The numbers that make the statement true are:
( -14, -∞ ) or [-15, -∞).
i.e -15, -16, -17, - 18, -19, ,,,,,,,,,-∞
Given,
Nine more than twice a number is less than negative nineteen.
We need to find all numbers that make this statement true.
What do the mathematical terms mean?More than - addition.
Twice - multiplication of 2.
Less than - <
How do we arrange integer numbers in ascending order?-∞.......-5 < -4 < -3 < -2 < -1 < 0 < 1 < 2 < < 3 ...........∞
Find the expression.
Let the number be M.
"Nine more than twice a number is less than negative nineteen".
We can write this statement as:
2M + 9 < -19
Find the number M.
2M + 9 < -19
2M < -19 - 9
2M < -28
M < -28/2
M < -14
Let us check the statement is true with M < -14.
2M + 9 < -19
2 x -15 + 9 = -19
-30 + 9 = -19
-21 < -19
This is true.
We see that all numbers below -14 will make the statement true.
So,
The numbers are -15, -16, -17, -18,..........-∞
Thus the numbers that make the statement true are ( -14, -∞ ) or [-15, -∞).
i.e -15, -16, -17, - 18, -19, ,,,,,,,,,-∞
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To solve the inequality, we need to translate the given statement into an algebraic expression and then solve for 'x' using subtraction and division.
Explanation:To solve the inequality, we will translate the given statement into an algebraic expression. Let's say the number is represented by 'x'. 'Twice a number' can be written as 2x. 'Nine more than twice a number' can be written as 2x + 9.
So, the inequality becomes 2x + 9 < -19.
To solve for 'x', we subtract 9 from both sides of the inequality, giving us 2x < -28. Then, we divide both sides by 2, resulting in x < -14.
Therefore, any number less than -14 will make the statement true.
Michelle Smith bought 30 shares of James Company stock at $34 per share. The company paid annual dividends of $0.42 per share. What is the total annual dividend? Show work
A) 9.78
B) 12.60
C) 1.69
D) 11.97
Answer:
The right option is B) 12.60
Step-by-step explanation:
We have given,
Number of shares = 30
Cost of each share = $34
Total cost of shares = 30 × 34 = $1020
Since the company paid annual dividends of $0.42 per share.
i.e Total annual dividend company paid = 0.42 × 30
Total annual dividend company paid = $ 12.60
Hence the right option is B) 12.60
What is the value of the expression (-8/9) divided by (-2/3) multiplied by (-4 1/2)
Final answer:
The value of the expression is -12, obtained by first converting mixed numbers to improper fractions, dividing and then multiplying the resulting fractions, and finally simplifying them.
Explanation:
The value of the expression (-8/9) divided by (-2/3) multiplied by (-4 1/2) is computed as follows:
Convert the mixed number (-4 1/2) to an improper fraction. (-4 1/2) = -4 - 1/2 = (-8/2) - (1/2) = (-9/2).Divide the fractions (-8/9) by (-2/3) by multiplying by the reciprocal of the divisor. (-8/9) ÷ (-2/3) = (-8/9) × (-3/2) = 8/3.Multiply the result by the improper fraction (-9/2). (8/3) × (-9/2) = -72/6.Simplify the resulting fraction, which gives -12 as the final answer.How do you write 9.7x10^4 (exponent 4) in standard form?
A.0.00097
B.0.000097
C. 97,000
D.970,000
Answer:
C. 97,000
Step-by-step explanation:
9.7x10^4 = 9.7 x 10000 = 97,000
Final answer:
To write 9.7x10^4 in standard form, you multiply 9.7 by 10,000, resulting in 97,000. Therefore, the correct answer is C. 97,000.
Explanation:
To write 9.7x10^4 in standard form, you multiply the coefficient (9.7) by 10 to the power of 4.
Since 10^4 means 10,000, you would perform the calculation 9.7 multiplied by 10,000. Doing this gives you 97,000. Therefore, the correct answer is:
C. 97,000
Here are steps to write numbers in scientific notation or standard form from the examples provided:
To convert the number 4,500 to scientific notation, you move the decimal three places to the left to get 4.5 x 10^3.
The number 2,220,000 would be 2.22 x 10^6 in scientific notation.
A smaller number like 0.0035 would be written as 3.5 x 10^-3.
For 0.7, the scientific notation is 7 x 10^-1.
The number 858.67 would be 8.5867 x 10^2 since the decimal is moved two places to the left.
[tex]16x - (8x + 6) =90[/tex]
Answer:
x=12
Step-by-step explanation:
16x - (8x + 6) =90
The first step is to distribute the - sign
16x -8x -6 =90
Now we combine the like terms
8x-6 = 90
Add 6 to each side
8x-6+6 = 90+6
8x = 96
Divide each side by 8
8x/8 = 96/8
x =12
It is suggested that an adult drink 64 fluid ounces of water every day. Josey, has already consumed 700 milliliters of water. How many more liters should he drink today?
Answer:
1.3 L more.
Step-by-step explanation:
Givens
8 fluid ounces = 1 cup.
240 mL = 1 cup
Solution
4 cups = 1 L
64 fluid ounces = x cups
8/64 = 1 / x Cross multiply
8x = 64 Divide by 8
8x/8 = 64/8
x = 8 cups
So we should be drinking 8 cups a day
1 L = 4 cups
x = 8 cups Cross multiply
4x = 8 cups Divide by 4
x = 8/4
x = 2 Liters.
1 L = 1000 mL
x L = 700 mL
700 * 1 = 1000 * x
Divide by 1000
x = 700 / 1000
x = 0.7 L
He needs to drink 2 L - 0.7L
1.3 more liters.
Answer: 1.3 L
Step-by-step explanation:
HELPPP PLZZ I REALLY NEED HELP
Answer: A.
The reason is because if you're adding a negative to a number, it's subtraction, which is in the expression.
Answer:
The answer is A.
Step-by-step explanation:
Adding a negative is the same as subtracting
The area of a trapezoid is 60 square inches. The sum of the bases is 20 inches. Find the height of the trapezoid.
Answer:
The area of a polygon is the number of square units inside that polygon. Area is 2-dimensional like a carpet or an area rug.
trapezoidA trapezoid is a 4-sided figure with one pair of parallel sides. For example, in the diagram to the right, the bases are parallel. To find the area of a trapezoid, take the sum of its bases, multiply the sum by the height of the trapezoid, and then divide the result by 2, The formula for the area of a trapezoid is:
area_trapezoid1.gif or area_trapezoid2.gif
Where b1.gif is base1.gif, b2.gif is base2.gif, h.gif is height and · means multiply.
Each base of a trapezoid must be perpendicular to the height. In the diagram above, both bases are sides of the trapezoid. However, since the lateral sides are not perpendicular to either of the bases, a dotted line is drawn to represent the height.
In Examples 1 and 3 below, the height is a side of the trapezoid since it is perpendicular to the base. In Example 2, the lateral sides are not perpendicular to the base, so a dotted line is drawn to represent the height.
Example 1: Find the area of a trapezoid with bases of 10 inches and 14 inches, and a height of 5 inches.
trapezoidSolution:
area_trapezoid2.gif
a_0.gif = one_half.gif · (10 in + 14 in) · 5 in
a_0.gif = one_half.gif · (24 in) · (5 in)
a_0.gif = one_half.gif · 120 in2
a_0.gif = 60 in2
Example 2: Find the area of a trapezoid with bases of 9 centimeters and 7 centimeters, and a height of 3 centimeters.
Solution:
trapezoidarea_trapezoid2.gif
a_0.gif = one_half.gif · (9 cm + 7 cm) · 3 cm
a_0.gif = one_half.gif · (16 cm) · (3 cm)
a_0.gif = one_half.gif · 48 cm2
a_0.gif = 24 cm2
Example 3: The area of a trapezoid is 52 square inches and the bases are 11 inches and 15 inches. Find the height.
trapezoidSolution:
area_trapezoid2.gif
52 in2 = one_half.gif· (11 in + 15 in) · h.gif
52 in2 = one_half.gif· (26 in) · h.gif
52 in2 = (13 in) · h.gif
52 in2 ÷ (13 in) = h.gif
h.gif = 4 in
trapezoidSummary: To find the area of a trapezoid, take the sum of its bases, multiply the sum by the height of the trapezoid, and then divide the result by 2, The formula for the area of a trapezoid is:
area_trapezoid1.gif or area_trapezoid2.gif
Where b1.gif is base1.gif, b2.gif is base2.gif, h.gif is height.
Step-by-step explanation:
There are 12 boys and 15 girls in your class.Four new students, 3 boys and 1 girl , join your class. Compare the ratio of boys and girls before and after the new students enrolled.
Answer:
4:5 ,15:16
Step-by-step explanation:
divide 12 and 15 by 3 to get 4 and 5
in a parking lot, 43% of the cars have GPS. express this percent as a decimal.
