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Math
Algebra
Problem 2601
Solve the equation
v
5
v
−
8
=
2
3
v
−
4
\frac{v}{5v-8}=\frac{2}{3v-4}
5
v
−
8
v
=
3
v
−
4
2
and express the solutions as integers or simplified fractions.
See Solution
Problem 2602
Solve for
x
x
x
in the equation
−
2
(
x
−
3
)
−
4
x
=
x
−
8
−
4
x
-2(x-3)-4x=x-8-4x
−
2
(
x
−
3
)
−
4
x
=
x
−
8
−
4
x
.
See Solution
Problem 2603
Write the following expressions in product form:
x
2
+
14
x
+
49
x^{2} + 14x + 49
x
2
+
14
x
+
49
and
x
2
−
1
x^{2} - 1
x
2
−
1
.
See Solution
Problem 2604
Evaluate the given expressions for the specified variable values: a)
3
r
+
2
r
+
1
3r+2r+1
3
r
+
2
r
+
1
where
r
=
7
r=7
r
=
7
, b)
6
s
+
4
−
s
6s+4-s
6
s
+
4
−
s
where
s
=
4
s=4
s
=
4
.
See Solution
Problem 2605
Find the missing number in the equation
x
−
13
=
−
429
x - 13 = -429
x
−
13
=
−
429
.
See Solution
Problem 2606
Bestimme die Länge der Strecke
x
x
x
mithilfe der Verhältnisgleichung
7.5
+
x
7.5
=
16
10
1.10
\frac{7.5+x}{7.5}=\frac{16}{10} 1.10
7.5
7.5
+
x
=
10
16
1.10
, die nach
x
x
x
aufgelöst
x
=
4.5
x=4.5
x
=
4.5
ergibt.
See Solution
Problem 2607
Prove the identity
a
=
a
a=a
a
=
a
.
See Solution
Problem 2608
Find the value of
t
t
t
that satisfies the equation
3
t
+
8
=
17
3t + 8 = 17
3
t
+
8
=
17
.
See Solution
Problem 2609
Find the value of
r
r
r
that satisfies the equation
3
(
r
+
2
)
−
r
=
r
−
4
3(r+2)-r=r-4
3
(
r
+
2
)
−
r
=
r
−
4
.
See Solution
Problem 2610
Solve the linear equation
−
27
=
5
y
−
7
-27=5y-7
−
27
=
5
y
−
7
for the variable
y
y
y
.
See Solution
Problem 2611
Simplify the expression
−
9
w
−
(
−
1.6
x
+
10
)
-9 w-(-1.6 x+10)
−
9
w
−
(
−
1.6
x
+
10
)
.
See Solution
Problem 2612
Solve the absolute value equation
∣
f
r
a
c
7
x
−
5
7
−
x
∣
=
8
|\\frac{7x - 5}{7 - x}| = 8
∣
f
r
a
c
7
x
−
5
7
−
x
∣
=
8
for
x
x
x
.
See Solution
Problem 2613
Solve the linear equation
2
⋅
x
+
5
=
10
2 \cdot x + 5 = 10
2
⋅
x
+
5
=
10
for the value of
x
x
x
.
See Solution
Problem 2614
Finden Sie den Schnittpunkt der Funktionen
f
(
x
)
=
−
0.5
x
+
2
f(x) = -0.5x + 2
f
(
x
)
=
−
0.5
x
+
2
und
g
(
x
)
=
x
−
1
g(x) = x - 1
g
(
x
)
=
x
−
1
.
See Solution
Problem 2615
Simplify the expression
(
13
x
+
21
)
−
(
5
x
−
9
)
(13x+21)-(5x-9)
(
13
x
+
21
)
−
(
5
x
−
9
)
into an equivalent binomial, then test the equivalence using a calculator and provide evidence.
See Solution
Problem 2616
Solve for
x
x
x
in the linear equation
y
=
4
x
+
8
y=4x+8
y
=
4
x
+
8
.
See Solution
Problem 2617
Solve the quadratic equation
x
2
+
7
x
=
3
x^2 + 7x = 3
x
2
+
7
x
=
3
and find the two real solutions.
