The constant term in the function f(x) = x² + 8x + 15 would be 15.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
A function f(x) has x-intercepts of –3 and –5 means
f(x) = (x+3)(x+5)
f(x) = a(x + 3)(x + 5), here a is a multiplier
let a = 1 then
f(x) = (x + 3)(x + 5) (expand factors)
f(x) = x² + 8x + 15
thus, 15 is the constant term
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Which algebraic expressions are polynomials? check all that apply. pi x minus startroot 3 endroot 5 y x2y 2 – 4x3 12y startfraction 4 over x endfraction – x2 – 16 3.9x3 – 4.1x2 7.3
By the definition of the polynomials, the expression [tex]3.9x^3 - 4.1x^2 + 7.3[/tex] is the only polynomials.
What are polynomials?Polynomials are those algebraic expressions that consist of variables, coefficients, and constants. The standard form of polynomials has mathematical operations such as addition, subtraction, and multiplication.
a. [tex]\pi x -\sqrt{3} +5y[/tex]
This expression consists of 2 variables so this is not a polynomial.
b. [tex]x^{2} y^{2} -4xy^{3} +12y[/tex]
This expression consists of 2 variables so this is not a polynomial.
c. [tex]\frac{4}{x} -4x^{2}[/tex]
Here variable x is in the denominator in term 4/x so this is not a polynomial.
d. [tex]3.9x^3 - 4.1x^2 + 7.3[/tex]
This expression satisfies all conditions of being a polynomial hence this is a polynomial.
e. [tex]\sqrt{x} -16[/tex]
Here the power of variable x is not an integer so it's not a polynomial.
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Answer:
A B E
Step-by-step explanation:
cuz i know
Mr. blue's first year salary is $30,000 and it doubles each year. what is the explicit rule for the sequence in simplified form?
Answer: Explicit Rule: a_n=30,000 • 2^n-1
Recursive Rule: a_n = 2a_n-1; a_1 = 30,000
Step-by-step explanation: the explicit rule for a geometric sequence is a_n = a_1 • r^n-1 and the recursive rule is a_n= r • a_n -1.
a_1 is the first term of the sequence, which is this case is 30,000. R is the common ration, which is 2 since it doubles each time. Substitute those numbers into the formulas and that’s what you’ll get. Hope this helps. God bless you!!!
The volume of a box is 124.4 in3. Find the volume of a larger, similarly shaped box that has a scale factor of 4. Round your answer to the nearest tenth.
Using the scale factor, the volume of the larger similar shaped box is 497.6in³.
What is a Scale Factor?A scale factor is simply the ratio of the corresponding sides of two similar objects. A scale factor of 4 simply means that the new shape is multiply four times the size of the original shape.
Given the data in the question;
Volume of original box V° = 124.4in³Scale factor SF = 4Volume of the larger box V = ?Since scale factor of 4 means that the new shape is multiply four times the size of the original shape.
Volume of the larger box V = V° × SF
V = 124.4in³ × 4
V = 497.6in³
Therefore, using the scale factor, the volume of the larger similar shaped box is 497.6in³.
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HELP!please HELP!please
Which of the following lists is in the correct order from smallest to largest? -13, -19, -21, -24 11, -12, 15, -19 -7, -3, 6, 2 -19, -14, 5, 11
Answer:
-24, -21, -19, -19, -19, -14, -13, -12, -7, -3, 2, 5, 6, 11, 11, 15
Step-by-step explanation:
Hey there!
To put the numbers in least to greatest form, you need to put the biggest numbers with a - sign in front of it
This means negative
Negative means below zero
Then after putting the big negative numbers, you put positive numbers going from smallest to largest
So the numbers in least to greatest is -24, -21, -19, -19, -19, -14, -13, -12, -7, -3, 2, 5, 6, 11, 11, 15
6th grade math!!
Please help me I have a unit test tomorrow, and I’m having a hard time figuring this out. So please be quick! I think we’re supposed to use a formula for rectangles but im not sure
The perimeter of thr rectangle shown is 36 inches. Write and solve an equation to find the value of x.
Answer:
X = 3
Step-by-step explanation:
(4x-6)+(4x-6)+12+12=36
Circle A has center of (2, 3) and a radius of 5, and circle B has a center of (1, 4) and a radius of 10. What steps will help show that circle A is similar to circle B?
Dilate circle A by a scale factor of 2.
Translate circle A using the rule (x + 1, y − 1).
Rotate circle A 180° about the center.
Reflect circle A over the y-axis.
