Answers to both subparts are given below:
(A) Yes, x = 6 is the solution of the equation 8x+8 = 56.(B) We need to add 24 on the right side of the equation when x = 9.What do we mean by equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.So, (A) x = 6 is the solution of equation 8x+8 = 56:
Substitute x = 6 in equation 8x+8 = 56 as follows:
8x+8 = 568(6)+8 = 5648 + 8 = 5656 = 56Yes, x = 6 is the solution of the equation 8x+8 = 56.
(B) The change on the right side if x = 9:
Substitute x = 9 in equation 8x+8 = 56 as follows:
8x+8 = 568(9) + 8 = 5672 + 8 = 5680 = 56Now,
80 - 56 = 24So, we need to add 24 on the right side of the equation when x = 9.
The answers to both subparts are given below:
(A) Yes, x = 6 is the solution of the equation 8x+8 = 56.(B) We need to add 24 on the right side of the equation when x = 9.Know more about equations here:
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HELP PLEASEEEEEEEEE!!!!!!!! ILL MARK BRAINLIEST
Answer:
I'm not %100 sure this is correct but it seems like it wants a decimal
Step-by-step explanation:
D is 0.37
R is 0.34
That's the only thing that makes sense.
Please mark brainliest if correct!
find the length of arc JL. Round to the nearest hundredth.(degrees)
Arc Length
Given a circle of radius r, the length of the arc formed by a central angle θ is given by:
[tex]L=\theta\cdot r[/tex]We are given the central angle ∠JKL = 144° and the radius r = JK = 6 units.
The angle must be converted to radians by using the equivalence π = 180°
Thus:
[tex]\begin{gathered} \theta=144\cdot\frac{\pi}{180} \\ \theta=2.51327\text{ rad} \end{gathered}[/tex]Calculating the arc length:
[tex]\begin{gathered} L=2.51327\cdot6 \\ L=15.08 \end{gathered}[/tex]The length of the arc JL is 15.08 units
f(x)=2x^3+6x^2-5x-3
Find (f-g)(x)
The solution to the function expression, (f - g)(x) is: D. 2x³ + 6x² - 8x + 1.
How to Subtract Functions?To evaluate or subtract functions that has polynomials, all we simply need to do is to pair like terms together and combine them.
Given the following:
f(x) = 2x³ + 6x² – 5x – 3 and g(x) = 3x – 4
Therefore:
(f - g)(x) = f(x) - g(x)
Substitute
(2x³ + 6x² – 5x – 3) – (3x – 4)
2x³ + 6x² - 5x - 3 - 3x + 4
Combine like terms
2x³ + 6x² - 5x - 3x - 3 + 4
2x³ + 6x² - 8x + 1
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Complete Question:
f(x) = 2x³ + 6x² – 5x – 3
g(x) = 3x – 4
Find (f - g)(x).
O A. (f - g)(x) = 2x³ + 6x² – 2x – 7
O B. (f - g)(x) = 2x³ + 6x² – 2x + 1
O c. (f - g)(x) = 2x³ + 6x² – 8x – 7
O D. (f - g)(x) = 2x³ + 6x² – 8x + 1
use the distance formula to find the distance between the two points (-4.75,-8) and (3.25,5.5)? round to the nearest tenths?
Let the coordinates of points be,
[tex]\begin{gathered} (x_1,y_1)=\mleft(-4.75,-8\mright) \\ (x_2,y_2)=\mleft(3.25,5.5\mright) \end{gathered}[/tex]The distance between the two points using distance formula is,
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ =\sqrt[]{(3.25-(-4.75))^2_{}+(5.5-(-8))^2} \\ =\sqrt[]{8^2+13.5^2} \\ =15.7\text{ } \end{gathered}[/tex]Therefore, distance between the two points is 15.7.
can someone help me with this
The exact values of the sine of the addition and subtraction of two angles are 576 / 1105 and 264 / 1105, respectively.
