Given
a = m(2) + 2value of a when m = -3Substitute m with -3
a = -3*2 + 2
a = -6 + 2
a = -4
Answer
The value of a when m = -3 is -4
Answer:
=11
Step-by-step explanation:
The equation given is a=m²+2
To find a when m= -3 , we substitute for m in the equation.
a=(-3)²+2
=9+2
=11
Therefore a=11 when m is -3
What is the surface area of the figure?
314 in.2
792 in.2
628 in.2
546 in.2
Answer:
628 n.2 is the correct answer
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? A] The test contains 4 three-point questions and 20 five-point questions. B]The test contains 10 three-point questions and 14 five-point questions. C]The test contains 14 three-point questions and 10 five-point questions. D]The test contains 20 three-point questions and 8 five-point questions.
Answer:
B. The test contains 10 three-point questions and 14 five-point questions.
Step-by-step explanation:
Let us first find the solution to the system of equations.
x+y= 24
3x+5y= 100
We use substitution method.
x=24-y
Replacing the value of x in the second equation.
3(24-y)+5y=100
Then solve for y.
72-3y+5y=100
2y=100-72
2y=28
y=14
To find x let us replace the value of y in x=24-y
x=24-14
x=10
This means that the test has 14 five-point questions and 10 three point questions.
Indicate which property is illustrated in step 8. A. Subtraction property of equality B. Simplification C. Distributive property D. Division property of equality
step 8: -3x/-3 = -7/3
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
[tex]-3x=7[/tex]
After Step 8 it becomes,
[tex]\dfrac{-3}{-3}=\dfrac{-7}{3}[/tex]
It indicated the Division property of equality.
To find the value of x, we need to divide the left hand side and right hand side by -3.
So, this property is known as "Division property of equality":
Hence, Option 'D' is correct.
Answer:
Option D - Division property of equality
Step-by-step explanation:
Given : Step 8 - [tex]\frac{-3x}{-3}=-\frac{7}{3}[/tex]
To find : Indicate which property is illustrated in step 8 ?
Solution :
Step 8 - [tex]\frac{-3x}{-3}=-\frac{7}{3}[/tex]
In step 8 we have seen that -3 is divided both side,
So, The division property of equality is applied to get the result.
[tex]\frac{-3x}{-3}=-\frac{7}{3}[/tex]
[tex]x=-7[/tex]
Therefore, Option D is correct.
Division property of equality
which decimal is equivalent to forty and seventy six thousands ? a.40.076 b 40.76 C 47.006 D 47.06
Answer:
A. 40.076
Step-by-step explanation:
Because B is forty and seventy six hundredths. C is forty-seven and six thousandths. D is forty-seven and six hundredths.
Seventy-six thousandths is written as .076, making the final answer 40.076.
The decimal equivalent to forty and seventy six thousandths is 40.076. This is because seventy-six is in the thousandths place after the decimal point.
The decimal equivalent to forty and seventy six thousandths is 40.076. To write this out, you place the decimal point after the whole number forty, then you need to ensure that seventy-six is in the thousandths place. When writing decimal numbers, the first place to the right of the decimal is the tenths place, the second is the hundredths place, and the third is the thousandths place. Therefore, seventy-six thousandths is written as .076, making the final answer 40.076.
Which of the following inequalities matches the graph?
[tex]x \leqslant 0[/tex]
[tex]x \geqslant 0[/tex]
[tex]y \leqslant 0[/tex]
[tex]y \geqslant 0[/tex]
which one is it 1,2,3,or the 4 one
Answer:
[tex]\large\boxed{x\leq0}[/tex]
Step-by-step explanation:
x ≤ 0 - the region below the line x = 0 (x axis)
x ≥ 0 - the region above the line x = 0 (x axis)
y ≤ 0 - the region on the left of the line y = 0 (y axis)
y ≥ 0 - the region on the right side of the line y = 0 (y axis)
all region with lines (axes)
We have the region below the x axis (x = 0).
Which expression has the same value as -18-(-9)?
0 -18+2
9 -12-(-3)
-10-5
Answer:
None of the given option is correct.
Step-by-step explanation:
The expression given is:
-18-(-9)
= -18+9
= -9
Now checking the options, which will have -9 as answer
1) 0 -18+2
= -18+2
= -16
As answer is not -9, so this is not a correct option
2) 9 -12-(-3)
= 9 - 12 + 3
= 0
As answer is not -9, so this is not a correct option
3) -10-5
= -10-5
= -15
As answer is not -9, so this is not a correct option
So, None of the given option is correct.
3. Write an equation in point-slope form for the line through the given point with the given slope.
(4, -6); m = 3/5
A. Y-4=3/5x (x+6)
B. Y+6=3/5(x-4)
C. Y+6=3/5x-4
D. Y-6=3/5(x+4)
Answer:
B
Step-by-step explanation:
recall that point-slope form of a linear equation is expressed as follows
y - y1 = m (x - x1)
where m = slope and (x1, y1) is the coordinate of any point on the line
so, here we have m = (3/5), x1 = 4 and y1 = -6
substitute these into the formula
y - (-6) = (3/5) (x - 4)
y + 6 = (3/5) (x - 4)----> answer
Answer:
[tex]\boxed{\text{B. }y + 6 =\dfrac{3}{5}(x - 4)}[/tex]
Step-by-step explanation:
The point-slope formula for a straight line is
[tex]y - y_{1} = m(x - x_{1})[/tex]
x₁ = 4; y₁ = -6; m = ⅗
Substitute the values
[tex]\begin{array}{rcl}y - (-6) & = & \dfrac{3}{5}(x - 4)\\\\y + 6 & = & \dfrac{3}{5}(x - 4)\\\\\end{array}\\\text{The equation for the line is $\boxed{\mathbf{y + 6 =\dfrac{3}{5}(x - 4)}}$}[/tex]
The figure shows the graph of the equation with slope ⅗ passing through (4,-6).
Solve for k k/2 + 1/2 = 3
k/2+1/2=3
Move +1/2 to the other side. Sign changes from +1/2 to -1/2
k/2+1/2-1/2=3-1/2
k/2=3-1/2
Find the common denominator for 3 and -1/2.
Common denominator is 2
k/2=3(2)-1/2
k/2= 6/2-1/2
k/2=5/2
Multiply k/2 with 2. Multiply 2 with 5/2
k/2 (2/1)=2(5/2)
Cross out 2 and 2. Divide by 2. Cross out 2 and 2 for 5/2(2). Divide by 2
k=5
Multiply. Express your answer in simplest form. 9 1/6 × 1 1/11
Answer:
10
Step-by-step explanation:
First convert the fractions.
9 1/6 to 55/6 and 1 1/11 to 12/11
With these fractions, you can cross out 11 and 6.
55 times 12 5 × 2
6 11 1 × 1
This equals 10/1 or 10
Final answer:
To multiply 9 1/6 by 1 1/11, first convert them to improper fractions, 55/6 and 12/11 respectively. Multiply the numerators together to get 660, and the denominators together to get 66. Simplify by dividing both by their greatest common divisor, which is 66, to get the simplest form, which is 10.
Explanation:
The question asks to multiply 9 1/6 by 1 1/11 and express the answer in simplest form. First, we will convert these mixed numbers to improper fractions. For the first number, 9 1/6, we multiply the whole number part by the denominator of the fractional part and add the numerator: (9 × 6) + 1 = 54 + 1 = 55, thus we get 55/6. For the second number, 1 1/11, we follow the same process: (1 × 11) + 1 = 11 + 1 = 12, resulting in 12/11.
Next, we multiply the resulting improper fractions. The numerators are multiplied together, and the denominators are multiplied together yielding 55 × 12 over 6 × 11 which equals 660/66. Simplifying by common factors, we notice that both the numerator and denominator have a common factor of 66. Dividing the numerator and denominator by 66 gives us the simplest form, which is 10/1 or simply 10.
Need some help ya plz
Answer:
C. (-5, 3)
Step-by-step explanation:
Point C is currently (5,3).
If it is reflected over the y-axis, that means while the y-coordinate stays the same, the x- coordinate is negative of what is was before.
C is the only answer that keeps the y-coordinate constant, so just by looking at that, we can say that the answer is C.
Answer:
C
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y )
Hence
C(5, 3 ) → C'(- 5, 3 ) → C
{(1,2), (-2,3), (1,3), (-2,2)} is what type of relation?
A. one-to-many
B. many-to-many
C. one-to-one
D. many-to-one
Answer:
B. Many-to-many
Step-by-step explanation:
We have the following ordered pairs:
(1,2)(-2,3)(1,3)(-2,2)First let's define the following concepts:
One-to-one: A function is said to be one-to-one if every y value has exactly one x value mapped onto it.Many-to-one: If there are y values that have more than one x value mapped onto them.One-to-many: If there are x values that have more than one y value mapped onto them. (NOT A FUNCTION)Many-to-many: If there are x values that have more than one y value mapped onto them and at the same time, there are y values that have more than one x value mapped onto them (NOT A FUNCTION)From all the ordered pairs, we find that the points (1,2) and (1,3) have the same x-value for diferent y-values. Also we find that the points (1,2) and (-2, 2) have different x-values for the same y-value.
Therefore, the ordered pairs DO NOT belong to a function and can be considered MANY-TO MANY.
The given relation is a many-to-one relationship.
The given relation {(1,2), (-2,3), (1,3), (-2,2)} is an example of a many-to-one relationship. In a many-to-one relation, multiple elements in the domain map to a single element in the range. Each x-value has a unique y-value.
find the equivalent expression using the same bases (46 x 59)^6
Answer:
46^6 x 59^6
Step-by-step explanation:
For properties (axb)^y has the equivalent expression of a^y x b^y
Then, (46x59)^6 can be written as 46^6 x 59^6
Answer: [tex]46^6* 59^6[/tex]
Step-by-step explanation:
Given the expression [tex](46* 59)^6[/tex], in order to find an equivalent expression using the same bases, you need to remember the following:
[tex](a*b)^n=a^n*b^n[/tex]
So, you can observe that, in this case:
[tex]a=46\\b=59\\n=6[/tex]
Therefore, substituting values, you get the following equivalent expression:
[tex](46* 59)^6=46^6* 59^6[/tex]
how many 1/4s fit in 1/2
Answer:
2
Step-by-step explanation:
1/4+1/4=1/2
Country days scholarship rounds receive a gift of $135000. The money is invested in stock, bonds, and CDs. CDs pay 2.75% interest, bonds pay 4.5% interest, and stocks pay 10.4% interest. Country days invests $70000 more in bonds than CDs. If the annual income from the investments is $8555, how much was invested in stocks, bonds, and CDs?
Answer:
CDs — $10,000bonds — $80,000stocks — $45,000Step-by-step explanation:
Let the variables c, b, s represent the dollar amounts invested in CDs, stocks, and bonds, respectively. Then the problem statement gives us 3 relations between these 3 variables:
c + b + s = 135000 . . . . . . . . . . . . . . . . . total invested
0.0275c +.045b +0.104s = 8555 . . . . . total income earned
-c + b = 70000 . . . . . . . . . . . . . . . . . . . . . 70,000 more was in bonds than CDs
Using the third equation to write an expression for b, we can substitute into the other two equations.
b = 70000 +c . . . . . . . . . . . . . . . . expression we can substitute for b
c + (70000 +c) +s = 135000 . . . . substitute for b in the first equation
2c +s = 65000 . . . . . . . . . . . . . . . . [eq4] simplify
.0275c +.045(70000 +c) +.104s = 8555 . . . . . substitute for b in 2nd eqn
.0725c +.104s = 5405 . . . . . . . . . . [eq5] simplify
Using [eq4], we can write an expression for s that can be substituted into [eq5].
s = 65000 -2c . . . . . . . expression we can substitute for s
0.0725c +0.104(65000 -2c) = 5405
-0.1355c = -1355 . . . . . . . . . . . . . . . . . . . . subtract 6760, simplify
c = 1355/.1355 = 10,000
s = 65000 -2×10000 = 45,000
b = 70000 +10000 = 80,000
The amounts invested in stocks, bonds, and CDs were $45,000, $80,000, and $10,000, respectively.
_____
Alternatively, you can reduce the augmented matrix for this problem to row-echelon form using any of several calculators or on-line sites. That matrix is ...
[tex]\left[\begin{array}{ccc|c}1&1&1&135000\\0.0275&0.045&0.104&8555\\-1&1&0&70000\end{array}\right][/tex]
Wendy is paid $12 per hour and plans to work between 30 and 35 hours per week. Identify the independent and dependent quantity in the situation. Find reasonable domain and range values.
weekly pay; hours worked; 30 to 35 hours; $360 to $420
hours worked; weekly pay; 30 to 35 hours; $0 to $420
hours worked; weekly pay; 30 to 35 hours; $360 to $420
weekly pay; hours worked; $360 to $420; 30 to 35 hours;
Answer:
See below.
Step-by-step explanation:
The independent variable is the number of hours worked and the dependent variable is the weekly pay.
The domain is 30 to 35.
The range is $360 to $420.
The graph shows the relationship between the price of frozen yogurt and the number of ounces of frozen yogurt sold at different stores and restaurants
Answer:
13
Step-by-step explanation:
If you look at where $5 crosses the line of best fit, you see it between 12 and 14 ounces. The answer is 13.
Answer:
13 oz
Step-by-step explanation:
The blue line here is the trend line of the function between cost and size.
The trend line is the linear equation approximation of the function
So, for predicting the size when $5 is paid we need to take the corresponding x axis value and the corresponding y axis value on the trend line.
Hence, the Size of frozen yogurt is between 12 and 14 oz which means the size is 13 oz.
(7z^3+42z^2-15z+1)- (36z^2+12z-21)
Answer:
7z^3+6z^2-27z+22
Step-by-step explanation:
The given question is of subtraction:
So,
(7z^3+42z^2-15z+1)- (36z^2+12z-21)
=7z^3+42z^2-15z+1-36z^2-12z+21
Combining alike terms to simplify
=7z^3+42z^2-36z^2-15z-12z+1+21
=7z^3+6z^2-27z+22
So the answer in simplified form is:
7z^3+6z^2-27z+22 ..
Answer:
7z³ + 6z² - 27z + 22
Step-by-step explanation:
It is given an expression in variable z,
(7z³ + 42z² - 15z + 1) - (36z² + 12z - 21)
To find the simplified form
(7z³ + 42z² - 15z + 1) - (36z² + 12z - 21)
= (7z³ + 42z² - 15z + 1 - 36z² - 12z + 21)
= 7z³ + 42z² - 36z² - 15z -12z + 1 + 21
= 7z³ + 6z² - 27z + 22
Therefore the simplified expression is = 7z³ + 6z² - 27z + 22
for questions 5-6 the functions are
f(x)=5x^2+3
g(x)=x^2-7
Answer:
see explanation
Step-by-step explanation:
Note that
(f + g)(x) = f(x) + g(x) and
(f - g)(x) = f(x) - g(x)
5
f(x) + g(x)
= 5x² + 3 + x² - 7 = 6x² - 4
6
f(x) - g(x) = 5x² + 3 - (x² - 7) ← distribute parenthesis
= 5x² + 3 - x² +7 ← collect like terms
= 4x² + 10
7
f(x) + g(x) = [tex]4^{x}[/tex] + 3x + 2x - 5 = [tex]4^{x}[/tex] + 5x - 5
Whitch expression is equivlent to the expression
7(3x-2) + 4(x+5)
Answer:
[tex]\large\boxed{7(3x-2)+4(x+5)=25x+6}[/tex]
Step-by-step explanation:
[tex]7(3x-2)+4(x+5)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=(7)(3x)+(7)(-2)+(4)(x)+(4)(5)\\\\=21x-14+4x+20\qquad\text{combine like terms}\\\\=(21x+4x)+(-14+20)\\\\=25x+6[/tex]
Answer:
[tex]\Huge \boxed{25x+6}[/tex]
Step-by-step explanation:
[tex]\large \textnormal{Distributive property}[/tex], [tex]\large \textnormal{A(B+C)=AB+AC}[/tex].
[tex]\displaystyle 7(3x-2)=21x-14[/tex]
[tex]\displaystyle 21x-14+4(x+5)[/tex]
[tex]\displaystyle 4(x+5)=4x,5\times 4=20, 4x+20[/tex]
[tex]\Large\textnormal{Solve to find the answer.}[/tex]
[tex]\displaystyle 21x-14+4x+20=25x+6[/tex]
[tex]\Large \textnormal{Correct answer is \boxed{25x+6}.}[/tex]
Q: Which best describes the demand for consumer goods in the 1920's.
Select one:
a. people were less likely to buy new goods.
b. the demand for consumer goods declined during the 1920's.
0 C. all of these are correct
d. people began buying more than they had the cash to pay for becaus
could access loans and buy things on credit.
NE
Answer:
d. people began buying more than they had the cash to pay for because they
could access loans and buy things on credit.
Step-by-step explanation:
In the 1920's, it was a period of prosperity and people in the middle class began to have more income available to purchase products. Also, there were more products available because of the assembly line production and the credits expanded which resulted in people being able to buy things that they couldn't purchase paying the full price. According to this, the answer is that the statement that best decribes the demand for consumer goods in the 1920's is that people began buying more than they had the cash to pay for because they could access loans and buy things on credit.
F(x)=3x+1 and g(x)= x^2-6 find (f•g)(x)
Answer:
Step-by-step explanation:
It never occurred to me that the closed circle meant multiplication. The most common symbol for multiplication here is *. If that is what is meant (closed circle = multiplication) then my answer is wrong.
f(x) = 3x + 1
g(x) = x^2 - 6
f(x)(g(x)) = (3x + 1)(x^2 - 6)
f(x)(g(x)) = 3x^3 - 18x + x^2 + 6 or more properly
f(x)(g(x)) = 3x^3 + x^2 - 18x - 6
[tex](f\cdot g)(x)=(3x+1)(x^2-6)=3x^3-18x+x^2-6=3x^3+x^2-18x-6[/tex]
What is the approximate radius of a sphere whose volume is 1349 cm?
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=1349 \end{cases}\implies 1349=\cfrac{4\pi r^3}{3}\implies 4047=4\pi r^3 \\\\\\ \cfrac{4047}{4\pi }=r^3\implies \sqrt[3]{\cfrac{4047}{4\pi }}=r\implies 6.85\approx r[/tex]
what is the slope of the line passing through the points (-5,9) and (2,-12)
Answer:
-3
Step-by-step explanation:
To find the slope of a line given two points, we use:
[tex]\frac{y_2-y_1}{x_2-x_1} \text{ when the points } (x_1,y_1) \text{ and } (x_2,y_2) \text{ are on the line }[/tex].
Or you could line up the points vertically and subtract the points vertically, then put 2nd difference over 1st difference.
That looks like this:
( 2 , -12)
-( -5 , 9 )
----------------
7 -21
So the slope is -21/7 which gives you -3.
Dakota believes there is a correlation between the number of texts sent in class and GPA. She collected data and found that the line of best fit for the data can be modeled by the equation y = 3.9 − 0.3x.
Identify and interpret the slope in this scenario.
a. The slope is −3.9. Starting at 0.3, the GPA will decrease by 3.9 for every text sent in class.
b. The slope is 3.9. Starting at 0.3, the GPA will increase by 3.9 for every text sent in class.
c. The slope is 0.3. Starting at 3.9, the GPA will increase by 0.3 for every text sent in class.
d. The slope is −0.3. Starting at 3.9, the GPA will decrease by 0.3 for every text sent in class.
Answer:
d. The slope is −0.3. Starting at 3.9, the GPA will decrease by 0.3 for every text sent in class.
Step-by-step explanation:
You can write the equation is the slope intercept form of y=mx+c
where m is the slope and c in the y-axis intercept
write the equation as;
y=mx+c
y= -0.3x+3.9
Here , you have a negative slope which means the GPA will reduce by 0.3 for every text sent in class.
See attached graph to visualize the y-intercept point
Answer:
The correct option is d.
Step-by-step explanation:
The given equation of best fit line is
[tex]y=3.9-0.3x[/tex] .... (1)
The slope intercept form of a line is
[tex]y=mx+b[/tex] .... (2)
where, m is slope and b is y-intercept or initial value.