Answer:
A
Step-by-step explanation:
To show that circle A is similar to circle B the step required is Dilate circle A by a scale factor of 2 option (A) is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have two circles:
Circle A has a center of (2, 3) and a radius of 5
Circle B has a center of (1, 4) and a radius of 10
The standard circle's equation can be written as:
(x - h)² + (y - k)² = r²
The equation for circle A:
(x - 2)² + (y - 3)² = 5²
The equation for circle B:
(x - 1)² + (y - 4)² = 10²
To show that circle A is similar to circle B:
It is required to perform the geometric transformation:
Dilate circle A by a scale factor of 2.
The radius of circle A is 5 units and after dilation by a scale factor of 2, the radius of the circle becomes 10 which is the radius of circle B.
Thus, to show that circle A is similar to circle B the step required is Dilate circle A by a scale factor of 2 option (A) is correct.
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Item 3 The Ferrells save $150 each month for their next summer vacation. Write an equation that they can use to find y, their savings, after x months.
Answer:
y = 150x
Step-by-step explanation:
If y = savings and they save $150 each month then you can just multiply $150 by each month to get the total savings
LOCKS SOON WILL GIVE BRAINLEST! 50 POINTS!!! For triangle xyz , the measures of angles x,y, and Z are known. Which method should be used to start solving triangle xyz?
law of sines
law of cosines
neither law can be used
both laws can be used
If the angles of measures of angles X, Y, and Z are neither law of sine and cosine can be used to solve the triangle.
What is the law of cosines and sines?The law of cosines can be used to determine the measures of the triangle if the angles are known. The law is given by:
a² = b² + c² - 2bc*cosA
a,b,c are the sides and A, B, C are the angles.
The law of sines are used to determine the measures of the triangle if the angles are known. The law is given by:
a/sinA = b/sinB = c/sinC
If the angles of measures of angles X, Y, and Z are neither law of sine and cosine can be used to solve the triangle.
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Value (in billions) 2017 2018
Total assets $16. 20 $16. 80
Total liabilities $14. 60 $14. 80
Deposits $11. 90 $12. 20
From 2017 to 2018, borrowings by commercial banks changed by $ _ billion (round your answer to two decimal places).
From 2017 to 2018, owner’s equity for commercial banks changed by $_ billion (round your answer to two decimal places)
Answer:
Borrowings = $0.10 Billion
Owner's Equity = $0.40 Billion
Step-by-step explanation:
Total liabilities = deposits + borrowings
Borrowings = total liabilities - deposits
Borrowings in 2017 = $14.60 - 11.90 = $2.70 billion
Borrowings in 2018 = $14.80 - $12.20 = $2.60 billion
Borrowings from 2017-2018= 2.60 - 2.70 = $0.10 billion
Owner's Equity= total assets - total liabilities
Owner’s equity in 2017 = $16.2 - $14.6 = $1.6 billion
Owner’s equity in 2018 = $16.8 - $14.8 = $2 billion
Owner's Equity from 2017-2018= 2 - 1.6 = $0.4 billion
Hope this helps!
The Owner's Equity for commercial banks in 2017-2018 is $0.4 billion.
The given is,
Borrowings = $0.10 Billion
Owner's Equity = $0.40 Billion
What is the formula for the total liabilities?Total liabilities = deposits + borrowings
So we have Borrowings = total liabilities - deposits
Borrowings in 2017
= $14.60 - 11.90
= $2.70 billion
Borrowings in 2018
= $14.80 - $12.20
= $2.60 billion
Borrowings from 2017-2018
= 2.60 - 2.70
= $0.10 billion
Owner's Equity= total assets - total liabilities
Owner’s equity in 2017
= $16.2 - $14.6
= $1.6 billion
Owner’s equity in 2018
= $16.8 - $14.8
= $2 billion
Owner's Equity from 2017-2018
= 2 - 1.6
= $0.4 billion
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Evaluate the expression:
Will mark brainlyest!!
Answer:
6
Step-by-step explanation:
pemdas=parenthesis, exponents, multiplication, division, addition, subtraction. with this, we multiply 2 x the absolute value of -3, which is just 3. therefore, 6. now we see we need to subtract the absolute value of 6 from the absolute value of 8, which gives us 2. and 2+4 is 6.
