4y + 9 = - 4y - 7. Please explain to me how to do it.

The domain of the heart rate function h(t) for a runner who completed a 10-mile run in 112 minutes is [0, 112] in interval notation.

In this scenario, the domain of the function h(t) is the time duration during which the runner is running. Thus, since the runner completed the 10-mile run in 112 minutes, the domain is from 0 (the start of the run) to 112 (the end of the run). We represent this in interval notation as [0, 112]. The square brackets indicate that the endpoints are included in the domain. So, the domain of the function h(t) in this context is [0, 112].

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Answer:

[tex]a \: \: x = \frac{ -1 ± i\sqrt{139}}{14} [/tex]

Explanation:

Since this is unfactorable, use the Quadratic Formula:

[tex]x = -b ± \frac{ \sqrt{ {b}^{2} - 4ac}}{2a} [/tex]

Now, take the information and input it:

[tex] -1 ± \frac{ \sqrt{1 - 4(7)(5)}}{2(7)} \\ \\ -1 ± \frac{ \sqrt{ -139}}{ 14} = \frac{-1 ± i\sqrt{139}}{14} [/tex]

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Answer:

Option 3 - five to the two thirds power

Step-by-step explanation:

Given : Expression 'the square root of 5 times the cube root of 5'.

To find : Simplify the expression ?

Solution :

Writing expression in numeric form,

The cube root of 5 means [tex]\sqrt[3]{5}[/tex]

The square root of 5 times the cube root of 5 means [tex]\sqrt{5\sqrt[3]{5}}[/tex]

Now, simplify the expression

[tex]\sqrt{5\sqrt[3]{5}}=\sqrt{5\times (5)^{\frac{1}{3}}}[/tex]

[tex]\sqrt{5\sqrt[3]{5}}=\sqrt{(5)^{1+\frac{1}{3}}}[/tex]

[tex]\sqrt{5\sqrt[3]{5}}=\sqrt{(5)^{\frac{4}{3}}}[/tex]

[tex]\sqrt{5\sqrt[3]{5}}=((5)^{\frac{4}{3}})^{\frac{1}{2}}[/tex]

[tex]\sqrt{5\sqrt[3]{5}}=(5)^{\frac{4}{3}\times \frac{1}{2}}[/tex]

[tex]\sqrt{5\sqrt[3]{5}}=(5)^{\frac{2}{3}}[/tex]

The expression is five to the two thirds power.

Therefore, Option 3 is correct.

The correct option is d. To simplify [tex]\(\sqrt{5} \cdot \sqrt[3]{5}\)[/tex], we get [tex]\(5^{5/6}\)[/tex]. Therefore, the correct answer is five to the seven sixths power.

To simplify [tex]\( \sqrt{5} \times \sqrt[3]{5} \)[/tex], we combine the radicals:

[tex]\[ \sqrt{5} \times \sqrt[3]{5} = 5^{1/2} \times 5^{1/3} \][/tex]

Using the property of exponents [tex]\( a^m \times a^n = a^{m+n} \)[/tex]:

[tex]\[ 5^{1/2} \times 5^{1/3} = 5^{1/2 + 1/3} \][/tex]

Now, find a common denominator for the exponents:

[tex]\[ \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \][/tex]

Therefore,

[tex]\[ 5^{1/2} \times 5^{1/3} = 5^{5/6} \][/tex]

So, the simplified expression is [tex]\( {5^{5/6}} \).[/tex]

This corresponds to option (d) in your choices: five to the seven sixths power.

The complete question is- Simplify the square root of 5 times the cube root of 5.

a. five to the five sixths power

b. five to the one sixth power

c. five to the two thirds power

d. five to the seven sixths power

Answer:

Step-by-step explanation:

Maybe if we defined a non terminating fraction first, a terminating one would make more sense to you.

non terminating means that it goes on forever.

1/3 = 0.3333333333333333333333333333333....333333333333333333...333

I/3 never really ends.

1/8 on the other hand had

1/8 = 0.125 as a value and that's all there is. We're done.

So a terminating decimal ends.

Answer:

y

Step-by-step explanation:

Anderson was unable to capitalize on her invention, and other companies were able to profit from her invention without paying her.