From (1) and (2), we get
[tex]m=-0.3[/tex]
[tex]b=3.9[/tex]
It means the slope is −0.3. Starting at 3.9, the GPA will decrease by 0.3 for every text sent in class.
Therefore the correct option is d.
Which expression is equivalent to the following complex fraction?
2-1/y / 3+ 1/y
Answer:
[tex]\frac{2-\frac{1}{y} }{3+\frac{1}{y} }[/tex] is equivalent to [tex]\frac{2y-1}{3y-1}[/tex]
Step-by-step explanation:
The given expression is :[tex]\frac{2-\frac{1}{y} }{3+\frac{1}{y} }[/tex].
We collect LCM in both the numerator and the denominator to obtain:
[tex]\frac{\frac{2y-1}{y} }{\frac{3y-1}{y} }[/tex]
Change to the normal division sign;
[tex]\frac{2y-1}{y} \div \frac{3y-1}{y}[/tex]
Multiply by the reciprocal of the second fraction:
[tex]\frac{2y-1}{y} \times \frac{y}{3y-1}[/tex]
Cancel out the common factors
[tex]\frac{2y-1}{3y-1}[/tex]
Therefore [tex]\frac{2-\frac{1}{y} }{3+\frac{1}{y} }[/tex] is equivalent to [tex]\frac{2y-1}{3y-1}[/tex]
Rachel is going to calculate the following expression: 3.32/1.66+18.4. She calculates the expression as it is written and then writes down the answer rounded to the nearest whole number. She then calculates it again, but rounds each of the 3 numbers in the expression to the nearest integer, and then performs the division and addition. She writes this answer down next to the answer she got before. What is the positive difference between the 2 answers she got?
Answer:
the answer is 0.5 lol
What type of function is represented by the table of values below?
8
12
16
20
Answer:
To be precise, I think it's a pattern question, where you have to add 4 to each number. I'm not very sure though.
Which of the following is the correct notation for the complex number
Answer:
1-4i
Step-by-step explanation:
[tex]i=\sqrt{-1}[/tex]
We have [tex]1-\sqrt{-16}[/tex].
Let's look at the [tex]\sqrt{-16}[/tex] part.
Since it has a negative inside the square root, it is imaginary. This is our imaginary unit [tex]i=\sqrt{-1}[/tex].
So [tex]\sqrt{-16}[/tex]
[tex]=\sqrt{16} i [/tex]
[tex]=4i[/tex]
So [tex]1-\sqrt{-16}=1-4i[/tex]
A 12-volume numbered set of books is placed randomly on a shelf. What is the probability that the books will be numbered in the correct order from left to right?
Answer:
Step-by-step explanation:
There is a 1/12 probability that volume 1 will be correctly put in position 1.
If we assume that volume 1 is right, then since there are then only 11 books left to choose from, there is then a 1/11 prob that volume 2 will be in position 2. And so on. By the same reasoning there is 1/10 prob that volume 3 is then right, 1/9 prob for volume 4, 1/8 prob for volume 5, and 1/7 prob for volume 6,
and 1/6 prob for volume 7,and 1/5 prob for volume 8,and 1/4 prob for volume 9,and 1/3 prob for volume 10,and 1/2 prob for volume 11,and 1/1 prob for volume 12.
So the probability is 1 /(12*11*10*9*8*7*6*5*4*3*2*1) = 1 / 479,001,600 ....
Simplify remove all the perfect squares from inside the square root 45
Answer:
3[tex]\sqrt5}[/tex]
The square root of 45 can be simplified by removing perfect square factors. In this case, the number 9 is a perfect square factor of 45, resulting in the simplification √45 to 3√5.
Explanation:To simplify the square root of 45 by removing perfect squares, we first need to identify the factors of 45 that are perfect squares. In this case, the number 9 is a factor of 45 and is a perfect square. Therefore, we can simplify √45 to √9*5 or 3√5. Simplifying square roots is a basic principle of Mathematics one should know as it is often applied in various middle school, high school, and even college math problems.
Learn more about Simplifying Square Roots here:https://brainly.com/question/1441039
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