To solve this word problem, set up the equation (1/5) x + (1/10) x = 42 and solve for x. The team scored 140 points.
Explanation:To solve this word problem, we can start by letting the total number of points scored by the team be represented by 'x'. Since Michaela scored one-fifth of the team's points, her score can be represented as (1/5)x. Similarly, Aleah's score can be represented as (1/10)x. Together, their scores add up to 42 points, so we can set up the equation:
(1/5)x + (1/10)x = 42
To simplify the equation, we can find a common denominator of 10:
(2/10) x + (1/10) x = 42
Combining like terms, we get:
(3/10) x = 42
To isolate x, we can multiply both sides of the equation by 10/3:
x = 42 * (10/3)
Simplifying further, we get:
x = 140
Therefore, the team scored 140 points.
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Find the perimeter of the rectangle.
If the rectangle has vertices M(−2,4), N(1,5), O(3,−1), and P(0,−2), what is the perimeter of the rectangle?
Round each side length to the nearest tenth, if necessary.
help plsss need this for tomorrow
Solve by factoring write the steps.
x2−7x+10=0
Please help show me all the steps and the answers
Which diagram could be used to prove △ABC ~ △DEC using similarity transformations?
(from top to bottom, first pictures top option is A for example)
A.
B.
C.
D.
To prove similarity, the triangles must have three angles or any three components must be equal. According to the statement, option A seems to be proof the triangles are similar to each other.
There are two images given in the question.
Let us segregate the images into image 1 and image 2.
Take image 1.
In image 1, three different triangles are given,
One angle is equal in all the triangles, which is represented as a single arc.Another angle is represented as a double arc is equal.If two angles are equal in triangles then the third angle is automatic get equal.According to the above bullet points, image 1 qualifies all the requirements for the similarity of the triangles.
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One number is one less than five times another. if their sum is decreased by three, the result is eight. find the numbers.
Can anyone answer this for me?
Line r passes through points (2, 11) and (10, 4). Line s is perpendicular to r. What is the slope of line s?
according to the tree diagram below what is the probability that someone buys a book that is paperback and fiction
see the attached figure to better understand the problem
we know that
[tex]0.65\ (65\%)[/tex] of the buyers buy paperback and [tex]0.45\ (45\%)[/tex] of them buy fiction.
Hence
The probability that they buy both fiction and paperback is equal to
[tex]0.65*0.45=0.2925[/tex]
the answer is
[tex]0.2925[/tex]
1.One of the lamp posts at a bank has a motion detector on it, and the equation (x+15)2+(y−12)2=25 describes the boundary within which motion can be sensed.
What is the greatest distance, in feet, a person could be from the lamp and be detected?
5 ft
10 ft
50 ft
125 ft
Answer:
5ft
Step-by-step explanation:
The required greatest distance, in feet, a person could be from the lamp and be detected is 5 ft. Option A is correct.
The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.
Here,
Given equation
(x+15)²+(y−12)²=25
The above equation is the equation of the circle, so the longest distance that person could be from the lamp and be detected is the radius of the circle,
Which is given as,
r² = 25
r = √25
r = 5
Thus, the required greatest distance, in feet, a person could be from the lamp and be detected is 5 ft. Option A is correct.
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On Monday Mrs. Wise bought 3 lbs of apples at $4 per lb. On Tuesday, apples were on sale for 20% off so she bought another 5 lbs. What was the price of apples on Tuesday? NEED ANSWER ASAP!
It is given that on Tuesday, apples were on sale for 20% off. Now, we know that on Monday Mrs. Wise bought 3 lbs of apples at $4 per lb. This means that if we have a 20% off on Tuesday then this must be with respect to the price on Monday which is $4. Thus the price of Tuesday can be calculated as:
[tex] 4-\frac{20}{100}\times 4=4-0.8=3.2 [/tex]
Thus, the per pound price of apples on Tuesday was $3.2
Please help!! Which of the following could represent the scale factor of the smaller figure to the larger figure?
Smaller figures volume is 216in.^3
Larger figures volume is 343in.^3
The scale factor from the smaller figure to the larger figure is found by taking the cube root of the ratio of their volumes, which is the cube root of 216/343.
Explanation:The student asked: Which of the following could represent the scale factor of the smaller figure to the larger figure? When comparing the volumes of two geometric figures, we can determine the scale factor of their linear dimensions by understanding the relationship between volume and linear scale factor.
Given that the smaller figure's volume is 216 cubic inches and the larger figure's volume is 343 cubic inches, we are looking for the cube root of the ratio of these volumes to find the linear scale factor.
To find the scale factor from the smaller figure to the larger figure, divide the volume of the smaller figure by the volume of the larger figure and then calculate the cube root: Scale factor = ∛(216/343). This calculation will give you the scale factor of the linear dimensions from the smaller figure to the larger figure.
what is the sum of the arithmetic series 18 t=1 (3t-4)
a. 234
b. 441
c. 25.5
d. 49
The given arithmetic series is
[tex] \sum_{t=1}^{18} (3t-4) [/tex]
When t =1, we will get the first term,a, which is
[tex] 3(1)-4 =3-4=-1 [/tex]
When t =18, we will get the last term,l , which is
[tex] 3(18)-4 = 50 [/tex]
Now we use the formula of sum of n terms which is
[tex] S = \frac{t}{2} (a+l) [/tex]
Substituting the values of t,a and l, we will get
[tex] S = \frac{18}{2} (-1+50) = 9*49 =441 [/tex]
Consider the arithmetic series [tex] _{t=1}\Sigma^{t=18} (3t-4) [/tex]
Let t=1 in the given series, we get
first term = [tex] a_{1} [/tex] = 3-4 = -1.
Let t=2 in the given series, we get
second term = [tex] a_{2} [/tex] = [tex] (3 \times 2)-4 = 2 [/tex]
Let t=3 in the given series, we get
third term = [tex] a_{3} = (3 \times 3)-4=5 [/tex]
Now, let t=18 in the given series, we get
last term = l = [tex] l = (3 \times 18)-4 = 50 [/tex]
We get the series as
-1, 2, 5,..... 50
Sum = [tex] \frac{n}{2}(a+l) [/tex]
= [tex] \frac{18}{2}(-1+50) [/tex]
= [tex] = 9 \times 49 [/tex]
= 441
Therefore, the sum of the given arithmetic series is 441.
Can someone please help? In the circle at right, AZB is a(n): (A) minor arc, (B) central angle, (C) major arc, (D) arcezoid, or (E). None of these? Thanks
In this question it has been clearly indicated that AZB is to be taken as an arc. This is because there is the arc symbol on top of AZB. Thus, we have [tex] \overarc{AZB} [/tex] and we need to answer what does the arc [tex] \overarc{AZB} [/tex] represent.
As we can see from the diagram, by visual inspection, that AZ is the chord which is lesser than the diameter and AZB is the segment on that lesser side of the circle. Therefore, the arc [tex] \overarc{AZB} [/tex] must be the minor arc.
Therefore, Option A, minor arc is the correct answer.
What is the equation, in slope-intercept form, of the line that is perpendicular to the line Y-4=-2/3(X-6) and passes through the point (-2,-2)
Answer:
d
Step-by-step explanation:
Factor completely. a2+3a−28 Enter your answer in the box.
Solution :
To factor completely
[tex] a^{2} + 3a-28 [/tex]
To factor it completely , first take the product of first and third term, and then break the second term in two parts in such a way that its sum equals the second term and the product equals the product of first and third term.
Product of first and third term is [tex] (a^{2})(-28) = -28 a^{2} [/tex]
Second term is 3a, Re-write 3a as sum of 7a and -4a.
Lets check it Product of 7a and -4a is [tex] -28 a^{2} [/tex] wich is eaqual to product of first and third term and sum of 7a and -4a is 3a which is the second term.
Now factorise, we get
[tex] a^{2}+3a-28\\\\ = a^{2} +7a-4a-28\\\\=a(a+7)-4(a+7)\\\\=(a+7)(a-4) [/tex]
Hence, [tex] (a+7)(a-4) [/tex] is the factor of [tex] a^{2}+3a-28 [/tex].
Select ALL the correct answers.
The square of the sum of a number and 6 plus twice the number is equal to 189.
Which equations could be used to represent this relationship?
(3x + 6)2 = 189
(x + 6)2 + 2x = 189
(x + 6)2 = 189 + 2x
x2 + 10x + 36 = 189
x2 + 14x + 36 = 189
x2 + 2x + 6 = 189
Answer:
[tex](x+6)^{2}+2x=189[/tex]
and
[tex]x^{2}+14x+36=189[/tex]
Step-by-step explanation:
Let
x -----> the number
we know that
The equation that represent the situation is
[tex](x+6)^{2}+2x=189\\ \\x^{2} +12x+36+2x=189\\ \\x^{2}+14x+36=189[/tex]
therefore
The equations that could be used are
[tex](x+6)^{2}+2x=189[/tex] and [tex]x^{2}+14x+36=189[/tex]
Answer:
(x+6)^{2}+2x=189
and
x^{2}+14x+36=189
Step-by-step explanation:
Which polynomial correctly combines the like terms and expresses the given polynomial in standard form? 8mn5 – 2m6 + 5m2n4 – m3n3 + n6 – 4m6 + 9m2n4 – mn5 – 4m3n3 n6 + 7mn5 + 14m2n4 – 5m3n3 – 6m6 –2m6 – 5m3n3 + 14m2n4 + 7mn5 + n6 14m2n4 + 7mn5 – 6m6 – 5m3n3 + n6 n6 – 6m6 + 7mn5 + 14m2n4 – 5m3n3
The correct combining of like term is
f(m, n) = [tex]n^{6}[/tex] + 7m[tex]n^{5}[/tex] + 14m²[tex]n^{4}[/tex] - 5m³n³ -6[tex]m^{6}[/tex] - 2[tex]m^{6}[/tex]
What is polynomial equation?A polynomial equation is the equation in which the unknown variable is one and the highest power of the unknown variable is n.
Given:
8m[tex]n^{5}[/tex] - 2[tex]m^{6}[/tex] +5m²[tex]n^{4}[/tex] - m³n³ + [tex]n^{6}[/tex] - 4[tex]m^{6}[/tex] + 9m²[tex]n^{4}[/tex] - m[tex]n^{5}[/tex] - 4m³n³
Now, Combining the like terms
(8m[tex]n^{5}[/tex] - m[tex]n^{5}[/tex]) + 5m²[tex]n^{4}[/tex] + 9m²[tex]n^{4}[/tex] - m³n³ - 4m³n³ + [tex]n^{6}[/tex] - 4[tex]m^{6}[/tex] - 2[tex]m^{6}[/tex]
=7m[tex]n^{5}[/tex] + 14m²[tex]n^{4}[/tex] - 5m³n³ - 6 [tex]m^{6}[/tex] + [tex]n^{6}[/tex]
now, arranging according to their powers
[tex]n^{6}[/tex] + 7m[tex]n^{5}[/tex] + 14m²[tex]n^{4}[/tex] - 5m³n³ -6[tex]m^{6}[/tex] - 2[tex]m^{6}[/tex]
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3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi.
I have the same problem but with 14 being 15 in and 9 being 7 in, can someone help?
What is the equation of the line described below written in slope-intercept form? the line passing through point (0, 0) and parallel to the line whose equation is 3x + 2y - 6 = 0
Answer:
The slope intercept form of the required line is [tex]y=\frac{-3}{2}x[/tex].
Step-by-step explanation:
If a line is defined as
[tex]Ax+By+C=0[/tex] ... (1)
Then the slope of the line is
[tex]m=\frac{-A}{B}[/tex]
The given equation is
[tex]3x+2y-6=0[/tex] .... (2)
From (1) and (2), we get
[tex]A=3, B=2, C=-6[/tex]
The slope of the line is
[tex]m=\frac{-3}{2}[/tex]
The slope of parallel line is same. So, the slope of required line is -3/2.
The slope intercept form of a line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
The slope of required line is -3/2 and y-intercept is at (0,0).
[tex]y=\frac{-3}{2}x+0[/tex]
[tex]y=\frac{-3}{2}x[/tex]
Therefore the slope intercept form of the required line is [tex]y=\frac{-3}{2}x[/tex].
Cassandra lives in Oklahoma and makes $60,000 a year. If the median annual income in Oklahoma is $64,105 and the median annual income in the United States as a whole is $50,233, is Cassandra likely to qualify for Chapter 7 bankruptcy?
Answer:
Cassandra is likely to qualify for Chapter 7 bankruptcy.
Step-by-step explanation:
Given scenario is : Cassandra lives in Oklahoma and makes $60,000 a year. The median annual income in Oklahoma is $64,105.
A person qualifies for chapter 7 bankruptcy, if his annual median income is below the median income of his state. So, here the annual median income of Cassandra is below the median income of her state, Oklahoma.
So, she will qualify for chapter 7 bankruptcy.
What is the slope-intercept form for each equation in this system? Compare the slopes and y-intercepts to describe the graph of the system. 3x - 4y = 28 4x + 10y = 20 A) y = 3 4 x − 7; y = −2 5 x + 2; one line B) y = - 3 4 x − 7; y = −2 5 x + 2; parallel lines Eliminate C) y = 3 4 x − 7; y = 2 5 x + 2; intersecting lines D) y = 3 4 x − 7; y = −2 5 x + 2; intersecting lines
The slope - intercept form of the equations are : [tex]y = \frac{3}{4} x - 7 [/tex] and [tex]y = - \frac{2}{5} x + 2[/tex]
Given the standard form of the equations :
3x - 4y = 28 - - - - (1)4x + 10y = 20 - - - - - (2)The General form of a slope - intercept equation :
y = bx + cFor equation (1) :
3x - 4y = 28
Make y the subject
-4y = 28 - 3x
Divide both sides by - 4 to isolate y
y = -7 + 3/4x
[tex]y = \frac{3}{4} x - 7 [/tex]
For equation (2) :
4x + 10y = 20
Make y the subject
10y = 20 - 4x
Divide through by 10 to isolate y
y = 2 - 2/5x
[tex]y =- \frac{2}{5} x + 2[/tex]
Hence, the slope - intercept equations are : [tex]y = \frac{3}{4} x - 7 [/tex] and [tex]y = - \frac{2}{5} x + 2[/tex]
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Write the equation of the line, in standard form, that passes through the origin and is parallel to x + y = 6. Include your work in your final answer.
I understand the answer is x + y = 0
I want to understand how that is determined. Using point slope form and all that.,
K - 263.48 = 381.09 solve this equation
Jalen traded $4100 for Mexican pesos, immediately changed his mind, and then promptly traded his Mexican pesos back into dollars. Which of these amounts is he most likely to have?
A. More than $0 but less than $4100
B. $0
C. $4100
D. More than $4100
APEX APEX APEX APEX APEX APEX APEX APEX APEX APEX
More than $0 but less than $4100
Please help me out :)
helppppppppppppppppppppp
Answer:
1/4
Step-by-step explanation:
Find the probability that when a couple has four four children, at least one of them is a girl girl. (assume that boys and girls are equally likely.)
If a circle has an diameter of 14, what would the area be?
Use 3.14 for π
The asymptote of the function f(x) = 3x + 1 – 2 is_________ . Its y-intercept is_____ .
Options for the first blank is
y= -2
y= -1
y= 1
y= 2
Options for the second is
(0,-2)
(0,-3)
(0,1)
(0,-1)
Answer:
In first blank : y = - 2,
In second blank : ( 0, 1 )
Step-by-step explanation:
Given function is,
[tex]f(x)=3^{x+1}-2[/tex]
The horizontal asymptote of the function f(x),
[tex]y=lim_{x\rightarrow \infty} f(x)[/tex]
[tex]y=lim_{x\rightarrow \infty} 3^{x+1}-2[/tex]
[tex]y=3^{\infty+1}-2[/tex]
[tex]y=3^\infty - 2[/tex]
[tex]y=0-2[/tex]
⇒ y = -2
First option is correct.
Also, the function has no vertical asymptote,
2. For finding the y-intercept, x = 0,
[tex]f(0)=3^{0+1}-2=3-2=1[/tex]
Hence, the y-intercept = (0,1)
Third option is correct.
Final answer:
The function f(x) = 3x + 1 – 2 is a linear function and does not have an asymptote, contrary to the options provided. The y-intercept is found by setting x to 0, which results in the point (0, – 1).
Explanation:
The function in question is f(x) = 3x + 1 – 2. To determine its asymptote and y-intercept, we analyze its structure.
Since this is a linear function and not a rational function, it does not have an asymptote like those found with rational functions, whose denominators can become zero. Instead, the original function is a modification of the function f(x) = 3x, with vertical shifts up by 1 and down by 2, effectively canceling each other out. Therefore, the asymptote is essentially the x-axis, which can be represented by the equation y = 0. However, since none of the provided options include y = 0, and the function we are analyzing is, in fact, linear without any asymptotes, there must be an error in the question regarding this part.
To find the y-intercept, we set x equal to 0 and solve for f(0):
f(0) = 3(0) + 1 – 2 = 1 – 2 = – 1.
Therefore, the y-intercept of the function is the point (0, – 1).
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