Answer: 0.43
Think of 43% as 43.0%
Move the decimal 2 spots to the left to go from 43.0 to 0.43
Alternatively, use a calculator to find that 43% = 43/100 = 0.43
"percent" means "per 100", so that's why we're dividing over 100.
A certain drug is made from only two ingredients: compound A and compound B. There are
milliliters of compound A used for every
milliliters of compound B. If a chemist wants to make
milliliters of the drug, how many milliliters of compound A are needed?
Answer:
425 milliliters of compound A are needed
Step-by-step explanation:
We were told that [tex]5[/tex] milliliters of compound A and [tex]6[/tex] milliliters of compound B is needed to make the drug.
This means that each drug contains 11 milliliters of both compounds.
[tex]\frac{935}{11}=85[/tex] milliliters is the volume of each drug.
Therefore the chemist needed [tex]5\times 85=425[/tex] millilirteres of compound A.
In order to find out how much of compound A is needed, we would set up a ratio using the amounts provided of compound A and B. Then, we cross multiply and solve for the unknown amount of compound A needed for the specific quantity of the drug.
Explanation:This problem is about ratios. We know that specific quantities of compound A and compound B are combined to make a certain amount of the drug. However, the quantities of compound A and B are not mentioned in the question. If they were provided, we would set up a ratio equal to the total amount of the drug and cross multiply to solve for the amount of compound A needed.
An example might look something like this: if the drug is made of 2 milliliters of compound A for every 3 milliliters of compound B and we wanted to make 5 milliliters of the drug. You would set it up like this:
2 (Compound A) / 3 (Compound B) = x (Amount of compound A needed) / 5 (Total Amount of drug needed)
Cross multiplying gives us: 2 * 5 = 3 * x
This simplifies to: 10 = 3x
Dividing each side by 3 then gives the amount needed of compound A: x = 3.33 milliliters.
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What degree of rotation is represented on this matrix
Answer:
Option B is correct
the degree of rotation is, [tex]-90^{\circ}[/tex]
Step-by-step explanation:
A rotation matrix is a matrix that is used to perform a rotation in Euclidean space.
To find the degree of rotation using a standard rotation matrix i.e,
[tex]R = \begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}[/tex]
Given the matrix: [tex]\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}[/tex]
Now, equate the given matrix with standard matrix we have;
[tex]\begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}[/tex] = [tex]\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}[/tex]
On comparing we get;
[tex]\cos \theta = 0[/tex] and [tex]-\sin \theta =1[/tex]
As,we know:
[tex]\cos \theta = \cos(-\theta)[/tex][tex]\sin(-\theta) = -\sin \theta[/tex][tex]\cos \theta = \cos(90^{\circ}) = \cos( -90^{\circ})[/tex]
we get;
[tex]\theta = -90^{\circ}[/tex]
and
[tex]\sin \theta =- \sin (90^{\circ}) = \sin ( -90^{\circ})[/tex]
we get;
[tex]\theta = -90^{\circ}[/tex]
Therefore, the degree of rotation is, [tex]-90^{\circ}[/tex]
The degree of rotation represented on a matrix is measured in angles, such as degrees or radians.
Explanation:The degree of rotation represented on a matrix is typically measured in terms of angles, such as degrees or radians. In order to determine the degree of rotation on a matrix, you need to identify the angle of rotation.
If the matrix is rotated clockwise, the angle is considered negative (-). If the matrix is rotated counterclockwise, the angle is considered positive (+).
For example, if a matrix is rotated 90 degrees counterclockwise, the degree of rotation would be +90°.
what is the value of y?
Answer: x=12, y=30
Step-by-step explanation: 180=40+5x+2y+20, 140=5x+2y+20, 120=5x+2y, 60+60=120, so 5*12=60, and 2*30=60
The value of y is determined by solving the algebraic equation presented, which after simplifying and isolating y, gives us a value of y equal to 3200.
Explanation:To find the value of y, we can use the given equations and perform the necessary algebraic manipulations. The question appears to contain a regression analysis problem where ŷ, read as 'y hat', represents the estimated value of y. This value is obtained from the regression line, which helps in making predictions about y based on corresponding values of x.
Here are the steps to solve the provided equations:
Begin by simplifying the equation with constants and coefficients next to y:
Consider the function ƒ(x) = 3x2 + 6x + 5.
Write the function in the form of ƒ(x) = a(x – h)2 + k, where a, h and k are constants.
Answer:
f(x) = 3(x + 1)² + 2
Step-by-step explanation:
Use the method of completing the square
3x² + 6x + 5
= 3(x² + 2x) + 5
add/ subtract (half the coefficient of the x-term)² to x² + 2x
= 3(x² + 2(1)x + 1 - 1) + 5
= 3(x + 1)² - 3 + 5
f(x) = 3(x + 1)² + 2 ← in vertex form
A friend rewrote the expression 5(x+2)as 5x+2. Wrote a few sentences to your friend explaining the error. Then, rewrite the expression 5(x+2)
Answer:
5x+2
Step-by-step explanation:
Ok so the expression 5(x+2) is not 5x+2 because you have to use the distributive property. So with that being said:
5(x+2)=5 times x and 5 times 2
so the realest answer is 5x+10 instead of 5x+2
EXPLANATION: The error in the rewritten expression done by your 'friend' is that he/she did not multiply the five in the parenthesis by ALL terms (meaning numbers and/or variables) as he/she should have done according to the distributive property. In the distributive property, you distribute equally to all numbers and parts in the equation or expression.
Take, For example, 7(x+4). Instead of just multiplying 7 times x in the parenthesis, you would also multiply seven times to four and add that to the end of the expression, making the rewritten expression 7x+28.
So, the correct rewritten expression for this problem is 5x+10.
EASY TO ANSWER HELPP PLEASE
Answer:
(17.8 , 1.6)
Find the total cost to the nearest cent. $58 bill; 20% tip
Answer:
$69.60
Step-by-step explanation:
20% of $58 is $11.60. So you add $11.60 + 58 which equals $69.60, so that is the total cost.
Answer:
$69.60
Step-by-step explanation:
The desired amount (total cost) is equivalent to the sum of the bill and 20% of the bill, or, equivalently, 120% of the bill.
1.20($58) = $69.60
The total cost is $69.60, including a 20% tip.
HELP you purchase a car using a $22,000 loan with a 6% simple interest rate for 5 years
(a) how much interest do you pay your loan? show your work
(b) what is the total amount that you will pay back? show your work
Answer: (a) $6,600
(b) $28,600
Step-by-step explanation:
Interest (I) = Principal (P) x rate (r) x time (t)
I = 22,000(0.06)(5)
= 6,600
Accrued (A) = Principal (P) + Interest (I)
A = 22,000 + 6,600
= 28,600
The graph of the equation y = x2 - 3 is shown. Which equation will shift the graph up 6 units?
Answer:
Here’s the graph
Step-by-step explanation:
Which system of equations has a solution of approximately (1.8,-0.9)
A. 6x-5y=15 and x+2y =0
B. 4x+5y=8 and 6x-5y=15
C.x-2y=4 and 4x+5y=8
D.6x-5y=15 and x-2y=4
A.
6x - 5y = 15
L = 6(1.8) - 5(-0.9) = 10.8 + 4.5 = 15.3
R = 15
L ≈ R
x + 2y = 0
L = 1.8 + 2(-0.9) = 1.8 - 1.8 = 0
L = R
B.
4x + 5y = 8
L = 4(1.8) + 5(-0.9) = 7.2 - 4.5 = 2.7
R = 8
L ≠ R
C.
x - 2y = 4
L = 1.8 - 2(-0.9) = 1.8 + 1.8 = 3.6
R = 4
L ≈ R
4x + 5y = 8
L = 4(1.8) + 5(-0.9) = 7.2 - 4.5 = 2.7
R = 8
L ≠ R
D.
6x - 5y = 15
L = 6(1.8) - 5(-0.9) = 10.8 + 4.5 = 15.3
R = 15
L ≈ R
x - 2y = 4
L = 1.8 - 2(-0.9) = 1.8 + 1.8 = 3.6
R = 4
L ≈ R
Yeah so your answer is gonna be
A.
After testing the approximate values (1.8, -0.9) in the systems of equations, only option A satisfies both equations with the solution approximately equal to (1.8, -0.9).
Explanation:To find which system of equations has a solution of approximately (1.8,-0.9), we need to substitute the x-value into each equation to see if the corresponding y-value is approximately -0.9. Whichever system satisfies both equations with these approximate values will be our answer.
For option A, substituting x ≈ 1.8 into the first equation 6x - 5y = 15 gives us 6(1.8) - 5y ≈ 15. This simplifies to 10.8 - 5y ≈ 15, leading to -5y ≈ 4.2, and y ≈ -0.84, which is close to -0.9. Checking the second equation, x + 2y = 0 with x ≈ 1.8, we get 1.8 + 2(-0.9) = 0, which is true. So, option A is a candidate.For option B, using the same method, we test the first equation 4x + 5y = 8 with the given x-value. Substituting x ≈ 1.8 gives 4(1.8) + 5y ≈ 8, which simplifies to 7.2 + 5y ≈ 8. Solving for y does not give us a value close to -0.9.Option C and D will also not yield the approximate y-value of -0.9 when substituting x ≈ 1.8 into their respective equations.Therefore, the correct answer is option A, as it satisfies both equations with the solution approximately equal to (1.8, -0.9).
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In a diagram shown,
PQRS is a rectangle
XY is parallel to PS
RY= 9cm
Area of PQRS = 84cm^2
Area of PXYS = 21cm^2
Work out the values of a and b
You must show all your working.
Answer:
a = 7cm
b = 3cm
Step-by-step explanation:
84 - 21 = 63cm²
XYRQ = 63cm²
63 / 9 = 7cm
a = 7cm
21 / 7 = 3cm
b = 3cm
What is 10 - (a + b)
If A=4.1 And B=5.7
Answer:
The answer is 0.2.
Step-by-step explanation:
10-(a+b)
A=4.1 B=5.7
10-(4.1+5.7)
10-4.1-5.7
10-9.8=
0.2
Gregg has a coin collection album with 275 pages. Each coin is displayed on 1/6 of a page. How many coins will fit in the page?
Answer:
1650
Step-by-step explanation:
If there are 275 pages and each page can fits 6 coins then you multiply 6 by 275.
Answer:
6 on each page; 1,650 in total coins for all the pages
Step-by-step explanation:
1. The first step is to multiply 1/6*6 to find out how many coins can fit on one page.
2.The second step is to multiply 6 *275. That equals 1,650
A pancake recipe calls 4 cups of loud and 3 cups milk. Does a recipe calling for 2 cups flour and 1.5 cups milk use the same ratio of flour to milk
Answer:
yes
Step-by-step explanation:
Because 4:3 simplifies to 2:1.5
Find the sale price of each item. Round to two decimal places when necessary. 8. Original price: $45.00; Markdown: 22% 9. Original price: $89.00; Markdown: 33% ___________________________________ ___________________ 10. Original price: $23.99; Markdown: 44% _______________________________ 11. Original price: $279.99, Markdown: 75% eh, might aswell do the last question too. sorry! :) 12. How can you determine the sale price if you are given the regular price and the percent of markdown?
Answer:
8) Sale price : 45* (100%-22%)= 45* 78/100= 35,1 $
9) 89* ( 100%-33%)= 89*67/100=59,63 $
10) 23,99* (100%-44%)= 13,43 $
11) 279,99*25/100= 69,99 $
12) Sell price= regular price* ( 100%- Markdown)
Step-by-step explanation:
How do I graph this?
Nancy also has a mirror that measures 20.32 centimeters long. What is the length of Nancy’s mirror in inches?
A. 1.45
B. 2.03
C. 8
D. 14
Answer:
C: 8.00
Step-by-step explanation:
1 in = 2.54 cm
l = 20.32 × 1/2.54
l = 8.00 in
The length of Nancy’s mirror is 8.00 in.
which expression is equivalent to the given expression after using the distributive property 6*13+6*7
Answer: 6*(13+7) = 60
Step-by-step explanation:
6*13+6*7
6*(13+7) = 6*10 =60
The required equivalent expression is [tex]6(13+7)[/tex].
Given:
The expression is:
[tex]6\times 13+6\times 7[/tex]
To find:
The equivalent expression of the given expression by using the distributive property.
Explanation:
Distributive property: If [tex]a,b,c[/tex] are three real numbers, then
[tex]a(b+c)=ab+ac[/tex]
We have,
[tex]6\times 13+6\times 7[/tex]
Using the distributive property, we get
[tex]6\times 13+6\times 7=6(13+7)[/tex]
Therefore, the required equivalent expression is [tex]6(13+7)[/tex].
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[tex]1 - \frac{1}{3} \div \frac{2}{3} [/tex]
Answer:
1/2
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] ÷[tex]\frac{2}{3}[/tex] equals 1/2 so 1 mius that will be 1/2
What is the probability of an individual being born on Feb.28?
Answer:
1/365 (or 1/366 in the case of a leap year.)
PLEASE ANSWER ASAP
Which table shows a proportional relationship?
b 1 4 5 7 11
c 3 12 15 21 33
p 1 3 5 7 9
q 0 2 4 6 8
r 3 6 10 12 15
s 2 4 6 8 10
x 1 2 3 4 5
y 9 10 11 12 13
Answer:
b
Step-by-step explanation: