The given equation is,
[tex]4p-9=2p+21[/tex]The equation can be solved as,
[tex]\begin{gathered} 4p-9=2p+21 \\ 4p-2p=21+9 \\ 2p=30 \\ p=\frac{30}{2} \\ p=15 \end{gathered}[/tex]Thus, the requried value of p is 15.N
A student finished 45 of her homework problems in class. If the ratio of problems shefinished to problems she still had left was 9:4, how many homework problems did shehave total?
The ratio between the amount of problems she finished and the problems she still had left is given by the division between those amount. Since this ratio is 9:4, if we call the amount of homework she still has left as x, we have the following relation
[tex]\frac{45}{x}=\frac{9}{4}[/tex]Solving for x, we have
[tex]\begin{gathered} \frac{45}{x}=\frac{9}{4} \\ \frac{x}{45}=\frac{4}{9} \\ x=\frac{4}{9}\cdot45 \\ x=\frac{4\cdot45}{9} \\ x=\frac{180}{9} \\ x=20 \end{gathered}[/tex]She still has 20 problems left to solve. The total amount of problems is given by the sum between the problems she already finished and the problems left to solve, then, the total amount of problems is
[tex]45+20=65[/tex]65 problems.
List the potential rational zeros of the polynomial function. Do not find the zeros.f(x) = -4x^4 + 2x^2 - 3x + 6A± , ± , ± , ± , ± 1, ± 2, ± 3, ± 4, ± 6B± , ± , ± , ± , ± 1, ± 2, ± 3, ± 6C± , ± , ± , ± , ± , ± 1, ± 2, ± 4D± , ± , ± , ± , ± , ± 1, ± 2, ± 3, ± 6
Answer:
±1,±2,±3 and ±6
Explanation:
We make use of the Rational Zero theorem below:
If a polynomial has integer coefficients, then every rational zero of f(x) has the form p/q where p is a factor of the constant term and q is a factor of the leading coefficient.
Given the function:
[tex]f\mleft(x\mright)=-4x^4+2x^2-3x+6[/tex]The steps to follow are given below.
Step 1: Determine all factors of the constant term and all factors of the leading coefficient.
The constant term is 6: Factors are ±1,±2,±3 and ±6
The leading coefficient is -4: Factors are ±1,±2, and ±4.
Step 2: Determine all possible values of p/q.
[tex]\begin{gathered} \frac{p}{q}=\pm\frac{1}{1},\pm\frac{2}{1},\pm\frac{2}{2},\pm\frac{3}{1},\pm\frac{6}{1},\pm\frac{6}{2} \\ =\pm1,\pm2,\pm1,\pm3,\pm6,\pm3 \\ =\pm1,\pm2,\pm3,\pm6 \end{gathered}[/tex]Therefore, the potential zeros are: ±1,±2,±3 and ±6.
A piece of wire 5/4 m long is to be cut into 20 pieces of the same length. What is the length of each piece?Each piece is ____ m long.(Simplify your answer. Type an integer or a fraction.)
When we divide a fraction by a number, that's equivalent to multiplying the first fraction by the inverse of that number.
In this problem, we need to divide the fraction 5/4 by 20. So we obtain:
[tex]\frac{5}{4}\colon20=\frac{5}{4}\cdot\frac{1}{20}[/tex]Now, we need to multiply the numerator of the first fraction by the numerator of the second one, and the denominator of the first fraction by the denominators of the second one:
[tex]\frac{5}{4}\cdot\frac{1}{20}=\frac{5\cdot1}{4\cdot20}=\frac{5}{80}[/tex]Now, we need to simplify the answer. To do so, we can divide both the numerator and the denominator by 5:
[tex]\frac{5\colon5}{80\colon5}=\frac{1}{16}[/tex]Therefore:
Each piece is 1/16 m long.
1. Consider the following functions. f(x) = 3x2 + x + 2 g(x) = 4x2 + 2(3x – 4) h(x) = 5(x2 - 1) a. Find f (x) - g(x). b. Find g(x) - h(x).
a.
Let's write function g(x) better:
[tex]g(x)=4x^2+2(3x-4)=4x^2+6x-8[/tex]Now we can do the substraction easier
[tex]f(x)-g(x)=(3x^2+x+2)-(4x^2+6x-8)_{}[/tex][tex]f(x)-g(x)=3x^2+x+2-4x^2-6x+8[/tex][tex]f(x)-g(x)=(3-4)x^2+(1-6)x+2^{}+8[/tex][tex]f\mleft(x\mright)-g\mleft(x\mright)=-x^2-5x+10[/tex]That's answer a
b.
