Answer:
(x - 5)(x - 3)
Step-by-step explanation:
You need two numbers that multiply to 15 and add to 8. There aren't many numbers that will do that.
15 and 1 is one pair of numbers. They multiply to 15 but don't add to 8.
6 and 2 add to 8 but don't multiply to 15.
5 and 3. This in some form is your answer, but handle it carefully.
(x - 5)(x - 3)
The 5 and 3 both have to be minus.
Answer:
(x-3)(x-5)
Step-by-step explanation:
The expression is:
x2 - 8x+15
Break the middle term:
Coefficient of first term will be multiplied by constant
1*15 = 15
Now we have to find out which numbers will be multiplied to get 15
and also by adding those numbers we get the middle term:
3*5=15
3+5 = 8
Now break the middle term:
x^2-3x-5x+15
x(x-3)-5(x-3)
(x-5)(x-3)....
The factors are (x-5)(x-3)....
Which of the following is a polynomial?
O A. x2-1
O B. -2
O c. 1 +2
OD.
a woman bought some large frames for $13 each and some small frames for $9 each at a closeout sale if she bought 21 frames for $209 fine how many of each type she bought.
Answer:
5 large frames
16 small frames
Step-by-step explanation:
$13 times 5 large frames = $65
$9 times 16 small frames = $144
144+65=209
For Sophia's graduation party, several tables of the same width will be arranged end to end to form a serving table with a
total area of 75 ft. The total length of the tables will be two more than three times the width. Find the length and width of
the serving table so that Sophia can purchase the correct table cloth. Round your answers to the nearest tenth.
Area: 75 ft
Bw + 2
Answer:
Width=4.7 ft
Length=16.1 ft
Step-by-step explanation:
Let the width of the table to be x ft
Then the length should be two more than three times the width= 2+3x ft
The area of the serving table should be 75 ft²
But you know the area of this table is calculated by multiplying the length by the width of the table
Hence, Area= length× width
Length=x ft and width =2+3x ft
75ft²= (x ft) × (2+3x ft)
[tex]75=x*(2+3x)\\\\75=2x+3x^2\\\\3x^2+2x-75=0[/tex]
Apply the quadratic formula to solve this quadratic equation
The formula is ;
x= (-b ±√b²-4ac)÷2ac
where a=3, b=2 and c=-75
x= (-2 ± √2²-4×3×-75)÷(2×3)
x=(-2±√4+900)÷6
x=(-2±√904)÷6
x=(-2±30.1)÷6
x=(-2+30.1)÷6=4.683⇒4.7(nearest tenth)
or
x=(-2-30.1)÷6= -32.1÷6=-5.35⇒ -5.4
Taking the positive value
x=width =4.7 ft
2+3x= length= 2+3(4.7)=16.1 ft
Which is the graph of linear inequality 2 y > x – 2?
Answer:
Third graph
Step-by-step explanation:
We are determine whether which of the given graphs is that of the linear inequality [tex]2y>x-2[/tex].
We know that, on the graph the greater than sign ([tex]>[/tex]) represents the shaded part above the line and less than sign ([tex]<[/tex]) represents the shaded region below the line.
While the signs [tex]\leq[/tex] or [tex]\geq[/tex] is denoted by a solid line on the graph.
Therefore, the third graph represents the given inequality.
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
2y > x-2
The solution of this inequality is the shaded area above the dotted line 2y=x-2
The graph in the attached figure
Students observing a caterpillar crawl on a tree noticed that the caterpillar crawled upwards 38 of an inch every minute. The caterpillar was already 4.5 feet off the ground when the students began observing.
Which function represents the total number of inches the caterpillar crawls after x minutes?
f(x) = 4.5x + 3/8
f(x) = 54x + 3/8
f(x( = 3/8x + 54
f(x) = 3/8x + 4.5
Answer:
f(x) = 4.5x + 3/8
Answer: Third Option
[tex]f(x) = \frac{3}{8}x + 54[/tex]
Step-by-step explanation:
We want to propose an equation that models the distance traveled by the caterpillar as a function of time, we have a constant initial quantity of 4.5 feet and then we know that every minute the caterpillar advances 3/8 of an inch
Then the distance that the caterpillar to advanced after x minutes is:
[tex]f(x) = \frac{3}{8}x[/tex]
Then we know that initially the caterpillar was at a distance of 4.5 feet or 54 inch
Then the equation for the distance in inch is:
[tex]f(x) = \frac{3}{8}x + 54[/tex]
Find the mean of the data set that consists of 3, 11, 4, 3, 10, 6, 4, 5.