The sequence of events that explains why Anderson did not make any money from her patent is as follows:

The image of Mary Anderson and the First Windshield Wipers confirms this sequence of events. The image shows Anderson with a model of her windshield wiper invention. The text below the image states that Anderson "failed to sell her patent to any manufacturer" and that "her patent expired in 1920 without her making any money from her invention."

In addition to the information in the image, we can also infer that Anderson did not make any money from her patent because she did not have the business acumen or resources to bring her invention to market. She was a single woman with no business experience. She also did not have the financial resources to manufacture and market her invention on her own.

Answer:

-3.6

Step-by-step explanation:

Since 32.5 is greater than 28.9, you just subtract 32.5 from 28.9 then add an equal sign. 32.5-28.9=3.6. With the negative, it would be -3.6

The value obtained by making the subtraction operation is -3.6

To perform the subtraction operation, the right hand side value is taken away from left hand side value .

Here , we have;

We obtained a negative value because the right hand value is greater than the left hand value.

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Answer:

=9

Step-by-step explanation:

7−(−2)

=7−(−2)

=7+2

=9

Answer:

1½

Step-by-step explanation:

[tex] \frac{1}{8}(12) = \frac{12}{8} = 1 \frac{4}{8} = 1 \frac{1}{2} [/tex]

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Answer: A. 0.01426

Step-by-step explanation:

divide the mass value by 100000

Answer:

A. 0.01426

Step-by-step explanation:

divide by 10000

The value of sec(θ) given [tex]\tan^2(\theta) = \frac{3}{8}[/tex] is [tex]\frac{\sqrt{22}}{4}[/tex]. Using the identity [tex]\tan^2(\theta) + 1 = \sec^2(\theta)[/tex], we find [tex]\sec(\theta) = \frac{\sqrt{22}}{4}[/tex].

To find the value of sec(θ) given that [tex]\tan^2(\theta) = \frac{3}{8}[/tex], we'll use the trigonometric identity:

[tex]\[ \tan^2(\theta) + 1 = \sec^2(\theta) \][/tex]

Given that [tex]\(\tan^2(\theta) = \frac{3}{8}\)[/tex], we can plug this into the identity:

[tex]\[ \frac{3}{8} + 1 = \sec^2(\theta) \][/tex]

[tex]\[ \frac{3}{8} + \frac{8}{8} = \sec^2(\theta) \][/tex]

[tex]\[ \frac{11}{8} = \sec^2(\theta) \][/tex]

To find [tex]\(\sec(\theta)\)[/tex], we take the square root of both sides, but since sec(θ) is always positive, we'll take the positive square root:

[tex]\[ \sec(\theta) = \sqrt{\frac{11}{8}} \][/tex]

[tex]\[ \sec(\theta) = \sqrt{\frac{11}{8}} \times \frac{\sqrt{8}}{\sqrt{8}} \][/tex]

[tex]\[ \sec(\theta) = \sqrt{\frac{88}{64}} \][/tex]

[tex]\[ \sec(\theta) = \frac{\sqrt{88}}{\sqrt{64}} \][/tex]

[tex]\[ \sec(\theta) = \frac{\sqrt{88}}{8} \][/tex]

[tex]\[ \sec(\theta) = \frac{2\sqrt{22}}{8} \][/tex]

[tex]\[ \sec(\theta) = \frac{\sqrt{22}}{4} \][/tex]

So, the value of [tex]\(\sec(\theta)\)[/tex] given [tex]\(\tan^2(\theta) = \frac{3}{8}\)[/tex]is [tex]\(\frac{\sqrt{22}}{4}\)[/tex].

Complete Question:

Given that tan²(θ) = 3/8, what is the value of sec(θ)?

The value of sec(θ) given that tan²(θ) = 3/8 is (1/4)√22.

To find the value of sec(θ) given that tan²(θ) = 3/8, we first need to recall the relationship between tangent (tan) and secant (sec) functions.

