Answer:
g = -30
Step-by-step explanation:
-15 - g/3 = -5
Add 15 to each side
-15+15 - g/3 = -5+15
-g/3=10
Multiply by -3 to each side
-g/3 * -3 = 10*-3
g = -30
Answer:
g= -30
Step-by-step explanation:
after writing down the problem, multiply both sides of the equation by 3 to get -45-g= =15. then subtract 15 from both sides to get g=-30, which is your answer. hope this helps!
If function g is defined by the equation y − 3x = -14, which equation represents the function in function notation?
Answer:
f(x) = 3x - 14
Step-by-step explanation:
note that y = f(x), thus rearrange the equation making y the subject.
Given
y - 3x = - 14 ( add 3x to both sides )
y = 3x - 14 , that is
f(x) = 3x - 14 ← in functional notation
A man lends 12,500 at 12% for the first
year, at 15% for the second year and at 18%
for the third year. If the rates of interest are
compounded yearly; find the difference
between the C.I. of the first year and the
compound interest for the third year.
Answer: $1398
Step-by-step explanation:
Given , Principal (P) = $12,500
Rate of interest for 1st year [tex](R_1)[/tex]= 12% =0.12
Rate of interest for 2nd year [tex](R_2)[/tex]= 15% =0.15
Rate of interest for 3rd year [tex](R_3)[/tex]= 18% =0.18
Interest for first year = [tex]I=P\times R_1\times T[/tex]
= [tex]12500\times 0.12\times 1[/tex]
= $1500
Now, For second year new principal [tex]P_2 = \$12,500+\$1,500 =\$14,000[/tex]
Interest for second year = [tex]I=P_2\times R_2\times T[/tex]
= [tex]14000\times 0.15\times 1[/tex]
= $2100
Now, For third year new principal [tex]P_3 = \$14000+\$2,100 =\$16,100[/tex]
Interest for third year = [tex]I=P_3\times R_3\times T[/tex]
= [tex]16100\times 0.18\times 1[/tex]
= $2898
Difference between the compound interest of the first year and the compound interest for the third year. = $2898 - $1500 = $1398
Hence, the difference between the compound interest of the first year and the compound interest for the third year is $1398 .
How to do this question plz answer me step by step plzz plz
Answer:
£13496.80
Step-by-step explanation:
We can ignore the £ sign for now, that is just units.
If we decrease a number by 4.5%, we will have to find [tex]100-4.5=95.5[/tex]% of 14132.77.
We can easily do this by setting up a proportion.
[tex]\frac{x}{14132.77} = \frac{95.5}{100}[/tex]
Multiply 14132.77 by 95.5:
[tex]14132.77\cdot95.5=1349679.535[/tex]
Divide by 100:
[tex]1349679.535\div100=13496.79535[/tex]
Rounding this to two decimal places, it simplifies to 13496.80.
Hope this helped!
10 points please help
Answer:
[tex]\frac{14}{55}[/tex]
Step-by-step explanation:
note that
n! = n(n - 1)(n - 2) .... × 3 × 2 × 1
Given
[tex]\frac{8!9!}{5!12!}[/tex]
Cancel the terms from 8! ( 5 × 4 × 3 × 2 × 1 ) with the same terms from
5! ( 5 × 4 × 3 × 2 × 1 ) leaving
8 × 7 × 6 = 336 on the numerator
Similarly
Cancel the terms from 9! and 12!
leaving 12 × 11 × 10 = 1320 on the denominator, thus simplifies to
[tex]\frac{336}{1320}[/tex]
= [tex]\frac{14}{55}[/tex]
This rectangle has side lengths r and s.
For each expression, say whether it gives the perimeter of the rectangle, the area of the
rectangle, or neither.
