To solve the 3 step equation, we have to solve the one equation in two variable. Then substituting the value in other equation and further solving according to the given rule.
In the substitution approach, we will examine the two equations and choose which variable is the most straightforward to solve for in order to transform one of the equations into x =, y =, or z =. The other equation's x, y, or z will then be appropriately replaced. The outcome will be an equation we can solve that has just one unknown. A variable whose coefficient is 1 or -1 should be isolated.
Use the steps below to solve systems using substitution:
(1) Choose an equation and determine the value of one of its variables.
(2) Substitute the variable you just solved in the other equation.
(3) Address the fresh equation.
(4) Enter the discovered value into any equation that calls for both variables, then get the value for the other one.
(5) Verify the answers to the two initial equations.
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3, -3/2, -6, -21/2… what is the explicit function that defines the sequence
The explicit function that defines the sequence is 15/2 - 9n/2
How to determine the explicit rule?The sequence is given as:
3, -3/2, -6, -21/2
The above sequence is an arithmetic sequence, with the following parameters
First term, a = 3Common difference, d = -9/2 i.e. -3/2 - 3The explicit formula is then calculated as:
T(n) = a + (n -1) * d
This gives
T(n) = 3 +(n -1) * -9/2
Expand
T(n) = 3 + 9/2 - 9n/2
Evaluate
T(n) = 15/2 - 9n/2
Hence, the explicit function that defines the sequence is 15/2 - 9n/2
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rewrite the exponential expression to have the indi cated base.
(1/8)2*, base 2
Answer:
2^-6
Step-by-step explanation:
(1/8)^2 = (2^-3)^2 = 2^-6
Chandra invests $75 every month at 4.8%/a compounded monthly for 8 years. What is the total amount of Chandra's investments after 8 years?
The total amount of Chandra's investments after 8 years is $110.03
Compound interestThe formula for calculating the compound interest is expressed as;
A = P(1+r/n)^nt
where
P is the amount invested = $75
r is the rate. = 0.048
t is the time =8years
n = 12 (monthly)
Substitute
A = 75(1+0.048/12)^96
A = 75(1.467)
A = 110.03
Hence the total amount of Chandra's investments after 8 years is $110.03
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If you flip the graph of the absolute value parent function, f(x)=|x|, over the x-axis, what is the equation of the new function?
The equation of the new function is f'(x) = -|x|
How to determine the equation of the new function?The function is given as:
f(x) = |x|
The rule of flipping the graph over the x-axis
(x, y) = (x, -y)
So, we have:
f'(x) = -f(x)
Substitute f(x) = |x|
f'(x) = -|x|
Hence, the equation of the new function is f'(x) = -|x|
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Brendan is 30. Anna is 5 years older than Cassie and 10 years younger than Brendan. How old is Cassie
Answer:
20 because Brendan is 30
What is the repayment amount after one month on a simple interest loan of $2,500 at 7% interest?
Payment Every Month = $2,514.58
Total of 1 Payments = $2,514.58
Total Interest = $14.58
What is simple intertest ?
Simple interest is calculated based on the principal of a loan or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accumulated.
Solution:
Principal value = $2500
Interest rate = 7%
Time = One month
Formula for simple interest calculation:
[tex]=\frac{Principalamount*rate *time}{100} \\=\frac{2500*7*(\frac{1}{12}) }{100}\\ =14.588[/tex]
Total Simple interest on $2500 for month $14.588.
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how meny yards are in 100 meters?
Answer:
109.36 yards to nearest hundredth
Step-by-step explanation:
1 meter = 1.09361 yards
So 100 m = 109.361 yards
Which statement defines a translation?
OA A translation proportionally stretches or compresses an object based on a given scale factor.
OB. A translation moves points a specified distance along a line parallel to a specified line.
OC. In a translation, each point in the preimage and its corresponding point in the image are at equal distances from a given line.
Also, the line segment joining two such points is perpendicular to the given line.
OD. A translation is when an object moves in a circular arc around a point
the statement which defines a translation is option A that is "A translation proportionally stretches or compresses an object based on a given scale factor".
What is Translation ?
"Translation" moves points the same distance along lines that are parallel to each other.
Translation involves the initial object called the pre-image and the final object called the image. As you can see in the picture above, the rust-colored item represents the pre-image, and the blue item represents the image. Because of the arrow, we can tell the direction in which the image was moved. For other images, you may receive instructions on which image is the pre-image, or you may be asked to find the pre-image from the image.