Answer: 6
Step-by-step explanation:
8-2 x 3+4
2x3=6
8-6+4
2+4
=6
hope this helps
1. Identify the reactants and the products in the following equation. (1 point)
CaO + CO2 → CaCO3
2. Show the molecular formula and electron structure of the simplest compound that forms with only carbon and hydrogen atoms. (1 point)
3. For each equation, state the reaction type and then balance the equation. (2 points)
a. ___Na3PO4 + ___HCl → ___H3PO4 + ___NaCl
b. ___KClO3 → ___KCl + ___O2
4. You have knowledge of the outermost electron states of the atoms, trends in the periodic table, and the patterns of chemical properties. Use that knowledge to predict the products of each of the following equations. Then explain how you made your predictions. Be sure to balance the equations. (4 points)
a. ___NaBr + ___Ca → _______ + _______
b. ___Mg + ___O2 → _______
5. Identify the products of this single-replacement reaction between sulfuric acid and aluminum. Then balance the equation. (2 points)
___H2SO4 + ___Al → ___ + ___
6. (6 points)
a. Write a balanced equation for the model of a chemical reaction shown below. (The white balls represent hydrogen atoms, the black balls represent carbon atoms, and the gray balls represent oxygen atoms.) Then complete the table with information about the atoms and molecules represented in the model. Show your work. (5 points)
chemical equation
Molecule name Methane Oxygen Water Carbon dioxide
Molecular formula
H2O
Elements in molecule
C, O
Molecular mass of molecule 16.05 g/mol
Total mass in reaction
64.00 g
Total mass of all reactant molecules
Total number of reactant atoms
Total mass of product molecules
Total number of product atoms
b. How does your second table support the claim that the number of atoms — and therefore mass — is conserved during a chemical reaction? (1 point)
7. (6 points)
a. Calculate the molar mass of sucrose: C12H22O11. Show your work. (2 points)
b. Calculate the molar mass of glucose, one of the products of photosynthesis: C6H12O6. Show your work. (2 points)
c. How many molecules are in 1 mole of sucrose? (1 point)
d. How many atoms are in 1 mole of sucrose? (1 point)
8. Baking soda (NaHCO3) and vinegar (HC2H3O2) react to form sodium acetate, water, and carbon dioxide. If 42.00 g of baking soda react, how many moles of carbon dioxide will form? Show your work. (3 points)
NaHCO3 + HC2H3O2 → NaC2H3O2 + H2O + CO2
The series of questions is based on the entire concept of chemical equations. This is shown by balanced reaction equations.
What is a reaction equation?A reaction equation shows the reactants and the products in a reaction. We shall now answer the questions individually;
1) The reactants in this equation are CaO and CO2. The product is CaCO3.
2) The simplest molecule that is formed between carbon and hydrogen is CH4 with the structure shown in the image attached.
3) The balanced equations are;
a) Na3PO4 + 3HCl -----> H3PO4 + 3NaCl
b) 2KClO3 → 2KCl + 3O2
4)
a. 2NaBr + Ca ----->CaBr2 + 2Na
b. 2Mg + O2 ------->2MgO
5) 3H2SO4 + 2Al -------> Al2(SO4)3 + 3H2
6) CH4 + 202 ---->CO2 + 2H2O
7)
a. molar mass of sucrose = 12(12) + 22(1) + 11(16) = 144 + 22 + 176 = 342 g/mol
b. molar mass of glucose = 6(12) + 12(1) + 6(16) = 72 + 12 + 96 = 180 g/mol
c. There are 6 * 10^23 molecules 1 mole of sucrose
d. There are 6 * 10^23 atoms 1 mole of sucrose
8) The equation of the reaction is; NaHCO3 + HC2H3O2 → NaC2H3O2 + H2O + CO2
Number of moles of baking soda= 42.00 g/84 g/mol = 0.5 moles
Since the reaction is 1:1, 0.5 moles of CO2 is formed.
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how do you solve this?
Answer:
X = 7.8
Step-by-step explanation:
First I will mark all the Information given to us:
Angle 1: 52 Degrees
Angle 2: 90 (Marked by the box) Degrees
Angle 3: 180-(90+52) Triangle Angle Sum Therom
Simplified Angle 3: 38 Degrees
Height: 10
Base: X
Hypo: ? (we will call this y)
In order to solve this problem we must use basic trig functions such as sin, cos and tan.
I will be applying sin for the degree measure of 52 as it is applicable there.
(Sin for refrence sin(angle measure)= side opposite to angle/hypo)
So this would be in our case:
Sin(52)=10/y
Simplify
y sin(52) = 10
y = 10/sin(52) (use a calculator make sure sin is in degrees not radians)
y=10/0.78801
y=12.69018 (We have our hypo value)
We can now apply a²+b²=c²
a²+10²=12.69018²
a²+100=161.040668432 (Calculator)
a²=61.040668432
a=√61.040668432 (calculator)
a=7.81285277168
Rounded to the nearest tenth
7.8 =a=x (X is the a value in this equation)
Simplify the expression. Write your answer as a power.