We write h(x) better too:
[tex]h(x)=5(x^2-1)=5x^2-5[/tex]And do the same as before:
[tex]g(x)-h(x)=(4x^2+6x-8)-(5x^2-5)[/tex][tex]g(x)-h(x)=4x^2+6x-8-5x^2+5[/tex][tex]g(x)-h(x)=(4-5)x^2+6x-8+5[/tex][tex]g(x)-h(x)=-x^2+6x-3[/tex]That's answer b
2. Which answer of
the following is an
example of a SUM?
A 12-3=9
B 12+3=15
C 12×3=36
D 12÷3=4
Answer: B : 12+3=15
Step-by-step explanation:
A sum is the answer of an addition problem
The side walls of a regular quadrilateral pyramid are equilateral triangles with sides equal to 8 cm. Calculate the pyramid:1) the sum of the lengths of all the sides;2) the area of the base;3) the length of the height of the side wall;4) the area of the side wall.
a) 64cm
b) 64 square cm
c) 4√3 cm
d) 16√3 square cm
Explanations:A regular quadrilateral pyramid with equilateral triangles is as shown below;
1) The pyramid has 8 side lengths, hence the sum of the length of all the sides is given as:
[tex]\begin{gathered} Sum\text{ of side lengths}=8\times8cm \\ Sum\text{ of side lengths}=64cm \end{gathered}[/tex]2) Since the triangular sides are equilateral, the base of the pyramid will be a square with side length of 8cm. The area of the base is expressed as:
[tex]\begin{gathered} A=length\times length \\ A=8cm\times8cm \\ A=64cm^2 \end{gathered}[/tex]3) Since one side wall is an equilateral triangle, the height will be perpendicular to the base as shown:
In order to determine the height, we will use the Pythagorean theorem as shown:
[tex]\begin{gathered} 8^2=h^2+4^2 \\ h^2=8^2-4^2 \\ h^2=64-16 \\ h^2=48 \\ h=\sqrt{48}=4\sqrt{3}cm \\ \end{gathered}[/tex]4) The area of the side wall is equivalent to the area of the triangle expressed as:
[tex]\begin{gathered} Area\text{ of side wall}=\frac{1}{2}\times base\times height \\ Area\text{ of side wall}=\frac{1}{2}\times8cm\times4\sqrt{3} \\ Area\text{ of side wall}=16\sqrt{3}cm^2 \end{gathered}[/tex]hello can u help me please5.Admission to the Basketball Hall of Fame in Springfield is $5.00 per student. A group of students bought admission tickets. One student spent an extra $9.00 for a poster. The total amount they spent was $34.00. How many students were in the group?a.4b.5c.6d.7
Given:
The price per student for the admission, m=$5.
Extra amount spent by a student, c=$ 9.
Total amount spent, T=$34.
Let x be the number of students. Then, the expression for the total amount is,
[tex]T=mx+c[/tex]Substitute values and solve for x.
[tex]\begin{gathered} 34=5x+9 \\ 34-9=5x \\ 25=5x \\ x=\frac{25}{5} \\ x=5 \end{gathered}[/tex]Therefore, the number of students is 5.
Option (b) is correct.
WILL MARK BRAINLIEST Rectangle PQRS is shown above. Point C is the center of the rectangle.Maggle claims that there are transformations that preserve the length of the rectangle's sides. Which of the following transformations could be used to support Maggie's claim? select all that apply1.) a translation of 10 units to the right2.) a rotation of 90' clockwise about vortex Q3.) a reflection over the side RS4.) a diation of scale factor 1 through contor5.) a vertical stretch of scale factor 2 through contor C
With the given options;
(1) A translation of 10 units to the right will only map the rectangle onto a different location, but the lengths would remain as it were
(3) A reflection over the side RS will turn the rectangle into a mirror reflection of itself, and this means the sides remain the same measurement but is now being observed from the opposite side (but top now bwcomes bottom and vice versa).
(4) A dilation of scale factor 1 through center
There are a total of 37800 members at club A and the ratio of club A to club B is 20:13. The ratio of 40 and older group is 70% of club B the ratio of under 40members in club A to club B is 176:39
Find the equation of the line through the given points. (-8, 6) and (-8, 0)
The equation of a line is typically written as y=mx+b, where m is the slope and b the y-intercept.
The slope can be calculated like this:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case you have x1=-8, y1=6, x2=-8 and y2=0. Replace this values on the slope formula
[tex]m=\frac{0-6}{-8-(-8)}=\frac{-6}{-8+8}=\frac{-6}{0}\text{ the slope is undefined}[/tex]An undefined slope indicates that you have a vertical line parallel to the y-axis.
This line will pass through all points in the plane with an x-coordinate=constant (c). In this case this constant will be -8
The equation is written in the form x = c, then the equation of this line will be
[tex]x=-8[/tex]i inserted a picture of the question can you make it very shorta -4 b 8c 4d -8
a. -4
Explanation
the average rate of change is given by:
[tex]\begin{gathered} rateofch=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ where \\ P1(x_1,y_1)\text{ is the start point} \\ P2(x_2,y_2)\text{ is the end point} \end{gathered}[/tex]then
Let
[tex]\begin{gathered} x_1=1 \\ f(x_1)=0 \end{gathered}[/tex]and
[tex]\begin{gathered} x_2=3 \\ f(x_2)=-8 \end{gathered}[/tex]hence
P1(1,0)
P2(3,-8)
now, replace in the formula
[tex]\begin{gathered} rateofch=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{rate of change=}\frac{-8-0}{3-1}=\frac{-8}{2}=-4 \\ \text{rate of change=-}4 \end{gathered}[/tex]therefore, the answer is
a. -4
I hope th
what is the slope of the line described by 5x+7y=19
Answer:
-5/7
Explanation:
Given the equation 5x+7y = 19
The standard form of an equation is y = mx+c
m is the slope
c is the intercept of a line
Make y the subject of the formula from the given equation
5x+7y = 19
7y = -5x + 19
Divide through by 7
7y/7 = -5x/7 + 19/7
y = -5/7 x + 19/7
Comparing with general formula;
mx = -5/7 x
m = -5/7
Hence the slope of the line is -5/7
PLEASE HELP ME ASAP PLEASE PLEASE PLEASE
jaren is selling lampshades at a craft fair. for the price per lampshade in dollars is f (x) and it is a function of the
Number of lampshades bought as shown by the graph below. What is the total cost of buying 10 lampshades from Janet's stall
According to the graphic the total cost of buying 10 lampshades is 8 dollars
determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. afterwards, determine two values of x that support your conclusion. 4(x+4) = 4x+16the equation has ____ solutions.a value of x that makes the equation true is __,which when simplified makes the equation turn into____=_____.a value of x that makes the equation false is____, which when simplified makes the equation turn into ___=___.
4(x+4) = 4x+16
Apply distributive property:
4(x)+4(4)= 4x+16
4x+16=4x+16
Add and subtract alike terms
4x-4x= 16-16
0=0
Since x can have many values, it has an infinite number of solutions.
we can replace x by 1, by 3, by 2 and the equality will remain.
the equation has an infinite number of solutions.
find the slope of the line through the points (-6,5) and (3, -2)
We have to find the slope of the line that pass through points P1=(-6,5) and P2=(3,-2).
We can calculate it as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-5}{3-(-6)}=\frac{-7}{9}=-\frac{7}{9}[/tex]Answer: the slope of the line is m = -7/9
Classify the following triangle as acute, obtuse, or rightO A. AcuteO B. ObtuseOc. RightOD. None of theseSUBMIT
Given:
Triangle is given with the angles.
Given triangle is Acute
solve equation. -2(y-1)=9
y = -7/2
Explanation:-2(y-1)=9
expand the bracket:
-2 × y -2 × -1 = 9
-2y + 2 = 9
collect like terms:
-2y = 9 -2
-2y = 7
Divide both sides by -2:
-2y/-2 = 7/-2
y = -7/2
A total of $54,000 is invested at an annual interest rate of 5.25%. Find the balance after 6 years if it is compounded monthly.
Using the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
A = Amount
P = Principal = 54000
r = Interest rate = 5.25% = 0.0525
n = Number of times the interest is compounded per year = 12
t = Number of years = 6
So:
[tex]\begin{gathered} A=54000(1+\frac{0.0525}{12})^{12\cdot6} \\ A\approx73943.18 \end{gathered}[/tex]Answer:
The balance is $73943.18
What percentage of 371 is 120?
This question is about percentages.
To know which percentage of 371 is 120, we just have to divide
[tex]\frac{120}{371}=0.32[/tex]Then, we multiply by 100 to express it in percentage
[tex]\text{0}.32\cdot100=32[/tex]Therefore, 120 represents 32% of 370, approximately.Miranda has $100.00 in a saving account that earns 10 percent interest, compounded annually. what wull the balance be after 1 year round to the nearest cent
Calculate the maximum number of cylindrical paint cans that carvers auto custom can stock if the paint comes in a 2-pack hazmat box that mesures 15 inches by 7 inches by 6 inches
The volume of Hazmat box is,
[tex]v=15\times7\times6[/tex][tex]v=630in^3[/tex]Convert inches to feet ,
[tex]undefined[/tex]The volume of the warehouse when half of the warehouse is painted with cams and rims is.
[tex]V=\frac{8000}{2}\times20ft^3[/tex][tex]V=80,000ft^3[/tex]SHOW THE PROPORTION YOU ARE SETTING UP.Four out of 10 adults in a certain city buy their drugs at large drug stores. If this city has 34,000 adults, how many of these adults would you expectto buy their drugs at large drug stores?
You know that 4 out of 10 adults buy their drugs at large drug stores. To calculate the value of the proportion you have to divide 4 by 10
[tex]\begin{gathered} p=\frac{4}{10} \\ p=0.4 \end{gathered}[/tex]The city has n=34,000 adults, to determine the expected number of adults that buy at large drugstores, you have to multiply the total number of adults by the proportion:
[tex]E(X)=np[/tex]n=34,000 and p=0.4
[tex]\begin{gathered} E(X)=34000\cdot0.4 \\ E(X)=13600 \end{gathered}[/tex]Out of the 34,000 you could expect 13,600 adults to buy at large drug stores.
Why is x² + 36 NOT factorable? In other words, why is it prime? What are twodetails that draw you to this conclusion?
SOLUTION:
Step 1:
In this question, we are given the following:
a) Why is x² + 36 NOT factorable?
b) In other words, why is it prime?
c) What are two details that draw you to this conclusion?
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} a)\text{ x}^2\text{ + 36 is not factorizable under of field of integers Z,} \\ since\text{ it cannot be expressed as product of two squares} \end{gathered}[/tex]b) In other words, why is it prime?
It is a prime polynomial because a prime polynomial is one that cannot be factored into the product of two polynomials, using integer values.
-
c) What are two details that draw you to this conclusion?
1) You can factor a difference of squares, but not a sum of squares.
2) A prime polynomial is one that cannot be factored into the product of two polynomials, using integer values.
-
question will be in picture
given:
[tex]-7\le x[/tex]so, the line that represents the given inequality will be: b
in pqr, what is the measurement of angle Q? 200 degrees871059010
In the triangle PQR we know that its angles have the following measures:
∠P=(6x+5)º
∠Q=(11x-5)º
∠R=xº
To determine the measures of ∠Q, you have to determine the value of x first. To do so you have to keep in mind that the measure of the inner angles of any triangle is 180º, so, for this triangle, the measure of the inner angles can be expressed as:
[tex]\begin{gathered} \angle P+\angle Q+\angle R=180º \\ (6x+5)+(11x-5)+x=180º \end{gathered}[/tex]From this expression, we can calculate the value of x.
-First, take the parentheses away, order the like terms together and simplify them:
[tex]\begin{gathered} 6x+11x+x+5-5=180º \\ 18x=180º \end{gathered}[/tex]-Second, divide both sides by 18 to determine the value of x:
[tex]\begin{gathered} \frac{18x}{18}=\frac{180}{18} \\ x=10 \end{gathered}[/tex]Now that we know that the value of x is 10º, we can determine the measure of ∠Q by replacing this value on the given expression for its measure:
[tex]\begin{gathered} \angle Q=11x-5 \\ \angle Q=11\cdot10-5 \\ \angle Q=110-5 \\ \angle Q=105º \end{gathered}[/tex]∠Q=105º, the correct option is the third one.
V11, -14 and w -19, 15 are the influence of the line segment what is the midpoint M of that line segment right the coordinates as decimals are integers
Step 1: Problem
Mid-point of V ( 11, -14 ) and W ( -19, 15 )
Step 2: Concept
[tex]\begin{gathered} coordinatesofthe\text{mid}-po\text{ int = ( x , y )} \\ x\text{ = }\frac{x_1+x_2}{2} \\ y\text{ = }\frac{y_1+y_2}{2} \end{gathered}[/tex]Step 3: Method
Substitute the given data to find the coordinates of the mid-point
Given data
x1 = 11
y1 = -14
x2 = -19
y2 = 15
[tex]\begin{gathered} x\text{ = }\frac{-\text{ 19 + 11}}{2}\text{ = }\frac{\text{ -}8}{2}\text{ = -}4 \\ y\text{ = }\frac{15\text{ +(-14)}}{2}\text{ = }\frac{1}{2}\text{ = }0.5 \end{gathered}[/tex]Step 4: Final answer
The coordinates of the mid-point = ( -4 , 0.5 )
what is the graph of x= 1 ?
The given equation x = 1 represents a horizontal lines that passes thourgh (1, 0).
Hence, the graph isThe answer is D.2.) Your unusual boss decided to offer you a fourthoption to complicate your decision.Your payment would be described by the functionP(x) = 95,000x + 200,000, with x representingdays you work and P representing dollars you earn.Explain the meaning of the function based on thissituation and then decide if you would take this optionover the other three choices.On the next slide, you use a graph to support yourdecision.
P(x) = 95,000x + 200,000
5 lb of apples cost $8.20. How much is it for 1 lb?
Its says for pi do 3.14 and round to tje nearest hundredth.
EXPLANATION
Measure of the rectangular window:
length = 24 inches
width = 18 1/4 inches = 73/4 inches = 18.25 inches
The area is given by the following relationship:
[tex]\text{Area}_{wi\text{ndow}}=\text{length}\cdot\text{width}=24\cdot18.25=438in^2[/tex]The picture is as follows: