To factor this expression we need to find two numbers which sum is 4 and the product is -21.
Now, 21 has only 2 factors (besides 1 and 21), 7 and 3, se we need to write them in a way such that they sum 4, so
[tex]x^2+4x-21=(x+7)(x-3)[/tex]we see that 7-3=4 and 7(-3)=-21, so the factorization is correct.
convert the equation into vertex form, then solve the equation: r^2– 4r – 91 = 7
We want to convert the equation to vertex form
[tex]\begin{gathered} r^2-4r-91=7 \\ r^2-4r\text{ = 98} \\ r^2-4r\text{ + }(-2)^2=98+(-2)^2 \\ (r-2)^2=102\text{ },(r-2)^2-102=0,\text{ This is the equation in vertex form} \\ r-2\text{ =}\pm\sqrt[]{102} \\ r\text{ = 2}\pm\sqrt[]{102} \\ \end{gathered}[/tex][tex]\begin{gathered} \text{Equation in vertex form, (r-2)}^2-102\text{ = 0} \\ \text{Solution, r = 2}\pm\sqrt[]{102} \end{gathered}[/tex]45*3/12+4.5697-3.12903
Answer: 12.69067
Step-by-step explanation:
If f(x) is an exponential function where f(4) = 7 and f(5.5) = 53, then find thevalue of f(5), to the nearest hundredth.
Given:
f(x) is an exponential function.
f(4) = 7.
f(5.5) = 53.
Since f(x) is an exponential function, f(x) can be expressed as,
[tex]f(x)=ab^x[/tex]Here, a and b are constants.
Hence, we can write
[tex]\begin{gathered} f(4)=ab^4----(1) \\ f(5.5)=ab^{5.5}\text{ ------(2)} \end{gathered}[/tex]Divide equation (2) by (1).
[tex]\frac{f(5.5)}{f(4)}=\frac{ab^{5.5}}{ab^4}[/tex]Substitute f(4) = 7 and f(5.5) = 53 in the above equation.
[tex]\begin{gathered} \frac{53}{7}=\frac{b^{5.5}^{}}{b^4} \\ \frac{53}{7}=b^{5.5-4} \\ \frac{53}{7}=b^{1.5} \\ \frac{53}{7}=b^{\frac{3}{2}} \\ b=(\frac{53}{7})^{\frac{2}{3}} \\ b=3.855 \end{gathered}[/tex]Now, the value of a can be obtained as,
[tex]\begin{gathered} f(4)=ab^4 \\ 7=a(\frac{53}{7})^{\frac{2}{3}} \\ a=\frac{7}{(\frac{53}{7})^{\frac{2}{3}}} \\ =1.815 \end{gathered}[/tex]What is slope-intercept form of m=-7,b=4
I need help to find the indicated measure of each angle. I will send the photo.
Explanation
Step 1
we have a rigth triangle, then
Let
[tex]\begin{gathered} \text{angle}=\emptyset \\ \text{adjacent side=14} \\ \text{opposite side= 12} \end{gathered}[/tex]hence, we need a function that relates, angle, adjacent side and opposite side
[tex]\tan \emptyset=\frac{opposite\text{ side}}{\text{adjacent side}}[/tex]now, replace.
[tex]\begin{gathered} \tan \emptyset=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan \emptyset=\frac{12}{\text{1}4} \\ \tan \emptyset=\frac{6}{7} \\ In\text{verse tan in both sides} \\ \tan ^{-1}(\tan \emptyset)=\tan ^{-1}(\frac{6}{7}) \\ \emptyset=40.60\text{ \degree} \end{gathered}[/tex]I hope this helps you
2: A game is played by tossing a single coin onto a square table. The square is 25 inches o each side, and the coin has a radius of 10 inches (it's old fashioned). If the coin lands entirely on the table (nothing hanging off the edge), the player wins a prize. What fraction of the table can the center point of the coin land on so that the player wins a prize?
Find the area of the square table:
[tex]\text{Area of the square = }L^2=25^2=625in^2[/tex]Find the area of the coin (area of a circle):
[tex]\text{Area of coin= }\pi r^2=\pi10^2=314.16in^2[/tex]To find the fraction of the table the center point of the coin lands, we have:
[tex]\frac{Area\text{ of coin}}{\text{Area of table}}[/tex][tex]=\frac{314.16}{625}\text{ = }0.50[/tex]Since we are to leave the answer in fraction, we have:
[tex]\frac{5}{10}=\text{ }\frac{1}{2}[/tex]9. Assessment Practice Diego wants to
find 8+ 9. 2.NSO.2.1
Which doubles fact can help him?
