Please help:y = x + 4y = x^4Graph your system of equations and show the solution graphically to verify your solution.
Answers
Given:
[tex]\begin{gathered} y=x+4 \\ y=x^4 \end{gathered}[/tex]Graphing:
green line is y = x + 4
blue line is y = x^4
The solutions are:
(-1.28, 2.72) and (1.53, 5.53)
Answer: (-1.28, 2.72) and (1.53, 5.53)
Related Questions
What value for x makes the following statement true?
Answers
Answer:
2
Step-by-step explanation:
we can isolate the variable by subtracting 3x from both sides
3x + 12 = 5x + 8
-3x -3x
12 = 2x + 8
and then subtracting 8 from both sides
12 = 2x + 8
-8 -8
4 = 2x
then we divide by 2 on both sides
4 = 2x
÷2 ÷2
2 = x
flip the equation to get:
x=2
checking the solution by plugging in 2 in place of x:
(3 * 2) + 12 = (5 * 2) + 8
6 + 12 = 10 + 8
18 = 18
since the equation is true,
the solution x = 2 is correct.
Using the formula for the area of the triangle area equals 1/2 times base times height write an expression for the area of triangle ABC. The line BD bisects the line AC perpendicularity hence this has made triangle ABD and BCD right triangles
Answers
Using the formula:
[tex]A=\frac{b\cdot h}{2}[/tex]Where:
b = base
h = height
From the diagram:
b = AC
h = BD
So:
[tex]A=\frac{AC\cdot BD}{2}[/tex]How do I graph y = -4x + 6 thanks!
Answers
We have that the equation represents a line in slope-intercept form:
[tex]y=mx+b\Rightarrow y=-4x+6[/tex]We have that m is the slope, in this case, m = -4, and 6 is the y-intercept (0, 6). The y-intercept is the point where the line passes through the y-axis - at this point x = 0.
Therefore, we still need another point to do the graph of the line. This point can be the x-intercept: the point where the line passes through the x-axis, and, at this point, y = 0. Then, to find it, we can proceed as follows:
y = 0
[tex]y=0\Rightarrow0=-4x+6[/tex]Subtracting 6 from both sides of the equation, we have:
[tex]-6=-4x+6-6\Rightarrow-6=-4x[/tex]Now, we can divide both sides of the equation by -4:
[tex]-\frac{6}{-4}=-\frac{4}{-4}x\Rightarrow x=\frac{6}{4}\Rightarrow x=\frac{3}{2}=1.5[/tex]Now, we have the y-intercept (0, 6) and the x-intercept (1.5, 0), and with these two points, we can graph the line. We need to remember that a line can be defined by two points.
The accompanying box-and-whisker plots can be used to compare the annual incomes of three professions. Based on the box-and-whisker plots, which statement is true?a - the median income for nuclear engineers is greater than the income of all musiciansb - the median income for police officers and musicians is the samec - all nuclear engineers earn more than all police officersd - a musician will eventually earn more than a police officer
Answers
a - Median income for nuclear engineers: $70,000. Some musicians earn more than $120,000. FALSE
b - Median income for police officers: $30,000
Median income for musicians: $30,000
TRUE
c - Some nuclear engineers earn between $50,0000 and $60,0000
Also, some police officers earn between $50,0000 and $60,0000
FALSE
d - box-and-whisker plots don't allow us to predict future events. Then, maybe or maybe not a musician will eventually earn more than a police officer
. Your friend has 2 credit cards with balances that he cannot afford to pay off all at once. A $500 balanceon a card with 15.99% APR and a $400 card with a 25.99% APR.2. Calculate the monthly finance charges for each credit card. (round to the hundredths place)
Answers
A $500 balance on a card with 15.99% (0.1599) APR:
[tex]\begin{gathered} Monthly\text{f}\imaginaryI nance=500*\frac{0.1599}{12} \\ \\ Monthly\text{f}\imaginaryI nance=6.66 \end{gathered}[/tex]A $400 card with a 25.99% (0.2599)APR:
[tex]\begin{gathered} Monthly\text{f}\mathrm{i}nance=400*\frac{0.2599}{12} \\ \\ Monthly\text{f}\mathrm{i}nance=8.66 \end{gathered}[/tex]Then, the monthly finance charge is: $6.66 for first credit card and $8.66 for second credit cardsolve triangles using law of sines , please show work thank you so much! find m
Answers
By Sine Rule,
[tex]\frac{b}{\sin B}=\frac{a}{\sin A}[/tex]Where b=14, a=12, sinA = sin57 and sinB = ?
[tex]\begin{gathered} \frac{14}{\sin B}=\frac{12}{\sin 57} \\ \text{Cross multiply to get} \end{gathered}[/tex][tex]\begin{gathered} 12\sin B=14\sin 57 \\ \\ \sin B=\frac{14\sin 57}{12}=\frac{14\times0.83867}{12}=0.978449 \end{gathered}[/tex][tex]B=\sin ^{-1}(0.978449)=78.08\approx78^o[/tex]A car wash uses 59 gallons of water every 40 seconds how much water does it use per second
Answers
Answer: 1.475 gallons a second
Step-by-step explanation:
just divide 59/40 and you get your answer for this question
Answer:
1.475
Step-by-step explanation:
59÷40
40 seconds =59
1 seconds=x
c.m
59×1=40x
59÷40
=1.475
Santa has 3/4 of a bag of grain left. His hens eat 1/6 of a bag of grain every day. How many days will he be able to feed his hens?
Answers
To find how many days he is able to feed his hens, divide 3/4 by 1/6.
[tex]\frac{\frac{3}{4}bag}{\frac{1}{6}\frac{day}{day}}[/tex]To solve it multiply the first fraction by the inverse of the second fraction.
[tex]\begin{gathered} \frac{3}{4}bag*\frac{6}{1}\frac{day}{bag} \\ \frac{6*3}{4}days \\ \frac{18}{4}days \\ 4.5days \end{gathered}[/tex]That means he will be able to feed his hens for 4 days.
Answer: 4 days.
Which of the following is equal to the rational expression when x + 1 or -1? 5(x-1) (x + 1)(x-1)
Answers
Answer
Option A is correct.
[tex]\frac{5}{(x+1)}[/tex]Explanation
We can see that the numerator and the denominator both contain (x - 1).
Hence, that expression cancels out and we are left with
5/(x + 1)
Hope this Helps!!!
Sally test grades in English and 75 and 80 what grade must she get on her next test so the average is in 85?
Answers
Explanation
We are told that Sally scored 75 and 80 on two English tests
We are then asked to determine the next grade she must have so that the average becomes 85
Thus
let the third grade be x
Hence
The total grades of the three tests will be
[tex]75+80+x[/tex]The average of the three tests will be
[tex]\frac{75+80+x}{3}[/tex]Since the average is 85, then we will have
[tex]\frac{75+80+x}{3}=85[/tex]We can now solve for x
[tex]\begin{gathered} 75+80+x=3\times85 \\ 155+x=255 \\ x=255-155 \\ x=100 \end{gathered}[/tex]Thus, she must score 100 on her third test
The drink booth at the school fair had these 4 types of drinks:root beer, ice tea, orange juice, and apple cider.The 16 students from Mr. Smith's class were asked which drink they ordered. Here are the results:root beer, root beer, apple cider, root beer, root beer, ice tea, orange juice, ice tea, apple cider, apple cider, apple cider, apple cider, apple cider, orangejuice, apple cider, ice teaDraw the bar graph for these data.Frequencyх?S716+5+3-2-0000root beerapple ciderice teaorange juiceType of drink
Answers
Hello there. To solve this question, we'll have to construct a bar graph using the data about the drinks ordered by the students.
From 16 students, we know that:
- 4 ordered root beer
- 6 ordered apple cider
- 3 ordered ice tea
- 3 ordered orange juice
The frequency is given by the number of times an option was ordered, therefore we build the following graph:
Factor using the GCF: 7x-19y
Answers
Answer:
1(7x-19y)
Step-by-step explanation:
these are both prime numbers so the gcf is 1
hopes this helps please mark brainliest
Answer: no solution
Step-by-step explanation: 1. Find the gcf for both numbers. The prime factorization for 7x is just 7 * x. The prime factorization for 19y is 19 * y.
2. 7x and 19y have nothing in common, so therefore it's not factorable
In ΔHIJ, the measure of ∠J=90°, the measure of ∠I=62°, and IJ = 86 feet. Find the length of HI to the nearest tenth of a foot.
Answers
To get the angle at H:
The total angle in a triangle = 180
< H = 180 - (90+ 62)
To get the length HI, the hypotenuse
[tex]\cos \text{ 62 = }\frac{86}{x}[/tex][tex]\begin{gathered} x\text{ = }\frac{86}{\cos \text{ 62}} \\ \\ x\text{ = }\frac{86}{0.4695} \\ x\text{ = 183.185 f}eet \end{gathered}[/tex]The length HI = x = 183. 2 Feet to the nearest tenth
I need help to find an surface area! I will include a full photo.
Answers
ANSWER:
99.9 square meters
STEP-BY-STEP EXPLANATION:
We have that the area of a cone is given by the following equation
[tex]A_T=A_L+A_B[/tex]Where the lateral area and the base area are calculated as follows:
[tex]\begin{gathered} A_L=\pi\cdot r\cdot g_{} \\ A_B=\pi\cdot r^2 \end{gathered}[/tex]Replacing in each case, g = 7.6 m and r = 3 m:
[tex]\begin{gathered} A_L=3.14\cdot3\cdot7.6_{}=71.6 \\ A_B=3.14\cdot3^2=28.3 \end{gathered}[/tex]Therefore the surface area would be:
[tex]\begin{gathered} A_T=71.6+28.3 \\ A_T=99.9 \end{gathered}[/tex]f (x) = 2x -1find f (-4)
Answers
f(x)=2x-1
we repleace the x with the number -4
f(-4)=2(-4)-1=-8-1=-9
f(-4)=-9
2.“Lucy”, a 12 year old 16 kg beagle needs a dose of the antibiotic cefazolin IV to treat her infected bite wound. The dose is 22 mg/kg IV. The concentration is 100 mg/ml. How many mgs of cefazolin will you give to “Lucy”? How many mls will you give to “Lucy”?
Answers
To determine the many mls will you give to “Lucy”:
Using a weight measurement by volume conversion
[tex]\text{Volume(ml)}=\frac{\text{mass(kg) x dose(mg/ml)}}{density\text{ (mg/ml)}}[/tex]Mass = 16kg
dose = 22mg/kg
density = 100mg/ml
How many mgs of cefazolin will you give to “Lucy
[tex]\begin{gathered} \text{mass (mg) = 22 mg / kg x 16kg} \\ \text{mass (mg) = 352 mgs} \end{gathered}[/tex]Hence the mass (mgs) of cefazolin given to lucy = 352 mgs
[tex]\begin{gathered} \text{Volume (ml) = }\frac{\text{22 x 16 mg }}{100\text{ mg/ml}} \\ \text{Volume (ml) = }\frac{88}{25}ml \\ \text{Volume = 3.52 ml} \end{gathered}[/tex]Hence the volume (mls) given to lucy = 3.52 ml
i’m a survey 49 peaiple revived a flu vaccine before the flu season and 63 people did not revive the vaccine
Answers
Using the information provided:
Let:
V = Number of people who received the vaccine before the flu
NV = Number of people who didn't receive the vaccine before the flu
F = Number of people who got flu
NF = Number of people who didn't get flue
Write a coordinate rule for the composition
Answers
The coordinate rule for the composition is (x,y) → (y/4, -x/4).
What is coordinate plane rule?
Rules for the coordinate plane are as follows: (x, y) → (x ± h, y ± k) , where h and k are the horizontal and vertical shifts. Recall that h is negative if movement is to the left. K is negative if movement is down.
The coordinate of the vertices of △LMN are L(4,8), M(8, 8), and N(16, 4).
The coordinate of the vertices of △QRS are Q(2,-1), R(2, -2), and S(1, -4).
Assume that the vertices of △LMN is represented by (x, y).
Then the vertices of △QRS can get by (y/4, -x/4).
The coordinate rule for the composition is (x, y) → (y/4, -x/4).
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Write the equation of a line parallel to the given line and passes through points (4, 6), and (-2, -6). Hints find the slope by using the slope formula and then write your equation in slope-intercept form show your work in order to get credit!
Answers
Answer:
y = 2x - 2
Step-by-step explanation:
Equation of a line:
In slope-intercept formula, it is:
y = mx + b
In which m is the slope and b is the y-intercept, which is the value of y when x = 0.
Passes through points (4, 6), and (-2, -6).
We find the equation using these two points.
First we find the slope, which is the change in y divided by the change in x.
Change in y: 6 - (-6) = 6 + 6 = 12.
Change in x: 4 - (-2) = 4 + 2 = 6
Slope: m = 12/6 = 2
So:
y = 2x + b
We select one of these points, two find b.
I will select the point (4,6), which means that when x = 4, y = 6. So
y = 2x + b
6 = 2*4 + b
8 + b = 6
b = 6 - 8
b = -2
So the equation of the line is:
y = 2x - 2
Find the measure of each angle in the proplem RE contains point P
Answers
In the given figure, line LP is lie on the line RE, thus from the linear property
Angle LPR + Angle LPE = 180°
It is given that Angle LPR = 3z, angle LPE = 2z
Angle LPR + Angle LPE = 180°
3z° + 2z° = 180°
5z° = 180°
z = 180/5
z=36
Substitute the value of z = 36 in the angle LPR;
Angle LPR = 3z
= 3(36)
=108°
Angle LPE = 2z
= 2(36)
= 72°
Answer : B) 108 and 72
Determine the equation of the line thatpasses through (0, 2) and (4, 5). Put inslope-intercept form.
Answers
Given:
Point ( 0, 2) and (4, 5)
The coordinates are:
x₁=0 y₁=2 x₂=4 y₂=5
First, we need to find the slope(m) using the formula below:
[tex]\text{slope(m)}=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute the values and evaluate.
[tex]\text{slope(m)}=\frac{5-2}{4-0}=\frac{3}{4}[/tex]Next, is to find the intercept(b) by substituting m=3/4 x=0 and y=2 into y=mx+b and then solve for b.
2 = 3/4 (0) + b
b=2
We can now proceed to form the equation by substituting the values of m and b into y=mx + b.
Hence, the equation of the line is:
[tex]y=\frac{3}{4}x\text{ + 2}[/tex]If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a 7 or 5? (Your answer must be in the form of a reduced fraction.)
Answers
In a deckk of 52 cards there are four 5 and four 7, so the probability to select randomly a 5 or a 7 is:
[tex]\begin{gathered} \text{prob}=\frac{success\text{ cases}}{total\text{ cases}} \\ \text{prob}=\frac{8}{52}=\frac{2}{13} \end{gathered}[/tex]The probability is 2/13
which would it be? …….
Answers
Answer:
A
Step-by-step explanation:
for the relationship to be a function, then each value from the input must map to exactly one unique value in the output.
This is the case here si represents a function.
What is an equation of the line that passes through the points (-1, -6), (6,1)?
Answers
y = x - 5
Explanation:Given:
The points are (-1, -6) and (6, 1)
To find:
the equation of line that pass through the points
To determine the equation of the line, it will be in the form:
[tex]\begin{gathered} y\text{ = mx + b} \\ m\text{ = slope, b = y-intercept} \end{gathered}[/tex]The slope formula is given as:
[tex]$$m\text{ = }\frac{y_2-y_1}{x_2-x_1}$$[/tex][tex]\begin{gathered} x_1=-1,y_1=-6,x_2=6,y_2\text{ = 1} \\ m\text{ = }\frac{1-(-6)}{6-(-1)} \\ m\text{ = }\frac{1+6}{6+1}=\text{ }\frac{7}{7} \\ m\text{ = 1} \end{gathered}[/tex]To get the y-intercept, we will use any of the given points and the slope
[tex]\begin{gathered} Using\text{ point \lparen6, 1\rparen: x = 6, y = 1} \\ y\text{ = mx + b} \\ 1\text{ = 1\lparen6\rparen + b} \\ 1\text{ = 6 + b} \\ 1-6\text{ = b} \\ b\text{ = -5} \end{gathered}[/tex]Next substitute the slope and y-intercept
[tex]\begin{gathered} y\text{ = 1\lparen x\rparen + \lparen-5\rparen} \\ \\ The\text{ equation od the line becomes:} \\ y\text{ = x - 5} \\ \end{gathered}[/tex]describe the transformation of the graph of the parent quadratic function then identify the vertex
Answers
The vertex of a quadratic function can be found by the following expression:
[tex]x=\frac{-b}{2a}[/tex]When we add a number to the argument of the function, "x", we shift the function left or right. If the number is positive the shift happens to the left, if is negative the shift happens to the right.
When we add a number to the whole function we shift the function up or down. If the number is positive the shift is on the upwards direction and if it is negative the shift is on the downwards direction.
When we multiply a function we are stretching or compressing it. If the number is greater than 1, we are compressing the function and if its smaller than 1 we are stretching i.
With this in mind we can find which transformations happened in each option. The original function is:
[tex]f(x)=x^2[/tex]27.
[tex]f(x)=3(x+2)^2+1[/tex]There is a number 3 multiplying the function, so it got compressed by a factor of three. There is a number 2 adding to the variable, so it got shifted left by 2. There is a number 1 adding the whole function, so it got moved upwards by 1.
The vertex of the original function is at (0,0). The function moved upwards by 1 this happens on the y-axis and left by 2 this happens on the x-axis, so the new vertex is (-2,1).
28.
[tex]f(x)=-4(x+1)^2-5[/tex]There is a negaive number, "-4", multiplying the function, so it got compressed by a factor of four and it also got inverted, because the number is negative. There is a number "1" adding the variable, so it got moved one unit to the left. There is a number "-5" adding the whole function, so it got moved five units down.
Since the function moved one unit to the left, changing the x-coordinate for the vertex by "-1" and it also moved five units down, changing the y-coordinate for the vertex by "-5", the new vertex is (-1, -5).
29.
[tex]f(x)=-2x^2+5[/tex]There is a negative number multiplying the function, so it got compressed by a factor of 2 and inverted. There is also a constant adding to the function, so it got moved up by 5 units.
Since the function didn't moved in the x-axis, but got up 5 units on the y-axis the new vertex is (0,5).
30.
[tex]f(x)=\frac{1}{2}(x-1)^2[/tex]There is a number "1/2" multiplying the function, since it is lower than 1, the function got stretched by a factor of 2. There is a constant adding "-1" to the variable, therefore the function got moved to the right by one unit.
Since the function moved 1 unit to the right the new vertex is (1,0).
Solve for x. x + 58 , x + 128
Answers
given angels are x+58 and x+128.
The sum of the angles in the straight line is 180 degree.
thus,
[tex]\begin{gathered} x+58+x+128=180 \\ 2x+186=180 \\ 2x=180-186 \\ 2x=-6 \\ x=-\frac{6}{2} \\ x=-3 \end{gathered}[/tex]subsitute x =-3 in the equations,
[tex]\begin{gathered} =x+58 \\ =-3+58 \\ =55^{\circ} \end{gathered}[/tex]Also,
[tex]\begin{gathered} =x+128 \\ =-3+128 \\ =125^{\circ} \end{gathered}[/tex]thus, the angles are 55 and 125 degrees.
find an equation for the line that passes through the points (-1,5) and (-5,1)
Answers
Answer:
x-y=-6
Explanation:
Given the points (-1,5) and (-5,1):
To find the equation of the line, we use the two-point formula:
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)=(-1,5) \\ \mleft(x_2,y_2\mright)=\mleft(-5,1\mright?) \end{gathered}[/tex]Substitute these points into the formula:
[tex]\frac{y-5}{x-(-1)}=\frac{1-5}{-5_{}-(-1)}[/tex]Then simplify:
[tex]\begin{gathered} \frac{y-5}{x+1}=\frac{1-5}{-5_{}+1} \\ \frac{y-5}{x+1}=\frac{-4}{-4} \\ \frac{y-5}{x+1}=1 \\ y-5=x+1 \\ -5-1=x-y \\ x-y=-6 \end{gathered}[/tex]The equation of the line is:
[tex]x-y=-6[/tex]Jason owns a small business selling bagels. He knows that in the last week 45
customers paid cash,
8 customers used a debit card, and 6 customers used a credit a
card.
Based on these results, express the probability that the next customer will pay with a
credit card as a decimal to the nearest hundredth.
Answers
The probability that the next customer will pay with a credit card is given by 0.10 approximately.
Given that 8 customers used a debit card and 6 customers used a credit card and 45 customers paid cash.
So the total number of customers = 6+8+45 = 59
The number of customers paid in credit card = 6
Hence the probability that the next customer will pay with a credit card = 6/59 = 0.10 (approximately)
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Express tante in terms of sec e for ein Quadrant I.
Answers
Explanation:
We would be applying the trigonometry identity that shows thr=e relationship between tanθ and secθ:
[tex]\sec ^2\theta=tan^2\theta\text{ + 1}[/tex]we make tanθ the subject of formula:
[tex]\begin{gathered} \text{subtract 1 from both sides:} \\ \sec ^2\theta-1=tan^2\theta\text{ + 1}-1 \\ \sec ^2\theta-1=tan^2\theta\text{ } \\ \text{square root both sides:} \\ \sqrt[]{\sec ^2\theta-1)}\text{ =}\sqrt[]{tan^2\theta\text{ }} \end{gathered}[/tex]Find the circumference of this circleusing 3 for T.C ~ [?]88C = id
Answers
We have that d = 8, using the formula:
[tex]C=\pi d[/tex]Where π = 3, then
[tex]\begin{gathered} C=\pi d \\ \\ C=3\cdot8 \\ \\ C=24 \end{gathered}[/tex]Then the circumference is 24
[tex]C=24[/tex]