factor outside
Let us take 24 outside, we get
24(2+3)=24.2+24.3=48+72
Hence applied
The required expression is [tex]24(2+3)[/tex] by using the distributive property.
Given:
The given expression is [tex]48+72[/tex].
To find:
The equivalent expression by using the distributive property.
Explanation:
According to the distributive property:
[tex]a(b+c)=ab+ac[/tex]
We have,
[tex]48+72[/tex]
It can be rewritten as:
[tex]48+72=24\times 2+24\times 3[/tex]
Using the distributive property, we get
[tex]48+72=24(2+3)[/tex]
Therefore, the required expression is [tex]24(2+3)[/tex].
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Twice the sum of a number and 2 is equal to three times the difference of the number and 8. find the number please help
Answer:
28
Step-by-step explanation:
Let n represent the number.
Twice the sum of the number and 2 is ...
2(n +2)
Three times the difference of the number and 8 is ...
3(n -8)
The problem statement tells us these quantities are equal, so ...
2(n +2) = 3(n -8) . . . . the given quantities are equal
2n +4 = 3n -24 . . . . . use the distributive property to eliminate parentheses
2n +28 = 3n . . . . . . . add 24
28 = n . . . . . . . . . . . . subtract 2n
The number is 28.
_____
Check
The sum of the number and 2 is 30; twice that is 60.
The difference of the number and 8 is 20; three times that is 60--the same number.
Determine the type and number of solutions of −4x^2 − 4x − 1 = 0
Help me please, I'm extremely behind in math
50 POINTS!!
What are the missing parts that correctly complete the proof?
Answer:- 2. ∠JKM≅∠LKM
5. MK≅MK
6. AAS congruence postulate.
7. Corresponding parts of congruent triangles are congruent.
8. Definition of equidistant.
Therefore the complete proof will be
Proof :- 1. KM is the line bisector of ∠JKL. [Given]
2. ∠JKM≅∠LKM [Definition of bisector]
3. ∠KXM and ∠KYM are right angles [Given]
4. ∠KXM ≅ ∠KYM [All right angles are congruent]
5. MK≅MK [reflexive property of congruence]
6. ΔKXM ≅ ΔKYM [AAS congruence postulate]
7. MX≅MY [Corresponding parts of congruent triangles are congruent]
8. Point M is equidistant from the sides of ∠JKL [Definition of equidistant]
Hence proved.
Decide whether the function is an exponential growth or exponential decay function, and find the constant percentage rate of growth or decay.
f(x) = 2479 ⋅ 0.9948x
The scale on a map shows that 2 inches represents 15 miles. Which proportion can be used to find the actual distance, x, represented by 30 inches on the map?
Answer:
I think it's 2/15 = 30/x
Step-by-step explanation:
sorry if it's wrong
Find the Least Common Multiple of these two monomials:
16jk^8m^5 and 20j^9k^4m^6
36j^9k^8m^6
80j^9k^8m^6
4jk^4m^5
80j^10k^12m^11
lcm 16 & 10 = 80
lcm j^8 & j^9 = j^9
lcm k^8 & k^4 = k^8
lcm m^5 & m^6 = m^6
answer is: 80j^9k^8m^6
How does doubling the side lengths of a triangle affect its area?
On Wednesday night in St. Petersburg, Russia, the temperature is -11°C. On the same night in Bombay, India, the temperature is 17°C. What is the difference in temperature? Show your work.
What is the diameter of a dime in inches?
PLEASE HELP ASAP!! Will give brainliest!
Decide which of the two points lies on the graph of the line
6x-2y= -4
A, -1, -1
B, -3,-2
. Catie is 3 years older than her brother. The sum of their ages is no more than 31. Write an inequality that can be used to represent this situation, where x represents Catie's brother's age. Don’t combine like terms.
Answer: So, the required inequality that can be used to represent this situation is [tex]2x+3\leq 31[/tex]
Step-by-step explanation:
Let the age of Catie's brother be 'x'.
Let the age of Catie be 'x+3'.
According to question, the sum of their ages is no more than 31.
So, it becomes,
[tex]x+x+3\leq 31\\\\2x+3\leq 31[/tex]
So, the required inequality that can be used to represent this situation is
[tex]2x+3\leq 31[/tex]
if right triangle LMN, L and M are complementary angles and sin (L) is 19/20 what is cos (M)
Answer: Value of cos(M) is
[tex]\cos M=\frac{19}{20}[/tex]
Step-by-step explanation:
Since we have given that
LMN is a right angled triangle where L and M are complementary angles ,
And,
[tex]\sin L=\frac{19}{20}=\frac{Perpendicular}{Hypotenuse}[/tex]
so, we will find base now by using "Pythagorus theorem":
[tex]H^2=B^2+P^2\\\\20^2=B^2+19^2\\\\400=B^2+361\\\\400-361=B^2\\\\39=B^2\\\\\sqrt{39}=B[/tex]
As we know that side opposite to mentioned theta is considered as perpendicular as shown in the figure ,
For M as [tex]\theta[/tex]
NL will be its perpendicular and MN will be its base and to find the cos(M) we use Base and Hypotenuse.
So, now we will find cos(M) i.e.
[tex]\cos M=\frac{Base}{Hypotenuse}=\frac{19}{20}[/tex]
Hence,
[tex]\cos M=\frac{19}{20}[/tex]
If i run 5 miles in 38 minutes how many miles can i run in 57
A toy manufacturer makes a toy truck, a toy car, and a toy boat. The production spreadsheet is:Toy Time to Produce Cost to Produce Profit for Each Truck 10 minutes $1.00 $1.00 Car 12 minutes $0.75 $1.50 Boat 8 minutes $0.80 $0.60 After accounting for breaks, a worker actually works 400 minutes each day. The manufacturer needs each worker to generate a potential profit of $35 each day. Write a system of inequalities that expresses these constraints
Bill earns $87.50 per week and Jack earns $70.00 per week. What percent of Bill's salary is Jack's?
Answer:
80%
Step-by-step explanation:
Let us suppose x percent of Bill's salary is equal to Jacks's salary.
Thus, we can write
x% of 87.50 = 70
Mathematically, we can write this as
[tex]0.0x\times87.50=70[/tex]
Solve the equation for x
[tex]0.0x=\frac{70}{87.50}\\\\x=\frac{70}{87.50}\times100\\\\x=80[/tex]
Therefore, Jack's salary is 80% of Bill's salary
The sum of the squares of two consecutive even integers is 452. find the integers.
The box plots show male and females grades in mathematics class: Which of the following best describes the information about the interquartile ranges?
Answer:
The interquartile ranges are quite close in value.
Step-by-step explanation:
We have been given two box-plots and we are asked to choose the correct statement about the interquartile ranges.
Since we know that interquartile range is difference between upper and lower quartile.
[tex]IQR=Q_3-Q_1[/tex]
Let us find IQR for the female grades in math.
We can see from box-plot representing female grades that upper quartile is about 90 and lower quartile is about 75.
[tex]\text{IQR of female grades}=90-75[/tex]
[tex]\text{IQR of female grades}=15[/tex]
Now let us find IQR for the male grades in math.
[tex]\text{IQR of male grades}=85-70[/tex]
[tex]\text{IQR of male grades}=15[/tex]
We can see IQR values for males and females are same, therefore, last statement is true.