How to find the exact value of the sine of the addition and the subtraction of two angles
Since angle A is in the fourth quadrant and B is in the second quadrant, then we find the following inequalities:
cos A > 0, sin A < 0
cos B < 0, sin B > 0
If we know that cos A = 13 / 85 and sin B = 12 / 13, then the missing trigonometric functions according to the fundamental trigonometric formula are:
sin A = - √(1 - cos² A)
sin A = - √[1 - (13 / 85)²]
sin A = - 84 / 85
cos B = - √(1 - sin² B)
cos B = - √[1 - (12 / 13)²]
cos B = - 5 / 13
And the exact value of the sine of the addition and subtraction of two angles is found by the following formula:
sin (A + B) = sin A · cos B + cos A · sin B
sin (A + B) = (- 84 / 85) · (- 5 / 13) + (13 / 85) · (12 / 13)
sin (A + B) = 576 / 1105
sin (A - B) = sin A · cos B - cos A · sin B
sin (A - B) = (- 84 / 85) · (- 5 / 13) - (13 / 85) · (12 / 13)
sin (A - B) = 264 / 1105
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Give a test to a group of students the grades and gender are summarized below if one student is chosen at random find the property ability that the student was female or got AB round the solution of 3 decimal places
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Data Table
Step 02:
probability (female) or probability (B)
probability = favorable outcomes / total outcomes
probability (female) = 32 / 55
probability (B) = 8 / 55
probability (female) or probability (B) = (32 / 55) + (8 / 55) - (32/55)*(8/55) = 0.6426
The answer is:
probability (female) or probability (B) = 0.643
An individual borrowed 84000 at an APR of 3% which will be paid off with monthly payments of $422 for 23 years
If an individual borrowed 84000 the Starting loan principal is $84,000; Interest rate is 3%; Number of payment per year is 12 payments per year; Loan term is 23 years; Payment amount is $422.
Principal loana. Identifying the starting loan principal, the interest rate, the number of payments per year, the loan term, and the payment amount.
Starting loan principal = $84,000
Interest rate =3%
Number of payment per year = 12 payments per year
Loan term = 23 years
Payment amount = $422
b. Total payment
There are 12 payments every year for 23 years, so
12 × 23 = 276
c. Total amount
Total amount 276× $422
Total amount = $116,472
d. Toward principal and interest
Toward Principal = $84,000
Toward Interest = $116,472 - $84,000
Toward Interest = $32,472
Therefore the starting loan principal is $84,000.
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The complete question is:
An individual borrowed 84000 at an APR of 3% which will be paid off with monthly payments of $422 for 23 years
a. Identify the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.
A. The amount borrowed is
The annual interest rate is
The number of payments per year is
The loan term is
The payment amount is
B. How many total payments does the loan require? What is the total amount paid over the full term of the loan?
C. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest?
The percentage paid toward the principal is
and the percentage paid for interest is:
What are the missing reasons in the proof?
50 points!
The missing reasons in the proof that shows that the triangles are congruent by SSS are:
3. Definition or parallelogram
4. Alternate interior angles theorem
5. Reflexive property of congruency
6. SSS Congruence Theorem
What is the SSS Congruence Theorem?The SSS congruence theorem is applicable when two triangles have three pair of corresponding side lengths that are congruent to each other. The SSS congruence theorem states that they are congruent to each other. This theorem can be used in proof where it is established that the three sides of two triangles are equal to each other.
What is the Reflexive Property of Congruency?A side is congruent to itself according to the reflexive property of congruency. This means that if two triangles share a common side, the two angles therefore have a pair of corresponding congruent sides in a proof.
Therefore, the missing reasons for the proof are explained below:
Statements Reasons
1. AD║BC 1. Definition or parallelogram
2. ∠ADB ≅ ∠CBD 2. Alternate interior angles theorem
3. AB║CD 3. Definition or parallelogram
4. ∠ABD ≅ ∠CDB 4. Alternate interior angles theorem
5. DB ≅ DB 5. Reflexive property of congruency
6. ΔABD ≅ ΔCDB 6. SSS Congruence Theorem
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Question is in the picture. No need for explanation. Just the answer is needed.
We have
[tex]\begin{gathered} y=7x+10 \\ y=-4x-23 \end{gathered}[/tex]we make the next equality
[tex]7x+10=-4x-23[/tex]then we sum like terms
[tex]7x+4x=-23-10[/tex][tex]\begin{gathered} 11x=-33 \\ x=\frac{-33}{11}=-3 \end{gathered}[/tex]Then we substitute the value of x in the first equation
[tex]\begin{gathered} y=7(-3)+10 \\ y=-21+10 \\ y=-11 \end{gathered}[/tex]ANSWER
x=-3
y=-11
your answer is
x=-3 or y=-11
CorrectQuestion of Step 1 of 10.3270.3250.2070.2070.2770.2890.3160.2900.2750.2820.2780.2790.3230.3160.2090.2830.2960.2810.3060.296Copy DataAnswerm Tables НЕ КеурKeyboard ShorSeparate multiple answers with commas, if necessary.Selecting a button will replace the entered answer value(s) with the button value. If the button is not selected, the entered answer is useMean: 0.2966Median:Mode: 0.297
Median:
To find the median, we first need to sort the values from smallest to highest.
The median separates the bottom 50% from the top 50%.
In a sorted set of n elements, which n is odd, the median is the element at the position: ((n+1)/2).
If n is even, the median is given by the mean of the elements at those following positions: (n/2, (n/2)+1).
Example:
Sorted: {1,2,3}
n = 3, element at the position (3+1)/2 = 2.
So the median is 2.
Sorted: {1,2,3,4}:
n = 4, so the mean between the elements at these following positions:
n/2 = 4/2 = 2, the element at the position 2 is 2.
(n/2)+1 = (4/2)+1 = 2 + 1 = 3, the element at the position 3 is 3.
The median is 2+3/2 = 5/2 = 2.5
In this question:
We have 20 elements.
The median will be the mean between the 10th and the 11th elements of the sorted set.
Sorted set:
In an ascending way.
{0.275, 0.277, 0.278, 0.279, 0.281, 0.282, 0.283, 0.289, 0.29, 0.296, 0.296, ...}
The 10th element is 0.296
The 11th element is also 0.296
(0.296 + 0.296)/2 = 0.296
The median is 0.296
James can type 40 words in 20 seconds. How many words can James's type in 30 seconds?
A, 60
B, 20
C, 30
D, 25
Proportionately, in 30 seconds, James can type A, 60 words since he can type 40 words in 20 seconds.
What is a proportion?Proportions set two ratios as equal to each other.
Proportions are the portions of a variable in another variable.
Proportions, like ratios, are stated in fractions, decimals, or percentages.
The number of words James can type in 20 seconds = 40 words
In 30 seconds, based on the above unit rate, James can type = 60 words (40/20 x 30)
Thus, based on the ratio of James' typing speed, in 30 seconds he can type 60 words.
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state the possible rational zeros for each function. The find all zeros. Use the example in the picture to solve: f(x)=2x^3-23x^2-28x-8
We have to find the zeros of the polynomial f(x) = 2x^3-23x^2-28x-8.
The independent coefficient is -8, that has factors ±1,±2,±4 and ±8.
The leading coefficient is 2, and has factors ±1 and ±2.
The possible rational zeros (p/q) are: ±1/2, ±2/2=±1, ±4/2=±2 and ±8/2=±4.
The possible rational zeros are: ±1/2, ±1, ±2 and ±4.
Julie can run 3 laps in 9 minutes. At this rate, how many laps can she run in 24 minutes?
In 24 minutes Julie can run 8 laps.
What is proportion ?
A proportion is an equation based on the equality of two ratios.
Here it is given that :
Julie can run 3 laps in 9 minutes that is :
in 9 minutes = 3 laps
Now, to find the laps covered by Julie in 24 minutes we first find the laps rate per minutes by dividing 9 both the side :
in 9/9 minutes = 3/9 laps
in 1 minutes = 1/3 laps
Multiply 24 both the side :
in 24 minutes = 24/3 laps
in 24 minutes = 8 laps
Therefore, in 24 minutes Julie can run 8 laps.
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Bob's yard is in the shape of a semicircle with a diameter of 14 feet. Bobwants to buy grass to cover the area of his entire yard. How many squarefeet of grass does Bob need? Round to the nearest tenth.
EXPLANATION
The area of a semicircle is given by the following relationship:
[tex]\text{Area}_{\text{semicircle}}=\frac{1}{2}\cdot\pi\cdot r^2[/tex]The radius of the semicircle is diameter/2=14/2 = 7 feet
Replacing terms:
[tex]\text{Area}=\frac{1}{2}\cdot\pi\cdot(7)^2[/tex]Computing the power:
[tex]\text{Area}=\frac{1}{2}\pi\cdot49[/tex]Simplifying numbers:
[tex]\text{Area}=24.5\cdot\pi=24.5\cdot3.14=76.93ft^2\approx77ft^2[/tex]In conclusion, the answer is the option D.
A construction crew is lengthening a road. The road started with a length of 54 miles, and the crew is adding 2 miles to the road each day.
Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D. Then us
this equation to find the total length of the road after the crew has worked 32 days.
Equation:
Total length of the road after 32 days: ___ miles
Answer: 456 Miles
Step-by-step explanation:
Solve for points please
During drought years, Lake Sakakawea water level lowers one inch per year. What integer represents the water level change after 8 years?
The water level change after 8 years is 8 inches if it is lowers one inch per year.
Integer representation of 8 = 1000 in binary .
A fixed-point number with the radix point placed after the least-significant bit is an integer. They differ from real numbers or floating-point numbers, where the radix point is always at the same place. You should be aware that computers handle integers and floating-point numbers differently. They are shown differently and processed differently (e.g., floating-point numbers are processed in a so-called floating-point processor). We'll talk about floating-point numbers later.