See Solution
Problem 2618
Find the value of
x
x
x
when
9
(
3
x
)
=
2
7
3
9(3^{x})=27^{3}
9
(
3
x
)
=
2
7
3
.
See Solution
Problem 2619
Solve for x in the equation
3
x
+
4
=
2
x
−
5
3x + 4 = 2x - 5
3
x
+
4
=
2
x
−
5
by subtracting 5 from both sides and then subtracting
2
x
2x
2
x
from both sides.
See Solution
Problem 2620
Solve the equation
5
x
−
2
=
4
+
2
x
5x - 2 = 4 + 2x
5
x
−
2
=
4
+
2
x
for
x
x
x
and enter the number in the green box.
See Solution
Problem 2621
Find the expression for the difference between 3 and 5 times a number.
See Solution
Problem 2622
Find the values of
x
x
x
and
y
y
y
that satisfy the linear equation
30
x
+
50
y
=
2400
30x + 50y = 2400
30
x
+
50
y
=
2400
.
See Solution
Problem 2623
Find the general form of the equation
x
=
1
3
y
x=\frac{1}{3} y
x
=
3
1
y
.
See Solution
Problem 2624
Solve the linear equation
2
x
+
75
=
102
−
x
2x + 75 = 102 - x
2
x
+
75
=
102
−
x
and prove that
z
=
9
z = 9
z
=
9
.
See Solution
Problem 2625
Find the number of boxes of candy if each box contains an unknown number of candies and the total number of candies is 3.
See Solution
Problem 2626
Solve the linear equation
6.81
−
4
x
7
=
21
6.81 - \frac{4x}{7} = 21
6.81
−
7
4
x
=
21
for the unknown variable
x
x
x
.
See Solution
Problem 2627
Solve for
b
b
b
in the equation
−
1
=
−
0.5
⋅
14
+
b
-1=-0.5 \cdot 14 + b
−
1
=
−
0.5
⋅
14
+
b
.
See Solution
Problem 2628
Find the values of
x
x
x
that satisfy the inequality
∣
x
∣
≤
3.5
|x| \leq 3.5
∣
x
∣
≤
3.5
.
See Solution
Problem 2629
Finden Sie die Nullstellen der Kubikfunktion
f
(
x
)
=
3
x
3
+
3
x
2
−
18
x
f(x)=3x^3+3x^2-18x
f
(
x
)
=
3
x
3
+
3
x
2
−
18
x
durch Ausklammern.
See Solution
Problem 2630
Find the value of
x
x
x
that satisfies the equation
21
=
3
x
21=3x
21
=
3
x
.
See Solution
Problem 2631
Solve the inequality
13.5
−
x
≠
6
13.5-x \neq 6
13.5
−
x
=
6
for real values of
x
x
x
.
See Solution
Problem 2632
Use the difference of two squares to find the following products:
34
⋅
26
34 \cdot 26
34
⋅
26
,
22
⋅
28
22 \cdot 28
22
⋅
28
,
17
⋅
7
17 \cdot 7
17
⋅
7
.
See Solution
Problem 2633
Solve the linear equation
2
n
+
11
+
4
n
+
3
=
8
n
2n + 11 + 4n + 3 = 8n
2
n
+
11
+
4
n
+
3
=
8
n
to find the value of
n
n
n
.
See Solution
Problem 2634
Find the quadratic function with points
(
0
,
5
)
,
(
2
,
11
)
,
(
−
1
,
14
)
(0,5), (2,11), (-1,14)
(
0
,
5
)
,
(
2
,
11
)
,
(
−
1
,
14
)
. The equation is
y
=
a
x
2
+
b
x
+
c
y=ax^2+bx+c
y
=
a
x
2
+
b
x
+
c
.
See Solution
Problem 2635
Finde die Nullstellen der quadratischen Funktion
f
(
x
)
=
x
2
−
10
x
+
25
f(x)=x^{2}-10x+25
f
(
x
)
=
x
2
−
10
x
+
25
.
See Solution
Problem 2636
Find the standard form equation for
y
=
3
x
−
1
5
y=3x-\frac{1}{5}
y
=
3
x
−
5
1
.
See Solution
Problem 2637
Determine if the equation
5
+
3
=
2
(
5
+
7
3
)
5+3=2\left(\frac{5+7}{3}\right)
5
+
3
=
2
(
3
5
+
7
)
is true, false, or an open equation.
See Solution
Problem 2638
Solve for x in the linear equation
−
10
+
x
=
18
-10+x=18
−
10
+
x
=
18
.
See Solution
Problem 2639
Solve the equation
2
+
3
(
2
x
−
4
)
=
3
(
4
x
−
2
)
2+3(2x-4)=3(4x-2)
2
+
3
(
2
x
−
4
)
=
3
(
4
x
−
2
)
. Which statement is true?
x
=
0
x=0
x
=
0
is a solution, or
x
=
−
2
3
x=-\frac{2}{3}
x
=
−
3
2
is a solution.
See Solution
Problem 2640
Solve the proportion
−
9
7
=
p
63
\frac{-9}{7}=\frac{p}{63}
7
−
9
=
63
p
and check. The solution set is {
p
p
p
}.
See Solution
Problem 2641
Solve for
x
x
x
given
m
∠
2
=
x
+
42
m \angle 2 = x + 42
m
∠2
=
x
+
42
and
m
∠
2
=
72
m \angle 2 = 72
m
∠2
=
72
.
See Solution
Problem 2642
Find the number that completes the perfect square for
x
2
+
8
x
+
□
x^2 + 8x + \Box
x
2
+
8
x
+
□
.
See Solution
Problem 2643
Solve
y
2
−
3
2
x
=
−
7
2
\frac{y}{2}-\frac{3}{2}x=-\frac{7}{2}
2
y
−
2
3
x
=
−
2
7
for y or x, or rearrange to slope-intercept or standard form.
See Solution
Problem 2644
Solve for
p
p
p
in the equation
11.9
p
+
23.1
=
273
11.9p + 23.1 = 273
11.9
p
+
23.1
=
273
.
See Solution
Problem 2645
Solve the inequality
w
−
3.5
≤
−
2
w - 3.5 \leq -2
w
−
3.5
≤
−
2
for the real number
w
w
w
.
See Solution
Problem 2646
Simplify the expression
7
x
2
+
3
y
2
2
\frac{7 x^{2}+3 y^{2}}{2}
2
7
x
2
+
3
y
2
with
x
=
4
x=4
x
=
4
and
y
=
2
y=2
y
=
2
.
See Solution
Problem 2647
Describe the graph of an odd function. Is it symmetric about
y
=
x
y=x
y
=
x
,
x
x
x
-axis,
x
=
0
x=0
x
=
0
, or the origin?
See Solution
Problem 2648
Find the coefficient of the variable
y
y
y
in the equation
−
30
y
+
4
=
64
-30y + 4 = 64
−
30
y
+
4
=
64
.
See Solution
Problem 2649
Add
t
t
t
and the sum of 8 and
u
u
u
.
See Solution
Problem 2650
Solve the linear equation
−
2
x
−
y
=
7
-2x - y = 7
−
2
x
−
y
=
7
for
y
y
y
in terms of
x
x
x
.
See Solution
Problem 2651
Identify the error in solving the equation
x
−
m
3
=
−
4
x - \frac{m}{3} = -4
x
−
3
m
=
−
4
and provide the correct solution.
See Solution
Problem 2652
Find the value of
y
y
y
for the quadratic function
y
=
−
x
2
+
6
x
−
5
y = -x^2 + 6x - 5
y
=
−
x
2
+
6
x
−
5
when
x
=
0.5
x = 0.5
x
=
0.5
.
See Solution
Problem 2653
Solve the linear equation
x
=
−
x
+
2
x=-x+2
x
=
−
x
+
2
for the value of
x
x
x
.
See Solution
Problem 2654
Publish a book:
25
x
+
1100
=
y
25x + 1100 = y
25
x
+
1100
=
y
. Find the startup cost and cost change per book.
