Answer:
y+1/2-2y-1/2=4
y-2y=4
-y=4
y=-4
Let me know if this helps!
In the figure below, triangle ABC is similar to triangle PQR:
A right triangle ABC with right angle at B and base BC is drawn. Length of AB is 4, length of BC is 2. A similar right triangle; triangle PQR, which is triangle ABC enlarged and reflected across a horizontal line, is drawn near it. The right angle is at Q. Angle A is congruent to angle P and angle C is congruent to angle R. The length of QR is 12.
What is the length of side PQ?
48
24
40
18
Answer:
24
Step-by-step explanation:
Since the triangles are similar the side lengths must be proportional
2/12 = 4/PQ cross multiply expressions
2PQ = 48 divide both sides by 2
PQ = 24
Find all three distinct roots for X³ =1. (two of them are complex mumber). And show that sum of all roots is zero.
x ³ = 1
x ³ - 1 = 0
x ³ - 1³ = 0
Factorize the right side as a difference of cubes:
(x - 1) (x ² + x + 1) = 0
Then
x - 1 = 0 or x ² + x + 1 = 0
The first equation yields x = 1 as a root.
For the other equation, rearrange and complete the square to get the other two roots,
x ² + x + 1/4 = -3/4
(x + 1/2)² = -3/4
x + 1/2 = ±√(-3/4) = ± i √3/2
x = -1/2 ± i √3/2
x = (-1 ± i √3)/2
Since complex roots occurs in conjugate pairs, taking the sum of these two roots eliminates the imaginary part:
(-1 + i √3)/2 + (-1 - i √3)/2 = (-1 - 1)/2 = -2/2 = -1
and adding to 1 indeed shows that the sum of roots is zero.
Write an
equivalent expression by distributing the
""
"sign outside the parentheses:
-(-9.1d - 6f +9.1)
Answer:
Submit Answer
Answer:
[tex] - ( - 9d - 6f + 9.1) \\ = 9d + 6f - 9.1 \\ thank \: you[/tex]
We want to factor the following expression: (x 3)^2 14(x 3) 49(x 3) 2 14(x 3) 49(, x, plus, 3, ), squared, plus, 14, (, x, plus, 3, ), plus, 49 We can factor the expression as (U V)^2(U V) 2 (, U, plus, V, ), squared where UUU and VVV are either constant integers or single-variable expressions. 1) What are UUU and VVV
Answer:
[tex]U = x[/tex]
[tex]V=10[/tex]
Step-by-step explanation:
Given
[tex](x +3)^2 + 14(x + 3) + 49 = (U + V)^2[/tex]
Required
Find U and V
We have:
[tex](x +3)^2 + 14(x + 3) + 49 = (U + V)^2[/tex]
Expand
[tex]x^2 + 6x + 9 + 14x + 42 + 49 = (U + V)^2[/tex]
Collect like terms
[tex]x^2 + 6x + 14x + 9 + 42 + 49 = (U + V)^2[/tex]
[tex]x^2 + 20x + 100 = (U + V)^2[/tex]
Expand
[tex]x^2 + 10x + 10x + 100 = (U + V)^2[/tex]
Group
[tex][x^2 + 10x] + [10x + 100] = (U + V)^2[/tex]
Factorize each group
[tex]x[x + 10] + 10[x + 10] = (U + V)^2[/tex]
Factor out x + 10
[tex][x + 10][x + 10] = (U + V)^2[/tex]
So, we have:
[tex][x + 10]^2 = (U + V)^2[/tex]
By comparison
[tex]U = x[/tex]
[tex]V=10[/tex]
(x − 5)∙ 3 = 2∙ 10 + 8
Answer:
x=17
Step-by-step explanation:
3x-15=20+16
3x-15=36
3x=36+15
3x=51
x=17
whats the differnce in (5x+4)-(x+2)
Answer:
4x+2
Step-by-step explanation:
(5x+4)-(x+2)=(5-1)*x+(4-2)=4x+2
17’4” multiply by 17’5”
The eighth term of a linear sequence is 26. The term-to-term rule is 'add 3
Work out the fourth term of the sequence.
Explain the method you used to solve this problem.
Let a be first term
[tex]\\ \rm\longmapsto a_8=a+7d[/tex]
[tex]\\ \rm\longmapsto 26=a+7(3)[/tex]
[tex]\\ \rm\longmapsto a=26-21[/tex]
[tex]\\ \rm\longmapsto a=5[/tex]
Now
[tex]\\ \rm\longmapsto a_4=a+3d[/tex]
[tex]\\ \rm\longmapsto a_4=5+3(3)[/tex]
[tex]\\ \rm\longmapsto a_4=5+9[/tex]
[tex]\\ \rm\longmapsto a_4=14[/tex]
Can someone help me with this question?
Answer:
y = ± 15
Step-by-step explanation:
Given
y² = 225 ( take the square root of both sides )
[tex]\sqrt{y^2}[/tex] = ± [tex]\sqrt{225}[/tex]
y = ± 15
That is y = 15, y = - 15
Since 15 × 15 = 225 and - 15 × - 15 = 225
y² = 225
y = √225
y = 15
y²= 225
y = √225
y = -15
y = ±15
Therefore values of y are 15 and -15
Must click thanks and mark brainliest
Helpppppppp pleaseeee!!!!!!!!
Answer:
29.5 square inches
Step-by-step explanation:
Let's divide the shape into 3 parts to make it easy for us to find the area.
- a wide triangle
- a triangle
- a shorter rectangle
For the wider rectangle, the area is;
A1 = 8 × 2 = 16 in²
For the triangle, the area is;
A2 = ½(7 - 2) × 3
A2 = 7.5 in²
For the shorter rectangle, the area is;
A3 = 3 × 2
A3 = 6 in²
Total area = A1 + A2 + A3 = 16 + 7.5 + 6 = 29.5 square inches
If S=4πr² , find
i) the value of S when r = 10
Answer:
S = 1256
Step-by-step explanation:
S = 4[tex]\pi[/tex][tex]r^2[/tex]
S = 4[tex]\pi[/tex][tex](10)^2[/tex]
S = 4[tex]\pi[/tex][tex](100)[/tex]
S = [tex]4(314)[/tex]
S = 1256
Answer:
400pi, or 1256.637...
Step-by-step explanation:
S = 4pir^2
S = 4pi(10^2)
S = 4pi(100)
S = 400pi
I NEED HELP
THERE ARE TWO OTHER QUESTIONS AS WELL
Answer:
Please find attached the drawing of ABCD, A'B'C'D', and A''B''C''D'', created with MS Excel
Step-by-step explanation:
The given composition of transformation is [tex]r_{y-axis} \ \circ \ r_{x = - 4}[/tex]
The transformation on the right, [tex]r_{x = - 4}[/tex], is carried out first as follows;
The point A with coordinate (-7, 7) reflected across the line x = -4, gives;
A(-7, 7) [tex]r_{x = - 4}[/tex] → A'(-1, 7)
Similarly, we have;
B(-5, 7) [tex]r_{x = - 4}[/tex] → B'(-3, 7)
C(-5, 1) [tex]r_{x = - 4}[/tex] → C'(-3, 1)
D(-7, 1) [tex]r_{x = - 4}[/tex] → D'(-1, 1)
Therefore, the image of the given rectangle after reflection across the lie, x = -4, is A'(-1, 7), B'(-3, 7), C'(-3, 1), and D'(-1, 1)
The second transformation, [tex]r_{y-axis}[/tex], is found as follows;
(x, y) [tex]r_{y-axis}[/tex] → (x, -y)
Therefore, we have;
A'(-1, 7) [tex]r_{y-axis}[/tex] → A''(-1, -7)
B'(-3, 7) [tex]r_{y-axis}[/tex] → B''(-3, -7)
C'(-3, 1) [tex]r_{y-axis}[/tex] → C''(-3, -1)
D'(-1, 1) [tex]r_{y-axis}[/tex] → D''(-1, -1)
The points ABCD, A'B'C'D', and A''B''C''D'' are plotted on MS Excel and the points joined with straight lines to form the drawing of the triangles as shown in the attached figure.
Pls Help, Thanks
According to the partial construction shown, what is the next step in constructing a line perpendicular to a point on the line?
Place compass at point D, and draw an arc that intersects the arc above line DF.
Place compass at point F, and draw an arc that intersects the arc above line DF.
Place compass at point P, and draw an arc above line DF
Place compass at point P, and draw an arc below line DF
Step-by-step explanation:
First draw a lign segment like DF
Next keep the point on D make an arc by increasing the length of compass
As same keep the point on F make an arc lile same as before
Next there is apoint name it as any meeting on drew arc
connect it to the point with P
The total cost of 2 bracelets and 3 necklaces is $15.50. The total cost of 4 bracelets and 1 necklace is $13.50. Let b represent the cost of each bracelet and n represent the cost of each necklace. This situation can be represented by the following system of equations.
{2b+3n=15.504b+n=13.50
What is the cost of one bracelet?
A
$2.50
B
$7.75
C
$5.00
D
$3.50
Answer:
A
$2.50
Step-by-step explanation:
b = cost of bracelet
n = cost of necklace
2b+3n = 15.50
4b+1n = 13.50
Multiply the first equation by -2
-4b -6n = -31
4b +n = 13.50
---------------------------
-5n = -17.50
Divide each side by -5
-5n/-5 = -17.5/-5
n = 3.50
Now we can find b
4b+n = 13.50
4b+3.50 = 13.50
4b+3.50-3.50 = 13.50 -3.50
4b = 10
Divide by 4
4b/4 = 10/4
b = 2.50
How do I find x and y?
Answer:
x = 20
y = 70
Step-by-step explanation:
Since B and D are parallel :
6x - 10 + 3x + 10 = 180 add/subtract like terms
9x = 180 divide both sides by 9
x = 20
angle represented by y and 6x - 10 are supplementary and their sum is 180
y + 6x - 10 = 180 replace x with 20
y + 6*20 - 10 = 180
y + 120 - 10 = 180
y + 110 = 180 subtract 110 from both sides
y = 70
Does anyone know the answer plz ?
Answer:
x = 5; y = 5
Step-by-step explanation:
One angle is a right angle, so its measure is 90 degrees.
One angle measures 45 degrees, so the unknown angle must also measure 45 degrees.
x and y are opposite two 45-degree angles, so x = y.
In a 45-45-90 triangle, the ratio of the lengths of the sides is
1 : 1 : sqrt(2)
We have
x : y : 5sqrt(2)
x/1 = 5sqrt(2)/sqrt(2)
x = 5
y = 5
In a survey of 850 students in a school, 90% reported having pets at home. If the margin of error is 3.4%, what is the interval that is likely to contain the exact percent of all people who have pets at home?
Between 3.4% and 90%
Between 90% and 93.4%
Between 86.6% and 90%
Between 86.6% and 93.4%
Answer:
Between 86.6% and 93.4%Step-by-step explanation:
To obtain the population proportion from the sample, we calculate the confidence interval ; Confidence interval = phat ± margin of error Phat = 90% ; margin of error = +3.4% 90% ± 3.4% (90 - 3.4)% ; (90 + 3.4)% 86.6% ; 93.4%We want to find the zeros of this polynomial:
p(x) = 2x^3 + 3x^2 - 18x -27.
Plot all the zeros (x-intercepts) of the polynomial in the graph.
Answer:
-3,-1.5,3
Step-by-step explanation:
(x+3) x=-3
(x-3) x=3
(2x+3) x=-3/2
15. 4 + 2x = 4x - 20
What is the value of X?
Answer:
[tex]x = 12[/tex]
Step-by-step explanation:
[tex]4 + 2x = 4x - 20[/tex]
[tex]4 + 20 = 4x - 2x[/tex]
[tex]24 = 2x[/tex]
[tex]x = \frac{24}{2} [/tex][tex]x = 12[/tex]
Hope it is helpful....Use the box plots comparing the number of males and number of females attending the latest superhero movie each day for a month to answer the questions.
Two box plots shown. The top one is labeled Males. Minimum at 0, Q1 at 1, median at 20, Q3 at 25, maximum at 50. The bottom box plot is labeled Females. Minimum at 0, Q1 at 5, median at 6, Q3 at 10, maximum at 18 and a point at 43
Part A: Estimate the IQR for the males' data. (2 points)
Part B: Estimate the difference between the median values of each data set. (2 points)
Part C: Describe the distribution of the data and if the mean or median would be a better measure of center for each. (4 points)
Part D: Provide a possible reason for the outlier in the data set. (2 points)
Answer:
The formula for iqr is q3 - q1
24
Step-by-step explanation:
The box plot is a visual way of presenting a dataset where the rectangle is used to represent the quartiles.
The IQR of the male dataset is 24.The difference in median of both datasets is 14.The best measure of center to use for the female box plot is the median. The best measure of center to use for the male box plot is the mean.A possible reason for an outlier is human error.The given parameters are:
Male: Female
[tex]Minimum = 0[/tex] [tex]Minimum = 0[/tex]
[tex]Q_1 = 1[/tex] [tex]Q_1 = 5[/tex]
[tex]Median = 20[/tex] [tex]Median = 6[/tex]
[tex]Q_3 = 25[/tex] [tex]Q_3 = 10[/tex]
[tex]Maximum = 50[/tex] [tex]Maximum = 18[/tex]
A. IQR for male dataset
The IQR is calculated as follows:
[tex]IQR = Q_3 - Q_1[/tex]
For the male's data:
[tex]IQR = 25-1[/tex]
[tex]IQR = 24[/tex]
Hence, the IQR of the male dataset is 24.
B. Difference in median values
We have:
[tex]Median = 20[/tex] ----- Male dataset
[tex]Median = 6[/tex] ----- Female dataset
So, the difference (d) is:
[tex]d = 20 - 6[/tex]
[tex]d = 14[/tex]
Hence, the difference in median of both dataset is 14.
C. Best measure of center
The female box plot (see attachment) has an outlier. This means that the measure of center to use for the female dataset is the median.
The male box plot has no outlier; this means that the mean can be used as a measure of center for the male box plot
D. Reason for outlier
There are several reasons that could cause an outlier in a dataset. One of the reasons is human error during data entry
Read more about box plots at:
https://brainly.com/question/1523909
Which situation is best represented using a negative integer?
Answer:
a
Step-by-step explanation:
PLZ HELP ASAP ITS KHAN WILL GIVE 5 STARS AND HEART AND 10 POINTS AND BRAINLIST
Answer:
14.4
Step-by-step explanation:
Cross multiply.
5x = 8 * 9
5x = 72
x = 14.4
Answer:
x= 14.4
Step-by-step explanation:
1. cross multiply
5*x and 8*9
5x=72
2. divide 72 by 5
x= 14.4
Express 1.2, 2.25, 3.5, 4.06 as a fraction in its simplest form
Answer:
1.2 = 12/10 = 6/5
2.25 = 225/100 = 9/4
3.5 = 35/10 = 7/2
4.06 = 406/100 = 203/50
The area of each square below is 1 square unit.
HELP PLEASE SO I CAN MOVE ON
find the measure of the indicated angle to the nearest degree
Answer:
16
Step-by-step explanation:
[tex] \tan(x) = \frac{13}{46} [/tex]
[tex] \tan {}^{ - 1} ( \frac{13}{46} ) = 16[/tex]
Solve the triangle. Round to the nearest tenth when neccesary or to the nearest minute as appropriate.
Answer:
Here is the detailed answer below
Step-by-step explanation:
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Answer:
300 yd³
Step-by-step explanation:
Volume = lwh
l = 6
w = 5
h = 10
so, 6×5×10 = 300 yd³
The interest of the sum of money at the end of 10 years is one third of the sum. Find the rate of interest
Answer:
3.33%
Step-by-step explanation:
Intrest = P. A. *Intrest Rate * Time
(1/3)*P. A. = P. A. *Intrest Rate * 10
Intrest Rate = 1/30)=3.33%
6. Use a one unit multiplier to convert 20 inches to centimeters.
7. Use two unit multipliers to convert 25 feet to centimeters.
Answer:
should be 15.
Step-by-step explanation:
solve the equation - 2(3x+5/x+2) -5(x+2/3x-5) = 3 , where x unequal -2 and x unequal 5/3
it's urgent
please quys
with solution
Answer:
Step-by-step explanation:
(a - b)(a + b) =a² - b²
(3x + 5)(3x -5) =(3x)² - 5² = 9x² - 25
(x +2)(x+2) = (x+ 2)² = x²+ 2*2*x+2² = x² + 4x + 4
(x+2)(3x -5 ) = x*3x - 5*x +2*3x +2*(-5)
= 3x² -5x +6x -10
= 3x² + x - 10
[tex]\frac{2*(3x+5)}{x+2}-\frac{5(x+2)}{3x-5}=3\\\\\frac{2*(3x+5)*(3x-5)}{(x+2)(3x-5)}-\frac{5*(x+2)(x+2)}{(3x-5)(x+2)}=3\\\\\frac{2*(9x^{2}-25)-5(x^{2}+4x+4)}{(3x-5)(x+2)}=3[/tex]
[tex]\frac{18x^{2}-25-5x^{2}-20x-20}{3x^{2}+x-10}=3\\\\\frac{18x^{2}-5x^{2}-20x - 25-20}{3x^{2}+x-10}=3\\\\[/tex]
13x² - 20x - 45 = 3*(3x² + x - 10)
13x² - 20x - 45 =9x² + 3x - 30
13x² - 9x² -20x - 3x - 45 + 30 = 0
4x² - 23x - 15 = 0
