Translate the sentence into an equation. Twice the difference of a number and 2 equals 9 . Use the variable y for the unknown number.
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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Find the 6th term of a geometric sequence t3 = 444 and t7 = 7104.
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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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
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]
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
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?
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
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]
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)
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.
(4.04 LC)
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
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
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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Use 1% or 10% to estimate 8% of 310.
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
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
Given: The universal set = {all animals}; A = {hogs}; B = {cows}; C = {horses}; D = {foals}; E = {mares}. Click on the diagram until you find the one that correctly represents the expression. (Note: mares are female horses, foals are baby horses).
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)
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.
If g is the number of girls in a class and b the number of boys and if there are five more girl) than boys (b) in a class, write an algebraic equation that shows this relationship.
(06.02 LC)
Which line best represents the line of best fit for this scatter plot?
Line P
Line Q
Line R
Line S
Answer:
The correct option is 3. Line R represents the line of best fit for this scatter plot.
Step-by-step explanation:
A straight line is called line of best fit if it minimize the sum of the squared prediction errors. It means the distance of all the points from the line is minimum.
The best fit line may or may not passes through the scatter points. Some scatter points lie above the line and some lie below the best fit line. In other words the best fit line passes through the middle points.
From the given graph it is clear that the line R passes through 3 points. The number of points above the line is equal to the number of points below the line. So, R is the line of best fit
Line R represents the line of best fit for this scatter plot. Therefore the correct option is 3.
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
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
The given series has six terms. what is the sum of the terms of the series? 10 + 20 + 30 + . . . + 60 420 120 210 240
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.
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?
If you flip a coin twice, what is the probability that you flip tails both times?
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.
For g(x)=9x^2-2x find g(-2)
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)
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
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)
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)
Paul planted 20 onion bulbs. Three-fourths of the bulbs sprouted. How many onion plants did Paul have?
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.
What expression is equivalent to (4y2)^3 (3y^2)
) 12y^8
) 12y^12
)192y^8
) 192^12
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.
if 7x+3=24, find the value of -5 - 6x.
a)-23
b)-7
c)1
d)17
Find the area of the regular polygon.
pentagon with a radius of 4 ft
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
When solving negative one over five -1/5 (x − 25) = 7, what is the correct sequence of operations
The solution would be like this for this specific problem:
[tex]\left( { - 5} \right) \cdot \left( { - \frac{1}{5}} \right) \cdot \left( {x - 25} \right) = 7 \cdot \left( { - 5} \right)[/tex]
[tex]\left( { - 5} \right) \cdot \left( { - \frac{1}{5}} \right) = 1[/tex]
The correct sequence of operations when solving negative one over five (x − 25) = 7 would be multiply each side by −5, and adding 25 to each side.
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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|