Reflection, on the other hand, moves points along a specified line in such a way that the line bisects each line segment connecting corresponding pre-image points and image points.
There, the statement which defines a translation is option A that is "A translation proportionally stretches or compresses an object based on a given scale factor".
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Answer:
The correct answer is: A translation moves points a specified distance along a line parallel to a specified line
Step-by-step explanation: I got it right on plato.
Simplify the expression.
Answer:
D
please mark brainiest
The 24 retail stores located in the Mall of America numbered 00 through 23 are: A systematic sampling procedure will be used. The first store will be selected and then every third store. Which stores will be in the sample
The stores that will be in the sample are - 00, 02, 05, 08, 11, 14, 17, 20, 23.
What comprises the sample?
An analytical subset of a larger population is referred to as a sample in statistics. A sample are used in research so that it can be done quickly and with more manageable data. However, obtaining such a sample may be costly and time-consuming. Randomly generated samples do not have significant bias if they are large enough.
Stores in the Sample
Since it is given that the sample is made up of every third store, starting from the first retail store. The stores have been numbered systematically from 00 to 23. Since a systematic sampling is done, after picking the first store, the third store will be picked, that is, 02, and then 05, and so on till 23.
Thus, the following retail stores will be present in the sample,
00, 02, 05, 08, 11, 14, 17, 20, 23
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NEED HELP PLEASE!!!!!
What is c−1(x) given c(x)=x3−5?
A. c−1(x)= ∛x+5
B. c−1(x)= ∛x+x
C. c−1(x)= ∛x- ∛5
D. c−1(x)= ∛x-5
Answer: A
Step-by-step explanation:
Let c(y)=x.
[tex]\implies x=y^3 -5\\\\x+5=y^3\\\\y=\sqrt[3]{x+5}\\\\c^{-1}(x)=\sqrt[3]{x+5}[/tex]
how meny grams are in 6 ounces?
Answer:
170.097 grams are in 6 ounces
Answer:
170.097 g to nearest thousandth
Step-by-step explanation:
1 ounce = 28.34952 g
6 = 170.09712 g
PLEASE HELP DUE TONIGHT
The height & speed are mathematically given as
t = 0.2 s
u = 4 m/s
What is the height & speed?Generally, the equation for height is mathematically given as
h = 0.2gt^2
Therefore
0.2 = 0.5 * 9.8 *[tex]t^2[/tex]
0.2 = 4.9 *[tex]t^2[/tex]
t = 0.2 s
b)
In conclusion, the initial speed is
s = ut
Therefore
u = 0.8 / 0.2
u = 4 m/s
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4+4-3-4-2-5-1-8-9-0=a+c=a
Simplification of the expression gives 2a + c = -24
How to simplify the equation
4+4-3-4-2-5-1-8-9-0=a +c + a
First, let's add
[tex]8 -3 -4-2-5-1-8-9-0 = a+ c + a[/tex]
Then, let's substract
[tex]-24 = a + c + a[/tex]
[tex]-24 = 2a + c[/tex]
We then have,
[tex]2a + c = -24[/tex]
Thus, simplification of the expression gives 2a + c = -24
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Thanks!
1) You know that for any , neither sin nor cos can be greater than 1. How can you explain this using the unit circle definitions of sine and cosine? How can you explain it using the right triangle definitions of sine and cosine?
As a follow-up question, consider why it is important to have both the right triangle definitions of sine and cosine and the unit circle definitions of sine and cosine.
2) Can you give examples of situations that might be modeled with trigonometric functions? That is, can you give examples of phenomena that take on a series of values over and over again?
The trigonometric function gives the ratio of different sides of a right-angle triangle. The value of sine and cosine will be always less than a unit.
How to explain the trigonometry?In a unit circle, the radius of the circle represents the hypotenuse of the triangle. Since the hypotenuse is the largest side of the triangle, the ratio of the perpendicular to the hypotenuse and the base to the hypotenuse both will be less than the hypotenuse, therefore, 1. Hence, the value of sine and cosine will be always less than a unit.
In construction, we use trigonometry. For figuring areas of triangular shapes, similar to many concepts and phenomena in mathematics.