1. rts
2. r.s
3. 2r + 2s
4.72 +82
Answer:
1.) Neither
2.) Area
3.) Perimeter
4.) Neither
Step-by-step explanation:
Given that the lengths of the rectangle are r and s
The perimeter of the rectangle will be:
Perimeter = 2r + 2s
Perimeter = 2(r+s)
While the area will be:
Area = r × s
Area = rs
For each expression, say whether it gives the perimeter of the rectangle, the area of the
rectangle, or neither.
1. rts = neither
2. r.s = Area of rectangle
3. 2r + 2s = Perimeter of rectangle
4.72 +82 = neither.
The sums of which two pairs from the table will give you the same result? For example, A + B = C + D.
Answer:
D + E = F + H
Step-by-step explanation:
We have to identify the two pairs from the give table which have the same result.
These pairs show the relation as A + B = C + D
We take a pair of expressions given in options (D) and (E)
By adding them,
D + E = (-4 + 9i) + (6 - 6i)
= 2 + 3i
Similarly we add the expressions given in options (F) and (H),
F + H = (-9 + 15i) + (11 - 12i)
= 2 + 3i
Therefore, D + E = F + H will be the answer.
what is the value of 14 - a² given a = -3? A. 23 B. 11 C. 8 D. 5
Answer:
The answer is D. 5
Step-by-step explanation:
14-(-3)^2=
14-9=5
The value of f(a) = 14 - [tex]a^{2}[/tex] at x = -3 is 5.
We have the following function of [tex]a[/tex] -
f(a) = 14 - [tex]a^{2}[/tex]
We have to determine the value of this function at a = -3.
What is the value of f(x) = 2x - 3 at x = 3?\The value of f(x) = 2x - 3 at x = 3 can be calculated as follows -
f(3) = 2 x 3 - 3 = 6 - 3 = 3
According to the question -
f(a) = 14 - [tex]a^{2}[/tex]
Now, the value of the function f(a) can be calculated as follows -
f(- 3) = 14 - [tex](-3)^{2}[/tex]
f(- 3) = 14 - 9
f(- 3) = 5
Hence, the value of f(a) = 14 - [tex]a^{2}[/tex] at x = -3 is 5.
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Solve D = ABC for C.
Answer:C=d/ab
Step-by-step explanation:
D=abc
D/ab=abc/ab (both side divided by ab)
Ab cancel by ab and c= d/ab remains
The solution of the given equation D = ABC for C will be D/(AB).
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
The equation must be constrained with some constraints.
As per the given equation,
D = ABC
The value of the above equation for C will be as,
D = (AB)C
C = D/(AB)
Hence "The solution of the given equation D = ABC for C will be D/(AB)".
For more about the equation,
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Add or subtract. Write your answer in scientific notation. 6.4 x 10^3+ 1.4 x 10^4+ 7.5 x 10^3
Answer:
2.79 * 10^4
Step-by-step explanation:
6.4 x 10^3+ 1.4 x 10^4+ 7.5 x 10^3
The exponents need to be the same
6.4 x 10^3+ 14 x 10^3+ 7.5 x 10^3
Add the numbers
6.4 + 14+ 7.5 =27.9
Multiply by the exponent
27.9 * 10 ^3
But this is not in scientific notation
Move the decimal one place to the left and add one to the exponent
2.79 * 10^4
Plz help Solve: y-17= -37
Answer:
-20
Step-by-step explanation:
First thing you do is set up your equation:
y-17= -37
+17 +17 Next you add 17 to both sides
------------- Follow your integer rules
y= -20
We can check this by putting it back into the solution
-20-17= -37 Integer Rules
You use KCC aka Keep Change Change
= -20+ -17= -37
What is the slope of the line that cuts through the points (1, 2) and (5, 4)?
Answer:
[tex]slope=\frac{1}{2}[/tex]
Step-by-step explanation:
Use the following equation:
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}[/tex]
Rise over run is the change in the y-axis over the change of the x-axis, otherwise known as the slope.