A 5+5=10
B6+6=12
C7+7= 14
D 8+8=16
They can use counters or their fingers, but they can also use doubles facts. If they know 5 + 5 = 10, they know that the sum of 5 + 6 will be one more.
What is meant by addition?One of the four fundamental mathematical operations, along with addition, subtraction, multiplication, and division, is addition.
The sum of 5 + 6.
They can utilize counters or their fingers, but they can even utilize doubles facts. If they understand 5 + 5 = 10, they know that the sum of 5 + 6 will be one more.
Therefore, 5 + 6 = 11.
Estimating other doubles-plus-one facts together, such as 3 + 4, 7 + 8, and 9 + 8.
Repeat the doubles facts so they can use them to solve equations.
They can also use doubles-minus-one facts to enable them solve equations.
Write down 9 + 10 and have your children find the sum.
If they know that 10 + 10 = 20, they know that the sum of 9 + 10 will be one less. Therefore, 9 + 10 = 19.
solving different number sentences together.
Therefore, they can utilize counters or their fingers, but they can even utilize doubles facts. If they understand 5 + 5 = 10, they know that the sum of 5 + 6 will be one more.
Therefore, the correct answer is option A) 5 + 5 = 10.
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12. How many centimeters are there in 740.2millimeters?A 7402 cm© 7.402 cmB 74.02 cmD 0.7402 cm
In this kind of question, we always need to know what is the equivalence between two measures:
We already know that in 1 centimeter there are 10 millimeters. With this equivalence, we can write:
740.2 millimeters * ( 1 centimeter / 10 millimeters )
When we have a unit in the numerator and also in the denominator, like millimeters, in this case, both units are converted in 1, and they do not need to be in the final answer (millimeters/millimeters = 1). Therefore:
740.2 * ( 1 centimeter / 10 ) =
( 740.2 / 10 ) centimeter =
When we divide a number by 10, 100, 1000, we write the decimal point to the left as many zeros have the 10, 100, 1000. In this case, we only have one zero.
Thus, we write the decimal part one digit to the left:
( 740.2 / 10 ) centimeter =
74.02 centimeter (this is the answer).
Therefore, there are 74.02 centimeters in 740.2 millimeters.
72 km/h converted into m/s
Answer: 20 meters per second
Step-by-step explanation:
please do complete and be quick
1. cube root - a number whose cube equals the original number.
2.irrational number -a number that cannot be written in the form a/b, where a and b are integers and b≠ 0
3.Product of powers property- To multiply two powers with the same base, keep the common base and add the exponents.
4.perfect cube- the cube of an integer.
5.perfect square- a number that is the square of an integer.
6.Power of powers property-To multiply two powers with the same exponent and different bases, multiply the bases and keep the exponent.
7.Powers of products property- when you have an exponent raised to a power ,keep the base and multiply the exponents.
8. scientific notation -a way to express a number as the product of two factors, one greater than or equal to 1 and less than 10 and the other a power of 10
9. square root - a number when multiplied by itself equals the original number
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Answer to the question
Step-by-step explanation:
Option Four is the correct answer.
Have a great day!
A bank features a savings account that has an annual percentage rate of 4.4 % with interest compounded quarterly. Natalie deposits $4,000 into the account.What is the annual percentage yield (APY) for the savings account? APY= %. Round to the nearest hundredth of a percent.
ANSWER :
4.47%
EXPLANATION :
The APY Formula is :
[tex]APY=\left(1+\frac{r}{n}\right)^n-1[/tex]where r = annual percentage rate
n = number of compounding in a year
From the problem, r = 4.4% or 0.044 and n = 4 (Quarterly)
That will be :
[tex]\begin{gathered} APY=\left(1+\frac{0.044}{4}\right)^4-1 \\ APY=0.0447 \end{gathered}[/tex]The APY is 4.47%
pls help i give brainliest
Answer: Please check attached image
in the diagram (triangle) ABC = (triangle) PQR. Reflect (triangle) ABC across the line y = x. Describe how to map image to (triangle) PQR.
First we have to find the line y=x so we can do the reflection:
now in the graph we can se that the lines RO and BC are parallel to the line y = x
and there you can see that they are the same by moving the triangle 5 units to the right.
Other way you can check they are iqual, is by calculate the area of the triangles.