The relationship is as follows:

[tex]\[ \tan^2(\theta) + 1 = \sec^2(\theta) \][/tex]

Given that [tex]\( \tan^2(\theta) = \frac{3}{8} \),[/tex] we can substitute this value into the equation above:

[tex]\[ \left(\frac{3}{8}\right) + 1 = \sec^2(\theta) \][/tex]

Now, let's simplify the expression:

[tex]\[ \frac{3}{8} + 1 = \frac{3}{8} + \frac{8}{8} = \frac{3 + 8}{8} = \frac{11}{8} \][/tex]

So, [tex]\( \sec^2(\theta) = \frac{11}{8} \).[/tex]

Now, to find the value of sec(θ), we take the square root of both sides:

[tex]\[ \sec(\theta) = \sqrt{\frac{11}{8}} \][/tex]

To rationalize the denominator, we multiply both the numerator and the denominator by [tex]\( \sqrt{8} \):[/tex]

[tex]\[ \sec(\theta) = \frac{\sqrt{11 \times 8}}{\sqrt{8 \times 8}} = \frac{\sqrt{88}}{8} \][/tex]

Now, we can simplify the expression under the square root:

[tex]\[ \sqrt{88} = \sqrt{4 \times 22} = 2 \sqrt{22} \][/tex]

So, the final expression for sec(θ) is:

[tex]\[ \sec(\theta) = \frac{2 \sqrt{22}}{8} \][/tex]

And if we simplify it further, we get:

[tex]\[ \sec(\theta) = \frac{\sqrt{22}}{4} \][/tex]

This is the final answer for the value of sec(θ) in terms of the given information.

The Complete Question:

Given that tan²(θ) = 3/8, what is the value of sec(θ)?

Final answer:

The curved surface area of a cone with a radius of 15 cm and a slant height of 16 cm is 753.982 cm², calculated using the formula A = πrl.

Explanation:

The question asks for the curved surface area of a cone with a given radius and slant height. To find the curved surface area of a cone, we use the formula:

A = πrl

where A is the area, π is pi (approximately 3.14159), r is the radius, and l is the slant height of the cone.

Here, the radius (r) is 15 cm and the slant height (l) is 16 cm. Substituting these values into the formula, we get:

A = π × 15 cm × 16 cm

A = 3.14159 × 15 cm × 16 cm

A = 753.982 cm²

Therefore, the curved surface area of the cone is 753.982 cm².

Answer:

False

Step-by-step explanation:

The sequence seems to be increasing by 3+3(-5+3=-2, -2+3+3=4, so on). By 13, the sequence is increasing by 11, making the next number 24.

Answer:

the answer is true

Step-by-step explanation:

I just took the test and put false it was wrong

Answer:

218 every part

Step-by-step explanation:

654/3 = 218

Step-by-step explanation:

Yes, I agree with her. If you multiply a number by .001 youll move the decimal point to the left 3 times. For example let's say 480. multiplied by .001. it will then become .480 or .48

Yes I agree I just did this in class

The simplification of the expressions give above would be = 32

To simplify the given expression the following steps needs to be taken as follows:

2²× 2³

Where;

2² = 2×2

2³ = 2×2×2

The simplification = 2×2×2×2×2= 32

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Answer:

B

Step-by-step explanation:

When Experimenting scientist must include every part of the experiment and not leave out details.

Answer:b

Step-by-step explanation:

Answer:

The correct next step is the answer choice

[tex]x^{2} +\frac{b}{a}x=-\frac{c}{a}[/tex]

Step-by-step explanation:

we have the quadratic equation in standard form

[tex]ax^{2}+bx+c=0[/tex]

The steps in the derivation of the quadratic formula by completing the square are

step 1

[tex]ax^{2}+bx+c=0[/tex] ----> given equation  

step 2

Move the constant term over to the right-hand side

[tex]ax^{2}+bx=-c[/tex]

step 3

The leading term is multiplied by a

so

Divide by a both sides

[tex]x^{2} +\frac{b}{a}x=-\frac{c}{a}[/tex]

step 4

Multiply the linear term by 1/2

[tex]\frac{b}{a}(\frac{1}{2})=+\frac{b}{2a}[/tex]

step 5

square this derived value

[tex]+\frac{b^2}{4a^2}[/tex]

step 6

Add this squared value to either side of the equation

[tex]x^{2} +\frac{b}{a}x+\frac{b^2}{4a^2}=-\frac{c}{a}+\frac{b^2}{4a^2}[/tex]

step 7

convert to the common denominator, and combine on the right-hand side

[tex]x^{2} +\frac{b}{a}x+\frac{b^2}{4a^2}=\frac{b^2-4ac}{4a^2}[/tex]

step 8

convert the left-hand side to completed-square form

[tex](x+\frac{b}{2a})^{2}=\frac{b^2-4ac}{4a^2}[/tex]

step 9

take the square roots of either side

[tex](x+\frac{b}{2a})=(+/-)\sqrt{\frac{b^2-4ac}{4a^2}} \\\\(x+\frac{b}{2a})=(+/-)\frac{\sqrt{b^2-4ac}}{2a}[/tex]

step 10

solving for the variable

[tex]x=-\frac{b}{2a}(+/-)\frac{\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-b(+/-)\sqrt{b^2-4ac}}{2a}[/tex]

Answer:

C on edge

Step-by-step explanation:

Answer:

(4, 0 ) and (0, - 10 )

Step-by-step explanation:

To find the x- intercept let y = 0 in the equation

5x - 0 = 20

5x = 20 ( divide both sides by 5 )

x = 4 ← x- intercept ⇒ (4, 0 )

To find the y- intercept let x = 0 in the equation

0 - 2y = 20

- 2y = 20 ( divide both sides by - 2 )

y = - 10 ← y- intercept ⇒ (0, - 10 )

The x- and y-intercepts of the equation 5x - 2y = 20 are 4 and -10 respectively. The x-intercept is obtained by setting y = 0, likewise, the y-intercept is obtained by setting x = 0.

The x-intercept and y-intercept of an equation can be found by setting the other variable to zero and solving for the remaining variable. In the equation 5x - 2y = 20:

So, the x-intercept is 4 and the y-intercept is -10 for the given equation.

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Answer:

A pound is a measure of weight and a cup is a measure of volume.

Step-by-step explanation:

You can't directly compare 1.07 pounds of sugar to 1.23 cups of sugar because they're measured in different units -- weight and volume -- and without a conversion factor (like density), they're not directly comparable. The solution is to convert one measurement to the other, such as by knowing that one cup of granulated sugar typically weighs about 0.44 pounds.

The reason you can't directly compare 1.07 pounds of sugar to 1.23 cups of sugar is because they're measured in two different units -- weight and volume, respectively. Without a known conversion factor (in this case, the density of sugar), you can't equate the two. It's like comparing apples to oranges, the two quantities just aren't compatible without some more information.

Let's consider a real-world example. Just like you can't compare how heavy an object is to how much space it takes up without knowing the material's density, the same goes for comparing sugar in pounds and cups.

The solution is to convert one measurement to the other. For instance, by knowing that one cup of granulated sugar typically weighs about 200 grams (or 0.44 pounds), you could convert your weights and volumes to make a meaningful comparison.

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Answer:

1.) 2

2.) 3

3.) 2

4.) 3

Step-by-step explanation:

Answer:

The coordinates of the vertex of the graph are (-2, -9).

Step-by-step explanation:

The quadratic function is described by the standard equation   The graph of a quadratic function is called a parabola.

We have the quadratic function

We identify the coefficients a, b, and c. For this equation,

The axis of symmetry is , i.e.,  Thus, the statement in the question for the symmetry axis x = -2 is correct.

The vertex (or turning point) is  where   or

The parabola opens upward because a > 0, resulting in a vertex that is a minimum.

Finding the minimum value is as follows:

Therefore, the coordinates of the vertex of the graph are (h, k), i.e.,

Other components:

The y-intercept of the quadratic function f(x) = x² + 4x - 5 is (0, c), i.e., the point

The factorization of f (x) = x² + 4x - 5 becomes f(x) = (x + 5)(x - 1). Then we get the x-intercepts at

Learn more

Which is the graph of f(x) = (x - 1)(x + 4) brainly.com/question/2334270  

Finding the y-intercept of the quadratic function f(x) = (x – 6)(x – 2) brainly.com/question/1332667

The midpoint brainly.com/question/3269852  

Keywords: the axis of symmetry, for a function, f(x) = x² + 4x − 5, x = −2, which is the graph of f(x) = (x - 1)(x + 4), what, the coordinates of the vertex of the graph, the x-intercept, quadratic function, a standard equation, the y-intercept, parabola, upward, the minimum value

Answer:

the vertex of the graph is (-2, -9)

Step-by-step explanation:

The given function is:

[tex]f(x)=x^2+4x-5[/tex]

Given x = -2 is the axis of symmetry and because we know that the vertex of the graph lies on its axis of symmetry

=> coordinate of vertex is (-2, y)

When x= -2 we have

 [tex]f(-2) =(-2)^2+4(-2)-5\\<=> y=4-8-5\\<=> y=-9[/tex]

So the vertex of the graph is (-2,-9)

Answer:

B.111

Step-by-step explanation:

111 is a composite number because the number can be divided evenly by more numbers than 1 and itself.