(xy)^7
Answer:
[tex](xy)^{7}[/tex]
↓
[tex]x^{7} y^{7}[/tex]
So the answer is [tex]x^{7} y^{7}[/tex].
The average temperature of the top 5 meters in April is 22,500 cubic meters. 2. Typical seawater has a salinity of 35 psu (practical salinity units). In which month is the difference in salinity of surface and bottom waters the greatest
The months where the difference in salinity of surface and bottom waters was the greatest was in April and September.
What is salinity?It should be noted that salinity simply means the accumulation of salt in land as well as water.
In this case, the months where the difference in salinity of surface and bottom waters was the greatest was in April and September.
This is because many events take place such as continuous flowing or river water into the sea, evaporation, and melting of ice.
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Given the following data points, calculate the curve of best fit. Show all steps.
The equation of curve of best fit is y = -30.17x + 14.49. To find the curve of best fit, we would require two equations which are explained in details below.
Equation of Straight LineData;
∑x = 16∑y = 50.9∑x^2 = 35∑xy = 24.6The equation of straight line is y = ax + b
If we modify it to fit into this problem,
[tex]\sum y = na + b \sum X ... equ(i)\\\sum xy = a \sum x + b \sum x^2 ...equ(ii)[/tex]
Let's substitute the values into the equations and solve
[tex]\sum y = na + b \sum X ... equ(i)\\\sum xy = a \sum x + b \sum x^2 ...equ(ii)\\50.9 = 6*a + b*16 ...equ(i)\\24.6 = a*16 + b*35 ...equ(ii)\\50.9 = 6a + 16b ...equ(i)\\24.6 = 16a + 35b ...equ(ii)[/tex]
Let's solve both equation (i) and equation (ii)
[tex]50.9 = 6a + 16b...equ(i)\\24.6 = 16a + 35b ...equ(ii)\\a = -30.17, b = 14.49[/tex]
We can substitute the values of a and b into the equation
[tex]y = ax + b\\y = -30.17x + 14.49[/tex]
The equation of curve of best fit is y = -30.17x + 14.49
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Henry calculated the mean absolute deviation of the points he earned throughout the year health and music
history: MAD 3.5
English: MAD: 2.65
health: MAD of 2.5
music: MAD of 3.28
in which class were his scores the closest together
health
English
music
History
Answer:
health class
Step-by-step explanation:
when the mean absolute deviation (M.A.D) is lower, that means the data is closer together. When it is higher that means the data is more spread out.
Answer:
its health
Step-by-step explanation:
i took the k12 test and got it wrong and it showed this one was correct
A shipping company charges $6 to ship a package that weighs up to 1 pound and $2 for each additional pound or portion of a pound. which equation represents the cost, in dollars, of shipping a package that weighs x pounds?
The equation represents the cost (in dollars) and shipping a package that weighs x pounds is y = 2(x - 1) + 6.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
A shipping company charges $6 to ship a package that weighs up to 1 pound and $2 for each additional pound or portion of a pound.
Let x be the number of pounds and y be the total cost, then we have
y = 2(x - 1) + 6
This is the required equation that describes the condition.
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Answer:
Its A on edge, f(x)=6+2[x-1]
Step-by-step explanation:
, where x > 0
What is the y-value of the vertex of the function f(x)=−(x+8)(x−14)?
Answer:
f(x) = -(x + 8)(x -14)
= -(x2 - 112 - 6x)
= -x2 + 6x + 112 --- (1)
We know the graph of an equation y = ax2 + bx + c where a ≠ 0 is a parabola. The parabola opens upwards if a > 0 and opens downwards if a < 0. The vertex of the parabola is the point where the axis and parabola intersect. Its x coordinate x = -b/2a and its y coordinate is found out by substituting x = -b/2a in the parabola equation.
The parabola given in the problem statement has a negative coefficient of x2 and hence it is a parabola which opens downwards. Also for the equation
a = -1, b = 6 and c = 112. Therefor the x-coordinate of the vertex is
x = -b/2a
= -(6)/[2(-1)]
= 3
Substituting the value of x = 3 in equation (1) we get,
Now y = -(3)2 + 6(3) + 112
= -9 + 18 + 112 = 121
So the vertex point coordinates are (3, 121) and the y value is 121.
The graph below verifies the vertex point.
vertex of the graph
What is the y-value of the vertex of the function f(x) = -(x + 8)(x - 14)?