Kali just started a new sales floor job to save for college. She earns 15.75 plus a flat fee of 50 . She wants to earn between 200 and 400 . The following inequality represents her earning potential
200 ≤ 15.75x + 50 ≤ 400 Solve the inequality PLEASE HELP ASAP
!!
Solving the inequality the range of x becomes 9.523 ≤ x ≤ 22.222.
The given inequality which needs to be solved is 200 ≤ 15.75x + 50 ≤ 400.
If 50 is subtracted from each part or side of the inequality we get,
200 - 50 ≤ 15.75x + 50 - 50 ≤ 400 -50 which will be equal to,
150 ≤ 15.75x ≤ 350, now to solve this inequality divide the given inequality with the coefficient of x which is 15.75 to get the range of x.
Hence the inequality becomes 150÷15.75 ≤ 15.75x÷15.75 ≤ 350÷15.75. solving this equation the value of x becomes 9.523 ≤ x ≤ 22.222.
So the range of inequality that represents Kalis earning potential ranges from (9.523,22.222) for the given question.
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f(m) = (x + 1)(x - 5)| has two solutions. What is the set of values for f(m)? How would you describe the locations of values in this solution set?
Answer:
x = {x: -1, 5}
Step-by-step explanation:
[tex]{ \rm{f(m) = (x + 1)(x - 5)}}[/tex]
- To find the values of function f(m), we consider its zero or its root by letting f(m) = 0
[tex]{ \rm{f(m) = 0 = (x + 1)(x - 5)}} \\ { \rm{(x + 1)(x - 5) = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
- Either (x + 1) or (x - 5) is equated to zero
For (x + 1);[tex]{ \rm{x + 1 = 0}} \\ { \rm{x = - 1}}[/tex]
For (x - 5);[tex]{ \rm{x - 5 = 0}} \\ { \rm{x = 5}}[/tex]
Therefore, x is -1 and 5
[tex]{ \bold{ \boxed{ \red{ \delta}}}}{ \underline{ \red{ \mathfrak{ \: \: creed}}}}[/tex]
3. Which of the following is true about the graph of y = -x] – 2? (A) The graph is increasing when x > -2. (B) The graph is decreasing when x > -2. (C) The graph is increasing when x < 0 (D) The graph is increasing when x > 0.
First let's draw the graph
Now, we can see that the graph is increasing when x<0! thus the answer is (C)
Question 10(Multiple Choice Worth 1 points)
(08.01 LC)
Susan wants to conduct a survey to find how much time the students of her school spent eating in a local cafeteria. Which of the following is an appropriate statistical question for this survey?
Who eats at the cafeteria on weekends?
How many students eat in the cafeteria on Mondays?
How many students eat in the cafeteria once a week?
How many hours during the week do you eat in the cafeteria?
The appropriate statistical question for this survey is D. How many hours during the week do you eat in the cafeteria?
What is a survey?It should be noted that a survey is used by researchers in order to get information about a particular thing.
In this case, Susan wants to conduct a survey to find how much time the students of her school spent eating in a local cafeteria.
It should be noted that a statistical question should be able to address the question asked. Therefore, the correct option is D.
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is negative 18/3 rational or irrational
Answer:
rational
Step-by-step explanation:
it is because
it can be written in p/q form as answer is -6
Classify the system as independent, dependent, or inconsistent.y=2x-1y=-2x+5
To classify the equations, we will need to define some terms:
Inconsistent equations: Inconsistent equations is defined as two or more equations that are impossible to solve based on using one set of values for the variables.
inconsistent equations of linear equations are equations that have no solutions in common.
An example of a set of inconsistent equations is x+2=4 and x+2=6.
Independent equation: The equations 3x + 2y = 6 and 3x + 2y = 12 are independent because any constant times one of them fails to produce the other one.
Dependent system: Equations in a dependent system can be derived from one another; they describe the same line
We can now proceed to classify the equations.
[tex]\begin{gathered} y=2x-1 \\ \text{and} \\ y=-2x+5 \end{gathered}[/tex]Equating the two equations
[tex]2x-1=-2x+5[/tex]simplifying further
[tex]\begin{gathered} 2x+2x=1+5 \\ 4x=6 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{6}{4}=\frac{3}{2} \\ x=\frac{3}{2} \end{gathered}[/tex]Since it has a solution (x=3/2), and also if we multiply each equation by a constant, we will have an uncommon equation.