Insert the values:
[tex](1_{x1},2_{y1})\\(5_{x2},4_{y2})[/tex]
[tex]\frac{4-2}{5-1}=\frac{2}{4} =\frac{1}{2}[/tex]
The slope is [tex]\frac{1}{2}[/tex].
:Done
Answer:
1/2
Step-by-step explanation:
The formula for slope is: y1-y2/x1-x2
The points given are: (x-coordinate, y-coordinate)
In the formula:
y1 is the y-coordinate of the first point
y2 is the y-coordinate of the second point
x1 is the x-coordinate of the first point
x2 is the x-coordinate of the second point
This said, we can plug our points in.
2-4/1-5
Subtract.
-2/-4
Simplify.
-1/-2
The negatives will cancel each other out.
1/2
The slope of the line that cuts through the points (1,2) and (5,4) is 1/2.
solution for x+4 is equal to 10
Answer:
x = 6
Step-by-step explanation:
x + 4 = 10
x = 10 - 4
x = 6
hope it helps
We can calculate EEE, the amount of euros that has the same value as DDD U.S. Dollars, using the equation E=\dfrac{17}{20}DE= 20 17 DE, equals, start fraction, 17, divided by, 20, end fraction, D. How many euros have the same value as 111 U.S. Dollar? euros How many U.S. Dollars have the same value as 111 euro? dollars
Answer: 1 U.S.dollar = 0.85 euro.
1 euro = 1.18 dollars.
Step-by-step explanation:
The given equation: [tex]E=\dfrac{17}{20}D[/tex]
, where 'E' is the amount of euros that has the same value as 'D' U.S. Dollars.
At D= 1,
[tex]E=\dfrac{17}{20}=0.85\text{ euro}[/tex]
i.e. 1 U.S.dollar = 0.85 euro.
At E= 1 , we have
[tex]1=\dfrac{17}{20}D\\\\\Rightarrow\ D= 20/17\approx1.18\text{ dollars}[/tex]
Hence, 1 euro = 1.18 dollars.
Escreva expressões algébricas mais simples e equivalentes às expressões abaixo.
Answer:
Step-by-step explanation:
(4a+8)/2 = 4a/2 + 8/2 = 2a + 4(5x + 6x + 22)/11 = (11x+22)/11 = 11x/11 + 22/11 = x + 2{6(x+2)-12}/3 = {6x+12 - 12}/3 = 6x/3 = 2x(Please answer ASAP. The question is down below
Answer: A
Step-by-step explanation:
Notes: Dividing by a fraction means to multiply by its reciprocal.
The denominator cannot equal zero.
[tex]\dfrac{5a^3bc}{8ab^3}\div\dfrac{-ab^2}{6a^5b}\cdot \dfrac{2a^2b^3}{3b}\qquad \rightarrow a\neq 0,b\neq 0\\\\\\=\dfrac{5a^3bc}{8ab^3}\cdot\dfrac{6a^5b}{-ab^2}\cdot \dfrac{2a^2b^3}{3b}\\\\\\=\dfrac{5\cdot 6\cdot 2\quad a^3\cdot a^5\cdot a^2\quad b\cdot b\cdot b^3\quad c}{8\cdot -1 \cdot 3\quad a\cdot a\qquad b^3\cdot b^2\cdot b \quad}\\\\\\=\dfrac{-60a^{10}b^5c}{-24a^2b^6}\\\\\\=\dfrac{-5a^8c}{2b}[/tex]
On a cold February morning, the temperature of the radiator fluid in Stanley’s car is . When the engine is running, the temperature of the fluid goes up per minute. Approximately how long will it take before the radiator fluid temperature reaches ?
Answer:
18.18 min
Step-by-step explanation:
The complete question is
On a cold February morning, the radiator fluid in Stanley’s car is -18F. When the engine is running, the temperature goes up 5.4 F per minute. Approximately how long will it take before the radiator fluid temperature reaches 80 F?
The initial temperature of the engine [tex]T_{1}[/tex] = -18 F
rate of increase in temperature r = 5.4 F/min
Final temperature [tex]T_{2}[/tex] = 80 F
Difference in temperature ΔT = [tex]T_{1} -T_{2}[/tex] = 80 - (-18) = 98 F
time taken to reach this 80 F will be = ΔT/r
where ΔT is the difference in temperature
r is the rate of change of temperature
time taken = 98/5.4 = 18.18 min
What is the slope of the line that passes through the points (-10, 8) and
(-15, – 7)? Write your answer in simplest form.
Answer:
[tex]slope=3[/tex]
Step-by-step explanation:
Use the following equation the find the slope:
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{rise}{run}[/tex]
Rise over run is the change in the y-axis over the change in the x-axis from one point to the other. This is also known as the "slope". Insert the known values:
[tex](-10_{x1},8_{y1})\\\\(-15_{x2},-7_{y2})\\\\\\\frac{-7-8}{-15-(-10)}\\\\\frac{-7-8}{-15+10}[/tex]
Solve:
[tex]\frac{-7-8}{-15+10}=\frac{-15}{-5}[/tex]
Simplify. Two negatives make a positive:
[tex]\frac{-15}{-5}=\frac{15}{5}[/tex]
Simplify fraction by dividing top and bottom by 5:
[tex]\frac{15}{5}=\frac{3}{1} =3[/tex]
The slope is 3.
:Done
The slope of the line that passes through the points (-10, 8) and (-15, -7) is 3 and thsi can be determined by using the point-slope formula.
Given :
The line that passes through the points (-10, 8) and (-15, -7).
The following steps can be used in order to determine the slope of the line that passes through the points (-10, 8) and (-15, -7):
Step 1 - The slope formula when two points are given is:
[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
where m is the slope and [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the points on the line.
Step 2 - Substitute the known terms in the above formula.
[tex]\rm m = \dfrac{-7-8}{-15+10}[/tex]
Step 3 - Simplify the above expression.
[tex]\rm m = \dfrac{15}{5}[/tex]
m = 3
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Drag a vertex of the triangle to change its shape.
Double-click or double-tap a vertex or side to prevent it from
changing.
Problem: Construct a triangle with interior angle
measures of 60° and 75°.
What is the measure of the third angle?
O 30°
2C = 41°
O 45°
48°
9.2
10
50°
ZA = 49°
6.0 ZB = 90°
Answer:
The correct option is;
45°
Step-by-step explanation:
By angle sum theorem, we have that the sum of angles in a triangle = 180°
Therefore, we have;
When the interior angles of the triangle are constructed to be 60° and 75°, we have by the angle sum theorem;
The third angle + 60° + 75° = 180°
Which gives;
The third angle = 180°- 60° - 75° = 180°- 135° = 45°
The measurement of the third angle by the angle sum theorem will be 45°
The correct option is ∠third angle = 45°.
Allie, Ben, and Cliff plant ceilings in the neighborhood park. Ali plans 40% of the total number of ceiling, then place 45% of the total number of seed wings, and Cliff plans the rest of the siblings. If Cliff +84 siblings how many seedling do the three boys play together
Answer:
The number of seedlings the three boys planted together is 560 seedlings
Step-by-step explanation:
The possible information in the question are;
Percentage of the seedlings planted by Ali = 40%
Percentage of the seedling planted by Ben = 45%
The percentage of the seedling planted by Cliff = The rest of the seedling
The number of seedling planted by Cliff = 84 siblings
Therefore, the percentage of the seedling planted by Cliff = 100% - 45% - 40% = 15%
Given that Cliff planted 15% of the seedlings, we have;
15% of seedlings Cliff planted = 84
Let X = the total number of seedlings
15/100 × X = 0.15×X = 84
X = 84/0.15 = 560
The total number of seedlings = The number of seedlings the three boys planted together = 560 seedlings.