A. 3 and 4
B. 4.5
C. 5.75
D. 5.25
Answer:
5.75
Step-by-step explanation:
[tex]3 + 11 + 4 + 3 + 10 + 6 + 4 + 5 = 46 \\ 46 \div 8 = 5.75[/tex]
The total amount of numbers are : 8
To find the mean, we calculate the sum of all values and divide that sum by the amount of numbers there are.
PLEASE DO MARK ME AS BRAINLIEST IF MY ANSWER IS HELPFUL :)
A triangle has two sides of lengths 10 and 14. What value could the third side be?
Answer:B, C, D, E.
Step-by-step explanation:
The third side of a triangle with two sides measuring 10 and 14 units must be greater than 4 and less than 24 units. This is determined using the Triangle Inequality Theorem.
The possible values for the third side of a triangle with sides of lengths 10 and 14 can be found using the Triangle Inequality Theorem.
Add the two given side lengths: 10 + 14 = 24.
To find the range of possible values for the third side, subtract the two given side lengths from the total: 24 - 10 = 14, and 24 - 14 = 10.
Therefore, the third side of the triangle must have a length greater than 4 but less than 24.
What is the solution to the equation below?
log 20х3 - 2logx = 4
x=25
x=50
x=250
x=500
Answer:
x = 500.
Step-by-step explanation:
log20x^3 - 2logx = 4
By the laws of logs:
log20x^3 - logx^2 = 4
log(20x^3 / x^2) = 4
20x^3 / x^2 = 10^4
20x = 10,000
x = 10,000 / 20
x = 500.
The solution of the given logarithmic equation is x = 500.
What is a logarithmic equation?Any equation in the variable x that contains a logarithm is called a logarithmic equation.
Given logarithmic equation
[tex]log20x^{3} -2logx=4[/tex]
Using [tex]mloga=loga^{m}[/tex]
[tex]log20x^{3} -logx^{2}=4[/tex]
Using [tex]loga-logb=log(\frac{a}{b})[/tex]
[tex]\frac{log20x^{3} }{x^{2} }=4[/tex]
[tex]log20x=4[/tex]
[tex]20x=10^{4}[/tex]
[tex]x=\frac{10000}{20}[/tex]
[tex]x=500[/tex]
The solution of the given logarithmic equation is x = 500.
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A car travelled a distance of D = 199 km (kilometers) for T = 4.3 hours at a constant rate. Use the formula
D=R.T
to find the speed (R) of the car in km per hour. Round your answer to the nearest tenth. Do not include the units in
your answer.
Answer:
i will answer this in 5 mins
Step-by-step explanation:
PLEASE ANYONE I NEED YOUR HELP. For the points A(-2, 10) and B(-4,6). Find each of the following.
a. AB
b. The coordinates of the midpoint of AB
c. The slope of AB
Answer:
a. _ √20 , about 4.472136
b - (-3, 8)
c- Slope of 2
Step-by-step explanation:
Calculator
Answer:
a. [tex]AB=2\sqrt{5}[/tex]
b. [tex](-3,8)[/tex]
c. [tex]2[/tex]
Step-by-step explanation:
You have the points:
A(-2,10)
where i will call: [tex]x_{1}=-2[/tex] and [tex]y_{1}=10[/tex]
B(-4,6)
where i will call: [tex]x_{2}=-4[/tex] and [tex]y_{2}=6[/tex]
for our calculations we are going to need the distance in x between the points ([tex]\Delta x[/tex] )and the distance in y between the points ([tex]\Delta y[/tex]):
[tex]\Delta x =|x_{2}-x_{1}|=|-4-(-2)|=|-4+2|=|-2|=2\\\Delta y =|y_{2}-y_{1}|=|6-10|=|-4|=4[/tex]
a. To find AB (the distance between point A and point B) you need The Pythagorean Theorem:
[tex](AB)^2=(\Delta x)^2+(\Delta y)^2\\(AB)^2=(2)^2+(4)^2\\(AB)^2=4+16\\\\AB=\sqrt{20}\\ AB=2\sqrt{5}[/tex]
b. to find the coordinates of the midpoint we average the x-coordinates and the y coordinates
[tex]x_{mid}=\frac{x_{1}+x_{2}}{2} =\frac{-2-4}{2}=\frac{-6}{2} =-3\\y_{mid}=\frac{y_{1}+y_{2}}{2} =\frac{10+6}{2}=\frac{16}{2} =8\\[/tex]
so the midpoint [tex](x_{mid},y_{mid})[/tex] is at: [tex](-3,8)[/tex]
c. For the slope we use the slope formula:
[tex]slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{6-10}{-4-(-2)}=\frac{-4}{-2}=2[/tex]
The slope is equal to 2.
The fuel consumption in miles per gallon for a car varies inversely with its weight. Suppose a car that weighs 2800 pounds get 33 miles per gallon on the highway. Write the equation that relates y, the fuel consumption in miles per gallon, to the car's weight, w pounds.
Answer:
y=0.01179/w
Step-by-step explanation:
First understand that the fuel consumption in miles per gallon is inversely proportional to the weight of a car.
If y is the fuel consumption in miles per gallon and w is weight of car in pounds . you can write the first statement as;
y∝1/w
Introduce a constant value for proportionality, k
y=k/w....................make k subject of the formula by multiplying both sides by 1/w
k=y/w
Given in the question that ;
w=2800
y=33
k=?
To find k , apply the formula that you derived above
k=y/w
k=33/2800 =0.011785⇒0.01178(4 significant figures)
Rewrite the formula as
y=k/w ⇒ y=0.01179/w
The equation that relates y and w is;
y=0.01179/w
The fuel consumption in miles per gallon for a car varies inversely with its weight and can be represented mathematically by the inverse proportionality relationship y = k/w. Substituting the given values gives us the constant k = 92400, so the final equation is y = 92400/w.
Explanation:This problem can be defined mathematically by an inverse proportionality relationship, expressed as y = k/w, where k is a constant, y is the fuel consumption in miles per gallon, and w is the weight of the car in pounds.
To find the value of k, we can substitute the given values into the equation. This gives us 33 = k/2800, which simplifies to k = 33 * 2800, or k = 92400.
So, the equation that relates the mileage per gallon, y, to the weight of the car, w, is y = 92400/w. This means the fuel efficiency of a car decreases as its weight increases, thus heavier cars tend to have lower miles per gallon.
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A: What are the solutions to the quadratic equation?
B: which statements accurately interpret the solution?
Answer:
A. x = -1 or x = 3B. firstStep-by-step explanation:
[tex]x^2-2x-3=0\\\\x^2+x-3x-3=0\\\\x(x+1)-3(x+1)=0\\\\(x+1)(x-3)=0\iff x+1=0\ \vee\ x-3=0\\\\x+1=0\qquad\text{subtract 1 from both sides}\\x=-1\\\\x-3=0\qquad\text{add 3 to both sides}\\x=3[/tex]
Write the expression in complete factored form. 2n^2(q+8)-(q+8)=
(q+8)(2n^2-1)
I think this is the correct form.
Express each ratio as a fraction in lowest terms.
1) 77 to 490
2) 35 to 135
3) 65:1001
Using the information given, determine the answer:
Circumference of a circle with area 36π square centimeters
Answer:
12π
Step-by-step explanation:
The area of a circle is π*r^2, where r is the radius. Therefore, given that the area is π*36, the radius is 6.
The circumference of a circle is 2πr, which in this case is 2*6*π=12π.
The area of the triangle is given by the functions area of triangle A:x2 + x area of triangle B: x2 - 3x which functions represents the sum of the areas of the two triangles? 1. 4x 2.-4x 3.x2-4x 4.2x2-2x
Answer:
4. 2x^2 - 2x.
Step-by-step explanation:
Adding the 2 functions:
Area of the 2 triangles = x^2 + x + x^2 - 3x
= .2x^2 - 2x
Answer:
OPTION 4
Step-by-step explanation:
Let be f(x) the function that represents the area of Triangle A:
[tex]f(x)=x^2 + x[/tex]
Let be g(x) the function that represents the area of Triangle B:
[tex]g(x)=x^2 - 3x[/tex]
Then, you need to add the area of Triangle A and the area of Triangle B in order to find the sum of the areas (Let be h(x) the function that represents the sum of the the areas of triangles A and B):
Therefore, this is:
[tex]h(x)=(x^2 + x)+(x^2 - 3x)=x^2 + x+x^2 - 3x=2x^2-2x[/tex]
You can notice that this matches with the option 4.
When Θ = 5 pi over 6, what are the reference angle and the sign values for sine, cosine, and tangent? Θ' = negative pi over 6; sine and cosine are positive, tangent is negative. Θ' = 5 pi over 6; sine and tangent are positive, cosine is negative Θ' = pi over 6; sine is positive, cosine and tangent are negative Θ' = negative 5 pi over 6; sine is positive, cosine and tangent are negative
Answer:
Option C is correct.
Step-by-step explanation:
[tex]\theta=\frac{5\pi }{6}[/tex]
We need to find reference angle and signs of sinФ, cosФ and tanФ
We know that [tex]\theta=\frac{5\pi }{6}radians[/tex] is equal to 150°
and 150° is in 2nd quadrant.
So, Ф is in 2nd quadrant.
And In 2nd quadrant sine is positive, while cos and tan are negative
The reference angle Ф' is found by: π - Ф
=> Ф = 5π/6
so, Reference angle Ф' = π - 5π/6
Ф' = 6π - 5π/6
Ф' = π/6
So, Option C Θ' = pi over 6; sine is positive, cosine and tangent are negative is correct.
Help please the graphs below Have the same shape. What is the equation of the blue graph
Answer:
D. G(x) = (x+2)^2
Step-by-step explanation:
We can easily solve this problem by graphing each case with a graphing calculator or any plotting tool.
The equations are
A. G(x) = (x-2)^2
B. G(x) = (x)^2 + 2
C. G(x) = (x)^2 -2
D. G(x) = (x+2)^2
Se attached image.
The correct option is
D. G(x) = (x+2)^2
Answer:
C. G(x)=x²-2
Step-by-step explanation:
The midpoint of the graph has been displaced from x=0 to x=-2. this is a negative displacement.
Therefore the new equation G(x)=x²-2
This is because there is no tilt in the graph so it is a replica of the red graph.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Check all that apply.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
Answer:
[tex]-6x+15< 10-5x[/tex]
Step-by-step explanation:
we have
[tex]-3(2x-5) < 5(2-x)[/tex]
solve for x
eliminate the parenthesis (apply the distributive property)
[tex]-3*2x+3*5 < 5*2-5*x[/tex]
[tex]-6x+15< 10-5x[/tex] ---> correct representation of the inequality
Adds (5x-15) both sides
[tex]-6x+15+5x-15< 10-5x+5x-15[/tex]
[tex]-x< -5[/tex]
Multiply by -1 both sides
[tex]x>5[/tex]
Which is the best estimate of the circumference of this circle?
Answer:
12 is the best estimate
Answer:
option A.
Step-by-step explanation:
We have to find the circumference of the given circle with radius 2 units.
Since formula to calculate circumference of a circle is = 2πr
Where r = radius of the circle.
Circumference = 2 × (3.14) × (2)
= 4 × 3.14
= 12.56
So approximate value will be option A.
What are the zeros of Ax) = x2 - 12x + 36?
O A. x= -6 and x = 6
O B. x=-6 only
O c. x = 6 only
O D. x=-4 and x = 9
SUBMIT
Answer:
The correct option is C
Step-by-step explanation:
x2 - 12x + 36
The coefficient of 1st term will be multiplied by the constant:
1*36 = 36
Now find two numbers whose product is 36 and whose addition is 12.
6*6 = 36
6+6 =12
Now break the middle term:
x^2-6x-6x+36 = 0
Now group the terms:
(x^2-6x) - (6x-36) = 0
Now take common of each group:
x(x-6)-6(x-6) = 0
(x-6) (x-6) =0
(x-6)=0 , (x-6) =0
x-6=0 , x-6=0
x=0+6 , x=0+6
x=6 , x=6
Thus the correct option is C. x=6 only....
What is the value of sin n
The value of sin n depends on the angle n and represents the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle.
Explanation:The value of sin n depends on the angle n. In mathematics, sine is a trigonometric function that represents the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle. It is a periodic function that oscillates between -1 and 1 as the angle increases or decreases.
For example, if n is 0 degrees, then sin n is 0. If n is 90 degrees, then sin n is 1. If n is 180 degrees, then sin n is 0 again. The values of sin n for angles in between can be determined using a calculator or trigonometric tables.
It's important to note that in mathematics, the angle n is typically measured in radians rather than degrees. In radians, a full circle is equal to 2π, so an angle of 360 degrees is equal to 2π radians.
which of the following is equal to the fraction below? (4/5)^6
Answer:
Step-by-step explanation:
Next time, please share the answer choices.
(4/5)^6 is equivalent to:
4^6 4096
---------- = -----------
5^6 15625
Answer:
4^6/5^6
Step-by-step explanation:
what is the mean between 500, 372,536, 369, 328, 412 & 561
Answer:
439.7.
Step-by-step explanation:
The mean of these number is
(500+372+536+ 328 +369+412+561) / 7
=439.7.
Final answer:
To determine the mean of the numbers 500, 372, 536, 369, 328, 412, and 561, you add them together and divide by the total count, which results in a mean of approximately 439.71.
Explanation:
To find the mean of a set of numbers, you add up all the numbers and then divide by the number of values in the set. The numbers given are 500, 372, 536, 369, 328, 412, and 561. Let's calculate the mean step by step:
Add up all the numbers: 500 + 372 + 536 + 369 + 328 + 412 + 561 = 3078.Count the number of values: There are 7 numbers in total.Divide the total sum by the number of values: 3078 ÷ 7 = 439.7142857.The mean (average) of the numbers is approximately 439.71.
The table shows the number of degrees the temperature increased or decreased over four days. On which day did the temperature change have the greatest magnitude?
Consider the polynomial p(x)=x^3-9x^2+18x-25, which can be rewritten as p(x)=(x-7)(x^2-2x+4)+3. The number blank is the remainder when p(x) is divided by x-7, and so x-7 blank a factor of p(x). Fill in the two blanks with is, 3, 7,is not, or 0!!!!
PLEASE HELP. WILL MARK BRAINLIEST!!
Answer:
[tex]\boxed{\text{3; is not}}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rcl}p(x) & = & (x - 7)(x^{2} - 2x + 4) + 3\\\\\dfrac{p(x)}{x - 7} & = &x^{2} - 2x + 4 + \dfrac{3 }{x-7 }\\\\\end{array}\\\\\text{The number }\boxed{\mathbf{3}}\text{ is the remainder when $p(x)$ is divided by $(x - 7)$,}\\\\\text{so $(x - 7)$ }\boxed{\textbf{is not}} \text{ a factor of $p(x)$.}[/tex]
A basket contains six apples and four peaches. You randomly select one piece of fruit and eat it. Then you randomly select another piece of fruit. The first piece of fruit is an apple and the second piece is a peach. Find the probability of this occuring.
Answer as a fraction: 4/15
Answer as a decimal: 0.267
The decimal version is approximate rounded to three decimal places.
=============================================================
Explanation:
6 apples, 4 peaches
6+4 = 10 pieces of fruit total
The probability of picking an apple is 6/10 = 3/5
After you pick and eat the apple, there are 10-1 = 9 pieces of fruit left. Also, the probability of picking a peach is 4/9, as there are 4 peaches out of 9 fruit left over.
Multiply out 3/5 and 4/9 to get (3/5)*(4/9) = (3*4)/(5*9) = 12/45 = 4/15
Using a calculator, 4/15 = 0.267 approximately.
Answer:
Fraction: [tex]\frac{4}{15}[/tex]
Decimal: [tex]0.2667[/tex]
Percent: 26.67%
Step-by-step explanation:
If the basket contains six apples and four peaches then the Total amount of fruit in the basket is (6+4) 10 pieces of fruit.
You reach in and randomly pick out an apple. Since there are only 4 apples, the probability of this happening was [tex]\frac{4}{10}[/tex] , and now there are only 9 pieces of fruit in the basket.
Now you reach in and randomly pick out a peach. Since there are 6 peaches, the probability of this happening is [tex]\frac{6}{9}[/tex]. Now we can find the probability of both of these things happening one after another by multiplying both probabilities together
[tex]\frac{4}{10} * \frac{6}{9} = \frac{24}{90}[/tex]
[tex]\frac{24}{90} = \frac{4}{15}[/tex] ...... simplified
So we can see that the probability of you picking out an apple and a peach in sequence is [tex]\frac{4}{15}[/tex] or [tex]0.2667[/tex]
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
A recipe for muffins calls for 1/2 quart of buttermilk, 1/3 quart of skim milk, and 1/16 quart of oil. How many total quarts of liquid ingredients does the recipe call for?
To find the total quarts of liquid ingredients for the muffin recipe, add together 1/2 quart of buttermilk, 1/3 quart of skim milk, and 1/16 quart of oil, resulting in 43/48 quarts in total after converting to a common denominator and summing up.
The question asks how many total quarts of liquid ingredients are called for in a muffin recipe, which includes 1/2 quart of buttermilk, 1/3 quart of skim milk, and 1/16 quart of oil. To find the total, you need to add these measurements together.
Adding the fractions:
1/2 quart of buttermilk1/3 quart of skim milk1/16 quart of oilFirst, find a common denominator, which would be 48 in this case. Converting each fraction:
24/48 (for 1/2 quart)16/48 (for 1/3 quart)3/48 (for 1/16 quart)Adding these fractions together gives us 43/48 quarts as the total amount of liquid ingredients needed for the recipe.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each exponential equation to its percent rate of change.
Answer:
60% growth, 40% decay, 20% decay, 80% decay, 40% growth. In that order :)
Step-by-step explanation:
The number inside the parenthesis is always 1+a number. So for every .1 up or down, that's 10% growth or decay(up being growth, down being decay).
Answer:
Step-by-step explanation:
A). In exponential equation [tex]80(1.6)^{t}=20[/tex], 1.6 is the common ratio which represents [(1 + 60% of 1) = 1.6] a growth of 60%.
B). In [tex]20(0.6)^{t}=1.2[/tex] common ratio is 0.6 [(1 - 40% of 1)] which represents 40% decay.
C). In [tex]60(0.8)^{t}=1.4[/tex] common ratio is 0.8 [(1 - 20% of 1)] which represents 20% decay.
D). In [tex]40(0.2)^{t}=1.6[/tex] common ratio is 0.2 [(1 - 80% of 1)] which represents 80% decay.
E). In [tex]1.2(1.4)^{t}=80[/tex] common ratio is 1.4 [(1 + 40% of 1)] which represents 40% growth.
5
6. 1-7x + 4) = 18
7. 5 p + 10 = 10
Answer:
[tex]\large\boxed{6.\ x=-\dfrac{12}{7}}\\\boxed{7.\ p=0}[/tex]
Step-by-step explanation:
[tex]6.\\\\1-7x+4=18\\(1+4)-7x=18\\5-7x=18\qquad\text{subtract 5 from both sides}\\-7x=12\qquad\text{divide both sides by (-7)}\\x=-\dfrac{12}{7}\\\\7.\\\\5p+10=10\qquad\text{subtract 10 from both sides}\\5p=0\qquad\text{divide both sides by 5}\\p=0[/tex]