Thus, we can classify the system as Independent
answers please
im failing
Answer:
y = -5, x = 5
Step-by-step explanation:
le brain
what is 338.8882 rounded to the nearest thousandth
Answer:
338.8882 rounded to the nearest thousandth is 338.888
hope it helps, mark as brainliest please :D
Justin earns a base salary of $1500 per month at
the jewelry shop. He also earns a 3% commission
on all sales. If Just sold $82,975 worth of jewelry
last month, how much would he make for the
month including his base salary and commission?
8)
He make $84475 for the month including his base salary and commission.
Define commission.The percentage or fixed payment attached to a specific volume of sales is known as the commission rate. For illustration, a fee can be $30 for each sale or 6% of sales. The payment that is either a fixed amount or a percentage of a sale is the commission rate. When they make a sale, people in commission-based professions like insurance brokers, real estate agents, and automobile salespeople get compensated. A business pays its employees according to the revenue they bring in through a commission structure. An employee receives a commission when they conduct business or provide a service, according to the definition of commission.
Given,
Salary = $1500
Commission = 3%
Sales = $82975
= 1500 + 82975 + [tex]\frac{3}{100}[/tex]
= 84475.03
84475(approximately)
He make $84475 for the month including his base salary and commission.
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On 25 March 1965, Martin Luther King led thousands of nonviolent demonstrators on a 5-day, 54-mile march from Selma, Alabama to the steps of the capitol in Montgomery, Alabama.
A court order restricted the number of marchers to 300 when passing over a stretch of two-lane highway. However, on the final day of the march, when the road reached four lanes the number of demonstrators swelled to 25,000.
What was the percentage of increase?
The percentage increase is 88%.
What is percent increase?The difference between the final value and the starting value, stated as a percentage, is known as a percentage increase. The initial value and the enhanced (new) value are required in order to calculate the percentage.
Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100
Given:
Initially, number of marchers = 300
Finally, number of marchers = 25000
Change in amount = 25000- 300 = 22000
Now, the percent increase
=22000 / 25000 x 100
= 22/25 x 100
=22 x 4
= 88
Hence, the percentage increase is 88%.
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Robert has a gross monthly income of $3690. According to Housing Recommendation #1, how much can he devote to monthly housing expenses?
In AKLM, 1 = 48 inches, _K=55° and L=46°. Find the length of k, to the nearest
inch.
We have a KLM triangle which as l = 48 in, the angle opposed to K = 55° and the angle opposed to L = 46°.
For this triangle, we have the following relation:
k^2 = l^2+m^2-2*l*m*cos 55°
Without m, we can't find k
Write the missing power of 10 in each equation a. 0.06 x ____=6 b. ___X 0.3 = 300
a) the expression can be writen as:
[tex]0.06\times10^2=6[/tex]because we move two units to the right the period.
b) the expression can be written as:
[tex]0.3\times10^3=300[/tex]because we move the period 3 units to the right
What are the intersection points of the parabola given by the equation y=x^2 - 9 and the line given by the equation y = x - 3?
Since we want the points where both the parabola and the line have in common (i.e., they intersect), then we have the following:
[tex]\begin{gathered} y=x^2-9 \\ y=x-3 \\ \Rightarrow x^2-9=x-3 \end{gathered}[/tex]Now we solve for x to find the first two values of the points that we are looking for:
[tex]\begin{gathered} x^2-9=x-3 \\ \Rightarrow x^2-9-x+3=0 \\ \Rightarrow x^2-x-6=0 \\ \Rightarrow(x-3)\cdot(x+2)=0 \\ x_1=3 \\ x_2=-2_{} \end{gathered}[/tex]Now we use these values of x to find other pair of values for y:
[tex]\begin{gathered} y=x-3 \\ x_1=3 \\ \Rightarrow y_1=3-3=0 \\ \Rightarrow(x_1,y_1)=(3,0) \\ x_2=-2 \\ \Rightarrow y_2=-2-3=-5 \\ \Rightarrow(x_2,y_2)=(-2,-5) \end{gathered}[/tex]Therefore, the intersection points are (3,0) and (-2,-5)
What is the value of X? 8X=63.2
the given expression is,
8x = 63.2
x = 63.2/8
x = 7.9
thus, the answer is x = 7.9
i have solved your problem in the answer tab.
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what the average for 68,68,84,73,100,91
Answer:
81
Step-by-step explanation:
mean average= sum of values / amount of values
484/6=80.66666666