Answer:

x = - 3

Step-by-step explanation:

Given

7(x + 2) = 2x - 1 ← distribute parenthesis on left side

7x + 14 = 2x - 1 ( subtract 2x from both sides )

5x + 14 = - 1 ( subtract 14 from both sides )

5x = - 15 ( divide both sides by 5 )

x = - 3

Answer:

[tex]\large\boxed{\dfrac{3}{4}-\dfrac{1}{3}=\dfrac{5}{12}}[/tex]

Step-by-step explanation:

[tex]\dfrac{3}{4}-\dfrac{\boxed{\ }}{3}=\dfrac{5}{12}\\\\\bold{METHOD\ 1:}\\\\LCD=12\\\\\dfrac{3\cdot3}{4\cdot3}-\dfrac{4\cdot\boxed{\ }}{4\cdot3}=\dfrac{5}{12}\\\\\dfrac{9}{12}-\dfrac{4\boxed{\ }}{12}=\dfrac{5}{12}\\\\\dfrac{9-4\boxed{\ }}{12}=\dfrac{5}{12}\iff9-4\boxed{\ }=5\qquad\text{subtract 9 from both sides}\\\\-4\boxed{\ }=-4\qquad\text{divide both sides by (-4)}\\\\\boxed{\ }=1[/tex]

[tex]\bold{METHOD\ 2:}\\\\\dfrac{3}{4}-\dfrac{\boxed{\ }}{3}=\dfrac{5}{12}\qquad\text{subtract}\ \dfrac{3}{4}\ \text{from both sides}\\\\-\dfrac{\boxed{\ }}{3}=\dfrac{5}{12}-\dfrac{3}{4}\\\\-\dfrac{\boxed{\ }}{3}=\dfrac{5}{12}-\dfrac{3\cdot3}{4\cdot3}\\\\-\dfrac{\boxed{}}{3}=\dfrac{5}{12}-\dfrac{9}{12}\\\\-\dfrac{\boxed{\ }}{3}=-\dfrac{4}{12}\\\\-\dfrac{\boxed{\ }}{3}=-\dfrac{1}{3}\to\boxed{\ }=1[/tex]

Answer:

D. 35%

Step-by-step explanation:

Note the percentage of each. You are trying to solve for the combination of homework and school.

In this case,

Homework = 10% of the pie chart.

School = 25% of the pie chart.

Add the two numbers together:

10 + 25 = 35

35% is your answer, or D).

~

Answer:

35%

Step-by-step explanation:

she spends 25% at or on school, and 10% on homework. all together (by adding) she spends 35%

Answer:

[tex] \frac{x}{3} = 3[/tex]

Step-by-step explanation:

[tex] \frac{1}{3} ≠ 3; \: \frac{9}{3} = 3[/tex]

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Final answer:

The equation for which x = 1 is not a solution is x/3 = 3, as substituting x with 1 gives 1/3, which is not equal to 3.

Explanation:

To determine which equation x = 1 would not be a solution for, we need to substitute x with 1 in each equation and see if it holds true:

x/1 = 1: Substituting x with 1 gives us 1/1 = 1, which is true. Therefore, x = 1 is a solution.

x/2 = 2/4: Substituting x with 1 gives us 1/2 = 2/4, which simplifies to 1/2 = 1/2, also true. Hence, x = 1 is a solution.

x/3 = 3: Substituting x with 1 gives us 1/3 = 3, which is false, because 1/3 is not equal to 3. Therefore, x = 1 is not a solution here.

x/4 = 1/4: Substituting x with 1 gives us 1/4 = 1/4, which is true. Thus, x = 1 is a solution.

The equation for which x = 1 is not a solution is x/3 = 3.

Answer:

1.5

Step-by-step explanation:

1 person = 3 hours

2 people = 1.5 hours

Answer:

1 hour and 30 minutes

Step-by-step explanation:

Each one of them needs 3 hours to paint the bedroom,but now they are 2 people who work at the same place so together,they only need half of the time.

Answer:

-4 + 4

Step-by-step explanation:

because when you add a negative number with a positive number the sum will always equal 0

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Answer:

-4+4

Step-by-step explanation: