Segment DE is midsegment of triangle ABC. What is the length of segment DE?
A) 5
B) 10
C) 15
D) 20
Answers
2X+10=X+15
X=5
A) 5 :)
Answer:
B) 10
Step-by-step explanation:
If DE is midsegment of the triangle, we know that AC measures twice as DE.
In the problem we have that AC = x + 15 and DE = x + 5
Writing this as an equation we have:
[tex]x + 15 = 2(x+5)\\x+15=2x +10\\15-10=2x-x\\5=x[/tex]
Therefore x = 5 and the length of segment DE is:
x + 5 = 5 + 5 = 10
Therefore the correct answer is B) 10
Related Questions
Which of the numbers listed below are solutions to the equation? Check all that apply. x2 = 81 A. 18 B. 40.5 C. -9 D. 162 E. 9 F. 6561
Answers
x = (+-) sqrt 81
x = (+-) 9
answers are : -9 and 9
x = ±√81
x = ±9
Answers are either C and E
Find the 6th term of a geometric sequence t3 = 444 and t7 = 7104.
Answers
So 7104 = 444 * r^4 -> solve for r, you will get r = 2 or -2
So, for r = 2, t6 = t7 / r = 7104 / 2 = 3552
For r = -2, t6 = -3552
The 6th term of the geometric sequence is 3552
How to determine the 6th term of the geometric sequenceTo find the 6th term of a geometric sequence, we need to determine the common ratio (r) first.
Given that t3 = 444 and t7 = 7104, we can use these two terms to find the common ratio.
t3 = t1 * r^(3-1)
444 = t1 * r^2
t7 = t1 * r^(7-1)
7104 = t1 * r^6
Dividing the two equations, we get:
7104/444 = (t1 * r^6) / (t1 * r^2)
16 = r^4
Taking the fourth root of both sides, we find:
r = ∛16 = 2
Now that we have the common ratio (r = 2), we can find the first term (t1) by substituting the values of t3 and r into the equation t3 = t1 * r^(3-1):
444 = t1 * 2^2
444 = 4t1
t1 = 111
To find the 6th term (t6), we substitute the values of t1 and r into the general formula for the nth term of a geometric sequence:
t6 = t1 * r^(6-1)
t6 = 111 * 2^5
t6 = 111 * 32
t6 = 3552
Therefore, the 6th term of the geometric sequence is 3552.
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Which of the following parent functions has the most restricted domain?
A.
y=1/x
B.
y=x^2
C.
y=square root x (i couldnt find the symbol)
D.
y = |x|
Answers
the area of the cross section of a sphere at the largest point is 100 Pi square miles. What is the total surface area of the sphere?
Answers
The cross-section of largest area is obtained when the cross-sectional plane, contains the center of the sphere.
That is, when this plane divides the sphere into 2 semi (half) spheres.
2.
This cross sectional region is a circle with surface area = 100 Pi square miles.
The area of a circle is [tex] \pi R^{2} [/tex], where R is the radius.
So
[tex]\pi R^{2}=100 \pi [/tex] square miles,
3.
The surface area of a sphere is given by the formula [tex]4\pi R^{2}[/tex]
So the surface area of this sphere is [tex]4\pi R^{2}=4*100 \pi =400 \pi [/tex] square miles.
Answer: [tex]400 \pi[/tex] square miles
Gary earns $12 an hour plus $16 an hour for every hour of overtime. Overtime hours are any hours more than 30 hours for the week. Part A: Create an equation that shows the amount of money earned, M, for working x hours in a week when there is no overtime. (3 points) Part B: Create an equation that shows the amount of wages earned, T, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 30 hours. (3 points) Part C: Gary earned $408 in 1 week. How many hours (regular plus overtime) did he work? Show your work. (4 points)
Answers
Part A.
Amount of money earned = Regular rate per hour * Number of working hours
M = 12 x
Part B.
Amount of wages earned = Regular rate per hour * Maximum number of regular working hours + Overtime rate per hour * Excess working hours
T = 12 * 30 + 16 * y
T = 360 + 16 y
or
T = 16 y + 360
Part C.
Given T = 408, find y:
408 = 16 y + 360
y = 3 hrs
Therefore the total hours Gary worked that week is,
x + y = 30 + 3 = 33 hrs
(x = 30 since that is the maximum limit for regular working hours)
Do the ratios 1/12 and 8/96 form a proportion? Explain.
Answers
cross multiply
(1)(96) = (8)(12)
96 = 96
yes, this is a true proportion...keep in mind, proportions are nothing but equivalent fractions
1 : 12 = 8 : 96
It's not all that hard, all you need to know is the ''cross-multiplication'' methods for testing this kind of stuff.
1 : 12 = 8 : 96 ?
1 * 96 = 12 * 8 ?
96 = 96 ?
96 = 96 ==> CORRECT
Choose the equation below whose axis of symmetry is x = 2.
y = x^2 + 4x + 2
y = x^2 - 4
y = x^2 - 2
y =x^2 - 4x + 2
Answers
Answer:
Hi!
The correct answer is y =x^2 - 4x + 2
Step-by-step explanation:
The axis of symmetry is the x-coordinate vertex of the parabola.
The general form to find the axis of symmetry is:
[tex]x=-\frac{-b}{2*a} [/tex]
For y =x^2 - 4x + 2, a=1, b=−4 and c=2:
[tex]x=-\frac{-4}{2*1} = - \frac{-4}{2} = -(-2) = 2[/tex]
[tex]x = 2[/tex]
The area of a triangular flag is 4242 square centimeters. its altitude is 2 centimeters longer than twice its base. find the lengths of the altitude and the base.
Answers
h = 2b + 2
A = 42
42 = (b(2b + 2)) / 2
42 = (2b^2 + 2b) / 2
42 = b^2 + b
b^2 + b - 42 = 0
(b + 7)(b - 6) = 0
b + 7 = 0
b = -7...nope..extraneous solution
b - 6 = 0
b = 6 <== base
h = 2b + 2
h = 2(6) + 2
h = 12 + 2
h = 14 <=== height (altitude)
Substituting x-4=y and -5y+8x=29
Answers
-5x+20+8x=29
3x+20=29
3x=9
X=3
The distance between two cities on a map is 3 1/2 inches. The actual distance between the two cities is 28 miles.
a. What is the scale used on the map?
b. If the scale on a different map of the same area is inch = 1 mile, how separate the same two cities?
Answers
Part B= if 1 inch is 1 miles then on this map the cities are 28 inches apart.
hope this helps!!! if so please help me out by marking as brainliest
The given series has six terms. what is the sum of the terms of the series? 10 + 20 + 30 + . . . + 60 420 120 210 240
Answers
Answer:
10+20+30+40+50+60=210
Step-by-step explanation:
Let's simplify the series and then apply a useful method.
The original series is:
10+20+30+40+50+60, which can be simplified as:
10*(1+2+3+4+5+6)
Considering that you have a new series starting in 1 and the following numbers are consecutive, then the Gauss equation can be used, which is:
S=n*(n+1)/2, where n is the last value of a consecutive-number series starting in 1.
Through this equation we can find the sum of 1+2+3+4+5+6 by using:
S=6*(6+1)/2=21
Since our expression was 10*(1+2+3+4+5+6) now we can use the expression:
10*(21), obtaining the answer 210.
So, 10+20+30+40+50+60 is equal to 210.
Translate the sentence into an equation. Twice the difference of a number and 2 equals 9 . Use the variable y for the unknown number.
Answers
The value of variable y in the equation,
2y + 2 = 9 is y = 7/2.
What is an equation?An equation is a pair of algebraic equations with the equal sign (=) in the middle and the same value.
Given:
A phrase: Twice the difference of a number and 2 equals 9.
Let the number be y.
Then according to the question,
twice the difference of a number means,
2 x y
= 2y.
And the 2y and 2 equals 9.
That means,
we have an equation,
2y + 2 = 9
Subtract 2 from both sides,
we get,
2y = 7
y = 7/2.
Therefore, the value of y is 7/2.
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Which equation represents a linear function?
Equation 1: y3 = 2x + 1
Equation 2: y = 3x + 1
Equation 3: y = 5x2 − 1
Equation 4: y = 4x4 − 1
A. Equation 1
B.Equation 2
C. Equation 3
D. Equation 4
Answers
B. Equation 2
What is the shape of the graph of any geometric sequence?
Answers
Final answer:
The graph of a geometric sequence forms either an exponential decay or growth curve, depending on the common ratio, with the sequence appearing as a straight line on a semi-logarithmic scale.
Explanation:
The graph of any geometric sequence takes on a distinctive shape. If the common ratio of the geometric sequence is between -1 and 1 (excluding 0), the points of the graph will form a curve that approaches the x-axis as the number of terms increases, which is known as an exponential decay if the common ratio is positive, and an oscillating decay if it is negative. Similarly, if the common ratio is greater than 1 or less than -1, the sequence will exhibit exponential growth with each subsequent term becoming larger, and the points will diverge away from the x-axis forming an upward curve if the common ratio is positive or oscillating upward if it is negative. The graph may have a y-intercept, where it crosses the y-axis, and when graphed on a semi-logarithmic scale, the sequence with a positive common ratio will appear as a straight line.
If you flip a coin twice, what is the probability that you flip tails both times?
Answers
1/2(1/2)= 1/4
The probability of flipping tails both times is 1/4.
Hope this helps!
Answer: 1/4
Step-by-step explanation: In this problem, we are tossing two coins and we want to find the probability of tossing a tails and a tails. Tossing two coins are independent events because the outcome of tossing one coin does not affect the outcome of tossing the other coin.
We can find the probability of independent events by multiplying the probability of the first event by the probability of the second event. Note that we are talking about the theoretical probability because we aren't going to actually toss the coins.
If we want to find the probability of tossing a tails and a tails, we multiply the probability of tossing a tails by the probability of tossing a tails.
Now, let's find the probability of tossing a tails on the first coin. Remember that a coin has two sides which are heads and tails. Tails is one of these sides so the probability of tossing a heads is 1 out of 2 or 1/2. On the second coin the same is true so the probability is 1 out of 2 or 1/2.
Finally, we can simply multiply 1/2 by 1/2 which gives us 1/4. Therefore, the probability of tossing tails and tails is 1/4.
Paul planted 20 onion bulbs. Three-fourths of the bulbs sprouted. How many onion plants did Paul have?
Answers
3/4(20) = 60/4 = 15 onion plants <=
Paul had 15 onion plants.
To solve the problem, we need to calculate three-fourths of the 20 onion bulbs that Paul planted, as this represents the number of bulbs that sprouted.
First, we find three-fourths of 20 by multiplying 20 by the fraction [tex]\(\frac{3}{4}\)[/tex]:
[tex]\[ \frac{3}{4} \times 20 = \frac{3 \times 20}{4} \][/tex]
[tex]\[ \frac{3 \times 20}{4} = \frac{60}{4} \][/tex]
[tex]\[ \frac{60}{4} = 15 \][/tex]
Therefore, 15 onion bulbs sprouted, which means Paul had 15 onion plants.
Use 1% or 10% to estimate 8% of 310.
Answers
To estimate the 8% of 310, we use 10% method since 8 when rounded off is equals to 10.
The 10% of a number can simply be obtained by moving the decimal place one point to the left.
Therefore using the 10% method, the 8% of 310 is approximately 31.0
Answer: 10% = 31.0
The width of a rectangle is 7 inches less than its length. The area of the rectangle is 120 square inches. Solve for the dimensions of the rectangle. Length: inches Width: inches
Answers
area = L x W
W=L-7
120 = L x L-7
120 = L^2-7L
L^2-7L+120 =0
(L-15) (L+8)
L=15, L=-8. It can't be a negative number so L=15
W=15-7 = 8
15*8 =120
length = 15 inches
width = 8 inches
Answer:
The dimensions of the rectangle. Length= 15 inches and Width= 8 inches
Step-by-step explanation:
Let width of rectangle be W and length be L then
L=W+7 ---- (A)
Also given that area of rectangle = 120 square inches
=> WxL=120 -----(B)
From equation (A) and (B)
Wx(W+7) = 120
=> [tex]W^{2}+7W-120=0[/tex]
=>[tex]W^{2}+15W-8W-120=0 =>(W+15)(W-8)=0[/tex]
=> [tex]W=-15 or 8[/tex]
Since the width can not be a negative quantity , so W= 8 inches
=> L= W+7= (8+7) inches = 15 inches
Thus the dimensions of the rectangle. Length= 15 inches and Width= 8 inches
Candida bought 334 yards of fabric. If she uses 23 of the fabric to make a dress, how much fabric will she have left?
Answers
just minus 23 from 334
23 yards are 828 inches
She has 11,196 inches or 311 yards left
ABC is similar to pqr. Ab corresponds to pq and bc corresponds to qr. if the length of ab is 9 units the length of bc is12units the length of ca is 6units and the length of pq is 3 units then the length of qr is ? Units and the length of rp is ? Units
Answers
if you multiply QP which equals 3, by 3, then you would get 9.
So you would divide BC by 3. 12/3= 4
Then divide AC by 3. 6/3=2.
Answer:
[tex]QR=4\ units[/tex]
[tex]RP=2\ units[/tex]
Step-by-step explanation:
we know that
If two triangles are similar
then
the ratio of their corresponding sides are equal
In this problem
triangle ABC is similar triangle PQR -------> given problem
so
[tex]\frac{AB}{PQ}=\frac{CA}{RP}=\frac{BC}{QR}[/tex]
we have
[tex]AB=9\ units, PQ=3\ units,CA=6\ units,BC=12\ units[/tex]
Find the length of side QR
[tex]\frac{AB}{PQ}=\frac{BC}{QR}[/tex]
substitute the values and solve for QR
[tex]\frac{9}{3}=\frac{12}{QR}[/tex]
[tex]QR=12*3/9=4\ units[/tex]
Find the length of side RP
[tex]\frac{AB}{PQ}=\frac{CA}{RP}[/tex]
substitute the values and solve for RP
[tex]\frac{9}{3}=\frac{6}{RP}[/tex]
[tex]RP=6*3/9=2\ units[/tex]
The proof that MNG ≅ KJG is shown.
Given: angle N and angle J are right angles; NG ≅ JG
Prove: MNG ≅ KJG
What is the missing reason in the proof?
the reflexive property
ASA
AAS
the third angle theorem
Answers
The line [tex]\mathbf{\overline{MK}}[/tex] is a bisector of the line [tex]\mathbf{\overline{JN}}[/tex], and both lines form part of
ΔMNG and ΔKJG.
Correct response:
The missing reason in the proof is; ASAMethod used to prove ΔMNG ≅ ΔKJG, and find the missing reasonA two column proof is presented as follows;
Statement [tex]{}[/tex] Reasons
1. [tex]\overline{NG}[/tex] ≅ [tex]\overline{JG}[/tex] 1. Given (hash marks representing equal length)
2. ∠N and ∠J are right angles 2. Given (symbol for right angle)
3. ∠MGN ≅ ∠KGJ 3. Vertical angle are congruent (theorem)
4. ∠N ≅ ∠J 4. Right angles are (all) congruent
5. ΔMNG ≅ ΔKJG 5. Angle-Side-Angle, ASA, congruency rule
The missing reason in the proof is; ASAAccording to the ASA congruency rule, if two angles and the included
side of one triangle are the same to two angles and the included side of
another triangle, the two triangles are congruent.
∠N, side [tex]\mathbf{\overline{NG}}[/tex]∠MGN in ΔMNG are congruent to ∠J, side [tex]\mathbf{\overline{JG}}[/tex]∠KGJ in ΔKJG
Therefore;
ΔMNG ≅ ΔKJG by ASA congruency ruleLearn more about ASA postulate here:
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What is the average of three checks, one for $16.00, one for $40.00 and one for $130?
Answers
add them then divide by 3
16.00 + 40.00 + 130 = 186.00
186.00/3 = 62.00
the average is 62.00
if the average (arithmetic mean) of two, seven, and X is 12, what is the value of X?
Answers
(2+7+x)/3=12
Multiply both sides by 3
2+7+x=36
Combine like terms
9+x=36
Subtract 9 from both sides
x=27
Final answer: x=27
Which expression is equivalent to (x^27y)^1/3?
A) x^3 (3√y)
B) x^9 (3√y)
C) x^27 (3√y)
D) x^24 (3√y)
Answers
(x²⁷.y)¹/³ = x⁽²⁷ˣ¹/³⁾. y¹/³
x⁽²⁷ˣ¹/³⁾. y¹/³ =x⁸. y¹/³ = x⁹. ∛y. NONE OF THE ANSWERS, UNLESS YOU HAVE OMITTED SOMETHING, JUST AS 27 IS THE EXPONENT OF X AND ALSO ANOTHER 27 THAT MULTIPLIES Y??, In this case, it will be b
Answer:
Option B).[tex]x^{9}.(\sqrt[3]{y} )[/tex].
Step-by-step explanation:
The given expression is [tex](x^{27}y)^{\frac{1}{3} }[/tex].
We have to further simplify so that we can get the answer as shown in the options.
[tex](x^{27}y)^{\frac{1}{3} }=(x^{27})^{\frac{1}{3}}(y)^{\frac{1}{3}}[/tex]
[ As [tex](x^{a}.y^{b})^{m}=(x^{a})^{m}.(y^{b})^{m}[/tex] ]
Now ([tex](x^{27})^{\frac{1}{3}}(y)^{\frac{1}{3}}=(x^{\frac{27}{3} }).(y^{\frac{1}{3} } )=x^{9}.(\sqrt[3]{y} )[/tex]
Therefore Option B. is the answer.
A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for football or baseball. Out of the total 77 people who liked football, 48 also liked baseball. There were 65 people who liked baseball. Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points)A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for football or baseball. Out of the total 77 people who liked football, 48 also liked baseball. There were 65 people who liked baseball. Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points) Like football Do not like football Total Like baseball A D G Do not like baseball B E H Total C F I Part B: What percentage of the survey respondents did not like either football or baseball? (3 points) Part C: Do the survey results reveal a greater dislike for football or baseball? Justify your answer. (2 points)
Answers
like baseball 48 17 65
dont like it 29 6 35
total 77 23 100
percent that did not like football or baseball : 6/100 = 0.06 = 6% <=
there is a greater dislike for baseball....because out of the 100 people, 35% dont like baseball, and 23% dont like football <=
Answer:
Part A: A=48 B=29 C=77 D=17 E=6 F=23 G=65 H=35 I=100
Part B: 6% of the survey respondents did not like either football or baseball.
Part C: The survey results reveal a great dislike for baseball this is because 35% of the survey respondents dislike baseball while only 23% of the survey respondents dislike football.
A quadratic equation is shown below:
25x2 + 10x + 1 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 4x2 − 4x + 1 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
Answers
hello :
help :
the discriminat of each quadratic equation : ax²+bx+c=0 ....(a ≠ 0) is :
Δ = b² -4ac
1 ) Δ > 0 the equation has two reals solutions : x = (-b±√Δ)/2a
2 ) Δ = 0 : one solution : x = -b/2a
3 ) Δ < 0 : no reals solutions
3x+2y+4z=12
X+y+2z=6
(X=0,y=4,z=1)
Determine if the given 2 lines intersect at the given point. Explain your reasoning.
-2x-4y+z=8
4x+2y=-5
(x=-2,y=0,z=3) same as up above
Answers
Given points x = 0, y = 4, and z = 1
Equation 1:
3x + 2y + 4z = 3(0) + 2(4) + 4(1) = 0 + 8 + 4 = 12
Equation 2:
x + y + 2z = 0 + 4 + 2(1) = 6
Both equation 1 and equation 2 give the intended answer; 12 and 6 respectively, hence the given point is the intersection point
---------------------------------------------------------------------------------------------------------------
Given point : x = -2, y = 0, and z = 3
Equation 1:
-2x - 4y + z = -2(-2) - 4(0) + 3 = 4 - 0 + 3 = 7
Equation 2:
4x + 2y = 4(-2) + 2(0) = -8
The answers are not as intended, hence the given point is not the intersection point
The perimeter of a scalene triangle is 14.5 cm. The longest side is twice that of the shortest side. Which equation can be used to find the side lengths if the longest side measures 6.2 cm?
Choose the correct answer.
6.2 + b = 14.5
9.3 + b = 14.5
12.4 + b = 14.5
18.6 + b = 14.5
Answers
6,2/2=3,1 cm (the shortest side)
6,3+ 3,1+b=14.5 cm
The correct anwser is 9,3+b=14,5
Find the area of the regular polygon.
pentagon with a radius of 4 ft
Answers
sin36∘4sin36∘8sin36∘n=.5n4=12n=n≈4.7 cos36∘=a44cos36∘=aa≈3.24
Using these two pieces of information, we can now find the area.
A=12(3.24)(5)(4.7)≈38.07 units^2.
Are 60 meters equal to, greater than, or less than 6 km?
Answers
Final answer:
60 meters is significantly less than 6 kilometers, as 6 kilometers is equal to 6,000 meters.
Explanation:
To answer this, we need to compare the two measurements in the same unit. We know that 1 kilometer is equivalent to 1,000 meters, so to convert 6 kilometers to meters, we multiply by 1,000:
6 km imes 1,000 = 6,000 m
Now we can compare the two measurements:
60 m
6,000 m
Since 60 is less than 6,000, we can conclude that 60 meters is less than 6 kilometers.