Answer:
The length of the base is [tex]b=17cm[/tex]
Step-by-step explanation:
We start by writing the equation of the base :
Given that the base of the triangle is seven less than twice its height we can write that
[tex]b=2h-7[/tex] (I)
Where ''b'' is the base and ''h'' is the height.
Now, the area of a triangle is [tex]\frac{bh}{2}[/tex]
We know that the area is [tex]102(cm^{2})[/tex] ⇒
[tex]\frac{bh}{2}=102(cm^{2})[/tex]
Now we can replace ''b'' by the expression in (I) ⇒
[tex]\frac{bh}{2}=102(cm^{2})[/tex]
[tex]\frac{(2h-7)(h)}{2}=102(cm^{2})[/tex]
Rearraging the expression :
[tex]\frac{(2h-7)(h)}{2}=102(cm^{2})[/tex]
[tex](2h-7)(h)=204(cm^{2})[/tex]
[tex]2(h^{2})-7h=204(cm^{2})[/tex]
[tex]2(h^{2})-7h-204(cm^{2})=0[/tex]
We need the values of ''h'' that satisfy the equation.
We can use the quadratic formula with
[tex]a=2\\b=-7\\c=-204[/tex]
The quadratic formula will be
[tex]h1=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex]
and [tex]h2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]
Using [tex]a=2\\b=-7\\c=-204[/tex] in the expression of h1 and h2 we find that
[tex]h1=12\\h2=-8.5[/tex]
Given that ''h'' is a length ⇒ [tex]h\geq 0[/tex]
We conclude that h1 = 12 cm is the correct value of ''h''
With this value of ''h'' we go to the expression of ''b'' ⇒
[tex]b=2h-7\\b=2(12)-7\\b=24-7\\b=17[/tex]
The value of the base ''b'' that satisfies the problem is [tex]b=17cm[/tex]
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:
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.
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]
How does doubling the side lengths of a triangle affect its area?
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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Determine the type and number of solutions of −4x^2 − 4x − 1 = 0
Help me please, I'm extremely behind in math
The sum of the squares of two consecutive even integers is 452. find the integers.
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.
There is an average of 3.5×10−2 kilograms of dissolved salt in each liter of seawater.
The Pacific Ocean contains approximately 6.6×1020 liters of seawater.
About how many kilograms of dissolved salt are in the Pacific Ocean?
Enter your answer, in scientific notation, in the boxes.
(blank) x 10(blank) kg
IT IS 2.31, I AM TELLING YOU THIS IS 2.31
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].
. 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]
PLEASE HELP ASAP!! Will give brainliest!
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?
If i run 5 miles in 38 minutes how many miles can i run in 57
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.
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.
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.
How do transformations in m and b effect the graph of y=mx+b
How many 12ths are equivalent to 1/3?
PLEASE HELP!!!!
What is the distance between points M and N?
___ meters.
Answer:
The distance between points M and N is 9.8m.
Step-by-step explanation:
It is given that JKL is a triangle and M and N are the mid points of the KL and JL respectively.
Now, if we join the mid points together that is MN, then we can see that the basic proportionality holds that is:
[tex]\frac{LM}{MK}=\frac{LN}{NJ}[/tex]
[tex]\frac{10.7}{10.7}=\frac{7.4}{7.4}=\frac{1}{1}[/tex] which holds.
And which also proves that MN is parallel to JK.
Now, if MN is parallel to JK, then the measure of MN will be half the measure of JK, that is:
[tex]MN=\frac{1}{2}JK[/tex]
[tex]MN=\frac{1}{2}(19.6)[/tex]
[tex]MN=9.8 m[/tex]
Thus, the measure of MN is 9.8 meters.
Answer:
yah its 9.8 meters bro
Step-by-step explanation:
best of luck to yall on assignment and happy new year!!!
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
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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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
What is the diameter of a dime in inches?
Donald baked 77 cookies in the morning and 83 cookies in the afternoon for 14 days how many total cookies did he bake
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
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:
given the equation -2x-13=8x+7, which order of operations completely solves for x
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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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