Summary:
The y-value of the vertex of the function f(x) = -(x +
Answer:
Step-by-step explanation:
D or 121 got it right on edgenuty
Does anyone know the answer for this?
Answer:
88
Step-by-step explanation:
Answer:
8(4+7)
Step-by-step explanation:
The GCF of 32 and 56 is 8. Then you divide by 8.
The diameter of a circle is 4 in. Find its circumference in terms of T.
Answer:
C = 12.57 inches
Step-by-step explanation:
C=2πr
C=πd=π·4≈12.56637in
What is the image of ( − 6 , 9 ) after a reflection over the y-axis?
Frances bought 144 shares of dwyn horticulture for $7.73 apiece. her broker charged her a commission of $46.15 for the purchase. if the yearly dividend on dwyn horticulture is 61 cents per share, what is the annual yield on frances’s stock? a. 0.0758 b. 0.0789 c. 0.0132 d. 0.0320
The annual yield on Frances’s stock approximately will be 0.0758. Then the correct option is A.
What is Algebra?Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.
Frances bought 144 shares of Dwyn horticulture for $7.73 apiece. her broker charged her a commission of $46.15 for the purchase.
Then the total amount spent by the company will be
→ 144 × $7.73 + $46.15 = $ 1159.27
If the yearly dividend on Dwyn horticulture is 61 cents per share, then the annual yield on Frances’s stock will be
[tex]\Rightarrow \dfrac{0.61 \times 144}{11592.27} \\\\\Rightarrow 0.07577[/tex]
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It took an airplane 3 hours to go 1725 miles.
How many miles per hour
Answer:
575 mph
Step-by-step explanation:
The plane is traveling at 575 mph.
1725/3
575
Which sum is equal to 3 1/4+1 2/5?
Answer:
[tex]\huge\boxed{\bf\: \frac{93}{20}=4.65}[/tex]
Step-by-step explanation:
[tex]3 \frac { 1 } { 4 } + 1 \frac { 2 } { 5 }[/tex]
Now,
[tex]3 \frac { 1 } { 4 } \\= \frac{4 * 3+1}{4}\\= \frac{13}{4}[/tex]
Then,
[tex]1 \frac { 2 } { 5 }\\= \frac{1* 5+2}{5} \\= \frac{7}{5}[/tex]
So,
[tex]3 \frac { 1 } { 4 } + 1 \frac { 2 } { 5 }\\= \frac{13}{4}+\frac{7}{5}\\ \\\mathrm{LCM = 20}\\\\= \frac{65}{20}+\frac{28}{20} \\=\boxed{\bf\: \frac{93}{20}=4.65}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
what would a proof look like for this equation?
5. Do 4 x (1 + 3%) and 4 x (1 + 3)' have the same answer? Explain.
Answer:
no. so the first answer I got was 4.12 and the other 16
Step-by-step explanation:
4×(1+3%)
3%=0.03
0.03+1= 1.03
1.03*4= 4.12
4*(1+3)
1+3=4
4*4=16
I hope that helps you
Can someone please help me it is due today! Thank you to whoever can help.
y = 0.6x + 3
How to determine the equation of the line?To determine the equation of the line, we need to determine the slope and the y-intercept. Then, we will substitute the slope and the y-intercept in the slope intercept form equation to obtain the equation in slope intercept form.
Slope of line:Two points that lie on line: (0, 3) and (-5, 0)
[tex]\implies \text{Slope} = \dfrac{\text{Rise}}{\text{Run}} = \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
[tex]\implies \text{Slope} = \dfrac{3 - 0 }{0- (-5)}\\[/tex]
[tex]\implies \text{Slope} = \dfrac{3 }{0+5}\\[/tex]
[tex]\implies \text{Slope} = \dfrac{3 }{5} = 0.6[/tex]
Y-intercept of line:[tex]\implies \text{Intersection of line on y-axis: 3}[/tex]
[tex]\implies \text{y-intercept: 3}[/tex]
Equation of line:Slope intercept form:
y = mx + b[Where "m" is the slope and "b" is the y-intercept]
Substitute the slope (m) and the y-intercept (b) in the formula;
[tex]\implies \text{Slope intercept form: y = (m)x + (b)}[/tex]
[tex]\implies \text{Equation of line in slope intercept form: y = (0.6)x + (3)}[/tex]
Open the parenthesis in the equation;
[tex]\implies\text{Equation of line in slope intercept form: \boxed{\text{y = 0.6x + 3}}}[/tex]
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Line m is represented by the equation y +2 = (x + 4). Select all equations that represent lines perpendicular to line
Answer
y = x + 2
hope this helped
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