See Solution
Problem 2655
Subtract
1
2
(
x
−
4
)
(
x
−
2
)
\frac{1}{2}(x-4)(x-2)
2
1
(
x
−
4
)
(
x
−
2
)
from
5
x
+
10
5x+10
5
x
+
10
and simplify to
6
+
8
x
−
1
2
x
2
6+8x-\frac{1}{2}x^2
6
+
8
x
−
2
1
x
2
.
See Solution
Problem 2656
Find the value of
x
x
x
given the equation
3
x
+
2
=
8
3x + 2 = 8
3
x
+
2
=
8
.
See Solution
Problem 2657
Find the value of
g
g
g
that satisfies the inequality
9
+
5
g
>
−
1
9 + 5g > -1
9
+
5
g
>
−
1
.
See Solution
Problem 2658
Find the property described by the statement: "If
a
=
b
a=b
a
=
b
, then either
a
a
a
or
b
b
b
may be the other in any equation."
See Solution
Problem 2659
Solve the absolute value equation
∣
7
x
−
5
∣
=
39
|7x-5| = 39
∣7
x
−
5∣
=
39
by finding two possible values for
7
x
−
5
7x-5
7
x
−
5
.
See Solution
Problem 2660
Solve the system of linear inequalities:
5
x
<
−
20
5x < -20
5
x
<
−
20
and
3
x
>
12
3x > 12
3
x
>
12
.
See Solution
Problem 2661
Describe the transformation of the linear function
f
(
x
)
=
1
3
x
f(x) = \frac{1}{3}x
f
(
x
)
=
3
1
x
.
See Solution
Problem 2662
Solve the absolute value inequality
∣
x
−
6
∣
−
4
<
4
|x-6|-4<4
∣
x
−
6∣
−
4
<
4
. First isolate the absolute value expression, then write the two inequalities to solve.
See Solution
Problem 2663
Solve the equation
x
5
+
11.3
=
−
1.2
\frac{x}{5}+11.3=-1.2
5
x
+
11.3
=
−
1.2
for
x
=
T
x=T
x
=
T
. Find the value of
T
T
T
.
See Solution
Problem 2664
Evaluate the expression
7
x
2
+
9
x
−
3
7x^2 + 9x - 3
7
x
2
+
9
x
−
3
when
x
=
3
x=3
x
=
3
.
See Solution
Problem 2665
Identify values in the interval
−
2
≤
x
≤
6
-2 \leq x \leq 6
−
2
≤
x
≤
6
from the given set:
x
=
0
,
−
1
,
−
4
,
3
,
6
,
−
5
4
x=0, -1, -4, 3, 6, -\frac{5}{4}
x
=
0
,
−
1
,
−
4
,
3
,
6
,
−
4
5
.
See Solution
Problem 2666
Find the error in the plant's growth rate of
0.2
cm/0.5 day
0.2 \text{cm/0.5 day}
0.2
cm/0.5 day
if it grows
3.6
cm
3.6 \text{cm}
3.6
cm
in
1.44
days
1.44 \text{days}
1.44
days
.
See Solution
Problem 2667
Solve for
x
x
x
in the inequality
4
(
x
+
1
)
≤
4
x
+
3
4(x+1) \leq 4x+3
4
(
x
+
1
)
≤
4
x
+
3
. The solution set is
x
≤
1
x \leq 1
x
≤
1
or
x
≤
7
x \leq 7
x
≤
7
.
See Solution
Problem 2668
Match the expressions in Column A with their respective equivalents in Column B.
Column A:
−
(
27
+
b
)
-(27+b)
−
(
27
+
b
)
,
−
(
27
−
b
)
-(27-b)
−
(
27
−
b
)
,
−
(
−
27
+
b
)
-(-27+b)
−
(
−
27
+
b
)
,
−
(
−
27
−
b
)
-(-27-b)
−
(
−
27
−
b
)
Column B:
−
27
−
b
-27-b
−
27
−
b
,
27
−
b
27-b
27
−
b
,
−
27
+
b
-27+b
−
27
+
b
,
27
+
b
27+b
27
+
b
See Solution
Problem 2669
Simplify the expression
7
(
x
+
3
)
7(x+3)
7
(
x
+
3
)
by distribution. Fill in the blanks with the simplified expression.