An integer is represented by a fixed number of bits in computers. Integers can be stored in 8-bit, 16-bit, 32-bit, or 64-bit formats. There are two representation techniques for integers in addition to bit-lengths:
Positive and zero integers can both be represented as unsigned integers.
Positive, negative, and zero are all represented by signed integers.
Hence , If the water level drops one inch per year for eight years, the decrease in water level will be 8 inches.
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What are the missing reasons for the proof?
URGENT
△ABD is congruent to △CDB (△ABD ≅ △CDB) under the SAS congruency condition.
What is the congruency of triangles?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, rotate, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. The relationship between equality and congruence is established by three key theorems. If and only if two angles have equal measures, they are said to be congruent. If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.So, △ABD ≅ △CDB:
AD || BD (Definition of parallelogram: Given)∠ADB ≅ ∠CDB (Alernate interior angles throrem: Given)AB || CD (Definition of parallelogram)∠ABD ≅ ∠CDB (Alternate interior angles throrem)DB ≅ DB (Common line)△ABD ≅ △CDB (SAS condition)Therefore, △ABD is congruent to △CDB (△ABD ≅ △CDB) under the SAS congruency condition.
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There are different types of proofs: two-column, paragraph and flow chart. Which of these type of proofs do you prefer? Why?
I prefer the two-column proof since it is the most common format in high school textbooks. One can easily find each of the steps of the proof, and one can correct any step so you can continue the next one step by step in a chronological list of them.
It is easy to audit this type of proof, and I am very comfortable using it.
Find the area of the polygon. 2 m 19 m 2 m 17 m The area of the polygon is (Type a whole number.)
If the polygon is redrawn and completed as shown below
The area of the polygon = area of the rectangle ABCD - ( area of the rectangle AEFG + area of the rectangle HBJI)
Area of rectangle = L x B
For ABCD
L = 17 + 2= 19 m
B = 19 + 2 + 2 = 23 m
Area = 19 x 23 = 437 square metre
For AEFG
L= 2 m , B = 2 m
Area = 2 x 2 = 4 square m
For HBJI
L= 2 m , B = 2m
Area = 2 x 2 = 4 square m
[tex]\begin{gathered} Area\text{ of the polygon = 437 - ( 4+ 4)} \\ =\text{ 437 - 8} \\ =429m^2 \end{gathered}[/tex]given the following system identify the type of system x+y=4x-y=6
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given system of equation
[tex]\begin{gathered} x+y=4----equation\text{ 1} \\ x-y=6-----equation\text{ 2} \end{gathered}[/tex]STEP 2: Solve the given equation
Subtract equation 2 from equation 1
[tex]\begin{gathered} (x-x)+(y-(-y))=4-6 \\ y+y=-2 \\ 2y=-2 \\ Divide\text{ both sides by 2} \\ \frac{2y}{2}=-\frac{2}{2} \\ y=-1 \end{gathered}[/tex]STEP 3: Solve for x
[tex]\begin{gathered} Substitute\text{ -1 for y in equation 1} \\ x+(-1)=4 \\ x-1=4 \\ x=4+1 \\ x=5 \end{gathered}[/tex]The values of x and y are 5 and -1 respectively meaning that the system has one solution, hence the type of system of equation given is a CONSISTENT system of linear equation.
Write a formula for the function obtained when the graph is shifted as described.
The given function is
f(x) = x^3
Recall, if a function, f(x) is shifted c units upwards, the new function would be f(x) + c. This means that if we translate the given function 3 units upwards, the new function would be x^3 + 3
Also, if a function, f(x) is shifted d units to the left, the new function would be
f(x + d). This means that if we translate x^3 + 3 7 units to the left, the new function would be (x + 7)^3 + 3
The function is
f(x) = (x + 7)^3 + 3
Required Question #7 7) 100^2 x 100^5 = 100^y y=?
Given the general rule for exponents:
[tex]a^n\cdot a^m=a^{n+m}[/tex]then, in this case we have the following:
[tex]\begin{gathered} 100^2x100^5=100^y \\ \Rightarrow(100^2)\cdot(100^5)=100^{2+5}=100^7 \\ \Rightarrow y=7 \end{gathered}[/tex]therefore, y=7
The cost of providing water bottles at a high school football game is $35 for the
rental of the coolers and $0.50 per bottle of water.
A. What does $35 represent in the function for this situation?
B. What does $0.50 represent in the function for this situation?
C. Write a function for the amount 'C, in dollars, of providing b water bottles.
D. What is an appropriate domain for the function?
E. Graph the function over the appropriate domain.
Answer:
Step-by-step explanation:
A.
35 dollars represents the cost of renting the coolers (I think it's a constant since it does not say it is the cost per cooler).
B.
0.50 cent represents the cost per water bottle in the function (the coefficient in front of b, the amount of water bottles being purchased).
C.
C is the total cost.
C = 0.50b + 35
D.
I'm not sure what this is asking. Y = 0.50x + 35's domain is all real numbers but I'm not sure what it means by "appropriate domain for the function" unless the problem is using the average statistics from actual high school football games based on how many water bottles are purchased or something else.
E.
The graph would be all real numbers unless I'm wrong. Which is very possible on d and e but I think I provided the correct info on the others.
5. Alex's friend Pablo comes
up with
an exact equation to find out how many bags he needs. Use his equation to find out how many bags will actually be needed if B=x(2x+7)+3(2x+7)+(x+4)(2x+7), where the quantity (2x + 7) equals 4. Show how you arrive at your answer.
8.5 bags will actually be needed if B=x(2x+7)+3(2x+7)+(x+4)(2x+7), where the quantity (2x + 7) equals 4
What is an Expression?Expression: An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.) Expressions can be thought of as similar to phrases. In language, a phrase on its own may include an action, but it doesn't make a complete sentence.
Number of bags needed B=x(2x+7)+3(2x+7)+(x+4)
where the quantity (2x+7)=4
2x+7=4
2x=4-7
2x=-3
x=-3/2
now we are given the no. of bags needed
B=x(2x+7)+3(2x+7)+(x+4)
substitute the value of x which is found above x=-3/2
B=(-3/2)(2(-3/2)+7)+3(2(-3/2)+7)+((-3/2)+4)
B=8.5
hence 8.5 bags are needed
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An order is received for 180 mL of a 2.5% solution to be prepared from diluting a 15% solution with water. How much of the stock 15% solution is needed?
a.
20 mL
b.
25 mL
c.
30 mL
d.
35 mL
We need 30 ml of the 15 percent solution to complete the order.
Here, we are given that we need to prepare 180 mL of a 2.5% solution by diluting a 15% solution with water.
the 180 ml 2.5% solution will contain-
2.5% pf 180 ml acid
= 2.5/100 × 180
= 25/1000 × 180
= 1/40 × 180
= 18/4
= 9/2
= 4.5 ml
Water in the 180 ml solution will be = 180 - 4.5 = 175.5
Now, we have say x ml of 15% solution
It must contain 4.5 ml of acid
Thus-
15% of x = 4.5
15/100 × x = 4.5
x = 4.5 × 100/15
x = 450/15
x = 30
Thus, we need 30 ml of the 15 percent solution, hence, option C.
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What is the slope of line AB, where the points are A (-1,5) and B (3,-1)
Explanation
Step 1
when you have 2 points of a line P1 and P2, you can easily find the slope using:
[tex]\begin{gathered} \text{slope}=m=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]Let
P1=A=(-1,5)
P2=B=(3,-1)
Step 2
replace
[tex]\begin{gathered} \text{slope}=m=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=m=\frac{-1-5}{3-(-1)}=\frac{-6}{3+1}=\frac{-6}{4}=-\frac{3}{2} \end{gathered}[/tex]I hope this helps you
The value of a stock decreases by an average of 17 dollars each week. Which of the following represents the total average decrease in the stock after 6 weeks?
6|−17| = 102 dollars
|−17| − |6| = 11 dollars
|−17| − 6 = 11 dollars
−6|17| = 102 dollars
Answer: It is C.
i did the exam.
Step-by-step explanation: It is really about how it is set up so C is the right one.
An object is thrown from one meter above the ground. Its height (in meters) above the ground at time t (in seconds) is given by the equation h(t) =120+-167 + 1.
How long will it take for the object to reach a height of 191 meters
The perimeter of a parallelogram is 120cm. If one of the sides is greater than the other by 10cm,
find the length of all the sides of the parallelogram
Answer:
Two of the sides are 25cm and the other two sides are 35cm.
Step-by-step explanation:
The perimeter is the distance all the way around the shape.
The shape is a parallelogram, so two sides across from each other are the same length. And the other two sides are also the same as each other. See image.
The shorter sides can be labelled x and the longer sides can be labelled x + 10. This is because the question said the long side is 10cm more than the short side.
see image.
Add up all the sides to make them equal to the perimeter. Set it equal to 120. See image.
Solve for x.
x + x+10 + x + x+10 = 120
4x + 20 = 120
Subtract 20.
4x = 100
Divide by 4.
x = 25
The short sides are 25cm and the long sides are 35cm.
Check:
25+35+25+35=
120 Check!