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A sample of workers exhibit the following production rates before and after a workshop. Worker Before After 1 20 22 2 25 23 3 27 27 4 23 20 5 22 25 6 20 19 7 17 18 The point estimate for the difference between the means of the two populations is: Group of answer choices
The point estimate here is 0.
Calculating the Mean of Each Set
The sample set of production rates exhibited by workers before workshop, S1 = {20, 25, 27, 23, , 22, 20, 17}
The sample set of production rates exhibited by workers after workshop, S2 = {22, 23, 27, 20, 25, 19, 18}
The mean of set S1 = (20+25+27+23+22+20+17)/7
= 154/7
= 22
The mean of set S2 = (22+23+37+20+25+19+18)/7
= 154/7
=22
Calculating the Point Estimate
The formula for point estimate is given as,
Point Estimate = The mean of set S1 - The mean of set S2
Point Estimate = 22-22
Point Estimate = 0
Therefore, the point estimate for the difference between the means of the two populations or sets is 0
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Given: quadrilateral MNOL with MN ≅ LO and ML ≅ NO
Prove: MNOL is a parallelogram.
Quadrilateral L M N O is shown. Sides M N and L O are congruent. Sides L M and O N are congruent.
Complete the paragraph proof.
We are given that MN ≅ LO and ML ≅ NO. We can draw in MO because between any two points is a line. By the reflexive property, MO ≅ MO. By SSS, △MLO ≅ △
. By CPCTC, ∠LMO ≅ ∠ and ∠NMO ≅ ∠LOM. Both pairs of angles are also , based on the definition. Based on the converse of the alternate interior angles theorem, MN ∥ LO and LM ∥ NO. Based on the definition of a parallelogram, MNOL is a parallelogram.
The answers to the quadrilateral are ONM, NOM, and alternate interior angles.
How to explain the quadrilateral?Based on the SSS postulate, the two triangles △MLO and △ONM are congruent since three sides of △MLO are respectively equal to the three sides of △ONM.
Based on CPCTC, all of the corresponding angles of △MLO and △ONM are congruent as well since the two triangles are congruent, that is,
∠LMO≅∠NOM and ∠NMO≅∠LOM.
Since the pair ∠LMO and ∠NOM as well as ∠NMO and ∠LOM are angles on the inner side of two lines but on opposite sides of the transversal MO, these pairs of angles are also alternate interior angles.
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Answer: ONM
NOM
alternate interior angles
Step-by-step explanation: Complete the paragraph proof.
We are given that MN ≅ LO and ML ≅ NO. We can draw in MO because between any two points is a line. By the reflexive property, MO ≅ MO. By SSS, △MLO ≅ △
✔ ONM
. By CPCTC, ∠LMO ≅ ∠
✔ NOM
and ∠NMO ≅ ∠LOM. Both pairs of angles are also
✔ alternate interior angles
, based on the definition. Based on the converse of the alternate interior angles theorem, MN ∥ LO and LM ∥ NO. Based on the definition of a parallelogram, MNOL is a parallelogram.
How many three-digit numbers use only the digits 0,1 and 5
Answer:
18
Step-by-step explanation:
3*3*3 = 27, assuming all 3 digits can occupy each space
However, 0 cannot start a number, so it becomes:
3*3*2, which is 18.
halp pls ok
x =x=x, equals
^\circ
∘
Answer:
60
Step-by-step explanation:
The yellow and green angles form a right angle, so the measures of those combined will be 90 degrees.
90 - 30 = 60
Please help me with this
Answer:
altitude: 16 cmbase: 12 cmStep-by-step explanation:
The given relation can be used with the formula for the area of a triangle to give an equation for the altitude or base.
SetupLet b represent the length of the base. Then the altitude (height) is (b+4). The area formula tells us the area is ...
A = 1/2bh
Using given values, the equation becomes ...
96 = 1/2b(b +4)
SolutionSimplifying the equation and multiplying by 2, we have ...
192 = b² +4b
Adding (4/2)² = 4 will complete the square.
196 = b² +4b +4 = (b +2)²
Taking the square root gives ...
14 = b +2 . . . . . . we are not interested in the negative root
12 = b . . . . . . . . subtract 2
16 = b+4 . . . . . find the altitude
The base is 12 cm; the altitude is 16 cm.
Can someone help me please?
The surface area of the cone is: A. 184π units².
What is the Surface Area of a Cone?Surface area of a cone = πr(l + r), where r is the radius and l is the slant height.
Given the following:
Slant height (l) = 15 unitsRadius = (r) = 8 unitsSurface area of a cone = π8(15 + 8)
Surface area of a cone = 184π units²
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The counting numbers beginning with 101 and ending with 200 are listed. How many of the numbers have a 6 as a digit
Counting numbers from 101 to 200, those with 6 as a digit are 19
The numbers
Let's start by listing all the number between 101 and 200
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
Now, let's count the numbers with 6 as a digit
= 19 numbers has 6 as a digit
Thus, counting numbers from 101 to 200, those with 6 as a digit are 19
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6x + -2y² + 4xy² + 3x² + 5xy² simplify it
[tex]\large\displaystyle\text{$\begin{gathered}\sf 6x+-2y^{2}+4xy^{2}+3x^{2} +5xy^{2} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Group\:like\:terms \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf =3x^2+6x-2y^2+4xy^2+5xy^2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Sum\:similar\:elements:\:4xy^2+5xy^2=9xy^2 \end{gathered}$}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf 3x^2+6x-2y^2+9xy^2 \end{gathered}$} }[/tex]
Helpppppp Asap!!!!!! The question is in the picture
The approximate length of side AB is 14.0. The correct option is B. 14.0 units
Law of sinesFrom the question, we are to determine the measure of side AB
First, we will determine the measure of angle A
A + B + C = 180° (Sum of angles in a triangle)
A + 65° + 35° = 180°
A = 180° - 65° - 35°
A = 80°
Now, using the law of sines
c/sinC = a/sinA
c = AB
a = BC = 24
Thus,
c/sin35° = 24/sin80°
c = (24×sin35°)/sin80°
c = 13.978
c ≈ 14.0
∴ AB = 14.0
Hence, the approximate length of side AB is 14.0. The correct option is B. 14.0 units
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2. Mary receives $2.00 weekly as an allowance. If
she saves $0.70 of it, what percent does she
save?
Answer:
35%
Step-by-step explanation:
She is saving $0.70/$2.00 weekly.
To convert this into a percentage we covert it to decimal then multiply by 100 :
$0.70/$2.00 = 0.35
0.35 × 100 = 35%
Our final answer is 35%.
Hope this helped and have a good day
y=x The point F is the foot of the perpendicular from the point (1, 9) to the line y=x. Find the coordinates of F.
Answer: (5,5)
Step-by-step explanation:
The perpendicular to y=x has slope -1, and thus the equation of the perpendicular from (1,9) is [tex]y=-x+10[/tex].
Finding the point where they intersect, since both equations are set equal to y, we know that -x+10=x, and thus x=5.
If x=5, then y=5 as well.
So, F has coordinates (5,5).
The product of the square of a number x and 2 subtracted from 3 is y.
The algebraic expression for the given statement is: 2x² - 3 = y.
How to Write an Algebraic Expression?To wrote an algebraic expression is translate a statement using numbers, variables, and mathematical sign into a mathematical statement.
Square of x is: x²
Product of x² and 2 is: 2x²
Thus, we would have:
2x² - 3 = y
The algebraic expression is: 2x² - 3 = y.
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pls help tysm!!!!!!!!!
Answer:
Second choice
Step-by-step explanation:
Analyse each sentences: The sum of x and y is 5 can be mathematically expressed as [tex]\displaystyle{x+y = 5}[/tex] since both are sum together and equal to 5.
Next, the value of y is one more than value of x can be mathematically expressed as [tex]\displaystyle{y=x+1}[/tex] because value of y is one more than value of x so y will be the value of x add with 1.
Therefore, form the simultaneous equation:
[tex]\displaystyle{\left \{ {{x+y=5} \atop {y=x+1}} \right}[/tex]
Hence, the answer is second choice.
Triangle ABC was dilated using the rule Do,4. Triangle
A'B'C' is the result of the dilation.
3
A
B
C
A'
В'
C
What is OB'?
O 1.5 units
3 units
O4.5 units
O6 units
The value of OB based on the information given about the triangle is 3 units.
How to illustrate the information?It should be noted that dilation is the process of enlarging or shrinking of an object.
In this case, the triangle is dilated. Therefore, the length of OB will be:
= 3/4 × 4 = 3 units.
Therefore, the correct option is B.
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What does 6 * b equal??
Answer:
6b
You can just simply combine the variable, 6, and the coefficient, b.