See Solution
Problem 2670
Find the polar form solution for the equation
z
4
+
16
p
2
i
=
0
z^{4} + 16p^{2}i = 0
z
4
+
16
p
2
i
=
0
, where
p
p
p
is a real number.
See Solution
Problem 2671
Prove that the equation
−
3
y
6
+
8
y
4
−
9
y
2
+
10
=
0
-3y^6 + 8y^4 - 9y^2 + 10 = 0
−
3
y
6
+
8
y
4
−
9
y
2
+
10
=
0
has exactly two real solutions. Find the discriminant of
−
3
x
2
+
2
x
−
5
-3x^2 + 2x - 5
−
3
x
2
+
2
x
−
5
. (2 marks)
See Solution
Problem 2672
Find the pattern in the cost sequence:
4.50
,
4.50,
4.50
,
6.75, $9.00, ...
See Solution
Problem 2673
Find the values of
x
x
x
where
f
(
x
)
=
−
x
(
x
+
4
)
2
(
x
+
1
)
(
x
−
6
)
6
≤
0
f(x) = -x(x+4)^{2}(x+1)(x-6)^{6} \leq 0
f
(
x
)
=
−
x
(
x
+
4
)
2
(
x
+
1
)
(
x
−
6
)
6
≤
0
.
See Solution
Problem 2674
Solve for the unknown variable
Z
Z
Z
given the equation
X
=
2
9
(
Y
+
Z
)
X=\frac{2}{9}(Y+Z)
X
=
9
2
(
Y
+
Z
)
.
See Solution
Problem 2675
Find the general form of a quadratic function
f
(
x
)
=
(
x
+
7
)
2
f(x) = (x + 7)^2
f
(
x
)
=
(
x
+
7
)
2
.
See Solution
Problem 2676
Expand the expression
f
(
x
)
=
(
2
−
x
)
2
f(x) = (2 - x)^2
f
(
x
)
=
(
2
−
x
)
2
.
See Solution
Problem 2677
Find all values of
x
x
x
that satisfy the system of equations
y
1
=
x
+
7
y_1 = x + 7
y
1
=
x
+
7
,
y
2
=
x
−
5
y_2 = x - 5
y
2
=
x
−
5
, and
y
1
y
2
=
13
y_1y_2 = 13
y
1
y
2
=
13
.
See Solution
Problem 2678
Solve
5
7
x
+
4
=
3
x
+
2
5^{7 x+4}=3^{x+2}
5
7
x
+
4
=
3
x
+
2
for
x
x
x
. Give the exact and decimal approximation to the nearest hundredth.
See Solution
Problem 2679
Find
p
p
p
when
q
=
9
q=9
q
=
9
and
q
q
q
when
p
=
3
p=3
p
=
3
, given
p
p
p
is directly proportional to
q
\sqrt{q}
q
and
p
=
5
p=5
p
=
5
when
q
=
4
q=4
q
=
4
.
See Solution
Problem 2680
Find the monthly cost for 34 minutes of calls given a linear function with a slope of
0.09
0.09
0.09
and a cost of
$
18.58
\$18.58
$18.58
for 38 minutes of calls.
See Solution
Problem 2681
Find the value of
r
r
r
in the equation
A
=
P
(
1
+
r
t
)
A=P(1+rt)
A
=
P
(
1
+
r
t
)
, given
A
=
1180.80
A=1180.80
A
=
1180.80
,
P
=
884.07
P=884.07
P
=
884.07
, and
t
=
3
t=3
t
=
3
.
See Solution
Problem 2682
Find the value of
x
x
x
such that
5
x
=
23
5^{x} = 23
5
x
=
23
.
See Solution
Problem 2683
Find demand equation
p
=
−
1
9
x
+
200
p=-\frac{1}{9}x+200
p
=
−
9
1
x
+
200
and revenue function
R
(
x
)
=
−
1
9
x
2
+
200
x
R(x)=-\frac{1}{9}x^{2}+200x
R
(
x
)
=
−
9
1
x
2
+
200
x
. Determine domain of
R
(
x
)
R(x)
R
(
x
)
.
See Solution
Problem 2684
Solve the linear equation
28
=
−
9
w
−
8
+
5
w
28=-9w-8+5w
28
=
−
9
w
−
8
+
5
w
for
w
w
w
and simplify the answer.
See Solution
Problem 2685
Find
m
m
m
in the equation
2701
=
m
3
2701 = m^3
2701
=
m
3
.
See Solution
Problem 2686
Evaluate the expression
3
a
2
+
2
b
2
3 a^{2} + 2 b^{2}
3
a
2
+
2
b
2
given
a
=
−
3
a = -3
a
=
−
3
and
b
=
6
b = 6
b
=
6
.
See Solution
Problem 2687
Solve the exponential equation
7
e
3
x
=
8
e
6
x
7 e^{3 x} = 8 e^{6 x}
7
e
3
x
=
8
e
6
x
for the value of
x
x
x
.
See Solution
Problem 2688
Solve the absolute value equation
11
⋅
∣
5
−
3
x
∣
=
3
11 \cdot |5-3x| = 3
11
⋅
∣5
−
3
x
∣
=
3
for
x
x
x
.
See Solution
Problem 2689
Solve the equation
10
x
−
(
9
x
−
11
)
=
6
x
+
16
10x - (9x - 11) = 6x + 16
10
x
−
(
9
x
−
11
)
=
6
x
+
16
and find the value of
x
x
x
.
See Solution
Problem 2690
Determine if the group
Z
6
=
{
0
,
1
,
2
,
3
,
4
,
5
}
Z_{6}=\{0,1,2,3,4,5\}
Z
6
=
{
0
,
1
,
2
,
3
,
4
,
5
}
under addition is cyclic.
See Solution
Problem 2691
Solve the equation
3
(
2
x
+
1
)
=
−
4
(
f
r
a
c
14
x
−
1
)
3(2 x+1)=-4(\\frac{1}{4} x-1)
3
(
2
x
+
1
)
=
−
4
(
f
r
a
c
1
4
x
−
1
)
and simplify the solution
x
=
[
?
]
x=[?]
x
=
[
?]
.
See Solution
Problem 2692
Two trains leave stations 306 miles apart at the same time, one at 80 mph and the other at 90 mph. How long until they meet?
See Solution
Problem 2693
Find the value of
m
m
m
in the equation
1
9
3
7
=
(
19
m
)
3
19^{\frac{3}{7}}=(\sqrt[m]{19})^{3}
1
9
7
3
=
(
m
19
)
3
.
See Solution
Problem 2694
Find the term that completes the statement: "An equation that is true for all real numbers for which both sides are defined is called a(n)
‾
\underline{\hspace{2cm}}
."
See Solution
Problem 2695
Write an inequality for the statement: "Ten is at least the product of a number
h
h
h
and 5."
The inequality is:
10
≥
5
h
10 \geq 5h
10
≥
5
h
See Solution
Problem 2696
Solve for
y
y
y
in the equation
8
x
−
3
=
5
+
4
y
8x - 3 = 5 + 4y
8
x
−
3
=
5
+
4
y
.
See Solution
Problem 2697
Solve for
x
x
x
in the equation
−
u
=
b
−
c
−
x
-u = b - c - x
−
u
=
b
−
c
−
x
.
See Solution
Problem 2698
Identify an absolute value equation with solutions
x
=
3.4
x=3.4
x
=
3.4
and
x
=
9.4
x=9.4
x
=
9.4
.
See Solution
Problem 2699
Solve the linear equation
4
x
+
2
=
6
4x + 2 = 6
4
x
+
2
=
6
and represent the solution using a 3x2 table.
See Solution
Problem 2700
Rewrite a two-variable equation equivalent to the function
f
(
x
)
=
−
2
(
x
−
4
)
f(x) = -2(x-4)
f
(
x
)
=
−
2
(
x
−
4
)
.
See Solution
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