PLEASE HELP!!!
Which expression shows a way to find the area of the following rectangle?
Answer:
B
Step-by-step explanation:
This rectangle appears to have 7 boxes on the bottom, and 3 box for the side.
Since area is base×height
It would be 7×3
Five different cookies and four different drinks are served at the Junior Honor Society reception. In how many ways can Sara select three different cookies and two different drinks?
A. 60
B.10
C.6
D.20
E.30
F.120
[tex]_5C_3\cdot _4C_2=\dfrac{5!}{3!2!}\cdot\dfrac{4!}{2!2!}=\dfrac{4\cdot5}{2}\cdot\dfrac{3\cdot4}{2}=2\cdot5\cdot3\cdot2=60[/tex]
Answer:
[tex]\large \boxed{\mathrm{A. \ 60}}[/tex]
Step-by-step explanation:
[tex]\displaystyle nC_r=\frac{n!}{r!(n-r)!}[/tex]
[tex]5C_3 \times 4C_2[/tex]
[tex]\displaystyle \frac{5!}{3!(5-3)!} \times \frac{4!}{2!(4-2)!}=10 \times 6 = 60[/tex]
Simplify this expression:
4(1 - 3x) + 7 x - 8
4(1-3x) + 7x -8
Use distributive property:
4 -12x + 7x -8
Now combine like terms:
-5x -4
Answer:
[tex]-5x-4[/tex]
Step-by-step explanation:
With the expression [tex]4(1-3x) + 7x - 8[/tex], we can simplify it down by applying the distributive property, then combining like terms.
[tex]4(1-3x)+7x-8\\\\4-12x+7x-8\\\\4-5x-8\\\\-5x-4[/tex]
Hope this helped!
A box has a base of 12 inches by 12 inches and a height of 30 inches. What is the length of the interior diagonal of the box? Round to the nearest hundredth.
This is a problem using the Pythagorean theorem.
The square of the length required is 122 + 122 + 302 = 1188
The length is the square root of this number; I will leave it to you to extract the square root.
Answer:
34.47
Step-by-step explanation:
IT IS FOR NOW IM GIVING BRAINLIEST HRRY UP AND 10 POINTS Simplify the expression. What classification describes the resulting polynomial? (8x2 + 3x) − (12x2 − 1) A. linear binomial B. quadratic binomial C. quadratic trinomial D. linear monomial
Answer:
The equation would be a quadratic trinomial
Step-by-step explanation:
Step 1: Expand the equation to remove the brackets
0 = 8x² + 3x - 12x² + 1
Step 2: Collect like terms
0 = -4x² + 3x + 1
Step 3: Count number of terms
0 = -4x² + 3x + 1
1 2 3
Therefore there are 3 terms and this is a quadratic equation making the answer B, a quadratic trinomial
1. Which of the following is a true statement?
?
a. To square a number, multiply the number
by 2.
b. The inverse of squaring a number is to
divide the number by 2.
c. To square a number, multiply the number
by itself.
d. A perfect square is a number who's
square root is an even number.
Answer:
C
Step-by-step explanation:
Definitely not a! To square a number you multiply it by itself. for example, if you were squaring 3, you would do 3x3.
Not b either! You will have to take the SQUARE ROOT of the number!
C is the right answer, as I said for a.
D is wrong! The perfect square 49 has a sqrt (square root) of 7. That is NOT even, so d cannot be true.
C is the only true statement. Also, if this is right, can I get branliest answer? Thx :)
martin ordered a pizza with a 16-inch diameter. Ricky ordered a pizza with a 20-inch diameter. What is the approximate difference in area of the two pizzas?
Answer:
14
Step-by-step explanation:
What the answer now
Answer:
Area of the triangle = 98.1 km²
Step-by-step explanation:
In the given triangle WXV,
m∠W + m∠X + m∠V = 180°
m∠W + 119° + 34° = 180°
m∠W = 180° - 153°
m∠W = 27°
By applying Sine rule in the given triangle,
[tex]\frac{\text{SInW}}{\text{XV}}=\frac{\text{SinX}}{\text{WV}}[/tex]
[tex]\frac{\text{SIn27}}{\text{XV}}=\frac{\text{Sin119}}{26}[/tex]
[tex]XV=\frac{26\times (\text{Sin27})}{\text{Sin119}}[/tex]
XV = 13.496 km
Area of the ΔWXV = [tex]\frac{1}{2}(\text{WV})(\text{XV})(\text{SinV})[/tex]
= [tex]\frac{1}{2}(26)(13.496)(0.55919)[/tex]
= 98.109
≈ 98.1 km²
What is the quotient ? -4 /5 divide 2 A . - 1 3/5 B . -2 /5 c. 1/2 D . 1 3/ 5
Answer:
[tex] \boxed{ - \frac{2}{5} }[/tex]Option B is the correct option.
Step-by-step explanation:
[tex] \mathrm{ - \frac{4}{5} \div 2}[/tex]
[tex] \mathrm{dividing \: a \: negative \: and \: a \: positive \: equals \: a \: negative \:. \: ( - ) \div ( + ) = ( - )}[/tex]
[tex] \mathrm{ - \frac{4}{5} \div 2}[/tex]
[tex] \mathrm{dividing \: is \: equivalent \: to \: multiplying \: with \: the \: reciprocal}[/tex]
[tex] \mathrm{ - \frac{4}{5} \times \frac{1}{2} }[/tex]
[tex] \mathrm{reduce \: the \: numbers \: with \: G.C.F \: 2}[/tex]
[tex] \mathrm{ - \frac{2}{5} }[/tex]
Hope I helped!
Best regards!
The quotient of -4 /5 divide 2 would be equal to -2/5 in simplified form.
What are the Quotients?Quotients are the number that is obtained by dividing one number by another number. We can use the fact that division can be taken as multiplication but with the denominator's multiplicative inverse.
We have been given that -4 /5 divide 2
Thus, we have to divide the terms as;
-4 /5 ÷ 2
Therefore, -4 /5 x 1/ 2
-2/5
Hence, the quotient of -4 /5 divide 2 would be equal to -2/5 in simplified form.
Learn more about the quotient;
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PLEASE HELP ME FAST...
Answer:
Sequence a) Pattern: (-2) -9, -11, -13, -15, -17
Sequence b) Pattern: (-5) -15, -20, -25, -30, -35
Sequence c) Pattern: (-6) -13, -19, -25, -31, -37
Hope this helps!
Hi there! Hopefully this helps!
-------------------------------------------------------------------------------------------------------------
A (Subtracting by 2): -9, -11, -13, -15, -17.
B(Subtracting by 5): -15, -20, 25, -30, -35
C(Subtracting by 6): -13, -19, -25, -31, -37
What is the standard form of function f ?
Answer:
f(x) = 4x² + 48x + 149
Step-by-step explanation:
f(x) = 4(x + 6)² + 5
The above expression can be written as: f(x) = ax² + bx + c, by doing the following:
1. Expand (x + 6)²
(x + 6)² = (x + 6)(x + 6)
(x + 6)(x + 6)
x(x + 6) + 6(x +6)
x² + 6x + 6x + 36
x² + 12x + 36
(x + 6)² = x² + 12x + 36
2. Substitute x² + 12x + 36 for (x + 6)² in
f(x) = 4(x + 6)² + 5
This is illustrated below:
f(x) = 4(x + 6)² + 5
(x + 6)² = x² + 12x + 36
f(x) = 4(x² + 12x + 36) + 5
Clear bracket
f(x) = 4x² + 48x + 144 + 5
f(x) = 4x² + 48x + 149
Therefore, the standard of the function:
f(x) = 4(x + 6)² + 5
is
f(x) = 4x² + 48x + 149
